How Old is Light? - Exploring Einstein's Theory

[Francis Ward]

Is that a problem for you?

No. On the contrary, it is probably the most magnificent concept I have heard. The imagery is awesome. Do you have thoughts on how such an event would be initiated?

 

[Drakkith]

No. On the contrary, it is probably the most magnificent concept I have heard. The imagery is awesome. Do you have thoughts on how such an event would be initiated?

Please stick to the main topic. If you have questions or comments regarding the BBT, then please make a new thread in the cosmology section.

 

[GeorgeDishman]

Well one could say an answer to the original question is that the oldest 'light' is the cosmic microwave background ;-)

 

[Simon Bridge]

Hi Simon,
That is precisely what I am trying to understand, and thank you for taking the time to depict it so well. I come from an engineering background and as I said I am new to pondering the whole relativity stuff. So my views are initially constrained by a very logical approach eg if you add speeds in a single direction there should be no limit how fast you can go.

... that would be common sense logic rather than logic based on very careful observation.
Common sense is what tells you the Earth is flat ... though, to be fair, common sense is pretty good for day-to-day experience.

So, pondering the many comments my initial post had generated, leaves many questions. For instance, that raised by the question of relative velocities, such as, to a person on the ground, observing an aircraft passing over head, they see it moving at, say, 600 km/h. However to the person on the aircraft, observing the person on the ground they see precisely the same of the person, that he is moving at 600 km/h. Simple and obvious stuff

... as an engineer you would know that those speeds are estimates. They should be quoted with their uncertainty.
So ... off those figures, the speed would be $600\pm0.5$kmph. This is important to notice since, for such slow speeds, the difference between common-sense and relativity is usually much smaller than the uncertainty.
The next thing I want you to notice is that you have described two inertial reference frames (apart from gravity being in both of them) ... so they are equivalent from the point of view of the physics you can do in them. The only way to distinguish them is to notice that the flying aircraft is making a lot of noise and is using up fuel ... but I'm sure you can think of a way to get rid of such clues.

Now, if we replace the aircraft with a rotating podium on which an observer, A, stands, and that podium is rotating at 6000 rpm. Then place another observer, B, a distance of 478 km from the podium. If my maths is right to A they will simply see B rotating at 100 hz, but to B they will see A flash past them at marginally higher than c, 100 times per second.

You no longer have the kind of equivalence you had with the aircraft example since A is in a non-inertial frame.
Rotating frames are accelerating.

The rotating observer thing is handled in general relativity.
http://abacus.bates.edu/~msemon/SemonMalinWortel.pdf
(Slideshow discussion... http://luth.obspm.fr/~luthier/gourgoulhon/fr/present_rec/imcce_syrte10.pdf )
... however, it is probably best to get used to special relativity first, otherwise you are trying to make links to things that are harder to understand from a fuzzy understanding of something else. The tldr answer is that the common-sense, euclidean, geometry you are used to becomes non-euclidean for rotating observers.

Now replace B with a light source emitting a straight source of light, which does not diverge. Build a circular wall at 478 km radius from B, on which the spot of light can project. To all observers in the frame of reference of the wall, that spot of light would travel at marginally higher than c (again assuming my maths is correct).

... there is nothing in relativity to contradict this, and the effect has been observed in Nature.
ie. http://www.mtu.edu/news/stories/201...may-help-illuminate-astronomical-secrets.html

Another example would be two spacecraft flying in opposite directions away from a space station, each at 0.6c wrt the station. Clearly an observer in the station will see the distance between the spacecraft getting bigger at the rate 1.2c.
Distant galaxies can also exceed c - due to cosmological expansion.

All observers measure the same speed for light in a vacuum ... this does not mean that nothing, no effect of any kind at all, can travel FTL, just that no message can be sent FTL.

 

[GeorgeDishman]

Now replace B with a light source emitting a straight source of light, which does not diverge. Build a circular wall at 478 km radius from B, on which the spot of light can project. To all observers in the frame of reference of the wall, that spot of light would travel at marginally higher than c (again assuming my maths is correct).

Replace B with a machine gun. Does any individual bullet move along the wall at greater than c? Or does each bullet move from the gun to the wall at the usual muzzle velocity, well below the speed of light?

You say you come from an engineering background, I'm in that discipline too, so make your light source an LED connected to a pulse generator. What happens to each flash of light emitted?

The situation you are describing is a variant of a paradox called the "Superluminal Scissors".

 

[Francis Ward]

Replace B with a machine gun. Does any individual bullet move along the wall at greater than c? Or does each bullet move from the gun to the wall at the usual muzzle velocity, well below the speed of light?

You say you're an engineer, me too, so make your light source an LED connected to a pulse generator. What happens to each flash of light emitted?

The situation you are describing is a variant of a paradox called the "Superluminal Scissors".

HI George,
Yes, that is exactly how I had been viewing it. I shall look up the Superluminal Scissors - thank you
One question that have not been able to clarify though is the impact of the sideways motion in that pulse of light. In this case, as Simon rightly put it, better to stay with the simpler non-rotational motion. So, going back to the light emitter traveling at 90 degrees to the direction of the light. With the 'physical' things, such as the bullets or the ball being fired/thrown, I can see clearly that the velocity of the train 'adds' to the velocity of the ball/bullet and gives a resultant. Can we apply the same principle to the pulse of light? As Brian Cox put in his book, does the light get a 'helping hand' from the motion of the train? My understanding, based on the fact that if you switch the direction of the light emitter to one that is parallel to the direction of the light, you cannot 'add' to the speed of the light, is that is should not. This was refuted by an earlier responder, saying that is was 'a demonstrably false assertion', and Einsteins light clock thought experiment seems to support this, inasmuch as the light travels from mirror centre to mirror centre, exactly as it would if the train were stationary. (Which of course, to the observer on the train, it might well be)

 

[Francis Ward]

... that would be common sense logic rather than logic based on very careful observation.
Common sense is what tells you the Earth is flat ... though, to be fair, common sense is pretty good for day-to-day experience.

... as an engineer you would know that those speeds are estimates. They should be quoted with their uncertainty.
So ... off those figures, the speed would be $600\pm0.5$kmph. This is important to notice since, for such slow speeds, the difference between common-sense and relativity is usually much smaller than the uncertainty.
The next thing I want you to notice is that you have described two inertial reference frames (apart from gravity being in both of them) ... so they are equivalent from the point of view of the physics you can do in them. The only way to distinguish them is to notice that the flying aircraft is making a lot of noise and is using up fuel ... but I'm sure you can think of a way to get rid of such clues.You no longer have the kind of equivalence you had with the aircraft example since A is in a non-inertial frame.
Rotating frames are accelerating.

The rotating observer thing is handled in general relativity.
http://abacus.bates.edu/~msemon/SemonMalinWortel.pdf
(Slideshow discussion... http://luth.obspm.fr/~luthier/gourgoulhon/fr/present_rec/imcce_syrte10.pdf )
... however, it is probably best to get used to special relativity first, otherwise you are trying to make links to things that are harder to understand from a fuzzy understanding of something else. The tldr answer is that the common-sense, euclidean, geometry you are used to becomes non-euclidean for rotating observers.

... there is nothing in relativity to contradict this, and the effect has been observed in Nature.
ie. http://www.mtu.edu/news/stories/201...may-help-illuminate-astronomical-secrets.html

Another example would be two spacecraft flying in opposite directions away from a space station, each at 0.6c wrt the station. Clearly an observer in the station will see the distance between the spacecraft getting bigger at the rate 1.2c.
Distant galaxies can also exceed c - due to cosmological expansion.

All observers measure the same speed for light in a vacuum ... this does not mean that nothing, no effect of any kind at all, can travel FTL, just that no message can be sent FTL.

Hi Simon,
Once again thank you for the time and effort you put into your responses. It is highly appreciated.
Can you explain the inertial/non-inertial frame? Do you refer to moving items with mass, and therefore inertia vs those without mass and therefore zero inertia?
Regards
Francis

 

[Simon Bridge]

Hi Simon,
Once again thank you for the time and effort you put into your responses. It is highly appreciated.
Can you explain the inertial/non-inertial frame?

Discussion: https://www.physicsforums.com/threads/what-is-an-inertial-frame-of-reference.183267/
Wikipedia actually takes some care: https://en.wikipedia.org/wiki/Inertial_frame_of_reference
tldr... it's like this: you are in a well equipped lab in a closed box and you are tasked to conduct an experiment to discover the state of motion of the box.
If there is no experiment that will do this, the box is in an inertial frame.

For instance, you can tell if the box is accelerating by observing the slope in the level of water in a container in different parts of the box... thus, an accelerating box is not in an inertial frame. Uniform motion, however, cannot be detected - thus: an inertial frame. For rotating observer: imagine the box is around the observer, rotating with her. Is there any experiment done inside the box that will determine that the box is rotating?

This is the idea in a nutshell.

 

[Drakkith]

So, going back to the light emitter traveling at 90 degrees to the direction of the light. With the 'physical' things, such as the bullets or the ball being fired/thrown, I can see clearly that the velocity of the train 'adds' to the velocity of the ball/bullet and gives a resultant. Can we apply the same principle to the pulse of light? As Brian Cox put in his book, does the light get a 'helping hand' from the motion of the train? My understanding, based on the fact that if you switch the direction of the light emitter to one that is parallel to the direction of the light, you cannot 'add' to the speed of the light, is that is should not. This was refuted by an earlier responder, saying that is was 'a demonstrably false assertion', and Einsteins light clock thought experiment seems to support this, inasmuch as the light travels from mirror centre to mirror centre, exactly as it would if the train were stationary. (Which of course, to the observer on the train, it might well be)

That's right. From the emitter's frame, the light pulse moves directly out from it, with no motion to either side or forward or backwards. From the frame of an observer in which the emitter is moving, the light pulse will move diagonally in such a way that the sideways component of its velocity is the same as the emitter's velocity. One thing to note: the emitter cannot travel at 90 degrees to the direction of the light. It either has no motion (emitter's frame) or its motion matches the sideways motion of the light, in which the angle between the two is less than 90 degrees.

Honestly, if you're set on learning special relativity, you should grab one of the many books dedicated to teaching it. Sitting down and working through a well-written book that contains diagrams, equations, thought experiments, and real-world experiments will beat trying to make your way through dozens of online references and forum posts/threads hands down. Not only that, but once you learn a little bit of the fundamentals, you can very easily take what you've learned and ask more specific questions here on the forums.

I'm sure someone here can recommend a good book on SR if one hasn't already been recommended in the thread.

 

[GeorgeDishman]

Can we apply the same principle to the pulse of light? As Brian Cox put in his book, does the light get a 'helping hand' from the motion of the train? My understanding, based on the fact that if you switch the direction of the light emitter to one that is parallel to the direction of the light, you cannot 'add' to the speed of the light, is that is should not.

Yes, you can apply the same principle but you have to use the relativistic maths, not conventional version that simply adds the velocities which only works for low speeds. For light parallel to the direction of motion, the combination of c and v gives c and still in the same direction. For light at any other angle, the angle changes but the speed remains c. That change of angle essentially throws the light from a moving source forward, it is sometimes called the "relativistic headlight effect" or "relativistic beaming" or aberration. A real world example occurs on the jets from some super-massive black holes, see the comparison of M87 and 3C31 in the following article. The jet moving away from us is so dim we cannot see it for this reason.

https://en.wikipedia.org/wiki/Relativistic_beaming

 

[Mister T]

Hi Simon,
So my views are initially constrained by a very logical approach eg if you add speeds in a single direction there should be no limit how fast you can go.

You can add speeds in a single direction, and there is no limit on the sum that you get when you do that.

But there are other ways besides addition that one can combine numbers. The logical question to ask is which is the right way to combine them when trying to figure out how fast something is moving. If B moves with respect to A at speed $v_{AB}$ and C moves with respect to B with $v_{BC}$, then what is the speed $v_{AC}$ that C moves with respect to A?

One possible way to figure that out is by adding $v_{AB}$ to $v_{BC}$. When you do that you of course get a speed, but it's not equal to $v_{AC}$.

Note that common sense is just something that appears to be true because it has been demonstrated to be true, and therefore appears to be obvious.

But in fact this way of combining speeds to get $v_{AC}$ works no better than it does when combining slopes. If you're on a roof that has a slope of 5/12, meaning it rises 5 inches for every 12 inches of run, and you place a rod on that roof so that it is tilted at a slope of 5/12 relative to the roof surface, then the rod will not have a slope of 10/12 relative to the horizontal. Instead, you would add the angles, which are the inverse tangents of the slopes. (Note though, that all you ever deal with is very small slopes, you find that adding the slopes works just as well as adding the angles. You don't notice that one way works better than the other until you have some experience with larger slopes. The same is true of slow speeds!)

Likewise, you would add the inverse hyperbolic tangents of the speeds. That's the right way to combine them.

 

[Mister T]

HI George,
My understanding, based on the fact that if you switch the direction of the light emitter to one that is parallel to the direction of the light, you cannot 'add' to the speed of the light, is that is should not. This was refuted by an earlier responder, saying that is was 'a demonstrably false assertion', and Einsteins light clock thought experiment seems to support this, inasmuch as the light travels from mirror centre to mirror centre, exactly as it would if the train were stationary. (Which of course, to the observer on the train, it might well be)

You do not add the speeds, you combine them in the way I described in my previous post. Likewise, when the direction of object's motion (light beam or ball) is tilted relative to the horizontal direction of the train's motion, you combine the horizontal components of the velocities in the same way.

 

[Battlemage!]

You can add speeds in a single direction, and there is no limit on the sum that you get when you do that.

But there are other ways besides addition that one can combine numbers. The logical question to ask is which is the right way to combine them when trying to figure out how fast something is moving. If B moves with respect to A at speed $v_{AB}$ and C moves with respect to B with $v_{BC}$, then what is the speed $v_{AC}$ that C moves with respect to A?

One possible way to figure that out is by adding $v_{AB}$ to $v_{BC}$. When you do that you of course get a speed, but it's not equal to $v_{AC}$.

Note that common sense is just something that appears to be true because it has been demonstrated to be true, and therefore appears to be obvious.

But in fact this way of combining speeds to get $v_{AC}$ works no better than it does when combining slopes. If you're on a roof that has a slope of 5/12, meaning it rises 5 inches for every 12 inches of run, and you place a rod on that roof so that it is tilted at a slope of 5/12 relative to the roof surface, then the rod will not have a slope of 10/12 relative to the horizontal. Instead, you would add the angles, which are the inverse tangents of the slopes. (Note though, that all you ever deal with is very small slopes, you find that adding the slopes works just as well as adding the angles. You don't notice that one way works better than the other until you have some experience with larger slopes. The same is true of slow speeds!)

Likewise, you would add the inverse hyperbolic tangents of the speeds. That's the right way to combine them.

Thanks for that. This is now my favorite analogy.

 

[GeorgeDishman]

The "stacked doorstop" analogy :-)

 

[Mister T]

This is now my favorite analogy.

Thanks, but I can't take all the credit. Most of it is adapted from Taylor and Wheeler. I threw in the part about the roof.

 

[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!