Certainly. Nothing is exactly that, no thing. How do you propose to make anything of nothing? When you multiply zero by an number, no matter how large, all you do is add up zeros and get zero.

If I have a something, then I have a something, and not nothing. Things do NOT simply vanish. They can be changed in form, but not vanished into nothing.

If either of these tenets are false, how can we hope to have a conservation law of any kind? For that matter, how could there be any order of any kind?

I would argue that if the universe is finite, then the conservation law is necessarily true. Whether we could make a determination or not would be irrelevant. On the other hand, if it can be shown that the universe is indeed infinite, and that must be shown, not merely asserted, the the conservation laws do not actually hold at all.

Here is the link:
http://en.wikipedia.org/wiki/Conservation_of_mass

Okay, I'll take your word for it. Notice, however, that they tie causality to the conservation laws.

I think it was Asimov who said that if Einstein had not derived E=mc^2 from his work that he would have heaved a great sigh and started over. And, I do recall that there was a considerable flapdoodle, especially from philosophers over the convertability of matter and energy. Still, ultimately, SR conserved both matter and energy, didn't it? It still does conserve matter and energy as far as I know. For that matter, you are telling me that GR does not really violate conservation laws until and unless we get into one of these time-shifting conundrums. These only occur at the extremes, so there is still clearly a need for a new theory. We cannot get GR to work with QM, or whatever we are calling QM nowadays.

This may seem obvious to physicists, but it is not so terribly obvious to me. At least some of that arises from my own ignorance, but we have had examples of nature being less than symmetric. Our own faces are rarely symmetric. Nearly all sea shells are "right handed" with only a few very rare exceptions. You can seldom find a tree with fully symmetric growth. Symmetric crystals are rare enough that they are treasured as gems. I might be comparing apples and oranges, here but exact symmetry seems to have always been fairly rare.

Within limits, I agree with you on this. However, all of physical theory relies on the conservation laws. We cannot rely on the conservation laws and rely on violating them at one and the same time. When we do that, it is time to look for a whole long list of shiny new laws.

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There is no God and Dirac was his prophet.

Ah, so this is just an a priori assumption on your part, that it's impossible to make something out of nothing, or vice versa. I'm afraid that we may indeed have an impasse, since, as far as physics goes, I'm only willing to accept premises that we can support through observation. In the case of the conservation laws, what we observe is nothing more nor less than the fact that the total energy of a closed system remains constant (and that if the total energy changes, the amount of the change is equal to the amount that enters or leaves the system). In a given interaction, we don't actually know whether the particles turn into other particles, or if some particles vanish utterly to be replaced by other particles, or even if the particles are teleported instantaneously back and forth from some reservoir at some great distance. We don't know, because these cases are experimentally indistinguishable. There's no way we can tell the difference between these events, so we can't hope to know which one is happening, unless, like you, we simply decide arbitrarily that one of them must be the case.

That's why the law of conservation of energy doesn't specifically talk about what happens to the various particles, but only talks about the total energy of the system. It refers specifically to measurable quantities, so that we're only talking about what we can observe and test. And the conservation laws work fine under those conditions.

I think you're misunderstanding what I mean when I talkabout whether we can define the energy of the system. Energy is a concept we developed to describe certain aspects of the universe. It was partly defined so that it would be conserved under the laws of mechanics and electrodynamics. When I say that we can't define the energy of the universe, I don't mean that it might have some value but we can't figure out what it is. I mean that it has no definite value. Our definition of energy, created for workign with local system, simply has no precise analog on the global scale. As for whether it's "necessarily true", I don't accept that. Whether or not energy is conserved is something that should be empirically determined, and there are certainly cases where it appears it is not. What do you think about the energy lost through cosmological redshift, for example?

Now you seem to be going in the other direction, and assuming that there's a situation in which conservation of energy must be logically false. Why would that be the case? It would seem in this case that we could still take a system, keep track of its energy over time, and compare any changes to the amount of energy we see pass through the boundary. Why would they necessarily have to differ?

Ah, there they are talking specifically about the conservation of mass. We've been using "conservation of energy" as shorthand (as is common) for the "conservation of mass and energy", but remember that these were actually separate, and are sometimes referred to separately. All that article is saying is that the law of conservation of mass, by itself, isn't valid under relativity, and that's true. They're just referring to the fact that the mass of a system might vary, by chaging some of that mass to energy, or vice versa.

Well, we do need to work out a theory that can unify general relativity and quantum theory, but it's not just weird situations that cause problems with conservation laws in general relativity. Cosmological redshift, and other issues involving the global curvature of spacetime cause problems, too. And note that it's not precisely a violation. It's that defining the energy of a system globally isn't possible (or at least not unambiguous), so it becomes meaningless to talk about whether energy is conserved or not for a global system. The differential version still works fine, and someone might come up with a revised definition of global energy that works well and is useful.

Sure, but the point is that conservation of matter and conservation of energy were rock-solid laws at that point. We were sure that they applied everywhere, and it only made sense. After all, how can you just destroy solid matter? That doesn't make any sense. And we didn't have any evidence that it could be destroyed or created, so here we had the case of something that seemed intuitively obvious, also supported by extensive experiment. But it turned out to be wrong. Or more precisely, the laws of conservation of mass and energy (separately) turned out to be special cases, rather than universal laws.

Let me try to be more clear about why this is dramatic. It's not some kind of statement that everything has to be symmetric. It's as though we could determine that, due to the laws of phyiscs, the farthest you could jump is two meters. But, that if we were to be able to magically replace you with your mirror image twin, you'd instead be able to jump three meters. Or that gravity works differently (say, it's only 90% as strong) for left-handed people than it does for right-handed people. That's the kind of symmetry violation that we're talking about. If someone claimed to have discovered that gravity worked differently for left-handed and right-handed people, I'd immediately assume that the experiment was flawed rather than thinking someone had discovered a new law of physics, wouldn't you? It was a huge shock to the physics community when parity violations were discovered, and rightly so.

It's true that physics relies on the conservation laws, but remember that the conservation laws that physics relies on are the formal, precise ones that we've talked about, and not just a layman's description of them.

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Conserve energy. Commute with the Hamiltonian.

Have we seen anything suddenly appear out of nothing? As I said, unless confronted with evidence to the contrary, I go with logic. Nothing is exactly that, nothing. There is no way to make something out of nothing. We have no evidence to suggest that anything was ever made from nothing. If we had, Hoyle et al might have been right.

There is nothing arbitrary about my decision. The assertion that particles can appear out of nothing is arbitrary. Where is the evidence of this? What we have on hand is that particles change into other particles, a combination of particles and energy, or simply energy. In some cases we see energy do the same thing. I know of no case where we have ever seen energy simply disappear into nothing and the same for matter. Absent any compelling logical reason to say that any of the strange things you mentioned happen, or observational evidence to support such claims, I am obliged to consider them as being nothing more than arbitrary assertions. So, I will again ask, do we have any reason, theoretical or otherwise, to suspect any of these extrarordinary events actually occur? If so, we have a basis to work from in designing experiments that might throw light on the subject.

Indeed they do, but how can they hold if matter or energy can come out of nothing at random? They cannot. All we have evidence for is that matter becomes energy or energy becomes matter. This shows that something which already exists never disappears. We have absolutely no evidence to the contrary that I know about. BTW, if this could happen, thermodynamics would fly to pieces on us as well.

If the universe is finite, and both logical reasoning combined with observational evidence say that it is, then it necessarily has a definite magnitude. If the universe did not have a definite value or magnitude, there would be no reason for the existence of conservation laws.

Reasoning why they are is presented above.


I agree that it should be empirically determined and it has been to very good precision and accuracy. Are you saying that we also have empirical evidence to the contrary, or are you saying there are conditions predicted by theory where they will not?


I don't know that there is energy lost due to red shift. I know that we see red shift, but we seem to be lacking a complete explanation as to what is causing the red shift. It would be a bit precipitous of us to conclude that the conservation laws do not hold without a complete explanation.

If the universe were to be infinite, what possible difference could the addition or deletion of energy make? We could vanish google-joules of energy and it would make no difference to the overall magnitude of the universe. BTW, if the universe were infinite, it would lack a definite quantity.

Then I will fault the quality of the article rather than its intent. Perhaps one of us should insert a note into Wikidpedia's discussion board for that article.

If the universe is finite, and all the evidence we have in both reasoning and empirical evidence we have says it is, then conservation laws hold for the universe at large because the universe itself is the system.

It is reminiscent of what happened at Marburg and the discovery of the "vacuum." Philosphers fainted, while some scientists were overjoyed and others were disgruntled. The debates raged for decades. In the end, we were placing an "aether" in the vacuum. Then Einstein replaced the vacuum and the aether with geometry which is and was very hard to understand. Now we are putting all sorts of things back into the vacuum, "virtual" particles, dark matter, dark energy, quintessence, inflation, the list has become astonishingly lengthy.

Einstein never dreamed of presenting a theory that would violate the conservation laws. Instead, he combined the conservation laws into one law. Personally, I have concluded that the conservation laws are fundamental to existence and it would seem that cosmologists have as well.

This remains unclear to me, and perhaps it is doomed to remain so unless and until I acquire the mathematical skills to follow the entire problem. Just on the face of it, however, I would suspect we found something that tells us that the theory we were using to arrive at that point is badly flawed. I did not realize that the symmetry problem had anything to do with gravity. I thought it had to do with the formation of certain kinds of particles predicted by theory.

Oh, I do not disagree with you there, but I think we have failed to take all the logical consequences of that law into account when we allow matter to simply disappear into nothing or think it may appear out of nothing. Barring compelling proof that the universe is infinite, the conservation laws must hold everywhere at all times for everything.

__________________
There is no God and Dirac was his prophet.

Remember, I'm not talking about something appearing from nothing without something else disappearing at the same time. Besides, you're "logic" is really just assuming your conclusion. You're claiming that you cannot create something out of nothing. But what initial postulates are you reasoning from to arrive at that conclusion? As far as I can tell, you're just stating that conclusion and claiming that you've arrived at it by logic.

Wait a minute. We've agreed that there's no possible way to distinguish the two cases described (case 1: particle A is transformed by some unknown method into particle B; case 2: particle A vanishes, particle B appears). Since there's no way to distinguish between the two, any decision that one takes place while the other does not must be an arbitrary one, pretty much by definition.

Yes, actually. I've been focusing on issues where conservation of energy holds, because that was where we started. But offhand, I can think of two cases where we actually have violations of conservation of energy, at least in the sense you're trying to use it. One is cosmological redshift. Photons lose energy, and that energy doesn't go anywhere. Some people are really bothered by this. This is the issue with not having a global reference frame that I mentioned. The other is virtual particles. I imagine you're especially unhappy about the latter, since they both appear out of nowhere and violate conservation of energy. Note that there are definite predictions from quantum theory about the effects that virtual particles should have, and these predictions are borne out by experiment, to a lot of decimal places.

Nobody said anything about coming out of nothing at random.

No. Again, we only have evidence that the total energy of a closed system remains constant. We have no way of know by what means that total energy remains constant. You've agreed that you cannot distinguish between the two cases experimentally, so unless you can come up with a way to do so, you cannot support this statement.

Of course not. Thermodynamics uses only the strict, formal definition of conservation of energy that we've agreed upon. It makes no presumption about the mechanism by which some particles are replaced by other particles. Frankly, I have a hard time seeing why this is such a big issue. We watch interactions. We see some particles at the beginning and other particles at the end, and we have a whole set of rules that describe what particles you might see at the end given the initial configuration. Trying to describe "how" the interaction takes place isn't particularly relevant, because, as we've agreed, it has no measurable effects.

Can you cite observational evidence that the universe is finite? Current theory leaves the question quite open. As for logical reasoning, well, I'd imagine that whether you can logically reason that the universe is infinite or finite rather depends on the axioms you choose. I expect that it's not possible to prove the universe is finite by logic without assuming an equivalent axiom.

Why does the universe need to have a definite value for a quantity defined by humans? Let me ask a related question. Does it make sense to talk about the average velocity of the particles making up the universe? I'd say no, since you have to define a reference frame to measure from for velocity to have any meaning. The same is true for energy; it's a reference frame dependent quantity. But since there are no reference frames which can apply to the entire universe, defining a global value for energy simply has no meaning. That, by the way, is why the loss of energy to cosmological redshift isn't a violation of the formal differential form of the law of conservation of energy. Because the total energy of the universe cannot be unambiguously defined. As for why that means there's no reason for the conservation laws, that simply doesn't make sense. The conservation laws apply on a local scale (which is where they're defined) perfectly fine whether or not the universe has a well-defined total energy.

See above for two instances where the informal definition of conservation of energy that you're using is violated.

You may be lacking a complete explanation of what is causing cosmological redshift, but it comes as a direct result of general relativity. You seem to be disputing general relativity because it doesn't jibe with your notions of conservation of energy, but that's not a sufficient reason for discarding a theory. Show me the experimental results that invalidate it, and we'll talk.

To the total energy, sure. But the law of conservation of energy isn't talking about the total energy of the universe. It's talking about the energy within a finite closed system, and how changes in that energy relate to the amount of energy entering or leaving that system. It's perfectly reasonable to have rules that apply to finite subsets of an infinite set, even though they wouldn't be well-defined when applying to the set as a whole. Or are addition and subtraction meaningless because there are infinitely many integers?

It is perhaps not entirely clear. I'll try to come up with a better way of phrasing it, and edit the article.

You said roughly the same thing above, and I'll repeat my response. Empirical evidence shows the finiteness or infiniteness of the universe to be tantalizingly indeterminate at the moment. And since there is no reference frame which can encompass the entire universe, and its meaningless to talk about the energy of a system without specifying a reference frame, the total energy of the universe cannot be defined unambiguously, whether the universe is finite or infinite. And remember, that's not saying that we just can't measure it, that's saying that it cannot be defined. Our human-defined concept of energy doesn't appear to apply at that scale.

Einstein was well aware that only the differential form of conservation of energy holds under general relativity, as are modern cosmologists. They do generally think that conservation of energy holds, but when they say that, they're talking about that strict formal definition.

Wait, are you saying that if someone claimed and experimental result that left handed people are affected by gravity more strongly, you'd actually question whether our theory of gravity is right, rather than assuming that the experiment must be flawed, at least until you could get a lot of really solid verification and repetition of the experimental results?

It's the weak force, rather than gravity, which violates parity. I was making an analogy. However, the conclusion is just as dramatic. A fundamental force of nature actually distinguishes between left-handed and right-handed interactions. It's just as profound a result as if gravity distinguished between the two, it's just harder to detect.

So long as the matter disappearing and reappearing does so under certain restrictions, it's completely indistinguishable from matter changing from one thing into something completely different (which, if you think about it, is just as weird, really). So how can there be any logical consequences?

Well, I'd say that it appears the conservation laws do hold, since there's nothing that says that they must hold. And I still don't understand why you'd think that relies on a finite universe, since all the laws of physics would work just as well in an infinite one.

__________________
Conserve energy. Commute with the Hamiltonian.

Then what we have evidence for is a change in state, not an argument that things disappear into nothing.

I have no evidence that any such thing ever happens. I have no reason to think that it does. Barring evidence or a supportable line of reasoning to suggest that it does, I have no reason to build an experiment to test the notion. Lacking a reason for such a phenomenon, I have no means of building an experiment to see if it might be so.

Not really. Have you ever seen anything simply vanish? I am not talking about conjurers' tricks here, I am talking about something that actually ceased to exist without a trace. Has anyone ever seen such an event? No. Have we ever seen anything ever appear out of nothing? No. What we have seen are situations wherein something undergoes a change. Without reason to think that one is destroyed, ie, removed from existence, while the other is made from nothing, I have no reason to believe that such a thing can happen. There is nothing arbitrary about the decision. I am going on the evidence I have in hand. Can you supply me with reasoning that suggests that this might be taking place? Absent such reasoning, I have no reason to think that it might.

Concerning spectral shifts, I take it that you are posing this as a problem whether we are talking about ordinary doppler shift or the so-called cosmological shift?

As for the virtual particles, I accept them as a tentative "something" physicists are using to fill what they once believed was a vacuum. It simply tells me that we do not know everything there is to be known yet. As I recall, these mysterious whatsits appear, annihilate one another, then disappear again. How is that a violation of the conservation laws by your standard definition? Or are you saying that there are violations in quantum theory?

But if things simply disappear into nothing and appear out of nothing, what is to prevent it from happening at random?

Barring evidence that things can and do cease to exist altogether, so far not provided, I cannot ignore the logical consequences.

But we do have the disagreement because it is of fundamental importance. Causality itself appears to be at stake. GR suggests that all kinds of disastrous things can happen, right? Either there is a built in mechanism protecting causality or we have no reason to be talking about "natural laws" because there aren't any.

I'll turn the question around. Can you show any evidence of why the universe must be infinite? I haven't seen any. I suspect that empirical evidence of an infinite universe will be exceedingly difficult to acquire.

All the infinities I know about, exist in the imagination of humans. We can always add one more. If we could not do that in our heads we would never be able to count, but it does not follow and there is no logical reason to assume that anything in nature does this. Everything that exists, exists as a definite quantity including the universe. Properly speaking, we are no long dealing with physics. We are dealing with ontology or metaphysics, depending on which philosopher you scratch, but the reasoning is not done without a basis in observation.

Infinities only exist in our imaginations. We cannot observe the whole of anything that is infinite, can we? To show that something is infinite we must find a causal link that proves that it MUST be infinite. So far, I have seen no such proof and physicists do everything they can to avoid results that yield infinities. Remember the tachyon flap?


Only if you can show that the universe must be infinite. Can you show me that the universe must be infinite?

And I would argue that either the theories are incomplete, in error, or both. If I can count as high as I want, there is no reason why I cannot account for it all, save for the arguments stemming from a theory that falls apart and destroys causality when followed to its logical conclusion. Our theories, as brilliant as they are, appear to be footed on faulty premises.

I have questions about those, asked previously in this post. BTW, have these "virtual" particles been observed?

Let's see, we cannot get the two great theories to jibe with one another. One of them suggests that causality can be violated in certain cases and the other only just barely makes any sense at all and has its own internal problems, something to do with "symmetry breaking" among other things. Are you saying that there are no major problems here? Typically when you hit upon problems like this you need to worry about the premises upon which your reasoning is built. I happen to think there is a faulty premise(s?) at the root of all this.

And I have no evidence that the universe is anything but a finite closed system. Where can anything go if it does not go somewhere-somewhen in the universe?


Addition and substraction hold up just fine, but double entry bookeeping will not work at all. There is no reason for it.


I am glad to hear this because I applaude the efforts being made by the Wikipedia group. They do their honest best and are providing an invaluable service.

Not as far as I can see. What seems to be in question is the ultimate fate of the universe. It may expand forever, but it could do that and still be finite. It may collapse into something like a black hole, in which case it is necessarily finite, or it may be "flat" in which case you only barely have a basis for saying that it might infinite, but are still obliged to show why it must be infinite before the infinity of the universe can be proclaimed as fact.


If the universe is finite, then there is a fixed amount of energy.

And the "explanation" we have allows for the violations of causality? This is reasonable?


Were any of them ever really comfortable with Hoyle's Steady State model? I don't think so, but I will accede to your assertion here because it seems possible.

I'm not sure of what you are asking me here. Would you be good enough to rephrase it?

As I understand it, the weak force is the force that prevents electrons from binding to the nucleus and thereby causes atoms to be mostly space. Is that right?

[CONTINUED IN THE NEXT POST]

__________________
There is no God and Dirac was his prophet.

Because I have no reason to assume that anything has ceased to exist or come out of nothing. Explain to me how something can be made from nothing. Barring a line of reasoning that says such a thing happens, or evidence to suggest that it happens, all I have is evidence that matter changes its state. I only have evidence for one possible conclusion. The other is a matter of speculation.

If the universe were infinite and millions of billions of joules of energy suddenly ceased to exist, what possible impact could there be for the universe? Could such an event possibly have any effect on the state of the universe? No. Indeed, if the universe were infinite, we could take an infinite number of joules of energy out by making it cease to exist and the uinverse would keep right on ticking as before.

__________________
There is no God and Dirac was his prophet.

I don't know. Have you ever seen anything be transformed into something completely different? As far as I can tell, the only candidates for either type of event are the fundamental particle interactions we've been discussing. Since you haven't been able to suggest any way to distinguish between these two types of eve