
The discrete-time physics hiding inside our continuous-time world - dnetesn
https://phys.org/news/2019-04-discrete-time-physics-continuous-time-world.html
======
king_magic
This immediately makes me think of Sabine Hossenfelder's book "Lost in Math".

Just because the math is pretty doesn't mean the universe actually works that
way. Maybe it does, maybe it doesn't. Sure seems like the universe doesn't
seem to care much about our math.

I think the authors of the paper are being perfectly straightforward (e.g.,
they explicitly include the phrase "in a certain very limited sense" RE: time
proceeding in discrete time steps), but the title of the article itself feels
a bit misleading.

~~~
toolslive
> Sure seems like the universe doesn't seem to care much about our math.

Well, some mathematical truths are so universal even the universe can't escape
them. the incompleteness theorems [0] come to mind.

Regarding the article, I think most physicists consider the continuous models
they use to attack the problems at hand a hack to make the mathematics
consumable. I don't think they consider the universe itself to be non-
discrete.

[0]
[https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...](https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)

~~~
tromp
Perhaps those who expect quantum computers to scale to millions of qubits do.
The amplitudes involved seem to defy discreteness...

~~~
krastanov
There are workarounds for that: for instance, do not use such a poorly
conditioned basis to describe the system. In particular, problems in physics
that appear only in one particular basis are probably human-created notation
issues, not something fundamental, as physics should be basis independent.

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oarabbus_
>Scientists believe that time is continuous, not discrete—roughly speaking,
they believe that it does not progress in "chunks," but rather "flows,"
smoothly and continuously.

Is this true? I didn't think there was any kind of consensus on this topic. I
also thought some scientists believe the Planck time(/length) is the smallest
unit of possible time i.e. they would say time is discrete

~~~
colmmacc
Just because Planck times are the smallest possible measurement of time
intervals doesn't mean that time progresses in discrete Planck time chunks.
That's obvious enough, but maybe seems unmeasurable ... and so what difference
does it really make?

A bigger way to think about it is ... is the a universe like a movie where
each still image lasts a Planck-time (or some other smaller chunk)? Is the
entire state of the universe encoded in stasis for that instant, and then boom
... it's time for the next "Planck frame".

It's really hard to resolve that kind of universal time chunkiness with the
ordinary time dilation effects that can be observed at relativistic energies.
Whose frame of reference counts? We do know that space-time can be warped ...
it's harder to imagine that this kind of warping and curving is discrete.
That's one reason why many believe it's a smooth flow.

~~~
jrochkind1
Yeah, but not just unmeasurable by like a guy with a measuring device,
unmeasurable in the sense that it _can't effect anything at all_, right? (if
it caused an effect of any sort you could eventually measure or observe in any
way... nope).

To say that time is "really" continuous under such circumstances seems like a
weird philosophical claim.

~~~
oarabbus_
Thank you, you eloquently expressed the point I was trying to make. To say "we
know that quantity Y can never be measurable or observable below discrete
length X... but also, Y is continuous and can be subdivided below X, just
trust us on this one" doesn't sound like science. Philosophical at best.

~~~
coldtea
Philosophy is not just saying random stuff and "trust us".

And inversely, science is not just measuring -- that's the naive positivist
(and later Popperian) view of what scientists do.

For example:

As Thomas Kuhn (1961) argues, scientific theories are usually accepted long
before quantitative methods for testing them become available. The reliability
of newly introduced measurement methods is typically tested against the
predictions of the theory rather than the other way around. In Kuhn’s words,
“The road from scientific law to scientific measurement can rarely be traveled
in the reverse direction” (1961: 189). For example, Dalton’s Law, which states
that the weights of elements in a chemical compound are related to each other
in whole-number proportions, initially conflicted with some of the best known
measurements of such proportions. It is only by assuming Dalton’s Law that
subsequent experimental chemists were able to correct and improve their
measurement techniques (1961: 173).

[https://plato.stanford.edu/entries/measurement-
science/#EpiM...](https://plato.stanford.edu/entries/measurement-
science/#EpiMea)

~~~
oarabbus_
>Philosophy is not just saying random stuff and "trust us".

Ok, enlighten me. I've read philosophical works where that certainly seemed to
be the case. There's also this weird thing where only a specific lineage of
schools of thought and certain ancient Western philosophers are "real
philosophy" and others (e.g. anyone with a non-Anglo last name) are "not real
philosophers". No True Scotsman at its finest.

>And inversely, science is not just measuring -- that's the naive positivist
(and later Popperian) view of what scientists do.

In graduate school, I worked at a lab in Stanford (I didn't attend there, but
was fortunate to have spent some time there). Your statement would certainly
be news to the PI I worked for, who was a heavy Popperian. You can't falsify
the existence of sub-Planck lengths or times, that's for sure. Science was
absolutely nothing more than that to him. And while you can certainly claim an
Appeal to Authority fallacy, Stanford, at least, considered my PI competent
enough to award him a PhD in a scientific discipline, so I'm not sure how much
I can agree with your post.

~~~
shstalwart
People like to say that "modern" science has moved past Popper. In my opinion,
this is because it allows them to attach the gravitas of Science [0] to
whatever their pet topic is, even when that topic does not admit
falsification.

This is not to suggest that we should not inquire on these topics, but rather
that they should fall under some other umbrella besides Science.

[0] Or whatever is left of it at this point.

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pvitz
I think this is highly interesting, but while reading the comments here, I
think one should be very careful about the actual content of the paper. It is
deriving results about the (phenomenological) master equation. It has been
some time since I have studied this, but we are not talking about some first
principles theory here. It is possible to derive master equations in some
limit from a fundamental theory, but the setting here is purely
phenomenological. I.e. the hidden states would be anyway present in the
fundamental theory and would be lost due to some integration and limit process
in order to arrive at the master equation.

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physicsyogi
> Scientists believe that time is continuous, not discrete—roughly speaking,
> they believe that it does not progress in "chunks," but rather "flows,"
> smoothly and continuously.

The jury may still be out on that. A few of the quantum gravity theories (like
loop quantum gravity, causal dynamical triangulation, or causal sets) propose
a discrete spacetime as a consequence of background independence.

Edit: formatting

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checkyoursudo
Interesting. Though I didn't read the underlying papers.

I'd still like to know _what_ either "flows" or "chunks".

Time? Sure, ok, time flows, or time chunks. But what exactly is it?

Time has been one of my favorite topics to read about in the last 20 or so
years, and I still feel like we have hardly made any progress in figuring it
out.

~~~
asark
It seems to me there's a bait and switch of sorts that we play on kids. We
tell them science can answer their questions about the world, or that they can
use science to answer those questions, but it kinda can't. Keep digging and
pretty soon you're lost in not-quite-accurate metaphors that may have nothing
to do with reality and "we can tell you how it behaves, it's [pages of
equations], isn't that good enough?"

It may be (probably is) that "what is this" or "why does it do that" are just
meaningless questions, in the sense a child (or adult who hasn't re-calibrated
their expectations of what science can tell them) means them. Which is
interesting itself, I suppose, but at that point just go study philosophy and
art, if that's why you were into science in the first place—and I think it's
why everyone at least _begins_ to be interested in science.

[EDIT] in particular it's frightening how fast kids' questions stymie an adult
because the adult realizes that they're only a step or two away from "why is
there something instead of nothing, and also what is _something_?" and... good
lord, at that point seriously just go become religious or get really into
philosophy or something, because you're outta luck, kid, sorry, we don't have
any actual answers, just observations about what all this stuff does, but no
we can't tell you what "stuff" or "does" are.

~~~
simiones
Noam Chomsky usually has this point, that the human mind seems limited in its
"native understanding" to a mechanistic view of the world - that is the only
kind of model that is truly satisfactory to us.

He also points out that, ever since Newton, the dream of mechanistic world was
shattered, and with it, any hope that science would help us "make sense of the
world" in a truly satisfying sense. Instead, we have become content with
modelling the world mathematically and predicting how it will evolve.

Of course, space-time and quantum mechanics have driven additional nails in
the coffin of a truly understandable world.

~~~
AgentME
>Of course, space-time and quantum mechanics have driven additional nails in
the coffin of a truly understandable world.

I'd think the opposite. The fact the world can work at least as strangely as
relativity and quantum mechanics suggest, and we still figured those out as
much as we have so far, reassures me in our ability to figure out the world we
exist in.

~~~
simiones
What I meant was: quantum mechanics and relativity have shown that not only is
the physical world _slightly_ different from the kind of world our mind can
picture (e.g. "mechanistic, but with the universal attraction force"), it is
in fact nowhere near our built-in mechanistic model, and we can never hope to
build a real intuition about the world.

However, we can still hope to model and predict it more accurately than we
would have ever hoped before, so there is that :)

------
cubano
I mean, I've always thought that Planck's constant _defines_ the discreteness
of time and, as it were, reality. Isn't it rather obvious that this is the
case?

"Planck time"..the unimaginably small 5.39 × 10−44 s, is as fundamentally
important to the fabric of the universe as it's much more well known
"brother", the speed of light in a vacuum _c_.

Now, we are nowhere near able to measure that short a time frame...we are
limited to around 10x-19 or so, but without a doubt time is discrete, we just
are unable to get there yet.

~~~
lodi
I'm no physicist, but the layman explanation I've heard is that the concepts
of Planck length and Planck time _do not_ imply that spacetime is discretized
into little "voxels"; instead these quantities are just limits on the
uncertainty of any possible measurement.

As I understand it there are two contributing facts:

a) the Heisenberg uncertainty principle states that there's a tradeoff between
certainty in position vs momentum, so if you're more certain in a particle's
position you're less certain of its momentum. (For photons, momentum is
proportional to frequency, i.e. wavelength, and frequency is proportional to
energy.)

b) By mass-energy equivalence, anything with energy has mass, therefore higher
frequency photons are more "massive". A single photon of sufficiently high
frequency would form a black hole.

Putting those two together, to measure a distances accurately, you need higher
and higher frequency photons with shorter and shorter wavelengths. For
example, radar creates blurry images at ~5cm wavelengths, while ordinary
photographs can be razor sharp at ~500nm. The Planck length is just the
wavelength at which the photon would have so much energy that it would
collapse into a black hole and break our current mathematical models. That's
why it's nonsensical--with current models--to talk about lengths smaller than
a Planck length, but it _doesn 't_ mean that space itself is quantized.
Similar argument for time.

(Also, the same logic applies to other particles like electrons, protons, and
even up to macroscopic items like baseballs; everything has a wavelength...)

------
based2
Like an atom and then its composition.

[https://nobeliefs.com/atom.htm](https://nobeliefs.com/atom.htm)

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ngcc_hk
What flip one bit must involve a hidden varable? Is that related it’s being
continious to discrete and vice visa?

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ngcc_hk
Some issues in the discussion:

Scope: Many equate maths physics and universe all and only science. Whilst
they may be “easy” science not all human observed phenomenon are reduced to
them. Even left and right wing ideology?

Process-wise: whether the in principle refutatable may be naive to describe
how human work (and likely we do not all do maths in axiomic way). It is a way
to make a distinction of science and myth (and in maths axiom is good for
proof not necessarily generate maths)

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madhadron
tl;dr: This is a (cute!) technical detail of an approximation technique used
in studying the thermodynamics of computation. It has nothing to do with
fundamental physics.

Imagine you have a system with N states, represented as a vector of length N.
You have a linear operator that transforms that vector into the state in the
next step of time. That's basic linear algebra. Now make the linear operator
random, so you have stochastic transitions. That makes it into something
called a Markov chain.

Now, physicists love differential equations. They've got lot of tools for
working with them, and to bring those tool to bear, some folks a while back
took a Markov chain and wrote down a set of linear differential differential
equations for how the probability distribution over states evolves in time.
That's called a "master equation."

Now say that you have an arbitrary function from initial state to final state.
Can you describe it as a dynamics governed by a master equation? Not in
general. That's not a huge surprise. We know there are lots of things you
can't describe with linear differential equations.

If you're working on thermodynamics of computation, though, it would be nice
to salvage the master equation framework because its relationship with
thermodynamics is well understood, and you don't have to rebuild that. And
getting to thermodynamics from straight up stochastic processes is beyond the
mathematical abilities of most physicists. That's not a slight on physicists.
The mathematical path from a stochastic process to a thermodynamics is an area
of deep, difficult specialization in mathematical physics and if you go down
that rabbit hole, it will likely be your career (see, for example, Elliott
Lieb).

There are two ways to extend this linear world to get better approximations of
things:

1\. Imagine you have two points on a curve. A linear approximation is drawing
a straight line between the two points. To get a better approximation, you
take some more points between the two on the curve and draw a sequence of
linear going through those points. The equations of each of those lines are
going to be different (they have different slopes and intercepts or however
you want to parameterize them). Or, in the context of master equations, you
insert some additional, "hidden" steps in between your primary time steps with
different stochastic matrices.

2\. Imagine you have a dynamical system that moves in time steps, and depends
on the last two steps for its current move. You can make it into a system that
depends only on the last step by expanding the state to include the previous
time step as well (that is, instead of the dynamics of x(t), I track the
dynamics of (x(t), y(t)) where y(t) = x(t-1)). These are called "hidden
variables." It's the same idea as hidden variables in quantum mechanics. Or
even in classical mechanics, I can't write down a first order equation for the
position of a classical particle...but I can write down a pair of first order
equations for the position and momentum.

Lots of folks working on thermodynamics of computation have done both these
things to patch their tool.

What this paper does is try to calculate how many hidden steps and how many
hidden variables you need to patch the tool for a given arbitrary function
that you're trying to approximate, and shows that if you use more hidden
variables you need fewer hidden steps and vice versa.

For thermodynamics of computation, they point out that if you are engineering
a system with master equation dynamics, you have to pay for the extra hidden
states/steps that you need, so the simple statement that invertible functions
are thermodynamically free and noninvertible ones require work isn't the only
cost accounting to do.

Aside: I have complained before about only whiz bang articles rising on HN.
Here we have a straightforward, technical calculation on the front page.
Progress!

