
#1
Apr511, 09:16 PM

P: 7

Suppose you have two ships departing from Earth at the same time, Ship #1 and Ship #2. Both ships depart Earth in the year 2000, both in the same direction from earth, and both Ships return to Earth in the year 2020, so 20 Earth Years for BOTH ships.....
Ship #2 does something somewhat different from Ship #1, you'll see From Earth's Reference Frame: Ship #1 Cruises at a Velocity of 86.6025% of C, which is a Lorentz Factor of 2.... for half the 20year duration.... then the ship returns to Earth. Based on Twin Paradox, the ship's clock ticks half of 20 years.... so the ship ages 10 years. Ship #2 Cruises at the same velocity as Ship #1, but only for the first 6 Earth Years of time. Between Years 7 thru 10: After 6 years time, Ship #2 gains additional velocity and passes ahead of Ship #1 at a Velocity of 98.7433% of C with respect to Earth (Lorentz Factor of exactly 7). Then at some point in time, Ship #2 deaccelerates to 0 km/h with respect to Earth and waits patiently for Ship #1 to catch up to Ship #2. Ship #1 catches up to Ship #2 after 10 Earth Years Time. Note Ship #1's Reference Frame Between But based on U  V / (1 + U*V), the Ship #2 was moving ahead of Ship #1 at 86.6025 of C, Lorentz Factor of 2.... and then would have appeared to head back towards ship #1 also at 86.6025% of C. After 10 Earth Years: Both Ship #1 and Ship #2 return to Earth side by side at 86.6025% of C with respect to Earth, arriving home to Earth in the year 2020.... Now looking at Years 7 thru 10, however much Ship #1 was aging, Ship #2 would be aging half as much, because with respect to Ship #1's frame of reference, Ship #2 accelerated to Lorentz Factor 2 speed.... then moved back towards ship #1 at Lorentz Factor 2 speed (while ship #2 was moving 0 with respect to Earth it was moving backwards with respect to Ship #1)....... Based on the same logic as the Twin Paradox.... this would result in a situation where Ship #2 aged one year less than Ship #1, because during the 4 Earth Years Ship #2 parted from Ship #1....... Ship #1 would age 2 years and Ship #1 would have aged half of that... 1 years less aging than Ship #2..... or is this wrong? During years 7 thru 10, Ship #1 did not exert any force as it kept its contant cruising velocity. The same would hold true for Earth.... eventhough they were traveling at different velocities. So here is what gets confusing to me. From Ship #1's Reference Frame: It would appear that between Earth years 710, Ship #2 spent 50% of the time moving farther away from Ship #1, and 50% of the time moving back towards Ship #1.... for with respect to the ship.... the relative speed of Ship #2 was 86.6025% of C From the Earth's Reference Frame: I would appear that between Earth years 710, Ship #2 spent much more time moving away from Ship #1 compared to the time it took Ship #1 to catch back up to Ship #2. Ship #2 would have appeared to move 98.7433% of C away from Earth while Ship #1 was cruising at 86.6025% of C away from Earth..... a velocity difference of only 12.1408% of C....! Then when Ship #2 stopped moving and waited for Ship #1 to catch up, this would have appeared to be a movement of 86.6025% of C for BOTH Earth and the ship... so what's confusing to me is given the Earth AND Ship #1 are not accelerating/deacclerating since only Ship #2 is exerting force and shifting in speeds.... Why does it make sense relativity wise that Earth and Ship #1 would disagree on the PERCENTAGE of duration it took Ship #2 to move farther away from Ship #1... VS. the percentage of duration the ship #1 was moving closer to Ship #2....? Can someone explain this discrepancy or correct me if my assumptions are incorrect? Thanks! 



#2
Apr511, 09:24 PM

Mentor
P: 16,484

This scenario does not disprove relativity. It only proves that you can make a scenario which is so absurdly complicated that it is confusing for a novice to describe or analyze.
The easiest way to approach this problem is to draw a spacetime diagram in the Earth frame and clearly label the t and x coordinates of each acceleration/deceleration event. Then simply use the spacetime interval formula to determine the aging along each segment. 



#3
Apr511, 09:34 PM

P: 7

My guess is that perhaps nothing can be said for time scales of vehicles moving at different velocities to be proportional to each other on a percent scale of total time elapsed..... only that the end results at the end of 20 years accumulate to the proportions that they are......
and so it cannot be determined in absolute time what percentage of clock ticks occurred before the Uturn of Ship #1, the Deacceleration of Ship #2.... none of the above.... if this isn;t true what I'm saying here..... then I can't think of another answer On another note, is it written down anywhere that this is true? Given Obect #1 Is traveling with Respect to the Earth at Lorentz Factor X And Object #2 Is Traveling with Respect to Object #1 at Lorentz Factor X Then Object #2 is Traveling with Respect to the Earth at Lorentz Factor 2*(xsquared) 1 I discovered this, I wonder if it is written anywhere or can I get credit for this equality. You can test it out and you'll see I'm correct. 



#4
Apr511, 09:50 PM

Mentor
P: 16,484

Does this scenario disprove relativity?
There is no absolute time, so obviously you cannot determine anything in absolute time.
Just go through the exercise I suggested to solve your scenario completely. 



#5
Apr511, 10:19 PM

Sci Advisor
P: 8,470

Perhaps you want to change the thoughtexperiment so that ship #2 initially accelerates to (0.866025c + 0.866025c)/(1 + 0.866025*0.866025) = 0.989743c relative to the Earth, then comes to rest at the turning point and waits for ship #1 to catch up, in which case in ship #1's frame ship #2 initially moves away at 0.866025c and then turns around and moves back towards ship #1 at 0.866025c until they meet at the turning point? 



#6
Apr511, 10:34 PM

P: 7

whoops I meant ship 2 Velocity with respect to earth would be 0.9897433186.... typo... I left out a nine.... it should then be exactly the same as the .8606 C
So knowing this, it would appear to Ship #1 that an equal amount of ship #1 clock tickings were during the getting surpassed by ship #2 as the time catching up to the ship.... Using intuition, no graph, I think what is happening here is that Ship #1's time relationship with Earth is not changing between Year 06 and 710..... The disagreement over the time of Uturn of Ship #2 purely has to do with Earth's relationship to Ship #2 in spacetime differing from Ship #1's relationship to Ship #2 in spacetime.... explained by a disagreement over how much Ship #2 is accelerating/deaccelerating........... from the perception of Earth compared to Ship #1's perception However, all 3 clocks are out of sync with each other until they meet each other so I can't use Earth's clock to measure aging of the ship's clocks except note that the total times accumulated at the end are what they are.... and trusting the formulas. 



#7
Apr511, 10:51 PM

Sci Advisor
P: 8,470

So is your question just about the fact that the first leg of ship #2's trip lasts 3.5 years and the second leg only lasts 0.5 years in the Earth frame, while in ship #1's frame both legs last for an equal time of 1 year? If that is your concern, I suggest you look into the relativity of simultaneity (also see this page for more info), which says that different frames disagree about which pairs of distant events happened "at the same time" (simultaneously). Specifically, in ship #1's frame the event of ship #2 coming to rest relative to the Earth happens simultaneously with ship #1's clock showing a time of 4 years and Earth's clock showing a time of 2 years, but in the Earth's frame the event of ship #2 coming to rest relative to the Earth happens simultaneously with ship #1's clock showing a time of 9.5/2 = 4.75 years and Earth's clock showing a time of 9.5 years. 


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