Close to the speed of light relative to what?

Hi
The presence of any kind of any energy, by any amount, distorts spacetime. Its just that the amount you and an ant distort spacetime, is very very very very small so people just forget about it.
Uniform motion is relative. So if we consider the frame A to be at rest and frame B to be moving with speed v w.r.t. A, we can also consider B to be at rest and A to be moving with velocity -v w.r.t. B. Then A sees that B's time slows down and B sees that A's time slows down and both of them are right.

 

No, it would not. Time always passes locally at one second per second. What is observed by a remote observer is not what happens locally.

 

No, time progressed for you at exactly the same rate as it did for the people on Earth, one second per second. The fact that you traveled along a different world line mean you AGED by a different amount while the time passed at the same rate. This is a confusing concept but it is the way it is.

 

Kinetic time dilation has nothing to do with local vs. remote, just with relative motion. A moving clock runs slower than a resting clock, even when they pass close to each other, and are observed locally.

 

DOH ! I knew that

 

I am confused by this concept. It implies clocks don't measure time, but merely "age".

 

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

 

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

 

I always thought ##d\tau## was a differential.

 

I re-read an old thread where I thought thoroughly about time & age and more less came to the conclusion that "age" is sequenced accumulation of physical occurrence to a "body/object" (or the display on an imperfect clock), and time is a component of spacetime geometry. As phinds said "rate" is distinctly different from age.

In that case only an idealized perfect clock measures time, and for example my mechanical watch that gains 2 minutes per day ages, the hourglass ages, and the most consistent measures of the "rate" c (such as a light clock) is a measure of strictly time, not merely an accumulation of "change" but the rate.

If I understand the concepts right, I am saying a proper clock measures lightlike intervals. Our "biological" clock, hour glass ect can be a measure of proper time, timelike intervals, which of course different from coordinate time and the lightlike intervals of a perfect clock.

So with coordinate time I see the light clock in motion has the same rate of c, but the accumulation of "ticks" (different from rate) takes longer (different path).

 

Yes there would be a frame where it is observed that you were in motion prior to going (according to your frame) 0.99 of c relative to Earth.

However it is not a simple sum, according to the frame that observed Earth (and you the time traveler) in motion, your rulers and clocks were contracted/dilated prior to you deciding to go 0.99 of c relative to Earth. So to that observer you never reached 0.99 of c relative to Earth, but your measures/observations/calculations tell you you have, again this is because your rulers 'n clocks are not making the same measurements as the frame that observed Earth in motion.

So just as your rulers and clocks aren't making the same measurements (in turn calculation of velocities) we cannot simply add velocities as x+y.

The concept is more easily understood with a car and it's headlights. First the posit c is invariant; regardless of comparative motion every observer calculates light to have the velocity of c. So when a car is driving down the road with it's lights on, the driver calculates the light emitted from the headlights to be c, and the observer at rest to the road also calculates the light from the headlights to be c, not simply the car velocity + c. The "mechanics" is the car driver's rulers and clocks were contracted/dilated compared to yours (from your frame) to a point where he/she calculates the lights velocity to be c and not the car velocity + the headlight light velocity...note according to the driver he/she is at rest and your rulers and clocks are contracted/dilated.

 

Usually, when we say that something is traveling at a particular speed, we mean with reference to a particular Inertial Reference Frame (IRF). So you could say that in your chosen IRF, the earth is traveling at some speed, say, 10% of the speed of light (we'll call that 10%c) in some particular direction, and then you could say that the rocket is traveling at 99%c according to that same IRF in the same direction (or any other direction). Then the speed of the rocket relative to the earth will not be 99%c. It won't generally be a speed that you could easily calculate off the top of your head but it can be determined based on your specification of your scenario.

But we can also specify a scenario by saying that something is traveling at a particular speed with reference to some other object and then we don't care what the speed of that object is with reference to any other object or IRF. We just use that second object as the definition for an IRF in which it is at rest.

So in your example, if you just say that the rocket is traveling at 99%c with respect to the earth, it doesn't matter if the earth is also traveling at some particular speed with respect to the sun or any other object, as long as you aren't interested in determining anything that is happening on that other object or what observers on that other object see or determine that is happening on the earth or on the rocket.

So when Stephen Hawking says that we can travel into the future by taking a rocket at 99%c and returning, he is assuming the IRF in which the earth is at rest. At that speed, the Time Dilation Factor is 7.1 so if you say that the rocket is gone for 10 years, you have to tell us if you meant 10 years on earth or 10 years on the rocket. If you meant 10 years on earth, then you would have aged only 10/7.1 by the time you got back which is equal to 1.4 years so you would have traveled 8.6 years into the future of earth which isn't very much. If you meant 10 years of the rocket's time then the earth would have aged 10 times 7.1 or 71 years by the time you got back so you would have traveled 61 years into the future of earth and you would see a huge difference.

By the way, when considering speeds close to that of light, the Time Dilation due to gravity can generally be ignored since its contribution to the problem is so slight.

So the bottom line is that you get to set up your scenario any way you want and if all you care about is the relative aging between the people on earth and the people on the rocket, then you don't have to take into account any other objects or their relative speeds to either the earth or the rocket. The only thing that matters is the speed of the rocket relative to the earth.

Does that make sense to you?