As you pointed out, it does have a singularity, just not a point singularity. There are a couple issues. First, if it's not spinning really fast, there's still that event horizon to deal with. You might be able to pass through the singularity, rather than striking it, but you still won't be able to get back out. It's possible that there might be other universes that you could get to, or you could get to another part of our own if our universe has a weird enough curvature, but there's not any evidence that either of those is the case.

For a Kerr black hole that's spinning fast enough, the event horizon does vanish, and we could in principle have a "naked singularity" that would allow time travel of the sort you suggest. Of course, there's no evidence that this actually could happen either, and many physicists think that naked singularities cannot exist (the cosmic censorship hypothesis).

Even if we assume that these problems can be overcome, there's still the tidal force to deal with as you get close. It may never be infinite, but it will still be really, really large. You'd have to be able to come up with a way to protect yourself from spaghettification on your trip, or your constituent atoms might make it back to an earlier time, but you wouldn't survive the experience.

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Conserve energy. Commute with the Hamiltonian.

Well, maybe I couldn't but an intelligent robot? (shades of Terminator! :-) )

Actually, I would argue that the fallling tree is the cause of the sound of a tree falling and it would make the noise whether heard or not, or even if it were possible for a living thing to hear it or not. The phenomenon does not have to be observed by anyone or anything for it to be real.

I would argue that the tree could rot and become part of the soil, or even be fossilized by geologic forces and never be witnessed by anything capable of being hearing and the noise of the tree would still have been made. No detection of the event is necessary. If it happened, then it happened.

[quote=Grey]The total mass is constant, but one of the postulated events making the total mass constant appears to be a violation of the law of conservation.


And by positing a machine that can deal with the conservation of mass problem that I believe is inherent in time travel we we arrive at several such problems.

Agreed.

Okay, I think I have spotted the problem. We have posited a machine that can do the impossible. It can make mass disappear for a length of time so that another mass can be transported back in time and thereby exist in two places at one and the same time. Nature has not made any such machine and does not appear to make one, not even in theory.

You cannot travel back into the past because you would increase mass in the past. By traveling forward in time, you create a gap in the existence of your mass. It's the conservation law at work.

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There is no God and Dirac was his prophet.

Are you suggesting that it's possible to make a sound which is impossible, even in principle, to hear? I disagree, and I'd ask for an example. In the example of the tree, even if nobody was there, they could have been. If they had been there, they would have heard the sound. This is not the case with the change in total mass. No matter what you do, you'll never be able to design an experiment which would show the total mass to have changed. It's not that if you do not measure something then it does not exist. It's that if you can not measure something under any possible circumstances then it does not exist, at least from a scientific standpoint.

You're again arguing that no detection was made or necessary. But there were many opportunities for detection to have been made in principle, had an observer been present.

This is a contradiction in terms. All conservation of energy states is that the total mass of a closed system will remain constant, as we agreed.

It's true that there is no example of such a device, and no likelihood that there ever will be. But to say that the device is impossible because existing in two places at once is impossible does not have anything to do with the conservation of energy.

Except that you've been provided an example of a hypothetical device that you agree cannot cause any measurable change in the total energy of the system, which is the definition of conservation of energy. Show me the point at which the total mass of the system described has increased or decreased.

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Conserve energy. Commute with the Hamiltonian.

No. I am saying that if something happened, it happened whether it was observed or not. Existence does not rely on consciousness, consciousness relys on existence.

I lay no claim to omniscience, and I do not think that is what you mean to imply here. I mention this only to head off confusion by anyone else following this thread. We are not omniscient and there may well be things we never discover. I agree, if it cannot be measured at all, then there is no reason to think it exists and there would be no way to prove that it exists. Further, such a condition would violate what I, with my philospher's hat on, think of as the law of identity. So, in this we are in full agreement.

Here is what I think we have done. You follow my line of thought and tell me what I have gotten wrong. Oh, and thank you very kindly for having the patience to bear with me this far. This has been most enjoyable for me.

I think the machine example is flawed and here is my reasoning for this conclusion.

If we send something, anything at all, back into the past, we increase mass in the past, clearly a violation of the laws of conservation.

If we send something into the future, we create a gap in the existence of the mass sent, that is equal to the magnitude of the forward leap in time, thus again violating the laws of conservation.

What we propose is a machine that can do two false things at one and the same time. We send mass P into the past by time Z and at one and the same time, send mass F into the future by the same magnitude of time, Z. Taken together, we do not appear to have violated the conservation law, but we propose to do this by violating the conservation laws twice in opposite directions. It's a sillygism. The conclusion is as true as its premises.

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There is no God and Dirac was his prophet.

Very good. This was indeed all I was suggesting, which was why I tried quickly to separate what I was suggesting from the "tree in the forest" question. The latter addresses whether things are real if they are observed, and I was only bringing up the question of whether something could be consider real if it was impossible to observe.

No trouble. I've enjoyed the conversation as well.

Let me suggest a parallel experiment, and ask why your argument does not show it to be just as impossible.

If we destroy two particles, we reduce the energy of the system by a certain amount, clearly violating conservation of energy.

If we create one or more photons out of nothing, we have likewise violated conservation of energy.

Yet we can in fact take an electron and a positron and destroy them, while at the same moment creating two 511 keV photons. Separately, these two events would violate the conservation of energy in opposite directions. However, if they happen at the same time, it's not only permissible, but a pretty common event.

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Conserve energy. Commute with the Hamiltonian.

As I understand this, we are converting matter into energy, which is permissable under the conservation laws. Nothing ceased to exist, but the state of existence changed. So we are faced with the question of whether or not a change in position along the time axis is actually a change in state, right?

Here is a potential problem I thought of prior to reading your current post.

Researcher P builds his time machine and patiently waits for two years before using it. Two years after its construciton he clambers into the machine, turns it on and--wa-la!--he travels backward in time two years and the machine sends the happy mix forward two years.

Now we have Researcher P and Researcher F in the lab (our box) while the happy mix now sits safely out of the way, two years in the future.

Let us agree that niether version of our duplicate hero ventures outside the laboratory and thereby avoids any overt trouble with causality.

But, let us assume that they become preoccupied and fail to pay heed to the calendar. Researcher F never gets into the machine and travels back to the future and the happy mix is still sitting in its tray.

Time marches on and two years after using the way-back machine, we have Researcher F, Researcher P, and the happy mix all in the same lab at one and the same time. The universe has now seen its mass increased by, what was it, 84 kilograms?

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There is no God and Dirac was his prophet.

I think you pegged it when you said, "moving along the time axis."

That's how we've got to think about this problem. I mean, does the universe really care about causality? Questioned in a way we can wrap our heads around: "Does the universe care if you're at X1,Y1,Z1 rather than X2,Y2,Z2?"
Extend that notion into the 4th dimension and you'll have your answer, I bet, as I'm not very skilled in the maths (yet, I'm teaching myself.)

A related question: Is there a violation of any law if a particle does some sort of quantum tunneling? When an electron appears on the other side of the wall, it's traversed the distance "in no time" at all...

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Feynman
>~~~~<
Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.

Religion is a culture of faith; science is a culture of doubt.

I'm not certain that time and causality are tightly bound. I suspect that time is a concept we use to guage the progress of various processes and that it might well be skewed into something we can easily apprehend rather than being fully reflective of reality.

Having said that much, you do have to wonder how there can be conservation laws of any kind if mass-energy can exist in any place at any time and thereby exist in two places at one and the same time.

Not that anyone has found, but it is a very puzzling phenomenon. We also must remember that we have never really developed a sound notion of what motion is to begin with. That remains an unsolved puzzle since the days of Parmenides. Xeno of Elea, a student of Parmenides, demonstrated that movement through a continuum is impossible, yet everything we know about is in motion--or appears to be.

With this I think we have an argument against the actual existence of a continuum and must conisder the continuum to be a conceptual tool. In other words there is no continuum. Everything is discrete. Having said that, we come up against QM.

I think that mathematics alone will help us solve this problem. Mathematics is the science of measurement. That implies that we must first understand what we are trying to measure or our mathematics will fail us. We may well need a completely new branch of mathematics, or there may be an obscure branch of mathematics that deals with the problem at hand and we do not yet realize it.

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There is no God and Dirac was his prophet.

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.

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.

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.

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.

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.

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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Conserve energy. Commute with the Hamiltonian.

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.

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".

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.

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.

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.

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.

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There is no God and Dirac was his prophet.

Definitely not. Electric charge is not a form of energy, and the other conservation laws are independent of the law of conservation of energy. A photon has unit spin, and, when measured in a particular direction, will be either aligned in that direction, or anti-aligned. The magnitude of the spin will be the same regardless of the energy of the photon. And in any interaction, the total spin will be the same at the end as it was at the beginning. Something similar is true of electric charge. Properties like spin and charge are conserved in all interactions, separately from energy.

Yes. That's the point, though. The total energy after the interaction is exactly equal to the total energy before the interaction. As long as this is true (as it is if we replace a mass of happy mix with an equal mass of researcher), conservation of energy is not violated.

I'd already pointed out that we'd need to address these conservation laws as well, but it's the same non-issue. As long as the total (charge, spin, baryon count, lepton count, energy, momentum, etc.) at the end of the interaction is the same as at the beginning, the various conservation laws are preserved. None of them say anything about the distribution, just the total. For example, for baryon number, it's fine to go from having 10 baryons to having 20 baryons and 10 antibaryons to having 1,010 baryons and 1,000 antibaryons, and it doesn't matter what kind of baryons. They could start out protons and stay protons, or instead be replaced by neutrons or some of the more exotic baryons (as long as charge was also conserved, of course).

No, this works out. Viewed along the timeline, we have the following events. Researcher P puts the bag of happy mix into the machine, in preparation for the anticipated arrival of researcher F. Researcher F appears at the same moment that the happy mix vanishes. Both spend the next two years in further research. Then researcher P notices that it's time for him to go. He steps into the machine and vanishes, replaced by the happy mix. So we have three stretches of time. In the first, Researcher P and the happy mix are present. In the second, researcher P and F are both present, but there's no happy mix. In the third, researcher F is now alone, and the happy mix is back.

Except that it doesn't work. It's possible preserve all of the conservation laws and yet violate causality. Heck, for causality violations we don't even need to have anything physical travel back in time at all. Just information travelling back in time is sufficient to violate causality.

I'll leave it to you to start if you wish to actually discuss the matter.

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Conserve energy. Commute with the Hamiltonian.

I had forgotten that you mentioned the conservation of other things previously. My apologies for the oversight.


But, this assumes that Researcher P steps into the machine. If he does not step back into the machine, do we have causality problem or do we have a conservation problem? If he fails to get back into the machine, we will have extra mass on hand.

What if we did the reverse. What if we sent inanimate objects in both directions along the time axis? This issue becomes even more problematical if we send one mass back into the past at a point in time prior to the machine's construction.

I still cannot see a way to travel in time without violating the conservation laws.

I would agree that simply transferring information alone back in time would violate causality, but how could that be accomplished? I know of no way to transmit knowledge without sending matter or energy.

There is another problem with time travel that I have not brought up, but it is not, strictly speaking, an objection based on anyhing in physics, so I am leaving it for discussion at a later time and possibly in another thread.