B Do photons travel instantaneously?

[Stevexyz]

No, this is not correct. The Lorentz transformation is simply not valid mathematically for $v = c$. And, as has already been pointed out, there is no valid "limit" in which we can let $v \rightarrow c$ in the Lorentz transformation formula and get a sensible result. Lorentz transformations simply act in fundamentally different ways on timelike vectors vs. null vectors. So the correct statement is that there is no valid "frame" at all for a photon, and the concept of "distance traveled" makes no sense along a null worldline any more than the concept of "elapsed time" does.

Does this mean the special relativity can't be used to imply or give insights about the "nature of time" when traveling at the speed of light? Thanks

 

[Stevexyz]

Because for things that traveling at the speed of light the concept of time is meaningless. How many times and in how many different ways are you going to want us to keep answering the same question? As we have told you over and over, the answer isn't going to change.

Is "travelling at the speed of light the concept of time is meaningless" a consequence of special relativity or the nature of time or something deeper? Thanks for your replies.

 

[weirdoguy]

So we can't expect special relativity to provide answers/insights about photons and time (and other particles that travel at the speed of light)?

It does provide answers and you were given them multiple times. You are not reading what others are saying.

 

[vanhees71]

No, this is not correct. The Lorentz transformation is simply not valid mathematically for $v = c$. And, as has already been pointed out, there is no valid "limit" in which we can let $v \rightarrow c$ in the Lorentz transformation formula and get a sensible result. Lorentz transformations simply act in fundamentally different ways on timelike vectors vs. null vectors. So the correct statement is that there is no valid "frame" at all for a photon, and the concept of "distance traveled" makes no sense along a null worldline any more than the concept of "elapsed time" does.

Lorentz transformations act on the components of all kinds of four-vectors in the same way, no matter whether they are space-, time-, or lightlike.

Of course the relative speed between two intertial frames (i.e., the velocity of the origin of one of the frames measured by an observer at rest within the other frame) must be $|\vec{v}|<c$. The momentum of a photon is lightlike, and this is a frame-independent qualtity, $p \cdot p=0$. It says that the photon's phase velocity is $c$. There's no restframe of a photon, i.e., there's no inertial reference frame, where the photon's three-momentum is (momentarily) at rest. Also photons must not be visualized as billard-ball like particles. They are never localized since the don't even have a position observable to begin with. It's more appropriate to think in terms of electromagnetic waves than in terms of particles.

BTW that's how Einstein, as a 16 year-old, started to be puzzled about the problem of the non-invariance of electromagnetic phenomena (i.e. Maxwell's equations) under Galilei transformations in asking how an electromagnetic wave looks for somebody running with $c$ in direction of the light wave.

 

[vanhees71]

Is "travelling at the speed of light the concept of time is meaningless" a consequence of special relativity or the nature of time or something deeper? Thanks for your replies.

The point is that no massive object can travel with a speed greater than light with respect to any (inertial) frame. The worldline of a massive object is necessarily always time-like.

The "deeper" consequence of special relativity is that the Newtonian spacetime model is only approximately describing the phenomena (in the limit of relative speeds between objects which are much smaller compared to the speed of light). It becomes invalid when the situation is such that the approximation of Newtonian spacetime descriptions is unjustified.

 

[Stevexyz]

It does provide answers and you were given them multiple times. You are not reading what others are saying.

Perhaps you could summarise them for me and others would have kindly posted here.

 

[Ibix]

Perhaps you could summarise them for me and others would have kindly posted here.

You cannot define time for a photon. Thus asking about its experience of time is meaningless.

 

[anuttarasammyak]

Some photons are traveling since the birth of the Universe and keep going forever. Some circularly polarized photons are created at light bulb, go 1m and annihilate in my eyes. @Stevexyz if photons were able to have conscience, would they recognize their life time forever/a period/zero period ? I am sorry for a silly story.

 

[Stevexyz]

You cannot define time for a photon. Thus asking about its experience of time is meaningless.

Is it therefore pointless trying to use special relativity to understand the "nature of time" for photons for other massless particles?

 

[weirdoguy]

Is it therefore pointless trying to use special relativity to understand the "nature of time" for photons

It's special relativity that tells us that you cannot define time for photons. This whole discussion is getting pointless, you're not trying to understand what people are saying.

 

[fresh_42]

The question, although inconsistent in itself, has been answered as good as possible ...

You cannot define time for a photon. Thus asking about its experience of time is meaningless.

... and we're running in circles.

Thanks for participating.

 

[Nugatory]

Is it therefore pointless trying to use special relativity to understand the "nature of time" for photons for other massless particles?

Not pointless - Special Relativity is the best starting point. But you will have to learn what SR says and to do that you’ll want to put some effort into a working through a good textbook; my favorite is “Spacetime Physics” by Taylor and Wheeler.