Alpha Centauri lottery

  • Thread starter Ookke
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  • #1
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A rocket is preparing for journey from Earth to Alpha Centauri. The Earth and Alpha Centauri systems are at rest with each other and have syncronized their clocks to time t=0.


________E__________________________________________________A (distance: 4 ly)
________R

Rocket speed is known to be 0.8c. From EA frame, we calculate that the journey will take 5 years. The A clock will show 5 years and rocket's clock 3 years when the rocket arrives (1).


Rocket starts its engines and accelerates quickly to 0.8 c.

______<-E____________________________<-A (distance: 2.4 ly)
________R

From rocket's perspective, the travel will take 3 years. A's clock will advance only 1.8 years => to be consistent with (1), A's clock has to show 3.2 years after the rocket has started its engines.

Ok so far, but now the rocket driver has second thoughts and stops. We are again in situation

________E__________________________________________________A (distance: 4 ly)
R

A's clock seems to show t=0 again.

Needless to say, the rocket can accelerate and stop again any number of times. From R's perspective, during acceleration A's clock advances 3.2 years; during braking, the A's clock gets back the same 3.2 years.

Say, a great lottery is drawn in Alpha Centauri at t=1 years. Its winner will get financically very independent, possibly happy too. During every rocket acceleration, the lottery is drawn; during every braking, time is reversed. Of course the rocket cannot directly observe this, but in principle,
this is really happening.

When accelerating and braking back and forth, will the same person/alien will every time? Will the lottery numbers be the same? If yes, should we believe in destiny? If not, do the several winners each continue their lives somewhere in the timespace?
 

Answers and Replies

  • #2
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no clock actually changes. but a line of synchronized clocks stretching from earth to alpha centauri would APPEAR to the rocket to be out of synch (even after you take light travel time into account).
 
  • #3
3,962
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... During every rocket acceleration, the lottery is drawn; during every braking, time is reversed. Of course the rocket cannot directly observe this, but in principle, this is really happening.
The person onboard the rocket can not see the lottery numbers and then arrive before the lottery numbers are drawn so there is no way for him to cheat and win the lottery. Transmission of information is limited to the speed of light so there is no way even in principle for the rocket man to see the lottery results and arrive before the draw, unless he can exceed the speed of light (which is very difficult :P). You acknowledge that when you said "Of course the rocket cannot directly observe this".
 
  • #4
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even though the clocks on earth and alpha centauri are synchronized, a person on earth looking through a telescope would see alpha centauri's clock having a different value. but when light travel time and the distance between them is compensated for then they are synchronized. when the rocket suddenly accelerates to relativistic speed then if he looks through a telescope at alpha centauri, he will see the same time that a person on earth would see but because he perceives the distance between himself and alpha centauri to be different then he will perceive that the clocks are not synchronized.

but at no point does any clock actually change.
 
  • #5
russ_watters
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during every braking, time is reversed.
No, it isn't. He'll see clocks on the planet speed up and slow down as he accelerates and decelerates, but at no time will he see those clocks go backwards. For that, he'd have to be traveling away from Alpha Centuari at greater than C.
 
  • #6
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It's not about seeing here, but knowing (calculating, determining) what time is at a distant place. When the rocket moves, it calculates the clock time at Alpha Centauri to be t=3.2 years. When the rocket is at stop, it calculates the Alpha Centauri time to be t=0.

Is it all wrong to say that during braking the rocket calculates Alpha Centauri time to go backwards? Or how should it be explained that time, which was t=3.2 years, seems now to be t=0.
 
  • #7
3,962
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It's not about seeing here, but knowing (calculating, determining) what time is at a distant place. When the rocket moves, it calculates the clock time at Alpha Centauri to be t=3.2 years. When the rocket is at stop, it calculates the Alpha Centauri time to be t=0.

Is it all wrong to say that during braking the rocket calculates Alpha Centauri time to go backwards? Or how should it be explained that time, which was t=3.2 years, seems now to be t=0.
It is about seeing if you want to win the lottery ;)

Say we had another star called Beta Centauri that is exactly the distance away as Alpha Centauri but in the opposite direction. As soon as you accelerate towards Alpha Centauri you calculate the clocks on Alpha have advanced 3.2 years relative to yours and the clocks on Beta Centauri have regressed 3.2 years. There is no way to actually observe these times and there is no way to use the theoretical time reversal of the time on Beta Centauri when you accelerate or on Alpha Centauri when you stop for time travel or winning lotteries.


However, if you had a very good telescope and if you could exceed the speed of light, you could accelerate away form Earth and observe dinosaurs roamng about on the surface of the Earth.
 
  • #8
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Hi kev, sorry about going on around this :)

As soon as you accelerate towards Alpha Centauri you calculate the clocks on Alpha have advanced 3.2 years relative to yours and the clocks on Beta Centauri have regressed 3.2 years. There is no way to actually observe these times and there is no way to use the theoretical time reversal
Yes, exactly like this. But about theoretical time shiftings, do you agree on this:
- during acceleration, the rocket observes the time in Alpha Centauri going 3.2 years forward (since usually in Relativity "observing" does not require "seeing", I won't require it either. Calculating will do: the time advancing is real)
- during braking, AC time goes 3.2 years backwards
- during another accreleration, AC time goes 3.2 years forward again

If we have two separate accelerations, do the things in Alpha Centauri proceed exactly the same way? Including the free will of Alpha Centauri citizens, and quantum mechanics, will these 3.2 year periods in Alpha Centauri nevertheless be identical.
 
  • #9
russ_watters
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If we have two separate accelerations, do the things in Alpha Centauri proceed exactly the same way? Including the free will of Alpha Centauri citizens, and quantum mechanics, will these 3.2 year periods in Alpha Centauri nevertheless be identical.
As far as Alpha Centuari is concerned, there is only one timeline and it continues normally.
 
  • #10
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As far as Alpha Centuari is concerned, there is only one timeline and it continues normally.
I don't think there should be multiple timelines either.

This forum isn't for discussing about validity of Relativity, but I can't help thinking that the relativity of simultaneity is just a mathematical trick to make dilation/contraction calculations consistent. It's not real.

If it were real, we had to accept that from rocket's point of view the Alpha Centauri time really goes backwards during braking. This idea obviously doesn't get support, and I don't advocate it either.

There is no harm done if the rocket calculates Alpha Centauri time to be t=3.2 years when moving, but this is just another calculation that can well be disputed. There is no way to check it physically, i.e. by experiment.

I'm beginning to think that "measuring" time at distant places is not only relative, but completely impossible. Time is local.
 

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