Inertial & Non-Inertial Frames: Light Wavelengths

[HALON]

When neglecting gravity and body size, if a body rotating at uniform angular velocity about a central body sends a light signal to the central body, the central body will receive the wavelength as longer by $1/γ$. Conversely, if the central body sends a signal to the rotating body, the rotating body will receive the wavelength as $γ$ times shorter. Is this correct?

 

[ghwellsjr]

When neglecting gravity and body size, if a body rotating at uniform angular velocity about a central body sends a light signal to the central body, the central body will receive the wavelength as longer by $1/γ$.

The wavelength is longer but I would say by $γ$ times. Or you could say the frequency of the light is slower by a factor of $1/γ$.

Conversely, if the central body sends a signal to the rotating body, the rotating body will receive the wavelength as $γ$ times shorter. Is this correct?

Again, it is shorter but I would say by $1/γ$ times and the frequency is $γ$ times faster.

But this may just be semantics.

 

[WannabeNewton]

Didn't we already talk about this exact same thing in a previous thread of yours? You asked literally the same question in https://www.physicsforums.com/showthread.php?t=762176 and got the same answer ghwellsjr gave you above.

 

[HALON]

The wavelength is longer but I would say by $γ$ times. Or you could say the frequency of the light is slower by a factor of $1/γ$.


Again, it is shorter but I would say by $1/γ$ times and the frequency is $γ$ times faster.

But this may just be semantics.

I see your point about the semantics, but essentially we are in agreement.

[EDIT] I began with $γ=(1-v/c)^{1/2}$ for an instant of angular velocity, then $f_{orbit}=f_{central}/γ$, which is simply $1/γ$
Using $c=fλ$
we get Orbit's view of light as $c=(1/γ*f)(γλ)$
And the reciprocal is Central's view of light $c=(γf)(1/γ*λ)$

Didn't we already talk about this exact same thing in a previous thread of yours? You asked literally the same question in https://www.physicsforums.com/showthread.php?t=762176 and got the same answer ghwellsjr gave you above.

Yes but... it was the last question I posted on that thread and I didn’t receive your reply. You implicitly answered it earlier in a very detailed (and for me complicated) way, which I took as agreement. Indeed my last question there was also rather longwinded. So I condensed the question (without all the equations) to seek clarification and confirmation.

If ghwellsjr is correct then it satisfies me and this thread may be closed.

 

[sardar]

Yes, this statement is correct. Inertial frames refer to frames of reference that are not accelerating, while non-inertial frames refer to frames that are accelerating or rotating. In the scenario described, the central body is in an inertial frame while the rotating body is in a non-inertial frame due to its uniform angular velocity.

In this situation, the central body will perceive the wavelength of the light signal from the rotating body as longer due to the phenomenon of time dilation. This is because time appears to pass slower in a non-inertial frame compared to an inertial frame. As a result, the wavelength of the light signal will also appear longer.

Conversely, when the central body sends a light signal to the rotating body, the rotating body will perceive the wavelength as shorter due to the phenomenon of length contraction. This is because objects in motion appear shorter in the direction of their motion. Therefore, the wavelength of the light signal will appear shorter to the rotating body.

Overall, this statement accurately describes the effects of time dilation and length contraction in inertial and non-inertial frames on the perception of light wavelengths.