B How Does Einstein's Theory Affect the Age of Light?

[Mark Harder]

the static observer.

Be careful here. I don't believe there is such a thing as a static observer, or a static anything. Only when a reference frame is specified can we talk about static and moving things, that is, static or moving with respect to that frame.

 

[Francis Ward]

Gents,
Thanks to all of you for the really kind and thoughtful responses. I have taken them all on board. I am in fact reading a book on Relativity, though it is very 'light' and so restricts to maths to pythagoras, or inversions of it. Hence it leaves more questions than answers.

If any of you have the patience - could you explain how the thought experiment works if the light clock runs parallel with the direction of the train? Sketching it on a flight to Sweden last week I came to the conclusion that the total distance traveled in the 'return' journey of the light would be the same for both the observer on the train and the one on the platform. However the 'ticking of the clock would be assymetric to the observer on the platform and is symmetric to the observer on the train, as it appears the light travels further when heading in the direction of train travel and less when returning. I must be wrong with this!

Secondly, how is the time that it takes for the light from the train to reach the observer on the platform accounted for? For the 'image' of the light clock to reach the observer on the platform, there must be a delay, albeit very small, and that delay is not the same at the start of the journey as it is at the end of it because the train is now further down the platform by distance vt) and therefore there would be an addition time for that light to travel vt, which would be vt/c. The only way this could be eliminated in the thought experiment is if the journey was circular, returning to the same spot it started, immediately adjacent to the platform observer. That then would make the journey subject to acceleration, which messes up the simple maths. (Sorry I had too much time to think on the flight)
Francis

 

[Nugatory]

as it appears the light travels further when heading in the direction of train travel and less when returning. I must be wrong with this!

Define a tick to be a round trip instead of a single leg and this problem goes away. It's surprisingly difficult to assign any sensible and observer-independent meaning to the one-way (as opposed to round-trip) speed of light - search this forum for threads about the one-way speed of light to understand the problem here.

Secondly, how is the time that it takes for the light from the train to reach the observer on the platform accounted for? For the 'image' of the light clock to reach the observer on the platform, there must be a delay, albeit very small, and that delay is not the same at the start of the journey as it is at the end of it because the train is now further down the platform by distance vt) and therefore there would be an addition time for that light to travel vt, which would be vt/c. The only way this could be eliminated in the thought experiment is if the journey was circular, returning to the same spot it started, immediately adjacent to the platform observer. That then would make the journey subject to acceleration, which messes up the simple maths. (Sorry I had too much time to think on the flight)
Francis

Replace the single observer on the platform with multiple observers all lined up along the platform. Each one observes only what happens right under his nose, records that and the time his wristwatch reads when it happens, and then after the fact we can collect all of their notes to construct the history of the light beam as seen from the platform.

 

[Simon Bridge]

...it appears the light travels further when heading in the direction of train travel and less when returning. I must be wrong with this!

I'm please you spotted this yourself - well done - I was aware of the problem of the one-way trip for light when I wrote post #30 and, if you had not spotted it, I would be forced to point it out or risk leaving a big pothole in your path to understanding.

Einstein was aware of this problem and defined his light-clock to use the return journey as well, for exactly this reason. As asserted above, it is really hard to define what you mean by time periods, in a rigorous and consistent way, without doing this.

Einsteins original paper is amazingly readable ... have a look:
https://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[Francis Ward]

Thanks both!

 

[Vitro]

If any of you have the patience - could you explain how the thought experiment works if the light clock runs parallel with the direction of the train?

An additional complication for the parallel light clock is the distance between the mirrors. In SR we have length contraction in the direction of motion. If you don't take it into account the derivation of the time dilation will be a bit off, but you also can't assume it upfront. You have one equation with two unknowns.

Using the perpendicular light clock the distance between the mirrors is the same in both frames so you can derive time dilation independently then use it in the parallel light clock to derive length contraction.

 

[Francis Ward]

Thanks Vitro,
Actually, ignoring the distance contraction, the parallel light clock appears to me to have the same total distance whether observed from the platform or from the train. On the train it is simple, just double the distance measured between the 2 mirrors (2*d). From the platform I think it is d+v*t for the outward journey (t = time for light to travel one way from mirror to mirror, v = speed of the train); then for the return journey it is d-v*t. Hence for the whole journey it is the sum of these 2, which is simply 2*d. Where is my mistake?

 

[Francis Ward]

Replace the single observer on the platform with multiple observers all lined up along the platform. Each one observes only what happens right under his nose, records that and the time his wristwatch reads when it happens, and then after the fact we can collect all of their notes to construct the history of the light beam as seen from the platform.

I see what you are saying, but isn't that in effect the same as the platform observer traveling with the train?

 

[Drakkith]

I see what you are saying, but isn't that in effect the same as the platform observer traveling with the train?

Nope. All the observers are stationary with respect to the platform and will see the train moving by at the same velocity.

 

[Vitro]

From the platform I think it is d+v*t for the outward journey (t = time for light to travel one way from mirror to mirror, v = speed of the train); then for the return journey it is d-v*t. Hence for the whole journey it is the sum of these 2, which is simply 2*d. Where is my mistake?

You don't have the same t in both directions.

 

[Francis Ward]

You don't have the same t in both directions.

Of course! So to the platform observer, the total distance traveled is c*(t1+t2) = 2d+v*(t1-t2). So to the observer on the train, the clock is assymetric?

 

[Francis Ward]

Nope. All the observers are stationary with respect to the platform and will see the train moving by at the same velocity.

Thank you. Of course the difference is the motion of the train, causing the time dilation, whereas the observers on the platform are stationary relative to the platform, and therefore for them time does not dilate.

 

[Vitro]

So to the observer on the train, the clock is assymetric?

No, to the observer on the train the clock is symmetric, the light pulse takes the same time in both directions. The simplified time dilation formula works for the total round trip time but not for the individual legs, you need to apply the full Lorentz transformation for those.

 

[Nugatory]

Thank you. Of course the difference is the motion of the train, causing the time dilation, whereas the observers on the platform are stationary relative to the platform, and therefore for them time does not dilate.

... And their clocks are synchronized, so combining all the reports taken at some given time is a valid procedure for finding what was happening at that time (using their common rest frame to define "at the same time").

 

[robphy]

Early in another current thread, I posted some images and applications of the "longitudinal light clock", where the light rays are spatially parallel to the separation of the light-clock mirrors.https://www.physicsforums.com/threads/twin-paradox-help.884180/#post-5558653
https://www.physicsforums.com/threads/twin-paradox-help.884180/page-2#post-5564060

https://www.geogebra.org/m/HYD7hB9v#

For a fuller development,
look at my recent insights
https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/
https://www.physicsforums.com/insights/relativity-rotated-graph-paper/

 

[Let'sthink]

Let me agree that Light or photon cannot be observer as it perhaps not have a collection of measuring rods and clocks and may be signalling facility. But that muon does not also have. When we talk about muon distance and muon time we take it as what we will measure if we sit on the muon. There is no way to find out the life time of a muon at rest but we take that equal to the life time of muon when it has been retarded enough. Also in all the replies above the distance contraction has not been taken into account. In my opinion they are related phenomena and not independent and the constant parameter the speed of light connects them. In muon's frame muon lives shorter but has a smaller distance to travel to Earth and in our frame muon has a longer time to travel the distance we measure. My last submission or counter question is that can we say time is dilated for photon and space is contracted so that it is everywhere at the same time.

 

[Nugatory]

can we say time is dilated for photon and space is contracted so that it is everywhere at the same time.

No, and you even explained why yourself: "When we talk about muon distance and muon time we take it as what we will measure if we sit on the muon". That doesn't work for a flash of light because we can't ride along with it - we'd be moving at the speed of light and that's not possible.

 

[Let'sthink]

Thank you, Nugatory. But you have not reacted on the dependence of time dilation and length contraction. Also does it mean that photon does not exist in the space-time we exist in. Then where does it exist? Could you also elaborate on the difference between photon which you call flash of light?

 

[Nugatory]

Thank you, Nugatory. But you have not reacted on the dependence of time dilation and length contraction.

It's been touched on in a number of posts earlier in this thread. It's not needed to analyze the crossways-to-motion light clock, but it is needed for the parallel-to-motion case - so we usually work with first one just because it's easier to analyze.

Also does it mean that photon does not exist in the space-time we exist in. Then where does it exist?

It does not mean any such thing. If I, watching something, can say that it is at a given place at a given time, then that something exists in spacetime - that's what spacetime is. Saying that a flash of light is reflected off a mirror here, travels through space, and reaches another mirror over there a moment later is no different than saying that a ball bounces off the floor and reaches my hand a moment later. It's true that nothing can keep up with the flash of light except another flash of light, but that doesn't mean it doesn't exist in spacetime, it means that it is moving through spacetime faster than anything else.

Could you also elaborate on the difference between photon which you call flash of light?

We have an entire thread and many more discussions on this topic over in the quantum physics section; you'll want to find some of those threads.

For now, suffice to say that a photon is not a little object that moves through space at the speed of light and a beam of light is not a stream of photons moving by the way a river is a stream of water molecules moving by. Einstein developed relativity using the classical definition of light as electromagnetic waves propagating at speed $c$, and that still works today. Photons only come into the picture when quantum mechanics is involved.

 

[Let'sthink]

Thanks once again, Nugatory, for your point-wise replies! But you have not committed anything on my assertion that time dilation and length contraction are dependent on each other. Hope I will be able to read and understand the references you are providing. But am I right if I think that all this confusion is there because the marriage between theory of relativity, which is basically classical and quantum mechanics, (which takes birth from the womb of classical mechanics, has some extraordinary non-classical postulates;) is not yet complete and one day we may be able to prove that it is not possible also? Kindly excuse my flowery and may be incorrect diction!

 

[Drakkith]

But you have not committed anything on my assertion that time dilation and length contraction are dependent on each other.

They aren't dependent on each other, they both are the result of the fact that light travels at the same speed for all inertial observers. I wish I could go into detail about this, but I confess I do not know the details!

But am I right if I think that all this confusion is there because the marriage between theory of relativity, which is basically classical and quantum mechanics, (which takes birth from the womb of classical mechanics, has some extraordinary non-classical postulates;) is not yet complete

Nope. Relativity is a classical (non-quantum) theory. Nothing in this thread has anything to do with quantum physics.

 

[Let'sthink]

How do you say that , Drakkith, photon is name given to the particle associated with electromagnetic waves/field hence quantum physics has to be very much in as was also hinted in Nugatory's response?

Also I do not buy that argument of introducing a parameter c (length/time) and assume that that makes the two effects independent. Rather Relativity broke the myth that time is absolute!

 

[Nugatory]

But you have not committed anything on my assertion that time dilation and length contraction are dependent on each other.

It's not so much that they are dependent on one another as that they're both manifestations of the same underlying fact, namely that the speed of light is the same for all inertial observers. But yes, you need both (along with the relativity of simultaneity, which in some ways is more fundamental than the other two) to construct an internally consistent theory with a constant speed of light.

But am I right if I think that all this confusion is there because the marriage between theory of relativity, which is basically classical and quantum mechanics, (which takes birth from the womb of classical mechanics, has some extraordinary non-classical postulates;) is not yet complete

That marriage was successfully consummated about 75 years ago, with the discovery of quantum field theory. Unfortunately, QFT charges a much higher mathematical price of admission than either special relativity or non-relativistic QM; it's not generally considered an undergraduate-level topic.

 

[Drakkith]

How do you say that , Drakkith, photon is name given to the particle associated with electromagnetic waves/field hence quantum physics has to be very much in as was also hinted in Nugatory's response?

While its true that photons are the quanta of the EM field, relativity treats light as a classical wave, not as photons. As I said before, quantum physics has nothing to do with anything in this thread. (In other words, the theory of relativity works just fine whether you treat light as a classical wave or as a quantum object)

 

[Let'sthink]

Thank you very much Nugatory, I cannot ask a question or comment anything in a field where I am not admitted. But I am sure the total story of space time mass and energy is not yet completely written or written off!

 

[Nugatory]

I am (almost) completely serious when I say that the best thing you can do is to try to forget that you ever heard the word "photon" until after you have learned special relativity and are starting in on quantum mechanics. Einstein figured out special relativity without photons, and you can too.

But if you aren't going to take this advice... Take a look at the papers referenced in the first two posts of this thread: https://www.physicsforums.com/threads/what-is-a-photon.879128/

 

[Let'sthink]

I welcome your zeal of replying, Nugatory! When I accept your first advice, the first thread of this discussion loses its place.
I shall follow your second advice and then come back to you with my confusions!

 

[Let'sthink]

I have read one of the articles you, Nugatory, referred to and and am able to appreciate that photon is quite different from any other particle. I am in the superposition state of clarified and confused ones and will take quite some time for wording a clear question. Thank you for all your answers! But I do not understand what is the great idea in letting the ug student treat photon as he wants and also answer his questions as per his understanding in a round about manner and ultimately let him know at pg level that photon is no particle at all. But that is just observation and not a question!

 

[Drakkith]

But I do not understand what is the great idea in letting the ug student treat photon as he wants and also answer his questions as per his understanding in a round about manner and ultimately let him know at pg level that photon is no particle at all. But that is just observation and not a question!

In a perfect world every student would be taught things in the clearest manner, the best order, by the best teachers, and with the best source material. Unfortunately perfection is in a superposition of "doesn't compute" and "pipe dream".

 

[Let'sthink]

Thank you Drakkith for your reply and for using similar diction!

 

[Herman Trivilino]

But I do not understand what is the great idea in letting the ug student treat photon as he wants and also answer his questions as per his understanding in a round about manner and ultimately let him know at pg level that photon is no particle at all. But that is just observation and not a question!

The relevant issue here is the meaning of the word "particle". In the classical particle model, it's simply something so small that its size can be ignored when compared to all other relevant distances involved. So a traffic engineer can model a car as a particle, but an auto mechanic cannot. When calculating a home run distance a baseball can be modeled as a particle, but a major league pitcher cannot use that model when executing his pitches.

In quantum mechanics the word "particle" means an entirely different thing. A photon is just such a particle, as is an electron. If you've ever taken a chemistry class you run into the seemingly senseless warnings about not thinking of an atomic electron as you would think of a planet orbiting its sun. The planet can in that case be modeled as a classical particle, but the electron cannot.

If you read an article written by a physicist like N. David Mermin you see that he speaks of photons bouncing off mirrors and traveling the length of a train car as he derives a formula for the relativistic addition of velocities. But he is a physicist, so he can get away with it! He knows the difference between a classical particle and a quantum particle. For someone who doesn't that practice can lead to all sorts of misconceptions.

 

[Let'sthink]

When I was a ug student I used to think em waves or Planck's photon as pure energy. Classically whenever we talk of energy it is of the particles only whether with classical particles or classical waves. For waves also because in the classical domain energy of the wave is ultimately the energy of the particles of the medium. In case of light and after advent of relativity we find there is no necessity of a medium. But em waves have energy. So these waves must be particles in the guise of waves. Also these so called particles are strange they cannot be retarded and hence can never come to rest and we have to presume their rest mass as zero. For other particles the contribution to energy comes both from mass and motion but in case of photons it is all motion. The discussion on this thread has broadened my idea of photon and now I think I can think it as a purely QFT object whose energy, direction and plorization can only be conceived and position is just indeterminate or un-conceivable naturally it follows it cannot have a conceivable velocity at a given time.

 

[GeorgeDishman]

we have to presume their rest mass as zero.

"Presume"? Try following the references here.

 

[Let'sthink]

Thank you George Dishman, I went through some references suggested by you some par in detail and others not in so much detail. It was a very fruitful and useful exercise for me.

 

[.Scott]

Light, we are told, cannot be influenced by the speed of it's source (we cannot add to the speed of light by putting the torch on the front of the train). Hence it should not be influenced either by the sideways motion of the train.

To be clear, the light will be affected - but not it's speed. Suppose we have a high speed train passing a stationary train on a side track. And we have two stationary photon detectors positioned in front of the trains - each measuring photons from one train. We look at the light from each just as it passes. Photons from each train arrive at the detectors at the same time, but the detector watching the moving train will see heavier, bluer photons.