Relativity Scenario Question

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

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

_{"Should have gone to Specsavers."}

Bazinga!

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.

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.

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

What equation did you use?

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.

That looks correct for coordinate time.

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

In which case, I get the same. Thanks!

"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)

I like that! Thanks for the response!

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

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.

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.

"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

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