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.
fbs7 said:
Question is: do we know enough about how time flows (in a frame of reference at rest)
As dpa pointed out, "at rest" is relative.
fbs7 said:
to assume that it has always flowed at the same rate, ever since the first plank time after the big bang?
Also, as dpa pointed out, the concept of "rate of time flow" as it stands isn't really well-defined. For example, you say:
fbs7 said:
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?
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.
fbs7 said:
do we know if the flow of time at rest is related to the speed of light?
This version of the question, IMO, requires even more care in answering. For example:
zhermes said:
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.
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:
zhermes said:
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.
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.
questionpost said:
an object going at the speed of light would not be effected by the flow of time.
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.
questionpost said:
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.
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":
https://www.physicsforums.com/showthread.php?t=511170
