The Relativity of Simultaneity

1. Jun 9, 2009

Gear300

I got lost somewhere in this deduction that time is not simultaneous/equivalent for different reference frames.

There are two points A and B that are distanced apart from each other along a railroad (the railroad will act as the reference body). Point M is the midpoint of segment AB. While testing the simultaneity of two lightning strikes (one at point A and the other at point B), an observer stands at point M to observe whether the strikes are simultaneous. The observer finds that they are indeed simultaneous. If we were to shift the reference frame to instead a train moving along the railroad towards point B, we would have points A' and B' (both points on the train), in which A' would coincide with A and B' would coincide with B' at the moment the lightning strike. If there was an observer at point M' (on the train), which coincides with M at the moment the lightning strike, then because the train is moving with a velocity in the direction of point B, the observer at M', unlike the observer at M (for when the railroad was the reference body), would see the lightning from point B' (which coincides with B) before the one from A'. Time is not simultaneous in both frames, thus the time in one frame is not necessarily equivalent to the time in another.

What I don't get is what they mean by time in different reference frames not being equal. Would time be analogous to velocity in this case?: If there were two reference bodies, one stationary (K) and one moving with a velocity (K'), and there is a moving object P, the velocity of P with respect to K is different than with respect to K', though the overall behavior of the phenomenon can be modeled so that its nature with respect to K does not contradict its nature with respect to K'.

Last edited: Jun 9, 2009
2. Jun 9, 2009

Staff: Mentor

Everyone agrees that A' coincides with A at the time that lightning strikes A and that B' coincides with B at the time that lightning strikes B. (But not everyone agrees that the two lightning strikes happened simultaneously or that A' coincides with A and B' coincides with B at the same time.)
According to the railroad observers, M' coincides with M at the moment the lightning strikes. (The train observers will disagree, of course.)
The railroad observers can deduce that the light from flash B must reach M' before the light from flash A. Everyone agrees with this, including observer M'. Observers on the train must deduce, since M' was equidistant from the flashes and since light travels at the same speed with respect to them, that flash B must have occured first.
Events simultaneous in one frame are not simultaneous in another.

3. Jun 9, 2009

Gear300

I guess the trouble I'm having here is that the difference seems to be one in perception. I suppose that there would be no way of saying that one reference frame is "more correct" than the other. However, doesn't this imply that we're dealing with a theory that leans more on subjective perception, considering that we do not have an absolutely objective perception (or am I just getting everything screwed up)?

4. Jun 9, 2009

Staff: Mentor

Relativity is what is left over after you properly account for "perception" or "optical illusion" effects due to the finite propagation speed of light. This is unfortunately a very common impression given to students by these types of thought experiments and the usual way of presenting SR, but it is not correct.

5. Jun 9, 2009

JesseM

The basic reason it's called "relativity" is that the theory says that certain things which were formerly thought to be absolute truths, like the question of whether two events happened "at the same time", are actually not things we can determine in any absolute way through experiments, we can only determine them relative to particular frames of reference and the laws of physics work exactly the same way in each frame so there's no basis for preferring one over another. However, there are a number of things which all frames do agree on, like proper time or whether two physical events will coincide at the same point in spacetime, and that's where the real physical content of the theory lies.

6. Jun 9, 2009

Gear300

So then what is meant by unequal time between frames of reference? What does it mean by unequal displacement?

7. Jun 9, 2009

Staff: Mentor

It means that even after you account for optical effects time and distance are frame-variant.

8. Jun 9, 2009

Gear300

I'm seeing it in some clearer light (just a bit clearer)...Thanks.

9. Jun 9, 2009

Staff: Mentor

No problem. It is too bad that the way this stuff is presented almost inevitably leads to your confusion.

10. Jun 10, 2009

Lok

The misconceptions in perception do not count for much as things just behave as they suppose to, but the fact that we can find out by what amount or form the two M & M' observations differ is the final success of relativity. Which in time and given lot's of weird thoughts makes perfect sense.

11. Jun 10, 2009

ZikZak

DaleSpam,

What is it about the way that Relativity is currently presented that you think contributes to the misconception that Relativity is about perception / illusion? How would you teach it?

12. Jun 11, 2009

Staff: Mentor

I think the whole approach of using thought experiments is not terribly useful.

I would concentrate much more on spacetime diagrams and the related Minkowski geometric concepts. Students have already been exposed to position-time graphs, so the idea of events and worldlines should not be too difficult, then you introduce the spacetime interval and proper time. For me, that is what finally made relativity click, after about 7 years of occasional study.

13. Jun 12, 2009

michelcolman

I disagree completely. I guess everybody is different, but I only started to understand relativity after reading many thought experiments. My favorites:

- Twin paradox: on his outward journey, you get the impression that the age difference is just a matter of observation, but when he gets back, he really IS younger
- Passing trains paradox: trains can pass each other on a section of double track that would be way too short without relativity, driving home the point that length contraction is not just an observational issue.
- Some situations I worked out myself, for example a spaceship passing a space station at high speed, they want to figure out whose time is going slower so the station sends a signal to the spaceship one second after it passed, and times the reply, only to find that both still consider the other's time to run more slowly.
- trip to Betelgeuse and back, how long does it take as seen from Earth, the ship, or Betelgueuse, and what time is it in all of these places as seen from the different points of view.

Once you started to understand these, you can use spacetime diagrams to refine your understanding (and indeed, it will finally be easier to understand relativity this way) but if you start out with pages of equations and diagrams without any real life examples, don't expect anyone to really grasp the concept. I know I didn't, anyway.

14. Jun 12, 2009

ZapperZ

Staff Emeritus
Actually, I think the continual use of the word "paradox" has created many misunderstanding (and even created many crackpots) in SR. Calling something a "paradox" means that there are at least 2 contradictory observations or conclusion that cannot be reconciled with one another. This, obviously, is patently false in SR. The whole idea of relativity is the ability to do the appropriate transformation of coordinate systems to arrive at the seemingly different observations.

You have brought up both the issue of the "twin paradox", which is a consequence of "time dilation" and "pole in the barn" paradox, which is a consequence of "length contraction". Both of these notions of "time dilation" and "length contraction" are beginning to be questioned, not in terms of the physics, but in terms of its usage and pedagogy, the same way the use of "relativistic mass" has been questioned. See, for example, Lev Okun's recent paper (L.B. Okun Am. J. Phys. v.77, p.430 (2009)), or this recent one, (http://arxiv.org/abs/0906.1919).

So the understanding of the concept of SR, especially to non-specialists, may have to start with the language that we use.

Zz.

15. Jun 12, 2009

Staff: Mentor

I agree; I think that working out thought experiments is essential to understanding elementary special relativity.

I think there are three equivalent ways to analyze the typical SR thought experiments and that all three approaches are needed for full understanding:
(1) Using the relativistic behavior of moving clocks and metersticks directly.
(2) Using the Lorentz transformations.
(3) Using spacetime diagrams (toss in rapidity for extra credit ).

In my opinion, spacetime diagrams provide the deepest level of understanding, but many beginners find them too abstract at first.

16. Jun 12, 2009

michelcolman

a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true

17. Jun 12, 2009

ZapperZ

Staff Emeritus
Ask many of the "students" or even layman who use that word with respect to SR's consequences, and see if that's what they really understand as the meaning of the word. Furthermore, is that the accurate context in which that word is used in this situation?

The fact here is that the "twin paradox" is not a paradox. In fact, many of the paradoxes in SR are not paradoxes.

Zz.

18. Jun 12, 2009

clem

Putting "paradox" into google shows that it has so many different definitions that it means only what the speaker means it to mean. At least, that's what I mean.
I have always taken paradox to mean the application of a theory that leads to a contradiction (conflicting results). As such, I would use paradox to mean that, if the "twin paradox" were a paradox (It isn't, it is only a mistake made in some gedanken experiments.), SR is wrong.

19. Jun 12, 2009

Staff: Mentor

Everyone is certainly entitled to their opinion, but the traditional thought-experiemnt approach didn't work for me at all and I am not in the minority. In fact, only 30% of graduate physics students and only 11% of introductory undergraduate students correctly understand the relativity of simultaneity and the concept of reference frames via traditional instruction (see: http://www.physics.umd.edu/perg/papers/scherr/ScherrAJP2.pdf Table 2).

For me, Minkowski geometry, spacetime diagrams, and four-vectors are what finally got me to understand SR, so I am biased in their favor, but I think the evidence is pretty clear that traditional instruction is very ineffective. I also think that the anecdotal evidence on this board is that thought-experiments are too confusing to serve well as teaching aids.

Last edited: Jun 12, 2009
20. Jun 12, 2009

Saw

I feel the same as DaleSpam.

When I read the thought experiments, they only managed to make me angry. The problem is that they are usually presented as if each of them individually, by sheer logic, proved something, while the truth is that each of them, individually, proves nothing. What is more, in the worst presentations, it is even suggested that they prove something without relying on the postulate that the speed of light is constant for all observers and that makes them look simply false.

It is only by considering all the effects together (constancy of the speed of light for all observers, RS, TD and LC) that the theory makes sense and you don’t see that until you draw a ST diagram…

I would dare to say that the problem with the usual instruction method is that it yields to the temptation of dazzling people with the weirdness of each individual effect, instead of stressing that the combination of all of them leads to quite commonsensical results: all observers agree on which events happen and which do not = there is discrepancy in the paths taken by different observers to find the solutions to practical problems, but full agreement on the ultimate solutions.