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## More Sweet Nothings …

I’ve had an interesting set of responses to my post “Of Nothing”, so I can’t resist a sequel. (I’m not really taking a position on who “won” the debate. I don’t really care. I’m just commenting on some of the issues raised.) Here, I’ll respond to a few more of Krauss’ comments on nothing and cosmology, this time from this article in the Wall Street Journal:

There are remarkable, testable arguments that provide firmer empirical evidence of the possibility that our universe arose from nothing. … the existence of dark energy and a flat universe has profound implications for those of us who suspected the universe might arise from nothing.  Why? Because if you add up the total energy of a flat universe, the result is precisely zero. How can this be? When you include the effects of gravity, energy comes in two forms. Mass corresponds to positive energy, but the gravitational attraction between massive objects can correspond to negative energy. If the positive energy and the negative gravitational energy of the universe cancel out, we end up in a flat universe.  Think about it: If our universe arose spontaneously from nothing at all, one might predict that its total energy should be zero. And when we measure the total energy of the universe, which could have been anything, the answer turns out to be the only one consistent with this possibility.  Coincidence? Maybe. But data like this coming in from our revolutionary new tools promise to turn much of what is now metaphysics into physics.

If you read the whole article, you quickly discover that Krauss simply doesn’t understand the question “why is there something rather than nothing?” – see my last post for more on that. Here, I will raise two issues with the quote above.

### The Energy of the Universe

It is not true that if the universe is flat then it has zero total energy. This idea relies on a Newtonian calculation of the gravitational potential energy of an expanding universe. However, such a calculation simply cannot be performed in general relativity (and even the Newtonian calculation is suspect because the Poisson equation has no solution for a uniform unbounded fluid. See Rindler 1977, pg 199). There is simply no way to calculate the total mass-energy of a general spacetime, and the energy of the gravitational field cannot be calculated in a coordinate invariant way. John Baez and Sean Carroll have excellent discussions of this point, as does Hartle in his GR textbook: “Conserved quantities … cannot be expected in a general spacetime that has no special symmetries”. Note that energy conservation is a consequence of time-translation symmetry, which an expanding universe (and its Robertson-Walker spacetime) does not possess. Here’s Gravitation by Misner, Thorne and Wheeler (MTW):

When evaluating the 4-momentum and angular momentum of a localised system, one must apply the flux integrals only in asymptotically Minkowskian coordinates. If such coordinates do not exist (spacetime is not flat at infinity), one must completely abandon the flux integrals, and any quantities that rely on them for definition: the total mass, momentum, and angular momentum of the gravitating source … ‘Total mass-energy’ is a limited concept, useful only when one adopts a limited viewpoint that ignores cosmology. (Pg 463)

The Robertson-Walker metric is an example of a spacetime that is not asymptotically flat, and thus attempting to calculate its total mass-energy will “easily and unavoidably produce nonsense” (MTW). (Don’t confuse the two different uses of the word flat above. Krauss is referring to the space curvature of an expanding universe, while MTW are referring to spacetime curvature. A spatially-flat expanding universe is not spacetime-flat.)

The point of the above passage is that we cannot in general add up the local contributions of the mass-energy of the universe to produce a total mass-energy. When it comes to gravitational energy, it gets even worse – we can’t even define it locally:

To ask for the amount of electromagnetic energy and momentum in an element of 3-volume makes sense. First, there is one and only one formula for this quantity. Second, and more important, this energy-momentum in principle “has weight”. It curves space. It serves as a source term on the righthand side of Einstein’s field equations. It produces a relative geodesic deviation … It is observable. Not one of these properties does “local gravitational energy-momentum” possess. There is no unique formula for it, but a multitude of quite distinct formulas … Moreover, “local gravitational energy-momentum” has no weight. It does not curve space. It does not serve as a source term … It does not produce any relative geodesic deviation … It is not observable. Anybody who looks for a magic formula for “local gravitational energy-momentum” is looking for the right answer to the wrong question. (MTW, pg 467)

The equivalence principle says that one can always find a local coordinate system in which gravity, and thus any concept of gravitational energy, vanishes. It is not that we do not know how to formulate gravitational potential energy in GR, or that we don’t know how to total up the mass-energy of a given spacetime. Such calculations, which were perfectly sensible within Newtonian gravity,  are simply meaningless in the context of general relativity.

Apologies for subjecting you to such long quotes, but I’ve heard the claim that the total energy of the universe is zero too many times to let it be. The total mass-energy of the universe is not well-defined; even if it was, it wouldn’t be conserved in Robertson-Walker spacetime; and gravitational energy is not a meaningful concept in GR.

### Nothing has no energy

My second problem with Krauss’ quote above is this claim: “If our universe arose spontaneously from nothing at all, one might predict that its total energy should be zero”. In my last post I argued that the idea that the universe came from nothing is simply nonsense. Nothing has no properties, and the ability to spontaneously create a universe is a rather spectacular property.

But suppose the universe could come from nothing. Would it follow that it should have zero energy? This claim seems plausible – what other energy could nothing have? My first problem is that having an energy, even if that energy is zero, is a property. It makes sense to say that some physical system (say, a collapsing cloud of gas) could have zero energy, but other things – say, the C major scale – simply do not have the property we call energy. There is a difference between “having an energy, and that energy is zero” and “not possessing the property of having an energy”. The C major scale does not have zero energy; it does not have the property at all, just as it has no colour, mass or taste. Thus, “having zero energy” is a property, and anything possessing a property cannot be nothing.

The English language is partially to blame here. The phrase “has no energy” is ambiguous. It could mean “having an energy of zero” or “not possessing the property of having an energy”. Nothing, which has no properties, has no energy in the latter sense. A universe that came from nothing would not involve a transition from a state with zero energy to another state with zero energy.

There is second problem lurking here, which we will tease out with a bit of mathematical formalism. The symbol $P(A|B)$ represents the probability of some event A given the information represented by B. For example, A could be “I win this hand of poker” and B is “I have just been dealt a royal flush”. Actually, we would need B to also specify the entire scenario, including the rules of poker, the number of players etc. The probability of A depends on B. If B were “I have just been dealt (2C, 3D, 4H, 6H, 9C)” then the probability of A would be significantly lower. We will call the place in $P(A|B)$ occupied by A the outcome slot, and the slot occupied by B the given slot. The given slot controls the outcome slot.

Now, suppose that Krauss were correct, and that we could predict that a universe which came out of nothing would have zero energy. In this case, the outcome slot would be occupied by A = “Universe with zero energy”. But what would be in the given slot? Nothing. Not anything. Remember: nothing is not a type of something. There is not a kind of thing out there called “nothing” whose properties we can place in the given slot to see what outcomes are possible. There is literally not anything in the the given slot. Nothing is given. We would be calculating $P(A|~)$.

If you have a sneaking suspicion that such a calculation is nonsense, then you’re starting to see things my way. But we can go a step further. Suppose that $P(A|~) = p$, where p is positive number. Let’s now ask: what is $P(C|~)$, where C = “Universe with positive energy”? Ordinarily, we would appeal to the information in the given slot to answer this question. But nothing is given. There is literally no possible reason why $P(C|~)$ should not also be some positive number. There is nothing, not anything, to control what outcomes are impossible or possible, improbable or certain. We must conclude that, if a universe with zero energy could come out of nothing, then so could a universe with positive energy. Similarly, a universe with negative energy could come out of nothing.

It gets worse, as you must have realised by now that C could be anything at all. No possible reason can be given for denying the possibility that a polar bear could come out of nothing. When we calculate the probability that a radioactive nucleus will emit an alpha particle, we appeal to the laws of physics and the properties of the nucleus in question. When we calculate that the probability of the nucleus emitting a polar bear is zero, we do so on the basis of the information in the given slot. If there is nothing in the given slot, then there is nothing to control the outcome slot. We can put any outcome we like in there, and calculate a non-zero probability that it will appear out of nothing.

Worse still, if something could come out of nothing at the beginning of the universe, then something could come out of nothing now. If polar bears need no necessary or sufficient conditions to spontaneously appear out of nothing, then the conditions in this room right now fit the bill perfectly. Further, there no reason why the probability of such an appearance should not be one. Remember: nothing is given! There is literally no possible reason for polar bears to fail to appear in this room right now.

We can then make the following prediction: if a universe with zero energy can appear out of nothing, then polar bears should be appearing out of nothing in this room right now. I would call this a clear case of reductio ad absurdum.

All this to say: if something can some out of nothing, then anything and everything can and should come out of nothing at all times and places. This, then, is the empirical evidence we would need in order to believe that the universe could come out of nothing.

### 28 Responses

1. You can’t suppose either P(A|) = p because P(A|) makes no sense. Its P(|A)P(A)/P(). Its not defined. You can’t suppose it is anything.

Second P(A|) should really be P(A|X) where X is “the universe came from nothing” rather than nothing, if your goal is an attempt to calculate the probability the universe has zero energy given it came from nothing?

What you are really arguing can be said much simpler than making a mess out of bayes theorem. If something can come from nothing, then there are no constraints on what could come, since for there to be constraints, it would have to be something.

2. Hence, why I said: “If you have a sneaking suspicion that such a calculation is nonsense, then you’re starting to see things my way.”

3. The argument through bayes theorem relies on placing a number to p(c|), but p(c|) isn’t a number so you can’t go about concluding things about its values.

I don’t disagree with your conclusion, but would you agree that your use of Bayes theorem doesn’t support the claim that:

>if something can some out of nothing, then anything and everything can and should come out of nothing at all times and places.

4. I see what you’re getting at. I would say that the conditional “If something can come out of nothing …” is equivalent to saying “if we can assign a number to p(c|) …”

My conclusion is that the idea that something coming from nothing is either nonsense (if we can’t assign a value to p(c|)) or disconfirmed by the fact that polar bears aren’t appearing in this room right now (if we can assign a value to p(c|).

Putting X = “the universe came from nothing” into p(C|X) doesn’t change much. There is still no information in X to control the outcome of something coming out of nothing.

5. Hi. This comment just popped into being from nothing.

6. If nothing can come out of nothing, how come God pulled (at least) a universe out of it?

Further more, if nothing is the absence of anything/everything and before the universe began there was nothing (there was the absence of anything/everything), then there was/is no God. Because if there was (a) God, then there was not the absence of anything/everything. Unless, God is nothing, that is the absence of anything/everything.

Your logic is just as valid as mine.

You are trying to use logic and math to prove God, when you cannot prove logic or math to be correct (complete and consistent). (Kurt Godel incompleteness theorems) Should we throw away logic and math because they are not perfect? No, because they are very good tools. Not perfect, but good enough to do a lot of things.
But, you have to use the right tool for the job. For proving God, logic and math are not the right tools. Then again, I cannot think any good tool to prove God.

7. “You are trying to use logic and math to prove God,”
I think you are making an unwarranted assumption here. I don’t think Luke is trying to prove anything more than that the idea of the universe arising out of nothing doesn’t make sense. He has left each of us to draw our on conclusions beyond that.

But could it be that your apparent antipathy to the idea of God may be colouring your conclusion?

• I agree with unkleE here, Luke didn’t mention God at all here, though the theist will probably see his comments supporting something like the first premiss of the kalam cosmological argument. One way out for the atheist would perhaps be to argue that the universe never began to exist.

8. […] few months ago, I wrote two posts on Lawrence Krauss’ take on the question of why is there something rather than nothing. In […]

9. […] on this subject, I recommend the following articles: On the Origin of Everything, Of Nothing, More Sweet Nothings… window.fbAsyncInit = function() { FB.init({appId: "", status: true, cookie: true, xfbml: true}); […]

10. […] of the writings of atheists Lawrence Krauss, Victor Stenger and PZ […]

11. on May 27, 2012 at 11:54 pm | Reply Big Blue Bump

Statement 1 “Nothing has no properties, and the ability to spontaneously create a universe is a rather spectacular property.”
Statement 2″ if something can some out of nothing, then anything and everything can and should come out of nothing at all times and places.”

But if statement 1 is true then the this ‘nothing” exists in no location and no time that we can ever observe so if if were true we could not make the observations you suggest.
So it seems to me what follows should be: if something can arise out of nothing then we would never ever observe it as quantum mechanics prevents us from observing a true “nothing”. So the statement “something cant come from nothing” can never be backed by any observation. Of course conversely it can never be verified by any observation either.
Maybe we can simply use logic rather than empiricism to answer the question. But i see a problem here too, to do this we need to assume “nothing” obeys logical laws but that would give it a property making it not “nothing”.

12. I’m not claiming that 1 follows from 2. They can’t both be true. My argument is: 1, and even if not-1, 2. If either is true, then talk of something coming from nothing is nonsense.

If statement 1 is true then it is nonsense to talk about “this nothing” existing, or obeying logical laws. Nothing is not a type of something. The word is an indefinite pronoun (http://www.englishclub.com/grammar/pronouns-indefinite.htm). It is a linguistic device that signifies the absence of a referent (http://en.wikipedia.org/wiki/Referent). For example …

* If I say “nobody cleaned the car”, I don’t mean that my good friend “Nobody Jones” came along and cleaned the car.
* If I say “if a nuclear bomb explodes overhead, then nowhere in this house is safe”, I don’t mean that we have a room marked “nowhere”, and as long as we’re in there then we’re OK.
* If I say “nothing stopped Lex Luther’s diabolical plan”, I don’t mean that … wait … up in the sky … it’s Nothing!!! We’re saved!!!
* If I say “If you don’t know the answer it’s best to say nothing”, I don’t mean that if faced with a difficult question it’s best to chant “nothing nothing nothing nothing …”

What one means by these sentences is that the car is still dirty, we are not safe in any room, Lex Luther’s plan was successful, and you should just keep your mouth shut. These negations – nobody, nowhere, nothing – do not refer to a particular person, place or thing. There is no “true nothing”, no “physical nothing”, no “philosophical nothing”.

13. on May 28, 2012 at 11:08 am | Reply Big Blue Bump

i understand what you are saying when you mean “nothing” , thats not where my concern lies. Perhaps i wasn’t asking myself clear. let me rephrase with a question.
let us suppose a polar bear did appear in your room right now, would it be an example of something coming from nothing?

14. “let us suppose a polar bear did appear in your room right now, would it be an example of something coming from nothing?”

Maybe a group of alien pranksters teleported it to its new location?

15. My first reaction would be to say that something must have caused the polar bear to appear in my room, so no.

If I thought it were possible that something could come from nothing, then we can test that hypothesis. That hypothesis, as I argued above, predicts that anything and everything can and should be appearing at all times and places. Thus, the hypothesis (if intelligible at all) is empirically disconfirmed.

16. on May 30, 2012 at 9:50 am | Reply Big Blue Bump

(Hi I tried to post something and it has not appeared, don’t know if I pressed the wrong button or whether you are vetting comments. So if there’s repetition here my apologies in advance.)

So what you are saying is that Polar bears don’t appear in your room so something can’t come from nothing. But if they did then something still can’t come from nothing.
Can you see why I’m having a problem ?
The very essence of good science I believe is the ability to change your conclusions in the light of observations. Do you not agree? It appears you are categorically stating your conclusions will remain unchanged no matter what the outcome of observations. Something must be wrong here
What appears wrong to me is that the prediction you have extracted I think do not follow from the hypothesis. The reason is your room is not nothing. Your room contains stuff. I don’t know exactly what stuff, but I feel pretty confident it has something in it. Even if you pumped out every atom out you can, QM tells us there will still be something there. So there are no circumstances we can envisage where you room counts as nothing. Hence whether it s a virtual particle or a polar bear , if it appears in your room or not it won’t tell us whether something can come from nothing.

17. Dear dr. Barnes,

http://freethoughtblogs.com/carrier/archives/468

Where he claims that granting the premise there was once absolutely nothing then the probability that our universe would exist is infinitely close to one hundred percent. In fact Carrier claims that there must exist an infinite multiverse as far as we know.
Any thought you might have will be greatly appreciated.

18. I don’t know much about Carrier. I’ve noted elsewhere (http://letterstonature.wordpress.com/2010/04/03/is-that-really-necessary-a-fine-tuned-critique-of-william-lane-craig-part-2/) that he once said this:

“in the 19th century there were some twenty to forty ‘physical constants,’ there are now only around six”.

which is so laughably ignorant of modern physics and cosmology that I’m not really interested in what else he has to say about what universes must exist.

19. His argument formalized goes like this:

The formalization of the argument proceeds as follows:

P1: In the beginning, there was absolutely nothing.

P2: If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.

C1: Therefore, in the beginning, nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.

P3: Of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing, one universe popping into existence is another thing, two universes popping into existence is yet another thing, and so on all the way to infinitely many universes popping into existence, and likewise for every cardinality of infinity, and every configuration of universes.

C2: Therefore*, continuing to be nothing was no more likely than one universe popping into existence, which was no more likely than two universes popping into existence, which was no more likely than infinitely many universes popping into existence, which was no more likely than any other particular number or cardinality of universes popping into existence.

P4: If each outcome (0 universes, 1 universe, 2 universes, etc. all the way to aleph-0 universes, aleph-1 universes, etc. [note that there is more than one infinity in this sequence]) is no more likely than the next, then the probability of any finite number of universes (including zero universes) or less having popped into existence is infinitely close to zero, and the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.

C3: Therefore, the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.

P5: If there are infinitely many universes, and our universe has a nonzero probability of existing (as by existing it proves it does, via cogito ergo sum), then the probability that our universe would exist is infinitely close to one hundred percent (because any nonzero probability approaches one hundred percent as the number of selections approaches infinity, via the law of large numbers).

C4: Therefore, if in the beginning there was absolutely nothing, then the probability that our universe would exist is infinitely close to one hundred percent.

——-

I have problems with P1 though, it seems to presuppose that there was a time at which nothing exist, but if nothing exist not even time would exist I think. Moreover I think P2 and P3 are plausibly false.

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21. […] going to jump back on one of my favourite high horses. I’ve previously blogged about Lawrence Krauss and his views on the question why is there something rather than nothing. […]

22. THANK YOU !

It seemed to me that Krauss was simply using the high school formula for the total energy of a system travelling at escape velocity to get his “zero energy” conclusion. I posted a question about total energy of the universe in GR and got a lot of different (sometimes confusing) answers.

Your post has clarified this beautifully.

So, not only is Krauss a poor philosopher, he seems to have forgotten his grad school physics as well.

23. […] energy is irrelevant, as we should be using Einstein’s theory of general relativity (GR). In GR, the energy of the universe (and gravitational energy in particular) is not well-defined, and […]

24. […] blog posts about the philosophical claims of Lawrence Krauss. This is something I’ve blogged about a few times. His most recent post on Krauss contains this marvellous […]

25. […] å rettferdiggjøre dette med at universet i sum har null energi. Irrelevant, men selv ikke dette har han grunnlag for å si. (Takk Gud for kritiske fysikere som Luke […]

26. […] why is there something something rather than nothing?, a question I’ve discussed on a few previous […]

27. […] also has a follow-on blog that is quite helpful where he […]