Doppler Effect and absolute simultaneity

[bernhard.rothenstein]

The Doppler shift formula relates two proper time intervals measured in I and I' respectovely
(tau)=D(tau)'
D representing a Doppler factor that depends on the relative speed of I and I'. By definition the events involved in I and I' respectively take place at the same point in space. If the two involved events are simultaneous say in I they are simultaneous in I' as well and vice-versa.
The time intervals measured by clocks synchronized using the "everyday clock" synchronization procedure are related by a Doppler shift like formula. Could that be an explanation of the absolute simultaneity: two events simultaneous say in I and taking place at the same point in space are simultaneous in all inertial reference frames.
We find the same situation in the case of Selleri's approach.

 

[DrGreg]

The Doppler shift formula relates two proper time intervals measured in I and I' respectovely
(tau)=D(tau)'
D representing a Doppler factor that depends on the relative speed of I and I'. By definition the events involved in I and I' respectively take place at the same point in space. If the two involved events are simultaneous say in I they are simultaneous in I' as well and vice-versa. The time intervals measured by clocks synchronized using the "everyday clock" synchronization procedure are related by a Doppler shift like formula.

If you look at the absolute simultaneity equation for "left-to-right" Leubner coords

$$t_S(I) = \gamma \left(1 + \frac{v}{c} \right) t_S(R)$$​

which I obtained in this post, you will see that

$$\gamma \left(1 + \frac{v}{c} \right) = \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}} = D$$​

which is precisely the doppler factor between the frames I and R. This is no coincidence.

Imagine light being sent event e at the origin of the R frame at time

$$t_S(R)(e) = \tau(R)(e)$$...(1)​

(remember Einstein-time, Leubner-time and proper time are all the same at the spatial origin).

It is received event r at the origin of the I frame at time

$$t_S(I)(r) = \tau(I)(r)$$...(2)​

But because of the way S-time is defined we must have

$$t_S(I)(r) = t_S(I)(e)$$ ...(3) and
$$t_S(R)(r) = t_S(R)(e)$$ ...(4)​

Combining (1) with (4), and (2) with (3), and using the doppler equation

$$\tau(I)(r) = D \tau(R)(e)$$​

we get

$$t_S(I)(e) = D t_S(R)(e)$$ and
$$t_S(I)(r) = D t_S(R)(r)$$​

the same absolute simultaneity equation (evaluated at both events e and r) as before.

Could that be an explanation of the absolute simultaneity: two events simultaneous say in I and taking place at the same point in space are simultaneous in all inertial reference frames. We find the same situation in the case of Selleri's approach.

I don't really understand this. The general absolute simultaneity equation

$$t_S(I) = a(I) t_S(R)$$...(A)​

is measuring the same event in two different coord systems I and R, whereas the doppler shift equation

$$t_S(I)(r) = \tau(I)(r) = D \tau(R)(e) = t_S(R)(e)$$​

is measuring two different events e and r in (effectively) two different coords systems I and R. It's only in Leubner coords we can link the two.

(NOTE: the absolute simultaneity equation (A) could also be written

$$\frac{\partial t_S(I)}{\partial x_s(R)} = 0$$​

 

[Entropia]

The concept of the Doppler Effect and absolute simultaneity are both important principles in understanding the behavior of time and space in different reference frames. The Doppler Effect, as described in the content, shows that the measurement of time can be affected by the relative speed of two reference frames. This means that the time intervals measured in two different reference frames will be different due to the Doppler factor.

On the other hand, absolute simultaneity refers to the idea that events happening at the same point in space can be considered simultaneous in all inertial reference frames. This is in contrast to the concept of relative simultaneity, where the simultaneity of events is dependent on the observer's reference frame.

The content suggests that the Doppler shift formula could potentially explain the concept of absolute simultaneity. This is because the formula shows that the time intervals measured in different reference frames are related by a Doppler factor, indicating a connection between the two frames.

Additionally, the use of "everyday clock" synchronization, where clocks are synchronized based on the speed of light, also supports the idea of absolute simultaneity. This is because the speed of light is considered constant in all reference frames, meaning that the time intervals measured using this method would be the same in all frames.

Similarly, Selleri's approach, which also supports the idea of absolute simultaneity, can be seen as another explanation for the relationship between the Doppler Effect and absolute simultaneity. This approach suggests that the speed of light is not the same in all directions, which could also affect the measurement of time in different reference frames.

In conclusion, the Doppler Effect and absolute simultaneity are two important concepts in understanding the behavior of time and space in different reference frames. While the Doppler shift formula and the use of "everyday clock" synchronization can provide some explanation for the idea of absolute simultaneity, further research and exploration are needed to fully understand this concept.