Special Relativity paradox

[Zeno]

Special Relativity:

Person C is at the exact middle of two points A and B like so.

A----------C----------B.

A and B both emit a flash of light that reaches person C at the same time.

Person D is moving at high velocity towards person C and reaches C at the same time that both flashes of light reach C. The flashes are emitted simultaneously for C but not for D.

Beneath A and B there are ramps leading down into a single hole like so:
A-----------B
--\--------/
---\------/
----\----/
-----\--/

when the lights flash they trigger a mechanism at each light which releases a bowling ball at the top of each ramp which is just small enough to fit through the hole at the bottom. So, from the point of view of person C, the bowling balls run into each other at the bottom and neither falls through. From the point of view of person D, one ball is released first, falls through the hole, followed by the second ball.

What's wrong?

 

[Arch_Rival]

length contraction A-C and C-B will be the same to D. Therefore the distance light travels from A to C is same as distance from B-C as seen by D. So the pulses of light will be simultaneous as observed by D.

 

[Zeno]

True, the pulses of light will be seen simultaneously by D, but according to D they will have not been emitted simultaneously.

 

[przyk]

True, the pulses of light will be seen simultaneously by D, but according to D they will have not been emitted simultaneously.

The pulses also don't travel the same distance. A and B are moving in D's rest frame. While D is the same distance from both at the time the pulses reach C/D, this isn't true at the time each pulse is emitted.

 

[(Q)]

Special Relativity:

Person C is at the exact middle of two points A and B like so.

A----------C----------B.

A and B both emit a flash of light that reaches person C at the same time.

Person D is moving at high velocity towards person C and reaches C at the same time that both flashes of light reach C. The flashes are simultaneous for C but not for D.

No, regardless of the fact that D is moving at high velocity, D will still measure the speed of light at c, and will observe the flashes simultaneously, since D would be in the same reference frame as C. The only difference would be dependent on which direction D was moving and may observe the flashes to be red-shifted and/or blue-shifted.

True, the pulses of light will be seen simultaneously by D, but according to D they will have not been emitted simultaneously.

That would depend on which direction D was traveling, away from A or away from B. If equal distance, D would observe the flashes to have been emitted simultaneously.

Beneath A and B there are ramps leading down into a single hole like so:
A-----------B
--\--------/
---\------/
----\----/
-----\--/

when the lights flash they trigger a mechanism at each light which releases a bowling ball at the top of each ramp which is just small enough to fit through the hole at the bottom. So, from the point of view of person C, the bowling balls run into each other at the bottom and neither falls through. From the point of view of person D, one ball is released first, falls through the hole, followed by the second ball.

What's wrong?

D is then traveling either away from A or away from B and is no longer in the same reference frame as C, and not of equal distance. If D observed simultaneity previously, then D may have changed direction at the point of C.

 

[Zeno]

“ True, the pulses of light will be seen simultaneously by D, but according to D they will have not been emitted simultaneously. ”

That would depend on which direction D was traveling, away from A or away from B. If equal distance, D would observe the flashes to have been emitted simultaneously.

It doesn't depend on the direction D was traveling. Because light is always measured as c, the length of time depends on the distance at the time of emission. For example, let's say D is traveling at high speed from A to B, when D reaches where C is at and sees both flashes of light, according to D the flash from B will have been emitted before the flash from A.

 

[(Q)]

So, essentially what you're saying is that D, while in the same rest frame and coordinate as C, will not see the flashes simultaneously, but C will?

 

[Zeno]

It doesn't depend on the direction D was traveling. Because light is always measured as c, the length of time depends on the distance at the time of emission. For example, let's say D is traveling at high speed from A to B, when D reaches where C is at and sees both flashes of light, according to D the flash from B will have been emitted before the flash from A.

Sorry, I stand corrected. I was assuming that people understood that D is moving from left to right or right to left in the problem and not coming straight down from above C.

So, essentially what you're saying is that D, while in the same rest frame and coordinate as C, will not see the flashes simultaneously, but C will?

How did you come to that conclusion? Confusion between 'occurred' and 'been emitted'?

 

[EndLightEnd]

How about the time difference would not be great enough and the bowling balls would get stuck anyway.

 

[Zeno]

How about the time difference would not be great enough and the bowling balls would get stuck anyway.

There really is no limit on how far away A and B may be from each other, the difference might be light-years and the time difference may be years. As far as the bowling balls getting stuck, that's a cop-out.

 

[przyk]

For example, let's say D is traveling at high speed from A to B, when D reaches where C is at and sees both flashes of light, according to D the flash from B will have been emitted before the flash from A.

Remember that from D's point of view, it is A and B who are travelling at high speed, so the two emitters are not at the same distance from D at the time each pulse is emitted.

There really is no limit on how far away A and B may be from each other, the difference might be light-years and the time difference may be years. As far as the bowling balls getting stuck, that's a cop-out.

You're also applying an old, superseded, non-relativistic law of gravity. You'd probably need general relativity to do a proper analysis of this problem.

 

[Pete]

Hi Zeno,
According to C, the bowling balls have the same speed.
According to D, they have different speeds.
The bowling balls reach the hole at the same time according to everyone.

Przyk,
Gravity isn't really relevant. The thought experiment would work equally well if the bowling balls were pushed toward the hole rather than falling under the influence of gravity.

 

[przyk]

Hi Pete,

Gravity isn't really relevant. The thought experiment would work equally well if the bowling balls were pushed toward the hole rather than falling under the influence of gravity.

You can easily transform the trajectories of both balls, but I'm not sure that the gravitation law Zeno is applying will be able to account for their transformed velocities. Even if it does it's not that interesting though, as classical gravity is known not to be a relativistic theory in general anyway.