Flat universe implies no Big Bang and Singularity at T = 0

[Alan Grayson]

If Flat implies infinite in spatial extent, it can't be realized instantaneously at T = 0 (a type of singularity IMO). AG

[John Clark]

On Mon, Sep 16, 2024 at 6:58 AM Alan Grayson <agrays...@gmail.com> wrote:

> If Flat implies infinite in spatial extent, it can't be realized instantaneously at T = 0 (a type of singularity IMO). AG

 

Regardless of if the universe is infinite or finite or flat or curved, we know that our current physics cannot tell us what things were like at T=0, and we will never know until we resolve the discrepancy between our best theory of gravity, General Relativity, and our best theory of the other three forces of nature, Quantum Mechanics. Both theories have been tested with incredibly precise experiments and both theories have passed with flying colors. Physicists have been trying for nearly a century to find a way to get those two very successful theories to play nice together, but so far no luck.

 John K Clark    See what's on my new list at  Extropolis

cfl

[Alan Grayson]

This issue has nothing to do with a possible unifying theory at t = 0, but what an infinite universe in spatial extent implies; namely, no big bang, since that would require creating infinite spatial extent instantaneously (a condition I associate with a type of singularity). AG 

[Alan Grayson]

Another way to look at it is this; if the universe was finite in spatial extent when the BB occurred, it will always remain finite, but if it was infinite in spatial extent when the BB "occurred", it was always infinite and the BB didn't occur. AG 

[John Clark]

On Mon, Sep 16, 2024 at 10:54 AM Alan Grayson <agrays...@gmail.com> wrote:

> At t = 0, what an infinite universe in spatial extent implies; namely, no big bang, since that would require creating infinite spatial extent instantaneously

 

Neither Quantum Mechanics nor General Relativity can explain how something with infinite spatial extent could instantaneously come into existence at t=0, but they can't explain how something with finite spatial extent could do so either.  If we can ever find a way to stop those two theories from fighting each other, maybe we could figure it out.

> Another way to look at it is this; if the universe was finite in spatial extent when the BB occurred, it will always remain finite, but if it was infinite in spatial extent when the BB "occurred", it was always infinite

As I said in my previous post, if it's infinite now then it was infinite at the time of the Big Bang, and if it was finite then it's finite now.

> and the BB didn't occur.

That does not compute.  

 John K Clark    See what's on my new list at  Extropolis

stn

 

 

[Alan Grayson]

While it's true that our theories cannot explain the creation of a finite or infinite universe, our measurements indicate an expanding universe. But an infinite universe cannot expand, so if one exists, it was uncreated. Thus no BB for an infinite universe. AG 

[John Clark]

On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson <agrays...@gmail.com> wrote:

>  an infinite universe cannot expand

NO! In an infinite universe the distance between every particle in it and every other particle in it can still increase indefinitely. If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".

 John K Clark    See what's on my new list at  Extropolis 

imd

[Jesse Mazer]

"Expansion of space" in the general relativity sense does not depend on the total volume of the universe increasing--imagine something like an infinite chessboard where all the squares are increasing in area while the pieces stay the same size and centered on their respective squares, so each piece's distance from its neighbors is continually growing.

Jesse

On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson <agrays...@gmail.com> wrote:

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[Alan Grayson]

On Monday, September 16, 2024 at 3:05:27 PM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson <agrays...@gmail.com> wrote:

>  an infinite universe cannot expand

NO! In an infinite universe the distance between every particle in it and every other particle in it can still increase indefinitely.

And your proof is what? AG

[Alan Grayson]

On Monday, September 16, 2024 at 3:05:27 PM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson <agrays...@gmail.com> wrote:

>  an infinite universe cannot expand

NO! In an infinite universe the distance between every particle in it and every other particle in it can still increase indefinitely. If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".

How would you map (0,1) 1-1 onto the real numbers? Both sets have the same cardinality. AG 

d

[John Clark]

On Mon, Sep 16, 2024 at 9:36 PM Alan Grayson <agrays...@gmail.com> wrote:

> How would you map (0,1) 1-1 onto the real numbers?

F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the range is (0.1)

> Both sets have the same cardinality.

 And a short line in a long line have the same cardinality, and there is a very simple geometric proof showing that they can be put into a one to one correspondence.  Just draw a triangle with a line from the apex running through the short line to the long line at the base of the triangle 

> If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".

> That's circular. AG 

Alan, if you open any book on set theory you will find that the formal mathematical definition of infinity is that something is infinite if and only if a proper subset of it can be put into a one to one correspondence with the entire thing. 

John K Clark    See what's on my new list at  Extropolis

ioi

[Alan Grayson]

On Monday, September 16, 2024 at 9:12:58 PM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 9:36 PM Alan Grayson <agrays...@gmail.com> wrote:

> How would you map (0,1) 1-1 onto the real numbers?

F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the range is (0.1)

This map isn't 1-1. Many x's correspond to the same point in (0,1). AG 

> Both sets have the same cardinality.

 And a short line in a long line have the same cardinality, and there is a very simple geometric proof showing that they can be put into a one to one correspondence.  Just draw a triangle with a line from the apex running through the short line to the long line at the base of the triangle 

> If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".

> That's circular. AG 

I deleted the post with the circular comment. Why are you responding to it? AG 

Alan, if you open any book on set theory you will find that the formal mathematical definition of infinity is that something is infinite if and only if a proper subset of it can be put into a one to one correspondence with the entire thing. 

Returning to the focus of this thread is my claim that an infinite universe cannot be created. If one exists, it is eternal. The reason is because the creation would require something non-physical; infinite spatial expansion instantaneously. So no BB for a spatially infinite universe. The situation for a finite universe is different. It can start small and expand, notwithstanding the fact that we don't know how any universe can be created. AG 

[John Clark]

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson <agrays...@gmail.com> wrote:

> How would you map (0,1) 1-1 onto the real numbers?

F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the range is (0.1)

> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG 

This is a graph of the Arctan function. Show me many X's, or even one X, that corresponds to the same point in y.

>> If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".

> That's circular. AG 

>I deleted the post with the circular comment. Why are you responding to it? AG

I responded to your email. Apparently you thought you knew a way to delete an email that was already on my computer or delete my memory of reading that email. Neither worked.   

>  an infinite universe cannot be created. If one exists, it is eternal. The reason is because the creation would require something non-physical; infinite spatial expansion instantaneously. So no BB for a spatially infinite universe.

 

I will now quote somebody named Alan Grayson "You keep doing the same thing; asserting a result without proving it " 

John K Clark    See what's on my new list at  Extropolis

agd

[Alan Grayson]

On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson <agrays...@gmail.com> wrote:

> How would you map (0,1) 1-1 onto the real numbers?

F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the range is (0.1)

> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG 

This is a graph of the Arctan function. Show me many X's, or even one X, that corresponds to the same point in y.

I'll get back to you on this. I was thinking, as x increases positively or negatively, the y values (angles) repeat multiple times, making the function many-to-one. In this case, we're mapping all the real numbers, to a subset of the y-axis. Am I mistaken? AG 

>> If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".

> That's circular. AG 

>I deleted the post with the circular comment. Why are you responding to it? AG

I responded to your email. Apparently you thought you knew a way to delete an email that was already on my computer or delete my memory of reading that email. Neither worked.   

I deleted it from the List, wherever it's located. AG 

>  an infinite universe cannot be created. If one exists, it is eternal. The reason is because the creation would require something non-physical; infinite spatial expansion instantaneously. So no BB for a spatially infinite universe.

 

I will now quote somebody named Alan Grayson "You keep doing the same thing; asserting a result without proving it " 

Actually, I did prove it, above. When a universe is created, or shall we say "comes into being" it can either be finite or infinite. If it's alleged to be infinite but doesn't include some spatial points, that would be a contradiction to the assumption that it's infinite, and thus it must be finite (since, as we agree, a universe cannot transform from finite to infinite, or vis-versa). OTOH, if it's really infinite and includes all of space, it couldn't have reached that state through any progressive evolution, as that would make it finite. So, if the universe is really infinite, it must be eternally infinite since it can't evolve to that state. Not every proof is mathematical. This one's based solely on logic. AG

[Alan Grayson]

On Tuesday, September 17, 2024 at 6:48:19 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson <agrays...@gmail.com> wrote:

> How would you map (0,1) 1-1 onto the real numbers?

F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the range is (0.1)

> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG 

This is a graph of the Arctan function. Show me many X's, or even one X, that corresponds to the same point in y.

I'll get back to you on this. I was thinking, as x increases positively or negatively, the y values (angles) repeat multiple times, making the function many-to-one. In this case, we're mapping all the real numbers, to a subset of the y-axis. Am I mistaken? AG 

Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  So your plot seems wrong, but it's what is on the Internet. AG 

[Alan Grayson]

That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I still think the plot keeps repeating as x increases or decreases. AG

[Alan Grayson]

It repeats as follows: Arctan(x) = Arctan(x + n*2*pi), n=0,1,2,3 ...  AG

[John Clark]

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson <agrays...@gmail.com> wrote:

I'll get back to you on this. I was thinking, as x increases positively or negatively, the y values (angles) repeat multiple times, making the function many-to-one. In this case, we're mapping all the real numbers, to a subset of the y-axis. Am I mistaken? AG 

Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  So your plot seems wrong, but it's what is on the Internet. AG 

That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I still think the plot keeps repeating as x increases or decreases. AG

1) The range of the Arctangent function is the interval (-π/2,π/2) and its range is all the real numbers.

2) By dividing by π,  the range scales to (-1/2, 1/2).

3) Adding 1/2 shifts the range to (0,1)

4) Thus for every real number x there is a unique number y between zero and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . As I said before, the domain is all the real numbers and the range is (0,1)

 John K Clark    See what's on my new list at  Extropolis

rdi

[Alan Grayson]

Yes, but initially you were seeking a 1-1 function, but this one is many-to-one. AG 

[John Clark]

 FOR DARWIN'S SAKE! I GIVE UP!

 John K Clark    See what's on my new list at  Extropolis

ugi

[Alan Grayson]

You ought to cease being a juvenile a'hole. At each x, we get a value of y, but this image repeats as x is incremented by 2pi. Same situation at every x in the domain. Thus, many-to-one. But what really interests me is my claim/proof that an infinite universe must be eternal and hence is not subject to a creation. AG

[Alan Grayson]

I could be mistaken about arctan function. I'll check this again. AG 

[Alan Grayson]

On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson <agrays...@gmail.com> wrote:

I'll get back to you on this. I was thinking, as x increases positively or negatively, the y values (angles) repeat multiple times, making the function many-to-one. In this case, we're mapping all the real numbers, to a subset of the y-axis. Am I mistaken? AG 

Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  So your plot seems wrong, but it's what is on the Internet. AG 

That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I still think the plot keeps repeating as x increases or decreases. AG

1) The range of the Arctangent function is the interval (-π/2,π/2) and its range is all the real numbers.

What's the protocol here; to rant about Darwin because you have a typo above? AG 

[Brent Meeker]

Could'a told ya.

Brent

[Alan Grayson]

Why are you so inclined to join the asshole club? I just made an error. Are you immune from that? AG

[Alan Grayson]

 I conjectured that Inflation caused the unobservable universe to come into existence, an original thought you ignore, but your inclination is to be petty. Too many physicists are revealed to be a'holes and I see no cure for that. AG

[Alan Grayson]

I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 0, and arctan 0 degrees = 0, I thought arctan 360 degrees is also 0, but it apparently isn't. This is how I concluded y = arctan(x) is many-to-one. AG

[Cosmin Visan]

Universe doesn't exist. "Universe" is just an idea in consciousness. The Big Bang never happened in any past, since past doesn't exist. Only the eternal present moment exist. And in the eternal present moment, Big Bang happens at all times, since each moment is a moment of creation in which the world is being imagined into existence by consciousness inside itself.

[Alan Grayson]

On Thursday, September 19, 2024 at 6:14:53 AM UTC-6 Cosmin Visan wrote:

Universe doesn't exist. "Universe" is just an idea in consciousness. The Big Bang never happened in any past, since past doesn't exist. Only the eternal present moment exist. And in the eternal present moment, Big Bang happens at all times, since each moment is a moment of creation in which the world is being imagined into existence by consciousness inside itself.

Your ideas are essentially profound, but not accessible to physicists primarily because of their subliminal vanity. On the other hand, your ideas are totally useless. They predict nothing and offer us nothing to discover and do. AG 

[Alan Grayson]

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:

I spoke to a friend who is Emeritus Professor in Mathematics at Cal  Poly Pomona. He says the inverse tangent function is MULTI VALUED.  AG

[Alan Grayson]

Is the arctan periodic, or multi-valued? Internet answer:

No, the arctangent (arctan) function is not periodic; it is considered a one-to-one function because its domain is restricted to an interval where the tangent function (which is periodic) is one-to-one, typically from -π/2 to π/2, ensuring that each output value corresponds to a unique input value. 

Explanation: 

• Tangent periodicity:

  The tangent function (tan(x)) is periodic with a period of π, meaning its values repeat every π radians. 
• Restricting the domain:

  To create an inverse function (arctan), we need to restrict the domain of the tangent function to an interval where it is not repeating, like (-π/2, π/2). 

• By restricting the domain in this way, the arctangent function is no longer periodic. 

IOW, the arctan is single-valued if its domain is restricted to (-π/2, π/2), but Clark defines its domain to all real numbers, making the arctan periodic and thus multi-valued. AG

[Alan Grayson]

This above is not quite right. Clark is using just the principle branch of the tangent function, to get its inverse, which is 1-1. But there are many, in fact an infinite number of branches and this is where the multi-value problem originates. AG 

[Cosmin Visan]

@Alan Maybe you should read more books.

[Alan Grayson]

On Sunday, September 22, 2024 at 5:26:45 PM UTC-6 Cosmin Visan wrote:

@Alan Maybe you should read more books.

Maybe you should realize by now that your POV can be simultaneously valid and useless. AG

On Friday 20 September 2024 at 05:55:02 UTC+3 Alan Grayson wrote:

On Thursday, September 19, 2024 at 6:14:53 AM UTC-6 Cosmin Visan wrote:

Universe doesn't exist. "Universe" is just an idea in consciousness. The Big Bang never happened in any past, since past doesn't exist. Only the eternal present moment exist. And in the eternal present moment, Big Bang happens at all times, since each moment is a moment of creation in which the world is being imagined into existence by consciousness inside itself.

Your ideas are essentially profound, but not accessible to physicists primarily because of their subliminal vanity. On the other hand, your ideas are totally useless. They predict nothing and offer us nothing to discover and do. AG 

On Thursday 19 September 2024 at 10:14:01 UTC+3 Alan Grayso 

On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson <agrays...@gmail.com> wrote:

I'll get back to you on this. I was thinking, as x increases positively or negatively, the y values (angles) repeat multiple times, making the function many-to-one. In this case, we're mapping all the real numbers, to a subset of the y-axis. Am I mistaken? AG 

Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  So your plot seems wrong, but it's what is on the Internet. AG 

That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I still think the plot keeps repeating as x increases or decreases. AG

1) The range of the Arctangent function is the interval (-π/2,π/2) and its range is all the real numbers.

2) By dividing by π,  the range scales to (-1/2, 1/2).

3) Adding 1/2 shifts the range to (0,1)

4) Thus for every real number x there is a unique number y between zero and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . As I said before, the domain is all the real numbers and the range is (0,1) 

> Yes, but initially you were seeking a 1-1 function, but this one is many-to-one. AG 

 FOR DARWIN'S SAKE! I GIVE UP!

Could'a told ya.

Brent

Why are you so inclined to join the asshole club? I just made an error. Are you immune from that? AG

 I conjectured that Inflation caused the unobservable universe to come into existence, an original thought you ignore, but your inclination is to be petty. Too many physicists are revealed to be a'holes and I see no cure for that. AG

[Cosmin Visan]

@Alan. Maybe you should realize that if you are in depression everything is useless. And if you are happy everything is useful.