Relativity Question

Originally posted by Mickey Knox
I'm hoping somebody who knows physics can help me out with this question...

If rocket A flys away from the earth at .866 the speed of light and rocket B flys away from the earth from the opposite side in the opposite direction at .866 the speed of light, then how can they still be moving < the speed of light away from each other?

I'm having trouble ...[text shortened]... in paradox is something else I don't get.

Thanks if you can explain it in an intuitive way

Unless I skimmed too fast, no one has really addressed the issue here. From the earth's frame of reference, each rocket is traveling at 0.866c--no violation of the speed of light. Relative to each rocket, the earth is traveling at 0.866c--no violation, again. Relative to rocket A, rocket B is NOT traveling at 1.732c (which would be a violation), because of time and distance dilation. B appears to take longer to travel a given distance from A's perspective--that is, B appears to be moving more slowly.

Originally posted by HolyT
Unless I skimmed too fast, no one has really addressed the issue here. From the earth's frame of reference, each rocket is traveling at 0.866c--no violation of the speed of light. Relative to each rocket, the earth is traveling at 0.866c--no violation, again. Relative to rocket A, rocket B is NOT traveling at 1.732c (which would be a violation), because of t ...[text shortened]... to travel a given distance from A's perspective--that is, B appears to be moving more slowly.

I addressed it.

Question (1):
Say two jetplanes, A and B, are going in opposite directions with Mach 0.866. Can one pilot in plane A generate sound (given loud enough) to the pilot in plane B and he can hear it (given big enough ears)?

Question (2):
Say two rockets, C and D, are going in opposite directions with 0.866c. Can one pilot in rocket C generate light (given strong enough) to D and the pilot D can see it (given strong enough vision)?

Question (3):
What is the difference in the questions (1) and (2) and would there be any difference in the answers?

Originally posted by AThousandYoung
The math doesn't work that simply at relativistic speeds. That's because there is a value called the Lorenz factor which depends on velocity. The Lorenz factor is:

L = 1/(1-(v^2/c^2))

At normal velocities, the Lorenz factor is approximately 1, because the value (v^2/c^2) is approximately 0. However as v (velocity) rises, this fraction becomes ...[text shortened]... what exactly is supposed to be happening. How do you decide which twin is the one moving?

It's quite easy.
Twin paradox is no paradox because their speed is not constant. There's a time when one of them changes directions to turn back to earth. While doing so, general relativity applies, not special relativity, and the guy gets a lot older.

Originally posted by FabianFnas
No.

It doesn't matter if you have a rope and measure its length in each time or if you measure the distance between the spacecrafts at each time. You will get the same answer. How could it be of any difference?

You would get the same size, but the guys travelling at that speed would see that rope with a different size, somewhat smaller

Originally posted by serigado
... and the guy gets a lot older.

Who says?
If you ask the travelling guy, does he really say that he's getting a lot older?
I wouldn't think so.

Originally posted by FabianFnas
Question (1):
Say two jetplanes, A and B, are going in opposite directions with Mach 0.866. Can one pilot in plane A generate sound (given loud enough) to the pilot in plane B and he can hear it (given big enough ears)?

Question (2):
Say two rockets, C and D, are going in opposite directions with 0.866c. Can one pilot in rocket C generate light (give ...[text shortened]... is the difference in the questions (1) and (2) and would there be any difference in the answers?

1) Making a sound louder doesn't make it go faster. But let's say he can send some kind of signal (radar, flashlight, anything else). The guy in B could receive the sign from A as long as the sign could go to a speed faster then B. Vice-versa.
2) Yes, explained in 1)... light can catch ANYTHING (except light itself). Because anything (with mass) can reach the speed of light.
3) It doesn't matter where the signal comes from. It only matters the speed it comes from it's origin.
If it's not light, it's harder to send such high-speed signal, because the initial inertia would have to be surpassed and then an additional energy spent to accelerate it up to the necessary speed.
Imagining sending the a non-light signal (something like a bullet with a message) from A to B:
A has speed 0.8, same as B in the opposite direction
A in it's referential sees B going at speed 0.975c
B in it's referential sees A going at speed 0.975c
A would have to accelerate it's signal up to 0.976c (in it's referential) to the signal be able to catch B.
B would see the signal coming really slow, something like 0.0001c. But it would reach him, someday 🙂
Someone just standing around would see the signal going at something like 0.81c in the direction of B.

(0.81, 0.0000001, 0.976 are just rough approximations, something to give a relative size of the speed, nothing exact)


If it was a light signal it would be a lot simple. No acceleration was needed, just a flashlight.
A would send the signal, and would see it going a 1.0c, B would see it coming at 1.0c, and the guy standing would see it going from A to B at 1.0c.
Why? Because the speed of light is absolute, in every inertial (non-accelerated) referential, doesn't matter which. Is it strange? YES. Because if this happens, all our everyday notions of relativity and adding speeds ARE NOT VALID!!!
It's been measured to high precision, and really happens, it's incredible.

Originally posted by FabianFnas
Who says?
If you ask the travelling guy, does he really say that he's getting a lot older?
I wouldn't think so.

We wouldn't say so while travelling at constant speed. While he is going straight, no one knows who's the right twin.
But when he changes direction when turning back, he WILL know, because we will suffer an HUGE acceleration, and his twin won't. A LOT of G's. Imagine a plane making a loop at 2 million KM/s.

Originally posted by serigado
We wouldn't say so while travelling at constant speed.

He wouldn't feel himself getting hugely older, even if he is in relativistic conditions.

"I get some sleep while turning the ship (*yawn*)" "Now I'm awake again and seems to have greyish hair and a meter long beard. Where is my Alzheimer pills, I seem to forget everything since I woke up."

No, he will feel nothing more than anyone that he is getting older. --->In his frame of observations

Originally posted by serigado
1) Making a sound louder doesn't make it go faster. But let's say he can send some kind of signal (radar, flashlight, anything else). The guy in B could receive the sign from A as long as the sign could go to a speed faster then B. Vice-versa.
2) Yes, explained in 1)... light can catch ANYTHING (except light itself). Because anything (with mass) can reach ALID!!!
It's been measured to high precision, and really happens, it's incredible.

1) Making a sound louder doesn't make it go faster. But let's say he can send some kind of signal (radar, flashlight, anything else). The guy in B could receive the sign from A as long as the sign could go to a speed faster then B. Vice-versa.

No, I didn't imply that the sound goes faster when louder. But it makes it more plausible for the other pilot to hear it.
If he just wanted to send a signal, it wouldn't be any problem.
I think you answered a question that has not been asked.

The problem here is if it is possible to send sound (by sound waves) from one plane to another who have the velocity of Mach 0.86 in opposite directions.

Originally posted by FabianFnas
The problem here is if it is possible to send sound (by sound waves) from one plane to another who have the velocity of Mach 0.86 in opposite directions.

If you set up the right conditions, it might just be possible for the sound wave to travel round the planet and reach the pilot from the opposite direction 🙂

Otherwise, no. Sound moves at a certain speed relative to a medium, so you can apply a Galilean transformation.

Originally posted by FabianFnas
[b]1) Making a sound louder doesn't make it go faster. But let's say he can send some kind of signal (radar, flashlight, anything else). The guy in B could receive the sign from A as long as the sign could go to a speed faster then B. Vice-versa.

No, I didn't imply that the sound goes faster when louder. But it makes it more plausible for the other waves) from one plane to another who have the velocity of Mach 0.86 in opposite directions.[/b]

You are right, I misread the first part... I didn't read 0.8 mach, but 0.8c.
For Mach 1 we can forget special relativity and do the approximation to galileu's relativity.
The sound produced from A to B would reach plane B, because he's going at a speed lower then sound.
"but don't the speeds add up, u may ask"
In this case, they don't. The sound made in A comes from A at the normal speed of sound, and not 1 - 0.866 mach.
"What changes, then?"
The frequency of the sound made, through doppler effect.
If there was a wind of 0.134 mach, the sound wouldn't reach, though.

Originally posted by mtthw
If you set up the right conditions, it might just be possible for the sound wave to travel round the planet and reach the pilot from the opposite direction 🙂

Otherwise, no. Sound moves at a certain speed relative to a medium, so you can apply a Galilean transformation.

The velocity of the sound doesn't change, only the frequency

May I interpret the answers in this way?
Yes, a wave of sound can move from plane A to plane B, when they move 2 times Mach 0.866 relative to each other, but the frequency will be changed. We don't need any of Einsteins postulate here.
Am I right in this interpretation?

Originally posted by AThousandYoung
I addressed it.

Yes, you did, and you were the only one. I skimmed past your introductory statement that said that you were calculating the speed of B with respect to A or vice versa. And that is the key point that needs to be emphasized. All this discussion about imaginary fixed frames of reference other than A, B, and C involved is irrelevant. Good job.