Time & Speed of Photon: Questions Answered

[ShamelessGit]

I know this thread is similar to another one that was posted recently (I really enjoyed reading it), but I think I have some other questions which aren't entirely redundant.

BTW, I'm not looking for really mathematically rigorous explanations, because I probably wouldn't understand them. About the most complicated thing I can do yet is use the special relativity transformations (special relativity version of gallilean transformations), and I don't understand all of it. If an explanation requires a lot of math, I will just take the most reasonable explanation on faith.

1) How fast does a photon travel compared to another photon?

2) If all photons travel at the speed C compared to mass particles, do all mass particles travel at C relative to a photon?

3) If #2 is correct, is it conceivable that photons travel at different speeds relative to each other in the same way that mass particles can move at variable speeds with respect to other mass particles, but that all mass particles will travel at C relative to massless particles and vise-versa?

4) If it is true that a photon experiences no time, as I have been told in person and I have seen in other posts, then how is it that maxwell's equations can possibly be satisfied? I have seen the derivation for the speed of light from maxwell's equations, and it requires constantly changing E and B fields, and I don't see how this can happen without time. Wouldn't this seem to say that light doesn't know that it exists? (because if there is no time at a speed of C, then light exists in a frame where maxwell's equations for light can't be satisfied) or is this one of those things where you have 0/0 and the limit approaches something that makes sense?

 

[PeterDonis]

1) How fast does a photon travel compared to another photon?

All photons travel at the same speed, the speed of light. Photons can differ in energy and momentum, but not speed.

2) If all photons travel at the speed C compared to mass particles, do all mass particles travel at C relative to a photon?

The concept of "speed relative to a photon" doesn't really make sense, because the concept of "the reference frame of a photon" doesn't make sense. (This was brought up in a recent thread which I think is the one your OP referred to, though I may be wrong--see below.)

3) If #2 is correct, is it conceivable that photons travel at different speeds relative to each other in the same way that mass particles can move at variable speeds with respect to other mass particles, but that all mass particles will travel at C relative to massless particles and vise-versa?

No. See above.

4) If it is true that a photon experiences no time, as I have been told in person and I have seen in other posts

If you've seen this in other posts, those other posts are incorrect. If you look at posts by me and other Science Advisors in this thread, they should make it clear that the statement "a photon experiences no time" is not really correct; it is more correct to say that the concept of "experiencing time" doesn't make sense for a photon. That thread I just linked to, btw, is the one I thought you were referring to in your OP, as I mentioned above, but given what I've just said, I'm no longer sure you have really read that thread.

how is it that maxwell's equations can possibly be satisfied? I have seen the derivation for the speed of light from maxwell's equations, and it requires constantly changing E and B fields, and I don't see how this can happen without time.

The derivation you refer to is done in a particular inertial reference frame, in which the concept of "time" makes sense. It does not require that the concept of "time" makes sense for a photon.

Wouldn't this seem to say that light doesn't know that it exists? (because if there is no time at a speed of C, then light exists in a frame where maxwell's equations for light can't be satisfied)

I'm not sure what you're getting at here, but I don't think it's a good way of looking at it.

is this one of those things where you have 0/0 and the limit approaches something that makes sense?

Not really, no.

 

[Nugatory]

1) How fast does a photon travel compared to another photon?

An observer watching two photons approaching from opposite directions will see them both moving towards him at c, and therefore the distance between the two photons will be shrinking by two light-seconds per second. You can get this result from the standard relativistic addition formula ##w=\frac{u+v}{\sqrt{1+\frac{uv}{c^2}}}## by setting ##u## and ##v## both to c.

2) If all photons travel at the speed C compared to mass particles, do all mass particles travel at C relative to a photon?

That's not quite right. All photons travel at c in all frames, and therefore travel at c in the particular frame in which a massive particle is at rest. However, another observer moving relative to that massive particle will not see the speed of the massive particle relative to the photon to be c. Again, the velocity addition formula works here.

3) If #2 is correct, is it conceivable that photons travel at different speeds relative to each other in the same way that mass particles can move at variable speeds with respect to other mass particles, but that all mass particles will travel at C relative to massless particles and vice-versa?

No, because #2 is not quite right. You can't really can't talk about anything "from a photon's point of view", and so when you're dealing with two photons you have to bring in some observer and talk about what he observes.

4) If it is true that a photon experiences no time, as I have been told in person and I have seen in other posts, then how is it that maxwell's equations can possibly be satisfied? I have seen the derivation for the speed of light from maxwell's equations, and it requires constantly changing E and B fields, and I don't see how this can happen without time. Wouldn't this seem to say that light doesn't know that it exists? (because if there is no time at a speed of C, then light exists in a frame where maxwell's equations for light can't be satisfied) or is this one of those things where you have 0/0 and the limit approaches something that makes sense?

This is one of about 93 bazillion good reasons why you should not say "A photon experiences no time"...

 

[PeterDonis]

This is one of about 93 bazillion good reasons why you should not say "A photon experiences no time"...

Technical point: what exactly is the definition of a "bazillion"?

 

[Nugatory]

Technical point: what exactly is the definition of a "bazillion"?

It is is the maximum number of items I can count before I lose patience, plus one.

 

[PeterDonis]

It is is the maximum number of items I can count before I lose patience, plus one.

Wow, you have a not more patience at counting things than I have...

 

[ShamelessGit]

So what I've seen so far from peterdonis is that light does not experience proper time, and they don't have a reference frame. So does that basically mean that my questions don't make sense?

The issue I was having was that even if you accept that a special object A (light) always travels at a certain speed C relative to object B, it seems absurd to say that the speed of A relative to B is not the same as speed B relative to A. Another problem I was having was that if from my perspective two photons are moving in the same direction one after the other, then it seemed absurd to me that that they might both think that the other was moving away (or towards) at the speed of light, because obviously their distance apart stays constant. But I suppose if there is no proper time or reference frame for a photon, then these questions don't make sense, and I will just have to accept that I cannot possibly imagine a photon.

So if a photon has no proper time, then does that mean that it thinks that everything that happens to it in its life happens instantaneously? Because obviously photons sometimes interact with matter, which means it changes from one state to another. Again, I can't imagine something going from one state to another without having time.

 

[PeterDonis]

So what I've seen so far from peterdonis is that light does not experience proper time

Not quite; it would be better to say that the concept of proper time does not apply to light.

and they don't have a reference frame.

Yes.

So does that basically mean that my questions don't make sense?

Pretty much, because the concept of "relative speed" requires a reference frame, and a photon doesn't have one. (Same for the concepts of "distance", "proper time", etc.)

I will just have to accept that I cannot possibly imagine a photon.

Don't give up too easily. You can't imagine it the way you imagine an ordinary object like a rock, but there are other ways of imagining it.

So if a photon has no proper time, then does that mean that it thinks that everything that happens to it in its life happens instantaneously?

No. It means the concept of "time" doesn't make sense for a photon. But the concept of "happening" can still make sense, even without proper time; see below.

Because obviously photons sometimes interact with matter, which means it changes from one state to another.

Yes, and that brings up an important point. Even though the concept of time doesn't make sense for a photon, a photon's worldline still has distinct events on it. You can't label the events with distinct proper times, but there are other ways of labeling them that work perfectly well (such a labeling is called an "affine parameter"). Any state change of a photon due to an interaction will happen at some particular event, which can be labeled with some particular affine parameter, so the notion of things "happening" to a photon still makes sense even though the notion of proper time of a photon does not.