Question about relativistic acceleration:

Can anyone here answer a question in relativistic acceleration? My question is this: You have a space craft, from zero relative velocity, it starts accelerating at 1 standard g, 9.8 meters per second per second, and so forth.

If relativity was not a factor, it would reach the speed of light in about one year of such acceleration.

My question is, if at the start you feel your normal weight, like I weigh 100 Kg, later on in that year of acceleration when you start getting really close to c, say 0.9c, at that velocity, ship time makes you feel like you are going about 2X c. So at 0.9c, you would reach Alpha Centauri in about 2 years instead of 4.4 years. That would be onboard ship time, 4.4 years still goes by on Earth.

So when you are at 0.9c and still the craft is getting the same thrust it had at the start, if you had a scale, would you still weigh 100 Kg like you did at the start or would it be different now?

Originally posted by sonhouse
Can anyone here answer a question in relativistic acceleration? My question is this: You have a space craft, from zero relative velocity, it starts accelerating at 1 standard g, 9.8 meters per second per second, and so forth.

If relativity was not a factor, it would reach the speed of light in about one year of such acceleration.

My question is, if at ...[text shortened]... ad a scale, would you still weigh 100 Kg like you did at the start or would it be different now?

According to the theory the same. In your instantaneous inertial frame you are stationary, everything else is moving towards you at 0.9c (on average).

The problem is the interstellar medium is length contracted so it appears more dense on board, at 0.9c the gamma factor is 2.3 (you have to multiply this by the density in your initial frame, there is also a pressure term, but I'm ignoring that as I'd guess it is small). If you carried on past Alpha Centauri eventually it would appear so dense it would create drag, causing your acceleration to drop and your rockets hull to heat up (a lot).

Originally posted by DeepThought
According to the theory the same. In your instantaneous inertial frame you are stationary, everything else is moving towards you at 0.9c (on average).

The problem is the interstellar medium is length contracted so it appears more dense on board, at 0.9c the gamma factor is 2.3 (you have to multiply this by the density in your initial frame, there is ...[text shortened]... t would create drag, causing your acceleration to drop and your rockets hull to heat up (a lot).

Not sure where you get the heating up thing, but if you had a thruster that put out 1 g of thrust at low velocities, wouldn't the given thrust at .9c mean that the actual g force would be less than half what it was at non relativistic velocity and therefore your weight would be noticeably less, 2.3X less, where now I weigh 43 Kg instead of 100 which is what my scale showed me when first we started the engines? Wouldn't that mean the actual g force would approach zero as the ship gets closer to c? Given a constant thrust of X newtons?

Originally posted by sonhouse
Not sure where you get the heating up thing, but if you had a thruster that put out 1 g of thrust at low velocities, wouldn't the given thrust at .9c mean that the actual g force would be less than half what it was at non relativistic velocity and therefore your weight would be noticeably less, 2.3X less, where now I weigh 43 Kg instead of 100 which is what ...[text shortened]... g force would approach zero as the ship gets closer to c? Given a constant thrust of X newtons?

No, you've missed the point. Say you start out with zero speed relative to the sun, then by time you are moving at 0.9c in your own instantaneous reference frame you are stationary and the sun is moving away from you at 0.9c. So you will still be accelerating at 1g. An observer stationary w.r.t. the sun will think your acceleration has reduced, but they are in a different reference frame.

Originally posted by DeepThought
No, you've missed the point. Say you start out with zero speed relative to the sun, then by time you are moving at 0.9c in your own instantaneous reference frame you are stationary and the sun is moving away from you at 0.9c. So you will still be accelerating at 1g. An observer stationary w.r.t. the sun will think your acceleration has reduced, but they are in a different reference frame.

But the effect of that acceleration is to not increase velocity at the same rate, right? If I am producing, say 1000 tons of thrust at zero velocity and 1000 tons of thrust at 0.9c, then that thrust is pushing against 2+ times the mass, wouldn't that result in a slower increase in velocity?

Originally posted by sonhouse
But the effect of that acceleration is to not increase velocity at the same rate, right? If I am producing, say 1000 tons of thrust at zero velocity and 1000 tons of thrust at 0.9c, then that thrust is pushing against 2+ times the mass, wouldn't that result in a slower increase in velocity?

This is frame dependent. We need three observers, You in the spaceship, me in a space station which we'll assume is stationary, and one other moving away from me at a constant 0.9 c. Initially you and I are stationary with respect to each other. You switch on your boosters and accelerate away at 1 g. I stay put. As you get to 0.9 c relative to me you will for an instant be stationary with respect to the Third Man. At that moment you and the third man will agree that your acceleration is 1 g. I will think it is less - relative to me you cannot accelerate past the speed of light.

Suppose you carry on accelerating at constant thrust until you are doing 0.9 c relative to the third man, then, because of the way velocities add you will be doing 0.9945 c relative to me (See page on "velocity addition formula" in Wikipedia).

Originally posted by sonhouse
But the effect of that acceleration is to not increase velocity at the same rate, right? If I am producing, say 1000 tons of thrust at zero velocity and 1000 tons of thrust at 0.9c, then that thrust is pushing against 2+ times the mass, wouldn't that result in a slower increase in velocity?

I think what you are missing, is that this is relativity we are talking about. So the question is: velocity with respect to whom?

Originally posted by sonhouse
Can anyone here answer a question in relativistic acceleration? My question is this: You have a space craft, from zero relative velocity, it starts accelerating at 1 standard g, 9.8 meters per second per second, and so forth.

If relativity was not a factor, it would reach the speed of light in about one year of such acceleration.

My question is, if at ...[text shortened]... ad a scale, would you still weigh 100 Kg like you did at the start or would it be different now?

Ok, you are sitting in your spacecraft having accelerated to 0.9c.

The Lorentz factor [given by 1/((1/((1-((0.9C^2)/(C^2)))^(1/2)) ] is ~ 2.294
[or the inverse ~0.4359]

So you go to measure your weight. Your relativistic mass is 2.294 times your initial
mass, so your mass is now 229.4 kg.

BUT.

Weight is a measure of force, not mass. Your spaceship is now accelerating at 0.4359 g
and not 1 g, because the spaceship masses in at 2.294 times it's initial weight.
So you are accelerating slower, but mass more... and so weigh exactly the same.

And, you think you are still accelerating at 1 g, because acceleration is change in velocity
over time. You are accelerating at 0.4359 times your former rate, but time for you is also
passing at 0.4359 times it's former rate [or 2.294 times slower].

Your engines are still firing out the same mass per second at the same exhaust velocity
as YOU measure it. And so still appear to YOU to be generating 1 g of acceleration.
But from a [relative] stationary external observer they are firing out 0.4359 times the
mass per second, and generating 0.4359 times the thrust.


Also, while it appears to you that you only take ~2 years to get to Alpha Centauri, you don't
think you are going faster than light, because you measure the distance between you and
Alpha Centauri to be shrunk, so you think you only travelled 0.4359 times the distance as measured
by an external observer. So you thus never measure your speed [relative to objects around you]
to be greater than C.

Originally posted by googlefudge
Ok, you are sitting in your spacecraft having accelerated to 0.9c.

The Lorentz factor [given by 1/((1/((1-((0.9C^2)/(C^2)))^(1/2)) ] is ~ 2.294
[or the inverse ~0.4359]

So you go to measure your weight. Your relativistic mass is 2.294 times your initial
mass, so your mass is now 229.4 kg.

BUT.

Weight is a measure of force, not mass. Your s ...[text shortened]... r. So you thus never measure your speed [relative to objects around you]
to be greater than C.

Thanks for that analysis. I knew the contraction formula, have it programmed into my old TI 84, but with what you said, I understand the implications a bit better, thanks everyone!

I was thinking about the clock situation and it occurred to me that a time hack signal sent from Earth to your ship, say you were on your way to Alpha Centauri, a really great first interstellar stop since you get three stars for the price of one, but besides that, if you lasered or RF'd a time hack signal from Earth, even though you would have to frequency shift at the receiver to get the signal, 1, just the change in frequency from a known accurate frequency can tell you how close you are to c and the time hacks sent could tell you exactly how far apart your clocks are and thus you know exactly how much longer your ship time would take to get to A.C. If TV shows were beamed up you would have to watch a LOT of TV to keep up with whatever series you were hooked on since Earth clock would be going a couple times faster than ship clock time!

Originally posted by sonhouse
I was thinking about the clock situation and it occurred to me that a time hack signal sent from Earth to your ship, say you were on your way to Alpha Centauri, a really great first interstellar stop since you get three stars for the price of one, but besides that, if you lasered or RF'd a time hack signal from Earth, even though you would have to frequency ...[text shortened]... you were hooked on since Earth clock would be going a couple times faster than ship clock time!

No, as you fly away from the Earth you observe events happening on the
Earth as being slower than for you.

And that's even without relativistic effects.

Lets say you are travelling at 10% C, below the threshold of significant relativistic
effects, away from the Earth.

We start with you 1 light day away from the Earth at t=0 [18:00 UTC] which is
when your favourite TV show is broadcast every night.

The signal takes 1 day 2hrs 40minutes to catch up with you. T= 1d 2hr 40m

At T=1d the next episode was broadcast.


The second broadcast takes 1 day 2hrs 56minutes to catch up with you. T=2d 2hr 56m

So from your perspective the second show turned up 1 day 16minutes after the first.

Or in other-words, 1 day on the Earth lasted [from your perspective] 16 minutes longer
than it should have.

And this effect gets worse the farther away you get, it takes longer and longer for each
program to reach you the farther away you get.

Originally posted by googlefudge
No, as you fly away from the Earth you observe events happening on the
Earth as being slower than for you.

And that's even without relativistic effects.

Lets say you are travelling at 10% C, below the threshold of significant relativistic
effects, away from the Earth.

We start with you 1 light day away from the Earth at t=0 [18:00 UTC] which ...[text shortened]... ay you get, it takes longer and longer for each
program to reach you the farther away you get.

Yes, but one of my jobs in the ancient past was in 1970 at Goddard Space Flight Center, working on Apollo Tracking and Timing. The tracking part was a transponder onboard the Apollo, and a radio link between Earth and Apollo as it was going to the moon.

The transmitter on Earth sends a signal with a time hack code that when it reaches Apollo, the transponder immediately resends back to Earth. The system then knows very accurately how far apart Earth is from Apollo, within 50 feet, which was plenty good enough for tracking but they knew they could get that accuracy down to about 6 inches if they wanted to but it was not needed ATT.

I think a similar system could work for relativistic craft because the time hack signal would reach the craft and once calibrated at low velocity, you get definite information about how close you are to c by the frequency you have to shift to to listen to the time hacks, since Doppler effects come into play. If you have a known frequency at the start, say 1000 Ghz, just to pick an example, and you are now going at 0.9c away from Earth, then the frequency would shift downwards by that time dilation rate, 2.3 times or so. So the new frequency you look at would come in at 434 Ghz or you would not be able to read whatever codes are modulated into the signal.

That alone can tell you how fast you are going I think. Now not so sure, if shipboard time shifts, maybe that would mess up the perceived frequency shift. Have to think about that.

Originally posted by sonhouse
Yes, but one of my jobs in the ancient past was in 1970 at Goddard Space Flight Center, working on Apollo Tracking and Timing. The tracking part was a transponder onboard the Apollo, and a radio link between Earth and Apollo as it was going to the moon.

The transmitter on Earth sends a signal with a time hack code that when it reaches Apollo, the transp ...[text shortened]... d time shifts, maybe that would mess up the perceived frequency shift. Have to think about that.

That alone can tell you how fast you are going I think.

In the theory of special relativity you are always stationary the rest of the universe is what is moving as far as you are concerned.

you get definite information about how close you are to c by the frequency you have to shift to to listen to the time hacks

If you measure the speed of light it always comes out at 299,792,458 m/s no matter what your speed is relative to any other given observer. It doesn't matter if you are accelerating or not. You can measure the rate your starting point, let's say the sun, is receding from you but you are always stationary. The sun is moving relative to the black hole at the centre of the galaxy, I copied and pasted this from Wikipedia to illustrate the point.

The Sun follows the solar circle (eccentricity e < 0.1 ) at a speed of about 255 km/s in a clockwise direction when viewed from the galactic north pole at a radius of ~8.34 kpc about the center of the galaxy near Sagitarius A*.

We don't get two different figures for the speed of light if we measure it in the direction of the sun's movement or against it. So as far as we can tell the sun is stationary.

The easiest way of telling your speed relative to the sun would be a little spectroscopy - just look at the Doppler shift in the absorption lines of the sun. The problem with a timing signal is that by the time you are a light year away the signal isn't going to be very easily detected.

Originally posted by DeepThought

That alone can tell you how fast you are going I think.

In the theory of special relativity [b]you are always stationary the rest of the universe is what is moving as far as you are concerned.

you get definite information about how close you are to c by the frequency you have to shift to to listen to the time hacks

If you m ...[text shortened]... is that by the time you are a light year away the signal isn't going to be very easily detected.[/b]

Yes, you should be able to look at spectrographic lines of the sun to check out Doppler shift but if you had a strong enough transmitter or laser it could be done also. There are schemes afoot that would use the sun as a giant lens to focus energy to drive a ship where all you need on board is fuel, you don't need to spend energy to speed up the fuel or you could use the collected energy to power a particle accelerator to get the exhaust close to c also which I think should increase your thrust since each particle would be 2.3 times its rest mass so getting the particles to 0.9 c should not be a problem as long as you have gigawatts of energy from whatever source you can use.

The sun can be used as a lens because its first focal point, the start of a focal line is more accurate, but that first focus is at about 580 AU, or about 86 billion Km away from the sun. Like if you had two laser beams very tightly focused and they were say 10 billion km away from the sun and you aimed them very carefully so one beam was say skimming the surface on the left side (with reference to the ecliptic) and the other skimming the surface on the right side, if the sun was not there, the two laser beams would continue to be 1.4 odd million km apart going in the same direction.

But because of the gravity of the sun, the two laser beams will converge around 86 billion km on the other side of the sun and of course will continue on that path till they encounter another large mass and they would separate at that famous 1.75 arc seconds Einstein predicted but this time 86 billion klicks from the sun. Anyway you could use that effect to focus energy to a ship on its way somewhere in interstellar space, like Alpha Centauri which is where I would put my money for a first interstellar voyage.
A three for one deal!

Originally posted by sonhouse
Yes, you should be able to look at spectrographic lines of the sun to check out Doppler shift but if you had a strong enough transmitter or laser it could be done also. There are schemes afoot that would use the sun as a giant lens to focus energy to drive a ship where all you need on board is fuel, you don't need to spend energy to speed up the fuel or you ...[text shortened]... uri which is where I would put my money for a first interstellar voyage.
A three for one deal!

I think you would be better off simply focusing the laser beams conventionally
using regular [if giant] optics.

Skimming laser beams over the suns surface looks good until you account for the
scattering and absorption caused by the plasma in the corona and the fact that
the sun is a wobbling a-symmetric irregular object that makes focusing very hard,
if not impossible.