The whole point of locality is to make sure that this isn't a problem, by asserting that information can't travel across spacelike intervals.
But, you know, there is such a thing as a timelike interval, that is, a pair of points such that in ANY frame, one is in the past of the other.
The existence of different reference frames does nothing to disprove determinism. Try to learn the physics before you start using it to make philosophical arguments. It makes it much more effective.
It is the theory that has been making steady progress since the introduction of quantum mechanics, using probabilistic interpretations. Progress like the development of quantum field theory, and the standard model.
Your complaints that that the consequences of probabilistic interpretations are absurd are like the complaints of opponents of relativity that relativity's consequences are absurd. The same sort of arguments that you're making now can be turned into arguments that we should be using an "ether-based" theory to explain electromagnetism. One which does all its work in some absolute reference frame, but makes the same predictions as relativity.
Yes, you can do it that way. But it's a pain in the ass, and the only benefit to it is that it pretends to satisfy the philosophical preconceptions of people who believe there's an absolute reference frame. It doesn't actually, it just pretends to. Same with Bohmian mechanics.
It is the nonprobabilistic interpretations that have run into a dead end, while the "a particle has no real position" crowd is happily making progress.
The way Conway and Kochen have defined "free will" is, loosely, any behavior that isn't determined by the past. So, no, there's no reason for a particle to be intelligent to "have free will". Plain old wavefunction collapse in the Copenhagen interpretation is a particle exhibiting free will.
Honestly, the actual result isn't particularly interesting, if you believe that human thought and behavior can theoretically be explained by traditional physical processes.
The interesting thing about the theorem is that the proof skips all that, and with a very simple setup, demonstrates that if humans can do something (pick which measurement to make) independently of the past, then elementary particles can too, without making any assumptions on what exactly makes humans act the way they do.
Not quite. The fact that the n-sphere is simply connected is pretty easy to prove.
Poincare asked whether every closed simply connected 3-manifold is a 3-sphere.
A surface is a 2-manifold. The sphere, plane, Mobius strip, Klein bottle, and so on are all 2-manifolds.
A 3-manifold is just a natural extension of that idea, except instead of a surface, you have a 3-dimensional object. They're a bit hard to visualize, since most of them don't "fit into" our notion of space, in the same way that a sphere doesn't fit into a plane.
Anyway, Poincare's original question In English: if you have a 3-manifold with no holes and no border, is it necessarily the 3-sphere?
Translating the more general version into English is a bit more difficult, and I'll leave it to those who actually have experience with the problem. I just read the Wikipedia article.
Just a bit more information from there that might be interesting: The problem is actually easier for higher dimensions. It was first shown for dimensions 7 and above, and then worked down to the lower dimensions.
So does it really matter whether "time itself" is slowing down or everything is simply going faster? To me, they're the same thing.
Of course, the whole "backwards in time" thing is a bit iffy, but the main point of relativity is that time dilation and space contraction effects (as well as enegry stuff) approach infinity as the your speed approaches c. Whether these effects are "time itself" changing or just the way you see things doesn't really matter. The effects prevent you from going above the speed of light anyway.
On that note, when people discovered that light was observed to move at the same speed in all reference frames, they tried to stick with the idea of ether, and put it a bunch of math that would account for the fact that light always travels at c. Well, all of this math eventually ended up being equivalent to relativity, as in, it made the same predictions. Your idea of "time itself", like the ether, is simply an artifact of your intuition. Your intuition was developed by observing things at small speeds moving relative to an absolute frame of reference (the Earth). As such, it is normal to expect that it might not apply in other environments, such as very high speeds, in the same way that your social experiences don't apply if you move to another country with a totally different culture.
This is all assuming, of course, that you agree with the mathematics of relativity. Recall that special relativity assumes only a few facts, such as that light travels at c whatever reference fram you're in, and derives all the math from there. In order to disagree with relativity you'd need to either disagree with those facts (which have been experimentally confirmed, mind you), or disagree with the derivations, which have been checked and rechecked a bunch of times.
Note also that relativity, especially special relativity, has a whole ton of evidence backing it up. Particle accelerators give electrons energies that, under Newtonian mechanics would put them well above c, but we observe them going no faster than c. The more energy you put in, the closer to c they go, but no matter how much you put in, the speed of the particle never surpasses c.
Dude, this is wrong even in Newtonian Mechanics. E = 1/2 m*v^2. Given an object of mass 2 kilograms, it takes 1 Joule to accelerate it to 1 m/s, but 4 Joules to accelerate it to 2 m/s. Therefore it takes 3 Joules to accelerate it from 1 m/s to 2 m/s.
E=mc^2 does not derive from E=mv^2. First of all, the correct formula is E = 1/2 mv^2. Second of all, E=mc^2 describes the rest energy of an object of mass m. This is the energy it has when it is not moving, i.e. v=0. Newtonian mechanics would give E=0. (Of course, the zero level of energy is more or less arbitrary.)
"Sorry, I also want to pont out that American kids in my opinion are often more well rounded at youth."
'Well-rounded', as you pointed out, is a matter of opinion. It means that a person has learned somewhat equal amounts in most subject areas. However, the definition of 'equal' is disputable. For example, how do you compare progress in mathematics to progress in writhing skills? Perhaps russians would consider american kids to not we well-rounded because they know too little math.
If only one of the 6 was there because she enjoyed the game, then the other 5 were 'there because of their boyfriends'. By the pigeonhole principle, at least one nerd/geek must be doing very well indeed.
Slashdot Mirror
No, the worst part is this.
''I was eliminated on the basis of my intellectual makeup,'' he said. ''It's the same as discrimination on the basis of gender or religion or race.''
I for one, think that eliminating people from being policemen on the basis of their intellectual makeup is a very good idea.
However, I assume both quotes were simply ripped out of their context and thrown into the article to make it more interesting.
no u
The whole point of locality is to make sure that this isn't a problem, by asserting that information can't travel across spacelike intervals.
But, you know, there is such a thing as a timelike interval, that is, a pair of points such that in ANY frame, one is in the past of the other.
The existence of different reference frames does nothing to disprove determinism. Try to learn the physics before you start using it to make philosophical arguments. It makes it much more effective.
It is the theory that has been making steady progress since the introduction of quantum mechanics, using probabilistic interpretations. Progress like the development of quantum field theory, and the standard model.
Your complaints that that the consequences of probabilistic interpretations are absurd are like the complaints of opponents of relativity that relativity's consequences are absurd. The same sort of arguments that you're making now can be turned into arguments that we should be using an "ether-based" theory to explain electromagnetism. One which does all its work in some absolute reference frame, but makes the same predictions as relativity.
Yes, you can do it that way. But it's a pain in the ass, and the only benefit to it is that it pretends to satisfy the philosophical preconceptions of people who believe there's an absolute reference frame. It doesn't actually, it just pretends to. Same with Bohmian mechanics.
It is the nonprobabilistic interpretations that have run into a dead end, while the "a particle has no real position" crowd is happily making progress.
The way Conway and Kochen have defined "free will" is, loosely, any behavior that isn't determined by the past. So, no, there's no reason for a particle to be intelligent to "have free will". Plain old wavefunction collapse in the Copenhagen interpretation is a particle exhibiting free will.
Honestly, the actual result isn't particularly interesting, if you believe that human thought and behavior can theoretically be explained by traditional physical processes.
The interesting thing about the theorem is that the proof skips all that, and with a very simple setup, demonstrates that if humans can do something (pick which measurement to make) independently of the past, then elementary particles can too, without making any assumptions on what exactly makes humans act the way they do.
There is no such thing as a uniform distribution over the real numbers. Assuming that there is is bound to lead to contradictions.
Er, but in order for you to watch in on TV, someone needs to film it first, no?
Not quite. The fact that the n-sphere is simply connected is pretty easy to prove. Poincare asked whether every closed simply connected 3-manifold is a 3-sphere. A surface is a 2-manifold. The sphere, plane, Mobius strip, Klein bottle, and so on are all 2-manifolds. A 3-manifold is just a natural extension of that idea, except instead of a surface, you have a 3-dimensional object. They're a bit hard to visualize, since most of them don't "fit into" our notion of space, in the same way that a sphere doesn't fit into a plane. Anyway, Poincare's original question In English: if you have a 3-manifold with no holes and no border, is it necessarily the 3-sphere? Translating the more general version into English is a bit more difficult, and I'll leave it to those who actually have experience with the problem. I just read the Wikipedia article. Just a bit more information from there that might be interesting: The problem is actually easier for higher dimensions. It was first shown for dimensions 7 and above, and then worked down to the lower dimensions.
That's brilliant.
E=1/2 mv^2 isn't even true in relativity, so that seems unlikely.
So does it really matter whether "time itself" is slowing down or everything is simply going faster? To me, they're the same thing. Of course, the whole "backwards in time" thing is a bit iffy, but the main point of relativity is that time dilation and space contraction effects (as well as enegry stuff) approach infinity as the your speed approaches c. Whether these effects are "time itself" changing or just the way you see things doesn't really matter. The effects prevent you from going above the speed of light anyway. On that note, when people discovered that light was observed to move at the same speed in all reference frames, they tried to stick with the idea of ether, and put it a bunch of math that would account for the fact that light always travels at c. Well, all of this math eventually ended up being equivalent to relativity, as in, it made the same predictions. Your idea of "time itself", like the ether, is simply an artifact of your intuition. Your intuition was developed by observing things at small speeds moving relative to an absolute frame of reference (the Earth). As such, it is normal to expect that it might not apply in other environments, such as very high speeds, in the same way that your social experiences don't apply if you move to another country with a totally different culture. This is all assuming, of course, that you agree with the mathematics of relativity. Recall that special relativity assumes only a few facts, such as that light travels at c whatever reference fram you're in, and derives all the math from there. In order to disagree with relativity you'd need to either disagree with those facts (which have been experimentally confirmed, mind you), or disagree with the derivations, which have been checked and rechecked a bunch of times. Note also that relativity, especially special relativity, has a whole ton of evidence backing it up. Particle accelerators give electrons energies that, under Newtonian mechanics would put them well above c, but we observe them going no faster than c. The more energy you put in, the closer to c they go, but no matter how much you put in, the speed of the particle never surpasses c.
Dude, this is wrong even in Newtonian Mechanics. E = 1/2 m*v^2. Given an object of mass 2 kilograms, it takes 1 Joule to accelerate it to 1 m/s, but 4 Joules to accelerate it to 2 m/s. Therefore it takes 3 Joules to accelerate it from 1 m/s to 2 m/s.
E=mc^2 does not derive from E=mv^2. First of all, the correct formula is E = 1/2 mv^2. Second of all, E=mc^2 describes the rest energy of an object of mass m. This is the energy it has when it is not moving, i.e. v=0. Newtonian mechanics would give E=0. (Of course, the zero level of energy is more or less arbitrary.)
There is no such thing as absolute speeds at all: only relative speeds. That is pretty much the basis of relativity.
"Sorry, I also want to pont out that American kids in my opinion are often more well rounded at youth." 'Well-rounded', as you pointed out, is a matter of opinion. It means that a person has learned somewhat equal amounts in most subject areas. However, the definition of 'equal' is disputable. For example, how do you compare progress in mathematics to progress in writhing skills? Perhaps russians would consider american kids to not we well-rounded because they know too little math.
10-6=4
If only one of the 6 was there because she enjoyed the game, then the other 5 were 'there because of their boyfriends'. By the pigeonhole principle, at least one nerd/geek must be doing very well indeed.