Understanding Special Relativity

[boswell]

Hi everyone! This is my first post so I hope I’m following all the correct rules and such. I am a second year Physics major and I’m having a bit of trouble with special relativity. I don’t have much trouble with doing homework problems, but I always stump myself when trying to understand SR for what it really is. Whenever I think about SR I find another logical problem with my understanding, and my textbook can’t answer me whenever I get stumped. So here is just one of many problems I’ve encountered when thinking about SR. This is not a HW problem; this is just a simple scenario I’ve envisioned. I’ve tried to make it as simple as possible:

A man is running with a speed of (0.5c) towards a photon of light that is heading towards him initially (4.5*10^8 m) away, all of this is with respect to a stationary observer. I assume that (c=3.0*10^8 m/s), so with respect to this stationary observer after one second has passed the light will have moved (3.0*10^8 m) towards the man, while the man will have run (1.5*10^8 m) towards the photon. Since the two were initially (4.5*10^8 m) apart, they should meet after one second with respect to the stationary observer.

But in the runner’s reference frame the runner views himself as stationary, while the photon heads towards him. I know that the distance between the runner and the photon should have contracted, and the time will also tick slower for the runner when compared to the stationary observer. So assuming I have done the Lorentz contraction and time dilation formulas correctly, t(runner)=0.866 t(stationary) and L(runner)=0.866 L(stationary). Since the stationary observer originally recorded one second for the two to meet, it should now take (0.866) sec, and since the stationary observer also recorded that initially they were (4.5*10^8 m) apart, they should now be (3.9*10^8 m) apart. However this would mean that the photon traveled (3.9*10^8 m) in (0.866 sec), which is a speed of (4.5*10^8 m/s), meaning c=1.5c. That can’t be right! Where is the flaw in my logic? What am I missing?

 

[cesiumfrog]

Did you assume simultaneity? That would be one obvious difficulty, since you're comparing events that occur in different places.

 

[boswell]

Ahh, so if I understand correctly you're saying:

The photon was emitted a bit sooner for the runner, just enough sooner to make the runner's c=(3.0*10^8 m/s)? If so, it's starting to make sense now, I always thought simultaneity was some separate concept not directly related to the time/length contraction topics. But I guess that's the wrong way of thinking about it.

 

[jtbell]

Yes, relativity of simultaneity is absolutely essential (on an equal footing with length contraction and time dilation) to understanding how events "fit together" consistently according to different observers. Unfortunately, many introductory first- and second-year textbooks don't make this point, or at least not as prominently as they should.

Many of the common "paradoxes" of relativity are resolved by taking relativity of simultaneity into account. Most of the rest can be resolved by recognizing that there is no such thing as a perfectly rigid object.

 

[Syed Waqar]

Dear Reader,

Do you think that the Realativity is correct. I have some doubt in it. may be that is in my understanding but I think that it should be clear. If some expert want to share it. I would be very much thnakful to him.

Regards,Syed Waqar

 

[malawi_glenn]

Why not sharing your doubts here so that someone who is expert can help you?

And also, read the forum rules, it is not good to put the e-mail in your post or elsewhere.

 

[Fredrik]

boswell: You seem to be on the right track now. You can use a Lorentz transformation to find out how much earlier the photon was emitted in the runner's frame.

Syed: You should also read the part in the forum rules about overly speculative posts. If you have a crackpot alternative to relativity, then we're not interested. If you have specific questions about details in the theory that seem weird to you, then go ahead and ask them here. We are not going to discuss it by E-mail.

 

[Naty1]

Do you think that the Realativity is correct

clearly NOT...but it's the best we have. It fails to match quantum mechanics (and quantum mechanics fails to match relativity) at places like singularities of black holes and big bang originations...so something is not quite right...but it's pretty good.

Try Wikipedia for a variation on Lorentz relativity :

http://en.wikipedia.org/wiki/De_Sitter_relativity

(for Relativity)Minkowski's unification of space and time within special relativity replaces the Galilean group of Newtonian mechanics with the Lorentz group. This is called a unification of space and time because the Lorentz group is simple, while the Galilean group is a semi-direct product of rotations and Galilean boosts. This means that the Lorentz group mixes up space and time so that they cannot be disentangled, while the Galilean group treats time as a parameter with different units of measurement than space...De Sitter special relativity postulates that the empty space has de Sitter symmetry as a fundamental law of nature. This means that spacetime is slightly curved even in the absence of matter or energy. This residual curvature is caused by a positive cosmological constant Λ to be determined by observation...

 

[malawi_glenn]

Quantum mechanics and special relativity is coherent, we have relativistic quantum field theory which works.

General relativity and quantum mech. is difficult to merge.

The difficulty lies in what one means by "correct". Is it that it coherent and have no internal paradoxes and contradictions. Or is it that it has not been falsified yet? In so far, relativity matches these requirements.

There is no a priori reason for why quantum mechanics and gravity MUST be combined, so one can not say that relativity is incorrect since it can't be described by quantum physics... Relativity makes no such claims either.

 

[Naty1]

There is no a priori reason for why quantum mechanics and gravity MUST be combined, so one can not say that relativity is incorrect since it can't be described by quantum physics... Relativity makes no such claims either

As a general comment I'd just point out that it sure is difficult to be really comfortable with the hodge podge of glued together ad hoc Standard Model constituents...

I'm not well versed enough in the fine points of the mathematics of GR/QM to have a personal opinion but I'll stick with Lee Smolin, for example, on this issue for the time being and disagree with the above quoted viewpoint.

In his 2007 book, THE TROUBLE WITH PHYSICS ,here is the first of Smolin's "five great problems in theoretical physics":

Combine general relativity and quantum theory into one theory that can claim to be the complete theory of nature...This is called the the problem of quantum gravity.

He notes:

General Relativity has a problem with infinities because inside a black hole the density of matter and the strength of the gravitational field quickly become infinite...Quantum theory has its own troubles with infinities. They appear whenever you atempt to use quantum mechanics to describe fields, like the electromagnetic field. (The values at every infinite point in space have uncontrollable variations and predict infinite results...we can't help but feel an essential part of physics has been left out.

He goes on to the other "great issues" to discuss foundational problems in quantum mechanics, trying to unify all particles and forces via a fundamental entity, and theoretically determing the free constants in the standard model...sounds to me like we have a long, long way to go.

 

[Fredrik]

Quantum mechanics and special relativity is coherent, we have relativistic quantum field theory which works.

This isn't 100% correct. My understanding is that there are no problems with the combination QM+SR, or with non-interacting QFTs in that framework, but some significant problems with QFTs with interactions in the QM+SR framework. Unfortunately, I don't understand the issues well enough to explain them.

I'm pretty sure that those "issues" can be removed in many different ways (e.g. by introducing an explicit cutoff) and that every one of those ways gives us a different modified version of QED which agrees with all the experiments that can be performed today. (I don't think those versions agree with each other to infinite precision though). This means that the issues are mainly of a philosophical nature, but that doesn't make them any less interesting to the mathematical physicists.

There is no a priori reason for why quantum mechanics and gravity MUST be combined,

I disagree with that too, because the right-hand side of Einstein's equation is a mathematical representation of the properties of matter*, and we know that matter can't be described very accurately by classical theories like GR. People have tried to just replace the stress-energy tensor with an expectation value of the corresponding QM operator, but they only got nonsense that way. (I think one of the appendices in Wald talks about this).

*) I see no reason to make a distinction between "matter" and "radiation" in this context.