The quotes below (in blue) are from another thread https://www.physicsforums.com/showthread.php?t=364893&page=5" , but since they are a slight digression from the topic of the original thread, I have decided to continue the conversation in this new thread.(adsbygoogle = window.adsbygoogle || []).push({});

Yes, that it what I am talking about. kev said: ↑Another example. I will call this the gravitational twin's paradox. The twins are initially together at the top of some great tower on a massive body. One twin descends to the bottom of the tower and remains there for some time. Each twin has a clock that emits signals at one second intervals. The twin at the top of the tower sees the clock at the bottom of the tower emit signals at a slower rate than his own clock or in other words he sees the signals from the lower clcok as red shifted. I have seen it argued on this forum that the this is an optical illusion brought about by the "stretching" of the light wavelength of the signal from the lower twin with the implication that the clock of the lower twin is not "really" running slower that the clock of the twin at the top of the tower. However, I guarantee that if the twin at the top of the tower were to descend down to the twin at bottom of the tower at the same rate as the first twin descended, that the twin that had been at the bottom of the tower the longest will have aged the least in a real physical sense...

Austin0 said: ↑I am happy to see that someone else has a problem with this common explanation of wavelength stretching due to transit up the gradient.

It is not just an idea presented in this forum but I have found it in accepted explanations of, for instance ; the red shift of light coming up the gravity well to reach earth.

Where it is proposed to be an in transit effect , happening after emission and no mention of the shift due to dilation of the frequency of the emitting electron due to position in the field. {which you seem to be talking about here]

You might be surprised to know I do know what you are talking about and your reasoning is sound with the given information, but there is actually more to the situation than first meets the eye. Essentially, both phenomena are happening, rather than an either/or situation. The wavelength is increasing in transit AND the frequency is reduced due to physical time dilation of the emitter. Austin0 said: ↑I have brought this up in several threads but the response has been they were just two different descriptions of the same phenomena. It seems to me that if the gravitational effect due to locale is valid , and it seems to be verified to a great degree, the a shift due to transit is not merely superfluous but simply invalid. That if it also occurred then there should be an additive quantitative red shift at the receiver beyond what is calculated and explained by the expected shift at emission. Does this make any sense ??? SO far nobody has seemed to know what I was talking about.

First I will describe a simple physical experiment that could be carried out in a classroom to demonstrate some basic physical principles that are required for the explanation and then I will describe what is "really" happening to a photon as it rises out of a gravitational well and what local observers in the gravitational well actually measure.

The classroom experiment.

Equipment: A flexible track, two steel balls, a tape measure, two clocks and a video camera mounted above the ramp (or a still camera that can be triggered by the steel ball).

Set up: One end of the track is mounted higher than the other end, to provide a ramp of variable curvature for the steel ball to roll down. The tape measure is laid flat on the table the ramp sits on, so that from above the tape measure runs alongside the ramp.

Method: The video camera is switched on and a steel ball is released from the top of the ramp. One second later a second ball is released from the top of the ramp. The video frame as the second ball is released will show the "wavelength" of the two balls, which is the distance the the first ball travels in the one second interval before the second ball is released as measured on the tape measure. The video frame taken as the first ball reaches the end of the track at time T1 will contain the final "wavelength distance" of the two balls. Finally the time T2 that the second ball arrives at the end of the track is recorded. If the track is well supported so that it does not flex and alter the paths as the balls roll down it, then the time (T2-T1) should always be one second, no matter how the track is set up and no matter how the "wavelength" changes during the journey. If the track is set up so that the steepness of the track increases towards the end the wavelength should increase and by some simple analysis it should be be simple to determine that the increase in wavelength is exactly proportional to the ratio of initial average velocity of the two balls to the final average velocity of the two balls.

Conclusions:

1) It is impossible to change the frequency in transit, if two successive balls or (or wave peaks) follow the same path.

2) Any change in wavelength in transit, is always accompanied by a change in velocity of the wave.

(This might make a interesting science fair project for someone).

Photon climbing out of a gravitational well.

Consider two shells in a gravitational well, such that the gravitational time dilation factor (gamma) at shell A low down in the well, is twice the gamma factor at shell B higher up. We know from the Schwarzschild metric that the coordinate speed of light is gamma^{2}and from the experiment described above we know that the physical frequency does not change during transit. Light pulses emitted at 1 second intervals from shell A arrive at shell B at 1 second intervals and the coordinate speed of the light pulses is 4 times greater at B than at A. Therefore the wavelength at shell B is 4 times as long as when it was emitted. However, the rulers of an observer located at shell B are twice as long as the rulers of an observer located at shell A, so B only measures the wavelength to be 2 times as long as the wavelength measured by A lower down. The clocks of observer B are running twice as fast as A's clocks so B measures the interval between pulses to be twice as long as that measured by A and therefore B measures the the frequency of the light pulses to be half that measured by A. So if A measures a frequency of 1 and a wavelength of 1 then B measures a frequency of ½ and a wavelength of 2, so both measure the the local speed of light to be 1 using the equation frequency*wavelength = speed of the wave. In order for both observers to measure an equal value for the local speed of light, it is a requirement that clocks lower down in a gravitational well are physically running slower than clocks higher up and not “just appearing to run slower”.

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# The Physical Meaning of gravitational time dilation

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