First recalling here that physical time is not time as understood by our Sensability & Intuition - the proper sense of time; we also recall that famously Newtonian or Einsteinian Physics do not have an arrow of time. The theory is time reversable. It was an urgent question to establish an arrow.

It is thermodynamics that provides such an arrow by using probability via entropy. However there is still no now; and other questions of time remain open.

Now, if no matter was available to universe, that is the universe was empty, one is somehow still convinced that time will flow in the same direction. This of course is a Gedanken experiment; it cannot be carried out ever.

One resolution is to embed thermodynamics in spacetime altogether by atomising spacetime and applying ideas of entropy to the atoms of space & time. Then one expects an arrow of time to emerge from the simple existence of the space-time manifold.

Does this solve the arrow of time question with respect to the Gedanken experiment described above?

Notably one attempt at doing this is through causal set theory where spacetime is taken as atomistic and relational.

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    A note on your thought experiment: your result is only meaningful if you assume an Idealist philsophy. It requires that a mind be capable of existence without matter. This complicates things when you then bring matter without mind into the mix!
    – Cort Ammon
    Commented Dec 19, 2014 at 1:30
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    This question appears to be off-topic because it is about physics.
    – Dave
    Commented Dec 19, 2014 at 14:45
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    @Dave: What do you say about the Stanford Encyclopedia of Philosophy entry on Being and Becoming in Modern Physics where they start of by explicitly asking "What is time, and is it real? If it is, does time flow or lapse or pass? Are the future or the past as real as the present? These metaphysical questions have been debated for more than two millennia, with no resolution in sight. Modern physics provides us, however, with tools that enable us to sharpen these old questions and generate new arguments. Commented Dec 20, 2014 at 16:20
  • Does the special theory of relativity, for example, show that there is no temporal passage or that the future is as real as the present?" Now I'm not asking about the special theory of relativity, but I am asking about time, and causal set theory was insp[ired by a particular theorem about geodesics in the space-time manifold. Commented Dec 20, 2014 at 16:21
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    @MoziburUllah -- the gedankenexperiment in the question, and the final sentence of your previous comments are questions asked and addressed in the context of physics; I don't know has has (or is) doing work on matter-free space times, but I'm quite certain that this has been looked at in the GR community.
    – Dave
    Commented Dec 21, 2014 at 2:03

5 Answers 5


If time exists separate from the course of increasing entropy, as imagined by Boltzmann, how could we know? Our memory is an exothermic chemical reaction, completely dependent on increasing entropy to store information. And the rest of our sense of time is an extrapolation of our experience of accumulating memory.

So, I would contend that sheer thermodynamics need not prove the direction of time, our physiology ties us to a single arrow, instead. But that is the arrow of increasing entropy, which may not align perfectly with any specific dimension of spacetime.

From this point of view, we must inhabit a part of the history of the universe where entropy is relatively low, and entropy must decrease fairly continuously as you move away from points of low entropy and toward points of high entropy in all dimensions, including any 'time' dimensions. But heat does this in space, and we can assume it would have to do so in time.

Indeterminacy can be accounted for in this model by the fact that the progression of entropy would be erratic, so time is not strictly unidirectional, only macroscopically so. The very high level of order in our local space would mean that time never moves backward very fast or for very long, upstream through the sort of 'osmotic pressure' of entropy along the temporal direction. As the 'fluctuation theorem' proves, this pressure remains very, very high until entropy becomes nearly maximal.

The proposed gedankenexperiment would not make sense in this kind of world. An empty space is automatically both minimal and maximal in entropy, and there would be no reason for time to 'move' forward from there. Only in a universe with enough complexity for accumulating entropy to appear continuous could there be something like time as we know it. So space might not have been 'initially' empty, and attempts to project time too far backward may lack logical content. Whatever the underlying structure of time is, against which entropy moves, it could act quite differently in a much simpler place.


Actually, thermodynamics all by itself does not provide an arrow of time, although it is often erroneously believed to do so.

Let's do a thought experiment: At time t = 0, place an ice cube (with random initial conditions) on a table in a room that is kept at room temperature. Now let the laws of physics run normally in positive time. The ice cube will almost certainly melt, as we expect. Now go back to t = 0 and instead turn on the laws of physics in negative time. With overwhelming certainty, the ice cube will melt just as it did in positive time.

It is only the combination of the Second Law of thermodynamics with the low-entropy initial conditions that we observe (for instance, stars that radiate in the positive direction of time) that results in entropy's increasing.

  • Negative time? WTH is this? If you assume ice could melt when time runs in reverse (for whatever that means) then of course thermodynamics can't provide an arrow of time. But that's just behind the question.
    – armand
    Commented Sep 4, 2021 at 4:57

The classical thermodynamic doesn't resolve the arrow of time problem, but confuses it even further: according to the 2nd law of thermodynamic the future is more deterministic than the past; however, we seem to remember past rather than the future.

However, there have been some interesting development in the last 5 years or so, relating some I would say philosophical issues of quantum mechanics with the arrow of time of statistical physics. An easy review is available here, and a more detailed one in the original article it references. There are many very interesting philosophical question arising from that work, a possible resolution of the arrow of time problem being one of them.

EDIT: an explanation for the 1st paragraph above. Here's what I meant:

The 2nd law of thermodynamics precludes one from knowing some things from the past. If you mixed hot water and cold water you cannot later tell from measuring the temperature of the mix how cold was cold water and how hot was the hot one. However, the future remains deterministic: you can predict the temperature of the mix by measuring the ingredients before mixing them. In a matter of speaking, the law of thermodynamics allow more knowledge of the future from the present state than knowledge of the past, also based solely on the present state.

The human experience is kind of opposite: in our present state we remember the past, but we cannot directly "remember" the future. We can predict certain things, with varying degrees of certainty, but almost never with the same clarity as we remember the past.

Thus we have the Arrow of Time enigma: the basic laws of mechanics are deterministic; the laws of thermodynamics (which is based in small scale on the laws of mechanics) are suddenly non-deterministic in "hiding past, not future" sort of way; and the human experience, as well as the desire for the existence of free will, calls for non-determinism in "hiding future, not the past" sort of way.

The "Quantum Arrow of Time" article I quoted attempts to resolve this problem.

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    I can't see what is meant by 'the future is more determinstic than the past'; or even if its plausible. Do you have a link that explainsd it further? I aware that thermodynamics doesn't solve the whole question about the direction of the arrw; but it seemed to be the first scheme that worked; even if it worked imperfectly, as you've suggested. Commented Jan 2, 2014 at 2:21
  • @MoziburUllah: an explanation wouldn't fit into a comment, therefore I added it to the original answer after the word "EDIT".
    – Michael
    Commented Jan 2, 2014 at 3:11
  • Its an interestig perspective - but I'm not sure that this is paradoxical. Being able to predict the value of one macro-variable - the temperature - isn't determinism as we know it from classical physics. The article you quote doesn't try to solve this problem. What it argues is that at the quantum level the second law of thermodynamics is a tautology. That is any violations of the law at this level aren't observable. Commented Jan 2, 2014 at 9:32
  • @MoziburUllah: that's the beauty of that paper: it resolves the apparent asymmetry of the arrow of time despite time-symmetric basic laws by showing that the apparent time arrow asymmetry may be a result of unobservability of, how should I say that, eh, the time-backwards processes. The basic processes - Newtonian, relativistic, quantum - are all time-reversible; however, it's sufficient for some of the processes to be unobservable, hidden from our experience, for the perception of the arrow of time.
    – Michael
    Commented Jan 4, 2014 at 5:00

Irreversibility studies are considered a part of thermodynamics. So, YES, thermodynamic arrow of time really solves the arrow of time question.


As Prigogine explains, determinism is fundamentally a denial of the arrow of time. With no arrow of time, there is no longer a privileged moment known as the "present," which follows a determined "past" and precedes an undetermined "future." All of time is simply given, with the future as determined or undetermined as the past. With irreversibility, the arrow of time is reintroduced to physics. Prigogine notes numerous examples of irreversibility, including diffusion, radioactive decay, solar radiation, weather and the emergence and evolution of life.

One example from the book was a stone dropping from the top of the mountain, - and you cannot predict where it will be land after falling.

Because the interaction between irregular and dynamically changing shape, material, surface properties of both mountain and rock (as the rock gets damaged in the process of rolling) and also minor factors, like current and future wind power and its pressure (which is affected by rock position and aerodynamic properties) are beyond measurement, and thus - unpredictable.

  • i would appreciate an explanation for the downvote.
    – c69
    Commented Dec 19, 2014 at 5:52
  • Boltzmann, the person who formulated the theory to begin with did not think it addressed this problem. He took Loschmidt (the primary anti-arrow-of-time spokesman, see Loschmidt's Paradox) seriously and carefully rewrote his work to avoid presuming this question had been solved.
    – user9166
    Commented Dec 27, 2014 at 17:24
  • Boltzman died 10 year before Prigogine was born. Why should we care about his opinion ? Because he invented thermodynamics ? With logic like that, we should ignore any advances in the field of philosophy after ancient greeks.
    – c69
    Commented Dec 27, 2014 at 20:07
  • OK, so this person 'aimed to solve' the problem and seems to have given the argument that indeterminacy is basic, but without proof. What an advance... Anyone can state an assumption and get the answer they wanted. The known statements of indeterminacy that everyone uses are still reversible. You should care because Boltzmann was an original thinker everyone eventually understood, and this guy does not seem to have convinced anyone, since people like Hawking are still proposing new concepts (like imaginary time) that try to explain the arrow of time. Solved means we agree. No one does.
    – user9166
    Commented Dec 28, 2014 at 14:35
  • this person got Nobel Prize for his work. In chemistry. So, please, at least read his nobel prize lecture, where he specificly states Obviously, the second law [of thermodynamics] expresses the fact that irreversible processes lead to one-sidedness of time. The positive time direction is associated with increase of entropy. So much for no one agrees.
    – c69
    Commented Dec 28, 2014 at 17:50

Some phenomenons suggest an arrow of time that are not (or loosely) related to thermodynamics and the 2nd law.

Take one of the most basic way humanity measured time, the cycle of the sun in the sky. What makes the sun go from east to west in a regular motion whose period we call a day? It's the momentum of Earth's rotation, which is always conserved according to Newton's laws of motion.

It can often be seen that "in Newtonian physics time can be reversed", but this is just a property of the model, not reality. Although it is true that in Newton's equations a negative time value can be plugged, it is never observed in reality that moving object reverse course or change velocity on their own, because their momentum is conserved at all time. Now that it is set on its path, Earth's motion around the sun can only happen in one direction, unless tremendous force is applied to it. This has nothing to do with thermodynamics and yet is the reason astronomical bodies' motion is so regular, and have been humanity's first way to keep track of time.

There are forces that apply only in one direction, like gravity. Objects fall, but never climb up on their own. That's one of the reason why, if we see a footage of a splashed egg on the ground reforming and jumping back into a cook's hand, we instinctively know it has been reversed, because gravity acts only one way, which is down. Again, this is not linked to thermodynamics.

There is also the notion of information and the loss thereof. Here by information I mean the relationship of parts of an object inside of it, the structure of the object. This is what makes the difference between a random ink spot on a paper and the same amount of ink used on the same paper to write a note: the amount and elements of atoms are the same in both, but the way they are disposed makes the difference.

In some events, this information is lost. Take the aforementioned drop of an egg: once the egg is broken, the information about its shape, which was contained in the egg itself, is lost forever. That is why it can be broken only once, with a clear distinction with before and after it was broken. Although this might be related to Boltzmann entropy (which I am not familiar with), this is not related to thermodynamics (the amount of heat exchanged in a egg breaking is negligible).

So although the fact that heat can transfer only from a hot source to a colder recipient is one example of irreversible phenomenon, we can see that momentum, the application of forces and the loss of information, none of which are related to thermodynamics, are also an illustration of the concept of time and why it flows only in one direction.

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