B Near C Speed Rockets: Time Dilation & The Twin Paradox

[kolleamm]

Suppose we had two rockets traveling in opposite directions at 0.99c each.

Would a rocket in one frame of reference see the other traveling at 1.98c?

The argument would be that we would observe the rocket going slower, since time would slow down at near c speeds but who does the time slow down for?

I'm guessing this ties in with the Twin Paradox where determining which brother gets older is a problem since motion is relative.

 

[axmls]

No, in special relativity velocities do not add like that. They will each see the other going closer to c, but still less than c.

 

[Nugatory]

Would a rocket in one frame of reference see the other traveling at 1.98c?

No. Google for "relativistic velocity addition" and search this forum for those keywords.

I'm guessing this ties in with the Twin Paradox where determining which brother gets older is a problem since motion is relative.

Almost no tie-in... For a clear explanation of the twin paradox, check out the online FAQ: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[Ibix]

Suppose we had two rockets traveling in opposite directions at 0.99c each.

Relative to what? Presuming you mean that these velocities are measured in the same frame of reference, then each one will measure a speed below c for the other. If, in some frame, you have an object doing v in the +x direction and another doing u in the +x direction then the one doing v will measure the one doing u as moving at u':$$u'=\frac {u-v}{1-uv/c^2} $$ In your case, one of the rockets has a negative velocity.

I'm guessing this ties in with the Twin Paradox where determining which brother gets older is a problem since motion is relative.

There is no such problem - which twin is older is well defined. The twin paradox (which is only actually a paradox to the flawed understanding of relativity that most people initially pick up) and its resolution are not really related to the velocity addition formula, except in the general sense that they are both basic results of special relativity.

 

[Vitro]

Suppose we had two rockets traveling in opposite directions at 0.99c each.

Would a rocket in one frame of reference see the other traveling at 1.98c?

That Galilean addition is only approximately correct at low speeds, the ones we are used to in everyday experience, it doesn't work at high (relativistic) speeds. Look up "relativistic velocity addition".

The argument would be that we would observe the rocket going slower, since time would slow down at near c speeds but who does the time slow down for?

Two observes in relative motion will measure each other's time to be slower, yet time doesn't slow down for either of them.

I'm guessing this ties in with the Twin Paradox where determining which brother gets older is a problem since motion is relative.

It's not a problem at all. It's always the twin who turns around that ages less, when only one turns around while the other remains inertial. If you have a scenario where both twins go out and turn back then either can age less, or they can age the same, depending on the details. The age difference is the difference in "length" of their worldlines between meetings.

 

[kolleamm]

I see. The velocity addition for near c speeds seems to be what I was missing.

 

[hsdrop]

you know i have had the same question in my head about the L.H.C.. that if that have two beams of whatever particles smashing into one another. from the outside point of view nothing is fester than c. but if i was to be one of the particles. it mite look (from the particle that point of view) that i was standing still. the ring would look like it was moving at near c but then from that point of view. what would the other particle coming at me look like it was moving at ??

 

[Ibix]

you know i have had the same question in my head about the L.H.C.. that if that have two beams of whatever particles smashing into one another. from the outside point of view nothing is fester than c. but if i was to be one of the particles. it mite look (from the particle that point of view) that i was standing still. the ring would look like it was moving at near c but then from that point of view. what would the other particle coming at me look like it was moving at ??

Nearer c than the ring. Look up a speed for the particles (or make one up) and use the formula that I quoted in #4 to get an exact answer. If u and v, your equal and opposite LHC frame velocities (expressed as a fraction of c), have a lot of nines after the decimal point then your particle frame velocity, u', will have even more.

 

[hsdrop]

is it like looking at the universe and everything in it(at least the math for it) all as if there was no place that anyone can call still or a start point so we look the speed of light and mesher from there as a point of refinances to base everything las off of like the values for time dilation and movement with everything else

 

[Herman Trivilino]

is it like looking at the universe and everything in it(at least the math for it) all as if there was no place that anyone can call still or a start point [...]

Not just for the math. For the physics, too. It seems to be a fundamental facet of Nature that anyone inertial reference frame is as good as any other. They are all equivalent. This is called the Principle of Relativity.

so we look the speed of light and mesher from there as a point of refinances to base everything las off of like the values for time dilation and movement with everything else

It's true that the speed of light in a vacuum is the same in all inertial reference frames, but measurements are taken from the reference frame itself. That is the very purpose of the reference frame.