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http://en.wikipedia.org/wiki/Closed_universe#Closed_Universe

I suspect a majority believe the universe is close to Ω = 1......and that seems reasonable

so far; but if history is any guide, that may not be very important.

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Well, the key is 'within one percent'. The mainstream view is that the early universe underwent an incredibly rapid expansion called inflation. One effect of inflation is make any region of the universe enormous. So, after inflation, any spatial curvature would become undetectable. Therefore, measuring the universe is close to flat may just mean that inflation made the universe large enough that no curvature can be detected with our current measurements. So, Vilenkin's model is perfectly valid.

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One percent is a pretty good margin of error I would say. Also, if any spatial curvature could not be detected anyway, then why does NASA and other websites claim it is flat wuth such accuracy? What is the point of this discovery which if one could just say "It's just as likely it is closed, but we just can't detect the evidence". Also, doesn't that assumption violate Occam's Razor? Doesn't it make more sense to say the universe is most likely flat based on all available evidence, until evidence contradicts it?Well, the key is 'within one percent'. The mainstream view is that the early universe underwent an incredibly rapid expansion called inflation. One effect of inflation is make any region of the universe enormous. So, after inflation, any spatial curvature would become undetectable. Therefore, measuring the universe is close to flat may just mean that inflation made the universe large enough that no curvature can be detected with our current measurements. So, Vilenkin's model is perfectly valid.

Regardless, if the universe is really closed then it would have a net energy which is negative. This would mean the universe doesn't really have a net energy of zero, which means Alexander's model fails. Only if the universe has a net energy of zero could it have possibly come from "nothing". Alexander Vilenkin claims that the positive and negative energy balance out, but this is only true under the assumption of a flat universe. With a closed universe, isn't there a negative net energy?

"The universe is neither spherical shaped, like the shape of a ball. That would be positive curvature, having net negative energy" - Neil deGrasse Tyson

"The gravitational energy which is always negative exactly compensates the positive energy of matter. So the energy of a closed universe is always zero" - Alexander Vilenkin

Can you explain how Alexander Vilenkin can get away with claiming a zero energy universe, if it is closed? Conventional wisdom is that a closed universe has a net negative energy based on what I have read, not a net energy of zero like in a flat universe.

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Chalnoth

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It only requires that the universe be

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How can the universe have a total energy of zero, if the universe is closed though? I thought that conventional wisdom told us that only provided the universe is flat, does the net energy equal zero. If it doesn't equal zero, then one is forced to ask where that little spark of energy came form. Thus, I still fail to see how Alexander's model works by assuming a closed universe. I'm not saying you are wrong, but would you please clarify your position? Thank you.It only requires that the universe beslightlyclosed. This is perfectly compatible with measuring near-flatness. It may even be compatible with measuring very slightly negative curvature, as we can only measure the curvature of our observable region, but the statement about a universe from a quantum tunneling event being closed is a global statement that doesn't necessarily rule out some sub-regions within the universe being open.

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Basically, Alexander Vilenkin can say the universe came from "nothing" if the total energy of the universe is zero (I guess this makes sense, because "nothing" would have a net energy of zero as well). This is what he does in fact claim. However, in a closed universe, there is a net negative energy based on what I have researched, and only in a flat universe do you get a net energy of zero.It only requires that the universe beslightlyclosed. This is perfectly compatible with measuring near-flatness. It may even be compatible with measuring very slightly negative curvature, as we can only measure the curvature of our observable region, but the statement about a universe from a quantum tunneling event being closed is a global statement that doesn't necessarily rule out some sub-regions within the universe being open.

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Chalnoth

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It is only for a closed universe that it is possible (so far as we are aware) to define a total energy such that the total energy is zero. I don't know where you got the idea that this result is for a flat universe.How can the universe have a total energy of zero, if the universe is closed though?

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"Alan Guth's term of inflation, which causes our universe to be flat, like inflating a ball decreases its surface curvature and makes it flat. Another factor proposed by Guth which should be considered is thatIt is only for a closed universe that it is possible (so far as we are aware) to define a total energy such that the total energy is zero. I don't know where you got the idea that this result is for a flat universe.

"A gravitational field has negative energy. Matter has positive energy.

Everything I have researched, concludes that if the universe is flat it has a net energy of zero, and if it is closed, it has a net negative energy.

"

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Chalnoth

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The statement that the universe has zero total energy comes from what is known as the Hamiltonian formalism of General Relativity. See here:"Alan Guth's term of inflation, which causes our universe to be flat, like inflating a ball decreases its surface curvature and makes it flat. Another factor proposed by Guth which should be considered is thatin such a flat universe, the total gravitational energy equals zero." - http://news.softpedia.com/news/Zero-Energy-and-the-Flat-Universe-98861.shtml

"A gravitational field has negative energy. Matter has positive energy.The two values cancel out provided the universe is completely flat. In that case the universe has zero energyand can theoretically last forever." - http://en.wikipedia.org/wiki/Zero-energy_universe

Everything I have researched, concludes that if the universe is flat it has a net energy of zero, and if it is closed, it has a net negative energy.

"The universe is neither spherical shaped, like the shape of a ball.That would be positive curvature, having net negative energy." - Neil deGrasse Tyson ()

http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

Looks like I was part-wrong, in that it is also possible to define zero total energy for a flat universe.

That said, one of the main problems here is that the pseudo-tensor approach which leads to the zero-energy result is somewhat arbitrary: it depends explicitly upon the coordinates used. There isn't any absolute sense in which it is possible to state that

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(i) A closed universe means positively curved, hence a negative net energy (no?). How can a closed universe have net energy zero? I am not saying you are wrong, but could you provide a source stating that a zero energy universe is also possible with with a closed universe? From what I have read, it is possible with a flat universe, but a closed universe would be negative (once more, I could be wrong)The statement that the universe has zero total energy comes from what is known as the Hamiltonian formalism of General Relativity. See here:

http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

Looks like I was part-wrong, in that it is also possible to define zero total energy for a flat universe.

That said, one of the main problems here is that the pseudo-tensor approach which leads to the zero-energy result is somewhat arbitrary: it depends explicitly upon the coordinates used. There isn't any absolute sense in which it is possible to state thatanyuniverse is or is not zero-energy, because there isn't any absolute way to define the total energy of a universe. To me, the zero-energy universe is just an interesting conceptual idea to understand how it is perfectly sensible for a universe to appear as a vacuum fluctuation, or for the apparent energy in matter fields to increase or decrease as the universe expands. It should not be taken as truth, or even as necessary. Because the simple fact of the matter is that in General Relativity,energy is not conserved.

(ii) I never said the zero-energy universe was absolute truth. However, with all the evidence we have it is entirely plausible, and an attractive idea on top of that.

(iii) How is energy

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“If the shape of the universe were anything else [besides flat], positively curved or negatively curved, it wouldThe statement that the universe has zero total energy comes from what is known as the Hamiltonian formalism of General Relativity. See here:

http://arxiv.org/PS_cache/gr-qc/pdf/0605/0605063v3.pdf

Looks like I was part-wrong, in that it is also possible to define zero total energy for a flat universe.

That said, one of the main problems here is that the pseudo-tensor approach which leads to the zero-energy result is somewhat arbitrary: it depends explicitly upon the coordinates used. There isn't any absolute sense in which it is possible to state thatanyuniverse is or is not zero-energy, because there isn't any absolute way to define the total energy of a universe. To me, the zero-energy universe is just an interesting conceptual idea to understand how it is perfectly sensible for a universe to appear as a vacuum fluctuation, or for the apparent energy in matter fields to increase or decrease as the universe expands. It should not be taken as truth, or even as necessary. Because the simple fact of the matter is that in General Relativity,energy is not conserved.

"The gravitational energy which is always negative exactly compensates the positive energy of matter. So the energy of a closed universe is always zero" - Alexander Vilenkin

Basically, both of the above statements cannot be true. Neil says that a closed universe could not have a net energy of zero, but Alex says the energy of a closed universe could always be zero. Who do you agree with?

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Chalnoth

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Not at all. I think you're mistaking the critical density for the density required for zero net energy. This isn't at all what that means.(i) A closed universe means positively curved, hence a negative net energy (no?).

I did, in the very post you're quoting. You can see the mentions in the introduction, and the calculation in section 3C, on pages 8-9.How can a closed universe have net energy zero? I am not saying you are wrong, but could you provide a source stating that a zero energy universe is also possible with with a closed universe?

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“If the shape of the universe were anything else [besides flat], positively curved or negatively curved, it would not have zero energy.” – Neil DeGrasse TysonNot at all. I think you're mistaking the critical density for the density required for zero net energy. This isn't at all what that means

I did, in the very post you're quoting. You can see the mentions in the introduction, and the calculation in section 3C, on pages 8-9.

So basically, what you are saying, is Neil DeGrasse Tyson is mistaken?

Also, yes you did provide a link, I see it now. Thank you.

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Chalnoth

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Yes. Which is perfectly understandable. It's not quite his field. He's an astronomer. This is about cosmology. And while there is some overlap, it isn't as much as you'd think.“If the shape of the universe were anything else [besides flat], positively curved or negatively curved, it would not have zero energy.” – Neil DeGrasse Tyson

So basically, what you are saying, is Neil DeGrasse Tyson is mistaken?

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This is false. The total energy of a closed universe is zero. A flat universe may have zero energy, if and only if it is finite in size. See MS Berman's derivation:Basically, Alexander Vilenkin can say the universe came from "nothing" if the total energy of the universe is zero (I guess this makes sense, because "nothing" would have a net energy of zero as well). This is what he does in fact claim. However, in a closed universe, there is a net negative energy based on what I have researched, and only in a flat universe do you get a net energy of zero.

http://arxiv.org/pdf/gr-qc/0605063.pdf

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By finite in size, do you mean, not expanding forever? If so, how can this be? Doesn't a flat universe necessitate the expansion of the universe slowing down, but never quite stopping?This is false. The total energy of a closed universe is zero. A flat universe may have zero energy, if and only if it is finite in size. See MS Berman's derivation:

http://arxiv.org/pdf/gr-qc/0605063.pdf

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I find it weird this video was released then, without it being peer-reviewed:Yes. Which is perfectly understandable. It's not quite his field. He's an astronomer. This is about cosmology. And while there is some overlap, it isn't as much as you'd think.

However, what you are saying makes sense. Therefore, I thank you for answering my questions, you have been a big help!

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Chalnoth

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No. What is meant is that any individual time-slicing of the universe at a finite time is finite in size. The size of the universe at infinite time is not relevant for this statement.By finite in size, do you mean, not expanding forever? If so, how can this be? Doesn't a flat universe necessitate the expansion of the universe slowing down, but never quite stopping?

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for open tunneling universeVilenkin has a model of cosmic which describes the coming into being as a event. The problem that I see with this, is that this requires the to be closed. However, we know the is probably with a margin of error of less than 1%. Does this , the model is a dud? Or, is there some way around it?

http://arxiv.org/pdf/gr-qc/9905056.pdf

....Restricting ourselves to the Tunneling boundary condition, and applying it in turn to each of these curvatures, it is shown that quantum cosmology actually suggests that the Universe be open, k = −1.....

http://arxiv.org/abs/gr-qc/9802038

If one uses the tunneling wave function for the description of creation of the universe, then in most inﬂationary models the universe should have Ω = 1, which agrees with the standard expectation that inﬂation makes the universe ﬂat.

Phys. Rev. D 59, 043509

We show that the instability of the singular Vilenkin instanton describing the creation of an open universe can be avoided using, instead of a minimally coupled scalar field, an axionic massless scalar field which gives rise to the Giddings-Strominger instanton.

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for open tunneling universe

Quantum Cosmology and Open Universes

http://arxiv.org/pdf/gr-qc/9905056.pdf

....Restricting ourselves to the Tunneling boundary condition, and applying it in turn to each of these curvatures, it is shown that quantum cosmology actually suggests that the Universe be open, k = −1.....

Quantum Creation of an Open Inflationary Universe

http://arxiv.org/abs/gr-qc/9802038

If one uses the tunneling wave function for the description of creation of the universe, then in most inﬂationary models the universe should have Ω = 1, which agrees with the standard expectation that inﬂation makes the universe ﬂat.

Nonsingular instantons for the creation of open universes

Phys. Rev. D 59, 043509

We show that the instability of the singular Vilenkin instanton describing the creation of an open universe can be avoided using, instead of a minimally coupled scalar field, an axionic massless scalar field which gives rise to the Giddings-Strominger instanton.

Ah but this presents another problem with quantum tunneling models. The universe is not in a supposition state. This means, an observer must have collapsed the wave-function of the universe (meaning the tunneling does not really happen "spontaneously"). Correct me if I'm wrong, but the collapse of wave-functions don't just happen, it requires an observer (correct?).

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Chalnoth

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Wave function collapse does not require an observer. Here is an experiment where they collapsed a wave function simply by bathing the system in photons, without ever looking at those photons:Ah but this presents another problem with quantum tunneling models. The universe is not in a supposition state. This means, an observer must have collapsed the wave-function of the universe (meaning the tunneling does not really happen "spontaneously"). Correct me if I'm wrong, but the collapse of wave-functions don't just happen, it requires an observer (correct?).

http://prl.aps.org/abstract/PRL/v77/i24/p4887_1

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What could have possibly caused the collapse of the universal wave-function though? Photons wouldn't have existed if the universal wave-function hadn't of collapsed yet, and was in a supposition state. They would have had to exist outside the universe to cause the collapse of the universal wave-function. Thus, you can't use them an an explanation for why the universal wave-function collapsed. There would have been nothing to cause the collapse of the universal wave-function unless due to an external measurement. Thus, these quantum tunneling models explain nothing, it just begs the question of who/ what measured the wave-function of the universe to cause it to collapse.Wave function collapse does not require an observer. Here is an experiment where they collapsed a wave function simply by bathing the system in photons, without ever looking at those photons:

http://prl.aps.org/abstract/PRL/v77/i24/p4887_1

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