Velocity dependent equations and frames of reference

[victorhugo]

With a velocity dependent equation such as de Broglie's λ=h/mv
There's just so many questions, where do I start...
In your frame of reference, an electron might be standing still but from an outside frame it could be moving at 0.1c
does that mean you'd see different wavelengths? What about when your frame accelerates, does the electron emit EMR?

 

[Orodruin]

does that mean you'd see different wavelengths?

Yes, wavelength is not frame invariant just as kinetic energy is not.

What about when your frame accelerates, does the electron emit EMR?

No.

 

[victorhugo]

Yes, wavelength is not frame invariant just as kinetic energy is not.

Prepare for questions from a level 1 newbie physicist... And of course, thank you so much for always answering my silly questions :)

1. [This question is covered in another thread split off from this one]

2. That makes sense, but does that mean that any velocity/energy dependent property of anything can only be described compared to a certain frame of reference? That is, having different observable characteristics at different frames.

3. So an observer seeing the electron accelerate, just not relative to its own 'spaceship' frame, would not see it emit EMR? To me it seems that it would, maybe I wasn't clear on my question enough. If we were to accelerate the electron alone or inside a jar, why would it make a difference whether it emits EMR or not?

 

[Orodruin]

That makes sense, but does that mean that any velocity/energy dependent property of anything can only be described compared to a certain frame of reference? That is, having different observable characteristics at different frames.

It does not mean anything else than that it is frame dependent.

So an observer seeing the electron accelerate, just not relative to its own 'spaceship' frame, would not see it emit EMR? To me it seems that it would, maybe I wasn't clear on my question enough. If we were to accelerate the electron alone or inside a jar, why would it make a difference whether it emits EMR or not?

You did not specify that the electron was also accelerating.

 

[victorhugo]

It does not mean anything else than that it is frame dependent.

Could you please elaborate on that then?

 

[Orodruin]

Could you please elaborate on that then?

I do not see how this can be misinterpreted. It is not something particular to SR and it is present already in classical mechanics.

 

[victorhugo]

I do not see how this can be misinterpreted. It is not something particular to SR and it is present already in classical mechanics.

Eg The wavelength (and anything else that is velocity dependent) of a particle is frame dependent? That is, different observers disagree on the wavelength because they observe different velocities?

 

[Orodruin]

Eg The wavelength (and anything else that is velocity dependent) of a particle is frame dependent? That is, different observers disagree on the wavelength because they observe different velocities?

Obviously, I do not see why you find this strange. Energy is different in different frames already in classical mechanics. Do you have a problem with that?

 

[victorhugo]

Obviously, I do not see why you find this strange. Energy is different in different frames already in classical mechanics. Do you have a problem with that?

Well, I'm still in school and started learning physics not even 2 years ago. We don't learn about any of this at school, only simple things like projectile motion, torque, basic particle physics etc.
No problems, I'm just finding all relativity strange, as expected.

 

[Orodruin]

Well, I'm still in school and started learning physics not even 2 years ago. We don't learn about any of this at school, only simple things like projectile motion, torque, basic particle physics etc.
No problems, I'm just finding all relativity strange, as expected.

Well, let us start with velocity itself - it is a measurable quantity. Do you find it strange that it can have different values in different inertial systems?

 

[Orodruin]

There is nothing a priori wrong with physical quantities that have different values in different frames. What we require is that the values of the properties obey the same laws in all frames. We like quantities that are the same in all frames (so much that we give them a name, invariants) because we can compute them in any frame and obtain their value in any frame, but they are by no means the only tool in the box.

 

[Ibix]

In that case the light clock is better to study since it allows you to derive the full Lorentz transforms. Those include both length contraction, time dilation and the relativity of simultaneity. After that I recommend looking up Minkowski diagrams, which are a very useful tool for seeing what is going on as viewed in different frames.