Actual earth measurement contradicts measurement predicted by special relativity

[ghwellsjr]

You can directly observe the Doppler-shifted frequency of the other clock. With appropriate assumptions you can translate that Doppler-shifted frequency into a time dilation. One of those assumptions is the choice of an inertial reference frame where the observing clock is at rest.

I understand that in SR, time dilation has a broader meaning which requires the specification of a frame to define the speed of a moving clock which can be independent of any observers but I wasn't using SR in my description. Isn't it just as legitimate to ignore any specification of a frame when going from the measured Doppler-shifted frequency to the calculation of the relative speed between the two clock/observers and then to the calculation of the time dilation of the other clock/observer? The only assumption that I was making is that we do this after the effects of the acceleration have passed so that the measured Doppler frequency has stabilized.

The reason that I am concerned about this detail is that I have been telling people on this forum that they have to analyze an entire scenario from one single frame of reference at a time. If they analyze one observer in one frame and another from another frame, we can get all kinds of apparent paradoxes. But if this is true, then how can the Twin Paradox (in which it is stated that each observer observes the other one's clock as going slower than his own) be analyzed from a single frame of reference where only one of the clocks is going slower?

 

[Dale]

I understand that in SR, time dilation has a broader meaning which requires the specification of a frame to define the speed of a moving clock which can be independent of any observers but I wasn't using SR in my description. Isn't it just as legitimate to ignore any specification of a frame when going from the measured Doppler-shifted frequency to the calculation of the relative speed between the two clock/observers and then to the calculation of the time dilation of the other clock/observer? The only assumption that I was making is that we do this after the effects of the acceleration have passed so that the measured Doppler frequency has stabilized.

Consider the reference frame where the source is at rest and the observer is moving. In this frame there is still the observed Doppler frequency, but the source is not time dilated. So you cannot go directly from an observed Doppler frequency to a source time dilation without some assumption of a particular reference frame (usually the inertial frame where the observer is at rest). That assumption may not be explicitly stated, but it is there.

The reason that I am concerned about this detail is that I have been telling people on this forum that they have to analyze an entire scenario from one single frame of reference at a time. If they analyze one observer in one frame and another from another frame, we can get all kinds of apparent paradoxes. But if this is true, then how can the Twin Paradox (in which it is stated that each observer observes the other one's clock as going slower than his own) be analyzed from a single frame of reference where only one of the clocks is going slower?

I guess I don't understand your concern here. Pick a frame, any frame will do. But I do agree with your point that you should analyze the entire scenario from one single frame. If you want to then look at a different frame you need to re-analyze the whole scenario in that other frame.

 

[Simplyh]

Sorry. I've introduced myself in the middle of your discussion with a quite different problem. I'll post it again for discussion some other time.

 

[JesseM]

Isn't it just as legitimate to ignore any specification of a frame when going from the measured Doppler-shifted frequency to the calculation of the relative speed between the two clock/observers and then to the calculation of the time dilation of the other clock/observer?

But these depend on the assumption that you want to use the measured frequency to calculate the speed/time dilation of one ship in the rest frame of the other. You could just as easily choose to use the measured frequency to calculate the speed of B in a frame where A is moving at 0.4c in the same direction as B, and calculate the time dilation in that frame; the calculation would just be a little different, that's all. Either way, the measured frequency is frame-independent (assuming you express it as a ratio of the rate signals are being received to the rate the receiver's own clock is ticking), but the subsequent calculation of velocity and time dilation depends on a choice of frame to use, so it's frame-dependent.

The reason that I am concerned about this detail is that I have been telling people on this forum that they have to analyze an entire scenario from one single frame of reference at a time. If they analyze one observer in one frame and another from another frame, we can get all kinds of apparent paradoxes.

It's usually good advice for beginners to analyze from one frame at a time, but you can use multiple frames to analyze different parts of a single problem as long as you're careful; for example, you could use one frame to calculate twin A's proper time between the two meetings, and a different frame to analyze twin B's proper time between the two meetings. What apparent paradoxes are you thinking of here?

But if this is true, then how can the Twin Paradox (in which it is stated that each observer observes the other one's clock as going slower than his own)

That's not part of the correct statement of the twin paradox, rather it's a false conclusion people draw by naively thinking that a non-inertial observer should still say that clocks moving relative to him run slower.

be analyzed from a single frame of reference where only one of the clocks is going slower?

One of the clock accelerates and thus changes velocities in all inertial frames, so some frame might say the clock was running slower than the inertial clock before the acceleration but faster after, or vice versa. In any case, all frames make the same prediction about the elapsed time on each clock when they reunite locally. I'm not sure if this answers your question since I don't really understand why you ask "how can the Twin Paradox ... be analyzed from a single frame of reference" in the first place; I don't see why doing so should conflict with your earlier statement about "telling people on this forum that they have to analyze an entire scenario from one single frame of reference at a time".