In a very small static universe with only a particle, does it make sense to talk about time?

I am sorry if this question is silly; it′s just one of those things I wished I asked before leaving university.

If there were a static universe only as big as the size of two particles, say electrons, and there were one electron in it going back and forth from point A to point B: would time also go back and forth in the future (point B) and in the past (point A), or would it be considered to go forward as it does for us? would it be possible to know how long that electron stayed at point A or point B, would it even make sense to ask? I guess what I am asking is: does time move forward only because there are so many particles moving in this enormous space that it is almost impossible they would all be back in the same position they held at least once before relative to each other? does time exist only as a consequence of a lot of particles and their position relative to each other, and the space for them, just like heat?

• ??? Static means time-independent, so time should play no role. But how can something go back and forth without a time? – Arnold Neumaier Oct 5 '12 at 19:32
• Can the particle talk? 8-)} – Keith Thompson Oct 6 '12 at 6:35
• – Artur Udod Oct 15 '12 at 7:58

There are levels of time definition., and all levels depend on change . Time is a mathematical construct of our mind abstracted from our biological experience.

The first level of time definition comes because we are living observers. We observe changes in our surroundings and ourselves. The changes we parametrize as "time" are strongly coupled in the biological cycle. Living beings have a timeline from birth to death. The giant astronomical clocks were used to correlate these changes with the timeline, defining time: day/night tides sun cycle. As our scientific observations progressed time has also been defined as vibrations of specific atoms, atomic clocks.

This time has as a beginning the emergence of homo sapiens who could organize a concept of dimensions and time. This time cannot be defined in a universe of two particles.

The next level of time is when we learned thermodynamics and statistical mechanics and discovered a microcosm of atoms and molecules and the concept of entropy, which can never become less and it can only grow. This direction gives also a direction for the so called "arrow of time". The number of microstates describing a system can only grow. In this definition of time's arrow two particles cannot create statistical quantities so there is no meaning to time other than mathematical.

Observation of change is important to defining a concept of time. If there are no changes, no time can be defined. But it is also true that if space were not changing, no contours, we would not have a concept of space either. A total three dimensional uniformity would not register.

In special relativity and general relativity time is defined as a fourth coordinate on par with the three space directions, with an extension to imaginary numbers for the mathematical transformations involved. The successful description of nature, particularly by special relativity, confirms the use of time as a coordinate on par with the space coordinates.

It is the arrow of time that distinguishes it in behavior from the other coordinates as far as the theoretical description of nature goes.

Your gedanken experiment of only two particles in a universe can only be a mathematical exercise, the time it has will be the time in the mathematical equations describing your creation and the forces involved. As was observed in the comments static means no time dependence and the problem should be better defined. If you have one hydrogen atom in the universe, that is static, until one goes to the nuclear dimensions, then a mathematical time is need to describe the system.

• Beautifully explained. I recently heard Sir Roger Penrose speak about his CCC theory at UC, San Diego. He derived the simple expression $\nu=m\frac{c^2}{h}$ to exemplify that "if all matter eventually decays" then so does time. I posted a question on that but it didn't receive much attention. And today found this post. Time indeed seems to race near the most massive objects, less so where matter is deplete. Which seems to me not necessarily tied to human observation. – docscience Feb 7 '18 at 18:19
• "The number of microstates describing a system can only grow" Are you sure? – Alex May 29 '18 at 15:17
• @Alex Yes. Just think of black body radiation that every matter system has to emit – anna v May 29 '18 at 15:50
• @annav For a particle physicist, that's an astonishing statement. – Alex May 29 '18 at 15:54
• @Alex why? black body radiation is par excellence quantum mechanical – anna v May 29 '18 at 15:55

Time is percieved to move forward, the only meaning we can give to time's foward motion is through our mind's computation and the associated entropy production. In a universe without a complex computing device, like a planet Earth, it is hard to know what it means for time to move forward in a positivistically satisfying way.

The question is largely meaningless because it is about the "flow of time" rather than about the measurements one can make on objects.

• Are you saying that experiencing the flow of time is like the philosopher's qualia about the experience of the color red? I never thought of it that way before, did you? – FrankH Oct 6 '12 at 5:39
• yes, this is standard physics philosophy since Boltzmann. – Ron Maimon Oct 6 '12 at 5:45
• I never heard something like the "qualia of the experience of the flow of time" before. I think I've heard we don't understand the psychological flow of time from a physics point of view, but not putting it on the same footing as the qualia of red. Can you point me to a physics reference like that? – FrankH Oct 6 '12 at 5:49
• @FrankH: It's just what I said above, it's not said explicitly in this form anywhere, but it's not original to me, it's just an implicit understanding in physics from Boltzmann onward, and the discussion of Boltzmann brains is the beginning (this was discussed on meta somewhere in a discussion involving me and anixx, and there was a reference to Boltzmann's article). The flow of time doesn't appear from this point on in physics as a concern. – Ron Maimon Oct 6 '12 at 5:53
• Ok. To me putting the qualifier "qualia" on the "flow of time" seems significant since I have always denigrated the philosopher's attempts to make the qualia of red mean something significant when, from my point of view, it is just a biological systems reaction to photons of certain wavelengths. So since cause and effect are closely related to the arrow of time experience, does that mean cause and effect is another qualia? I guess this is not the time or place to get into these "meta-philosophical" questions - so no reply is required or expected.... – FrankH Oct 6 '12 at 6:02

Well, i'm not a physicist, so my answer could sound a lil bit naive, but =)) As far as i remember from the "Brief History Of Time" by Hawking, a common view on time is that it's not a separate entity existing in isolation from space, but a part of the space–time continuum or simply, spacetime.

Time can be considered as a measure of entropy of space. Imagine that someone could somehow manage to 'rollback' the state of matter & energy to the state at which it was yesterday. Would this be time travel? I don't see reasons why it wouldn't.

Time is relative. If time was independend from space then we would be able to talk about absolute time. We know from the theory of general relativity that time can 'flow' differently for different observers.

If there are no particles, or they remain absolutely static, then notion of time is irrelevant. So it's irrelevant to talk about time before the Big Bang.

Also, i suppose that answer to your question should depend on the definition of 'time'. I'm not aware of the modern scientific definition of time, and probably, things are far more complex then I imagine, but from the POI I've just described, the answer to your question would be Yes.

PS: some of the text here is duplicated from my answer in understanding time: Is time simply the rate change?