From this link http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html I don't understand the following..."Does time stop for a photon?. . . It is really not possible to make sense of such questions and any attempt to do so is bound to lead to paradoxes. There are no inertial reference frames in which the photon is at rest so it is hopeless to try to imagine what it would be like in one." In particular this statement "There are no inertial reference frames in which the photon is at rest". Can anyone explain that to me?
I believe the answer to your question is that light is defined as photons, so photons are, always, traveling the the speed of light ([itex]c[/itex]). This is why photons are said to have [itex]0[/itex] mass.
One of the postulates of Special Relativity is that light moves at the same speed, c, in vacuum, in all inertial reference frames. This postulate immediately says that there is no reference frame in which the light is NOT moving at c, and "at rest" is definitely not moving at c.
In SR and GR there is a well-defined mathematical procedure to calculate proper time for moving objects along trajectoreis through spacetime (as measured by a co-moving clock). Applying this procedure to a light-like trajectory (along which photons move) the result is always zero, i.e. proper time for photons vanishes. In that sense photons are 'timeless'.
Although one could possibly device some frame of reference in which a photon is at rest, that frame is not a Lorentz inertial system of spacetime coordinates (called "inertial reference frame" for short). An inertial frame is one in which the principle of relativity holds - relative to an inertial frame, moving faster but at constant speed, the laws of physics take the "same form" as when one is not moving. This is due to a symmetry in the laws of physics called "Poincare invariance".
I do not like the argument that because we cannot make a frame of reference the question is nonsensical. Frames of reference have no physical significance as they do not exist in nature. As tom.stoer pointed out one does not need a frame of reference to demonstrate that the total elapsed time for the path of a photon between two events is zero.
I don't agree fully with the first statement since with special relativity, inertial frames of reference are privileged because of Poincare symmetry, which is absolute. I do agree with the second statement as providing a good meaning to "time stops for a photon".
I think a better way to put this might be that Lorentz boosts take timelike lines into *other* timelike lines, and spacelike lines into *other* spacelike lines, but they take null lines into themselves. So a "frame" constructed using null axes (two null and two spacelike axes for a standard set of null coordinates) will behave fundamentally differently under Lorentz boosts than an ordinary inertial frame constructed using one timelike and three spacelike axes. Since the "frame of a photon", in so far as one can construct one, would have to be constructed using null axes, it is a fundamentally different type of object than an ordinary inertial frame. That's why saying that "time stops for a photon" is not really a good way, IMO, to convey the difference between null objects and timelike objects, since it invites the inference that a "photon frame" is just like an ordinary inertial frame, only "moving at c". Saying that the "length" of a photon's worldline is always zero between any two events on it is better, but calling that length "elapsed time" is still dodgy, IMO, because it again invites the erroneous inference. I would say that the concept of "proper time" or "elapsed time for the object" simply doesn't apply to objects that move on null worldlines. If amplification is needed, see my first paragraph above.
PeterDonis, I, of course, have no technical disagreement with what you say, only a poetic one - we shouldn't have to give up our favourite kludges, I think;)
But Peter, don't you think a frame is just a mathematical object? For instance asking "What would the rate of a clock be if we discount the light travel time of a given Doppler shift of an object which is in relative motion to us" is interesting for professors to ask students in a test but apart from that what is the scientific value of those questions, frames or planes of simultaneity do not really exist, or do you disagree?
The planes of simultaneity certainly exist, at least to the same extent that the spacetime as a whole exists. If you adopt the viewpoint that spacetime, as a whole, is a 4-dimensional geometric object, then obviously you can "cut" particular spacelike 3-surfaces out of that 4-dimensional object that are orthogonal to particular timelike worldlines at particular events. The worldlines and the 3-surfaces themselves are coordinate-independent geometric objects, and they are as "real" as the overall geometric object that they are parts of. Labeling the coordinate-independent geometric objects with particular coordinates is arbitrary and doesn't affect the physics. So I would agree that "frames", in the sense of particular coordinate labelings, "do not really exist". But the things that the coordinates label do (at least in the same sense that spacetime itself does). If the question you quoted in the above is equivalent to the question "How much proper time elapses along this timelike worldline between events A and B?", then that question seems to me to have a direct physical meaning, since the proper time in question is directly measurable by a clock traveling along the given worldline. Questions about "proper length" and more generally about surfaces of simultaneity are more complicated to correlate to direct physical measurements, since you first have to talk about clock synchronization and the relativity of simultaneity. But it can still be done. Whether or not it is *useful* to do it depends on the problem. Over small distances it seems to me to be useful; for example, it's hard to talk about local inertial frames and what happens in them without talking about proper length measurements within those frames. But it can be problematic when people try to extend it out over large distances, such as the recent threads about what is happening "now" on Mars or in the Andromeda galaxy. In those cases I agree that trying to assign some sort of "real meaning" to a particular surface of simultaneity causes confusion and doesn't help with understanding the physics.
No of course it is not. But even in this case another observer can calculate the total time on the other clock by observing the Doppler shift between the events. No such planes of simultaneity are neccesary. I think that if we stick to relativistic Doppler shift, proper distance and proper velocity (celerity) special relativity becomes a lot simpler.
Huh? Either I'm misunderstanding you or you misunderstood what I said. I said that the proper time elapsed along a given timelike worldline is directly measurable by a clock moving along that worldline. Are you disputing that? Or are you just saying that wasn't the same question you were describing with "What would the rate of a clock be if we discount the light travel time of a given Doppler shift of an object which is in relative motion to us"? If the latter, I'm not sure I understand what question you were describing.
Every aspect of any model is a mathematical object. If you claim you want to eliminate them and only with what there is in nature, you would have empirical evidence and exactly zero theories to explain anything. "The sun is here at this time, the sun is here at this later time and here at this later time. We do not seek to explain why." So, your attempt to dismiss mathematical objects would stop inquisitiveness in its tracks.
"Of course it is not equivalent." That is what I meant. There is a difference to me between how allegedly two clocks are running with a different rate when they are in relative motion and two clocks going between two events with a different path in spacetime. The first can never be proven while the second obviously can.
SR predicts that if you try to experimentally set-up a global inertial frame, you can succeed. GR predicts that you will fail. So the existence of global inertial frames is a prediction of SR (which has been falsified by GR). So inertial frames are very important in SR.
I think I do. It is quite a simple concept. You take for granted most mathematical constructs in science. This one rubs you the wrong way so you want to weaken it by claiming it doesn't exist in nature. Well, neither does relativity or spatial curvature or geodesics. I would be interested to see you have any further meaningful discussion in this thread (let alone on PF) without resorting to some aspect of a model that does not exist in nature.