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Member (Idle past 4843 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
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Author | Topic: Age of the Universe | |||||||||||||||||||||||
Taco Inactive Member |
Mike,
I agree that it is general relativity that equates acceleration to gravity. However, as I understand it one can calculate the effect of Joe (or Moe) deccelerating by treating his speed at every infinitessimally small time delta(t) as an inertial system (and therefore described by special relativity). Integrating all his speeds over time will then give you the necessary effect to break the paradox.
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JustinC Member (Idle past 4843 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
deleted
[This message has been edited by JustinCy, 10-27-2003]
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JustinC Member (Idle past 4843 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
quote:Yeah, I knew a little bit about QM before, but this is kindof insane. I can accept a photon somehow going through two holes and interferring with itself, I can even accept an electron somehow travelling through two holes and interferring with itelf, but an atom? And what about an observer collapsing a wave function? Two particles being linked across space, where collapsing the one collapses the other instantaneously? What is one to make of all this? JustinC
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NosyNed Member Posts: 8996 From: Canada Joined: |
The quote is: (don't remember source)
"The universe is not only stranger than we imagine, it is stranger than we can imagine."
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JustinC Member (Idle past 4843 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
That sounds like a rip off of this one
Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose. -J. B. S. Haldane
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NosyNed Member Posts: 8996 From: Canada Joined: |
Thank you, you are right. I 'membered wrong (not for the first or last time).
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Mike Holland Member (Idle past 483 days) Posts: 179 From: Sydney, NSW,Auistralia Joined: |
Hello Taco,
Sorry I could not get back sooner. We have just had a catastrophe with house damage due to a hailstorm. I understand what you are saying regarding integrating over inertial frames, but I don't believe it solves the problem. The twin paradox arises because each sees the other's clock running slow while they are in relative motion, so that when they come together Joe says 'your clock is slow', and Moe says 'Your clock is slow'. The answer is that Moe sees Joe's clock running fast while he turns around, and this makes up the difference. I think we agree up to this point. But there is nothing in Special Relativity that allows for a speed-up of a moving clock relative to a stationary observer. Each of your intermediate inertial frames would see Joe's clock running slow. You cannot integrate a collection of negatives and get a positive. Only General Relativity caters for remote clocks speeding up, as is the case for satellites above our heads. And it provides the correct adjustment for the twin paradox. Mike.
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Primordial Egg Inactive Member |
So here is an interesting puzzle. Despite my agreement, it turns out that there is a difference between the elevator accelerating at 1g, and standing on the surface of the earth. What observations could someone perform if they were trapped in an elevator and needed to tell whether they were located on Earth, or accelerating uniformly through empty space? You may assume whatever measuring equipment you need, but you can't look outside the elevator. I'd do some sort of experiment based on the Coriolis effect (maybe Foucault's pendulum?). - or use a compass- or check to see how good the reception was on my mobile phone PE
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Percy Member Posts: 22391 From: New Hampshire Joined: Member Rating: 5.2 |
Today I realized that checking for a gravity gradient in the elevator wouldn't work because the force might be centrifugal, ie, due to rotation, and would therefore also have a gradient.
The recent suggestion about checking for a Coriolis effect wouldn't be conclusive for the same reason. Angular momentum would have it, gravity on a non-rotating mass would not. --Percy
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Taco Inactive Member |
Hello Mike,
Sorry to hear about the hailstorm. Some things are not so relative after all (if you'll forgive me the bad joke). It is a difficult puzzle, but I now think you are right. It seems I remembered my relativity lectures wrong. As I now understand it, according to general relativity, the fact that one system has an acceleration breaks the symmetry. The systems are therefore no longer equivalent. But all one can do with special relativity is add the infinitessimal timeintervals, to get (tau = clock 1, t is clock 2): tau2-tau1 = integral(from t1 to t2) [dt* sqrt(1-(u(t)/c)^2)] < t2 - t1 Forgive me the poor formula writing but I don't know how to make it come out better.The variable u(t) can still be allocated to both systems since every moment dt both systems are inertial systems. The (apparent) paradox still exists. Only general relativity breaks it. Sorry to all if this goes a bit too far.
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Taco Inactive Member |
JustinC,
I know, QM is insane. The entanglement riddle is solved (as I understand it) by the fact that there is no exchange of information, and therefore there is still no faster than light "travel". Interfering atoms stretch the imagination, but the world is a weird place. I read an excellent book by Brian Greene called "The Elegant Universe". It deals mainly with superstring and M-wave theory, but also goes into QM and relativity. Recommended to those who are interested, but be prepared for ever increasing weirdness. BTW, the book contains a topical quote from Richard Feynman (one of the greatest post-war physicists):"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity one way or another, certainly more than twelve. On the other hand I think I can safely say that nobody understands quantum mechanics." [This message has been edited by Taco, 10-29-2003]
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Sylas Member (Idle past 5260 days) Posts: 766 From: Newcastle, Australia Joined: |
Percipient writes: Today I realized that checking for a gravity gradient in the elevator wouldn't work because the force might be centrifugal, ie, due to rotation, and would therefore also have a gradient. The recent suggestion about checking for a Coriolis effect wouldn't be conclusive for the same reason. Angular momentum would have it, gravity on a non-rotating mass would not. The gravitational field due to a massive object cannot be reproduced by any motion. You can reproduce the effect locally, but gravity introduces effects of space curvature which can be detected with measurements of sufficient accuracy over a sufficient portion of the space. The pages we have cited are not kidding when they state the rotational motions and accelerated motions can all be handled without invoking general relativity. General relativity is based on an insight that gravitational forces are locally indistinguishable from internal forces. That does not mean general relativity is redundant, and it does not mean that the mathematical tools for motions will manage all aspects of gravity. The field over a region of space is different, and this is why general releativity is required for handling gravity, whereas special relativity is sufficient for accelerated motions. Whether you can detect the differences within a restricted space like an elevator will depend on various considerations. You can tell the difference between gravitational forces at the surface of the earth and a straight line acceleration using existing technology. But you will not be able to tell the difference between a 1g straight line acceleration and the gravitational field due to a more massive object at a greater distance. The difference is still real; but reduced below the range of detection with existing technology. I think rotational motions would be substantially worse for reproducing the field we experience at Earth's surface. Your last sentence is a bit hard to follow. The coriolis effect from circular motions would be a dead easy way to recognize that the elevator was not simply at rest on Earth's surface. Also bear in mind that the gradient from a circular motion would follow an inverse law; not an inverse square relation. Such a second order difference would be much harder to exploit than the coriolis effects, but it is a real difference nevertheless, and continues to underline the basic point that yes, really and truly, general relativity is not required for accelerated motions and it is required to handle gravity. It is a true generalization of a simpler case. I am confident that no motion of any kind could reproduce the effects of gravitation felt at earth's surface with sufficient fidelity to prevent detection with existing technology over a region of space encompassing, say, three meters in diameter. Cheers -- cjhs [This message has been edited by cjhs, 10-29-2003]
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Sylas Member (Idle past 5260 days) Posts: 766 From: Newcastle, Australia Joined: |
Taco writes: Forgive me the poor formula writing but I don't know how to make it come out better. The variable u(t) can still be allocated to both systems since every moment dt both systems are inertial systems. The (apparent) paradox still exists. Only general relativity breaks it. Sorry to all if this goes a bit too far. No problem. But your point that only general relavity resolves the paradox is incorrect. The resolution is in observing that the twins are not equivalent. The solution works fine in special relativity. You can handle motions using special relativity and a bit of calculus. General relativity is a more complete framework which is overkill for a problem due to motions only. Applying general relativity to this problem is a useful way to help see how inertial forces and gravitational forces are equivalent and managed all within a single framework, but that is not what resolves the paradox. The paradox is resolved by seeing that only one of the twins remains in a single inertial frame. From the same page cited previously (The Travelling Twins Puzzle):quote: [This message has been edited by cjhs, 10-29-2003]
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JustinC Member (Idle past 4843 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
quote:According to the book I'm reading, it seems it can. Say an atom emits two photons (going different directions), but the photons can be either polarized one of three ways. According to QM, the photons have a probability of being polarized one of the three ways, and it doesn't 'decide' which way until you it is observed. So once you observe it, it decides what angle it is polarized at, and the other photon (which may be light years away) instantaneously changes to one of the other polarized angles. According to this book, its been proven statistically that the odds of getting one of the three angles for the polarized light is different if it 'decides' once its observed rather than the atom emitting a certain angle from the start and we just don't observe it. And the experiments have proven QM correct. Is that not considered information? I've only read the first two chapters, so I think he might come back to this subject and you may be right that is technically not 'information'. But to me, right now, it seems it is. JustinC [This message has been edited by JustinCy, 10-30-2003]
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Percy Member Posts: 22391 From: New Hampshire Joined: Member Rating: 5.2 |
JustinCy writes: Is that not considered information? Yes, this is not considered information. Take your example of three possible polarities. Let's say you want to send a message to your partner about whether to buy, sell or stand pat on a stock. You agree that polarity A means buy, polarity B means sell, and polarity C means stand pat. So now you're watching the stock market and you need to send a message to your partner to buy. How do you guarantee that he sees polarity A? Don't waste too much time thinking about this - it isn't possible to control the polarity. --Percy
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