Comparing Time in Different Galaxies: A Dilemma?

[Janus]

Originally posted by yogi
A little more to add to the above - Janus - your analysis is parallel to that given by Born in his book on SR - but if you go through Born's math you see he made a critical flaw in arriving at the time dilation for the turn around - he use a time period for the acceleration that corresponded with the total outward time interval- but this period did not involve an acceleration - that took place only during the turn around - you cannot make up for the acumulated loss of time that occurs with years of near c velocity travel with a short period of turn around acceleration (even if acceleration per se altered clock rates) - the formulas derived for the acceleration time dilation are typically based upon some metaphore like having a clock in the nose of an accelerating spaceship and one in the tail - and both are subjected to the same acceleration field (they are both in the same vehicle) so there is a difference in the rate at which signals arrive from front to end and vice versa - this gives the correct formula for time dilation in a G field (somewhat surprizingly) but as I previously said - clocks subject to acceleration by some means other that a G field do not exhibit time dilation.

Again, no one is saying that acceleration effects clocks per se (or that velocity effects clocks per se either) We are saying that relative velocity effects how clocks measure each other, and acceleration felt by one clock effects how it measures others along the line of the acceleration it feels.

With the astronaut during turnaround, it is not only the strength of the acceleration he feels, but the distance and direction from him of the other clock he is measuring, that effects how he measures that other clock's rate.

Thus for an astronaut that has drifted at near c for years will be very far away from Earth, and the combined effect of this increased distance and the acceleration he feels during turnaround that will account for the speed up in time rate he sees for Earth. The longer he drifts, the further Away from Earth he is at turn around, and the greater the rate increase he sees in Earth's clock. So yes, a short turnaround can make up the difference.

So what happens is that from Earth the following is measured:

Twin 2 accelerates up to near c, coast for a while to some distance as measured form Earth, turns around and comes back. During this perod of The Earth observer will see twin 2's clock run slow for at varying rates due to the relative velocity of Twin 2 alone. (no additional time dilation is seen due to Twin 2's acceleration)

Twin 2 measures the following:

As he feels the acceleration and the distance between him and the Earth increase, he will measure the Earth's clock run slow due to the Increased relative velocity and the aceleration he feels at a changing rate. (since he is close to the Earth during this period, the acclerations effect on his measurements will be fairly small)

The force felt to acceleration is cut off, and now he measures only time dilation due to relative motion. The distance beween him and the Earth will increase unitl he reachs turnaround point. But because of length contraction, the distance between him and Earth will be less by his measurements than by the Earth's measurements. (If he coasted at .866c it will be just about 1/2 the distance as measured from Earth.)
Thus both he and the Earth will agree as what his clock reads at turnaround. (The Earth will say that he traveled a distance of x at .866c, and took T time to do so, but because twin 2 clock underwent time dilation it will only read 1/2 T. Twin 2 will say that the distance between the Earth and him increased to a distance of 1/2 x at .866c and it took, by his clock 1/2 T to do so. )

Up until now, twin 2 wil measure less time as passing on Earth than for him.

But now, as he feels the force due to turnaround, The Earth is in the opposite direction with respect to this force than it was earlier, and much further away. He will measure the Earth time rate as moving very fast during this period.

Once again, the force will stop and he will only measure the time dilation due to relative motion (earth clock running slow.)

The force of acceleration is felt again as he brakes, and he measures the combined effect of acceleration and relative velocity, both decreasing as the distance to Earth decreases and the relative velocity lowers. This continues until twin 2 and Earth are at rest wrt each other again.

Due to the various measurments each made of each other clocks for the duration, each will agree who experienced less time and by how much. However, they won't agree as to how that time difference was reached. And neither is more correct than the other.

 

[yogi]

Good Post Janus - and I agree that one can arrive at the correct time discrepancy between the two clocks back on Earth by this means - but you can also get to the same result by the much simplier hypothesis that velocity with respect to space alters the actual rate at which time passes - moreover, in the case where there is an inbound traveler who merely observes the outbound twin's clock - there is a discontinuity in the analysis - I know the standard (if there is such a thing) explanation of the lost time -

Take the case of the one way traveler - he passes Earth at 0.8c and syncs his clock as he passes by - then continues at the same speed straight to Alpha Centuri - how much will he have aged when he arrives? - how much time will have accrued on the clock back on earth?

 

[Janus]

Originally posted by yogi
Good Post Janus - and I agree that one can arrive at the correct time discrepancy between the two clocks back on Earth by this means - but you can also get to the same result by the much simplier hypothesis that velocity with respect to space alters the actual rate at which time passes

No, you don't get the exact same results. For example in relativity if an astronaut throws a ball forward, he only has to account for the ball's relative motion to him to determine its time dilation and length contraction wrt to hiim it doesn't matter how fast you consider the astronaut as moving himself. In the absolute motion to space notion you have to consider the ball's relative motion to space and the astronauts relative motion to space and compare the ratio. Thus if the astronaut is traveling very near the speed of light, even a small diference in velocity between him and the ball will cause a large difference in time rate between the two as measured by the astronaut). In Relativity a smal difference of velocity between the two would only cause a very small time rate difference between the two as measured by the astronaut.

A practical example is done everyday in particle accelerators. Particles are accelerated in opposite directions to near c and collided. If absolute motion wrt to space was the culprit, you would at times have the Earth's motion through space added to particles going in one direction and subtracted from those going in the other. This would produce an asymetry in the particles' time dilation and energy content. We never see this, we always get symetrical collisions no matter what time of day or year or what direction the accelerators are pointed.

In order for an "absolute motion to space" hypothesis to give the results we actually get, you have to create all kinds of ad-hoc explanations that don't naturally arise from the absolute motion hypothesis. (You to include additional hypotheses)

You then no longer have a "simpler" Theory.

moreover, in the case where there is an inbound traveler who merely observes the outbound twin's clock - there is a discontinuity in the analysis - I know the standard (if there is such a thing) explanation of the lost time -

What discontinuity?

Take the case of the one way traveler - he passes Earth at 0.8c and syncs his clock as he passes by - then continues at the same speed straight to Alpha Centuri - how much will he have aged when he arrives? - how much time will have accrued on the clock back on earth?

He will have aged 3.225 yrs. By his reckoning because the distance from Earth to Alpha C is 2.58 ly( due to length contraction) and that's how long it takes to traverse this distance at .8c

By Earth's reckoning he will also have aged 3.225 yrs, because by Earth time he took 5.375 yrs to traverse 4.3 ly at .8c, but his time rate ran at .6 of Earth time.

 

[yogi]

Janus - Things appear to be symmetrical with respect to the Earth centered reference system - one of the theories that has been advanced is that space is conditioned by the local gravitational field - I brought this up in one of my earlier posts - this explains why MMx and KT experiments fail to detect the Earth's motion relative to local space - but we can still detect the Earth's motion relative to distant light sources such as the CBR and starlight aberration. Gravitation conditioning of space is local - it differs from ether drag - which is disproven by aberration.

There are no experiments that I have come across that distinguish between Lorentz Ether theory and SR - they both lead to the same results - but in the former, time dilation is actual not observed - but the two theories rely opon exactly the same math (derived first as you know by Lorentz). The objection to Lorentz Ether Theory as originally propounded, is that it does require some actual physical deformation - which admittedly is hard to visualize and - as you and others would point out - makes the theory "not simple" But you can arrive at a free space result w/o the hypothesis of physical contraction - if time dilation is actual then length contraction is apparent (consequent to the fact that two observers in relative motion will measure the relative velocity between them as equal to v.


If the Alpha C traveler ages 3.2 years by his own calculation in his own environment (and I don't care what the Earth guy calculates for the traveler). What I am saying is - if the traveler ages 3.2 years when he arrives -and the Earth clock has logged 5 years or whatever when he arrives - how can time dilation not be actual? (The Earth twin can determine when the traveler arrives on Alpha by having the traveler send a light signal and subtract 5 years off his clock when it arrives back at earth). This is the extended lifetime of the high speed muon problem, cloaked in astronomical fiction - I know its possible to weasel-word through it using SR - I am not unfamiliar with the many treatise on the subject - but they do not all agree and in fact there seems to be no official consensus

Several months ago there was a posting on these boards re data from clocks on board the space station. The applet depicted how the on- board clocks were observed to run at different speeds depending their velocity orientation vector as the station moved in its orbit about the earth. How say you on this.