Einstein's cat

[monoman]

Hi All,

I’m familiar with the special relativity thought experiment involving a train carriage travelling to the right at a uniform velocity close to the speed of light. Two pulses of light are emitted, at the same time, from the centre of the carriage in opposite directions left and right. To an observer stood in the centre of the train (Einstein), the light pulses hit the carriage walls at the same time. To an observer on the platform (Me), the light pulse that is travelling left will hit the wall first because the wall is moving towards it.
Therefore, the simultaneity of the events depends on the frame of reference.

So, let’s say that the simultaneity of the events determines whether Einstein is going to shoot his cat or not. (There’s a cat and gun in the carriage too). If Einstein sees the two beams of light hit the carriage walls at the same time then the cat dies.
Now to me, I don’t mind the fact that the event’s simultaneity depends on the frame of reference but I can’t have the cat entering a quantum world of dead or alive depending on who observed the event. However, I think there’s no paradox here. As I observe the light beam going to the left, it reflects off the wall first but then has some chasing up to do to get to Einstein’s eyes which are now moving away from him. I think the reverse situation happens with the light beam going to the right so that both beams hit Einstein’s eyes at the same time. Is this right, or have I taken leave of my senses??

I’ll assume it’s right and enter another variable into the equation. As soon as the left beam hit’s the wall, Einstein pulls the emergency cord, which ignites a rocket on the right side of the train, and brings the train to a very quick halt relative to me. (If this causes problems with metal warping, spilt tea etc then just imagine an incredibly large carriage that we can bring to a halt at a nice reasonable pace over time).

I’ve now just realised typing this that my original question probably now doesn’t hold. I was assuming that both beams of light would still, according to Einstein, hit his eyes simultaneously but because the carriage is now accelerating this may not hold. Is this right?
Let me waste our time for moment and assume they do hit his eyes simultaneously, wrt him. So, the left beam, which has reflected from the wall, now has the advantage that Einstein is moving away from it slower & slower, wrt me, and vice versa for the right beam (after it has reflected off the wall). At the point where the carriage is at a stand still wrt me, both beams must be an equal distance from Einstein’s eyes to ensure that the cat dies wrt both of us.
How is this so? It obviously has something to do with general relativity due to the acceleration. Does the thrust on the right side of the carriage cause more length contraction on the right side, or time dilation or …spilt tea?…… Jesus, help!

Sorry for the long post

Oh, one more thing. What is it fundamentally about General Relativity that requires it to be described in terms of warping space. Could the equations also be described in terms of a classical force?

[Dancing David]

I am not sure but I think that the observer on the platform will see the light strike both walls simultaneously.

Poor cats, ever since Scroedinger, they are always under threat.

[davidhorman]

Caveat: I only got about halfway through your post before I got confused... :)

Now to me, I don’t mind the fact that the event’s simultaneity depends on the frame of reference but I can’t have the cat entering a quantum world of dead or alive depending on who observed the event.

It won't, since:

If Einstein sees the two beams of light hit the carriage walls at the same time then the cat dies.

The cat's life is only dependent on what Einstein sees. You'll just disagree with Einstein over what you saw. Einstein only sees one outcome, and shoots poor kitty. Thanks to Einstein's theories, you can calculate what Einstein would have seen and you'll understand why he shot the cat.

I think the reverse situation happens with the light beam going to the right so that both beams hit Einstein’s eyes at the same time. Is this right, or have I taken leave of my senses??

I think you're right. If Einstein isn't accelerating, he may as well be in a stationary carriage, and we know that in that case he'd see the two light beams hit the walls simultaneously.

David

[LostAngeles]

Originally posted by Dancing David
I am not sure but I think that the observer on the platform will see the light strike both walls simultaneously.

Poor cats, ever since Scroedinger, they are always under threat.

So wait, should we be concerned with the Quantum pharmacists (read: homeopaths. I think Kumar or someone responding to him called them something like that) who let their kitties suffer and die horribly, or the Quantum physicists who kill thought kitties in their cruel thought experiments?

[FireGarden]

I think the reverse situation happens with the light beam going to the right so that both beams hit Einstein’s eyes at the same time. Is this right, or have I taken leave of my senses??
It doesn't matter.
In relativity, an observer refers to someone who can collect infomation. Einstein would not report what he had seen. He would report to you what happened in his frame of reference. EG: To answer the question "did the light beams reach the ends of the train at the same time?", he would have accurate clocks at both ends of the train and some mechanism that records the arrival of the beams of light. He would then simply compare times and then conlude that the beams of light arrived at the same time. (Why kill the cat?)

As a different observer, you would not have access to Einstein's clocks. You would have to get your infomation from stationary clocks in your own reference frame. In the thought experiment, it is assumed that you have a clock at every point in space. You'd have to find the two that record the arrival of the light beams, but it is assumed that this problem can be overcome.


Of course, this thought experiment is normally for special relativity and constant motion.

[Ziggurat]

Originally posted by monoman

Oh, one more thing. What is it fundamentally about General Relativity that requires it to be described in terms of warping space. Could the equations also be described in terms of a classical force?

Shorty answer: freefall in a uniform gravitational field is an inertial reference frame (that is, there's no way to tell from local information that you're falling and not floating in deep space). But of course, gravity is not uniform globally. But because we want to treat falling reference frames as inertial frames, that means they have to be "geodesics". It's sort of like how a straight line on the surface of a sphere becomes a great circle around the sphere. In order for what looks like a curved path of a falling object in a gravitational field to be equivalent to a straight path in the absence of gravity, we need space-time to be curved, so that in this four-dimensional space, it actually *is* straight in some sense (in the same sense that a great circle around the surface of a sphere is a straight line on the surface).

Hope that doesn't confuse things more than they already were. But no, you cannot describe general relativity in terms of a classical force.