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eric_marsh
2008-Aug-18, 12:59 AM
I've been mulling over the subject of relativity for a while now. I've got a question that I'd be interested in hearing an answer to.

Suppose that you have a planet rushing throw space a .9C. The people of that world launch three rockets, each with exactly the same mass, exactly the same amount of propulsive force and each containing an atomic clock. One rocket is launched in the direction that the planet is moving, one in the opposite direction and one perpendicular to the direction of the planet's travel.

What would an observer on the planet see as she watched each of those atomic clocks?

Gigabyte
2008-Aug-18, 01:25 AM
Same thing any other planet would see. It doesn't matter how fast you are moving, to the planet, you are not moving. Just like on Earth. When we launch rockets, the relative motion doesn't matter much. (Except for orbital mechanics).

To understand this, ask how is the speed of the planet being measured? Relative to what?

For the rockets and clocks, the starting point is stationary. You could describe the same situation by saying the rest of the Universe is moving at .9C

See? This is why light always travels at the speed of light. The source of the light is always not moving, at least to the source of the light. Everything else is moving.

Measuring speed (velocity) is a matter of where you are measuring from. If all your rockets are starting from the same point, motion doesn't matter, to the observer on the planet.

If you pick the right point to measure the speed of our Planet, you could say it is moving at .9C right now.

Motion is relative to the observer.

eric_marsh
2008-Aug-18, 02:14 AM

Here's what I'm trying to get my head around. As I understand it the rocket moving in the direction of travel will be gaining mass as it approaches C and the rocket moving away from the direction of travel ought to be losing mass. Wouldn't this effect the total amount of acceleration of each rocket relative to the planet? Do I completely misunderstand the implications of this? I also understand that time dilation (along with mass) becomes asymptotic as one approaches C. It intuitively (and yes, I know that intuition doesn't get far in the world of physics) seems that as you push the amount of fuel up to high enough levels on one extreme the rocket would approach C and it's clock would appear to stop. Would the other rockets with the same amount of fuel appear to behave the same way?

The relative to what question is a good one and I don't have an answer to that one. It's evidently the crux of the issue. I'll probably mull it over a bit more and see where it leads me.

Cougar
2008-Aug-18, 05:46 PM
Suppose that you have a planet rushing [thru] space a .9C.....

According to the famously failed experiment of Michelson and Morley (http://en.wikipedia.org/wiki/Michelson-Morley_experiment), space cannot be considered to be a static background that things happen within. So when you say something is cutting along at .9c, this has no meaning until you indicate .9c relative to what.

Argos
2008-Aug-18, 06:21 PM
Here's what I'm trying to get my head around. As I understand it the rocket moving in the direction of travel will be gaining mass as it approaches C and the rocket moving away from the direction of travel ought to be losing mass. Wouldn't this effect the total amount of acceleration of each rocket relative to the planet? Do I completely misunderstand the implications of this?

Thereīs no mass gain or loss in the reference frames of any of the rockets. They will remain as massive as before in their own frame, no matter how fast they move. Now, their relativistic mass [thatīs what yourīre referring to] depends on the reference frame of the observer.

Relativistic mass is a tricky concept. So be careful with it.

Cougar
2008-Aug-18, 08:27 PM
Relativistic mass is a tricky concept. So be careful with it.

How true that is. I've seen some extremely long discussions on this topic, but I guess the main problem is in considering mass not as mass in the "ordinary" sense, but as an energy-momentum four vector, which is what actually increases as velocity approaches c.

Then (I just now notice) that generalizing Special Relativity's definition to general relativity is problematic, to say the least; in fact, it turns out to be impossible to find a general definition for a system's total mass (or energy).

Tricky indeed!

Jeff Root
2008-Aug-18, 09:44 PM
The relative to what question is a good one and I don't have an
answer to that one. It's evidently the crux of the issue.
That's exactry right: it is the crux of the issue.

Your question is actually quite simple, as relativity questions go.
One rocket has a speed away from the planet in one direction, the
other rocket has the same speed away from the planet in the opposite
direction. That's it. That's all there is to it. The motion of the planet
and the rockets relative to something or someone else (such as the
Sun, or another star, or the center of the Galaxy, or the matter which
emitted the cosmic background radiation) has no role.

-- Jeff, in Minneapolis

eric_marsh
2008-Aug-19, 01:20 PM
Thanks. Now another question.

If you have two rockets and one of them accelerates from the other, the occupants of each rocket would see the occupants of the other rocket slowed down. Correct?

I've been told that if the moving rocket turns around and returns to the non-moving rocket it's occupants will be older than the occupants of the non-moving rocket. What if the first rocket just started to accelerate and caught up with the second rocket?

Jeff Root
2008-Aug-20, 03:23 AM
If you have two rockets and one of them accelerates from the other,
the occupants of each rocket would see the occupants of the other
rocket slowed down. Correct?

I've been told that if the moving rocket turns around and returns to
the non-moving rocket it's occupants will be older than the occupants
of the non-moving rocket.
The other way around. The occupants of the unaccelerated rocket
would be older.

What if the first rocket just started to accelerate and caught up with
the second rocket?
I'm pretty sure that the larger acceleration and speed required for the
second rocket to catch up with the first would exactly balance the
longer time that the first rocket was in flight, so that there would be
no difference in ages when they meet up.

-- Jeff, in Minneapolis