my discussion...

[spikenigma]

Ok, myself and a mate were having a discussion about these two all morning and so I thought I'd throw them to the board....

1.

A variation on the old twins paradox.


There are two twins born from artificial wombs. Twin A is born on earth. Twin B is born on a relativistic laser propelled rocket doing a CONSTANT 0.86c with no acceleration relative to earth (the rocket did all its accelerating before Twin B was born).

After its acceleration for an arbitrary amount of time its engines are turned off and it travels at a constant 0.86c relative to earth, Twin B is born shortly after.

The twins are both born at the exact same time in respect to each other just as the rocket goes past earth.

General relativity as I understand it states that all frames of reference are completely equal; thus Twin B on the rocketship can state that earth is travelling away from him at 0.86c, whilst he himself is stationary relative to it

After a while the rocket returns to Earth.

Which twin is older?


2.

Quantum entanglement as I understand it happens instantaneously over any distance. i.e. a particle (and its twin) are both in a superposition of all their possible states. When a measurement of particle A happens, particles A and B will instantly collapse into a known state, they are entangled because you can tell the state of particle B from the measurement of particle A, also when one collapses the other will do the same

disclaimer: Now I know this can't be used to send classical FTL information blah blah blah, classical medium of information transfer to show correlation between the results has to be used bling bling blah!
however


2 Trillion entangled particles are created on earth (each one particle entangled to another one particle and no other). Particle group B is put onto the old relativistic rocketship, which travels at 0.6c (time dilation ratio for every 1 second on the ship 1.25 on earth), which is accelerating up to 0.86c. Particle group A is on earth.


Particle groups A and B are measured both during the rockets acceleration and the constant 0.86c

The rocket gets back to earth and he results are compared


* Quantum Theory (AIUI) states that the results will show that the collapse was (and will always be) instantaneous
* General Relativity (AIUI) states that everything inside the ship will experience time dilation, so thus the particles on the ship cannot collapse into known states instantaneously with their twins

do the results show that the collapse happened instantaneously or not?

that's all, grateful for the input

[Surlethe]

Ok, myself and a mate were having a discussion about these two all morning and so I thought I'd throw them to the board....

1.

A variation on the old twins paradox.


There are two twins born from artificial wombs. Twin A is born on earth. Twin B is born on a relativistic laser propelled rocket doing a CONSTANT 0.86c with no acceleration relative to earth (the rocket did all its accelerating before Twin B was born).

After its acceleration for an arbitrary amount of time its engines are turned off and it travels at a constant 0.86c relative to earth, Twin B is born shortly after.

The twins are both born at the exact same time in respect to each other just as the rocket goes past earth.

General relativity as I understand it states that all frames of reference are completely equal; thus Twin B on the rocketship can state that earth is travelling away from him at 0.86c, whilst he himself is stationary relative to it

After a while the rocket returns to Earth.

Which twin is older?

If the rocket was moving away from Earth, how does it return to Earth without accelerating?

[spikenigma]

If the rocket was moving away from Earth, how does it return to Earth without accelerating?

I suppose it would have to, but for the return trip back the acceleration and subsequent speed are negligable and non-relatavistic so as to allow any further time dilation be completely disregarded

[LadyTevar]

If the rocket was moving away from Earth, how does it return to Earth without accelerating?

I suppose it would have to, but for the return trip back the acceleration and subsequent speed are negligable and non-relatavistic so as to allow any further time dilation be completely disregarded

Or maybe it was just set up in a long orbit?

[Surlethe]

In either case, the rocket must accelerate: if it's in a long orbit, it's accelerating already, and it's in a gravitational field, so SR doesn't apply; and if you're going to turn around and go back, you first have to turn (an acceleration) and then get your speed from 0.86c to -0.86c, which is an acceleration. And if it accelerates, you can't expect SR to hold.

[Lord Zentei]

General relativity states that the laws of physics have the same form in all frames of reference. It does NOT state that all frames are equal with regards to time dilation.

Special relativity (and general relativity) states that all inertial frames are equal with regards to dilation, but that does not lead to a paradox because they cannot interact locally more than once without one or both observers experiencing accelleration, so the frame(s) are no longer inertial.

[drachefly]

* Quantum Theory (AIUI) states that the results will show that the collapse was (and will always be) instantaneous
* General Relativity (AIUI) states that everything inside the ship will experience time dilation, so thus the particles on the ship cannot collapse into known states instantaneously with their twins

There is no way to tell what order they collapsed in. If the state of an entangled system just collapsed in respect to a distant system, there is no way to tell until you compare notes, so you won't know when it happened.

To put it another way, if you ditch Copenhagen and just go strict QM, then replace all instances of 'collapse the wavefunction', which is global, with 'become entangled with the macrostate', which is local. The predictions come out the same, and simultaneity doesn't even come up.

[Miles Teg]

Or maybe it was just set up in a long orbit?

"Acceleration" is defined (roughly) as any change in speed or direction of travel (or a combination). If you are in a car going a constant 50MPH, and you turn, you are still accelerating (even if your speed stays exactly 50MPH). The idea is that your speed in the direction you were traveling decreases, while your speed in the new direction (which was initially 0) increases. Does that make any sense?

Miles Teg

[Surlethe]

Or maybe it was just set up in a long orbit?

"Acceleration" is defined (roughly) as any change in speed or direction of travel (or a combination). If you are in a car going a constant 50MPH, and you turn, you are still accelerating (even if your speed stays exactly 50MPH). The idea is that your speed in the direction you were traveling decreases, while your speed in the new direction (which was initially 0) increases. Does that make any sense?

Miles Teg

You could also think of it from the reference frame of the car: it appears, to anyone riding in the car, that there is a centrifugal force pulling against the direction of the turn. The reference frame is therefore not inertial.

[Teleros]

Which twin is older?

Depends on if you allow for the time dilation. If you do, the one on Earth is older, if you don't they're both the same age.

do the results show that the collapse happened instantaneously or not?

They won't - for one thing, quantum entanglement isn't instantaneous - New Scientist reported a lower limit for its effect of umpteen thousand times the speed of light, and an upper limit that was one of those stupidly big numbers you hear about (millions / billions / whateverillions of times the speed of light). I'll try to find it later (it's gone midnight and I'm tired ).
Not sure how much this helps your question however: I'm no quantum physicist so I can't tell you what effect such a high velocity will have on entanglement timings (what effect does it have with say black holes people? You get time dilation there with the event horizon, so maybe that'll offer a clue)...

[Kuroneko]

There are two twins born from artificial wombs. Twin A is born on earth. Twin B is born on a relativistic laser propelled rocket doing a CONSTANT 0.86c with no acceleration relative to earth (the rocket did all its accelerating before Twin B was born). After its acceleration for an arbitrary amount of time its engines are turned off and it travels at a constant 0.86c relative to earth, Twin B is born shortly after. The twins are both born at the exact same time in respect to each other just as the rocket goes past earth.

Alright. The simultaneity criterion makes sense iff the two twins are not spatially separated at the moment of birth (or only negligibly so). Otherwise, what's simultaneous according to A would not be simultaneous according to B.

I suppose it would have to [accelerate], but for the return trip back the acceleration and subsequent speed are negligable and non-relatavistic so as to allow any further time dilation be completely disregarded

That's true enough, but what cannot be disregarded is the fact that even if B's acceleration is negligible, B still has at least two different intertial frames throughout this experiment, while A only has one. Although B can consider A receding and then incoming, B is the one who accelerated and therefore switched inertial frames. The situation is therefore asymmetric. This becomes completely obvious if one consideres the spacetime trajectories. From A's point of view:

Code: Select all

^t  (t,x)-coordinates
+(2d/v,0)
|\  ^  B travels with outward speed v, i.e., along the
| \ |  line x = vt for the first part of the trip, and
|  \|  then with inward with the same speed, i.e., along
|   +  the line x = d-vt for some distance d at which the
|  /|  turnaround [+(d/v,d)] occured.
| / |
|/  |
*---+---->x