# Is the flow of time at rest a universal constant?

1. Jan 25, 2012

### fbs7

Hello again! Another silly question from a silly engineer if you guys would help, please?

Question is: do we know enough about how time flows (in a frame of reference at rest) to assume that it has always flowed at the same rate, ever since the first plank time after the big bang?

I mean, I assume (but I really don't if that is feasible or not) we can study the light from galaxies very far away and gather some conclusions how time flowed there when they emitted their light, but that was from 480 million years after the big bang. How about the initial 479 million years?

Thanks all!

ps: a side question - do we know if the flow of time at rest is related to the speed of light?

2. Jan 25, 2012

### dpa

i don't think there is such thing as absolute rest frame to make valid your assumption.

Further the notion that rate of flow of time might itself is flawed. You could say interval between two events.

3. Jan 25, 2012

### zhermes

Some great questions.

All things move through space-time at a constant velocity; namely, the speed of light. If an object is traveling through space near the speed of light; it travels very slowly through time. If an object is at rest, it travels at the speed of light through time.

The speed of light and the rate time progresses for an observer are fundamentally connected.
Time is measured by processes and physical interactions (e.g. the ticking of a clock, the oscillations of a crystal, the aging of cells, etc etc) all of which are governed(/limited) to the speed of light.

Current accepted theories believe the speed of light has remained constant over time, and thus it would seem that the flow of time has remained constant.

4. Jan 25, 2012

### questionpost

Time flowing at all is relative. Einstein figured that if nothing goes faster than light, then not even time would go faster than light, so if an object traveled at the speed if light, from the point-of-view or frame-of-reference of the light-speed object, time would be traveling at the same speed as it and thus an object going at the speed of light would not be effected by the flow of time. It's no different than noticing that two cars along side each other at the same speed will not notice one going ahead of the other.
Because of this, we know that by not traveling at the speed of light that from out frame-of-reference that time is flowing.

5. Jan 25, 2012

### Staff: Mentor

This is one of those questions that can lead to a lot of different answers to slightly different versions of the question. Some versions, IMO, aren't really physically meaningful, and all versions require some care in making sure the concepts you're working with are well-defined.

As dpa pointed out, "at rest" is relative.

Also, as dpa pointed out, the concept of "rate of time flow" as it stands isn't really well-defined. For example, you say:

We can indeed study light from faraway galaxies that was emitted long ago, as well as other phenomena such as radioactivity that give indications of time, and from that try to draw conclusions about whether the values of various physical constants, like the fine structure constant, have changed over the intervening time. See, for example, this page of the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/constants.html

However, whether you interpret any such variation in constants (so far nobody has found any evidence for such variation, but suppose someone did someday) as a "change in the rate of time flow" is a matter of interpretation. So to really get an answer to your question, you first have to decide what you think would count as a change in the rate of time flow. See further comments below.

This version of the question, IMO, requires even more care in answering. For example:

This is not wrong, exactly, but this way of putting things can very easily lead to confusion. The underlying physics that zhermes is describing here is this: objects in spacetime have associated with them a 4-momentum, which is their energy and momentum wrapped up into a single mathematical object that transforms in an appropriate way under Lorentz transformations--meaning that it properly represents how the object's energy and momentum appear to change when you change how you are moving relative to the object. If you take an object's 4-momentum, and divide by the object's rest mass, you get a mathematical object called the 4-velocity. This 4-velocity is the 4-D spacetime analogue of an ordinary vector, and the length of this vector is, in conventional units, the speed of light.

So we can, by properly interpreting the expression "move through spacetime at a constant velocity", make zhermes' statement above true. However, suppose we then ask the question: what is the speed through spacetime of a photon? There is no answer; if you try to apply the definition of 4-velocity I gave above, it doesn't work, because a photon's rest mass is zero and you can't divide by zero. However, a photon has a perfectly well-defined 4-momentum; it has energy and momentum just like everything else, and the 4-momentum describes it the same way it describes the energy and momentum of an object with nonzero rest mass. So 4-momentum is really the more fundamental concept; the idea of "speed through spacetime", 4-velocity, is a derived concept that can't always be applied.

And once again, what part of this corresponds to "rate of time flow" is a matter of interpretation:

If by "governed", you mean "is affected by the values of physical constants, one of which is the speed of light", then yes, all these processes that we use to measure time are governed by the speed of light. But they are also governed by other physical constants; the speed of light is not the only one. And you can use these processes to define "rate of time flow" in a way that can be physically tested and used as a measuring standard. For example, 1 second is currently defined, in SI units, as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

http://en.wikipedia.org/wiki/Second

But this definition, of course, *assumes* that each "period of radiation" marks out a constant interval of time. How do you test that? The only way is to compare it with some other physical process. But what if they vary with respect to each other? Which one is the "right" one? The second used to be defined in terms of the Earth's rotation, until atomic clocks got accurate enough to actually measure, directly, the gradual decrease in the Earth's rotation rate due to tidal effects from the Moon and Sun. That was what prompted the change to the cesium atom standard for the second. But interpreting the measurements as a "decrease in the Earth's rotation rate" assumes that the atomic clock standard is a "more constant" interval of time. Someday we may find that atomic clock rates can vary too, by one part in a quadrillion, say, and then we'll have to switch to something even more constant. There is no way to know for sure if there will ever be an end to this type of thing; there may always be some standard more accurate than our current one, that we just haven't figured out yet.

This is another statement that has to be interpreted carefully. What you're referring to is the fact that the length of a photon's 4-momentum vector is zero, which is equivalent to saying that a photon has zero rest mass. But note that neither of those ways I just stated it requires any assumption about the "flow of time" for a photon. Interpreting the zero length of the 4-momentum as "time does not flow for a photon" is an interpretation, and one that can lead to confusion, just as the statement about "speed through spacetime" quoted above can.

Not quite: this would apply to any pair of objects at rest relative to each other, but photons can't really be "at rest". See the PF FAQ on "rest frame of a photon":

6. Jan 26, 2012

### zhermes

@PeterDonis thanks for your additions, they certainly clarified both the OP's answer and my own understanding of things.

I should have said, 'any massive object'. Clearly time durations observed by a photon are undefined.

Here I disagree with you. Just because the second is now defined without regard to electromagnetism doesn't mean the temporal-nature of it isn't determined by the speed of light---which determines the rate of all fundamental interactions (gauge bosons).

Without interactions (via the fundamental forces) there is no concept of time progressing. Every hint, evidence, feature, and progression that goes with time's arrow are determined entirely by the rate at which fundamental interactions act. I'm saying that you can change the rate of time-travel if and only if you change the speed of light. Similarly, changing the speed of light will correspondingly change all of the measures of time-travel. Thus it seems it could be said that the speed-of-light 'governs' the rate of time-travel. No?

Last edited: Jan 26, 2012
7. Jan 26, 2012

### Staff: Mentor

There are several issues coming into play here (some of which involve quantum physics as well as relativity); it might help to try and disentangle them:

(1) Not all gauge bosons are massless; the W and Z bosons of the weak interaction have nonzero rest mass, so they don't travel at the speed of light. So it's not true that *all* interactions "flow" at the speed of light, even if we agree to call the speed of the gauge boson the "rate of flow" of the interaction (see below).

(2) The gauge bosons that actually mediate interactions are virtual particles, not real particles. Virtual particles don't have to travel at the "correct" speed for their rest mass (the technical term is that they can be "off the mass shell"); so massless virtual particles don't have to travel at the speed of light. (Strictly speaking, virtual particles, and indeed quantum particles in general, don't even have a well-defined "speed".)

(3) The speed at which the gauge boson travels (assuming we can come up with a reasonable meaning for that expression--see above) is not what determines the "rate" of the interaction as you are using the term. For example, the number of oscillations of the cesium atom that are defined to make up one standard second has nothing to do with the time it takes light to cross the atom, or any other parameter that could be related to the "speed" of photons within the cesium atom. So even though the oscillations are "governed" by the exchange of virtual photons between the electrons and the nucleus of the atom, the rate of oscillation can't be related to the speed of those photons.

(4) If changing the speed of light changed *all* of the measures of the "rate of time travel", how would you know anything changed? The "rate of time travel" is a *relative* concept; there is no absolute "rate of time travel". You have to be able to detect differences from one place to another, or one time to another, to know that anything changed at all.

For example, if we found evidence that the speed of light was different 10 billion years ago than it is now, we could interpret that as evidence that the "rate of time flow" was different then than now. (Although, as I said before, that would only be one possible interpretation.) But to even find such evidence, there would have to be something that *didn't* change from 10 billion years ago to now, something that was *not* affected by the change in the speed of light, in order for us to have some common standard against which to detect the change. If the "change" in the speed of light changed *everything* that we could possibly use to measure it, we would not detect any change at all. So the speed of light can't be the only thing "governing".

8. Jan 26, 2012

### fbs7

What I was trying to ask (in an imprecise way) is this: if I measure an object that is far away, and has a zero speed relative to me, can we assume its flow of time is the same as mine?

Say time was flowing slower to him when he emitted his light. Then the frequency of light will be lower and he would seem to redshift, so I could come to a conclusion that he is red-shifting because he is moving away from me, when actually he has zero speed.

Conversely, if I see someone that is far away and he seems to red-shift... can I tell for certain that he is moving away at speed and can I exclude the possibility that time just flows slower at the location he is at (or was slower when he emitted the light)?

From what I understand from the posts up so far, the whole thing seems to be tied up to the speed of light, right? Perhaps the question could be rephrased as "why do we assume the speed of light is constant in the universe, throughout the entire life of the universe" - is that the same question?

9. Jan 26, 2012

### fbs7

What a mind-boggling concept! This is a really exciting perspective.

So nothing is at rest - everything moves. Doesn't it kinda kills the concept of kinetic energy, through, because there's no energy associated with with moving through time?

Anyway, that's a fantastic though. Ill try to learn it better - thank you.

10. Jan 26, 2012

### Staff: Mentor

Only if there is no gravity. If gravity is present, you can't make this assumption.

Yes, this can happen if gravity is present. Take a look at the Pound-Rebka experiment:

http://en.wikipedia.org/wiki/Pound–Rebka_experiment

Not if gravity is present. [Edit: I should also note that interpreting an observed redshift of light emitted by an object as a difference in its "rate of time flow" is, as I noted before, only one interpretation. There are other ways of interpreting what's going on that don't involve "rate of time flow" at all.]

Not quite. See my previous posts. The answer to the question just quoted is that we assume speed of light is constant everywhere and at all times because it appears to work; we can construct theories of physics and make accurate predictions using that assumption. Also, as I noted in an earlier post, the speed of light is not the only physical constant that plays into all of this; the same question could be asked about Newton's gravitational constant, or Planck's constant, for example, and the answer is the same.

Please read my post #5 before reading too much into zhermes' statement. What he said does not imply that "nothing is at rest". His perspective can be a useful one, but it can also invite confusion.

Last edited: Jan 26, 2012
11. Jan 26, 2012

### Staff: Mentor

Sure there is. E=mc²

12. Jan 26, 2012

### jfy4

Indeed, $u_{\alpha}=\langle E,\vec{p} \rangle$, shows that E is your temporal speed. The flow of time is determined by this, and this is relative, clearly in a local coframe, $u_0=m$. The properties of the "passage" of time, have to do with the structure of the manifold in that "direction" though.

13. Jan 26, 2012

### fbs7

Wow, all these are super answers! All of them are very elucidating, and will keep me busy for a lot of time.

Thank you dpa, zhermes, questionpost, PeterDonis, DaleSpam and jfy4. It's amazing how we have here so many very incredible people that offer their time and knowledge to help others understand all sorts of things.

It's also amazing how relativity is so much more elegant and intuitive than quantum mechanics (where everything is odd, incredibly strange and seems to be taken out of the hat or imagined out of Alice in Wonderland).

Thanks again!