Tuesday, November 10, 2015

Dear Dr. B: What do physicists mean when they say time doesn’t exist?

That was a question Brian Clegg didn’t ask but should have asked. What he asked instead in a recent blogpost was: “When physicists say many processes are independent of time, are they cheating?” He then answered his own question with yes. Let me explain first what’s wrong with Brian’s question, then I’ll tell you something about the existence of time.

What is time-reversal invariance?

The problem with Brian’s question is that no physicist I know would ever say that “many processes are independent of time.” Brian, I believe, didn’t mean time-independent processes but time-reversal invariant laws. The difference is important. The former is a process that doesn’t depend on time. The latter is a symmetry of the equations determining the process. Having a time reversal-invariant law means that the equations remain the same when the direction of time is reversed. This doesn’t mean the processes remain the same.

The mistake is twofold. Firstly, a time-independent process is a very special case. If you watch a video that shows a still image, it doesn’t matter if you watch it forward or backward. So, yes, time-independence implies time-reversal invariance. But secondly, if the underlying laws are time-reversal invariant, the processes themselves are reversible, but not necessarily invariant under this reversal. You can watch any movie backwards with the same technology that you can watch it forwards, yet the plot will look very different. The difference is the starting point, the “initial condition.”

The fundamental laws of nature, for all we know today, are time-reversal invariant*. This means you can rewind any movie and watch it backwards using the same laws. The reason that movies look very different backwards than forwards is a probabilistic one, captured in the second law of thermodynamics: entropy never decreases. In large open systems, it instead tends to increase. The initial state is thus almost always very different from the final state.

Probabilities enter not through the laws themselves, but through these initial conditions. It is easy enough to set up a bowl with flour, sugar, butter, and eggs (initial condition), and then mix it (the law) to a smooth dough. But it is for all practical purposes impossible to set up dough so that a reverse-spinning mixer would separate the eggs from the flour.

In principle the initial state for this unmixing exists. We know it exists because we can create its time-reversed version. But you would have to arrange the molecules in the dough so precisely that it’s impossible to do. Consequently, you never see dough unmixing, never see eggs unbreaking, and facelifts don’t make you younger.

It is worth noting that all of this is true only in very large systems, with a large number of constituents. This is always the case for daily life experience. But if a system is small enough, it is indeed possible for entropy to decrease every once in a while just by chance. So you can ‘unmix’ very small patches of dough.

What does any of this have to do with the existence of time? Not very much. Time arguably does exist. In a previous blogpost I explained that the property of being reality isn’t binary (true or false), but it is graded from “mostly true” to “most likely false.” Things don’t either exist or don’t exist, they exist at various levels of immediacy, depending on how detached they are from direct sensory exploration.

Space and time are something we experience every day. Einstein taught us space and time are combined in space-time, and its curvature is the origin of gravity. We move around in space-time. If space-time wasn’t there, we wouldn’t be there because there wouldn’t be any “there” to be at, and since space and time belong together time exists the same way as space does.

Claiming that time doesn’t exist is therefore misusing language. In General Relativity, time is a coordinate, one that is relevant to obtain predictions for observables. It isn’t uniquely defined, and it is not itself observable, but that doesn’t make it non-existent. If you’d ask me what it means for time to exist, I’d say it’s the Lorentzian signature of the metric, and that is something which we need for our theories to work. Time is, essentially, the label to order frames in the movie of our universe.

Why do some physicists say that time isn’t real?

When physicists say that time doesn’t exist they mean one of two things: 1) The passage of time is an illusion, or 2) Time isn’t fundamental.

As to 1). In our current description of the universe, the past isn’t fundamentally different from the future. It will look different in outcome, but it will be made of the same stuff and it work the same way. There is no dividing line that separates past and future, and that demarks the present moment.

Our experience of there being a “present” comes from the one-sidedness of memory-formation. We can only form memory about things from a time where entropy was smaller, so we can’t remember the future. The perception of time passing comes from the update of our memory in the direction of entropy increase.

In this view, every moment in time exists in some way, though from our personal experience at each moment most of them are remote from experience (the past) or inaccessible from experience (the future). The perception of existence itself is time-dependent and also individual. You might say that the future is so remote to your perception, and prediction so close to impossible, that it is on the level of non-existence. I wouldn’t argue with you about that, but if you learn some more General Relativity your perception might shift.

Now this point of view irks some people, by which I mean Lee Smolin. Lee doesn’t like it that the laws of nature we know today do not give a special relevance to a present moment. He argues that this signals there is something missing in our theories, and that time should be “real.” What he means by that is that the laws of nature themselves must give rise to something like a present moment, which is not presently the case.

As to 2). We know that General Relativity cannot be the fundamental theory of space and time because it breaks down when gravity becomes very strong. The underlying theory might not have a notion of time, instead space and/or time might be emergent – they might be built up of something more fundamental.

I have some sympathy for this idea because I find it plausible that Euclidean and Lorentzian signatures are two different phases of the same underlying structure. This necessarily implies that time isn’t fundamental, but that it comes about in some phase transition.

Some people say that in this case “time doesn’t exist” but I find this extremely misleading. Any such theory would have to reproduce General Relativity and give rise to the notion of time we presently use. Saying that something isn’t real because it’s emergent is a meaningless abuse of terminology. It’s like saying the forest doesn’t exist because it’s made of trees.

In summary, time is real in a well-defined way, has always been real, and will always be real. When physicists say that time isn’t real they normally use it as a short-hand to refer to specific properties of their favorite theories, for example that the laws are time-reversal invariant, or that space-time is emergent. The one exception is Lee Smolin who means something else. I’m not entirely sure what, but he has written a book or two about it.

* Actually they’re not, they’re CPT invariant. But if you know the difference then I don’t have to explain you the difference.


  1. What do you think of Julian Barbour's claim that time doesn't exist. (If he is wrong then, echoing Fermi (or was it von Neumann?), probably on a higher level.) Have you read anything by him?

  2. Hi Phillip,

    I haven't read anything by Julian, but I've met him many times and heard several of his lectures. I would say the same thing about his claim that "time doesn't exist" - it's an abuse of language. What he means is that fundamentally there is no time. Since he too must reproduce General Relativity, emergent time must still exist.

    About his idea in general. It's either too much or too little I'd say. If you take away time and argue that our perception of time does not come about because moments are actually connected, but because at each moment it appears to us as if they were, then why not do away with space as well and go to full blown solipsism. What do you need a full universe for when Julian Barbor's brain at one moment of time will do?

    It's good there are people willing to be so radical and to question everything. I just personally think that quantizing gravity doesn't necessitate it. Best,


  3. on a (simplistic) tangent:

    Some talking at fundamental cross-purposes in such discussions

    Humans are capable of only the vaguest adumbration of reality as science knows it.

    To take simplest things: We look at our neighbour and see brown hair; that colour is merely our labelling of a frequency of light; we touch their hand and it is solid: yet it is almost entirely empty space; we look at the sky and see a pattern that does not exist now and never did exist; some stars are seen where they were a handful of years ago, others where they were billions of years ago.

    And once we start talking about deep issues like time . . .

    We tiny fractions of the universe can only grasp the universe as science understands it by ceasing to be human, splitting from our usual selves.

    Science can allow us to manipulate the deeper reality to some degree, and to understand in a shadowy way, but never more.

  4. Julian Barbour's style of writing is so convoluted as to be almost unreadable.
    The problem (well, one of the problems) I had with Lee Smolin's book is that he said some physicists believe time doesn't exist, which - as you say - is clearly misrepresenting their views. If you merely accept general relativity, you are saying time exists (as you say, it's just a coordinate). He didn't explain anything in detail, didn't explain the block universe model, and it left you wondering what he was actually arguing about. Really strange.

  5. General Relativity by itself gives no meaning to the present, but what about with Quantum Mechanics grafted onto it, with past, present and future measurements?

  6. Arun,

    I think George Ellis has been hitting on this drum, but I've never managed to make sense of his modified block universe. The measurement process isn't fundamental - it can't be because "detectors" aren't fundamental. The problem is that nobody knows how it 'emerges' (which I think, btw, is a totally under-investigated question). I think most physicists presently believe the measurement is yet another type of entropy increase. See, waving your hands and saying 'quantum mechanics' doesn't get you off the hook when you are asking which space-time slicing is the one to define the 'present' moment. The only way you can do this is to introduce a preferred slicing. Which leads to Lorentz-invariance violation, which leads to a problem. I don't see how to get around this. I'm a big fan of the block universe with all its eternal presence. Best,


  7. "But it is for all practical purposes impossible to set up dough so that a reverse-spinning mixer would separate the eggs from the flour." Maybe,


    "space-time, and its curvature is the origin of gravity." ECKS gravitation; spacetime torsion overall, Weitzenböck for a metric. Testable on a bench top in existing equipment. Chirality is a strong arrow of time,

    Phys. Rev. D 88, 044024 (2013), arXiv:1307.2229, doi:10.1103/PhysRevD.88.044024
    Nature 463 210 (2010), doi:10.1038/nature08680
    Phys. Rev. D 71 057501 (2005)), doi:10.1103/PhysRevD.71.057501
    Phys Rev Lett. 91(24) 247404 (2003), doi:10.1103/PhysRevLett.91.247404
    Chem. Phys. Lett. 173(5-6) 485 (1990), doi:10.1016/0009-2614(90)87240-R

    Politics denies time. Infrastructure has always been, society is redefined at will, no future will be held accountable for finance.

  8. Isn't the big insight about time in special relativity, which carries over to general relativity, that the rate at which time flows in local and individual, rather than being a global dimension or coordinate? Or, to be more precise, that the arrow of time may be global, but the metric of time is not?

  9. Andrew: Yes, it's what I mean when I wrote that time isn't uniquely defined.

  10. Here's my take on it : There are (at least) 2 interpretations of time. We can't remember the future because it hasn't happened yet. We can remember the past because is has happened. That's how we experience time in an absolute way. Then there's time in Relativity. The most general description of time here is : Time is what clocks measure. Mixing those 2 notions of time leads to a pile of nonsense. Side note: A classic spring clock would not respond the same way an atom clock does, so time as measured in Relativity is a process not yet fully understood ( in spite of excellent mathematical descriptions). I think if understood those details, we would have an viable angle to construct a theory of quantum gravity. Greetings. Everything should be debatable, so shoot.

  11. What about the Wheeler-DeWitt equation and the fact that time evolution is a Hamiltionian constraint(HΨ=0)? People often begin discussion regarding the "problem of time" by referring to this.

  12. Giotis,

    I was thinking that would be too technical. In my perspective this "problem of time" merely means, as in classical GR, that one has to pick a time coordinate by hand, or use one that is defined from the flow of some matter field. I don't really understand why this is a problem. Best,


  13. Can you explain more about the concept of time as it relates to quantum entanglement? If one particle of an entangled pair is distant, accelerating away, and in the neighborhood of a gravity well, isn't it hard to synchronize time between the two particles so that an "instantaneous" correlation between the particles makes any sense as a concept.

    To my layman's understanding, time at the quantum level looks a lot like an absolute thing in contradiction to SR and the relativity of simultaneity.

  14. Michael,

    An excellent question! Speaking of an "instantaneous correlation" doesn't make sense. The particles are correlated, period. It is correct that it "looks like" a contradiction to SR. But it isn't. There isn't anything observable in this description that contradicts SR. Yes, some people don't like the "instantaneous" collapse, but it's just this: a disliking. There's no internal contradiction. George Musser has written an excellent book about this, that I can warmly recommend. Best,


  15. Slightly off topic, but George Musser has an article in SciAm on nonlocality (I presume to promote his book that you reviewed):


    He claims that objects fall "because Earth's mass warps time. The warping of space plays only a minor role in these cases"

    Is this right?

  16. Waterberg,

    It's an extract from his book (which I mentioned above). I took the sentence you quote to mean that in the Newtonian limit it's only the tt-component of the metric that enters, so in that interpretation it's correct. Roughly speaking, the reason is that every contribution from a space-coordinate is suppressed by v/c which, for objects we deal with, is always << 1. Best,


  17. Thanks Sabine. Can you recommend a online resource that provides a good introduction to General Relativity for someone with a science background who isn't afraid of maths?

  18. From what I can see of George Musser's book courtesy of Amazon.com it looks like it's mostly (or even all) psiontology. He says, "in the case of nonlocality, even the most die-hard skeptic accepts that something very weird is going on, something that forces us to go beyond our deepest-held notions of space and time." Really? So where does that leave the (neo-)Copenhagenist, the QBist or the Relationalist?

  19. Dear Sabine,
    After thinking it over, I do wish to say I don't believe your attitude befits someone who very clearly wishes to be taken seriously. I am hoping sincerely that you might come around to agree with me.

    I came to your blog last night from Motl's. He had used your name in an offhanded way to characterize something as easy to understand while also making a definitive statement about your intelligence.

    Subsequently I read you entry regarding him and his disreputable behavior towards you, and it informed me.

    And so it pained me to read this unfortunate entry. I don't know how Mr. Smolin could have personally offended you, but this is not the place to seek retribution, particularly as you know he will not respond to this type of nonsense. It further pains me that in his books which are exceedingly easy to understand and written in plain and proper English he makes exactly the same statement more or less that you make here in the last paragraph. Finally, the gross inappropriateness of this offhand statement of yours makes a joke that you are missing. I don’t want to spell it out because you will be offended, but It would be better if you did not force your reader to evaluate this condition.

    Please consider removing the reference to Mr. Smolin altogether. As you suggested more or less in discussing Motl, it would be better to address a person's ideas after you have read them and are certain you understand them. I think you know what you were attempting here, perhaps it felt good at the time, but it is beneath anyone who is a scholar and a writer.

    Should you decide to make the necessary correction, please also delete this comment. Thank you.
    Mike Asher

  20. Mike,

    I have honestly no clue what you are talking about. All that I am trying to say is: If you want to understand what Lee says, you should read his book, and not listen to me. If you found it "easy to understand," then I am curious to hear what you think he means with "time being real." If you think he means the same as I mean, then I think you misunderstood either me or him.

    I assure you that Prof. Smolin has not personally offended me, and I am not "seeking retribution" on anything. If you though my comment was anything else than a humorous recommendation to buy-the-book, you misread it. Best,


  21. Hello Sabine,

    In your explanations above you say : "In this view, every moment in time exists in some way."
    Can you explain how this conclusion is reached, starting from the GR definition of time, where time is what clocks measure. We could indeed observe many clocks, each at for instance a different radius from the earth, and notice that they each will indicate a different time, according to gravitational time dilatation. "In some way" : could you clarify in what way you have intended this ?

    Thank you,


  22. Hi Noa,

    I explained this several years ago here. Looking at this now, I'm not sure how comprehensible it is, but give it a try. If that doesn't help, I'll give it another go ;) Best,


  23. Some thoughts on time;
    We experience reality as flashes of cognition and so think of time as the point of the present moving from past to future events. Physics essentially codifies this by treating it as measures of duration, from one event to the next.
    The basic reality though, is that it is a changing configuration creating and dissolving these events, such that they go future to past. To wit, tomorrow becomes yesterday because the earth turns, relative to the sun.
    Duration then, is the state of the present, as these events come and go. What is measured is frequency and this makes time an effect of action, similar to temperature, which is an effect of masses of frequency and amplitude.
    What creates the directionality of time is the inertia of action. It is a physical fact that the earth turns one way and not the other. Time is not simply a scalar measure, but an effect.
    So causality yields determination, not the other way around, as events are first in the present, then in the past. The input into any event only fully arrives with its occurrence and there is no view outside of space and time to recognize it prior to that. So if input cannot be known, then neither can output.
    Alan Watts used the example of a boat and its wake to describe this relationship between the present and the past, in that the boat creates the wake, not the wake directing the boat.
    The illusion of determinism comes from the inertia of energy, but this also means the energy is conserved as the present moment and so there is none to physically manifest prior or succeeding moments. So it is actually the present moment that is constantly reconfiguring prior formations and so adapting the prior formations to current frames, much as memory constantly edits itself. Even as they occur, events are recognized as subjective, so receding into the past doesn't make them objective. Time then is more a loop, of a tapestry being woven of strands pulled from what had been woven.
    We equate temporal sequence with causality, but it is an effect, not the basis of that process. Yesterday didn't cause today, rather the sun shining on a spinning planet created this effect of days.
    The reason clocks can run at different rates and still remain in the same present is that they are separate actions. A faster clock uses energy quicker and so will recede into the past faster. The tortoise is still plodding along, long after the hare has died. As the twin in the faster frame ages quicker.
    So time is emergent at the level of measurable change, just as temperature is emergent at the level of measurable activity.

  24. "buy-the-book"

    A real rarity: too many hyphens!

  25. @Mike The past 45 years of non-classical gravitation summed are non-empirical - assuming the Equivalence Principle (Einstein's elevators). Given Newton's assumptions, where is GR, QM, and stat mech? Derivation cannot detect weak postulates. Crackpot Bolyai said a triangle's three interior angles can sum to other than Euclidean 180 degrees, like 300+ degrees,

    71.295556 -156.766389 Barrow, AK
    -1.469167 -78.817500 Mt. Chimborazo, Ecuador
    3.133333, 101.683333 Kuala Lumpur, Malaysia

    Calculate it exactly
    The EP might fall to test mass geometry not composition.

  26. Ok Sabine, i've read your expose, it is very informative and didactic, thank you.
    The following is rather a long paragraph, but i hope you will take the time to look into it.
    I'm trying to get a grasp of this 'time' by hypothetically putting myself at a spot outside of the universe, to get an understanding as a non-participant so to speak. Taking the phylosophical starting view that everything is made of 'stuff', in the broadest sense of the word, visible matter, the vacuum, dark matter, ...litterally everything.
    Ok, what i see then is that any clock rate and any experience of time is emerging from interaction of this 'stuff', even without specifying what 'interaction' and 'stuff' would entail precisely.
    This results in a very dry and unspectacular understandi g of 'time', meaning that it is just not out there to be found anywhere. Past, present, future, ticking rates, all of it has its origin from 'stuff interacting'.
    The universe seen as 'a bucket' full of hydrodynamical processes, just stuff, and it moves, be it in highly specific ways and according to highly specific laws.
    This helicopter visions pulls the plug on abstract concepts and puts your feed firmly on the ground. At least , this is a view i wanted to share in response to a.o. the Block Universe concept and the Presentism you discussed in that post. Demystification has always been an important role for science throughout the course of history, no ? Interpreting SR and GR towards explanations that objectify the meaning of what sits behind the equations in this case.
    Would you agree with such a view, or ?
    Greetings, Noa

  27. George,

    I have always made it clear that it's perfectly fine by me to say that free will is emergent - a forest made of trees. The problem is that people want it to be a forest that isn't made of trees, and last time I looked you were one of these "people". I somehow lost track of this, sorry. I will come back to it eventually... Best,


  28. @George

    Well I haven't read your book so I've no idea what your argument is but it's implausible to me that one exists that would support your claim. Copenhagists and QBists don't only argue for their interpretations by poking holes in other interpretations. Once you've interpreted QT as, fundamentally, the application of (non-commutative, 'subjective') probability theory to physics, it just doesn't make sense to demand the kind of positive account of correlations - possibly involving dramatic revisions to our understanding of spacetime - which it does make sense to demand of psi-ontic interpretations.

    Rovelli's idea is compatible with MWI/EQM rather than equivalent to it.

  29. Slight tangent to your post. Well, I guess it's coming at the nature of time from a different direction.

    Specifically, I'm thinking of Aharonov's and Tollaksen's Time Symmetric Quantum Mechanics (TSQM). I've been following this theory for a little over 10 years now. At first, it didn't seem very popular. But, it seems like lately it's gaining some ground, with more folks considering that possibility reality might just consist of this ever-so-subtle type of retrocausality found in TSQM.

    Anyhow, seems like a whole 'nother spin on the question "what is the nature of time". Just curious what you make of their ideas?

    For some reason, I can't help but feel TSQM and "standard" QM might be analogous to Lagrangian/Hamiltonian and Infinitesimal methods under Newtonian physics. Mathematically, you get all the same predictions from both formulations (just like with TSQM and "standard" QM). But, one, or the other, is more useful in certain areas for problem solving, or for providing better, different insights on reality (once again, just like with TSQM and "standard" QM). But, reality is apparently rich enough to take on the appearances given by both points of view.

    I can't help but think that time (w/e it is) might ultimately be rich enough such that it takes on the linear appearance under "standard" QM, as well as the "bi-linear" appearance under TSQM. Perhaps the next big theory will tell us why?

  30. Sabine: You say that "time is real in a well-defined way" -- So, what is that definition of time that you mention? All I can find is, "Time in physics is defined by its measurement: time is what a clock reads." (en.wikipedia.org/wiki/Time_in_physics) Can you help me out, please?

  31. Time is a coordinate of a differentiable space-time manifold with Lorentzian signature. It's the one with the odd signature out, depending on convention that's either plus or minus. That's the definition. You can't define time as the thing that a clock reads because for that you'd first have to define what a clock is. Once you introduce matter, you can define a clock and you'll find that (in suitable approximations) clocks read time. In both cases there are infinitely many parameterizations of time.


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