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Originally Posted by Grey
Well, it is possible, but saying that nothing ceased to exist is simply false. There were some particles with measurable properties, like charge, spin, mass, and so forth (as well as some properties that are less definite, like position and momentum). Afterward, there are some different particles, with different values for charge, mass, spin, position, etc. Your argument would seem to apply here just as well, but we know that this is possible.
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As I understand them, charge and spin are forms of energy as is momentum. I assume, perhaps blythely, that the energy of the photons produced from such a collision conserves all of that. Is this not true? As for position, we don't know of anything that is absolute rest so it changes with time anyway and there is nothing there to conserve.
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Originally Posted by Grey
Let me anticipate some of the possible differences between this situation and the happy mix/researcher exchange, and try to explain why they shouldn't be relevant. In the positron-electron annihilation, I'm creating massless photons ("energy") from the particles. But I could just as easily give the electrons enough energy to instead form a muon-antimuon pair (or a proton-antiproton pair, or anything else), so I'm destroying one set of particles and creating a different set of particles. So it can't just be that its the conversion to energy that's special.
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But, the mass and energy emitted from such reactions always adds up to the same thing on both sides of the equation, right? Boiling water, a change of state, does not violate the conservation laws, although one might be forgiven for thinking that the water was "destroyed".
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Originally Posted by Grey
You could complain that in these examples I'm always using particle-antiparticle pairs. But that comes from a different conservation law, one that has nothing to do with conservation of energy. Specifically, baryon number and lepton number are conserved. I can have all kinds of reactions that transform one set of particles into another set, but as long as the total energy, total count of baryons, total count of leptons (of each type), total spin, and so on, of the two system are the same, there's nothing that prohibits the change.
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Okay, so there are actually more conservation laws at work than I considered. At first blush, this would strengthen my case rather than weaken it. Time travel would necessarily make a mess of these other laws as well.
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Originally Posted by Grey
Actually, it would be perfectly fine for reasearcher F to stay around. What has to happen is for researcher P to step in, and the happy mix will reappear. If another bag of happy mix happens to be sitting there, too, no big deal.
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If neither researcher travels forward in time after shoving the happy mix forward two years in time, they will both be present with the happy mix two years after the time travel expedition began. This results in the increase of mass in the present and following future, a clear violation of conservation law.
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Originally Posted by Grey
But what's more important is that the situation you describe has lots of problems that have nothing to do with conservation of energy. Why do you assume the happy mix will suddenly reappear if researcher never gets into the time machine. Here you're touching on the issues of causality and self-consistency that John was touching on. We know that researcher P has to get in the machine and go back in time (and be replaced by the bag of happy mix), because we've already seen the effects of it. Whatever happens, the set of events that transpires has to be self-consistent.
The fact that we see the effect before the cause, and that we therefore imagine that we could choose not to perform the action that is the cause (i.e., we see the researcher appear from travelling back in time, but then the researcher changes his mind and decides never to go back in time after all) is the difficulty here. That's the reason most physicists think that backward time travel is not possible, and it has nothing to do with conservation of energy.
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I agree, that it plays havoc with causality. I am arguing that the conservation laws protect causality because it is impossible to move in time without violating them in some way.
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Originally Posted by Grey
Although quantum mechanics does suggest that many things are discrete (not everything, though; some things can take on a continuum of values in quantum mechanics), I don't think that Xeno proved that it has to be so. That is, I think there are some obvious flaws in his paradoxes that have long since been shown, and his philosophical musings do not prove that motion through a continuum is impossible. But that's perhaps a subject for a different thread.
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Not that I have seen. Newton more or less said that "we get close enough that it won't matter" when he developed calculus and the theory of limits, but that is not really an adequate answer to the problem.
Even so, I would agree with you that this really should be the subject of another thread.