SR and classical Doppler shift

[shadowofra]

Wow. This is like questioning dogma in old times. Get properly done for it.

 

[JesseM]

If I am interpreting your question correctly, you're commenting on the fact that clocks run at the same rate on all galaxies that are exactly comoving with the Hubble flow, which is correct.

Actually I don't think shadowofra's question had anything to do with galaxies or cosmology, it seemed to just be about the SR twin paradox. If that's right, the answer to this question is that the classical Doppler effect alone cannot account for the amount a clock moving away from you seems to slow down--the relativistic Doppler effect predicts that it will appear to slow down even more, and that extra slowdown is due to actual time dilation. Another way of putting this is that time dilation is still present after you correct for the fact that the light from different events took different amounts of time to reach you.

 

[shadowofra]

Correct JesseM, maybe this accounts for the difference in shifts nutgeb originally referred to. The very non-21 century math question then is why? Further if one object remains stationary and multiple objects move at various near-C velocities relative to it who's clocks change nd on what physical basis? Is it a dilation and constriction of rotational systems (egs constituent atoms) that alter the actual frequency of event occurrence at near-C? Is the ubiquitous gravitation and its imagined cousin inertia, equal in all directions due to infinite universal mass offset by massive (distance)^2 in all directions, the new "ether"?

Again, no elegant math here but maybe helpful musings in nutgebs quest for non-math physical meaning.

 

[JesseM]

Correct JesseM, maybe this accounts for the difference in shifts nutgeb originally referred to. The very non-21 century math question then is why? Further if one object remains stationary and multiple objects move at various near-C velocities relative to it who's clocks change nd on what physical basis?

There's no such thing as objective velocity in relativity--something moving at "near-C" in one inertial frame will be at rest in some other inertial frame, and all inertial frames are considered equally valid in relativity. So by the same token, there is no objective answer to the question of which of two clocks is running slower at any given instant. But there is an objective answer to the question of how much time elapses on a clock between two events on its worldline, like the event of it leaving Earth and the event of it returning (or arriving at some other planet)--regardless of which inertial frame you use to calculate this elapsed time, you get the same answer. So it is an objective truth that if two clocks depart from a single location and later reunite at a single location, then if one of the clocks moved inertially while the other clock accelerated at some point in its journey, the clock that accelerated will always have elapsed less time.

 

[shadowofra]

Thanks JesseM I'll need to educate myself on worldlines. Your acceleration point is interesting as this can be measured absolutely without external reference. Also interesting in relation to C as acceleration could continue indefinitely without limit.

 

[JesseM]

Thanks JesseM I'll need to educate myself on worldlines. Your acceleration point is interesting as this can be measured absolutely without external reference. Also interesting in relation to C as acceleration could continue indefinitely without limit.

Yup, but note that there is a difference between "proper acceleration" and "coordinate acceleration"--a ship's proper acceleration determines the actual G-forces felt on board, while coordinate acceleration determines how its velocity changes relative to some fixed choice of inertial observer calculating the ship's motion in her own inertial rest frame (proper acceleration and coordinate acceleration coincide instantaneously if you pick the inertial frame where the ship is instantaneously at rest). A ship could experience the same proper acceleration forever, but relative to some inertial observer the coordinate acceleration would be continually getting smaller in magnitude, so the ship would never actually reach light speed in that observer's frame (or in any other inertial frame)--see http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html . On the other hand, if it were somehow possible to give a ship constant coordinate acceleration until it reached light speed, the proper acceleration (and thus the G-forces felt on board) would go to infinity as it approached light speed, and the energy required to maintain this ever-increasing proper acceleration would also go to infinity (which is one way of understanding why it's impossible to accelerate to light speed).