Ideas for small special relativity wiki-page

[Shukie]

Hi all,

We recently got an assignment from our professor to make a small wiki-like page on Blackboard about a topic related to special relativity. The article should have about 1500 words and it should be 'inviting' for others to discuss or edit. Ideally it should be something that's not cookie cutter stuff like time dilation or the doppler effect, which is already covered in the textbook extensively, but perhaps interesting side-effects of SR for instance or the history of SR (but that one has been snapped up already by others). Does anyone have any ideas? I can't really think of anything.

P.S.: I posted this here and not in the homework forum, as it doesn't really seem like a homework problem.

 

[Fredrik]

These are some ideas, but they may be too difficult:

1. How does Lorentz contraction affect a solid accelerating rod and a solid rotating (massless) disc, and why?
2. What exactly is the definition of "special relativity"?
3. A mathematically rigorous derivation of the Lorentz transformation from a well-defined version of Einstein's postulates.
4. Proof that the Poincaré group is the isometry group of Minkowski space.

I can't think of anything that's easy and also not totally standard. The derivation in 3 is easy, but it's difficult to see how to make the postulates well-defined. 2 is much more difficult than it seems. 4 requires some knowledge of differential geometry. (Nothing about curvature, but you'd need a solid understanding of coordinate systems, tensors and the definition of an isometry). 1 is the easiest of these suggestions, but I'm not sure it's easy enough. The first half of it probably is.

 

[Shukie]

Thanks for your suggestions, that's exactly the sort of stuff I'm looking for. I'm a first year university student, so I'm not sure the level of the topic is really supposed to be up to par with your suggestions, because I've never even heard of Poincare groups for example. Does 1 have to do with rigidity? Because the professor did mention that in his first lecture.

 

[Fredrik]

The Poincaré group is just one specific group. It consists of the homogenous Lorentz transformations plus translations, so it can be defined as the set of functions from \mathbb R^4 into \mathbb R^4 of the form

x\mapsto\Lambda x+a

where \Lambda is a linear function satisfying \Lambda^T\eta\Lambda=\eta. (Recall that linear operators can be represented by matrices, so \Lambda x can be interpreted as the product of a 4x4 matrix and a 4x1 matrix).

Yes, 1 has to do with rigidity. The impossibility of absolute rigidity in SR is a consequence of the relativity of simultaneity. Imagine giving your rod a boost so that it changes its velocity from 0 to v almost instantly. If it was rigid in the pre-relativistic sense, every part of it would change its velocity at the same time, but in SR, if the different parts change their velocity at the same time in one frame, they're not doing it at the same time in other frames.

The rotating disc is even worse. It's easy to see (if you can figure out what you should be looking at, which is difficult) that it's not possible to get something to start rotating without forcefully stretching it. The rod will at least be approximately rigid at small length scales, but the disc isn't even that.

The solid accelerating rod is probably a good topic for an article. And a study of the Poincaré group might be too. You'd have to do some work just to show that it is a group and find out what its interesting subgroups are.

 

[Phrak]

Fredrick! she did say first year

 

[atyy]

One thing I would like to know is how we know that the one-way speed of light is the same in all inertial reference frames (assuming we set our clocks so that slow motions are described by Newton's laws).

 

[DrGreg]

One thing I would like to know is how we know that the one-way speed of light is the same in all inertial reference frames (assuming we set our clocks so that slow motions are described by Newton's laws).

I doubt this is a suitable subject for Shukie, but the answer is "by definition". Given that the two-way speed of light is experimentally confirmed to be the same in all inertial frames, we choose to synchronise our clocks to make the one-way speed the same. ("Einstein's synchronisation convention".)

If you want to discuss this further, I'd suggest creating a new thread, unless Shukie actually wants to pursue this topic.

 

[Fredrik]

Fredrick! she did say first year

That's why I focused on the easiest aspects of my original four suggestions. But you're right. The acceleration/rigidity stuff must be very difficult for a first year student. Finding the subgroups of the Poincaré group might be easy enough (after looking up what a group is), but the point of that exercise would be almost impossible to understand.

How about this then?

5. Define rapidity and write as much about it as you have time for. (Roughly the same thing that DrGreg did here).

 

[Naty1]

make a small wiki-like page on Blackboard about a topic related to special relativity. The article should have about 1500 words and it should be 'inviting' for others to discuss or edit

How about "Observational frames and the speed of light"...

I've been thinking about that for some months, part time, and still find aspects confusing...

Put down some facts, some theory, pose some questions...then answer them...let people who think they understand answer before reading yours.

Nothing much is cookie cutter in special relativity...careful thought about cnsequences or concepts always leads to interesting situations...

I'd start with something like "Only certain observers see the speed of light as "c": those in an inertial frame who are not in a gravitational field and those freely falling observers who are in a gravitational field." All other observers will not record constant "c" and in general will record different values.

After some explanation consider different obeservers in different situations: A distant observer sees light (and mass) slow (blue shift) as a black hole is approached and never see the light reach the event horizon; a freely falling obeserver sees the light pass a "c", yet observes the light at the horizon itself as stationary. You could also use the acceleration/gravitation "equivalence" to explain how observers will see light in a general accelerating frame...Everybody else sees the speed of light vary.

Who sees red shift and blue shift? How does an accelerating source appear to distant observers? lots of confusing perspectives and they are all "true and accurate and correct"...When can you "see" electromagnetic radiation...I am still trying to sort out the different situations...
Relate relativity, perhaps, to electric charge which all observers see as fixed, as they do potential energy...but kinetic energy is observer dependent...why??

Why are interplanetary distances precise in Newtonian physics but ambiguous in relativity? You could even carry the theme down to Planck length: Is Planck length constant like the speed of light?? will moving observers see the same Planck length as stationary ones? If not, how can Planck length be a minimum size? If so, is this an exception to relativity, like the speed of light.

This is about 1/5 of what you need and I haven't even explained much yet!

 

[Naty1]

And if you wanted another example: use the "Photon velocity and Pythagorean Theorem" thread just posted...