The discrete-time physics hiding inside our continuous-time world

The discrete-time physics hiding inside our continuous-time world
Markov processes have been used to model the accumulation of sand piles. Credit: Santa Fe Institute Press

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. So they often model the dynamics of physical systems as continuous-time "Markov processes," named after mathematician Andrey Markov. Indeed, scientists have used these processes to investigate a range of real-world processes from folding proteins, to evolving ecosystems, to shifting financial markets, with astonishing success.

However, invariably a scientist can only observe the state of a system at discrete times, separated by some gap, rather than continually. For example, a stock market analyst might repeatedly observe how the state of the market at the beginning of one day is related to the state of the market at the beginning of the next day, building up a conditional probability distribution of what the state of the second day is given the state at the first day.

In a pair of papers, one appearing in this week's Nature Communications and one appearing recently in the New Journal of Physics, physicists at the Santa Fe Institute and MIT have shown that in order for such two- dynamics over a set of "visible states" to arise from a continuous-time Markov process, that Markov process must actually unfold over a larger space, one that includes hidden states in addition to the visible ones. They further prove that the evolution between such a pair of times must proceed in a finite number of "hidden timesteps", subdividing the interval between those two times. (Strictly speaking, this proof holds whenever that evolution from the earlier time to the later time is noise-free—see paper for technical details.)

"We're saying there are hidden variables in dynamic systems, implicit in the tools scientists are using to study such systems," says co-author David Wolpert (Santa Fe Institute). "In addition, in a certain very limited sense, we're saying that time proceeds in discrete timesteps, even if the scientist models time as though it proceeds continually. The scientists may not have been paying attention to those hidden variables and those hidden timesteps, but they are there, playing a key, behind-the-scenes role in many of the papers those scientists have read, and almost surely also in many of the papers those scientists have written."

In addition to discovering hidden states and time steps, the scientists also discovered a tradeoff between the two; the more hidden states there are, the smaller the minimal number of hidden timesteps that are required. According to co-author Artemy Kolchinsky (Santa Fe Institute), "these results surprisingly demonstrate that Markov processes exhibit a kind of tradeoff between time versus memory, which is often encountered in the separate mathematical field of analyzing computer algorithms.

The discrete-time physics hiding inside our continuous-time world
The minimal configuration for flipping a bit of information from 1 to 0 requires three states and three sequential time steps. Credit: David Wolpert

To illustrate the role of these hidden states, co-author Jeremy A. Owen (MIT) gives the example of a biomolecular process, observed at hour-long intervals: If you start with a protein in state 'a,' and over an hour it usually turns to state 'b,' and then after another hour it usually turns back to 'a,' there must be at least one other state 'c'—a hidden state—that is influencing the protein's dynamics. "It's there in your biomolecular process," he says. "If you haven't seen it yet, you can go look for it."

The authors stumbled on the necessity of hidden states and hidden timesteps while searching for the most energy-efficient way to flip a bit of information in a computer. In that investigation, part of a larger effort to understand the thermodynamics of computation, they discovered that there is no direct way to implement a map that both sends 1 to 0 and also sends 0 to 1. Rather, in order to flip a bit of information, the bit must proceed through at least one hidden state, and involve at least three hidden time steps. (See attached multimedia for diagram)

It turns out any biological or physical system that "computes" outputs from inputs, like a cell processing energy, or an ecosystem evolving, would conceal the same hidden variables as in the bit flip example.

"These kinds of models really do come up in a natural way," Owen adds, "based on the assumptions that time is continuous, and that the state you're in determines where you're going to go next."

"One thing that was surprising, that makes this more general and more surprising to us, was that all of these results hold even without thermodynamic considerations," Wolpert recalls. "It's a very pure example of Phil Anderson's mantra 'more is different,' because all of these low-level details [hidden states and hidden timesteps] are invisible to the higher-level details [map from visible input state to visible output state]."

"In a very minor way, it's like the limit of the speed of light," Wolpert muses, "The fact that systems cannot exceed the speed of light is not immediately consequential to the vast majority of scientists. But it is a restriction on allowed processes that applies everywhere and is something to always have in the back of your mind."


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The cost of computation

More information: Nature Communications (2019). DOI: 10.1038/s41467-019-09542-x
Provided by Santa Fe Institute
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Apr 15, 2019
Time for all pinheads who like to hear themselves type to come out of the woodwork and pretend they have something intelligent to say... (DONT forget the CAPS...)

Apr 15, 2019
Thank you Herr Leader Ghost of Otto von Shikelgruber for leading us into virtue signaling

I like Lee Smolin's background free physics and advance of time as real with space contingent. Time endures eternally and does not increment tick-tock.

A challenge to infinite time is Poincare Recurrance requiring (infinite) repetition of now and, uggh!, "TheGhostofOtto1923."

Apr 15, 2019
I guess kamerade dougie hasn't become sensitized to all the nonsense this particular topic generates from pinheads such as SEU/pirouette/racistblackguy/obamasocks/pussycat_eyes et al and other such resident pinheads. I dunno maybe you enjoy such turdflingingfests?

Do 900 ft tall martians have wristwatches or do they just 'know' what time it is?

Apr 15, 2019
Thank you Herr Leader Ghost of Otto von Shikelgruber for leading us into virtue signaling

LMAO.
Well, it's high time, you get his name right. That's "Schizergruber" and, as time has confirmed, is incapable of taking his own advice.

Apr 15, 2019
Heisenberg uncertainty should be extended to time; time at the greatest magnification is wavelike, not particle-like, and so on discrete quantum-like or particle-like temporal intervals exists.

Apr 15, 2019
I don't see the relevance to the real world of quantum physics which explicitly has no hidden variables, from entanglement is not necessarily Markov [ https://en.wikipe...ov_chain ], and by quantum field theory is continuous at the very least down to Planck scales. (And by supernova experiments may be continuous "all the way 'around' [as string theory would have it]".)

Specifically chemical reactions of cells are basically quantum, not always easily modeled as classical systems.

Apr 15, 2019
A challenge to infinite time is Poincare [sic] Recurrance [sic] requiring (infinite) repetition of now
.

I don't see how. Only if you assume the universe derives from a local "big bang" volume that was rejected 4 decades ago. Instead of the current, most likely (i.e. unconstrained physics) eternal process, spatially flat (i.e. most likely infinite extent and time) cosmology we have observed with Planck et al data. Inflation seems to remove any Planck size bottleneck in the topology and thus a singularity problem of cosmological Poincaré recurrence of the ad hoc chosen observable universe volume.

That is another problem with "discrete" physics, in cosmology general relativity rescales the volumes on Planck scales ... eh ... continuously. That would mote the recurrence conditions as per above.

Apr 15, 2019
Heisenberg uncertainty should be extended to time

It has been extended to that a long time ago (in the late 1920's by Nils Bohr).
There are many so called 'complementary variables' that obey an uncertainty relation - not just space and impulse

(e.g. time (duration) is a complementary variable to energy....more generally the field value and the change of that field form complementary values. Hence the intimate connection between time and entropy )

Apr 15, 2019
The disgusting and dishonorable liar antigoracle wrote:
Thank you Herr Leader Ghost of Otto von Shikelgruber for leading us into virtue signaling

LMAO.
Well, it's high time, you get his name right. That's "Schizergruber" and, as time has confirmed, is incapable of taking his own advice.


Well, since you are so stupid that you make up a figure of 6% and then post a link saying 14% to "prove" the figure you just made up, you really shouldn't talk.

You are a shameless lying scumbag and a coward to boot.

Apr 15, 2019
All you crazy nerds bickering at each other here like any of it matters is really too much. They should disable comments on this site

Apr 15, 2019
The disgusting and dishonorable liar antigoracle wrote:
Thank you Herr Leader Ghost of Otto von Shikelgruber for leading us into virtue signaling

LMAO.
Well, it's high time, you get his name right. That's "Schizergruber" and, as time has confirmed, is incapable of taking his own advice.


Well, since you are so stupid that you make up a figure of 6% and then post a link saying 14% to "prove" the figure you just made up, you really shouldn't talk.

You are a shameless lying scumbag and a coward to boot.
Looks like the little Pudel with the weak bladder is going to be following me around now.

Watch your step.

Apr 15, 2019
Hey TQ! I thought insulting the looneytoons was my schtick...
A big, hardwood schtick to belabor their mass insanity.

stepinlively. I'd guess from your sensitive nature?
You have never attended a professional academics debate or a scientific symposium?
Cause, those boys get rough!

Though I still think for choice, literate insults?
Either Jesuits Or Rabbis are the most savage.

Apr 15, 2019
Okay, I think my own small ability acquire a feeble understanding of the rationality of Continuous Time.

The possibility does not seem unreasonable to my stochastic viewpoint of how I think the Universe actually works.

However, I am of a definite opinion that the concept of Discreet Time Is an abstraction of improbable events from Human imagination?

That the idea of Discreet Time, is unbelievable to me personally.
Because this is where I experience Time.
Which seems to be a Human invention to muddle simplification of what we are experiencing at our mundane level.

It also seems interesting to me. That Time & Gravity share as many similar descriptions as they do.
Eternal, infinite,
Increasing without decreasing.
A force but not an energy.
Uni-directional.
Yeah? you've verified those claims?
& repeated the experiments?

Okay, once you've done that, including the peer-review process? Then come back to me & I'll probably still refuse to agree...

Apr 15, 2019
The graphic showing a 1 bit changing to a 0 bit is grossly misleading. It's actually showing (without showing it) an exchange of a 1 bit and a 0 bit.

Programmers will recognize the following:

temp = x;
x = y;
y = temp;

That's actually what the graphic is showing. It's a swap of the values of two variables.

However, what is stated is true -- it takes a "hidden variable", which is "temp" in my example code, and three steps.

Performing

x = y;
y = x;

merely assigns the value of y to both x and y. The "hidden variable" is necessary.

In order to change a bit to a 1 if it's a 0, or to a 0 if it's a 1, requires

if (x == 0)
x = 1;
else
x = 0;

The "hidden variable" here is the value against which x is tested; it still requires three steps, which are:

test
assign
skip statement

or:

test
skip statement
assign

depending on the value of x.

The proof mentioned in the article is correct.

Apr 15, 2019
@observer, it's only correct if you postulate discrete states. As opposed to states that continuously change.

And that's an interesting conversation.

Apr 15, 2019
@Da Schneib,

Discrete background states are still required.

Apr 15, 2019
Well, that settles it. We are a simulation, in which a significant portion is executing in "hidden" background processing, concealing hidden states. No worries, the CPU is running smoothly in continuous-time, however, its physical limitations constrains multi-tasking to discrete-time steps.

Apr 15, 2019
stephencrowley214
All you crazy nerds bickering at each other here like any of it matters is really too much. They should disable comments on this site

Didn't Ozzie sing a song bout you?

Apr 15, 2019
auntieoral. you are arguing that "hidden states" are incomprehensible to you, therefore that state cannot possibly exist.

Thereenforeunupon, I will assist you by describing an experiment you can perform to determine the actual existence of "hidden variables".

Ask your local GOP gaultier & party boss for an introduction to your neighborhood pastor's floating crap game.

Place your bet, throw the dice. When those stop bouncing? You have just revealed the "hidden value".

Too amuse me, please explain to the pit boss that hidden variables are impossible. & thereinforth you are taking your bet back as proof of your theorem.

Oh My! A laugh Riot!

Apr 15, 2019
To my mind time is a continueous phenomenon which depends upon the actions As the action changes time also change its path. Thus time moves in a helical path.

Apr 15, 2019
Hidden discrete states describe actions that have to take place (equivalent to information being retained or used) so that the next continuous time state can be reached.

Conceptually, to exchange the values of two bits, that's a continuous event, because it happens "instantaneously" from the point of view of an observicist (me). However, for that "conceptually instantaneous" event to take place, certain things must happen in the background, and they must happen in a certain order, which is why they are discrete states. From the point of view of thermodynamics, they can't take place instantaneously, because they use energy and are subject to entropy. We have what appears to be a continuous flow, but in the background, it's anything but. That continuous flow is chopped up into discrete chunks.

Apr 16, 2019
From the quantum point of view, the switch of a memory cell from positive to negative is not instantaneous. Electrons are inserted or withdrawn from the cell, and when the threshold is passed, then it turns from 1 to 0 or vice versa. This is not from the intrinsic view of the cell; it is measured from outside using criteria that are not determined by the cell.

I'm going to have to read the paper. Then I'll decide.

Apr 16, 2019
Naww, not buyin' it. The hypothesis proposed is based on Markovian discrete states. This is circular reasoning: discrete states result in discrete states.

Apr 16, 2019
The disgusting and dishonorable liar antigoracle wrote:
Thank you Herr Leader Ghost of Otto von Shikelgruber for leading us into virtue signaling

LMAO.
Well, it's high time, you get his name right. That's "Schizergruber" and, as time has confirmed, is incapable of taking his own advice.


Well, since you are so stupid that you make up a figure of 6% and then post a link saying 14% to "prove" the figure you just made up, you really shouldn't talk.

You are a shameless lying scumbag and a coward to boot.
Looks like the little Pudel with the weak bladder is going to be following me around now.

Watch your step.


I'm sorry, are you unable to tell yourself apart from antigoracle, even when that name is explicitly mentioned at the very top of the post in question?

Apr 16, 2019
Well, that settles it. We are a simulation, in which a significant portion is executing in "hidden" background processing, concealing hidden states. No worries, the CPU is running smoothly in continuous-time, however, its physical limitations constrains multi-tasking to discrete-time steps.

Antigoracle and his puppets live inside their own simulation inside his head, i don't think he understands the meaning of what he actually said

Apr 16, 2019
@Da Schneib,

I strongly suspect time, and everything else, is quantized, so, discrete states, it is.

Apr 16, 2019
@observer, I have considered this many times and have never come to a sound conclusion. But my feeling is different than yours; I feel that the mathematical difficulty with quantum gravity is precisely because spacetime is not quantized.

Apr 16, 2019
@Da Schneib,

I suspect spacetime is quantized at below the Planck level, which is why we're having problems with quantum gravity and finding dark matter. Such quantization would also give the illusion of non-quantization.

I know that right now there's no way to check which one of us is correct. That's why I wrote "I suspect" instead of "I hypothesize" -- if we ever locate dark matter, that may give us a hint. I have some suspicions about dark matter that I'm not going to put into print.

Apr 16, 2019
Thanks DS & Ob for your opinions & explanations.

As little as I understood!

- sigh -

right bow i am imaging myself chopping at the stream of Time with a butcher's cleaver. To achieve "discreet" portions.

Oh yes, that'll make some sense of this subject.

Apr 16, 2019
The cosmos -- 'tis a thing passing strange; difficult to understand.

That's why nobody really does. Not yet. And every time we think we're close, some observation comes along and throws a monkey wrench into the works.

Which is why it's so much fun.

Apr 16, 2019
Sorry, time is not quantized. In fact it is only a man-made metrical mapping of relative motions using convenient "clocks" (orbits, rotations, etc.).

Apr 16, 2019
Sorry, time is not quantized. In fact it is only a man-made metrical mapping of relative motions using convenient "clocks" (orbits, rotations, etc.).


I'm glad you're so certain.

Apr 17, 2019
I am thinking once again we are bollixed by the words. terms. designations we use for phenomena & concepts.

The word "temperature" means something different to everyone.
Not just the Layman such as myself.
But every scientific & medical specialization has their own technology & interpretations of the data.
Astronomers use Kelvin to measure Star colors & mass. Which leaves many people staring blankly.

Now here we have Time.
& the dispute (to me) is whether "Time" is a "concept"

Or a "phenomena"?

Does Time physically exist as the popular meme of the
"4th Dimension of Time"?

Or is Time (not so) simply our experience of Entropy. Whatever the Hufflelump that critter is assumed to be?

If we cannot agree of which words to use, specifically?

We must all curse that the meanings of those words will be in a constant flux...

As a satirist, I will voraciously abuse this opportunity to create bad jokes mangling words.
Did-knot I warn you?
I am a devotee of
Coyote Trickster Goddess.

Apr 17, 2019
Sorry, time is not quantized. In fact it is only a man-made metrical mapping of relative motions using convenient "clocks" (orbits, rotations, etc.).
says TimLong2001

Absolutely correct. Many of us have discussed this issue before of whether or not the concept of "time" could be classified as a 'Dimension' additional to the 3 Dimensions of Length, Width, Depth.
I have asked of some of the bozos here who were in those other phorums to explain "what is time made of", and never got a satisfactory reply - but only abuse and words of insults that belied their inability to discuss the issue objectively rather than subjectively. Time cannot be quantised except in the form of clocks/timing instruments and the sunrise to sunrise cycle, simply due to it only being a concept progressing from the human mind with the intent to describe the duration of Actions and Events as well as Distance measurements. IOW, "time" is not generated from quantum particles, like Space, which is.

Apr 17, 2019
Heisenberg uncertainty should be extended to time; time at the greatest magnification is wavelike, not particle-like, and so on discrete quantum-like or particle-like temporal intervals exists.
says RobertKarlStonjek

Have you then accomplished the "magnification" of the concept of 'time' as a Wave or wave-like? From whence does it emanate or progress out of?
Would you care to share that source of magnification as a real image, rather than a graph? Please include the link to the literature and photo.

Apr 17, 2019
Every argument in the comments so far is the same as saying Sample rate is Frequency.

Apr 17, 2019
What is time made of?
An interesting quandary.
From what little knowledge I have of this subject?

Y would tentatively speculate that since Time & Gravity share so many aspects. That, as Gravity goes down to the Planck foundational gravitron particles.
Will it be proven or disproven that there are Time Particles. Or are the quantum particles of Gravity & Time entangled? Or better, enmeshed for that smooth continuity?

Would this explain the Relativistic Time effect forced by Gravity from across the Event Horizon?

Apr 17, 2019
Finally
TimLong2001> Sorry, time is not quantized. In fact it is only a man-made metrical mapping of relative motions using convenient "clocks" (orbits, rotations, etc.).

The pennies dropping, time does not exist
except
in
These Shadows of this Mind

Apr 17, 2019
Every argument in the comments so far is the same as saying Sample rate is Frequency.
And frequency is 1/time. That's its definition. Denying time is denying frequency. This "debate" should have been done long ago. If the trolls even understood what was being said, it would be. But they don't; they don't have math, they are innumerate, so they don't understand what 1/something means.

Major hint: when you "tune" your radio, you are adjusting its frequency detection spectrum. This is why radio stations are a certain minimum frequency apart, so they don't interfere with one another in the radio receivers' tuners.

Apr 19, 2019
Finally
TimLong2001> Sorry, time is not quantized. In fact it is only a man-made metrical mapping of relative motions using convenient "clocks" (orbits, rotations, etc.).

The pennies dropping, time does not exist
except
in
These Shadows of this Mind
says granville

There are "some" here on physorg who cling steadfastly to certain errors in Relativity as though belief in it will miraculously make it undeniably so. The concept of "time" is such an error that was defined as a 'dimension' along with Space and then reclassified as 'Spacetime', which seemed to give the time hoax a bit more plausibility and seemingly logical, but without evidence as to time's existence and its properties. The truth being that time is but a 'concept' that has no properties whatsoever, except for such as are assigned to it by those who insist that time is a real object, which it isn't.
And yet, those whose belief in that falsehood continue to use the term "spacetime' anyway.

Apr 23, 2019
@Da Schneib,

I strongly suspect time, and everything else, is quantized, so, discrete states, it is.
its true for gravity too. since if you take out time in bits on a tabletop, you take out gravity too in bits. watch
https://www.youtu...g68VE-Ys

3 hours ago
Finally
There are "some" here on physorg who cling steadfastly to certain errors in Relativity as though belief in it will miraculously make it undeniably so. The concept of "time" is such an error that was defined as a 'dimension' along with Space and then reclassified as 'Spacetime', which seemed to give the time hoax a bit more plausibility and seemingly logical, but without evidence as to time's existence and its properties. The truth being that time is but a 'concept' that has no properties whatsoever, except for such as are assigned to it by those who insist that time is a real object, which it isn't.
And yet, those whose belief in that falsehood continue to use the term "spacetime' anyway.
spacetime is a lot of hogwash, but according to my experimental results, Time is a physical object

3 hours ago
Care to elaborate on that Bruddah Savvys ?

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