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Relativity Scenario Question

05/10/2012 7:33 AM

This is something I have wondered about for a long time but my understanding of the time dilation effect predicted by the general theory of relativity is very poor.

Can anyone help?

Here is the scenario; You have a space ship equipped with a drive system that can accelerate the ship at a constant one gee (roughly 10 meters per second per second)

You set up a relay station to beam either a RF signal or a laser beam containing your favorite radio station to your ship.

I calculate that accelerating at one gee you would attain 99% of the speed of light in just under one year. At which point you switch off the drive and coast weightless for another year, you then turn around the ship 180 degrees, switch on the drive and decelerate at one gee until your velocity is zero (ie one year later)

The big question is; what would you hear at;

A. The acceleration period.

B. The coasting phase.

C. The decelerating phase.

And a supplemental question; how much time would have passed on Earth relative to your own ships clock showing three years have passed.

Any answers greatly appreciated.

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#1

Re: Relativity scenario question.

05/10/2012 7:39 AM

Units failure alarm! Acceleration has dimensions of [length]/[time]^2. Arroooooooooooooogah!

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#2
In reply to #1

Re: Relativity scenario question.

05/10/2012 7:54 AM

10 meters per second per second (which is what he stated) IS acceleration (m/s2).

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#3
In reply to #2

Re: Relativity scenario question.

05/10/2012 9:16 AM

"Should have gone to Specsavers."

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#10
In reply to #2

Re: Relativity scenario question.

05/10/2012 8:02 PM

Bazinga!

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#4

Re: Relativity Scenario Question

05/10/2012 2:19 PM

At 10 m/s/s your calculated time to reach 99% C is pretty far off.

At that rate of acceleration you reach 99% C at about 5.03 years ship time and 13.34 years on Earth.

If you performed the maneuver you suggested with the acceleration phase to 99% C, coasting phase, and deceleration phase to zero V, after all that time what you would hear would probably be the radio station going off the air.

The total elapsed passage of Earth time would be just over 30 years and your ship clocks would say about 11 years have passed.

What you would hear would be the same thing we see when observing the universe. There would be a perceived non-linear red shift over ship time as you receded from Earth under acceleration, followed by a constant red shift in frequency while coasting, then a non-linear redshift in the opposite direction as you decelerated.

Your radio station would soon shift off the original receiver's set frequency as you travel relativistically.

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#5
In reply to #4

Re: Relativity Scenario Question

05/10/2012 2:47 PM

Is it time dilation that accounts for the difference in between what the OP calculated for acceleration time and yours?

EDIT: It has been quite some time since I've looked over those equations and came up with 6.7 years... probably my error. I'm sure you're right.

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#6
In reply to #5

Re: Relativity Scenario Question

05/10/2012 2:59 PM

I posted both ship time and Earth time for constant acceleration at 10 m/s/s until V = .99C.

What equation did you use?

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#7
In reply to #6

Re: Relativity Scenario Question

05/10/2012 3:08 PM

I used...

V = a * t / sqrt [ 1 + (( a * t)/c)^2 ]

v = velocity at time t

a = acceleration

t = time

c = speed of light

Like I said, it's been a long time since I've looked at the actual equations so I may be applying things incorrectly.

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#8
In reply to #7

Re: Relativity Scenario Question

05/10/2012 4:19 PM

That looks correct for coordinate time.

As a function of proper time it would be: v(T) = c tanh(g T/c)

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#9
In reply to #8

Re: Relativity Scenario Question

05/10/2012 5:54 PM

In which case, I get the same. Thanks!

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#14
In reply to #5

Re: Relativity Scenario Question

05/11/2012 12:09 PM

"Is it time dilation that accounts for the difference in between what the OP calculated for acceleration time and yours?"

Indeed, it is. The OP apparently calculated the time for 0.99c the Newtonian way, giving around 1 year, because 1g ~ 1 light year per year squared. Incidentally, this is also what will happen if the acceleration is kept at 1g in Earth coordinates rather than according to the ship's accelerometer.

With the approximation 1g ~ 1 ly/y^2, i.e. a ~ 1, the equations become exceptionally simple, because in such units c = 1 ly/y, hence:

v(t) ~ t / sqrt [ 1 + t2] and v(T) ~ tanh(T)

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#15
In reply to #14

Re: Relativity Scenario Question

05/11/2012 12:25 PM

I like that! Thanks for the response!

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#12
In reply to #4

Re: Relativity Scenario Question

05/11/2012 9:13 AM

AH wrote: "At that rate of acceleration you reach 99% C at about 5.03 years ship time and 13.34 years on Earth."

I looks like you may have a factor 2 error on both and that ChaoticIntellect may be right with the coordinate time. I got T=2.515 yr and t=6.7 yr respectively. Or am I missing something?

-J

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#13
In reply to #12

Re: Relativity Scenario Question

05/11/2012 9:39 AM

You are right! Think of it as an off-by-one problem. That is. one bit left shifted. :)

The acceleration calculation was off by a factor of two. The time calculations for the coasting phase should be correct.

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#11

Re: Relativity Scenario Question

05/11/2012 5:58 AM

The big question is; what would you hear at;

A. The acceleration period. your radio station, with incremental increase in signal delay

B. The coasting phase. your radio station with incremental increase in signal delay

C. The decelerating phase. your radio station with incremental decrease of the signal delay

Rationale: 'C' is only approached, never attained; direction of travel is a straight line; and the laser/ radio wave is already at 'C', so the vehicle never 'overtakes' the signal. Any vehicle capable of approaching 'C' would have on-board frequency compensation /adjustment for any shift away from linear in any case. While you are coasting, the distance is from the transmitter is constantly increasing.

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#16
In reply to #11

Re: Relativity Scenario Question

05/11/2012 12:46 PM

"The big question is; what would you hear at; ..."

The delay is one thing, but the real issue is that the frequency of the carrier signal would have decreased by a factor 14 when you reach 0.99c. During the cruise phase it would remain constant, increasing steadily during the turn-around acceleration, until it is a factor 14 higher than the original. One would need quite a fancy tuner to stay in connection during these accelerations...

If you could somehow stay tuned, the music and voice frequencies would also have gone down and up by these factors. What would it have sounded like?

-J

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#17
In reply to #16

Re: Relativity Scenario Question

05/14/2012 2:40 AM

I'm sure I've heard that music here on earth just recently....can't remember the name of the DJ....