"Entropy" (1854 - 2021)

Jul 24, 2020
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Rob Sheldon: “It From Bit” Is Winning The Cosmology Wars
Posted on September 21, 2021
----------------------
Ethan Siegel,
“Are we approaching quantum gravity all wrong?” at Big Think (September 16, 2021) -----
“gravity is emergent” from entropy that you can calculate based on the microscopic quantum state
of all the particles aggregated together.
Lee Smolin:"
the role of entropy in cosmological theory is something we have to get our heads straight about. “
Ethan :
“information” emerges from the particles . . . .
“entropy” or “information” emerges from the particles
Not only is “entropy” or “information” fundamental in the 21st century view of physics,
but in quantum information theory it is now held that “we wouldn’t say entropy is a property of a system,
but a property of an observer who describes a system.”,,,
Renato Renner, a professor ;
Fifteen years ago, “we thought of entropy as a property of a thermodynamic system,” . . .
“Now in (quantum) information theory, we wouldn’t say entropy is a property of a system,
but a property of an observer who describes a system.”,,,
“entropy is (not) a property of a system, but a property of an observer who describes a system.”
is with the quantum Zeno effect.
The reason why I am very impressed with the preceding experiments demonstrating that
“entropy is (not) a property of a system, but a property of an observer who describes a system”
is because entropy is very foundational in our scientific descriptions of the world.
As the following article states, “Entropy explains time; it explains every possible action in the universe;,,”,,
“Even gravity,,,, can be expressed as a consequence of the law of entropy.,,,”
Shining Light on Dark Energy – October 21, 2012
Excerpt: It (Entropy) explains time; it explains every possible action in the universe;,,
Even gravity can be expressed as a consequence of the law of entropy.,,,
The principles of thermodynamics are at their roots all to do with information theory.
Information theory is simply an embodiment of how we interact with the universe —,,,
Big bang by chance (?):
"The explosion in which our universe began was not a messy event." . . . .
And if you talk about how messy it could have been, this is what the Penrose calculation
is all about essentially. . . . This number has 10^123rd zeros.
Thus, considering entropy’s central importance in scientific explanation, (as well as in our own lives),
the statement “we wouldn’t say entropy is a property of a system, but a property of an observer
who describes a system.” is just fascinating!
===========
Where can "entropy" be used?
Entropy - in cosmological theory
Entropy - in quantum information theory
Entropy - is not only a property of a system, but also a property
of an observer who describes a system.
Entropy - can explain time
Entropy - can explain quantum gravity
Entropy - can explain every possible action in the universe
==========
John von Neumann said to the "father of information theory" Claude Shannon:
"Call it 'entropy', then in discussions you will get a solid advantage,
because no one knows what 'entropy' in general is."
------
"Entropy" (1854 - 2021)
==================
 
Entropy - can it decrease (overall) if the Universe contracts? (As in cyclic scenarios).

Cat :)
I was hoping my post

https://forums.space.com/threads/dark-matter-vs-mond-vs-gravity-by-em-waves.47222/post-554768

would answer some questions about entropy. It seems to have been completely unnoticed. Maybe you thought the ideas were not good or maybe because I mentioned they were from my book I'm not sure which?

Anyway, have another look and see if it helps. I think it might relate to IG's post as well. :)
 
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Catastrophe

The devil is in the detail
David,
I have looked at your referenced post #4. In fact this idea has been around for some time, and I have used it in the cyclic Universe context. I was not the first to refer to it either by a long chalk.

Where I used it was not in the context of localised reduction in entropy in a small part of the Universe, but in total reduction in entropy necessary to go from the maximum extent of the Universe to a Black Hole to Big Bang occurrence between one phase of a (the) cyclic Universe and the next.

I totally agree with what you suggest about contraction of molecular clouds.

Cat :) :) :)
 
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David,
I have looked at your referenced post #4. In fact this idea has been around for some time, and I have used it in the cyclic Universe context. I was not the first to refer to it either by a long chalk.

Where I used it was not in the context of localised reduction in entropy in a small part of the Universe, but in total reduction in entropy necessary to go from the maximum extent of the Universe to a Black Hole to Big Bang occurrence between one phase of a (the) cyclic Universe and the next.

I totally agree with what you suggest about contraction of molecular clouds.

Cat :) :) :)
If gravity can do it for molecular dust clouds ie nebula, then why can't it do it for a universe? it's the same principle. When gravity collapses something, it concentrates all the energy, all the matter and all the information and order all in one go.

By the way, did you mean to use an uppercase U for universe? In that case you can't speak of the Universe collapsing because it is probably infinite IMO. Only a local universe lower case u can collapse back into a black hole I think. You can't have the whole infinite Universe go through your nexus idea, it's too big it won't fit! :)
 
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Catastrophe

The devil is in the detail
First Universe. If it is the Universe going through phases separated by BH -> BB nexus, then I use U for the one Universe going through 'phases'.

The dust cloud is just a limited part of the Universe which is allowable in classical physical. What is "not allowed" is total reduction in entropy for the whole Universe.

BTW, you say the whole Universe will not go through a nexus. But, according to the BB, it all starts in a singularity.

Cat :)
 
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Catastrophe

The devil is in the detail
David,
The problem with cyclic Universe is that entropy increases (overall) from BB to state of maximum expansion. Contraction is then required to get through a nexus to the next BH/BB. My question, which I have posed and nobody has answered, is how the entropy gets back to a low level before the next nexus. Entropy must decrease as the Universe gets more and more closely packed together - in analogy to crystallization.

If entropy keeps increasing, nexus after nexus, then the cyclic process cannot be sustained.

Cat :)

Added 00.15 BST:
"It just says that the total entropy of the universe can never decrease. Entropy can decrease somewhere, provided it increases somewhere else by at least as much. The entropy of a system decreases only when it interacts with some other system whose entropy increases in the process."
 
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First Universe. If it is the Universe going through phases separated by BH -> BB nexus, then I use U for the one Universe going through 'phases'.

The dust cloud is just a limited part of the Universe which is allowable in classical physical. What is "not allowed" is total reduction in entropy for the whole Universe.

BTW, you say the whole Universe will not go through a nexus. But, according to the BB, it all starts in a singularity.

Cat :)
BTW, you say the whole Universe will not go through a nexus. But, according to the BB, it all starts in a singularity.
I think The Big Bang theory has done more damage and caused more confusion to science than anything else.

First is the singularity concept, this requires the there is a single infinitely small point with an infinite density. I find that completely stupid and unscientific, sorry, I know that statement is also unscientific but there you go.

Then - "according to the BB, it all starts". That's another nonsense because it is not known what 'all' is so no theory can say how it 'all' starts, it's a non starter to start with.

Then when people ask what is beyond the universe the experts quote that the universe created all of space so there is nothing beyond it. There's a similar response when people ask what was before The Big Bang and again the answer comes back there's nothing before because The Big Bang was the beginning. Again I find both these to be another nonsense. Stephen Hawking even solidified this thinking with his expression "it's like asking what's north of the North Pole".

My reason for thinking this is nonsense is as follows;

1. The big bang started from a hot dense patch, NOT a sngularity and so started with a finite size.

2. It's undergone finites rates of expansion

3. It has a finite age.

I suggest all of which means it has a finite size now, and so is an object. Objects exist in a space, they do not create all of space as the BB theory suggests. If space consists of 'something', then the BB may well have created its own internal space, but at the same time it must have existed in a pre-existing space, the Universe.

I suggest the big bang was the beginning of our local finite sized universe and not the infinite Universe.

For me the next line of thinking is, is there only our one finite universe sitting in an otherwise infinite emty space or, is space full of an infinite number of other finite universes? It's easy to understand an infinite number but you would have a very hard time explaining why there would be only one. Even more strange why you would only get one undergoing a cyclic process on its own forever in the middle of nowhere!

If you agree with my line of thinking then, IMO, you cannot have an infinite ( anyone care to dispute that) Universe which contains my suggested infinite universes, become a black hole and then go through a nexus. It's too big, it wont fit. I suggest your idea works well if you have just finite universes going through a nexus.

The final nonsense for me is the indefinite expansion of our universe, that is, the heat death of our universe. Again, with my above line of thinking our universe will stop expanding when it hits some of the other universes in the rest of the Universe.

Sorry, not the final nonsense, the final one is that the BB theory says there's no center or edge to our universe. However it's clear from my suggestion of our universe being a finite object, that it does have a center and an edge!

Back to the dust cloud. If gravity can do it for molecular dust clouds ie nebula, then why can't it do it for a finite universe or universe size clump of something? it's exactly the same principle. When gravity collapses something, it concentrates all the energy, all the matter and all the information and order all in one go. The difference with my thinking is that it's not the whole infinite Universe collapsing, which would be nonsense. :)
 
David,
The problem with cyclic Universe is that entropy increases (overall) from BB to state of maximum expansion. Contraction is then required to get through a nexus to the next BH/BB. My question, which I have posed and nobody has answered, is how the entropy gets back to a low level before the next nexus. Entropy must decrease as the Universe gets more and more closely packed together - in analogy to crystallization.

If entropy keeps increasing, nexus after nexus, then the cyclic process cannot be sustained.

Cat :)

Added 00.15 BST:
"It just says that the total entropy of the universe can never decrease. Entropy can decrease somewhere, provided it increases somewhere else by at least as much. The entropy of a system decreases only when it interacts with some other system whose entropy increases in the process."
My question, which I have posed and nobody has answered, is how the entropy gets back to a low level before the next nexus.
I've answered it several times in these forums with my dust cloud analogy.
Entropy must decrease as the Universe gets more and more closely packed together - in analogy to crystallization.

If entropy keeps increasing, nexus after nexus, then the cyclic process cannot be sustained.
You said it, it must work, it's part and parcel of your cyclic theory.

The fact that after an infinite time there is still some low enropy left proves there must be a mechanism to reset it to a lower level. After an infinite time no overall heat death has occurred because we are here. That means it never will occur!:)
 
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Catastrophe

The devil is in the detail
David,
"I think The Big Bang theory has done more damage and caused more confusion to science than anything else.

First is the singularity concept, this requires the there is a single infinitely small point with an infinite density. I find that completely stupid and unscientific, sorry, I know that statement is also unscientific but there you go."

On this we are totally agreed, If I could agree (much, much more) than than 100%, I would. It is openly admitted that division by zero steps outside the bounds of science and, therefore, that the singularity concept is unscientific.

I have to disagree about the Universe / universes issue, on which I have made my ideas clear on (many) more than one occasion. The terminology needs correcting before a sane discussion is possible. Some new word is necessary to get around this. I do not hold out much hope, since 'multiverses' seems too strongly entrenched to correct. I shall just have to accept that I will not live to see it changed, and leave it alone to fester.

Anyway, I am pleased that we agree on the (pseudo) BB and singularity issues.

Cat :) :) :)
 
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"Yet the thought has many times occurred to me, how many and how great are the benefits which accrue to states through History, which transmits to future generations the memory of those who have gone before, and resists the steady effort of time to bury events in oblivion...." -- Procopius, 'Buildings', Book I, Chapter I.
 
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If entropy keeps increasing, nexus after nexus, then the cyclic process cannot be sustained.
That seems to be how it is taken.

Interestingly, Dicke, at the time Penzias and Wilson called him to question their microwave noise, had computed about 5K for the universe. What I just learned was this was based on his "oscillating" universe idea (i.e. cyclical) where the build-up of entropy would result over time as you suggest. I'm not totally convinced the author I'm reading is right since it raises a number of questions to get a hard value. But it's interesting.

Dicke held that contraction could not be so perfect that it would go to a singularity but rather more of a blob before bouncing back.

However, Hawking, and I think Penrose or Wheeler, did work to argue that the initial singularity would be a must, which makes sense given the grav field surrounding any "blob".

But the author doesn't address David's point for a singularity. My understanding is that physics breaks down at t=0, and I have seen nothing to change that. It's not that illogical for some, but it's metaphysics AFAIK.
 
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Catastrophe

The devil is in the detail
Just my guess, but, of course, forget the impossible (division by zero). What's wrong with a concentrated blob squeezing through the nexus? Better than division by zero any day.

In my guessed cosmology, and I am still happy if I am the sole owner ;)
, entropy will decrease with contraction as plasma goes to gas to liquid to solid
and, as a joyful blob,. squeezes through its wondrous, excited nexus, accelerating into a new phase of relaxing, increasing entropy.

Cat :)
 
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Just my guess, but, of course, forget the impossible (division by zero). What's wrong with a concentrated blob squeezing through the nexus?
I would assume that the problem is in the instability of small blobs near one another due to unimaginable gravitational attraction to one another. We certainly see stable binary stars, but there seems to be something extra at work at this level due to the spacetime bending under GR. This, just guessing, is what turned Dicke away from his blob view.

Better than division by zero any day.
Yes, and let's say its infinitely better. ;) The author (same book), and other authors, would be better served if they treated the BB as something approaching a singularity when we rewind the clock.

We have discovered over time that there are strange forces that do things like constrain collapse for white dwarfs, and for neutron stars. There is no reason in my mind that some new process or force might emerge during the intensity of the first Planck second. Perhaps reversing entropy in some way if in a collapse, not that I support this supposition. But the point is no one knows, IMHO. If they did, we would have nice working equations from t=0, and we don't.

In my guessed cosmology, and I am still happy if I am the sole owner ;)
, entropy will decrease with contraction as plasma goes to gas to liquid to solid
Humpty Dumpty might have something to say about that. ;)
 
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Catastrophe

The devil is in the detail
Helio, my understanding (or my imagined version) of the blob was that there is only one, which, as it squeezed through the nexus, did narrowly miss being a singularity.
As far as Humpty Dumpty is concerned, I am happy if he falls through the nexus masquerading as a blob. I would never sanction his becoming a singularity ;)

Cat :)
 
David,
"I think The Big Bang theory has done more damage and caused more confusion to science than anything else.

First is the singularity concept, this requires the there is a single infinitely small point with an infinite density. I find that completely stupid and unscientific, sorry, I know that statement is also unscientific but there you go."

On this we are totally agreed, If I could agree (much, much more) than than 100%, I would. It is openly admitted that division by zero steps outside the bounds of science and, therefore, that the singularity concept is unscientific.

I have to disagree about the Universe / universes issue, on which I have made my ideas clear on (many) more than one occasion. The terminology needs correcting before a sane discussion is possible. Some new word is necessary to get around this. I do not hold out much hope, since 'multiverses' seems too strongly entrenched to correct. I shall just have to accept that I will not live to see it changed, and leave it alone to fester.

Anyway, I am pleased that we agree on the (pseudo) BB and singularity issues.

Cat :) :) :)
I am very dissapointed that I did not make my ideas clear in post 11 regarding Universe/universes. I thought I had used an agreed convention, i.e., Universe means all that exists and universes are individual finite entites such as bubble or pocket universes in eternal inflation theory, parallel universes in the "many worlds" interpretation or in my theory individual Big Bang finite universes. Also, the dictionary definition of Universe means it must at least include the multiverse. Incidently I don't use the word multiverse when expressing my ideas, though some might see it that way. Just an infinite Universe full of an infinite number of finite size universes is good enough for me. I thought I had made that clear in post 11, but obviously not.

I'm also sad that It's not possible to have "a sane discussion" about the Universe on a space forum.

Regarding the recent discussions about entropy. In order to have a view on this, it's necessary to have a viewpoint of the Universe or our universe, for example, whether or not it's a thermodynamically open or closed system etc. Since no one has given much attention to or understood my viewpoint of the Universe in post 11, I'm wondering whether its worth joining in or not.
 
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I'll share my thoughts on some of your important points, since you seem interested in comments...

I think The Big Bang theory has done more damage and caused more confusion to science than anything else.
Yes, because people quickly push BBT, as a great science theory, to places it can't go.

First is the singularity concept, this requires the there is a single infinitely small point with an infinite density. I find that completely stupid and unscientific, sorry, I know that statement is also unscientific but there you go.
I disagree that it's stupid since gravity doesn't get weaker near a singularity. But I do agree that it may well be unscientific since I don't know of equations that can accurately handle, even remotely, singularities, but there sure is a lot of stuff out there as if some folks, like Hawking, have done so.

Then - "according to the BB, it all starts". That's another nonsense because it is not known what 'all' is so no theory can say how it 'all' starts, it's a non starter to start with.
This is why I prefer to present BBT as it was discovered.... today then rewind the clock and go as far as science will take you.

Then when people ask what is beyond the universe the experts quote that the universe created all of space so there is nothing beyond it.
I haven't seen much of that. Science normally says that whatever, if anything, that was around before the Big Bang is outside our ability to see it or even understand it, at least until some objective evidence comes our way.

There's a similar response when people ask what was before The Big Bang and again the answer comes back there's nothing before because The Big Bang was the beginning. Again I find both these to be another nonsense. Stephen Hawking even solidified this thinking with his expression "it's like asking what's north of the North Pole".
Right. Physics can get close to the first Planck second but beyond that is either metaphysics or pseudoscience, or just hand-waving, IMO.

My reason for thinking this is nonsense is as follows;

1. The big bang started from a hot dense patch, NOT a sngularity and so started with a finite size.
These should be ignored or corrected when you see them.

Science doesn't know its origin.

2. It's undergone finites rates of expansion
The original paper from Lemaitre showed an early accelerated rate followed by a more linear rate. He understood well that he didn't have enough evidence to produce reliable estimates of expansion rates. This was 1927.

If and when we get a handle on DE, there may come much better estimates of an expansion rate and it may be fairly constant if our curvature is nearly "flat", for now, which it seems to be.

3. It has a finite age.
Why is this a problem? Rewind the clock and look at the CMBR, etc. and it can be determined with some degree of accuracy, within a 100M years or so is where we are now.

I suggest all of which means it has a finite size now, and so is an object. Objects exist in a space, they do not create all of space as the BB theory suggests. If space consists of 'something', then the BB may well have created its own internal space, but at the same time it must have existed in a pre-existing space, the Universe.
All we have to work with is the physics that lets us see that the great early phase of energy-only can expand and produce matter, and DM, apparently. It's logical that it produced spacetime as well.

I suggest the big bang was the beginning of our local finite sized universe and not the infinite Universe.
Agreed, but if you find another, you'll enjoy your reward in Sweden. :)

For me the next line of thinking is, is there only our one finite universe sitting in an otherwise infinite emty space or, is space full of an infinite number of other finite universes? It's easy to understand an infinite number but you would have a very hard time explaining why there would be only one. Even more strange why you would only get one undergoing a cyclic process on its own forever in the middle of nowhere!
Many likely hold this view. I favor a more teleological one, which also isn't objective-based science.

The final nonsense for me is the indefinite expansion of our universe, that is, the heat death of our universe.
The more the universe expands the cooler it gets. It's down to about 2.7K now and getting cooler. :) This is also an area where science writers do little to "eschew obfuscation".

Again, with my above line of thinking our universe will stop expanding when it hits some of the other universes in the rest of the Universe.
Yes, this would be objective evidence. This was proposed many years ago as a way to support M-theory (i.e. branes colliding with us). No evidence for such has been seen... so far.

Sorry, not the final nonsense, the final one is that the BB theory says there's no center or edge to our universe. However it's clear from my suggestion of our universe being a finite object, that it does have a center and an edge!
If any two laser beams can travel parallel and appear to curve due to spacetime, per GR, until they return to us from behind. Then where will you go to find a center.? The idea that the surface of a sphere has a center is the 2D example of this.

Back to the dust cloud. If gravity can do it for molecular dust clouds ie nebula, then why can't it do it for a finite universe or universe size clump of something?
Indeed, Einstein soon realized that he had to add something to prevent the universe from collapsing, so he added his cosmological constant. He later dismissed it when he finally accepted the GR work of Lemaitre, as well as others that encouraged him like de Sitter and Eddington. The original problem for all but Lemaitre and the math of Friedman was they were stuck in their dogmatic Static model view for the universe.
 
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That seems to be how it is taken.

Interestingly, Dicke, at the time Penzias and Wilson called him to question their microwave noise, had computed about 5K for the universe. What I just learned was this was based on his "oscillating" universe idea (i.e. cyclical) where the build-up of entropy would result over time as you suggest. I'm not totally convinced the author I'm reading is right since it raises a number of questions to get a hard value. But it's interesting.

Dicke held that contraction could not be so perfect that it would go to a singularity but rather more of a blob before bouncing back.

However, Hawking, and I think Penrose or Wheeler, did work to argue that the initial singularity would be a must, which makes sense given the grav field surrounding any "blob".

But the author doesn't address David's point for a singularity. My understanding is that physics breaks down at t=0, and I have seen nothing to change that. It's not that illogical for some, but it's metaphysics AFAIK.
However, Hawking, and I think Penrose or Wheeler, did work to argue that the initial singularity would be a must, which makes sense given the grav field surrounding any "blob".
I don't understand your position on singularities. Here you seem to be dissagreeing with me and agreeing with them. Further down you seem to agree with Catastrophe who agrees with me. Can you clarify for me please.
But the author doesn't address David's point for a singularity. My understanding is that physics breaks down at t=0, and I have seen nothing to change that. It's not that illogical for some, but it's metaphysics AFAIK.
Can I suggest that reality or physics don't break down at t = 0 and that it's only our understanding which breaks down. For me things like this are damaging to science, Any thing that gets a beyond understanding label on it becomes open to abuse, for example the mysteries suurrounding black holes leads to worm-holes to other universes etc. Likewise the lack of knowledge about t = 0 allow all sorts of creationist theories or something from nothing theories to flourish.
 
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I don't understand your position on singularities. Here you seem to be dissagreeing with me and agreeing with them. Further down you seem to agree with Catastrophe who agrees with me. Can you clarify for me please.
Sure. Singularities are a logical assumption for the result of almost infinite gravitational attraction. What is there to avoid it all collapsing into a point? The problem is that we don't have, IMO, hard science that knows how to address them. We can more easily describe space around them and their effects. Indeed, this is how we discovered them. They can only be seen indirectly.

I have no idea how far over my head Hawking and others are but I do have a telescope. :) So, perhaps there are those who can claim with evidence that there is a physics solution to them. But infinites are usually highly shunned.

Can I suggest that reality or physics don't break down at t = 0 and that it's only our understanding which breaks down.
Agreed, but if our understanding breaks down it's a sure sign the physics isn't there either. And I'm convinced it's not.

For me things like this are damaging to science, Any thing that gets a beyond understanding label on it becomes open to abuse, for example the mysteries suurrounding black holes leads to worm-holes to other universes etc. Likewise the lack of knowledge about t = 0 allow all sorts of creationist theories or something from nothing theories to flourish.
These things do seem to stir the imagination. We certainly need a better way to travel to the stars. :)
 
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I'll share my thoughts on some of your important points, since you seem interested in comments...

Yes, because people quickly push BBT, as a great science theory, to places it can't go.

I disagree that it's stupid since gravity doesn't get weaker near a singularity. But I do agree that it may well be unscientific since I don't know of equations that can accurately handle, even remotely, singularities, but there sure is a lot of stuff out there as if some folks, like Hawking, have done so.

This is why I prefer to present BBT as it was discovered.... today then rewind the clock and go as far as science will take you.

I haven't seen much of that. Science normally says that whatever, if anything, that was around before the Big Bang is outside our ability to see it or even understand it, at least until some objective evidence comes our way.

Right. Physics can get close to the first Planck second but beyond that is either metaphysics or pseudoscience, or just hand-waving, IMO.

These should be ignored or corrected when you see them.

Science doesn't know its origin.


The original paper from Lemaitre showed an early accelerated rate followed by a more linear rate. He understood well that he didn't have enough evidence to produce reliable estimates of expansion rates. This was 1927.

If and when we get a handle on DE, there may come much better estimates of an expansion rate and it may be fairly constant if our curvature is nearly "flat", for now, which it seems to be.

Why is this a problem? Rewind the clock and look at the CMBR, etc. and it can be determined with some degree of accuracy, within a 100M years or so is where we are now.

All we have to work with is the physics that lets us see that the great early phase of energy-only can expand and produce matter, and DM, apparently. It's logical that it produced spacetime as well.

Agreed, but if you find another, you'll enjoy your reward in Sweden. :)

Many likely hold this view. I favor a more teleological one, which also isn't objective-based science.

The more the universe expands the cooler it gets. It's down to about 2.7K now and getting cooler. :) This is also an area where science writers do little to "eschew obfuscation".

Yes, this would be objective evidence. This was proposed many years ago as a way to support M-theory (i.e. branes colliding with us). No evidence for such has been seen... so far.

If any two laser beams can travel parallel and appear to curve due to spacetime, per GR, until they return to us from behind. Then where will you go to find a center.? The idea that the surface of a sphere has a center is the 2D example of this.

Indeed, Einstein soon realized that he had to add something to prevent the universe from collapsing, so he added his cosmological constant. He later dismissed it when he finally accepted the GR work of Lemaitre, as well as others that encouraged him like de Sitter and Eddington. The original problem for all but Lemaitre and the math of Friedman was they were stuck in their dogmatic Static model view for the universe.
Thank you so much, Helio! at least you have understood my ideas. I disagree with most of your responses, but here in the dis-UK it's past my bedtime, so I'll continue later.
 

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