# Light clock and teaching of special relativity

1. Jun 24, 2006

### bernhard.rothenstein

do you think that the light clock is a good pedagogical tool for introducing special relativity? a teacher of mine told us that there is no advantage without disadvantage!
sine ira et studio

2. Jun 25, 2006

### pmb_phy

I, personallly, think that its an excellant tool. It allows one to understand time dilation qualitatively.

Pete

Last edited: Jun 25, 2006
3. Jun 25, 2006

### robphy

In fact, by using a higher-dimensional (e.g. circular and spherical) lightclock and drawing "spacetime diagrams of lightclocks", you can also do length contraction and relativity of simultaneity, as well as the doppler effect and twin paradox/clock effect.... and you can do it by "counting ticks". In fact, one can highlight the invariance of the interval.

http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/ [Broken]
arxiv.org/abs/physics/0505134

One "problem" to overcome in teaching with "lightclock diagrams" is getting students to understand spacetime diagrams... and appreciate the geometry first, and (if necessary) the algebra later. The physical interpretation is much clearer when viewed geometrically first.

Last edited by a moderator: May 2, 2017
4. Jun 25, 2006

### bernhard.rothenstein

i think that the light clock approach obscures its relationship with the Einstein's clocks. the light clock, in its rest frame, is associated with two Einstein clocks located at the two mirrors respectively. They are located in front of Einstein clocks of the reference frame relative to which it moves. Taking them into account we are able to describe all the relativistic effects.
sine ira et studio

5. Jun 25, 2006

### robphy

Is there an implicit assumption that "Einstein's clocks" are [necessarily] superior?

Of course, one advantage of the light clock is its operational definition of time along a worldline... using radar methods. This is arguably a "more physical" approach. This advantage has been raised in various references:

e.g.,
American Journal of Physics -- February 1969 -- Volume 37, Issue 2, pp. 178-189
Operational Approach to Space and Time Measurements in Flat Space
James L. Anderson and Ronald Gautreau

(see others in the references of the article in my previous post)

Last edited by a moderator: May 2, 2017
6. Jun 25, 2006

### Hurkyl

Staff Emeritus
Maybe I'm off base, but I feel like that a little too much emphasis is placed on motivating SR than teaching SR... the way I usually see the light clock used tends to fall in the motivation category.

7. Jun 25, 2006

### robphy

In my opinion, one does have to overcome "that layer of prejudices laid down upon the mind prior to the age of eighteen" [AE]. At one extreme, one could simply teach SR without motivation by just stating that we are studying a vector space with a Minkowski metric... and taking it from there.

In my opinion, your observation on the light clock in the "motivation[-but-not-much-as-teaching] category" is due to the limited treatment of light clocks via purely-spatial diagrams in textbooks. As I said above, with a spacetime diagram approach, one can actually use the light clock to calculate (in some nice cases, counting ticks of) spacetime intervals, as well as provide a physical, operational meaning to them... rather than relying on [often specific cases of] merely algebraic formulas to obtain the usual results. (Of course, after sufficient conceptual and computational motivation with the spacetime light-clock diagrams, one can then shift the emphasis to the now geometrically-motivated algebraic formulas and deal with more complicated problems that are tedious to handle with diagrams.)

my \$0.02

8. Jun 25, 2006

### rbj

and quantitatively.

9. Jun 26, 2006

### bernhard.rothenstein

light clock

What is the meaning of I'm off base?. What is the difference between teaching and motivating?

10. Jun 26, 2006

### Hurkyl

Staff Emeritus
I feel that too much emphasis is placed on answering the question "Why would we ever have thought of SR?" instead of answering the questions "What is SR?" and "How do we use SR?"

11. Jun 26, 2006

### actionintegral

I didn't find light clocks very helpful really. The concept of the "wristwatch" was most helpful to me personally.

12. Jun 26, 2006

### robphy

Of course, a "wristwatch" emphasizes that [proper-]time is a local concept associated with an observer [as opposed to a global time associated with "absolute time"]. This idea alone does not explain why the moving wristwatch is observed to behave differently from a wristwatch at rest. A light clock provides a relativity-friendly mechanism for the wristwatch's behavior.

13. Jun 26, 2006

### masudr

Is there a simple one-line argument that says why time experienced by a massive observer between $[a,b]$whose worldline is given by $x^\mu(\lambda),$ where $\lambda$ is a parameter is

$$\tau = \int^{\lambda=b}_{\lambda=a} d \tau = \int^b_a \sqrt{\pm\frac{dx^\mu}{d\lambda} \frac{dx_\mu}{d\lambda}} d\lambda\ \ \mbox{the sign depending upon the choice of metric}$$

Last edited: Jun 26, 2006