Twin paradox thought experiment

[guy_incognito]

I've been wracking my brain for days trying to comprehend everything that deals with the twin paradox. I have a vague understanding of relativity and its effects, but am massively confused by most of the explanations given on this forum and other places. I think perhaps it extends from my lack of total understanding of the theories involved. So here goes, and please point out anything that it seems I don't understand:

Everything is from MY (twin A) point of view.

Two twins (A and B) synchronize their clocks. One gets in a spaceship (B), the other stays on Earth (A). Twin A walks 100 feet in front of the spaceship (im assuming this small distance/acceleration is negligible and both clocks can be assumed synchronized still). The spaceship accelerates to near light speed almost instantly, and is already cruising at a constant velocity as it passes twin A. The exact moment it passes twin A it drops its own internal time stamp on twin A. From there it continues out in a straight line to a planet 1 light year away (as measured by twin A). Twin B does not stop, but keeps going, but as he passes the planet he transmits his internal clocks time stamp to the planet. The planet in question is exactly the same mass/size of Earth and is not moving relative to earth. As soon as the timestamp is received it is transmitted back to twin A on earth.

What is the discrepancy between A and B's time stamp the moment after takeoff? ie what effect does massive acceleration have on the clocks.

I am assuming that a planet not moving relative to Earth with the same gravity which is 1 light year away (as calculated from my point of view on earth) will be able to calculate real times based on signals sent back and forth. What I mean is this planet has some information (my twins time stamp as he passed by), and they beam it back to earth. On Earth I receive this signal, and I know it has taken exactly 1 year according to my clock to travel the distance between us, therefor I can simply subtract one year from my clock to know what my clock read at the time the time stamp was produced.

Does that logic work? If so what would my twins corresponding "local time" be at each point?

I'm not looking for real numbers here, just generalizations.

Like at At=0, Bt=0
then B accelerates quickly and sends a time stamp as he passes, so At=0.01 (or something super small) and Bt=? less than my time? or more?

then right as twin B passes the planet 1 light year away (from A's point of view) At=1yr, Bt=??

At= time read on twin A's clock from A's own perspective
Bt = time read on twin B's clock from B's own perspective.

 

[guy_incognito]

Also I am making an assumption that twin B is traveling so close to light speed I am just assuming he is at light speed (even though its technically less). So I know the planet is 1 light year away, and even though I don't observe twin B actually passing the planet at my 1 year mark, I know it must have happened.

 

[dx]

In the reference frame of A, B's clock ticks slower. So if B is moving away from A at a speed v, then when A's clock reads 1 second, B's clock reads less than 1 second (you can imagine this to be a 'time stamp' left by B on another plant if you want).

Numerically, B's clock reads

$$\sqrt{1 - \frac{v^2}{c^2}}$$

when A's clock reads 1.

 

[guy_incognito]

So if I define each starting point as "1", the first pass on Earth as point "2", and the point B passes the 2nd planet as "3"...

between points 2 and 3 one year will have elapsed on A's clock. less than one year will have elapsed on B's clock.

What about between points 1 and 2? Only a fraction of a second will pass on A's clock. What will that acceleration from point 1 to point 2 be like for B though? How much time will B and his clock experience between those points?

 

[dx]

The acceleration is really an irrelevant complication here. We can just imagine that B accelerates to his final velocity instantly. So if a small time ε elapses between "point 1" and "point 2" on A's clock (i.e. between the events "B starts off" and "B passes A"), then B's clocks would have ticked an amount ε√(1 - (v²/c²)), which is smaller than ε.

 

[guy_incognito]

I didn't know what effect, if any, acceleration would have.

Now say clock A has a synchronized counterpart clock A' that's located on the other planet. Am I correct to assume that A and A' will always be synchronized because they are experiencing the exact same gravitational force, and are not moving relative to each other? and if instant acceleration and deceleration is negligible, when twin B gets to the other planet and stops his clock will be significantly behind A' (and thus A). B will only have aged a fraction of a year. Then B travels back at nearly the speed of light to earth. According to clock A his round trip took 2 years, but clock B will once again show his trip lasted less than a year, so in total clock B gains less than 2 years. This is what should happen according to relativity as is my understanding.

Now what if twin B just sits in his spaceship and doesn't accelerate. The Earth and the other planet 1 light year from Earth instantly accelerate to light speed (all movement of Earth is mirrored exactly by the other planet) and instantly decelerate the moment the other planet is right under twin B. And then both planets simultaneously go back to their original starting points so twin B is right next to twin A when the planet decelerates. Now it was twin A who traveled some distance away from B, then turned around and came back. Shouldnt the opposite effect have happened on the clocks with twin A aging slower?

This seems like a paradox to me which is why I though the act of accelerating and decelerating relative to something else might have some effect on time.

 

[dx]

Your first paragraph is completely correct. This same situation cannot be analyzed in the same way from B's point of view, however, because he is not an inertial observer. When I said the acceleration was not relevant, I meant that the precise way in which he accelerates is not relevant, and that we may as well assume that he does it instantly. But the fact that he does accelerate means that from his point of view, we cannot analyze the situation in the same way A analyzes it from an inertial frame.

 

[guy_incognito]

but in the 2nd paragraph B is in an inertial frame. He never moves or accelerates. The Earth and other planet do the accelerating and traveling. So from his point of view twin A races some distance away, then returns. Now say B sees 2 years pass as he sits in his spaceship just waiting for Earth to return. What will clock A say when they meet back up? I'm inclined to guess clock A will age less than B. The only difference I see between the 2 opposite scenarios is which clock accelerates-decelerates-changes direction-accelerates-decelerates.

 

[dx]

The point is, the observer B is not undergoing a uniform inertial motion.

The argument which A uses to conclude that B's clocks lag behind his is simply not valid from B's point of view, i.e. he can't apply it to A. This is because this argument only works in an inertial frame, and a coordinate system attached to B is not inertial.

 

[guy_incognito]

The point is, the observer B is not undergoing a uniform inertial motion.

The argument which A uses to conclude that B's clocks lag behind his is simply not valid from B's point of view, i.e. he can't apply it to A. This is because this argument only works in an inertial frame, and a coordinate system attached to B is not inertial.

can you clarify which scenario you are referring to? My first scenario is B jetting off, then returning. A second completely separate scenario is A along with the Earth moving away from a stationary B, then returning.

scenario 1 = A never accelerates in any direction. B accelerates-decelerates-changes direction-accelerates-decelerates

scenario 2 = B never accelerates in any direction. A (along with the earth) accelerates-decelerates-changes direction-accelerates-decelerates

 

[dx]

Are these two separate scenarios, or the same situation viewed by two observers?

 

[guy_incognito]

separate. it was initially one up until this paragraph:

"Now what if twin B just sits in his spaceship and doesn't accelerate. The Earth and the other planet 1 light year from Earth instantly accelerate to light speed (all movement of Earth is mirrored exactly by the other planet) and instantly decelerate the moment the other planet is right under twin B. And then both planets simultaneously go back to their original starting points so twin B is right next to twin A when the planet decelerates. Now it was twin A who traveled some distance away from B, then turned around and came back. Shouldnt the opposite effect have happened on the clocks with twin A aging slower?

This seems like a paradox to me which is why I though the act of accelerating and decelerating relative to something else might have some effect on time."

which I started talking about a completely separate scenario.

The second scenario seems to make the whole thing a paradox to me.

 

[dx]

If they're separate scenarious, how can there be a contradiction? You're right, If B just sat still in an inertial frame, and it was A who accelerated away and came back, it will be A's clock which lags behind B's clock.

 

[guy_incognito]

because in either scenario maximum velocity is achieved instantaneously. and once they are traveling at a constant velocity I don't understand how one is different from the other.

For example a 3rd separate scenario. clock B is already traveling near light speed. it passes earth, and as it does it reads exactly 0, so A can synchronize his clock to what B was at the exact time it passed. So at the time B passes Earth both clocks are set to zero. B continues on and passes A' at practically light speed and keeps going. The moment B passes A' the reading on A as well as on A' should be exactly 1 year. What time will A' read on B as he passes? And what will B read on A' clock as he passes?

I assume A' will see Bs clock and it will read less than a year. And B will look at A' and see 1 year. Is that correct? And if so, how can you possibly differentiate between who is really moving (assuming these are the only 3 objects in the universe) when no one accelerates at any point?

 

[dx]

because in either scenario maximum velocity is achieved instantaneously. and once they are traveling at a constant velocity I don't understand how one is different from the other.

One of them feels an acceleration, and the other does not. It may be true that for most of his trip, B is also an inertial observer, but there are points during his journey where he accelerates, and this makes them non-equivalent.

For example a 3rd separate scenario. clock B is already traveling near light speed. it passes earth, and as it does it reads exactly 0, so A can synchronize his clock to what B was at the exact time it passed. So at the time B passes Earth both clocks are set to zero. B continues on and passes A' at practically light speed and keeps going. The moment B passes A' the reading on A as well as on A' should be exactly 1 year. What time will A' read on B as he passes? And what will B read on A' clock as he passes?

I assume A' will see Bs clock and it will read less than a year. And B will look at A' and see 1 year. Is that correct?

Yes, that's correct.

And if so, how can you possibly differentiate between who is really moving (assuming these are the only 3 objects in the universe) when no one accelerates at any point?

You're right, in this 3rd scenario, there is no one accelerating. But where do you see a contradiction in this 3rd scenario?

 

[yuiop]

In the scenario you described in the first post of this thread, you can ignore acceleration. From the time B drops his initial time stamp on Earth until B passes the second planet and drops his second time stamp, the velocity of B is constant. The time interval between B's two time stamps will be less than the time interval measured by A who is using two clocks in two different places (A and A'). However, B does not consider A and A' to be synchronised from his point of view. Remember, what is considered to be simulataneous from one observer's point of view is not simulataneous from the point of view of another observer who is not at rest with the first observer. B will agree that his clock shows less elapsed time than the difference between A' and A, but that is because from his point of view, A' is ahead of the clock back on Earth (A). B will still measure the instantaneous clock rate of A' (and A) to be running at a slower rate than his own clock.

Google "relativity of simultaneity".

 

[guy_incognito]

You're right, in this 3rd scenario, there is no one accelerating. But where do you see a contradiction in this 3rd scenario?

What exactly makes B experience time slower than A or A'? They are moving exactly the same speeds relative to each other.

 

[dx]

B does not experience time slower. It is just that, from the point of view of A, B's clock ticks slower that A's own clock. From B's point of view, A's clock ticks slower than B's own clock.

 

[guy_incognito]

i think I am getting tripped up by relative simultaneity, which I do not fully grasp. It still seems intuitive to me that things happen absolutely regardless of your frame of reference, and your frame of reference should only change the way you perceive the events happening. Even though from what I've read that's not the case.

For example the clock A and A' being synchronized at a distance of 1 light year. It seems to me that they are in fact synchronized even though I know Einstein says otherwise.

 

[dx]

I strongly suggest familiarising youself with the 'spacetime diagram'. It makes everything clear.

A very good book is "Spacetime Physics" by Taylor and Wheeler. You can read the first chapter for free here: http://www.eftaylor.com/download.html#special_relativity

 

[starthaus]

I've been wracking my brain for days trying to comprehend everything that deals with the twin paradox. I have a vague understanding of relativity and its effects, but am massively confused by most of the explanations given on this forum and other places. I think perhaps it extends from my lack of total understanding of the theories involved. So here goes, and please point out anything that it seems I don't understand:

Everything is from MY (twin A) point of view.

Two twins (A and B) synchronize their clocks. One gets in a spaceship (B), the other stays on Earth (A). Twin A walks 100 feet in front of the spaceship (im assuming this small distance/acceleration is negligible and both clocks can be assumed synchronized still). The spaceship accelerates to near light speed almost instantly, and is already cruising at a constant velocity as it passes twin A. The exact moment it passes twin A it drops its own internal time stamp on twin A. From there it continues out in a straight line to a planet 1 light year away (as measured by twin A). Twin B does not stop, but keeps going, but as he passes the planet he transmits his internal clocks time stamp to the planet. The planet in question is exactly the same mass/size of Earth and is not moving relative to earth. As soon as the timestamp is received it is transmitted back to twin A on earth.

What is the discrepancy between A and B's time stamp the moment after takeoff? ie what effect does massive acceleration have on the clocks.

I am assuming that a planet not moving relative to Earth with the same gravity which is 1 light year away (as calculated from my point of view on earth) will be able to calculate real times based on signals sent back and forth. What I mean is this planet has some information (my twins time stamp as he passed by), and they beam it back to earth. On Earth I receive this signal, and I know it has taken exactly 1 year according to my clock to travel the distance between us, therefor I can simply subtract one year from my clock to know what my clock read at the time the time stamp was produced.

Does that logic work? If so what would my twins corresponding "local time" be at each point?

I'm not looking for real numbers here, just generalizations.

Like at At=0, Bt=0
then B accelerates quickly and sends a time stamp as he passes, so At=0.01 (or something super small) and Bt=? less than my time? or more?

then right as twin B passes the planet 1 light year away (from A's point of view) At=1yr, Bt=??

At= time read on twin A's clock from A's own perspective
Bt = time read on twin B's clock from B's own perspective.

Your question is explained very well here.