You are completely misunderstanding what I am saying. Yes you can have a global reference frame for flat spacetime outside the hole (so yes, you can talk about the size of the EH) but you can’t have a global reference frame that includes both the exterior and interior of the hole or any other curved region of spacetime.
Jeez. YES, there is communication between the entangled pairs but, NO, you cannot use this superluminal communication for any kind of macro world transfer of information. In other words you cannot communicate with someone via the collapse of the wavefunction of entangled conjugate pair.
Two points: First, entangled particles “communicating”. What happens is, two particles are created together in some sort of superposition state: For instance, each particle has a 50% chance of having its spin point up, and a 50% chance that it points down, and we don’t know yet which it is. We let the particles move very far apart (say, a few light years) without disturbing them, and then observe one. Suppose we measure that one partice to be spin up. If someone else observes the other particle a minute later, there’s a 100% chance that they’ll find spin down. On the other hand, if we had observed down, they’d be guaranteed to find up. The observed states are correlated, but we have no way to control whether the particle we observe turns out to be up or down, so we can’t send messages this way. In other words, the particles can talk to each other, but we can’t tell them what to say.
Secondly, about relativity of motion: It is impossible to say who is moving and who is stopped. If DrMatrix and I are both in spaceships, and we pass each other at a very high speed, then I can say that I’m at rest, and he’s moving, so if I sneak a peek at his clock, I’ll say that it’s going slower than mine. On the other hand, he’ll say that he’s at rest and I’m moving, so when he looks at my clock, he’ll say it’s slow. The easiest way to think of this is in terms of rotations. By way of analogy, consider two trains: I’m on a train facing due north, and DrMatrix is on a train facing due northeast. Both trains are three cars long, and they’re parked caboose to caboose. When I look out my window, I see that the back of his train is at the same place as the back of mine, and the front of his is a little bit behind the front of the center car of mine. I then conclude that his train is shorter than mine. However, he looks out his window, and sees something similar, so he concludes that my train is shorter. In my frame of referece, I’m perfectly correct, and in his frame of reference, he’s perfectly correct.
Unless i’ve been lied to my whole life, you are wrong. Since the speed of light is a constant, you can measure your absolute velocity by measuring the relative (to you) speed of light in 3 directions (each direction 90 degrees from the other two). From that you can deduce your relative speed compared to a fixed point in space.
I will concede that DrMatrix could be right if time difference can be negative. For instance, if you approach an object at a high speed, your time relative to that object is slower, but as you move away from that object at high speed, your time relative to that object is faster (or the other way around). But to say that your time will always be slower relative to another moving object would create an impossible paradox.
Excellent explanations, as usual. I really like your comparison to rotation. Let me take it one step further. If time is taken as an imaginary distance coordinate, then relativistic contractions and time dialations are the result of a rotation of the time axis and a space axis pointing in the direction of motion. Your axes are rotated from my point of view and mine are rotated from your point of view.
Monocracy,
You are clinging to the notion that there is some reference frame that is “at rest” and has some proper time. Discard that notion. It is false and misleading. Special Relativity assumes that all motion is relative. That is the “relative” in Relativity. If you and I are coasting past each other and I measure your speed relative to mine as .9c. I can consider myself stationary and that you are moving. I would notice your clocks running slow and I would notice that you are contracted in the direction of your motion. You would consider yourself as stationary and I was moving past you. You would observe my clocks running slow and observe that I was contracted in the direction of motion.
The only speed that is absolute is c. Contrary as it seems, every inertail reference frame measures the speed of light as the same. If you measure the speed of light relative to your rocket, you will get the same value, namely c, no matter what your velocity is.
Don’t listen to him.
Ring,
I found the following in an excellent explanation of Bell’s inequality:
If time slows relative to the stationary frame, then there must be at least two ways of measuring time: the “stationary” time, and the “moving” time. So there’s more than one time, which contradicts your statement that there is only one time.
Monocracy
Do you really think that after nearly a century, physicists have simply not noticed these alledged paradoxes? Say you and I are going 3/5 light speed relative to each other, and we start at the same place with both our clocks saying 12:00. When my clock says 12:25, I will measure your time to be 12:20 (4/5 of 25 minutes). When your clock says 12:20, you will measure my time as 12:16. You’re probably thinking that there’s a paradox because my clock can’t be at 12:25 and 12:16 at the same time. But there is no paradox. Go back to my previous statements. What does it mean to say “When my clock says 12:25, I will measure your time to be 12:20”? It means that I think that the event of my clock reaching 12:25 and the event of your clock reaching 12:20 happened at the same time. But in relativity, there is no absolute “same time”. While I say these two events happen at the same time, you say that actually, the event of my clock saying 12:25 happened long after the event of your clock saying 12:20.
The rotation analogy isn’t perfect, but it can be useful. Suppose that two people disagree as to which way is north by slightly less than 30 degrees, and they both start walking at 5 miles an hour in the direction they think is north. Each person will think that they are getting 5 miles closer to the north pole every hour, but that the other person is only getting about 4 miles closer every hour (because the other person isn’t going directly north). So when the first has gotten what he considers 25 miles closer to the north pole, he considers the other guy to have gotten only 20 miles closer. And when the second guy has gotten what he considers to be 20 miles closer to the north pole, the first guy has only gotten 16 miles closer. So each think that the other person is going northward slower than he is. But there is no contradiction.
That is a legitimate problem. At relativistic speeds, even a single atomic particle is dangerous. That’s what a cosmic ray is. And they won’t give you super powers a la the Fantastic Four.
Good question. Best answer is that space is relatively empty and the odds of a spacecraft hitting something as large as even a baseball is quite small, especially outside the solar system.
“c” is constant & is the max. speed of light.
The speed of light is constant for a given medium (or vacuum) that the light is passing through for any observing reference frame. Observer A and Observer B may see relativistic differences between their own movements but they will see the same speed for a beam of light.
I didn’t mean to imply that there was only one time. I meant that every clock is equally valid; that no clock can be singled out as proper. And that it is arbitrary which inertial reference frames is considered stationary.
** Monocracy**,
OK, that is a contradiction. The first statement should have been that all inertial motion is relative. Those two statements (if worded properly) are the basis of Special Relativity. All of Special Relativity rests on two assumptions:
[li]Every inertial reference frame is equally valid.Light travels at the same speed relative to any inertial reference frame.[/li]
This implies that you cannot determine you speed by comparing the speed of light in various directions. You will always measure the speed of light relative to you as c.
Phobos,
That is not correct.
Every time I say “speed of light” without qualification, please read “speed of light in a vacuum”. The speed of light in a vacuum is constant. The speed of light in a medium is relative and if you define a reference frame moving at the speed of light in your medium in the direction opposite to the direction of your beam of light, light will stand still in while travelling through your medium. The speed of light in a vacuum, however, will still be moving at c relative to the reference frame.
In a medium other than the vacuum the speed of light is still c. The apparent slowing of light is caused by the time delay of the absorption and readmission of photons by the medium
I’m sure you know this, but in a medium the speed of light is still c. The apparent slowing of light is caused by the time delay of the absorption and readmission of photons by the medium
I still don’t understand how c can be relative and absolute at the same time … but anyways, i want to try to understand this impossible paradox that everyone says is not impossible. Example:
Jerry and Yolanda are born on the same day. Jerry is immediately thrown on a spaceship and zips away at .5c for about ten years, then turns around and heads back to Earth at the same speed after the pilot realises that he may have left his stove on. Now, from Jerry’s point of view, 20 years has passed for him, but only 17 have passed on Earth. From Yolanda’s point of view, 20 years have passed for her, but only 17 have passed on the spaceship. If Jerry and Yolanda have sex, who gets charged with statutory rape?
[QUOTE]
*Originally posted by Monocracy *
I still don’t understand how c can be relative and absolute at the same time
[quote]
“Relative” simply means that one can get a different answer. It doesn’t mean that one will.
No, frames of reference are attached to velocities, not people. Since Jerry changed velocities, he has no single frame of reference to work in. If he chooses one and sticks with it, everything makes sense. It’s only when he can’t make up his mind and switches frames midcalculation that he’s left scratching his head.
This is a bit of a hijack, of course, but so far as I know, U. S. law currently contains no provisions for time dilation. Age is defined in terms of a reference frame on the surface of the Earth, so J and Y would legally be considered the same age.
Asimov (I think) actually wrote a short story about this, with a criminal using a time machine to evade a statute of limitations.