Thoughts on so-called Twin Paradox?

Question

So the Twin Paradox is resolved by the fact it doesn't account for the three frames of reference for the traveler (e.g. the ac/deceleration at the turn). Relativity is not proven wrong (not proven right either, but that's a different issue). Fine.

Several explanations talk about the relativisitic doppler effect. For example, traveler sends a signal (like radar) every year (as measured by traveler). To homebody, it appears to come faster or slower due to doppler effect.

However, the relativistic doppler effect refers to the frequency of the wave (radar), not the frequency at which we turn the radar on and off.

The radar signal would be red or blue shifted, which *would* be determined by the relativistic formula. My claim is the "acoustic", not relativistic, doppler effect should apply to the frequency of messages (frequeny of radar turned on/off).

Agree?

Answer 1

Both the observed frequency and the frequency of the signal emissions are the same thing: waves separated in time. The only difference is the time scale. During a signal flash from the spaceship, you might see 300 billion wave crests from the radar go by each second. The flashes themselves can be considered wave crests, or waveform spikes, arriving at the rate of one per year, or almost. Both the frequency of the flashes and that of the quanta in the flash are affected by both Doppler and relativity.

A travelling spaceship moving away from you, sending you radar beeps at intervals of exactly one year of ship's time will be received by you at intervals larger than one year. And you will see them red-shifted, relative to their frequency at their source.

But if you correct for the frequency drop from the Doppler, you notice that there's still a discrepancy. The signals are still arriving little longer apart than the Doppler correction can account for, and, furthermore, the radar wavelength is a little "redder" than it would be if Doppler were the only effect in play.

The discrepancies in both the radar frequency and in the intervals at which the radar signals come are explained by special relativity.

Answer 2

No. Exercise for the brain. If I understand your question correctly, you are referencing the differential speed between the traveler and earth. Hense, the blue or red shift Doppler effect. If the time of both traveler and earth were equal, the frequency of the radar AND the turn/on-turn/off frequency would be equally displaced. However, and this is where it starts messing with the mind, if the traveler is traveling at great enough speeds or experiencing a larger gravitational field - his clocks run slower than ours, and the difference in frequency we receive has both the Doppler effect AND the actual frequency being transmitted (Hz - formally cycles per second. Because his seconds are longer than ours, his tranmission frequency will be less right from the source.) And the "twin paradox" lives to boggle yet another mind.

Answer 3

No, because the acoustic doppler formula applies to acoustic waves, which travel in a material medium with a defined frame of rest (the frame in which the medium has zero velocity). Light travels in vacuum, which has no rest frame of motion.

Turning on and off any electromagnetic signal (light, radar, infrared, x-rays, etc.) is superposing two electromagnetic frequencies, one at a very low frequency and the other at a very high frequency. Just because the very low frequency happens to have the same frequency as acoustic waves does not make the EM waves at that frequency acoustic; they are still EM waves traveling in a vacuum, not pressure waves traveling in a material medium.

Answer 4

First I must commend and thank you for approaching a topic so controversial in the theories applied to it as well as one so fascinating in its implications.

Give this exercise a go: Please try to think outside the constraints of convention and "common sense." There is no "twin" therefore there is no paradox; the particle is the same, not two different particles derived from another.

This will certainly ruffle some feathers because the issues of space and time (Relativistic or otherwise) will undoubtedly rear their ugly heads. However they are not applicable when referring to the particle itself. Hence the seemingly impossible display of faster than light communication.