Time dilation due to relative velocity

[barnesbb]

Hi all,

I have been interested in the Theory of Special Relativity for the past few years, and there is something I'd like to discuss. Somebody else may be discussing this elsewhere but if there is I haven't been able to find them.

I have never felt comfortable with time dilation due to velocity as inferred from the light clock thought experiment (for those unfamiliar with this thought experiment, see 'Simple inference of time dilation due to relative velocity' at http://en.wikipedia.org/wiki/Time_dilation). When thinking about this experiment, it occurred to me that it was impossible for the observer moving past the clock to see the light pulse traveling between the two mirrors. Surely any light that the observer sees is different to this light pulse.

I thought that this might just be a shortcoming of that particular experiment, so I went to as pure a source as I could find - the English translation of 'Relativity - The Special and General Theory' at Bartleby Online (http://www.bartleby.com/173/). I could have gone purer but I really didn't want to spend time learning German when there are plenty of people out there who can do it better than me anyway.

I was surprised to find that this oversight seems to exist there as well. In Chapter 7 'The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity', Einstein describes a thought experiment where the ubiquitous railway carriage is traveling parallel to a ray of light, and tries to explain why the light must appear to have the same speed to both the observer on the railway carriage and the observer on the embankment.

The answer Einstein gives is that time slows down as an observer approaches the speed of light, but surely this contradicts the principle of relativity where nobody is 'really moving'. As long as there is no net force acting on an observer (ie. no acceleration), all observers can apply the same laws. This means that time should slow down equally for the observer on the railway carriage and the observer on the embankment.

I think the answer to the problem of incompatibility lies in the fact that the observer on the railway carriage could never see that ray of light that is traveling parallel to him, because that would require another ray of light to travel from the first ray to the carriage. The only observer that would see the first ray of light would be someone standing next to the railway track in the path of that ray. And it's a good thing that there is no air in this experiment, otherwise the turbulence created by a supersonic train would surely wipe this poor observer from existence.

Therefore, the observer on the carriage could never judge the speed of that ray of light and there is no incompatibility - each individual ray of light can only be observed by one observer, and therefore time dilation as described in these instances can't exist.

To state it a little more succinctly - light and the constant speed it travels in a vacuum is required for special relativity to apply, so surely we can't apply the principles of relativity to part of the system that supports it?

Any comments, questions or derisions are welcome.

Cheers.

 

[JesseM]

I have never felt comfortable with time dilation due to velocity as inferred from the light clock thought experiment (for those unfamiliar with this thought experiment, see 'Simple inference of time dilation due to relative velocity' at http://en.wikipedia.org/wiki/Time_dilation). When thinking about this experiment, it occurred to me that it was impossible for the observer moving past the clock to see the light pulse traveling between the two mirrors. Surely any light that the observer sees is different to this light pulse.

The light clock thought experiment just deals with the coordinate description of the light's path in each frame (a frame is just a type of coordinate system which labels every point in spacetime with position and time coordinates), so what anyone "sees" visually isn't really an issue. If you like you could imagine each observer has a set of light detectors at rest at different positions in their frame, with each detector recording the time that light passes through it.

I thought that this might just be a shortcoming of that particular experiment, so I went to as pure a source as I could find - the English translation of 'Relativity - The Special and General Theory' at Bartleby Online (http://www.bartleby.com/173/). I could have gone purer but I really didn't want to spend time learning German when there are plenty of people out there who can do it better than me anyway.

In general I'd say there's no real reason in science to see the first sources that discussed a theory as having greater "purity" than later ones, pedagogical approaches are constantly being revised and sometimes the understanding of theories themselves can change over time, so it's more often the more recent sources that are better for learning about a theory. But in this case, the thought-experiment Einstein is talking about is still widely used in introducing relativity.

I was surprised to find that this oversight seems to exist there as well. In Chapter 7 'The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity', Einstein describes a thought experiment where the ubiquitous railway carriage is traveling parallel to a ray of light, and tries to explain why the light must appear to have the same speed to both the observer on the railway carriage and the observer on the embankment.

The answer Einstein gives is that time slows down as an observer approaches the speed of light,

Actually I think you misunderstand his answer to the problem posed in section 7, which he gives in section 8 and section 9. His solution is not to invoke time dilation, but rather to invoke the relativity of simultaneity--there's a good visual explanation of the train thought-experiment and how it can be used to derive the relativity of simultaneity on this page. The relativity of simultaneity says that two events which happen at the same time-coordinate at different spatial coordinates in one frame will have happened at different time-coordinates in other frames (unless the second frame is moving exactly perpendicular to the axis between the two events in the first frame).

but surely this contradicts the principle of relativity where nobody is 'really moving'.

Time dilation is reciprocal, so it doesn't imply anyone is "really moving". If you are moving relative to me, then in my rest frame your clock is running slow (i.e. your clock advances less than one second for every second of coordinate time in my frame), but in your rest frame it is my clock that is running slow, by exactly the same amount. Length contraction is reciprocal in the same way. And likewise, if I have two clocks at different locations which are synchronized in my frame (i.e. the events of each clock showing a reading of, say, 5 seconds occur simultaneously in my frame), then these clocks will be out-of-sync in your frame, and vice-versa. For a visual illustration of how this reciprocity can be possible without it leading to any contradictions, see my example in this thread.

As long as there is no net force acting on an observer (ie. no acceleration), all observers can apply the same laws. This means that time should slow down equally for the observer on the railway carriage and the observer on the embankment.

No, it doesn't mean that. "All observers can apply the same laws" just means that in each frame, a clock with a greater velocity in that frame is running slower in that frame--in the rest frame of the carriage the clock on the embankment is running slower than the clock on the carriage by a factor of [tex]\sqrt{1 - v^2/c^2}[/tex], while in the rest frame of the embankment the clock on the carriage is running slower than the clock on the embankment by the same factor of [tex]\sqrt{1 - v^2/c^2}[/tex]. So, the same time dilation law applies in both frames--regardless of what frame you're in, a clock moving at speed v in that frame will be running slower than a clock at rest in that frame by a factor of [tex]\sqrt{1 - v^2/c^2}[/tex].

I think the answer to the problem of incompatibility lies in the fact that the observer on the railway carriage could never see that ray of light that is traveling parallel to him, because that would require another ray of light to travel from the first ray to the carriage. The only observer that would see the first ray of light would be someone standing next to the railway track in the path of that ray. And it's a good thing that there is no air in this experiment, otherwise the turbulence created by a supersonic train would surely wipe this poor observer from existence.

Again, these sorts of thought-experiments don't deal with what is seen visually by any observer, but rather with the position and time coordinates assigned to different events by each observer. If you know when and where the original flashes that created the light occurred (say, because they left scorch marks on the ground), and you know when and where both beams were detected (say, because both observers had light detectors at just the right position so that light from both flashes hit both sides of the detector at the same moment, causing the detector to flash green or start honking or whatever), then you can use (difference in position)/(difference in time) to measure the coordinate speed of the light from the flashes in your frame.

Therefore, the observer on the carriage could never judge the speed of that ray of light and there is no incompatibility - each individual ray of light can only be observed by one observer, and therefore time dilation as described in these instances can't exist.

To state it a little more succinctly - light and the constant speed it travels in a vacuum is required for special relativity to apply, so surely we can't apply the principles of relativity to part of the system that supports it?

If something seems odd to you about some explanation in relativity, you'll learn more if your first instinct is "I'm probably misunderstanding something here, let's try to figure out what it was" and not "thousands of smart scientists must have been missing some very simple flaw in the theory for over a century"...the latter attitude leads to situations like this:

If you hang out in a science forum for a while (especially a physics forum) you'll see people acting like this all the time...my advice to you is, try not to become one of them!

 

[barnesbb]

Hehe - I do like that xkcd comic (and xkcd in general - many boring afternoons have been spent continuously clicking the 'Random' button. Hope my boss isn't a forum subscriber).

Sorry if i came across arrogant. I've read and thought and assumed my misunderstanding a lot and it was time for me to ask someone. Got a little carried away with my own thoughts. :)

However, I am very keen to discuss this more as I still have questions. I'm reading through your other posts and the links you included and I'll do some more thinking and get back to you very soon.

My last wish is to be viewed as a clueless neophyte so I'm thinking and being as skeptical as I can. Although - if I am making a fool of myself, I'm glad I'm doing it on the nameless, faceless Internet. :)

 

[matheinste]

My last wish is to be viewed as a clueless neophyte so I'm thinking and being as skeptical as I can. Although - if I am making a fool of myself, I'm glad I'm doing it on the nameless, faceless Internet. :)

Don't worry, all the responders on this forum have trodden the same path that you are starting out on, I am still treading it. It is a very wise man who negotiates the pitfalls of SR at the first attempt.

Matheinste.

 

[barnesbb]

I understand a bit more about where I went wrong now. I can see now that it is possible to track light without seeing it. I need to take some time to do some more thinking, research, and possibly even a course.

Thanks for your help and time - now I need to get back to doing what I get paid for to make up for the time I spent posting yesterday. :)

 

[granpa]

he can measure the velocity of photons moving in all directions in his own frame.
why should he assume that photons near himself behave any differently when they are somewhere else?

 

[Dale]

It is a very wise man who negotiates the pitfalls of SR at the first attempt.

It took me 7 years of admittedly very sporadic effort. I am not very wise.