10 ms·

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

106 points by dnetesn 8y ago

king_magic 8y ago
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.
- whatshisface 8y ago
  Good luck telling in advance which math is pointless guessing and which math is the groundwork for the next revolution in our understanding.
- samstave 8y ago
  Reminds me of a haiku i wrote a long while ago: —- Movement and measure How to discern life through time Everything is change —- Time and the inherent math of the universe is amazing to think upon, especially when you look back upon the wisdom of ancient humans who were able to perceive cycles of the stars that were many thousands of years long whilst human conscious life is so fleetingly short. Its interesting that we do not try to ask HOW civilizations past could have been aware of cycles that last for tens of thousands of years. And now humans are so myopic on what is in front of them, we hardly look up.
  - Retra 8y ago
    If you wanted to look up, you wouldn't be quoting yourself, writing poetry, or and navel-gazing at your emotional response to mystery. You'd be studying the world as it is, not as the story you want to tell about yourself.
    - catawbasam 8y ago
      “The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom the emotion is a stranger, who can no longer pause to wonder and stand wrapped in awe, is as good as dead —his eyes are closed. The insight into the mystery of life, coupled though it be with fear, has also given rise to religion. To know what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms—this knowledge, this feeling is at the center of true religiousness.” -- Albert Einstein
      - Retra 8y ago
        Curious that he's not famous for saying that. It's almost like his actual physics were more relevant than his poetic reflections.
        samstave 8y ago
        I find it abhorrent that people cannot place into the same realm physics with 'poetic reflections' Tiring is the limiting of mind and creativity such that one thinks that science and reflection are not, intrinsically, the same thing.
        Retra 8y ago
        If they are the same thing, why prefer Einstein to Chopra? Why quote Einstein's fluff, rather than his science? Why shouldn't we give samstave a Nobel Prize for his poem?
  - dpark 8y ago
    > Its interesting that we do not try to ask HOW civilizations past could have been aware of cycles that last for tens of thousands of years. That’s probably because they weren’t. What “cycles of the stars that were many thousands of years long“ were ancient peoples aware of?
    - jcranmer 8y ago
      Precession of the equinoxes? For Earth, this is circa 25,000 years, although I don't believe there's a reasonably accurate measurement of this value in Antiquity.
      - dpark 8y ago
        I'm not sure that meets the criteria for a "cycle of the stars" since it's a planetary change, but I guess for Hipparchus it probably did look like a celestial change. It definitely doesn't match the claim that "we do not try to ask HOW civilizations past could have been aware", though. We know exactly how Hipparchus recognized this. Nonetheless, this is a reasonable response to my question. Noting a long-term cycle of equinox precession is impressive but also not terribly surprising. If you can note the change, you can reasonably assume it's cyclical (because the alternative is that it's going to suddenly stop moving at some point in the future).
    - Izkata 8y ago
      The Mayan Long Count calendar? If I remember right, it's method of counting leap years is more accurate than the modern Gregorian calendar.
      - jcranmer 8y ago
        The Mayan calendrical system uses a "year" of 360 days without attempting to account for leap days. Essentially, the long count (the classic 13.0.5.7.6 style system) is a base-20 count of the number of days from the epoch, with one of the digits being base 18 instead. The other components are the 260-day year of 20 "months" of 13 days, the 365-day year of 18 months of 20 days (with 5 extracalendrical days), (and together these two things create a 52-year cycle that's the "Short Count" calendar), a week-ish system (of 9 days), a lunar cycle count, a correction to the lunar cycle because it's annoyingly 29.5 days long, and a 819-day cycle we don't understand yet. Their calendrical system did not attempt to correct for leap years, but we do know that they knew the length of the year to roughly the same precision as the Gregorian approximation.
- toolslive 8y ago
  > 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_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
  - tromp 8y ago
    Perhaps those who expect quantum computers to scale to millions of qubits do. The amplitudes involved seem to defy discreteness...
    - krastanov 8y ago
      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.
  - j7ake 8y ago
    Could you give examples on how the incompleteness theorem explains physical phenomena? I would be curious.
    - krastanov 8y ago
      I would suggest Aaronson's "NP-complete problems and physical reality" for this type of thinking (public PDF on his academic page). It is short and has a ton of examples. I really like the style, but it is not a common view among working physicists (yet? It is just not particularly practical for the moment).
  - krastanov 8y ago
    I am a physics in academia and no, most physicists do not think that (especially given that most physicists are not quantum foundations physicists, and even then). It is an interesting question, and if I am forced to guess on its answer I would even agree with you, but good science would be to not speculate the way you imply.
- sorokod 8y ago
  Are we not looking at a mathematical result that constraints what the universe "can do"?
- stabbles 8y ago
  Which neither means that beautiful math is necessarily describing the world inaccurately. Taken to the extreme, the best description of the world is a long list of all events and facts. No beauty in that. Now science tries to compress this list of events to a simple model that explains it best. Like in statistics, one should aim for the simplest model predicting most of the data. I'd argue that if you think of science as an attempt to compress all the data in the world, then OP's statement is obvious, and at the same time there's good reason to value beautiful (i.e. short & simple) explanations higher provided they generalize well.
  - eridius 8y ago
    You say "best", except a long list of events and facts has no predictive power, no way to infer what the future will be, only describes what the present is. The whole point of a model is to be able to predict the future. So in that sense, a long list of all events and facts is the worst description.
    - Xcelerate 8y ago
      Not sure why you’re being downvoted; what you’re saying is true. A model whose length is the same as the data it is describing has no predictive power. A perfect model what be the size of the minimum program that prints out all of the events in the universe (that is, the program whose size matches the Kolmogorov complexity of the universe).
- JKCalhoun 8y ago
  > Just because the math is pretty doesn't mean the universe actually works that way. Interesting thought ... is mathematics really orthogonal to the universe or does it "result from" or fall out as a result of the universe within which it was described? Getting philosophical, I know, but if you follow, then perhaps the degree to which you don't have to twist mathematics to describe the universe might suggest you are in fact on the right path....
- ngcc_hk 8y ago
  Agreed. Easy and intuitive as Euclidean geometry it is not right. It is not easy ask anyone doing proof in that paradigm. Getting more mtr complicate not meaning they are right.
checkyoursudo 8y ago
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.
- jchanimal 8y ago
  You might enjoy this one https://en.wikipedia.org/wiki/The_Unreality_of_Time https://en.wikipedia.org/wiki/The_Unreality_of_Time
  - checkyoursudo 8y ago
    Yes! I do know this one. And it is very interesting to me.
- systemfreund 8y ago
  > The Planck time is by many physicists considered to be the shortest possible measurable time interval; however, this is still a matter of debate. [0] So, if this is true, then does it mean that time does not 'flow', but rather 'chunks'? [0]: https://en.wikipedia.org/wiki/Planck_time https://en.wikipedia.org/wiki/Planck_time
  - TheRealPomax 8y ago
    In a very real sense, we may never know. The problem of natural language is that it doesn't really work all that well for scientific purpose: talking about chunks and flows comes with a human's lifetime's worth of thinking they know what those words imply, and so we don't use them except in popular science articles. Time could be discrete, or it could be continuous, but while in normal life the difference between those two is easily determined, this is not the case in physics at all: in order to say "which of the two it is" you first need to have an idea where the boundary between the two would have to be. (even at the macro level, a river that moves a specified number of molecules per time unit doesn't "flow", it's technically moving discrete "chunks" of water, we just don't say it's moving chunks of water because no one cares about the "well, technically..." in normal conversation. We know what's meant and what to ignore. Physics doesn't have that luxury) We have no idea where that boundary can even be found; it would certainly have to be below the Planck length, but we have nothing that allows for that kind of precision. The only thing physics can say right now, and possible even ever can, is that nothing we have at our disposal allows us to conclude time "actually is" discrete. We can come up with mathematical frameworks that assume time is a discrete dimension, but even if those yield super accurate predictions that are then verified through experiment, all that does is confirm that a continuous dimension can be reduced to a discrete one without loss of precision.
cubano 8y ago
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.
- danharaj 8y ago
  > 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. It is not. It would violate special relativity. No such violation has ever been observed.
- lodi 8y ago
  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...)
pvitz 8y ago
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.
physicsyogi 8y ago
> 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
madhadron 8y ago
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!
oarabbus_ 8y ago
>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 8y ago
  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 8y ago
    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.
    - whatshisface 8y ago
      Fortunately it's not a philosophical claim - after all even if it was demonstrated experimentally that time moved in frames like a movie, it could still be a movie played on a projector whose reels spun in continuous time. There's no way to know "what it ultimately is," only the most ultimate thing seen so far.
based2 8y ago
Like an atom and then its composition. https://nobeliefs.com/atom.htm https://nobeliefs.com/atom.htm
ngcc_hk 8y ago
What flip one bit must involve a hidden varable? Is that related it’s being continious to discrete and vice visa?
ngcc_hk 8y ago
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)

106 points by dnetesn 8y ago

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.

whatshisface 8y ago
Good luck telling in advance which math is pointless guessing and which math is the groundwork for the next revolution in our understanding.
samstave 8y ago
Reminds me of a haiku i wrote a long while ago: —- Movement and measure How to discern life through time Everything is change —- Time and the inherent math of the universe is amazing to think upon, especially when you look back upon the wisdom of ancient humans who were able to perceive cycles of the stars that were many thousands of years long whilst human conscious life is so fleetingly short. Its interesting that we do not try to ask HOW civilizations past could have been aware of cycles that last for tens of thousands of years. And now humans are so myopic on what is in front of them, we hardly look up.
- Retra 8y ago
  If you wanted to look up, you wouldn't be quoting yourself, writing poetry, or and navel-gazing at your emotional response to mystery. You'd be studying the world as it is, not as the story you want to tell about yourself.
  - catawbasam 8y ago
    “The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom the emotion is a stranger, who can no longer pause to wonder and stand wrapped in awe, is as good as dead —his eyes are closed. The insight into the mystery of life, coupled though it be with fear, has also given rise to religion. To know what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms—this knowledge, this feeling is at the center of true religiousness.” -- Albert Einstein
    - Retra 8y ago
      Curious that he's not famous for saying that. It's almost like his actual physics were more relevant than his poetic reflections.
      - samstave 8y ago
        I find it abhorrent that people cannot place into the same realm physics with 'poetic reflections' Tiring is the limiting of mind and creativity such that one thinks that science and reflection are not, intrinsically, the same thing.
        Retra 8y ago
        If they are the same thing, why prefer Einstein to Chopra? Why quote Einstein's fluff, rather than his science? Why shouldn't we give samstave a Nobel Prize for his poem?
- dpark 8y ago
  > Its interesting that we do not try to ask HOW civilizations past could have been aware of cycles that last for tens of thousands of years. That’s probably because they weren’t. What “cycles of the stars that were many thousands of years long“ were ancient peoples aware of?
  - jcranmer 8y ago
    Precession of the equinoxes? For Earth, this is circa 25,000 years, although I don't believe there's a reasonably accurate measurement of this value in Antiquity.
    - dpark 8y ago
      I'm not sure that meets the criteria for a "cycle of the stars" since it's a planetary change, but I guess for Hipparchus it probably did look like a celestial change. It definitely doesn't match the claim that "we do not try to ask HOW civilizations past could have been aware", though. We know exactly how Hipparchus recognized this. Nonetheless, this is a reasonable response to my question. Noting a long-term cycle of equinox precession is impressive but also not terribly surprising. If you can note the change, you can reasonably assume it's cyclical (because the alternative is that it's going to suddenly stop moving at some point in the future).
  - Izkata 8y ago
    The Mayan Long Count calendar? If I remember right, it's method of counting leap years is more accurate than the modern Gregorian calendar.
    - jcranmer 8y ago
      The Mayan calendrical system uses a "year" of 360 days without attempting to account for leap days. Essentially, the long count (the classic 13.0.5.7.6 style system) is a base-20 count of the number of days from the epoch, with one of the digits being base 18 instead. The other components are the 260-day year of 20 "months" of 13 days, the 365-day year of 18 months of 20 days (with 5 extracalendrical days), (and together these two things create a 52-year cycle that's the "Short Count" calendar), a week-ish system (of 9 days), a lunar cycle count, a correction to the lunar cycle because it's annoyingly 29.5 days long, and a 819-day cycle we don't understand yet. Their calendrical system did not attempt to correct for leap years, but we do know that they knew the length of the year to roughly the same precision as the Gregorian approximation.
toolslive 8y ago
> 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_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
- tromp 8y ago
  Perhaps those who expect quantum computers to scale to millions of qubits do. The amplitudes involved seem to defy discreteness...
  - krastanov 8y ago
    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.
- j7ake 8y ago
  Could you give examples on how the incompleteness theorem explains physical phenomena? I would be curious.
  - krastanov 8y ago
    I would suggest Aaronson's "NP-complete problems and physical reality" for this type of thinking (public PDF on his academic page). It is short and has a ton of examples. I really like the style, but it is not a common view among working physicists (yet? It is just not particularly practical for the moment).
- krastanov 8y ago
  I am a physics in academia and no, most physicists do not think that (especially given that most physicists are not quantum foundations physicists, and even then). It is an interesting question, and if I am forced to guess on its answer I would even agree with you, but good science would be to not speculate the way you imply.
sorokod 8y ago
Are we not looking at a mathematical result that constraints what the universe "can do"?
stabbles 8y ago
Which neither means that beautiful math is necessarily describing the world inaccurately. Taken to the extreme, the best description of the world is a long list of all events and facts. No beauty in that. Now science tries to compress this list of events to a simple model that explains it best. Like in statistics, one should aim for the simplest model predicting most of the data. I'd argue that if you think of science as an attempt to compress all the data in the world, then OP's statement is obvious, and at the same time there's good reason to value beautiful (i.e. short & simple) explanations higher provided they generalize well.
- eridius 8y ago
  You say "best", except a long list of events and facts has no predictive power, no way to infer what the future will be, only describes what the present is. The whole point of a model is to be able to predict the future. So in that sense, a long list of all events and facts is the worst description.
  - Xcelerate 8y ago
    Not sure why you’re being downvoted; what you’re saying is true. A model whose length is the same as the data it is describing has no predictive power. A perfect model what be the size of the minimum program that prints out all of the events in the universe (that is, the program whose size matches the Kolmogorov complexity of the universe).
JKCalhoun 8y ago
> Just because the math is pretty doesn't mean the universe actually works that way. Interesting thought ... is mathematics really orthogonal to the universe or does it "result from" or fall out as a result of the universe within which it was described? Getting philosophical, I know, but if you follow, then perhaps the degree to which you don't have to twist mathematics to describe the universe might suggest you are in fact on the right path....
ngcc_hk 8y ago
Agreed. Easy and intuitive as Euclidean geometry it is not right. It is not easy ask anyone doing proof in that paradigm. Getting more mtr complicate not meaning they are right.

checkyoursudo 8y ago

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.

jchanimal 8y ago
You might enjoy this one https://en.wikipedia.org/wiki/The_Unreality_of_Time https://en.wikipedia.org/wiki/The_Unreality_of_Time
- checkyoursudo 8y ago
  Yes! I do know this one. And it is very interesting to me.
systemfreund 8y ago
> The Planck time is by many physicists considered to be the shortest possible measurable time interval; however, this is still a matter of debate. [0] So, if this is true, then does it mean that time does not 'flow', but rather 'chunks'? [0]: https://en.wikipedia.org/wiki/Planck_time https://en.wikipedia.org/wiki/Planck_time
- TheRealPomax 8y ago
  In a very real sense, we may never know. The problem of natural language is that it doesn't really work all that well for scientific purpose: talking about chunks and flows comes with a human's lifetime's worth of thinking they know what those words imply, and so we don't use them except in popular science articles. Time could be discrete, or it could be continuous, but while in normal life the difference between those two is easily determined, this is not the case in physics at all: in order to say "which of the two it is" you first need to have an idea where the boundary between the two would have to be. (even at the macro level, a river that moves a specified number of molecules per time unit doesn't "flow", it's technically moving discrete "chunks" of water, we just don't say it's moving chunks of water because no one cares about the "well, technically..." in normal conversation. We know what's meant and what to ignore. Physics doesn't have that luxury) We have no idea where that boundary can even be found; it would certainly have to be below the Planck length, but we have nothing that allows for that kind of precision. The only thing physics can say right now, and possible even ever can, is that nothing we have at our disposal allows us to conclude time "actually is" discrete. We can come up with mathematical frameworks that assume time is a discrete dimension, but even if those yield super accurate predictions that are then verified through experiment, all that does is confirm that a continuous dimension can be reduced to a discrete one without loss of precision.

cubano 8y ago

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.

danharaj 8y ago
> 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. It is not. It would violate special relativity. No such violation has ever been observed.
lodi 8y ago
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...)

pvitz 8y ago

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.

physicsyogi 8y ago

> 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

madhadron 8y ago

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!

oarabbus_ 8y ago

>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 8y ago
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 8y ago
  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.
  - whatshisface 8y ago
    Fortunately it's not a philosophical claim - after all even if it was demonstrated experimentally that time moved in frames like a movie, it could still be a movie played on a projector whose reels spun in continuous time. There's no way to know "what it ultimately is," only the most ultimate thing seen so far.

based2 8y ago

Like an atom and then its composition. https://nobeliefs.com/atom.htm https://nobeliefs.com/atom.htm

ngcc_hk 8y ago

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

ngcc_hk 8y ago

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)