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'Dark fluid' with negative mass could dominate the universe (theconversation.com)
409 points by pavel_lishin 5 days ago | hide | past | web | favorite | 286 comments





Paper: https://arxiv.org/pdf/1712.07962.pdf

Not a physicist, but my summary of the author's point would be:

If you allow for matter with a negative mass and plug it into a n-body simulation. You seem to get what looks like dark matter from first principles. Namely, a halo of non interacting matter around galaxies in just the right "non-cuspy" shape. Their conclusion is that this is worth considering, as almost all mainstream cosmology makes the assumption that mass >= 0, despite the fact mass <=0 doesn't seem to violate any physical invariants we know.

The idea is persuasively simple. Every other force besides gravity is polarised, so why not also gravity? It seems interesting to me, but I'm nowhere near knowledgeable enough to know whether it can be easily refuted.


Here's an argument:

If you think about it, "mass" actually means two different things. One one hand, there is mass as the "charge" of gravitational interaction, that is, the gravitational field generated by a body is proportional to its mass. Let's call this concept "gravitational mass". On the other hand, you have mass in the sense of "intertial mass", a body's resistance to change of velocity. Although we kinda take it for granted, it's weird that these two concepts coincide, and not something that would be necessarily true a priori.

Asserting this equivalence as a principle is the starting point for Einstein's theory of General Relativity, which is one of the most beautiful and thoroughly tested theories in modern physics.

On the other hand, you can show that the inertial mass cannot be negative (else the Lagrangian would not be bounded from below and therefore you could not minimise it; the whole of physics then comes crumbling down). Therefore, if that equivalence stands, the gravitational mass also cannot be negative.


> On the other hand, you can show that the inertial mass cannot be negative (else the Lagrangian would not be bounded from below and therefore you could not minimise it; the whole of physics then comes crumbling down).

Here's a purely thought-experiment argument for inertial mass not being negative:

If you had an object with negative inertial mass, then pushing on that object would cause it to accelerate into your hand. This is a positive feedback loop that immediately results in the object and your hand exerting infinite amounts of force on each other, because applying force just leads to applying more force.


Here's a thought experiment that shows that there can't be electrons:

"If you had an object with negative charge, then putting that object near a positive charge would cause it to accelerate towards the positive charge." Getting closer increases the force. "This is a positive feedback loop that immediately results in the object and the positive charge exerting infinite amounts of force on each other, because" getting closer "just leads to applying more force."

Thus, there are no electrons.

So, I don't think the thought experiment rules out negative mass. In fact, the article explicitly says "if a negative mass was pushed, it would accelerate towards you rather than away from you.", and I assume that if that's an obvious contradiction, the author would have caught it.


So, electrons are attracted to protons by the electromagnetic force, but they don't make it all the way there because they are repelled by some other force. You don't have a paradox because our model of the electromagnetic force doesn't specify that it's the only force there is.

But if a negative mass is moving towards you and encounters a repulsive force, that repulsive force will, by definition, move the negative mass further toward you. It would need to encounter an attractive force to reach equilibrium.

Note that, unlike in the electron example, it doesn't matter what kind of force is being applied; the object's negative mass tells us that the response to any repulsive force is acceleration towards the force.


> they don't make it all the way there because they are repelled by some other force

A repulsive force is not the best way to think about it. The potential of the nucleus is the usual -1/r, and goes to (negative) infinity at zero. A repulsive force would be incorporated into the potential and appear as a bump around the nucleus, and would mess up the electron orbital.

A hand-wavy explanation of why the electron doesn't fall in: if you try to push the electrons into the nucleus, you necessarily localize the electron into a smaller volume; this means its wavefunction must get "spikier" and therefore it has more kinetic energy. This kinetic energy rises faster than the potential energy drops, so the state of lowest energy is actually found at an average radius > 0.

Note that it took quantum mechanics to rescue the atom. A classical electron could fall into the nucleus.

I do not see any problem with a negative-mass particle accelerating towards the force. The analogy with opposite charges seems right to me.


A different hand-wavy explanation. The places that an electron can be found are described by a wave pattern. If the electron is staying in place around a nucleus, that wave pattern has to be a standing wave that reinforces itself. To reinforce itself it has to wrap around the nucleus an integer number of times.

This explanation doesn't just explain why it doesn't fall in, it also explains why there are discrete shells that it could be found in, corresponding to how many times it wraps around the nucleus. (It doesn't explain why only a finite number can fit in each shell though. Or why bigger shells can have more electron orbitals. Or...well the actual theory has to be good for something!)


This is the Bohr model of the atom, but was replaced by a proper quantum theory.

Yes. Which is why I called it "a different handwavy theory". And also listed some of the things that it didn't explain.

I'm not really interested (here) in the reality of the interaction between the electron and the nucleus. I don't think the existence of an electromagnetic field is a good argument against its own existence as argued by FabHK further up.

I also don't think FabHK's argument works as an analogy to my problem with negative mass. The electromagnetic field is not self-reinforcing in the same way.

Imagine that you're holding a marble of negative glass in your fist. Negative glass is indistinguishable from ordinary glass except that its mass is negative rather than positive.

As we all know, the first step in solving any physics problem is to draw a free-body diagram. ( http://www.smbc-comics.com/comics/20130616.png ) Let's draw one here. First, we'll do one for an ordinary marble:

1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass.

2. The marble cannot accelerate downward, because it's stuck in your fist. Your fist experiences a downward force equal to the weight of the marble.

3. By Newton's third law, your fist exerts an upward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, but in the opposite direction. The two forces cancel, and the marble is at rest.

Now for the negative marble:

1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass. Because that mass is negative, the marble attempts to accelerate upward.

2. The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to the weight of the marble.

3. By Newton's third law, your fist exerts an downward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, and in the same direction, effectively doubling the marble's weight. The marble is now trying twice as hard to accelerate upward into your fist.

2. (Again.) The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to double the weight of the marble. Nothing has moved; we're still just trying to work out the balance of forces within the system at rest.

3. (Again.) You can see where this is going.

What is the conceptual breakthrough that rescues negative mass from this trap? (Note that saying the marble has negative inertial and gravitational mass, as opposed to negative inertial mass and positive gravitational mass, doesn't help: the marble will be trying to accelerate downward instead of upward, but it will still be doing it with infinite force.)


Maybe that's precisely why objects with negative mass do not exist on the Earth? But what stops them to exist in the void of space, between regular matter? And it doesn't need to be actual "objects", but isolated particles or a particle gas. In relativistic physics mass is dependent on the body's energy, so negative mass implies negative energy.

This is an argument that negative mass cannot be contained, not that it does not exist.

(Though it escapes me why you would assume that I believe in theories about negative mass, which actually seem to me to be very speculative and not very likely.)


> that repulsive force will, by definition, move the negative mass further toward you.

only if the repulsive force is negative gravity.

If a positive-mass electron attracts a negative-mass electron, the repulsive electromagnetic force will still keep them from making it all the way there.


>> that repulsive force will, by definition, move the negative mass further toward you.

> only if the repulsive force is negative gravity

We're talking about negative inertial mass, not negative gravitational mass. Negative inertial mass means accelerating against the direction of any force applied to you, including but not limited to gravity.


> But if a negative mass is moving towards you and encounters a repulsive force, that repulsive force will, by definition, move the negative mass further toward you

I am not sure you understand what "repulse" means..

Joking aside, it's easy enough to imagine negative gravity. Do you mean that such counter intuitive behavior would be the natural consequence of negative inertial mass?


The problem with these papers is there is no compilers to perfectly test the logic except peer review so no one knows if its horse shit or not until someone comes along and comes up with some way to prove it wrong, so I would not be so quick to say “if that’s an obvious contradiction, the author would have caught it”

Physics is highly mathematical and as such, can indeed be "tested" (i.e. proven) to be consistent with mathematical laws. This is fairly straightforward (for suitably mathematically literate people). The real issues are:

1. can the theory make testable predictions that can be verified by observation? e.g. string theory has had issues with this.

2. what does <wierd-mathematical-construct> "mean"? e.g. negative mass, spooky action at a distance, spacetime singularity.

In practice, only 1 really matters. However, 2 tends to bug a lot of people (consider the arguments around what the quantum world really represents). I'm one for whom 2 is important. "But what does it really mean?"

Back to your original point, looking at the paper [0], it doesn't seem too ridiculously hard to validate the math for someone familiar with this space (see what I did there?), unlike me who has forgotten everything I was taught [1].

[0] https://arxiv.org/pdf/1712.07962.pdf

[1] I have a physics degree but that was 33 years ago and I've been doing nothing but IT since.


1. OpenGL makes good predictions. Why not to switch to OpenGL terms when talking about physics?

Because physicists would find it totally unsuitable for their requirements?

Why match is better for that? To compute prediction, you will need to use computer and compiler, so it better to talk directly in these terms because of (1) (see above).

You should go back to 1910 and tell Einstein he can't start for another 50 years.

Einstein used the best tool he had at hands - math. Now we have mach better tools: computer models, knowledge databases, AI. Math is good because math formulas are very compact, so they are easy to play with, but computer models are much better, because computer can visualize them directly, calculate values correctly, and verify result automatically. Think about Computer Aided Science.

I'm confused - are you trolling us? You do realise that computer science is based on math right? All the calculations that that OpenGL does are mathematical calculations. Even databases are based on relational algebra. AI - linear algebra, probability, multivariate calculus, optimization etc. There would be no computer science without math.

> If you had an object with negative inertial mass, then pushing on that object would cause it to accelerate into your hand. This is a positive feedback loop that immediately results in the object and your hand exerting infinite amounts of force on each other

No, it doesn't; since this turns the repulsion of normal objects (which is what makes them resist interpenetration) into attraction by switching the orientation of the resulting acceleration, what it results in isn't more force at the boundary (the boundary is a repulsive effect), but interpenetration, which results in force declining to zero as the masses centers are at the same place. (And then switching directions as they cross.)


What makes us think the objects would actually interact at all?

I'm assuming that you can push in the classical sense but for what negative mass does to the equations, but sure, if you can't then the whole question is moot.

This assumes that the objects of opposite inertial mass are able to interact in the way you describe.

Specifically the interaction is: objects with positive inertia being able to 'push' objects with negative inertia.

This brings up an interesting question, is gravity about exchanging momentum? My mental model of gravity being spacetime curvature would imply no, but that intuition is likely wrong.


That's assuming your hand has negative inertial mass.. which I'm assuming it doesn't.

Your scenario could create a black hole if I'm understanding correctly. Enough 'negative inertial mass' trapped in a feedback loop..


If inertia is resistance to change then negative inertia would be promotion of change? I really dont know, the idea of negative inertia seems wildly counterintuitive.

Inertia isn't "resistance to change". It's defined by Newton's second law, F = ma. Force and acceleration are directional vectors, and mass is scalar.

In the form of the equation favored by my high school physics teacher, a = F/m, we see that when a force is exerted on an object with positive mass, the object will accelerate in the same direction as the force, in inverse proportion to its own mass.

But it's very easy to put a negative number in for the mass, and then you see that such an object would accelerate in response to force just as much as an object of equal positive mass, but in the opposite direction.


Thanks, that's obviously a much better way to think about it. However, you're wrong in at least the typical physics definition of inertia found in dictionaries is in fact, "resistance of change (velocity, acceleration, momentum)."

In that same framework, the maths definition of inertia is also momentum = mv and a google search confirms this. What would negative momentum even look like? Because that's not just movement in the opposite direction.


Velocity, the v in the definition of momentum, is also a vector, so yes negative momentum is just momentum in the opposite direction from positive momentum, whatever direction that may be.

Inertia is generally not defined as being momentum, because an object's momentum in any direction increases along with its velocity in that direction, while we like to think of inertia as being determined solely by mass.

https://en.wikipedia.org/wiki/Inertia begins "Inertia is the resistance, of any physical object, to any change in its velocity". That's specifically resistance to acceleration ("change in velocity"), not resistance to the concept of change in general.

(It does go on: "In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" (which is quantified by its mass), or sometimes to its momentum, depending on the context.")


But that's what I just said: resistance to change in v, a, p are the dictionary definitions I found on Google.

You're right about v. I thought a negative velocity was equally absurd, but it looks like it's defined as a vector which makes sense of course. The last time I took a proper physics course was in high school. How embarassing though, as I've read and watched more popular science/physics material than most people, probably. Hah.


Dictionaries are not written by physicists.

Positive mass has a speed limit though, so I think there would be an upper limit on the amount of force returned?

How do you think Thor’s hammer works when it’s sitting on the toilet seat?

Obviously, toilets are capable of exerting more upward force than any mere mortal.

What happens if the gravitational mass is the exact negative of the inertial mass for some fraction of matter, though? Does that break GR?

Perhaps gravitational mass is indeed polarised and inertial mass corresponds to the absolute value of the gravitational mass?

Another framing of the issue with negative inertial+gravitational mass is that it would result in perpetual acceleration.

E.g. assume two bodies, one with mass M, the other with mass -M. The standard gravitational model describes a "repulsive" force on each of these objects, in the direction opposite each other. However, since the object of mass -M has negative inertial mass, this force would cause it to accelerate toward the object of mass M.

This results in these objects not accelerating relative to each other, and perpetually accelerating relative to an independent observer. One might attempt to explain this by saying that the negative mass has a growing negative kinetic energy level, but (it seems as a layman) this would violate the second law of thermodynamics.

Edit: Actually just negative inertial mass does this all by itself; it is just in the opposite direction if the gravitational mass is positive.


Actually the lagrangian is not minimized, it is merely stationary. An example of this is the harmonic oscillator, the lagrangian is clearly not bounded from below.

Yes, I realised that but I couldn't edit the post anymore :) I mean the action, not the Lagrangian, must have a minimum.

The action of a trajectory is not minimized either, it is usually at a saddle point, maximal relative to some trajectories and minimal to others. The linked paper has a detailed discussion of this.

http://www.eftaylor.com/pub/Gray&TaylorAJP.pdf


Well, even the possibility of inertial mass not exactly equaling gravitational mass on interstellar scale open a big can of worms for physics

I’m not sure this stands true when you think about fields.

Think of charged particles in a magnetic field and how polarity and and strength of the charge impacts their interaction the strength would do the same thing for both particles while the polarity would mirror their interaction.

I need to read the paper a few more times tho.


I was thinking, what if body's resistance is actually the norm, even when there is no change of velocity ? But the negative mass would provide the energy to let the body's in movement ? From our point of view it seems that body's can move by theirselves and it seems also that we have to provide energy to change their velocities. But if we think the universe as a fluid, body's should be constantly slowed. It's very strange to have two distinct behavior, except if we have a negative mass in the universe.

Don't you have two things that can generate gravitational fields though? As distortions in spacetime can be caused by either mass or the momentum of massless particles, such as photons. Or do I have that wrong and photons merely follow the distortions and not cause any of their own? As presumably, you could have a negative gravitational field from a photon traveling backward in time, without having any issues with changes in inertial mass.

> Or do I have that wrong and photons merely follow the distortions and not cause any of their own?

You have that wrong in the momentum of massless particle has mass, independently of its carrier. Massless particles do not actually exist, what exist are particles with zero "mass at rest" and that are never at rest.


You're talking about relativistic mass, but that isn't a commonly used concept anymore. Today it is indeed the norm to think of "mass" as being the mass at rest. Massless particles are really massless and have momentum without having mass.

In which case, we seem back to having two things distorting spacetime. Could mass just be the momentum of massless particles going in really small circles such that you can pack them together and call them matter?

What you described sounds like a geon.

https://en.wikipedia.org/wiki/Geon_(physics)


Oh, cool, yep. I didn't know that's what they are. I have basically been wondering if all matter is variations of those.

Energy distorts spacetime. Mass only distorts spacetime because it is a form of energy. Light is also a form of energy.

Space is distorted by the stress-energy tensor field. Mass is only a component of that.

If you use "mass" to mean the rest mass of something. If you use it meaning the relativistic mass, it's the entire value, not a component.

Yes, using it as the relativistic mass leads to confusing papers and equations, so it's better avoided. Yet, the press does that, what makes everything very confusing for lay people. I should have clarified that the OP usage of the term wasn't optimal (although common on the media he sees), but this following discussion about word definitions seems to be completely missing the point.


Ahh, I was getting a bit confused from photons distorting spacetime off their wavelength and plank's constant, given they also apparently have no mass. Thanks for that. I have to go and re-read a lot of stuff now though. ;)

You may like to make a quick read of this:

https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati...

Besides it being a basic relation for relativity, there's also an entire "parallel" quantum mechanics for particles that have too much energy at the momentum component based on it.


I think this might be dumb, but, what if negative mass was just positive mass in some alternative dimension? If mass could be negative with respect to our observable space time, does that actually mean it is a binary kind of thing, or could there be lots of mass in lots of others semi-or-non-interacting dimensions? Maybe even the mass we can observe is only part of anything’s actual substance...

"Every other force besides gravity is polarised, so why not also gravity?"

Gravity is mediated by a spin-2 gauge boson, the graviton, whereas the other known fundamental forces are mediated by vector (spin-1) bosons. There is an exercise in Peskin & Schroeder (I believe) working out the lack of a gravitation "repulsion" resulting from this difference.

That being said, I think this kind of phenomenology is excellent and raises lots of interesting questions. There may be reason to rule out this author's new idea, or maybe rethink an established tenet. That's why science is such an exciting field.


That's what the article (https://arxiv.org/pdf/1712.07962.pdf) says:

> In theories of quantum gravity, gravitation is mediated by the graviton – a massless, spin-2, boson. This means that any pair of negative masses would attract, and not repel as suggested in this theory. However, there are also theoretical arguments that gravitons cannot, and will not ever, be detected experimentally (Rothman & Boughn 2006). There appear to be two options: either it is possible that the graviton could be modelled as a bound state of a positive and a negative mass, in a theory of composite gravity or some other mechanism which provides a modification of graviton properties. Alternatively, this could also indicate that the proposed theory cannot be modelled by real, physical, particles, but rather by the presence of effective negative masses within a superseding theory.


Given there have been no detections of individual gravitons, saying it's a spin-2 gauge boson is speculation at best (though it might be what the model predicts)

If it weren't, general relativity would be wrong as well and we know that (in its domain of applicability) it's a highly accurate model. GR models gravity as fluctuations in the metric tensor of spacetime, which is a symmetric rank-2 tensor. This is all you need to know to conclude that a graviton (a quantize fluctation of that tensor) must be spin-2.

https://en.wikipedia.org/wiki/Graviton mentions "[I]t can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way that gravitational interactions do. This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton." It links to other resources from there.


Well, in classical GR, which is still our best and most accurate theory of gravity, gravity is only an apparent force and thus isn't (or can't be) mediated by anything. Stating as fact that a graviton must exist or otherwise GR "would be wrong" is a bit of stretch IMHO. The graviton is plausible speculation, backed by some theoretical justifications, but nothing more yet.

disclaimer: IANAP.

as far as I understand, the space-time curvature is just an interpretation of the math. Another perfectly acceptable interpretation is as a relativistic classical field that couples with the stress-energy tensor field (thus, indirectly, with any other field).

In fact I think it is possible to come up with a space-time curvature interpretation of the EM field, for a toy universe where everything has a EM charge.

Now, given that the gravitational field couples with other fundamental fields and those are quantized, the gravitational field must necessarily also be quantized. The math straight forward quantization works fine for low energies, thus the spin-2 boson described elsethread. The issue is that at low energy, the gravitational effects are so small that it is impossible to come up with an experiment that would detect the difference between a classical field and a quantized field.

At high energy the straightforward derivation breaks down because of infinities (other quantum fields had similar issues, but the math tricks used to resolve them do not work with the gravitational field). There are multiple theories (string theory, loop gravity, etc) that try to resolve this problems, but the experimental apparatus required to distinguish between them are colossal (as in particle accelerators with radii measured in AU).


Well GR is potentially very wrong both at very large scales (seemingly requiring dark matter and dark energy) and very small scales (due to known present incompatibilities with quantum mechanics). It's only been shown to be a highly accurate model everywhere in between.

I think both dark matter and dark energy are perfectly consistent with GR. Hitherto unobserved matter would contribute to the stress energy tensor and dark energy is (I believe - has this changed?) the cosmological constant.

Yes, they are consistent. In fact, they are the result of the following line of thinking: given that we are observing unexpected results once we account for (using the GR paradigm) all the clearly apparent mass and energy, what else could we change so that GR doesn't have to change? In other words, the consistency with GR is already baked in. That's not to say that the approach doesn't have huge merit.

One model for dark energy is indeed the cosmological constant, but there are other approaches, most notably quintessence (https://en.wikipedia.org/wiki/Quintessence_(physics)).


> GR models gravity as fluctuations in the metric tensor of spacetime, which is a symmetric rank-2 tensor.

IANAP, and don't get the full picture. But isn't that definition itself derived by the fact that gravity has a single polarity?


Yes but while we don't have the unification between QM and GR we don't have the full picture.

We know what fits GM, but we don't know if it's the only solution.


>"If it weren't, general relativity would be wrong as well and we know that (in its domain of applicability) it's a highly accurate model."

Somehow I doubt it. I bet as a save someone would propose "dark spin" or some elaborate calculations that shows a few factors happen to cancel out exactly but no one noticed before now.


Dark spin? It spins in a direction that nothin else can?

I was thinking something like it spins along a dimension so small it can't be detected without a particle collider the size of the solar system.

My understanding is that the entire existence of the graviton is still theoretical. Has that changed recently?

Please see my comment above. You can use the language of gravitons and Feynman diagrams even for classical gravitational physics, but the calculations will be intractable for strong fields. See https://en.wikipedia.org/wiki/Graviton#Gravitons_and_renorma... for example

It's hypothetical, but less so than a lot of the things theoretical physicists consider.

Any quantum theory which reduces to general relativity in the classical limit will look like a theory of gravitons when quantum effects are small. This is just how the math works out in effective quantum field theories involving massless spin-2 particles.


I don't think its even a part of the standard model, still just a hypothesis.

Um, correct my amateur understanding if it's wrong, but... we don't actually have a working quantum theory of gravity, do we? So how certain are we that gravity is mediated by a spin-2 gauge boson?

Yes, because they are fluctuations of the metric tensor field, a symmetric rank-2 tensor. Take a look at https://en.wikipedia.org/wiki/Graviton#Gravitons_and_renorma... for details.

That does not appear to have any details that relate to your comment whatsoever. All it says is that renormalization doesn't work on gravitons.

However, if I understand your comment correctly, you're saying that the underlying non-quantum theory (GR) uses a symmetric rank-2 tensor, therefore you have to have a spin 2 particle - as opposed to photons, whose underlying non-quantum theory has an antisymmetric rank-2 tensor, and therefore give rise to a spin 1 particle. Do I have that right? If so, could you point me to something that would explain why?


Two-days-later addition: If you drop the # and following from the URL, it does have details that relate to duality's comment.

I recollect that Feynman's Lectures on Gravitation (Frontiers in Physics) has an amazing and detailed explanation.

"Quantum field theory in a nutshell" also covers this well.

The definitions you brought are tailored to what is our best understanding of the universe. Nobody ever said that these are immutable. Newtonian physics also must have felt rock solid, time and time again explaining new phenomena until it did not and there came about a better explanation.

Sidenote, but I think it is very important to emphasize that Newtonian physics is actually still quite rock-solid under certain conditions. These conditions are actually quite common and useful for humans. Many engineers utilize Newtonian physics everyday.

> raises lots of interesting questions

Exactly. What I liked about MOND was that it basically amounted to "we don't know." The populist notion that dark matter is conclusively matter, and dark energy is energy seems a bold claim for such a young species.

Crazy theories like non-universal constants are probably crazy, but they do explore unconventional lines of thought. One of those, most likely an unknown unknown, may be answer. Focusing all our energy on one explanation (that has been falsified more than once) seems like a waste.


> that has been falsified more than once

What has been falsified more than once?


Lots, we just patch it and move on. Iron orb should glow blue unless this one variable is this one value? "patch it" by calling that one value plank's constant and see, the models still good!

Our math says the universe comes up short on mass by over 3/4ths? Must be invisible matter we can't see or interact with see, the models still good!

Over simplification in the extreme, but also a far cry from the rock solid foundations it claims to be.


We haven't observed any of the predicted WIMPs at the LHC, as one example. They were subsequently relegated to a higher energy level.

That doesn’t disprove the “matter-like” observed behavior, it just shows that the particular assumptions under which exactly these non-found WIMPs were imagined were false.

If you have an infinite space of particle parameters and a series of tests keeps eliminating large swaths of this space, at some point it feels like you're playing a god of inbetweens game a la creationists arguing using gaps in the fossil record. There is a categorical difference, of course, but as a practical matter the parallels are useful, at what point do we table (for now) the search for the populist position and break for alternatives?

It's not "populist" anything. It's the best science that can be done:

https://medium.com/starts-with-a-bang/five-reasons-we-think-...

"Five Reasons We Think Dark Matter Exists: No other idea explains even two of these."

"1.) Galaxy Clusters"

"2.) Galactic Rotation Curves"

"3.) The Cosmic Microwave Background"

"4.) The Bullet Cluster"

"5.) Large-Scale Structure Formation"

From these 5, only dark matter matches all. Whereas MOND theories match only one, the "item number 2" and only as an attempt to after-the-fact-explanation of what's anyway observed, not as any prediction of anything new.

As I've quoted in my another message here:

"the predictions of dark matter were first made in the 1970s and 1980s, and were observationally confirmed later. This is not a case of tweaking the model to fit the data; this is a case of the best kind of science you hope for: where you make predictions, make the observations, and what you see validates and confirms the predictions you had made."

Moreover, there's nothing "large" of the possible space that is now excluded. The possible space includes everything that "behaves like matter". What's (still just "probably") eliminated is just what were for us, humans, in this particular moment of our history very convenient to happen: that the energies needed are exactly such that WIMPs that were conveniently postulated to be such can be generated by the device which design and maintenance costs less than 2% of the total cost of the F-35 fighter planes (the money invested and planned to be invested in F-35 is 75 times bigger than the international investment in LHC). It would have been luck if it had happened, but the possibilities are much bigger and include such which are going to remain physically unreachable to be produced by our technologies.

That we, humans, can't produce some particles doesn't disprove that dark matter exists when we have precise observations that can only be explained by dark matter and effectively by nothing else.


>"only dark matter matches all."

Dark matter can be placed arbitrarily so it can match pretty much anything. I remember recently there was a galaxy with negligible deviation of the GR-predicted rotation curve and that was taken as evidence for dark matter too (even though MOND was still the better fit for that case).

"Dark Matter" started out ok but has become a "god of the gaps" argument, I expect eventually MOND or similar solutions will be developed for all those issues.

Also, I gather that while MOND does seem not predict these observations exactly, it is not fully developed yet and often the presence of some "normal" cold gas (undetectable via light) could make it fit. Also, to get dark matter to fit the observations requires post-hoc assumptions and parameter adjustments. Eg:

"The amplitude of the third peak observed by WMAP merely falsifies the simple ansatz I used to make the prediction, not MOND itself. Indeed, I pointed out in the original papers that the ansatz must fail at some level, so I am hardly surprised that it does. All this means is that there are degrees of freedom (like a scalar field) that can oscillate separately from baryons in whatever the relavistic parent theory of MOND might turn out to be. The real test was for ΛCDM: the third peak had to be higher than predicted by pure baryonic damping. ΛCDM survives this test. It "wins ugly" in that, in order to obtain a fit, we have had to nearly double the baryon density over what it was so confidently known to be before it wasn't. That, and the no-CDM prediction for the second peak is still bang on. Amazing coincidence, that." http://astroweb.case.edu/ssm/mond/

>"the predictions of dark matter were first made in the 1970s and 1980s, and were observationally confirmed later."

I'm afraid I have never seen this although I have looked into this topic (as a layperson). Can you give an example of this? It would make the dark matter idea much more convincing.


> Dark matter can be placed arbitrarily so it can match pretty much anything.

Quite the opposite, and that statement is obviously uninformed. The science behind dark matter is very precise and exact. That's why the alternative theories can't come even near: once the same rigor which was applied to test dark matter is applied to the alternatives, the alternative theories simply break.

> I'm afraid I have never seen this ... Can you give an example of this?

I've given you the link to the complete articles and also highlighted the major points. Try to read and understand them fully, then search for more. For example, even on the MOND page that you linked you can read:

"2013: ΛCDM provides an excellent fit to the improved CMB data just as MOND provides an excellent fit to improved rotation curve data. As before, one's interpretation depends entriely upon which you find more impressive."

Note: "rotation curve" from that quote is the "item 2" from my posts before. So, no, still the match of the single "item 2" is definitely not "more impressive." The "CMB" mentioned on your page is the "item 3" from all 5 which are explainable by ΛCDM (and specifically, ΛCDM is the model part of which the "dark matter" is: https://lambda.gsfc.nasa.gov/education/graphic_history/univ_... see there 4 and 5).

Edit: response to your later response below:

> The claimed predictions from the 1970s and 1980s are not mentioned on that page.

They are mentioned even on the very page that you linked to: that page, among other points, followed the history of the tests and effectively concludes that, yes, finally, in 2013 ΛCDM wins the "item 3". Read carefully. Learn what ΛCDM is. MOND can still only claim "item 2." Which actual "authority" can show anything else? Also, behind "darkmattercrisis" blog are just a few guys with very fringe positions.


>"Quite the opposite, and that statement is obviously uninformed. The science behind dark matter is very precise and exact."

From what I have seen they can get precise post-dictions but not precise pre-dictions because there are so many free parameters (basically you can put dark matter wherever you need it).

>"I've given you the link to the complete articles and also highlighted the major points. Try to read and understand them fully, then search for more."

The claimed predictions from the 1970s and 1980s are not mentioned on that page.

Also, that "startswithabang" guy is more like a catholic inquisitor than a scientist. I wouldn't consider him a reliable source because this behavior indicates he lacks the required capacity for curiosity, he can only repeat what authority figures say:

"The blogger (@StartsWithABang) contacted @scilogscom on January 24 by replying to a 15-day old tweet that announced our blog’s move to the new domain. He tweeted “Bummed that @scilogscom is in the business of promoting contrarian scientist viewpoints.”, and asks the SciLogs.com community manager (@notscientific) “[Why] are you allowing @scilogscom to promote contrarian voices that undermine public understanding of [science]?”, adding “You have taken on “Dark Matter Crisis” blog, whose mission is to undermine all of physical cosmology & promote MOND.”

The two agreed to discuss the issue via email, with the blogger adding that he was “personally worried that you are promoting clicks & false controversy over quality science content”, and states that he is “very, VERY disappointed about this move that @scilogscom has made”.

By now the SciLogs.com community manager has explained to us what happened after these tweets. He and the publishing director responsible for SciLogs.com unfortunately assumed that the blogger’s criticism was justified. They decided to close our blog without conferring with others or asking us for a statement. After we complained about the discontinuation, they performed an internal investigation, which involved reaching out to astrophysicists and other people, and have realized that discontinuing our blog was a big mistake. We attribute SciLogs.com’s poor judgement to two factors: neither the community manager nor the publishing director has an (astro)physical background, it was the first time that SciLogs.com had experienced an attack against one of its blogs." https://darkmattercrisis.wordpress.com/2013/03/08/the-dark-m...

Anyway, I can tell you know even less about this topic than me so let's leave it at that.


> The claimed predictions from the 1970s and 1980s are not mentioned on that page.

They are mentioned, they just aren't elaborated: you have to do your own homework if you apparently "understand" the subject enough to claim your own opinion. A begin of that homework, however, as I've already written, you even have on the initial page that you chose to post, specifically:

"2013: ΛCDM provides an excellent fit to the improved CMB data"

As I've said, that's the "item 3" from the 5 item list, and it's ultimately confirmed by ESA's Planck satellite results in 2013. That is a strong confirmation.

Note: more details and the timeline are on the very page you've initially posted. Ad hominems don't change the facts.


>"They are mentioned"

No, they were not mentioned. If they were, you would be quoting it.

>'"2013: ΛCDM provides an excellent fit to the improved CMB data"

As I've said, that's the "item 3" from the 5 item list, and it's ultimately confirmed by ESA's Planck satellite results in 2013. That is a strong confirmation.'

You have to read the entire quote. This "fit" was a post-diction, not a pre-diction: "in order to obtain a fit, we have had to nearly double the baryon density over what it was so confidently known to be before it wasn't."

Post-dictions can be interesting as part of model development but are unable to confirm a model. The new, (possibly adjusted) model then need to be checked against new data.


What is your support for that claim? Can you quote other sources? I can quote my sources: Here are documented two independent approaches in estimating baryonic density: one is calculations based on the Big Bang Nucleosynthesis D/H ratio and another one is the values measured by the satellites observing the SMB. Note the two decades of similar values using both approaches:

https://lambda.gsfc.nasa.gov/education/graphic_history/baryo...

"There is general good agreement between the recent CMB and D/H+BBN determinations shown in the figure."

I don't see the "double" anywhere there. And the values could be traced to all the sources mentioned there.


>"I do disagree with the assertion that I often see, and remains a widespread misconception among scientists, that MOND does not do a good job of explaining cosmic phenomena. I’ve been through all that, and it is simply incorrect to say dark matter is always better outside of galaxies. Sure, it has shortcomings, but often dark matter only appears to be better because it declines to make a comparably testable prediction. Clusters of galaxies are a great example: MOND is off by a factor of 2 in mass (20% in velocity). Dark matter makes no prediction. Anything over the luminous mass is OK. The rest is dark. It doesn’t matter if that’s a factor of 2 or 5 (the modern value) or 6 (the cosmic value) or ~100 (Zwicky’s value). Being a factor of 2 off only sounds bad because there is a definite prediction! With dark matter we don’t care what that factor is because we have no prediction – at least, not one that can not be fudged."

Here in a recent comment he addresses the "galaxy cluster" issue: https://tritonstation.wordpress.com/2018/11/21/hypothesis-te...


My source is Stacy McGaugh (the guy who wrote that page). On the same page as the original link I found this: http://www.astro.umd.edu/~ssm/mond/BBNLCDMMOND.jpg

He is currently active at this blog: https://tritonstation.wordpress.com/

It looks like this doubling happened in ~2000 so it wouldnt show up in your chart.


> It looks like this doubling happened in ~2000 so it wouldnt show up in your chart.

Since 2000 many new satellite measurements were done and the values improved. As I've quoted your page Planck in 2013 ultimately made the most precise CMB measurements that most conclusively fit the "dark matter" model and provably don't fit the "MOND" model. And for that proof there were no "factor 2" corrections, as you also confirm, at least since 2000. The way you wanted to believe, and how you quoted some other parts of the same document, was that that had to be done for that 2013 proof, and it obviously haven't had. BTW the nature of the measurements, especially those made decades ago, is such that when we started with some value and then later measured something only 2 times smaller or bigger (but then all repeated measurements remain closer to one another), it's still OK. It's not the absolute values that prove this or that, it's the measured shapes that match or not the very complex calculations. And that's what happened in 2013 with Planck: what was measured for more than a decade with other satellites, and finally most precisely with Planck, shows the shape that in practice can't match the MOND predictions but nicely matches what the "dark matter" model predicts.


>"Since 2000 many new satellite measurements were done and the values improved."

The point is that "suddenly" people started measuring a higher baryon density to make it fit what was required for lambda-CDM model to fit the CMB measurements. Ie, the lambda-CDM model did not pre-dict the spectrum beforehand, they had to tune it to match the data.

And see how the squares and triangles start moving upwards once the blue circles appear: http://www.astro.umd.edu/~ssm/mond/BBNLCDMMOND.jpg

Remember the oil drop experiment mentioned by Feynman in his cargo cult science talk? That is what this looks like to Mcgaugh: http://calteches.library.caltech.edu/51/2/CargoCult.htm

I have to say, it is very frustrating to discuss this since you seem to misunderstand every simple point being made, and before that has been corrected you have gone on to miss another point that needs to be addressed. We are not discussing this at a very deep level... Perhaps English is not your native language, but I am just letting you know. I hope no offense is taken.


> The point is that "suddenly" people started measuring a higher baryon density to make it fit what was required

W...what? Do you really believe that different scientific organizations in different countries around the world financed and sent different satellites into space but misrepresented the actually measured values only to "fit" some old theoretical predictions?

Really?

Then there's really no point discussing anything about science with you.


There's no point to you discussing science with scientists then. Because that is exactly what scientists are worried about. Why? Because it happens all the time.

> Dark matter can be placed arbitrarily

Yes.

> so it can match pretty much anything

At the time you do the initial placement. But that's not the only relevant time.

You can scatter any type of DM on a spacelike hypersurface any way you want, but then you have to figure out the successor (and predecessor) spacelike hypersurface, and there you have to bite a bullet: you can constrain the DM or throw away the well-posedness of the initial-value problem.

Your constraints are dominated by the hyperbolic-elliptic PDEs. The hyperbolic portion lets you lay down initial values for your dark matter on a spacelike slice. You then need an equation of motion for your DM, as you do for your visible matter, so that you can evolve the contents of that initial spacelike slice in time. The elliptical portion are the Hamiltonian and momentum constraints.

Without satisfying these constraints you tend to lose uniqueness, which destroys the predictive power of your model.

If you're spraying down a dust of non-interacting DM particles within some spacelike region, as you evolve from your initial configuration you end up with each particle growing into an everywhere-timelike worldtube. (Non-(self-)interaction is just to make this really clear without the distractions of decays or daughter products from scatterings. Each dark matter particle has its own worldtube extending arbitrarily far in to the future or past.)

The simplest Cold Dark Matter models have a conventional nonrelativistic and relativistic dynamics determined by two parameters: particle rest-mass and interaction cross-section. In our simple non-interacting cold DM dust case the interaction is purely gravitational, so we're left with every particle having an identical rest mass.

Now, lay down the visible matter in a galaxy (or cluster!). You can lay down the dark matter dust arbitrarily to form a halo which could support a realistic galaxy rotation curve on your initial surface. You are right that you can put it practically anywhere, and are not restricted to uniform density. However, when you evolve in time, you inevitably find that you are stuck with a narrow range of mass densities at various points in the galaxy (or cluster!), but still have freedom to set down differing particle number density, higher numbers at lower particle mass. If your particles are too light, the gravitational coupling with the visible matter is too slight; worse, the gravitational coupling between the DM particles is too slight too, and your galaxy quickly disassembles. If your particles are too heavy, instead you get dynamic heating of hydrogen gas, and you get far too much star formation and metal enrichment.

You can go the other way too: first put down a test particle DM halo and then add hydrogen gas, or a modern galaxy, or whatever else, and see how the system evolves. It is a feature of the standard galaxy astrophysics that DM and visible matter do not have to be near each other at all times. (This gets important when you consider galaxy clusters rather than just galaxies; laying out CDM is hard work, as I've been describing, but you can't just drop in MOND. It's also testable at solar-system scales; we can look for post-Newton dynamics in the Jupiter system, or in the inner solar system, and test whether it's compatible with General Relativity (with a fine dark matter dust of up to a few Phobos-masses inside Neptune's orbit) or whether it's compatible with a different post-Newtonian dynamics, like MOND, where the galaxy's MOND corrections will generate a quadrupole anomaly stronger around the outer planets and their moons than around the inner planets).

More complicated particle CDM theories are still stuck with the general rules of the simple model above: the stress-energy in the large has to hang around in the right places for long periods of time; the stress-energy can't just pop in and out of existence at a point (it needs to be thermal, so its worldtubes cannot even be nearly lightlike, let alone timelike); and it has to have a reasonable number density). Crucially, non-gravitational coupling to the Standard Model imposes further restrictions on the initial surface, it does not relax them.

More complicated particle CDM is usually motivated by problems in particle physics, models for for which galaxy (and cluster!) astrophysics can provide observational evidence. Some WIMP models are good tests for SUSY models, so one experimental search might test two models grown from very different underlying theories. One does not have to believe the "WIMP miracle" conjecture when one can outright test it observationally and in a laboratory setting.

> MOND

By construction you can't put MOND just anywhere on your initial values surface; it is a phenomenon arising from visible matter. You can't put down MOND first and then add matching matter and see what happens. (Well, there are relativistic theories which start by taking MOND and then proceed to take General Relativity by introducing one or more fields until they get a good match with MOND. Some of those approaches might let you put down a "MOND field" first and add matter that -- Famaey and McGauch have a good, if aging, overview in Chapter 7 of https://arxiv.org/abs/1112.3960 -- but at some point you might ask if you can start with an already-relativistic theory like General Relativity and recover MOND from that instead. MOND does appear to work for galaxies, after all, even if it needs modification for much larger and much smaller structures.)



> If you have an infinite space of particle parameters and a series of tests keeps eliminating large swaths of this space, at some point it feels like you're playing a god of inbetweens game a la creationists arguing using gaps in the fossil record.

Or you're getting closer to finding out what the real parameters are?

If you eliminate all possibilities and have to make up some new parameters, sure, that feels like you're not doing science and might as well be a creationist. But what you describe, narrowing down the space of possible explanations from infinitely many to only a few, is the dream of every theoretical physicist.


> Or you're getting closer to finding out what the real parameters are?

By that metric, epicycles were rock-solid.


“What’s most impressive is that the predictions of dark matter were first made in the 1970s and 1980s, and were observationally confirmed later. This is not a case of tweaking the model to fit the data; this is a case of the best kind of science you hope for: where you make predictions, make the observations, and what you see validates and confirms the predictions you had made. And yet, even 35 years later, there are no modifications of gravity that achieve the galaxy-scale successes of MOND that also explain these other observations. The best tests of dark matter vs. MOND, which are on large, cosmic scales, have a clear winner and a clear loser.”

https://medium.com/starts-with-a-bang/theres-a-debate-raging...

In short: looking at everything we can observe and can model, we do know that the “dark matter” is matter. Because we first made predictions (“it should behave as matter”), then confirmed them, many times. And MOND can’t even explain that what’s already observed.


That's putting the effect before the cause. The dark matter map can also be a map of "how wrong we are," not only "how much invisible mass is there." An incomplete periodic table of physics, if you will.

We need to produce a WIMP here, on Earth, and watch it decay. That's a "thruthifiable" experiment, but it'd be enough to convince me that we've found the correct line of thinking (which the popular opinion could very well be, don't get me wrong - I simply believe that we're overconfident).


> We need to produce a WIMP here, on Earth, and watch it decay.

No. You can't "need" something if that is simply unreachable. There’s reasonable chance that to produce the particles (which still don’t have to be the WIMPs as we imagined them, and still would be „matter“) the energies needed are simply beyond those that will ever be available to humanity. It wold not mean more than that: that we, humans, just can't repeat with our technology the extreme conditions that the Universe had/has.

The WIMPs in the form discoverable by the energies that are available to us at the moment would have been nice luck, but the existence of dark matter is not anything less certain when the dark matter is simply different from that. It would still be "matter" and not something else.


"Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks."

- Karl Popper


The Bullet Cluster seems pretty conclusive though.

Please post links to the arXiv abstract pages, everyone: we don't always want to download a PDF just to read the abstract!

https://arxiv.org/abs/1712.07962

Edit to add: the abstract pages also often contain useful extra information, such as (in this case) a link to YouTube videos of the simulations -- https://www.youtube.com/channel/UC8ltFtaETXDphec0l-VxMsg -- or the publication history (in this case, a DOI is given).


I am of the opposite opinion. Don't post links to the abstracts as the pdf's contain them too. But the pdf's also contain figures and other things which make it easier to browse, whereas the arXiv abstract page contains a lot of unnecessary fluff.

But from the abstract it's one click to the pdf, while from the pdf it's manual URL editing to get to the abstract.

I actually started a Firefox extension that made a popup to redirect Arxiv PDF links to the abstract page, but never finished it for some reason.

Is it true that every other forces besides gravity is polarised? There's a repulsive nuclear strong force and an attractive nuclear weak force?

EDIT: Partial answer is that there is a three-"color" polarization for strong force. I feel like it somewhat weakens the argument of "everything else is polarized, why not gravity" if the other forces are polarized in unique ways.


Strong nuclear force is always attractive.


Apologies, you are correct, jumped the gun a bit there.

It's repulsive at short distances, attractive at longer distances. And oddly, the longer the distance, the stronger the force, it doesn't follow the inverse square law!


Why strange, rubber also works like that.

Also not a physicist.

AFIAIK the "dark matter & energy might be negtive mass" idea has popped up before but has been dismissed because our current observations show that it's gravitational effect isn't lessened by the expansion of the universe.

He addresses this in section 2.3.1 by adding a "creation term" to balance universe expansion with the creation of new negative mass, but that just seems like a dirty hack to me.

Albeit, the cosmological constant was a dirty hack too, so that doesn't really necessarily discount anything.


Are they pretty sure it’s different than antimatter? Last I heard we weren’t sure if it has negative gravity or not.

Matter-antimatter annihilation would produce gamma rays that are detectable. I believe there was a study that went looking for that but didn't find anything.

To clarify (presuming I understand correctly): Antimatter might have negative gravity, but dark matter can't be antimatter, because we'd see the gamma rays from the collisions.

But if they’re repelling each other and for billions Of years. Why should there be any collisions?

Because it's still in places where there's interstellar gas (if this theory is right). And repelling each other gravitationally doesn't work very well at the molecular level.

Maybe there's a matter/antimatter Leidenfrost effect?

https://en.wikipedia.org/wiki/Leidenfrost_effect



If it's antimatter why isn't it coalesced into antigalaxies that we would be able to see visibly, and is instead diffused as a dark fluid?

It is, we can't see them because they emit dark energy "light". /s

We would see gamma radiation producing events at the interaction interface, even if it is just interstellar gas occasionally colliding.

Not to mention the occasional universe bleaching bursts of energy that comes from an antimatter galaxy colliding with a regular matter galaxy.


I know you put the "/s", but in case anyone isn't aware, as far as we know the photon is its own anti-particle. So light from anti-matter stars would still just be light.

Given the spacetime interval between photon creation and destruction is always zero, I'd find it moderately bizarre if there was an antimatter version of them.

They could repel each other gravitationally too. Seems like that’s how antigravity would would work. I don’t even think we know that about antimatter yet.

Looks like the rest of the world is about to catch up with Jean-Pierre Petit's theories about negative masses surrounding positive mass objects like galaxies and holding them together... Even the proposal for the modification of Einstein's theories... Times are a'changin.

It took almost ten years (2007-2017) from JPP being shunned by the scientific community (and the highly politicised French Wikipedia) to others "discovering" the same things he had been saying all along. https://arxiv.org/abs/0712.0067

http://jp-petit.org/papers/cosmo/2018-AstrophysSpaceSci.pdf

You may give yourselves the smallest pat on the back in the universes.


figure 1 of that paper is virtually identical to the galaxy rotation curve of the current paper! both were N body simulations

thanks for pointing out this earlier work


I found the author's Twitter summary of the paper useful as well: https://twitter.com/Astro_Jamie/status/1070302359325151233


I've personally verified this part of the paper:

> Observations clearly indicate that the Universe is not empty.

EDIT to add: Another nice, slightly Douglas-Adams-y quote:

> This implies that our Universe is just one of those things that happen on occasion, and we can simply think of its existence as being illustrated by a 1 billion-σ statistical event.


>The gravity from the positive mass galaxy attracts negative masses from all directions, and as the negative mass fluid comes nearer to the galaxy it in turn exerts a stronger repulsive force onto the galaxy that allows it to spin at higher speeds without flying apart.

I don't get this, seems contradictory.


Maybe it was modeled as a curvature of space? So positive masses curve space so that everything moves toward them - including light, massless particles, and negative mass. And negative mass repels everything, including other negative mass, by shaping space differently.

[Edit: jbay808 has a better explanation below, and negative mass attracts negative mass.]

That behavior is described here https://en.wikipedia.org/wiki/Negative_mass#Runaway_motion but it's not what I was expecting either.


Yeah this helped me create a mental picture that kind of makes sense. It would clarify why negative mass is also concentrated in areas of high mass, and could also provide the mechanism for constant universe expansion, as the space between masses is constantly being pushed away by the diffuse negative mass. Heh, armchair physics is fun :)

Huh, very interesting. Definitely not intuitive by comparison to electric charge.

Negative mass inverts signs in ways that are not intuitive. Best explanation is a diagram from the author's twitter page [0][1].

When a positive and negative mass particle interact gravitationally the positive mass is repelled and the negative mass is attracted.

[0] https://twitter.com/Astro_Jamie/status/1070303556266283008

[1] https://i.redd.it/qt2tf2tbni221.jpg


I think what they're saying is that positive mass galaxies attract the negative mass, even as the negative mass repels the positive mass (and all other negative mass). In a stationary system, eventually the two will reach an equilibrium.

However, the effects of this in a system in which the positive mass galaxy is spinning is that the negative mass counteracts the forces of inertia, allowing the galaxy to spin at higher speeds without shattering like a cd spun too quickly. Now, whether the math of all that makes sense, I'm am not in a position to comment on.


Wouldn't that allow for a "perpetual motion" setup where a blob of normal mass is in front of a blob of negative mass? The negative mass would push the positive mass forward, and then be attracted to it and follow. What am I misunderstanding?

You can't ignore the gravitational force of the normal mass. The two would rapidly reach a zero-value equilibrium at some point where the repulsive force of the negative mass is perfectly cancelled out by the attractive gravity of the positive mass, so you have a net force of 0 at some distance.

For an easier to visualize example imagine placing one magnet positive pole up inside of a tube, and then you place another magnet positive pole down in the same tube. It would create a similar effect. There is a repulsive force being perfectly balanced out by an attractive force and the two reach an equilibrium where the magnet on top is 'floating' with the net of all forces in this closed system being 0.


Screwily to our intuitions negative mass goes in the opposite direction of its acceleration.

It still goes away but the acceleration is in the same direction. It is weird and easy to be confused.


I think you meant to say that the mass accelerates opposite to forces acting upon it.

An idealized -M + M = 0 pair of particles (one normal, one negative mass) could experience runaway acceleration. Author touches on this in the paper as a potential source for the incredibly high-energy extra-galactic cosmic rays.

Granted, the paper describes a model in which something that acts like a particle with negative mass exerts this force upon things, but has no claims as to what a physical manifestation of this would look like.


Damn, you're right, there goes the hoverboard.

It would be perpetual motion, but momentum and energy would remain the same. Both depend on mass (so negative mass accelerating creates negative momentum and energy).

That's an interesting point. Thank you!

The galaxy is in the center, and with a large positive mass it attracts negatively-massed matter towards it. But the negatively-massed matter repulses rather than attracting, so it has the effect of "squeezing" the galaxy in on its self.

Negative mass is like playing opposite day. Negative mass is attracted to other negative mass, but because of the inverse acceleration to force relationship of negative mass the end result is that it is pushed away from other negative mass. Negative mass would also repel positive mass, which is straightforward for the positive mass but for the negative mass (again, inverse acceleration) it would end up with an "attractive" motion toward the positive mass.

I was just about to quote that same sentence.

How can positive matter attract negative matter which at the same time is repelling positive matter?

The author is described as an Astrophysicist at Oxford (a reputable place) so I assume I'm either just not getting it or this is poorly worded.


To approximate with Newtonian laws:

F=ma

Meaning that positive and negative masses will accelerate in opposite directions in response to the same applied force. The effect is different, but it's a bit like how when you are in a car and hit the gas pedal, and your kid is in the back seat holding a helium balloon, the kid feels pushed backward into the seat but the balloon flies forward toward the windshield.

F = GMm/r^2

Meaning that gravitational forces between opposite signed masses is the opposite direction from the force between masses of the same sign.

Thus, the gravity force repels the normal mass away, but this repulsive force actually drags the negative mass along with it, because the negative mass accelerates the wrong way when "repelled".


We have an intuitive ~~example~~ approximation of this in real-life: balloons in a car[1].

[1]: https://www.youtube.com/watch?v=uAJlg8MDAlU


I'm intrigued. Isn't the reason a balloon moves forward more of buoyancy? If you do the same experiment with the window open, doesn't it do as expected by most people?

I didn't read that positive matter is attracting negative matter. What I gathered is that the presence of a cloud of negative matter in the right place would be held in place by mutual repulsion of the outer arms of the galaxy and the inner galaxy. And that the neg matter supplies enough repulsion to the diffuse outer galaxy that it can spin a bit slower than it would have to otherwise.

Positive matter creates a gravity well. This much most people are familiar with.

Seems to me what they're saying is that this well will pull in negative matter until a balance is reached, this will, in turn exert force on the internal structure of the galaxy.


Think of it as one pushes while the other one pulls.

> Air bubbles in water can be modelled as having a negative mass.

Forgive the naive take on this, but it's a weird point to me... if air bubbles in water can be modelled as having negative mass, but clearly do not (they are made of particles with positive mass), then they are only "negative" in relation to the material surrounding them. So even if they can be modelled this way successfully, clearly the model doesn't imply for certain that they do have negative mass. So by analogy, just because a negative-mass model can explain the observations of dark matter, doesn't it still leave the question of whether anything "real" is implied by it? Perhaps it's just a reflection of a negative relative to some unknown bias (field), like the Higgs field, but in "absolute" terms is not actually negative.

(Not sure "absolute" has any meaning here..)


The concept of whether something is "real" is a metaphysical amusement. And it is never meant to be answered in modern physics. Physics has come a long way into what it is today from natural philosophy. I believe all physicists in this day and age subscribe to the notion of model-dependent realism in one way or another. https://en.m.wikipedia.org/wiki/Model-dependent_realism

Perhaps someday in the distant future we will discover that many assumptions in physics are simply wrong since we really do indeed live in a computer simulation and it is one where the Von Neumann architecture holds so it is always possible to alter "physics laws" like the Pauli exclusion principle and "physics constants" like the speed of light. And these "physics laws and constants" do get altered under certain if-statements or else there will be bugs and the simulation will crash, rebooting itself as a result.

Or perhaps this simulation does crash and reboot itself very often. It's like elixir. We simply are not aware of it. Maybe that could be why we have things like the Heisenberg uncertainty principle and quantum tunnelling.


Or not so distant future. There has been a relative standstill in physics in spite of perhaps more 'known unknowns' than ever before. The problem with models independent of 'reality' is a lack of falsifiability. This in turn means the model itself becomes indefinitely self sustaining even when it's completely wrong as each wrong prediction is then simply massaged back into the model to artificially produce a correct answer.

For instance a recent conversation I had was discussing the big bang and the cosmic microwave background radiation. Somebody thought that the CMB was evidence of the big bang. Of course when the CMB was first observed/measured it completely falsified our idea of a big bang due to the horizon problem -- regions of space that should not be causally connected are somehow homogeneous, which should be impossible. But instead of this observation != prediction indicating some fundamental problem we instead add in a magical hyper-inflation period to the model of the big bang so that the model can now "predict" what we see. And now you have people that believe that the CMB itself is evidence of the model's accuracy, when in reality the CMB refuted our models and we were forced to massage it back into the model in a rather arbitrary fashion. There is absolutely no physical reason to accept hyper-inflation other than 'if we add this magic event, then we can keep using this model.'

For a less contemporary example consider geocentricism - the idea that everything rotated around the Earth. Prior to Newtonian mechanics and other 'real' systems of interaction, we simply used models for orbital mechanics. And these models ended up being quite rediculous. You had planets doing magical swirlies, stopping and going backwards, and all other sorts of things. But because you can't falsify models detached from reality, everybody just shrugged their shoulders and accepted it for something on the order of centuries. And as time passes these models become even more difficult to replace because it ends up meaning you'd basically have to toss something on the order of decades, if not centuries, of past work. In this particular case astrology, for instance, was in the past a scholarly and academic field analogous in many ways to psychology today. Refuting geocentricism involved completely scrapping this entire field, and centuries of work within it, due to the fact it took things such as Mercury going backwards as key components of its analysis of human psychology.

The point of this all is that as you accept models, it can be that you're searching for answers at the entire wrong level of a problem. For instance astronomers in times of a geocentric universe may have been trying to explain why Mercury went backwards during its orbit, yet it's extremely difficult to answer something when you start with a wrong assumption -- in that case that the planet does indeed go backwards at some point, planets have these orbital swirlies, and so on. People like to rewrite history to blame geocentricism on the church, but inertia is not limited to divine belief.


Okay, but does this stuff break the weak energy condition? Could we build Krasnikov tubes with it?

If anyone is interested in dark matter and dark energy I recommend this book: https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Re...

Written by this guy http://web.mit.edu/physics/people/faculty/tegmark_max.html is does a fantastic job of going from really simple concepts/experiments to blowing your mind.


Would this be only gravitational mass that's negative or would it be both gravitational mass and inertial mass? Because negative inertial mass is zany and wierds me out. Negative gravitational mass behaves in a way that makes sense to me.

Has to be gravitational only. Otherwise positive mass is repelled from negative mass, but the negative mass accelerates towards it. So both masses accelerate in the same direction, until they have infinite kinetic energy!

Conservation of energy & momentum would still hold, because negative mass would have negative energy & momentum, cancelling out that of the positive mass.

But the above surely would be an 'unphysical' situation.


>Negative masses are a hypothetical form of matter that would have a type of negative gravity – repelling all other material around them. Unlike familiar positive mass matter, if a negative mass was pushed, it would accelerate towards you rather than away from you.

Pretty sure the author means both.

A continuously accelerating system seems "unphysical", but we have an example already: the accelerating expansion of the universe.


The paper uses the version where both gravitational and inertial mass is negative. This means that everything wants to accelerate towards positive mass and away from negative mass. So positive mass naturally forms clusters (galaxies) and negative mass naturally spreads out evenly but concentrates around the galaxies (forming the dark-matter halos).

Surely its inertial mass is going to remain the same? In the same way that positive and negatively charged objects behave more or less the same way.

It's explained in the paper.

I'm curious about the idea of "allow[ing] negative masses to not only exist, but to be created continuously." Given the law (in the scientific sense) that matter/energy cannot be created or destroyed, on a scale of 1 to FTL travel, how crazy is this idea?

He points out that it's a mathematical tool and may not result in particles, e.g. matter or energy, as we currently think of it.

It could be a property of space-time, as space is always expanding everywhere, space it self could have a negative mass.

This could even be some sort of weird energy-neutral balancing mechanism (e.g. some sort of energy - my bet is on potential energy, like how gravity causes things to accelerate through the potential energy of the arrangement - is lost that accounts for the creation of negative mass particles or whatever; conservation is observational, but we don't really know what 95% of the stuff being conserved is in the first place).

Hence it can be consistent with the conservation of mass and energy.


Probably more close to 1 to than FTL travel.

This is very new research without a deep check by other groups and without experimental support, so wait 5-10 years before getting too attached to this result. Anyway, there are weird somewhat similar things that are cannon https://en.wikipedia.org/wiki/Vacuum_expectation_value

The technical details and the experimental support are very very very important to distinguish between weird things that are true and weird things that are false.


I thought it was less a law and more of an observation.

Scientific laws are just quantified observations.

Yup, that part seemed like a stretch to me too. Besides which, it doesn't seem to address any of the conflicts between QM and GR, so I'm not seeing it as a terribly interesting path. Not saying it's wrong, but it's not where I'd put my money.

This is at the "would lead to FTL" level.

This then leads to the inevitable questions, is an Alcubierre Warp Drive possible, since one of its pre-requisites was particles of negative mass?:

https://en.wikipedia.org/wiki/Alcubierre_drive

>>a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created

If this matter is popping into space continuously as the author describes, it could be possible to harvest it. The question is, how much of it is popping into existence in lets say a square km of space (something we could feasibly cover with our current tech), and how do we detect and capture it.

The author does readily admit that his theory may be wrong, but useful as a mathematical tool. It's like saying "My theory may be the Newtonian Mechanical model of dark matter + dark energy, but not the quantum (read: real) theory." I sure as hell hope he is correct and its a real particle we could capture. It could open up technology we have yet to realize and get us off this rock.


Sounds a lot like the concept of the Dirac sea to me.

https://en.wikipedia.org/wiki/Dirac_sea

Rather than have dark matter particles, have negative mass dark matter particles in every other location instead.


This is explicitly very different from that. There's no claim of "negative mass dark matter particles" in _ever_ location, rather, they have a specific distribution.

That distribution being all the places that aren't normal matter particles. So primarily outside of galaxies.

No. The negative mass matter clusters around galaxies because it accelerates towards positive mass and away from other negative mass. The area between galaxies becomes largely empty in the simulations.

I recall reading article in a popular science magazine about hypothetical negative mass with exactly these properties. It was about 25 years ago and the magazine was Russian language. Unfortunately, I can't recall its name now.

Oh, thanks to the power of the internet search, I found a scan of that article: http://epizodsspace.airbase.ru/bibl/tm/1990/10/otrits-massa.... The journal is "Техника-молодежи" (a Soviet style name that I am incapable of translating to English) and the article is from 1990.

And that article refers to a publication by Robert Forward in a journal with a name like Aerospace Technology or Aerospace Engineering. But I found an article in on the same topic in NewScientist: https://www.newscientist.com/article/mg12517084-200-the-powe...

Wikipedia, of course, has an article on Negative mass as well.


Thank you! The first thing I did when coming to this thread was search for posts containing "Robert Forward", as any discussion of negative inertial mass is incomplete without mentioning his work. So, kudos.

Anyone interested in the implications of negative mass should probably check out Timemaster, a sci-fi novel by Forward. Negative mass can hypothetically do some interesting things. Things such as allowing lightspeed travel by matching negative mass to positive mass in equal amounts, leaving a non-photon object with rest mass = 0, or producing energy by accelerating negative mass to high velocities.

Unfortunately, Forward is much better as an idea guy than he is as an author. The scene where the hero travels back in time and has a threesome with himself and his wife is a bit awkward...


What's the relationship between negative mass and negative gravity and anti-gravity? Dark fluid is repulsive, so is it theoretically possible to collect a ball of it, put it between you and another positive mass, and fly apart?

Yes, that is essentially my understanding

Two passages from the article:

> Negative masses are a hypothetical form of matter that would have a type of negative gravity – repelling all other material around them. Unlike familiar positive mass matter, if a negative mass was pushed, it would accelerate towards you rather than away from you.

> The gravity from the positive mass galaxy attracts negative masses from all directions

...why aren't these contradictory?

intuitively... wouldn't a negative mass be repelled by positive gravity?

(I am not a physicist of any kind, obviously)

In the author's Twitter thread https://threadreaderapp.com/thread/1070302359325151233.html

there is this image: https://pbs.twimg.com/media/Dtp7YjWW4AEIvSp.jpg

..which seems to answer my question

If I understood the picture:

- positive mass gravities attract each other and result in acceleration towards each other

- negative mass gravities attract each other, but the negative mass means this attractive force results in an opposite acceleration (they behave as if repelled)

- a positive mass and a negative mass have gravities which repel each other so the positive mass accelerates away from the negative, but the negative mass inverts its gravitation repulsion into an acceleration towards the positive (I find it hard to imagine how this interaction actually plays out, it's a bit counter-intuitive.. I guess they must cancel out rather than chasing each other faster and faster?)


Sounds a lot like phlogiston, especially since it apparently must be continuously created to matched observable behavior.

  Beware the Physical Chem, my son!
  The laws that arn’t, the constants that vary.
  Beware the phlogiston, my little one
  And of the molality be wary.

  He took his entropy in hand
  Long time the adiabatic foe he sought
  So rested he by the delta T
  And stood awhile in thought.

  And as in Newtonian Thought he stood
  The Physical Chem with Beer’s Law Plot,
  Came Bohring through the orbital wood
  And took quantum leaps when hot!
  PV! RT! And with fugacity,
  The entropy discharged his wrath.
  It reached a degenerate state, and being late,
  He returned by the mean free path
I wonder if anyone will recognize this. :)

If by recognize you mean that it's a variation/remix of "Jabberwocky"[1], then yes.

The second corresponding verse (so this corresponds to "He took his entropy in hand"), so others can see the resemblance (I chose the second since the first is a bit harder to see):

  He took his vorpal sword in hand:
  Long time the manxome foe he sought—
  So rested he by the Tumtum tree,
  And stood awhile in thought.
[1]: https://en.wikipedia.org/wiki/Jabberwocky

Very cool. Today I learned something about a AXE (Alpha Chi Epsilon chemistry fraternity).

But perhaps its continuous creation explains why the universe seems to contain so much of it?

Here's an article describing the theory that sound waves have negative mass. It also describes it in terms of the behavior of fluids.

https://www.realclearscience.com/articles/2018/08/11/could_p...

Maybe these phenomena are linked, and it's more immediate than cosmology.

via: https://twitter.com/robinhanson


Interesting rebuttal from someone in the field (who is actually quoted in the paper): http://backreaction.blogspot.com/2018/12/no-negative-masses-...

One of the most interesting properties of matter with negative mass is that if something collides with it it accelerates in the opposite direction of the incoming object.

https://en.m.wikipedia.org/wiki/Exotic_matter#Negative_mass


Titles that describe poorly understood scientific phenomena as "bizarre", "mysterious" etc., hurts science, IMO. I would expect this from a journalist (though not excuse it), but an academic?

Why not something like "Negative mass dark 'fluid' halos around galaxies as an alternative to dark matter"?


My favorite bit from the author on Twitter: https://threadreaderapp.com/thread/1070302359325151233.html

> The next-generation radio telescope - the Square Kilometre Array @SKA_telescope will be able to test this theory, and directly confirm or invalidate its predictions. 13/17 It is rather surprising that the model predicts the properties of a LambdaCDM universe.

As a casual observer this is is what gets me excited! We'll get our answers one way or another.


Stupid non-physicist question here: we know the universe is expanding, but where does it expand at? Are there physical areas which we can observe growing? And if so, shouldn't that mean that we observe distant objects as lighter than their interactions with closer objects would imply?

Space expands everywhere, also right in front of you, it is just a very small effect over short distances. Two points one meter apart expand away from each other with a speed of 0.07 nanometers per year. For short distances electromagnetic and strong forces just pull everything immediately back together as things want do move apart. Over larger distances, think the scale of galaxies, gravitational forces keep the stars, the gas, and all the other stuff together and prevent galaxies from expanding.

But once you move beyond the scale of galaxies and galaxy clusters there are no longer any forces strong enough to counter the expansion of all that space between galaxies and so in general the distances between galaxies are increasing. There are still exceptions, in clusters of nearby galaxies gravitational forces can still bind those galaxies together but with increasing distances between galaxies the expansion finally overpowers gravitational attraction.

It is important to remember that not only are all forces becoming weaker as distances increase but also that points are expanding faster away from each other as their distance increases. As said, two points one meter apart move away from each other with 0.07 nanometers per year but two points one kilometer apart move away with 70 nanometers per year because there are a thousand meters in between them, all of them simultaneously expanding at 0.07 nanometers per year.


> Space expands everywhere, also right in front of you, it is just a very small effect over short distances ... .07 nanometers per year but two points one kilometer apart move away with 70 nanometers per year because there are a thousand meters in between them

No, what you wrote is contradicted by evidence from within the inner solar system (MESSENGER's observations of solar mass loss were highly sensitive; we have excellent VLBI too), from other star systems, especially eclipsing binaries and systems with occluding planetary systems) and from galactic dynamics (LSR tests, peculiar motions, and lots of DM/dynamics evidence for galaxies at different redshifts). It is not how the standard model of cosmology works either. Grossly, 0.07 nanometers per metre per year expansion everywhere would be impossible to hide from solid state physics, and even several everyday polymers and ceramics; an expansion term would have to appear in accurate descriptions.

We cannot say there is no expansion at these scales, but the expansion is highly constrained and evidence requires that it effectively vanishes. A fifth-force mechanism like quintessence requires a shutdown mechanism inside galaxies that contain star systems like ours or TRAPPIST-1 or PSR~J0337+1715. Additionally it likely would need a shutdown in small structures (like asteroids) ejected from galaxy clusters by violent events, although we will not spot those in practice any time soon. Where there's a shutdown mechanism there's also a wake-up mechanism that has to be considered too, and high-redshift observations constrain the wakeup of quintessence action to relatively late times. What suppressed quintessence for a bit more than three billion years after the formation of the cosmic microwave background?

These type of modellers run into the hard problem that as they work out the parameters of their theory, they (so far) find they all are consistent with the standard cosmology. (That shouldn't be too surprising; LambdaCDM, the standard cosmology, was carefully built to concord with evidence "forward-compatibly".)

One way to put it is in the name: cosmic expansion, rather than universal expansion, distinguishing between effects apparent at the largest scales, and effects apparent everywhere in the universe, at all scales.

LambdaCDM is a model of an universe well-described by an expanding Robertson-Walker metric and matter in the large obeying the Friedmann equations. The expanding metric includes a term for the cosmological constant. The matter is essentially a space-filling fluid at rest, isotropic, homogeneous, and being diluted away by the expansion of the background Robertson-Walker spacetime. (It is in a special frame of reference in this model in which Dark Energy arises as a non-diluting homogeneous fluid imposing constant isotropic tension on the matter fluids. In general frames Dark Energy is just the cosmological constant.)

On the LambdaCDM model we can overlay the 'swiss cheese' model; this is standard too, but we are departing from cosmology and heading toward astrophysics. The motivation of 'swiss cheese' is simple: at the largest scales, the Friedmann Robertson-Walker model sketched above describes all observations between well and extremely well. However, it does not describe gravitationally-bound systems like galaxy clusters, galaxies, or star systems. Those are much much better described with conventional clumping matter (and dark matter) inside a collapsing Tolman spacetime. Notably, none of these systems are homogeneous (they contain lumpy bits like planets and stars, and sparse bits like the interstellar medium) and all of them contain radiating orbiting material; that they are radiating implies gravitational collapse (there's also plenty of other evidence for that). The Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model does not describe these systems.

In 'swiss-cheese', the FLRW cosmological model is the cheese. If we treat the cosmological-scale matter fluid as a dust that is only homogeneous at the largest scales, the dust can be lumpier in some places and sparser in others. The lumpiest bits represent galaxy clusters that remain gravitationally bound over cosmological times. We then "swiss" this lumpy cheese procedurally: we cut out a region of the Friedmann matter on the Robertson-Walker background and replace it with a region of galaxy-cluster matter on a Tolman background, and stitch the two together using junction conditions on the boundary. (Typically we do this to the densest lumps, the galaxy clusters, but we could do the same procedure in deep intergalactic space instead. A spherical region of that will not be exactly void, since it will contain at least photons and neutrinos produced in the early universe, likely a bit of baryonic matter from big bang and supernova nuclear synthesis, and possibly a small amount of dark matter too: however all this stuff is so sparse that it would not generate a collapsing spacetime metric -- calculated out, it would resemble a slightly perturbed expanding Robertson-Walker metric. So we don't put "holes" there; our "holes" contain galaxies.).

In a swiss-cheese model there is simply no expansion in the "holes", because the Tolman backgrounds that work do not contain a cosmological constant term. (The typical problem is that something that does contain expansion, like a Kottler vacuole, evolves away from a mass-compensating comoving void, e.g., the hole grows much too fast or in strange ways that do not match any of the tens of millions of galaxy clusters in our sky).

Since Tolman/FRW swiss cheese models [a] are tractable in practice and [b] match observations extremely well, it is perfectly reasonable to take the hint that nature doesn't expand at all inside the holes. That is, the non-expansion of the hole background carries down hierarchically; you don't need to introduce an expansion term into a metric describing an individual star or planet.

It would be very exciting to find any metric expansion within the solar system, or in another solar system under close scrutiny, or at any scale smaller than that of the swiss-cheese "holes".

Since real matter systems like stars and planets can be very well described as a "hole" generating a metric like Schwarzschild out to some boundary, there is no motivation to add in a metric expansion term (it would just vanish within the boundary).

Finally, inhomogeneous cosmologies generally import these results, just like they import the local and global measurements of H_0. The viable scale of fluctuations in the Hubble parameter in such approaches is large compared to solar systems. So there's no relief in a "well, your model is wrong" (incidentally, I'd agree, there are some real problems with swiss-cheese).

In summary, the evidence is against your claim, and other strands of evidence support theoretical frameworks in which there is no metric expansion around Earth/Earth-Moon. That includes frameworks in which one has explicit terms for such expansion: those terms must vanish around here.

- --

See also: the much less wordy way of taking the same position at http://curious.astro.cornell.edu/about-us/97-the-universe/ga...

Compare: https://medium.com/starts-with-a-bang/ask-ethan-if-the-unive...


I don't think this is correct:

"Grossly, 0.07 nanometers per metre per year expansion everywhere would be impossible to hide from solid state physics, and even several everyday polymers and ceramics; an expansion term would have to appear in accurate descriptions."

On a small scale, the effects of the expansion are overcome by other forces -- this doesn't mean that the expansion doesn't occur - merely that its effect is locally overcome and so it doesn't pull apart arrangements of atoms and molecules which are bound together by other forces.

This is even described in your second link.


My model was the following. Take the classical rubber sheet, place two marbles on it, then stretch the rubber sheet. The marbles are unbound and therefore expand away from each other with the expanding rubber sheet. Now connect the two marbles with a spring and again stretch the rubber sheet. The rubber sheet expands everywhere just as before but now the spring prevents the marbles from being pulled apart and makes them slip across the rubber sheet.

I can see where this model might be misleading or go wrong, it requires some friction between the marbles and the rubber sheet because all massive things are bound together at least by a tiny force and without friction the weakest imaginable spring would still prevent the marbles from separating. I have to think about this more carefully and try to figure out how badly this affects the model, maybe it's actually a really bad model.

But as far as I can remember, whenever raattgift said I am wrong, I was wrong. So I will reserve some time this evening for trying to work through his answer. I also skimmed the Ask Ethan article and at least at first it sound like what I intended to say, especially the following paragraph. On the other hand I did not notice any of raattgift's points in this article on a first quick pass.

The reason for this is subtle, and is related to the fact that the expansion itself isn’t a force, but rather a rate. Space is really still expanding on all scales, but the expansion only affects things cumulatively. There’s a certain speed that space will expand at between any two points, but if that speed is less than the escape velocity between those two objects — if there’s a force binding them — there’s no increase in the distance between them. And if there’s no increase in distance, that impetus to expand has no effect. At any instant, it’s more than counteracted, and so it never gets the additive effect that shows up between the unbound objects. As a result, stable, bound objects can survive unchanged for eternity in an expanding Universe.


Your italicized paragraph is a good clue.

I started a reply which was getting too long and technical, with the aim of looking at three prongs. Post-Newtonian elements are at work, and it is easy to fool oneself thinking of the underlying one: metric gravitation and how it manifests within extended objects. (It does; we can see that from the figure of the Earth and its internal structure, and from other roundish celestial bodies.) Where self-fooling is easiest is in thinking (1) in terms of forces, (2) using too large a set of local coordinates or inappropriate coordinates, and (3) studying an object that extends beyond the boundaries of "local".

I have some things to do but will return to your comment and its parent in a few hours with a more detailed comment that hopefully won't stray off into the weeds of technicalities. :D


After reading the Karen Masters link and your first response a few times, I think I am starting to understand what you want to point out. If the universe were empty and expanding, then some light non-interacting test dust would indeed get pulled apart everywhere and at all length scales. But when we add matter and let it collapse, the collapsing matter kind of pulls spacetime with it as it collapses and may eventually reach a kind of equilibrium where the effects of the expansion and the collapsing matter cancel out locally leading to a non-expanding region. If this is kind of correct, I have a very wrong model of the effect of mass on spacetime and have to rewatch Susskind's lectures on general relativity.

I'm not sure this is the conclusion of the part you italicized above, which I read as - space continues to expand but matter holds together (it counteracts the effects of expansion in that the matter doesn't drift apart - but that doesn't mean that space stops expanding around the object - it merely means that the object isn't slowly pulled apart by this expansion, because it is held together by forces that are stronger).

No, you misunderstood this. The paragraph I quoted seems to me to support what I thought and wrote initially. What I laid out in my last comment is different from that and the result of rereading and some additional reading. But I didn't yet manage to read much, so this more like a vague idea not backed up by much.

Yes, good, you've saved me some typing along these lines. (Well, in retrospect, maybe not that much :D )

In typical vacuum solutions of the Einstein Field Equations the metric is what determines the available geodesics[0]. Putting an isolated object into a vacuum solution causes it to "select" an appropriate geodesic from the ones available, and if left alone, that object will at every time be somewhere on that geodesic. A "test object" is pointlike and massless, so adding it to the vacuum does not change the background metric at all. But if we make it heavier, or bigger and rotating or oscillating, then the spacetime is no longer exactly modelled by the vacuum solution. At that point one might use perturbation theory, and consider the vacuum metric as a background and the metric the not-quite-a-test-object itself generates as a perturbation field overlaid on that.

The algebra usually looks like g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu} where the greek subscripts are the usual indices running 0,1,2,3 in 4-dimensional Lorentzian spacetimes (like ours, and most that you'll ever run into), \eta is the chosen background field, h is the perturbation field, and g is the "true" metric. One can also add perturbation fields or play around with higher-order contributions from self-interactions (say if the not-a-test-object is a black hole binary, or a solid fragment of a supernova (an Earth-massed blob of hot metal?) moving relativistically).

If we start with an expanding Robertson-Walker spacetime vacuum (no matter, not even dark matter), and add a single galaxy cluster, we need to figure out the metric to see how it evolves (or to see what geodesics are available for test particles we throw in as probes).

We can do this in a couple of ways: either using perturbative methods like above, e.g. g = {RW} + {galaxy}, or start with a single g for the whole spacetime from a known set of appropriate solutions like Schwarzschild-de Sitter or Kottler, or by engaging in "inside"/"outside" stitching together of metrics like I described earlier (swiss-cheese). (There are other approaches too!)

Each has advantages and drawbacks.

The middle option has the problem that a galaxy cluster will only look like a Schwarzschild source from so far away that it shrinks to a point. Closer observers will see (optically, even!) that it's lumpy, and if they have sufficiently sensitive gravimeters or a probe like Synge's "five-point curvature detector" they will see that Schwarzschild is not quite accurate. In particular, the geodesics the components of the gravimeter or probe "find" are not the ones that would be generated in the model metric.

The first option is hard to do and usually leads one into numerical relativity. That's not such a bad thing these days, thanks to modern codes and supercomputers. However, it's often hard to extract intuitions from numerical solutions, and even harder to boil down into an explanation for others ("just run this code and you'll see" is not very satisfying).

The last option has been around for decades and is a bit half-way. Its advantage is that you generally can say intelligent things about what's going on far from the thin shell boundary, and can develop a good map between the evolution of the configurations of matter within the "inside" metric and that outside. Its disadvantage is that it is a painful amount of work that computers aren't very good at helping with yet.

Which one chooses will depend on some combination of the problem being studied, personal preference, and trade-offs between manual work, accuracy, and comprehensibility. One can combine the perturbation approach with the inside/outside approach, so that one has (dropping the indices) g_{outside} = \eta_{outside} + h_{outside} and g_{inside} = \eta_{inside} + h_{inside} and an Israel-Darmois junction between g_{inside} and g_{outside} which is at least in principle something one can think about functionally (a test object crossing the junction will have its momentum altered; if it just drifts across, the junction is something like a "kink" linking two otherwise smooth geodesics).

Now, back to the standard cosmology, using the "inside"/"outside" approach. In the "outside", the Robertson-Walker vacuum does just what you say:

> [as the] universe [is] empty and expanding, then some light non-interacting test dust would indeed get pulled apart everywhere and at all length scales

and then

> But when we add matter and let it collapse

... we can no longer describe the whole spacetime as a Robertson-Walker vacuum that we're simply probing. Our matter perturbs the RW metric, so the true metric g must be the combination of RW and whatever metric the introduced mass generates. Since the introduced mass is collapsing, it's probably approximately described some sort of Tolman dust. So we select e.g. the Lemaître-Tolman-Bondi metric and perturb that in turn, so g = RW + LTB + O(h) + O(h^2) + ... where h is the deviation of the matter we introduced from exact LTB, and h^n is higher-order perturbations.

This g, like any other metric, will generate a set of geodesics throughout the spacetime. If our collapsing matter was a dust, then each of the individual particles will select its own metric. Flashes of light will find their own null geodesics determined by the metric, and so forth. The results are different from Robertson-Walker, at least close to the matter that we introduced. At even fairly short distances the higher order terms in h fall into irrelevance, and at large distances h itself becomes negligible.

I want to write a bit about extended objects, but that'll have to wait until a bit later. The key feature there is that the individual components of such objects are stuck together, so they don't find their own individual geodesics. The behaviour of extended objects in curved spacetime is fun!

> may eventually reach a kind of equilibrium where the effects of the expansion and the collapsing matter cancel out locally leading to a non-expanding region

You can move the thin shell of the junction around to explore that kind of thing. Or taking a purely perturbational approach you can look for regions of spacetime where geodesics have the characteristics you want (drop down test objects near point in spacetime near a suspected "cancelling-out" region and see if the inertially-moving test objects eventually collide or separate).

How you represent what's happening there is up to you. You could use your colloquial expression, a line from the Karen Masters link or something like it, or talk about the mathematical structures. The theory underdetermines the precise mathematical expression (there are lots of exactly equivalent ways of writing it down, and lots of so close it doesn't matter approximations); the English has it even worse. :/

However, the key thing is that exact vacuum solutions stop being exact when you add matter. Matter rarely cooperates with exact non-vacuum solutions (they typically are maximally symmetric: spherical arrangements of matter of uniform density, with no multipole moments from internal motions, etc. which is far from what we see measuring Earth's or Moon's gravitational fields with e.g. GOCE and GRAIL, and solar prominences big and obvious, galaxies can be spiral, a tiny black hole orbiting a large one will induce tides on the large one, and so on.)

- --

[0] I'm deliberately going to avoid talking about non-geodesic trajectories through spacetime for now. May come back to that when discussing extended objects in a followup.

- --

ETA: I should add that the metric expansion is not really an expansion of space, but rather an extra term tacked onto the metric g. So following the perturbation notation above we could start with flat spacetime \eta and say g = \eta + {expansion} and end up with g = {expanding Robertson-Walker}.

This is quite common: the "true" background is Minkowski flat-space, and then the vacuum eternal spherically-symmetric black hole is a perturbation on that, and then there may be other perturbations. (Instead of starting with the "true" background of Schwarzschild.) This kind of thing leads to some insights about asymptotic flatness.

So for an expanding cosmos, we can start with a perfect flat non-expanding one and perturb that, expanding the metric.

(This is being really loose with terminology, but I think gets the point across reasonably. It's the metric expansion of space because there is a time parameter in the line-element of the metric; spatial distances are determined by when (coordinate-time) you are. g = \eta + f(t), where f is a function taking a time coordinate and generating a perturbation field; maybe better to write g(t) = \eta(t) + f(t) where g(t) is the metric's spatial distance functions for all events on a slice of space that where everything is at the same time coordinate t; but this dives into 3+1 spacetime splittings which is another big can of worms...).

- --

ETA2: the Overview section of this puts it well in a different way. (No claims about the other sections, I haven't read them yet.) https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/m/Metric...


A couple little things I won't turn into literal ETA3, just in case you've already been reading the long post above. :)

(2) below is also mostly for me, I think.

1. Thanks, Michael Weiss. This is essentially the same argument I'm making, only terser. http://math.ucr.edu/home/baez/physics/Relativity/GR/expandin...

2. One important thing about the expansion of the universe is that people hear "expansion of space" and reasonably think space has physical properties. https://arxiv.org/abs/0707.0380 is a good rant about that, and https://arxiv.org/abs/0809.4573 is another interesting take. There's a sort of Betteridge effect going on, in that none of the authors think that the concept of expanding space is awful, but they're instead capturing the "gotchas" that befall even working relativists stray into what philosophers call manifold substantivalism. (I hope that doesn't attract house philosophers, no offence. I don't think my text is all honey!)


Could I interpret it this way?

In the EFE, if we move the cosmological constant factor to the right handside, where the stress–energy tensor is, then stress–energy tensor and the cosmological constant factor have opposite signs and stress–energy tensor can overcome the cosmological constant factor.

When we say EM-forces/Strong/Weak forces "cancel out" the expansion of the universe, it isn't because of those forces are holding matters together. But they contribute to the stress–energy tensor and "offset-ed" the effect of the cosmological constant factor.

Even without those forces, as long as the stress–energy tensor is greater than the cosmological constant factor, the solution of EFE will be non expanding.

Does this sound right to you? Thanks.


Well, so you write down an initial values surface with that approach and let the matter evolve: either you get something physically plausible or you don't. We have some guides as to what is physically plausible, and of course evidence that any of them is wrong would be very interesting.

More theoretically, the LHS doesn't care about how you arrange the RHS at all. More finely, the metric does not care how you compose the metric. If you do it perturbatively, the leading term could be Minkowski or Gödel for all it cares, as long as the sub-leading terms then present a useful background for small perturbations that remain small (or better, vanish) rather than explode into large perturbations. Inside the solar system, Schwarzschild gets that right, and nobody has shown you need to correct for the global behaviour of the cosmic expansion.

> ... if we move the cosmological constant factor to the right handside ..

Before the 1920s (!) there was a discussion about where to put an everywhere isotropic tension in the EFEs. https://arxiv.org/abs/1211.6338

In section 3, the author quotes Einstein's response about how to determine the density. The part after, "Later, he finishes with..." seems especially germane, and cf. section 4 especially its last sentence (wherein "dark energy" in that context means a source field with a potential and dynamics and a coupling to the other source fields and a set of initial values).

[Heh, typo in the second sentence of the last paragraph of §3, "vale" instead of "value".]

> (matter forces) contribute to the stress-energy tensor

Ok, but if you hold that the CC acts isotropically everywhere you can think about decomposing the curvature tensor into its Ricci (and Weyl) components. Weyl tensor encodes the stretch-squash astigmatism: a spherical volume in the presence of a nonvanishing Weyl start to look more like a U.S. football. Ricci scalar encodes the isotropic change in volume. For a volume, nonvanishing Weyl with a vanishing Ricci is volume-preserving; a vanishing Weyl and a nonvanishing Ricci is a contraction or expansion.

The cosmological expansion at cosmological scales clearly is Ricci scalar rather than Weyl, since matter in the large remains isotropic and homogeneous.

Shuffling \Lambda over to the source side does not change that observation: we don't see broken cosmological-scale isotropy, so we must still have a vanishing Weyl and a nonvanishing Ricci scalar on the LHS. How does that happen? Presumably in the metric, since it's the obvious choice of dynamic field (although of course you could insist on making the RHS as complicated as you like, and there have been cases where having the metric maximally static with gravitational dynamics shuffled into "fake" matter is useful -- the original Hawking Radiation paper did just that, for instance; and of course you might want a quintessence-style field instead of a CC, and bite the bullet on recovering observations through that field's behaviour).

Ultimately what we care about is that we have the correct EOMs, and for test particles the EOMs in our labs and in our experimental platforms elsewhere in the solar system, and observed for astrophysical objects throughout our galaxy and the cluster it's in, are nowhere near the EOMs of FLRW. They are much nearer to Schwarzschild.


I read your response like five minutes after you posted it as I just replied to cbzbc at that time. Thanks a lot for the effort! It's already pretty late here, so a real response will have to wait till tomorrow, but I guess I was able to get quite a few things from your responses. Especially probably somewhat related to your second point in the last comment, namely that I kind of really want to avoid the math and use analogies but without realizing or knowing well enough where those analogies break. Not because I don't like math but because as a layman I mostly consume it passively when reading or watching lectures. In consequence I can follow a presentation but doing calculations myself would be a very different thing and so I also lack mathematical intuition when it comes to the math used in physics.

And as I am already typing, I will just add the first question I got when reading your response because I already typed it out. In the second paragraph - not counting the first sentence - you write »[...] \eta is the chosen background field, h is the perturbation field, and g is the "true" metric.« When you say »chosen«, are you only referring to the choice between signatures (1,3) and (3,1) or do you want to allow eta to be something other than the Minkowski metric there? Probably not to important overall but the first thing that I marked.


> When you say "chosen"

I mean that neither nature nor theory requires one to choose Minkowski as the background spacetime, although it is the most popular choice in perturbative General Relativity.

I've been avoiding sign conventions and coordinates deliberately; I think they would be more distracting here, and of course the choices made have no physical implications.

(Using \eta without it necessarily meaning Minkowski spacetime is arguably an abuse of notation, if that's what you mean. :D)


I'm afraid I'm gonna have to drop the ball on discussion of extended objects. I can't shake the seeming-realization that restorative forces within the extended object must generate a gravitational backreaction, and down that path lies too much math to write down first (in order to summarize later), and I don't trust that starting with an English description avoids a gross mis-characterization.

However, I made a point about the expansion being in the curvature scalar, and Carroll has a lecture which supports this view for lambdavacuum (eqn 15 at https://ned.ipac.caltech.edu/level5/Carroll2/Carroll1_3.html ), which convinces me that I am not too addle-brained.

(The curvature scalar is the Ricci scalar, g^{\alpha\beta}R_{\alpha\beta}, written as R in the Carroll reference in the previous paragraph. Since the metric is Lorentzian a positive scalar curvature still leads to diverging parallel geodesics. Consequently we can say things about the positive energy theorem, and we don't have to introduce things like negative mass (and specify active, passive, or inertial mass when we do). By comparison, if we have a positive definite metric (+,+,+,+ signature) parallel geodesics converge in the presence of a positive scalar curvature. The sign difference for the timelike coordinate in our Lorentzian spacetime makes all the difference!)

Why does this matter? Because, at the Carroll reference, we can add terms for matter to the action integral, and following the logic in Carroll's subsequent paragraph, the scalar curvature is influenced by the matter. But note that by adding matter to eqn 15 we are making R even more positive. But in our universe with known matter, we can't make R go below zero. That's the conceptual keystone for me: quantum foobar doesn't lead to any energy state lower than that of vacuum any more than classical dynamics can, so there doesn't seem to be any room for expansion in local quantum systems or extended classical objects. (I guess the Newtonian-limit argument then goes that in vacuum if \nabla^{2}\Phi = 0 then you can't get an expansion force by adding matter.)

Finally, in part just because I love the image here, http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/n2ext.h... It's related to the first paragraph: if you spin an object this way it will shed gravitational waves (the metric isn't spherically symmetrical at any time) and at some level that must couple to the restorative forces that keep the wrench looking wrench-like rather than deforming during its spin. Turn the metal wrench into plasticine, for example, and it will deform while spinning, and the new shape will generate yet another different metric. If we put a fairly heavy weight on top of the metal wrench when it's on the ground, the metal wrench stays wrench-shaped; but the plasticine wrench would deform (and also heat!). Capturing all of this in general curved spacetime is not so easy, and for just weak Schwarzschild (as in the diagram, presuming the ground is our Earth) or even that and sliced de Sitter I don't trust the results to be general, so I kinda give up the moment. :/

My total guess though was that if the CC acts in the solar system than everything in the solar system, including metal and plasticine wrenches, need a tiny restoration force to avoid deforming. Could the notional equivalent of the spinning plasticine wrench in a comoving Cavendish appratus directly measure an expansion force within the plasticine? Likewise, does the CC affect the temperature of the deforming weighted grounded plasticine wrench? Not sure. I'm attracted by a comparison with a binary NS or BH system, treating BIGns----smallNS : Bigend--handle where the --- has been thinned out to almost nothing. We can extract local expansion from NSNS gravitational wave astronomy in principle. (A test system would probably galaxy-cluster scales in spatial extent or mass, though, see below.)

Undoubtedly these ideas will resurface in some future conversation.

Lastly, Cooperstock et al. https://arxiv.org/abs/astro-ph/9803097v1 grinds up some numbers; they take seriously cosmological correction to local EOMs at several sub-cosmological scales, and find out they're extremely extremely small, and compatible with not existing. Note that we've had 20 years of numerical relativity and physical cosmology not reflected in that paper.


Think of if space were just two dimensions and it was on the surface of a balloon. Space is expanding in the sense of inflating the balloon. Every point on the balloon is getting farther away from every other point.

If you stand on the balloon it doesn't make sense to ask "where is the balloon expanding from?". Its expanding in every direction. Every observer on the balloon sees all points around them getting farther away.

Now try to picture that but in 3d. It might help to think of it as like a cake with raisins in it expanding in the oven.


> If you stand on the balloon it doesn't make sense to ask "where is the balloon expanding from?".

Sure it does, and there is a well-defined answer, it's just the answer does not lie on the surface of the balloon. (And for a perfectly spherical balloon, is equidistant from every point on the surface.)


That of course only works because the surfaces of balloons we are used to are always embedded in spacetime. There is however no [good][known] reason to assume that spacetime itself is embedded in any space.

I've always thought this would be an interesting experiment. Assume that spacetime does live in a higher dimensional space, and try to arrange masses so that spacetime is forced to intersect itself. See if anything interesting happens.

Of course this probably requires some stellar engineering.


The explanation I've heard is that it's just space being created everywhere at once. There's no center from which everything expands.

This VSauce video explains it better than I can (later in the video): https://youtu.be/3pAnRKD4raY


Imagine a flat ‘universe’ on the surface of a balloon which is being inflated. There would be no centre of expansion on the surface of the balloon, the space would appear everywhere equally.

Presumably you could describe this as a theory of levity. For happy spacetimes.

The possibilities for Star Wars puns are endless.

There are alternative explanations that theorized that the 2nd law is not linear for extremely weak forces.[1] Thus, two masses that were sufficiently far apart would experience an attraction larger than that predicted by an inverse square law.

I think some particular applications of these theories were proved wrong some years ago, but I can't find those results.

[1] https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics


Actually, Star Trek had an episode where a giant space amoeba pulls the Enterprise into a "zone of darkness" where thrust towards the amoeba pushes the enterprise away from the amoeba. Sounds similar. Of course they destroyed the creature with some antimatter.

https://en.wikipedia.org/wiki/The_Immunity_Syndrome_(Star_Tr...


Negative mass... holy shit with this we could break the speed of light

How?

By offsetting the mass of a system, to produce a zero mass vehicle.

Take a net negative mass vehicle, and accelerate it by having it collide with its propellant. Would this be an anti-rocket?

How does it come to a stop, the vehicle gains too much mass?

The mass part of the vehicle could either detach from the negative mass component. Or the vehicle could eject mass to reduce velocity.

Very cool stuff

“Negative masses are not a new idea in cosmology. Just like normal matter, negative mass particles would become more spread out as the universe expands – meaning that their repulsive force would become weaker over time. However, studies have shown that the force driving the accelerating expansion of the universe is relentlessly constant. ”

Is it though? How can you measure a universe-size force that takes billions of years to “move” on a human lifetime scale?


Neither an experimental physicist nor cosmologist, but another possibility is that our universe shares very slight space-time interactions with other universe(s) in a multiverse where its mass-energy casts negative mass "shadows" in ours. Blackholes in one creates areas of repulsion and expansion in the other. Maybe this is where the missing mass-energy is? It's there, but it's not in our universe.

Not a physicist. If negative mass exists, is it featureless, or is it composed of units which can combine to form analogous negative mass atoms, negative mass molecules, etc?

It would presumably be composed of units which could well join together into larger structures. But these would have to be small scale (the size of atoms or molecules) because gravity causes negative masses to move away from each other. So it wouldn't clump together into planets and galaxies.

Would this also explain galactic voids as regions of large negative mass? It would seem that deviations in the Hubble constant bear a void would confirm this theory.

> Negative masses are a hypothetical form of matter that would have a type of negative gravity – repelling all other material around them. Unlike familiar positive mass matter, if a negative mass was pushed, it would accelerate towards you rather than away from you.

That assumes that inertial mass = gravitational mass, which is assumed to be true, not not proven.


> That assumes that inertial mass = gravitational mass, which is assumed to be true, not not proven.

The assertion has been tested experimentally. Inertial and gravitational mass are seen to be equivalent within the bounds of experimental accuracy. The wikipedia article on the "Equivalence Principle" has lists of tests for various versions of the principle: https://en.wikipedia.org/wiki/Equivalence_principle#Modern_u...


And the negative mass postulated here? We don't know if it's still equivalent there because we have never tested it.

It would be a lot simpler if inertial mass was negative gravitational mass in this theory.

Then you have repulsive gravity with normal behavior under force.


I see I misunderstood that you were specifically questioning the equivalence for this postulated negative mass. I thought your statement was a more general one.

I love the choice of the word "could" for this title. Makes it sound like the plot for a science fiction book X-D

Here comes the Alcubierre Warp Drive!

To quote the author https://twitter.com/Astro_Jamie/status/1070343971338153984

> It is quite likely that the negative masses in this study are a mathematical tool, rather than real physical matter. This rules out a lot of sci-fi, which is disappointing of course!


To be clear, the author IS proposing that there MAY be negative mass particles, not that this is all mathematical. That statement was simply a tip of the hat to the fact that none have yet been detected and its possible his theory is just a "accurate way to model" dark matter/+dark energy. It's just a nice way saying "My thoery might be the Newtonian Mechanics of Dark Matter/Energy, close but possibly wrong."

Why crap on the fact that this may lead to a warp drive.


Exactly where my mind went. Does the perspective described in the paper make the Alcubierre drive seem more plausible? Or is there something about the nature of the dark fluid hypothesized that would make it useless for something like that?

>Or is there something about the nature of the dark fluid hypothesized that would make it useless for something like that?

Assuming it was, literally, some kind of magical FTL juice... it all seems to be outside the galaxy, which means tens of thousands of years' travel just to get to it. If we're willing and able to do that, why bother with FTL at all?


He is also implying that it spontaneously emerges from space on a continuous basis. If that's the case then it may be possible to setup a harvester of negative mass. The question is how much of it emerges in so many square km of empty space. It could be 1 particle per light year.

I'm not a huge fan of the Fermi paradox but if it has any validity, it would seem to suggest the problem is difficult to say the least.

Or extremely easy if you believe the UFO reports... the only incorrect assumption is that they would initiate contact. Even Dawkings knew that this would be a stupid assumption:

https://www.richarddawkins.net/2017/11/we-just-sent-a-messag...

If they show up every couple thousand years and don't say anything, would we even notice?

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