Clock Synchronization: Teaching Special Relativity

[bernhard.rothenstein]

Please tell me if it is compulsory to start teaching special relativity with describing the clock synchronization procedure?
Which is the best way to do it in your opinion?
Thanks

 

[Dale]

I would start with the two postulates. The Einstein synchronization procedure is a direct result of the second postulate.

 

[bernhard.rothenstein]

I would start with the two postulates. The Einstein synchronization procedure is a direct result of the second postulate.

Thanks for your answer and I agree with you. Do you consider that x=ct and x'=ct' are equivalent with clock sybchronization? Do you consider that it is correct to arrive at the Lorentz transformations without to mention the concept of clock and to make a link between the involved time coordinates and the readings of clocks? I know a lot of such examples.
Regards

 

[Dale]

Thanks for your answer and I agree with you. Do you consider that x=ct and x'=ct' are equivalent with clock sybchronization?

The equation x=ct describes a light cone originating from the origin propagating at c. Then x'=ct' is simply a restatement of the second postulate, i.e. the light cone from the origin also propagates at c in the primed frame.

Do you consider that it is correct to arrive at the Lorentz transformations without to mention the concept of clock and to make a link between the involved time coordinates and the readings of clocks? I know a lot of such examples.

It can certainly be done correctly, but I have never taught relativity, so I don't know if it would be clear to a student. I tend to think that a derivation of the Lorentz transform and an introduction to Minkowski geometry and spacetime diagrams should be done as early as feasible, but I don't know exactly when that is.

 

[pervect]

Please tell me if it is compulsory to start teaching special relativity with describing the clock synchronization procedure?
Which is the best way to do it in your opinion?
Thanks

For some research into how students learn relativity, and specifically how they learn about clock synchronization, look up Scherr from U of W. One paper is http://arxiv.org/abs/physics/0207109 Another paper is http://aapt-doorway.org/TGRU/articles/Vokos-Simultaneity.pdf also at arxiv http://arxiv.org/abs/physics/0207081

(Both papers were published in journals as well as being on arxiv).

Some of the results are pretty gloomy looking. Especially with traditional instruction, students never really learned relativity properly, i.e. they couldn't get the test answers right, even after taking a course in relativity :-(.

It does (in at least one of the above papers) appear to be helpful to review some basic non-relativistic concepts first, at least part of the problem was an incorrect student understanding of synchronization even without relativity. The classic example is confusing seeing two events at the same time with having them occur at the same time.

Some of the statistics are really pretty depressing :-(.

VII. CONCLUSION
This investigation has identified widespread difficulties that students have
with the definition of the time of an event and the role of intelligent observers. After
instruction, more than 2/3 of physics undergraduates and 1/3 of graduate students
in physics are unable to apply the construct of a reference frame in determining whether
or not two events are simultaneous. Many students interpret the phrase “relativity of
simultaneity” as implying that the simultaneity of events is determined by an
observer on the basis of the reception of light signals. They often attribute the
relativity of simultaneity to the difference in signal travel time for different observers. In
this way, they reconcile statements of the relativity of simultaneity with a belief in
absolute simultaneity and fail to confront the startling ideas of special relativity.

Experienced instructors know that students often have trouble relating
measurements made by observers in different reference frames. It is not
surprising that students, even at advanced levels, do not fully understand the
implications of the invariance of the speed of light. What is surprising is that most
students apparently fail to recognize even the basic issues that are being addressed.

Students at all levels have significant difficulties with the ideas that form the
foundations of the concept of a reference frame. In particular, many students do not
think of a reference frame as a system ofobservers that determine the same time for
any given event. Such difficulties appear to impede not only their understanding of the
relativity of simultaneity, but also their ability to apply correctly the Lorentz
transformations.

 

[robphy]

My personal opinion is that part of the problem that such misconceptions and misunderstandings continue in special relativity is that the introductory textbooks still focus on the spatial-viewpoint of "moving frames of reference" (following Einstein's presentation) rather than a spacetime-geometric-viewpoint (developed by the mathematician Minkowski, and subsequently being developed by modern-day relativists).

 

[country boy]

Please tell me if it is compulsory to start teaching special relativity with describing the clock synchronization procedure?
Which is the best way to do it in your opinion?
Thanks

For the novice student, it may be best to begin with the basic concepts of coincidence (two things happening at the same time and place) and simultaneity (two things happening at the same time at different places). These are central to understanding relativity and do not require math in the initial discussion. Coincidence is a good place to start, because it is not an inherently relativistic concept, and the student usually has a good idea of it's meaning already. Simultaneity is harder, because it seems to be the same thing as coincidence until the student is shown how the finite speed of light makes the timing of separated events relative. Clock synchronization can then be introduced to explain how the observer defines simultaneity.

 

[bernhard.rothenstein]

Thanks to all participants. Do you consider that testing what students respond to different tests without analysing the ways in which they were tought lead to relevant results?
A student who states "The Lorentz transformation relates the space-time coordinates of two events (x,x') which take place at the same point in space when the clocks of the involved inertial reference frame located at that point and synchronized a la Einstein read t and t' respectively" would pass the examination?

 

[Dale]

For some research into how students learn relativity, and specifically how they learn about clock synchronization, look up Scherr from U of W. One paper is http://arxiv.org/abs/physics/0207109 Another paper is http://aapt-doorway.org/TGRU/articles/Vokos-Simultaneity.pdf also at arxiv http://arxiv.org/abs/physics/0207081

(Both papers were published in journals as well as being on arxiv).

Thank you very much for these references. I did not appreciate how fundamentally difficult the relativity of simultaneity is to grasp for a typical student. Although, now that I have read these it makes sense that most of the "paradoxes" I have seen invented by crackpots simply reduce to a failure to correctly apply the relativity of simultaneity. I struggled for years, but I attributed it to a poor textbook presentation rather than an inherent difficulty in the concept. Maybe my textbook wasn't so bad.

 

[Dale]

My personal opinion is that part of the problem that such misconceptions and misunderstandings continue in special relativity is that the introductory textbooks still focus on the spatial-viewpoint of "moving frames of reference" (following Einstein's presentation) rather than a spacetime-geometric-viewpoint (developed by the mathematician Minkowski, and subsequently being developed by modern-day relativists).

You and I have discussed this point before, and I am inclined to agree with you. My own personal experience is that relativity made no sense until I discovered spacetime diagrams, Minkowski geometry, and spacetime intervals. Then it suddenly "clicked".

I note that the presentations and questions in the articles referenced above were all from a traditional "spatial-viewpoint". With this approach it required the pretty drastic "tutorial workgroup" approach to get even a 50% success with some concepts. That success only came after the students were required to directly confront and discard their assumptions themselves.

I wonder if the geometric-viewpoint that you and I like would result in students that could work problems but would still hold to the underlying incorrect assumptions. In other words, would they avoid challenging their preconceptions altogether, or would the geometric approach give students the tools they need to challenge their fundamental assumptions more successfully? I really don't have a good idea.

 

[robphy]

I wonder if the geometric-viewpoint that you and I like would result in students that could work problems but would still hold to the underlying incorrect assumptions. In other words, would they avoid challenging their preconceptions altogether, or would the geometric approach give students the tools they need to challenge their fundamental assumptions more successfully? I really don't have a good idea.

Until so-called "relativistic effects" become a part of daily life, I think that many preconceptions will persist. However, as you suggest, the more tangible geometric approach would provide tools to help students analyze problems and try to overcome misconceptions.

In similar sense, a free-body diagram can be used to analyze problems and overcome misconceptions in mechanics.