
Why Understanding Space Is So Hard (2016) - dnetesn
http://nautil.us/blog/-this-is-why-understanding-space-is-so-hard
======
js8
It is hard. There are cellular automata, which are result of discrete local
functions evolving in fixed space.

But what if we had something like "foam automata", discrete local functions
that could alter the space they operate on? For example, if we represented the
underlying space as graph, could we have functions that evolve as to change
(reconnect) the edges and add/remove vertices of said graph?

Aside from 1D case, I was unable to figure out a set of rules that wouldn't
quickly devolve into something that's either locally too dense or too sparse
or disconnected. And making it follow some laws of conservation seems even
harder.

Maybe some smarter readers of HN will figure it out, I would certainly be
delighted.

~~~
TheOtherHobbes
Not sure why you're being downvoted.

What you're describing isn't too far from Causal Dynamical Triangulation.

[https://en.wikipedia.org/wiki/Causal_dynamical_triangulation](https://en.wikipedia.org/wiki/Causal_dynamical_triangulation)

~~~
js8
> Not sure why you're being downvoted.

Thanks, I was also confused, but according to some weird social customs
enforced on HN, I cannot sincerely ask that question. On the other hand, I am
not sure about the upvotes either.

I actually didn't mean to develop some new physics theory, I just wanted to
play a mathematical game (like Game of Life, for example), which would alter
its own space/geometry. And this seemed as a good place to mention it, and get
some feedback if somebody was aware of something similar. Because I found it
quite nontrivial (to make it work "decently", in a vague sense), despite my
lack of ambitions to explain physics.

CDT looks interesting, but it's not quite what I had in mind.

------
goldenkey
This article is pretty much a copy of a much more detailed Scientific American
piece posted 3 months ago. I highly recommend it, a great read.

The Forgotten Mystery of Inertia
[https://news.ycombinator.com/item?id=15487928](https://news.ycombinator.com/item?id=15487928)

Regarding the topic on hand -- Is it possible for the net statistical
acceleration of the charged virtual particles of the quantum vacuum to be used
as an absolute reference frame in order to gauge absolute velocity/intertial
mass? Does anyone know if this idea or similar has ever been tested
experimentally?

~~~
tim333
>Is it possible for the net statistical acceleration of the charged virtual
particles of the quantum vacuum to be used as an absolute reference frame in
order to gauge absolute velocity/intertial mass?

I very much doubt you could use that as an absolute reference frame. It would
contradict the ideas of relativity and no one has observed such a thing as far
as I know.

~~~
goldenkey
The partial differential equations of relativity consider spacetime and
matter/energy to be infinitely divisible. Particles are neither supported nor
rejected. Blackholes seem to indicate that relativity performs well in
matching reality despite lacking any notion of particles. But who
knows..relativity could be at odds when it comes to the vacuum.

The reason if any, to think there might be something interesting here-- All
objects as they move through the vacuum, leave a disturbance, a "wake" of
sorts, in all quantum fields. These disturbances can appear as real particles
to some observers, while being virtual particles for others. It may be
possible then, for relativity to be satisfied considering this observer-
dependent visibility. In fact, perhaps a binary statistical measure on the
number of real particles may be the key to getting the absolute measurements.

------
mabbo
I know that, given the greatest minds in history have worked so hard on the
problem, I'm missing something. What is it?

When I think about the problem on an individual atom level, the rising up the
bucket doesn't seem hard to explain at all. Friction from the bucket to the
outer molecules makes the water molecules want to move in the same direction
(slowing the bucket sightly, I'd imagine). Once those ones start moving, they
too will pull along the nearby molecules via friction. Then momentum will
cause them to move towards the outer edge of the bucket, pushing each other
and pushing some up the walls of the bucket.

I'm not being facetious here- what's the problem? Have we tried the same
experiment with extremely low-friction buckets?

~~~
T-A
The problem is: how does the bucket know that it's rotating, and not the rest
of the universe that's rotating around it?

Maybe this will help: [http://www-groups.dcs.st-
and.ac.uk/history/HistTopics/Newton...](http://www-groups.dcs.st-
and.ac.uk/history/HistTopics/Newton_bucket.html)

~~~
trevyn
> _Tie two rocks together with a rope, he suggested, and go into deep space
> far from the gravitation of the Earth or the sun...Rotate the rope about its
> centre and it will become taut as the rocks pull outwards. The rocks will
> create an outward force pulling the rope tight. If one does this in an empty
> universe then what can it mean for the system to be rotating. There is
> nothing to measure rotation with respect to. Newton deduced from this
> thought experiment that there had to be something to measure rotation with
> respect to, and that something had to be space itself._

Eh? You measure the rotation against the thing that performed the “rotate the
rope” step in the experiment.

Thought experiments that contain the step “now magically remove X from the
observable universe” should be treated with caution! :-)

If you change it to just “There exists a universe empty except for a rotating
set of rocks connected by a rope”, rotation needs no meaning as it’s one of
the axioms. Also, there is no observer in that universe, so you’re making a
pretty dangerous assumption about the ability to observe a universe without
being a part of it.

~~~
dullgiulio
Well, it's a thought experiment. You can think of the same with two rocket
powered capsules, tied with a rope, so that nothing has to disappear. If they
are rotating, they are rotating against something (space itself), if they are
not rotating, rocket power is strangely not having any effect, which violates
Newton's Third Law.

~~~
trevyn
That’s easy then; they’re rotating relative to the exhaust stream that they’re
creating.

Now if you’re talking quantum vacuum thrusters, exploring exactly how that
works should also give you a good idea of what space is! ;-)

~~~
mustacheemperor
But, how could you measure or perceive that rotation, relative only to the
exhaust stream created by each rocket? If you are picturing the rockets doing
any more than pulling the rope taut with the force of their motion, ie the
rockets are turning around like a wheel in your mental image, you are actually
picturing them rotating relative to _you,_ the stationary observer.

The conundrum is: what is the rotation without the relative perspective of the
stationary observer? What pulls the rope taut?

~~~
trevyn
> _What pulls the rope taut?_

Ok, this seems to be a clash of intuitions explained by reference frames —

When you imagine an object in deep space or its own empty universe, you
intuitively use an “inertial reference frame”, where “the physics of a system
in an inertial frame have no causes external to the system”. I.e. you do not
see any “fictitious” forces like the centrifugal force, so the rope would not
be taut.

[https://en.m.wikipedia.org/wiki/Inertial_frame_of_reference](https://en.m.wikipedia.org/wiki/Inertial_frame_of_reference)

If you _are_ imagining the rope to be taut, you are imagining a force pulling
it taut, but this force that you’re imagining is only explained by physics if
you’re using a rotational ( _non-inertial_ ) reference frame.

So if your system has unexplained “centrifugal” forces, those forces can be
modelled as the system rotating within an inertial reference frame, without
having any evidence of any “non-rotating” matter.

It just so happens that deep space is pretty close to an inertial reference
frame, so your mind sort of makes that assumption.

Or, in other words, you could measure and perceive the rate of the rope’s
rotation by _analyzing the forces in system_ , without having any physical
external point of reference.

------
philipov
> _although Einstein’s theory demolished Newton’s absolute space, it gave us
> something else in its place—a four-dimensional structure known as
> spacetime—and this, Greene argues, is absolute._

And yet, it is now thought that spacetime itself can not be absolute, and must
emerge from more fundamental structures, such as combinatorial geometries:
[https://youtu.be/qTx98PUW6lE?t=13m7s](https://youtu.be/qTx98PUW6lE?t=13m7s)

~~~
andrepd
I wouldn't go so far as to say that "it is now thought". More like some people
that are researching this problem are proposing some solutions. We are far
from a definite answer.

~~~
philipov
Sorry, I thought the video made that clear. What is now thought is not an
answer, but a perspective on the question. That the way to resolve the
paradoxes between quantum mechanics and general relativity is not to find a
quantum mechanical theory of gravity, but that both quantum mechanics and
spacetime must emerge together from something more fundamental. In this sense,
it is now thought that spacetime is not absolute. This sentiment appears
widespread in the physics community, but as to precisely what this more
fundamental theory should be, that answer has not yet been found.

------
state_less
These are fun questions to ask. If you take away everything in the thought
experiment except a single hydrogen ion, what can it rotate about? What does
rotation mean in a universe without anything except a single atom? What does
inertia mean without respect to something else? Can such a particle have a
velocity?

~~~
whatshisface
If all you have is a single hydrogen ion (proton? I assume you mean H+), then
you will always be able to choose a coordinate system where it is neither
moving nor rotating. You can also do this if there _is_ a universe outside.

Alternatively, you can choose a coordinate system where the particle is
rotating, accelerating, or moving however you like. Your choice will be
determined by the goals you have. (Without the laws of motion, there is no
reason to prefer even intertial frames over nonintertial ones.)

~~~
state_less
Yep, I was thinking about a proton. I probably should have been more explicit.

Is the particle moving or is the coordinate system?

It seems, like you say, to be arbitrary. Without something else in the
universe, the particle could have any rotation, velocity, inertia, etc...
depending on which coordinate system you choose. The coordinate system seems
to be layered on, from a universe where the idea of space and time were more
useful.

~~~
vorg
There must be something else in the Universe to observe the single proton for
it to have rotation, etc, according to quantum physics. Extend this idea to
the centrifugal force on the water in the bucket in a Universe with nothing
else in it, and the centrifugal force is similarly both there and not there,
in a quantum superposition until observed. The value of Planck's constant is
thus a function of the large-scale distribution of energy in the Universe,
rather than a fixed property of spacetime itself.

~~~
testestx
> There must be something else in the Universe to observe the single proton
> for it to have rotation, etc, according to quantum physics.

No, according to the Copenhagen interpretation.

~~~
whatshisface
Even in the Copenhagen interpretation states can have well-defined angular
momenta before wavefunction collapse.

~~~
vorg
I thought in QM you couldn't know both the degree of rotation and the
direction of the axis for a particle. If so, I wouldn't call that "well-
defined".

------
kapv89
Few years back, I was brushing up on some topology I studied in college. One
thing lead to another and I came up with the idea that there are 5 dimensions
of the absolute nature of our natural universe. Wrote it down as a medium post
last year: [https://medium.com/@kapv89/logically-there-is-a-5th-
dimensio...](https://medium.com/@kapv89/logically-there-is-a-5th-dimension-
fcc51cca9e94)

~~~
eximius
I mean, your post posits a logical possibility but merely posing the
possibility does not make it likely (like your post seems to imply).

Also, a dimension has some degree of continuity or, at least, regular discrete
nature that I'm not sure your idea for the 5th dimension really fits
naturally. Surely, we can relate to positions in your concept of a dimension,
but does a relation require a dimension? I'm not sure. Maybe it does. Maybe my
above thoughts are all locked in the concept of a euclidean geometry. My
topology studies were always in the context of function spaces, so it was a
bit too abstract to think about it this way.

------
mikhailfranco
Nice time-less relational formulation of Newtonian gravity:

[http://fqxi.org/data/essay-contest-
files/Barbour_The_Nature_...](http://fqxi.org/data/essay-contest-
files/Barbour_The_Nature_of_Time.pdf)

~~~
8bitsrule
Nice. Things moving around in the Eternal Now
([https://en.wikipedia.org/wiki/Philosophical_presentism](https://en.wikipedia.org/wiki/Philosophical_presentism)).
What is duration if not a fiction of memory?

------
platz
1\. The Higgs field goes one better: By offering resistance to anything that
passes through it, it may explain why objects have inertia in the first place.

Why doesn't the higgs field slow down objects moving in space?

2\. If gravity is simply the curvature of spacetime itself, the higgs field
gives particles mass, and mass curves spacetime, what is the relationship
between the curvature of spacetime and the higgs field exactly, is it special
somehow? (It seems somehow the way the higgs "offers resistance" is related to
the curvature of spacetime)

~~~
psadauskas
As far as I understand it, the Higgs field isn’t resistance to motion but
rather resistance to acceleration.

------
colordrops
I don't understand why the bucket example implies absolute space. When looked
at from a reductionist perspective, each atom is still travelling inertially
with respect to other atoms, but they are constantly changing direction based
on mutual forces applied to each other. The fact that from a macroscopic
perspective they appear to be "spinning" doesn't mean that "spinning" is
actually a fundamental and inherent form of motion relative to some static
background.

~~~
ithkuil
But they are not changing position nor velocities with respect to each other
while rotating, they are changing positions and velocities against other
frames of references.

~~~
colordrops
They are though. Structures are not rigid, but more elastic. They only appear
rigid and monolithic from a macroscopic perspective. One atom moves relative
to another , and then exerts electromagnetic force on another which then moves
a bit itself, and when all are seen together they appear to be a single unit
that is spinning, but that is an illusion.

------
dang
Discussed at the time:
[https://news.ycombinator.com/item?id=10979418](https://news.ycombinator.com/item?id=10979418)

------
woodandsteel
As a non-expert, it seems to me the question is whether space is fundamental,
or whether it is produced by something else more fundamental, and if so, what.

------
fmihaila
(Apologies for the long post. I can’t point off the top of my head to a
textbook reference, but [1] may be enough for a start.)

This is not an unsolved problem. The key is to understand how inertial motion
and inertial forces are explained in Newtonian mechanics vs. general
relativity.

Let’s take two friends, Charlie and Isidor. Charlie is sipping coffee while
reading a book sitting on a chair in his home, while Isidor is reading the
same book while floating freely on the International Space Station. At first
glance, it may seem that Charlie is experiencing inertial motion (with
velocity 0, since he is at rest) and Isidor is in accelerated motion around
the earth at a very high speed, since he is moving in a circular orbit.
(Recall that in Newtonian mechanics, circular motion is always accelerated
motion since the velocity vector varies with time, even though only in its
direction.)

However, this is backwards. In fact, Charlie feels the constant force of the
chair pushing on his bum and lower back, which is why he keeps changing his
position when it gets uncomfortable, while Isidor is weightless, experiencing
no forces acting on his body whatsoever. Also, absent any collision or
explicit application of rocket thrust, the ISS and Isidor inside will maintain
their current trajectory forever, while maintaining Charlie’s ‘at-rest’
position requires the constant application of force on his body, which is why
when the chair eventually breaks (Charlie is a heavy dude), Charlie moves
quickly towards the ground, spilling his coffee.

This observation is at the core of general relativity. Einstein remarked that,
if we surround Charlie with a tent, he cannot possibly tell whether he is
sitting on the beach or whether his chair is actually on the floor of a rocket
accelerating constantly at 9.81 m/s^2 towards Alpha Centauri. At the same
time, if the ISS had no windows, there is no experiment Isidor can conduct
that would tell him whether the ship is orbiting the earth or is hurtling
unaccelerated in a straight line in deep space. IOW, Charlie is in fact the
one experiencing accelerated motion, while Isidor is in inertial motion.

So what, then, is inertial motion? In general relativity, a body is in
inertial motion if its trajectory _in spacetime_ follows a local spacetime
geodesic. Earth’s gravity distorts space time around it to a shape in which
the trajectory of the ISS at that altitude and velocity is actually a straight
line according to the local metric imposed by the Earth’s gravitational field.
Conversely, if we plot Charlie’s at-rest position on the beach through the
same spacetime according to the same metric, it corresponds to a trajectory
that deviates from the geodesic right up until the moment when the chair
breaks, when for a very brief duration, his motion will actually follow the
local geodesic.

What does this have to do with the water in the bucket? Once the water
molecules rotate in sync with the bucket, their trajectories all deviate from
the local geodesic lines. We can see that by imagining the bucket wall
instantly disappearing; the water molecules would cease following the
previously enforced circular trajectories, and they would start traveling in
inertial motion away from the bucket, freely falling towards the ground (i.e.,
inertial motion in the Earth’s gravitational field). The sum of the forces
required to maintain the water molecules on circular trajectories happen to
lead to a curved water surface. The water molecules at rest in the non-
rotating bucket are still in non-inertial motion similar to Charlie’s, but the
forces acting on them to maintain those particular trajectories simply lead to
a flat surface.

The point is that every time we want a body to deviate from its free, inertial
trajectory in its local spacetime, we must apply a force. The water curvature
is a direct result of all the forces which are necessary to steer the water
molecules away from the local spacetime geodesics.

[1]
[https://physics.stackexchange.com/a/3988](https://physics.stackexchange.com/a/3988)

~~~
mrule_
I like this explanation. I've found that frame dragging
([https://en.wikipedia.org/wiki/Frame-
dragging](https://en.wikipedia.org/wiki/Frame-dragging)) completes this
intuition. In a hypothetical reference frame where the universe is rotating
around the bucket, the effect of the rotating mass "drags" space-time such
that the geodesics are curved and the water experiences an outward "force".

~~~
fmihaila
The way I understand it, frame-dragging is negligible if, as in your example,
the bucket is by itself in deep space, far away from any massive object.
Frame-dragging affects the nearby space around a rotating massive object (that
induces a strong gravitational field). The mass of the water is very small and
induces an extremely weak gravitational field, so even though it's rotating,
its frame-dragging would be exceedingly small. Likewise, the gravitational
influence (and consequently, any frame-dragging effect) of the rest of the
universe on the bucket is very close to zero, owing to the extreme distances
involved.

~~~
mrule_
My understanding is that in the case of an extremely massive object, frame
dragging leads to local changes in spacetime that amount to "changing" what
the "background" reference frame looks like? If the bucket _were truly
massive_ it would indeed start to look a little bit like space were rotating
around the bucket, and not the other way around? Since the bucket is of
negligible mass, of course, it is the mass of the rest of the universe that
"sets" the reference frame. This is my layperson's understanding. For me the
important point is that it is the global arrangement of mass in the universe
that determines the reference frame. Conceptually, I find it helpful to think
that, indeed, you can make the universe spin around the bucket, if your bucket
contains a fair portion of the mass in the universe? Perhaps I have
misunderstood something, however.

------
d13
"Something makes the water rise up against the side of the bucket"

We really have no idea?? Wow, it shows how little we really know about
anything.

~~~
tim333
No idea is a bit strong - we understand quite a lot about it. But not
everything by a long shot.

~~~
chiefalchemist
We believe we understand a lot about it, but we're not - yet? - absolutely
certain.

That is, once we get to the end, then and only then will we be certain of what
it took to get there.

Yes, no idea isn't accurate. We've got ideas. We just can't say the ideas are
correct.

------
z3t4
If nothing would exist, who would be there to tell ?

