RTT’s mind boggling Time Dilation Paradox

[RawThinkTank]

A train is moving relative to earth at such a high speed that the clock on the train slows down to half rate compared to clocks on earth. A rocket is launched in the opposite direction train is moving to such a high speed that the clock on the rocket slows down to half rate compared to the clock on train.

 

What will be the rate of clock time on rocket compared to that of clocks on earth ?

[RawThinkTank]

A train is moving relative to earth at such a high speed that the clock on the train slows down to half rate compared to clocks on earth. A rocket is launched in the opposite direction train is moving to such a high speed that the clock on the rocket slows down to half rate compared to the clock on train.

 

What will be the rate of clock time on rocket compared to that of clocks on earth ?

[mossoi]

1/4 - but that's not including any time dilation theory just using the numbers you have stated.

[mossoi]

1/4 - but that's not including any time dilation theory just using the numbers you have stated.

[maverick88]

Thr rocket and Earth will have the same time I suppose

Because rocket's and Earth's time relation to the train are same

Aren't they?

[maverick88]

Thr rocket and Earth will have the same time I suppose

Because rocket's and Earth's time relation to the train are same

Aren't they?

[cyeokpeng]

The answer is that such a system will be impossible. The speed of the rocket with respect to the Earth will be zero if you do the relativistic time-dilation calculations, so it is impossible for the rocket to be moving in the opposite direction with respect to the train.

[cyeokpeng]

The answer is that such a system will be impossible. The speed of the rocket with respect to the Earth will be zero if you do the relativistic time-dilation calculations, so it is impossible for the rocket to be moving in the opposite direction with respect to the train.

[maverick88]

The answer is that such a system will be impossible. The speed of the rocket with respect to the Earth will be zero if you do the relativistic time-dilation calculations, so it is impossible for the rocket to be moving in the opposite direction with respect to the train.

 

That's exactly what I said...

This system is possible when the rocket symply doesn't move..

Thr rocket and Earth will have the same time ----> she can't move(rocket)

but why impossible...the directions are opposite because train is moving in the opposite direction relatively to the rocket and Earth...

O_o

[maverick88]

The answer is that such a system will be impossible. The speed of the rocket with respect to the Earth will be zero if you do the relativistic time-dilation calculations, so it is impossible for the rocket to be moving in the opposite direction with respect to the train.

 

That's exactly what I said...

This system is possible when the rocket symply doesn't move..

Thr rocket and Earth will have the same time ----> she can't move(rocket)

but why impossible...the directions are opposite because train is moving in the opposite direction relatively to the rocket and Earth...

O_o

[mossoi]

If we assume what's stated in the question to be correct then:

 

"the clock on the train slows down to half rate compared to clocks on earth" and "the clock on the rocket slows down to half rate compared to the clock on train" - ie: 1/2 * 1/2 = 1/4

 

The answer is written there regardless of what time dilation tells us. Unless, of course, the information in the question is wrong.

[maverick88]

If we assume what's stated in the question to be correct then:

 

"the clock on the train slows down to half rate compared to clocks on earth" and "the clock on the rocket slows down to half rate compared to the clock on train" - ie: 1/2 * 1/2 = 1/4 QUOTE]

 

Ohh yea you are right

I though rocket's speed is compared to Earth like train's velocity

never mind

[Janus]

If we assume what's stated in the question to be correct then:

 

"the clock on the train slows down to half rate compared to clocks on earth" and "the clock on the rocket slows down to half rate compared to the clock on train" - ie: 1/2 * 1/2 = 1/4

 

The answer is written there regardless of what time dilation tells us. Unless' date=' of course, the information in the question is wrong.[/quote']

 

What's missing in the question is the reference frames from which these clock comparisons are made.

 

For example, if you say that the train's clock runs half as fast as the Earth clock, we can assume that he means as measured from the Earth. But when he says that the rocket clock runs at half speed to the train clock are we measuring this from the Earth or from the train?.

 

If from the train, then the rocket is fired so that it will be motionless with respect to the Earth and will have the same time rate as the Earth.

 

If measured from the Earth, then the rocket must be fired at a speed of .968 c with respect to the Earth. Then the rocket's clock will run at 1/4 of that of the Earth's as measured from the Earth. This means that it would have to be fired at .9977c relative to the rocket as measured by the train, which means that the rocket's clock would run at .0678 the rate of the train clock as measured by the train, and .1356 the rate of the Earth clock as measured from the train (measured from the train, the Earth clock runs half as slow).

 

To anticipate the next question: If everybody measures different time rates then how we say, for instance, that if a person flies off into space at .866c for 2 years Earth time, he will return having aged only 1 year?

 

To explain this, let's use the train-rocket example, but let's say that after a given time on the Earth, 1 year, The train fires a rocket back towards the Earth, such that it travels back to the Earth at the same rate as the train is moving away as measured from the Earth. IOW, the train is moving at .866c away from the Earth and the Rocket is fired so that it is moving towards the Earth at .866c.

 

Now let's examine what happens according to the Earth and Train.

 

Earth: the Train travels at .866c for one year and fires the rocket back to the earth after this time At this point it will be .866 ly from the Earth. According to the Time dilation measured by the Earth, the Train clock and rocket clock will both read 6 mo.s at this time. 1 year later the rocket reaches the Earth, having aged according to time dilation an additional 6mo. for a total of one year. Earth time: 2 yr, Rocket time 1 yr

 

Train: Due to length contraction, the same distance measured as .866 ly by the Earth will be measured as .433 ly according to the Ship. In order for the train to fire its rocket at the same point in space as seen from the Earth, it must do so when after it has traveled .433 ly by it own measurement. It took 6 mo. by its and the rocket's clock at .866c to reach this distance and the launch the rocket. Also, according the train, the Earth clock has been running at half speed and now reads 3 mo.

 

In order for the rocket to travel a .866c with respect to the Earth as measured from the Earth it must be launched at .9897c with respect to the train as measured by the train (Relativistic addition of velocities). This means that it has a respective velocity to the Earth as measured from the Ship of .9897-.866 = .1237c. Since the distance between rocket and Earth was .433 ly as measured by the Train, according to the train's clock it will take 3.5 yr for the rocket to reach the Earth.

Since the Rocket is moving at .9897c wrt the train as measured from the train, the rocket's clock will run at .1429 the rate of the Train clock according to the train. This means that, according to the train, 3.5*.1429 = .5 yr = 6 mo. will accumulate on the Rocket clock during its return to the Earth. Since it accumulated 6 mo at the time of launch it will have aged a total of 1 year during the full round trip.

 

Also, according to the train the Earth clock is still running at 1/2 the rate of the train clock. Thus the time accumulated on the Earth clock between the firing of the Rocket and its reaching the earth is 3.5 yr * .5 = 1.75 yr = 1yr 90mo. Adding this to the 3 mo. the Earth aged before the rocket was launched gives us a total of 2 years. Earth time: 2 yr, Rocket time: 1 yr

 

Both ship and Earth Agree as to the realtive aging that takes place.

 

If you want to determine what happens according to the rocket, you have to take into account the acceleration it undergoes when it it fired from the ship to head back towards the Earth. During this period it will be in an accelerated frame, and you have to make special calculations to determine what measurements are made from within an accelerated frame according to Relativity.

[Saint]

If you want to determine what happens according to the rocket' date=' you have to take into account the acceleration it undergoes when it it fired from the ship to head back towards the Earth. During this period it will be in an accelerated frame, and you have to make special calculations to determine what measurements are made from within an accelerated frame according to Relativity.[/quote']

 

See, here's the problem with the relativity calculations - the differences in clock rate and length contraction are supposed to be based soley on relative velocity wrt some "inertial" frame. In that world, every "inertial" frame can claim that ever other clock in the universe is moving at a slower rate than the "inertial" clock. That is obviously not the case. Throwing in acceleration is really only an attempt to make some sense of that rediculous world. It's an attempt at trying to figure out which of the frames is actually "moving". Acceleration is not relative. Acceleration is a real, physical phenomenon. If it wasn't, then it would simply be defined as the change in velocity wrt the "inertial" frame. It could simply be covered under an integral of the tiny changes in velocity (and the associated changes in clock rate and length contraction at each of those individual steps) wrt the "inertial" frame. It isn't dealt with that way because it's a physical reality. It is unrelative - or only relative to absolute space.

[RawThinkTank]

I know what is twins paradox; Can anybody tell me what is a triplets paradox ?