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The BVG Theorem

themohawkninja
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10/29/2013 10:15:41 AM
Posted: 3 years ago
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?
"Morals are simply a limit to man's potential."~Myself

Political correctness is like saying you can't have a steak, because a baby can't eat one ~Unknown
Rational_Thinker9119
Posts: 9,054
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10/29/2013 10:20:56 AM
Posted: 3 years ago
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

Don't answer a question with a question.
themohawkninja
Posts: 816
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10/29/2013 10:22:41 AM
Posted: 3 years ago
At 10/29/2013 10:20:56 AM, Rational_Thinker9119 wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

Don't answer a question with a question.

I can't answer a question if I don't fully understand it.
"Morals are simply a limit to man's potential."~Myself

Political correctness is like saying you can't have a steak, because a baby can't eat one ~Unknown
Enji
Posts: 1,022
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10/29/2013 3:02:24 PM
Posted: 3 years ago
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]
Enji
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10/29/2013 3:08:16 PM
Posted: 3 years ago
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).
Rational_Thinker9119
Posts: 9,054
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10/29/2013 3:08:44 PM
Posted: 3 years ago
At 10/29/2013 3:02:24 PM, Enji wrote:
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]

Read the last paragraph on page 3. It specifically states that the result shows that inflation must be finite in the past, and there must be space-time boundary.
Enji
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10/29/2013 3:26:28 PM
Posted: 3 years ago
At 10/29/2013 3:08:44 PM, Rational_Thinker9119 wrote:
At 10/29/2013 3:02:24 PM, Enji wrote:
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]

Read the last paragraph on page 3. It specifically states that the result shows that inflation must be finite in the past, and there must be space-time boundary.

You tend to be the first person to point out that a finite past does not imply a beginning. As they discuss in the following paragraphs, a beginning is a possibility but it's not necessary.
Rational_Thinker9119
Posts: 9,054
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10/29/2013 3:30:53 PM
Posted: 3 years ago
At 10/29/2013 3:26:28 PM, Enji wrote:
At 10/29/2013 3:08:44 PM, Rational_Thinker9119 wrote:
At 10/29/2013 3:02:24 PM, Enji wrote:
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]

Read the last paragraph on page 3. It specifically states that the result shows that inflation must be finite in the past, and there must be space-time boundary.

You tend to be the first person to point out that a finite past does not imply a beginning.

A finite past does not necessarily imply a "coming into being". It certainly implies a beginning.

As they discuss in the following paragraphs, a beginning is a possibility but it's not necessary.

They discuss no such thing. The paper specifically states that inflation cannot be eternal. Thus, a beginning follows from this.
Enji
Posts: 1,022
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10/29/2013 3:40:50 PM
Posted: 3 years ago
At 10/29/2013 3:30:53 PM, Rational_Thinker9119 wrote:
At 10/29/2013 3:26:28 PM, Enji wrote:
At 10/29/2013 3:08:44 PM, Rational_Thinker9119 wrote:
At 10/29/2013 3:02:24 PM, Enji wrote:
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]

Read the last paragraph on page 3. It specifically states that the result shows that inflation must be finite in the past, and there must be space-time boundary.

You tend to be the first person to point out that a finite past does not imply a beginning.

A finite past does not necessarily imply a "coming into being". It certainly implies a beginning.

As they discuss in the following paragraphs, a beginning is a possibility but it's not necessary.

They discuss no such thing. The paper specifically states that inflation cannot be eternal. Thus, a beginning follows from this.

If you consider an initial singularity to be a beginning, then the basic answer is yes - the BVG theorem shows that all inflationary models (and some others) have a beginning. There's a few subtleties - if the universe violates the initial assumption that the average rate of expansion is positive then the theorem doesn't hold, so it doesn't prove that the oscillatory model must have a beginning - but generally yes.
Enji
Posts: 1,022
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10/29/2013 3:43:43 PM
Posted: 3 years ago
At 10/29/2013 3:40:50 PM, Enji wrote:
At 10/29/2013 3:30:53 PM, Rational_Thinker9119 wrote:
At 10/29/2013 3:26:28 PM, Enji wrote:
At 10/29/2013 3:08:44 PM, Rational_Thinker9119 wrote:
At 10/29/2013 3:02:24 PM, Enji wrote:
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]

Read the last paragraph on page 3. It specifically states that the result shows that inflation must be finite in the past, and there must be space-time boundary.

You tend to be the first person to point out that a finite past does not imply a beginning.

A finite past does not necessarily imply a "coming into being". It certainly implies a beginning.

As they discuss in the following paragraphs, a beginning is a possibility but it's not necessary.

They discuss no such thing. The paper specifically states that inflation cannot be eternal. Thus, a beginning follows from this.

If you consider an initial singularity to be a beginning, then the basic answer is yes - the BVG theorem shows that all inflating* models (and some others) have a beginning. There's a few subtleties - if the universe violates the initial assumption that the average rate of expansion is positive then the theorem doesn't hold, so it doesn't prove that the oscillatory model must have a beginning - but generally yes.

fixed
themohawkninja
Posts: 816
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10/29/2013 8:26:10 PM
Posted: 3 years ago
At 10/29/2013 3:08:16 PM, Enji wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).

I just clicked on the first relevant link.

It only works if the Hubble constant remains greater than zero. If the universe lacks enough dark energy, it would probably collapse back in on itself, and make another "big bang", therefore possibly not having a provable finite past (unless each successive "big bang" was less powerful than the last).
"Morals are simply a limit to man's potential."~Myself

Political correctness is like saying you can't have a steak, because a baby can't eat one ~Unknown
Enji
Posts: 1,022
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10/29/2013 8:34:54 PM
Posted: 3 years ago
At 10/29/2013 8:26:10 PM, themohawkninja wrote:
At 10/29/2013 3:08:16 PM, Enji wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).

I just clicked on the first relevant link.

It only works if the Hubble constant remains greater than zero. If the universe lacks enough dark energy, it would probably collapse back in on itself, and make another "big bang", therefore possibly not having a provable finite past (unless each successive "big bang" was less powerful than the last).

Sorry, should have specified average Hubble constant - but you're correct; with an oscillatory model of the universe which can have a negative or 0 average Hubble constant the theorem doesn't hold.
Rational_Thinker9119
Posts: 9,054
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10/29/2013 10:06:39 PM
Posted: 3 years ago
At 10/29/2013 8:34:54 PM, Enji wrote:
At 10/29/2013 8:26:10 PM, themohawkninja wrote:
At 10/29/2013 3:08:16 PM, Enji wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).

I just clicked on the first relevant link.

It only works if the Hubble constant remains greater than zero. If the universe lacks enough dark energy, it would probably collapse back in on itself, and make another "big bang", therefore possibly not having a provable finite past (unless each successive "big bang" was less powerful than the last).

Sorry, should have specified average Hubble constant - but you're correct; with an oscillatory model of the universe which can have a negative or 0 average Hubble constant the theorem doesn't hold.

Isn't it more likely than not that the assumption of the BVG Theorem holds?
themohawkninja
Posts: 816
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10/29/2013 10:45:58 PM
Posted: 3 years ago
At 10/29/2013 10:06:39 PM, Rational_Thinker9119 wrote:
At 10/29/2013 8:34:54 PM, Enji wrote:
At 10/29/2013 8:26:10 PM, themohawkninja wrote:
At 10/29/2013 3:08:16 PM, Enji wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).

I just clicked on the first relevant link.

It only works if the Hubble constant remains greater than zero. If the universe lacks enough dark energy, it would probably collapse back in on itself, and make another "big bang", therefore possibly not having a provable finite past (unless each successive "big bang" was less powerful than the last).

Sorry, should have specified average Hubble constant - but you're correct; with an oscillatory model of the universe which can have a negative or 0 average Hubble constant the theorem doesn't hold.

Isn't it more likely than not that the assumption of the BVG Theorem holds?

Technically, yes, because our universe, being the only evidence we have, fulfills all of the theorem.

That being said, oscillating universes that lack sufficient dark energy (until dark energy can be explained with evidence that dark energy can't not exist in such quantities/ratios) should be taken as a possibility. After all, until it was discovered that the universes' acceleration is expanding, the "big crunch" theory was one of the most popular in science.
"Morals are simply a limit to man's potential."~Myself

Political correctness is like saying you can't have a steak, because a baby can't eat one ~Unknown
Such
Posts: 1,110
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10/29/2013 10:48:59 PM
Posted: 3 years ago
At 10/29/2013 3:02:24 PM, Enji wrote:
The actual conclusion of their paper is that " inflation alone is not sufficient to provide a complete description of the Universe", and a beginning is one possible solution - not that the universe must have a beginning. [http://arxiv.org...]

I think this is a very important statement. I'll bet a major hindrance to the actual understanding of many physical concepts is the belief that an explanation for physical phenomena is linear or immutable.
Enji
Posts: 1,022
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10/30/2013 8:58:49 AM
Posted: 3 years ago
At 10/29/2013 10:06:39 PM, Rational_Thinker9119 wrote:
At 10/29/2013 8:34:54 PM, Enji wrote:
At 10/29/2013 8:26:10 PM, themohawkninja wrote:
At 10/29/2013 3:08:16 PM, Enji wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).

I just clicked on the first relevant link.

It only works if the Hubble constant remains greater than zero. If the universe lacks enough dark energy, it would probably collapse back in on itself, and make another "big bang", therefore possibly not having a provable finite past (unless each successive "big bang" was less powerful than the last).

Sorry, should have specified average Hubble constant - but you're correct; with an oscillatory model of the universe which can have a negative or 0 average Hubble constant the theorem doesn't hold.

Isn't it more likely than not that the assumption of the BVG Theorem holds?

Yes. But it's probably worth noting that the theorem doesn't take into account quantum mechanics which would be important at the time of the singularity - quantum mechanics doesn't really jibe with singularities, so although the singularity is a result of relativity it probably doesn't reflect reality.
Rational_Thinker9119
Posts: 9,054
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10/30/2013 11:21:41 AM
Posted: 3 years ago
At 10/30/2013 8:58:49 AM, Enji wrote:
At 10/29/2013 10:06:39 PM, Rational_Thinker9119 wrote:
At 10/29/2013 8:34:54 PM, Enji wrote:
At 10/29/2013 8:26:10 PM, themohawkninja wrote:
At 10/29/2013 3:08:16 PM, Enji wrote:
At 10/29/2013 10:15:41 AM, themohawkninja wrote:
The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.

What does it mean to have an expansion greater than 1?

I'm not sure where you got the original quote - it actually states that the theorem holds if the Hubble constant is positive (greater than zero).

I just clicked on the first relevant link.

It only works if the Hubble constant remains greater than zero. If the universe lacks enough dark energy, it would probably collapse back in on itself, and make another "big bang", therefore possibly not having a provable finite past (unless each successive "big bang" was less powerful than the last).

Sorry, should have specified average Hubble constant - but you're correct; with an oscillatory model of the universe which can have a negative or 0 average Hubble constant the theorem doesn't hold.

Isn't it more likely than not that the assumption of the BVG Theorem holds?

Yes. But it's probably worth noting that the theorem doesn't take into account quantum mechanics which would be important at the time of the singularity - quantum mechanics doesn't really jibe with singularities, so although the singularity is a result of relativity it probably doesn't reflect reality.

Doesn't the BVG theorem hold regardless of any description of the early universe?

"What makes their proof so powerful is that it holds regardless of the physical description of the universe prior to the Planck time. Because we can"t yet provide a physical description of the very early universe, this brief moment has been fertile ground for speculations. (One scientist has compared it to the regions on ancient maps labeled "Here there be dragons!""it can be filled with all sorts of fantasies.) But the Borde-Guth-Vilenkin theorem is independent of any physical description of that moment." - William Lane Craig
Enji
Posts: 1,022
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10/30/2013 11:50:47 AM
Posted: 3 years ago
At 10/30/2013 11:21:41 AM, Rational_Thinker9119 wrote:
At 10/30/2013 8:58:49 AM, Enji wrote:

Yes. But it's probably worth noting that the theorem doesn't take into account quantum mechanics which would be important at the time of the singularity - quantum mechanics doesn't really jibe with singularities, so although the singularity is a result of relativity it probably doesn't reflect reality.

Doesn't the BVG theorem hold regardless of any description of the early universe?

"What makes their proof so powerful is that it holds regardless of the physical description of the universe prior to the Planck time. Because we can"t yet provide a physical description of the very early universe, this brief moment has been fertile ground for speculations. (One scientist has compared it to the regions on ancient maps labeled "Here there be dragons!""it can be filled with all sorts of fantasies.) But the Borde-Guth-Vilenkin theorem is independent of any physical description of that moment." - William Lane Craig

No, I don't know why WLC would think the theorem would hold if relativity doesn't.
Enji
Posts: 1,022
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10/30/2013 12:18:57 PM
Posted: 3 years ago
At 10/30/2013 11:50:47 AM, Enji wrote:
At 10/30/2013 11:21:41 AM, Rational_Thinker9119 wrote:
At 10/30/2013 8:58:49 AM, Enji wrote:

Yes. But it's probably worth noting that the theorem doesn't take into account quantum mechanics which would be important at the time of the singularity - quantum mechanics doesn't really jibe with singularities, so although the singularity is a result of relativity it probably doesn't reflect reality.

Doesn't the BVG theorem hold regardless of any description of the early universe?

"What makes their proof so powerful is that it holds regardless of the physical description of the universe prior to the Planck time. Because we can"t yet provide a physical description of the very early universe, this brief moment has been fertile ground for speculations. (One scientist has compared it to the regions on ancient maps labeled "Here there be dragons!""it can be filled with all sorts of fantasies.) But the Borde-Guth-Vilenkin theorem is independent of any physical description of that moment." - William Lane Craig

No, I don't know why WLC would think the theorem would hold if relativity doesn't.

To quote Sean Carroll, "Most importantly, I don"t think that any result dealing with classical spacetimes can teach us anything definitive about the beginning of the universe. The moment of the Big Bang is, if anything is, a place where quantum gravity is supremely important. The Borde-Guth-Vilenkin results are simply not about quantum gravity." Whatever your opinions are of him as a debater, physics and cosmology are his area of expertise.
Rational_Thinker9119
Posts: 9,054
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11/2/2013 11:56:18 PM
Posted: 3 years ago
At 10/30/2013 11:50:47 AM, Enji wrote:
At 10/30/2013 11:21:41 AM, Rational_Thinker9119 wrote:
At 10/30/2013 8:58:49 AM, Enji wrote:

Yes. But it's probably worth noting that the theorem doesn't take into account quantum mechanics which would be important at the time of the singularity - quantum mechanics doesn't really jibe with singularities, so although the singularity is a result of relativity it probably doesn't reflect reality.

Doesn't the BVG theorem hold regardless of any description of the early universe?

"What makes their proof so powerful is that it holds regardless of the physical description of the universe prior to the Planck time. Because we can"t yet provide a physical description of the very early universe, this brief moment has been fertile ground for speculations. (One scientist has compared it to the regions on ancient maps labeled "Here there be dragons!""it can be filled with all sorts of fantasies.) But the Borde-Guth-Vilenkin theorem is independent of any physical description of that moment." - William Lane Craig

No, I don't know why WLC would think the theorem would hold if relativity doesn't.

"A remarkable thing about this theorem is its sweeping generality. . . . We did not even assume that gravity is described by Einstein"s equations. So, if Einstein"s gravity requires some modification, our conclusion will still hold. The only assumption that we made was that the expansion rate of the universe never gets below some nonzero value" - Alexander Vilenkin