Temporal finitism is wrong in assuming the beginning of time.

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I found this on wikipedia:

If time were infinite, then as the universe continued in existence for another hour, the infinity of its age since creation at the end of that hour must be one hour greater than the infinity of its age since creation at the start of that hour. But since Aristotle holds that such treatments of infinity are impossible and ridiculous, the world cannot have existed for infinite time.
Indeed, such a treatment of infinity is ridiculous, but treatments exist in our head and not in the universe. The universe did exist for an infinite time, but us humans have chosen to begin counting from a certain point, which is why an infinite past is possible.

What do you say to this?
 

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  • #2
bcrowell
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The universe did exist for an infinite time, but us humans have chosen to begin counting from a certain point, which is why an infinite past is possible.
In the standard description of cosmology according to general relativity, the beginning of time is the big bang, which is not arbitrarily chosen.

The WP article you're referring to seems to be http://en.wikipedia.org/wiki/Temporal_finitism , which is about ancient and medieval philosophy, not modern science.
 
  • #3
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I'm sorry. I can't even say oops.

Before the big bang, however, did "things" exist? Particles? I know there is no specific answer yet, but surely, there must be assumptions... which I cannot find anywhere...

That suggests that we chose to count time from the Big Bang... but the flow was always there?

I really don't want this turning into a theological debate. Kindly refrain from all references to holy stuff.
 
  • #4
Nabeshin
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Before the big bang, however, did "things" exist? Particles? I know there is no specific answer yet, but surely, there must be assumptions... which I cannot find anywhere...
This is... perhaps one of the most unsatisfying issues for people when they hear about the big bang. I have for a long time thought that the question itself is meaningless. Certainly, within the context of classical general relativity, you cannot even ask what happened before the big bang. The analogy I always use (is this courtesy of hawking?) is that it's like asking what's north of the north pole.

I do know that there is some effort into attempting to extend some kind of theoretical framework back past the epoch of the big bang. Other people here on the forum know much more about these efforts than I do and can probably point you to some articles -- I merely know they exist!
 
  • #5
bcrowell
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In standard general relativity, there was no time before the big bang. There are alternative theories that do allow time to be extended back before the big bang.
 
  • #6
Chronos
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You run into the same problem with singularities. We are pretty confident they exist , but, unable to explain what happens inside the event horizon.
 
  • #7
zonde
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In standard general relativity, there was no time before the big bang.
I would like to ask why do you view general relativity as equal with big bang model?
As I understand general relativity with cosmological constant can have different solutions like big bang model or static universe model just as well.
 
  • #8
zonde
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Before the big bang, however, did "things" exist? Particles? I know there is no specific answer yet, but surely, there must be assumptions... which I cannot find anywhere...

That suggests that we chose to count time from the Big Bang... but the flow was always there?
Big bang can be just an artefact of chosen coordinate system. Say you can redefine some "normal" time axis t that way: t'=-1/t. On that new coordinate axis t' you will approach t'=0 as you move toward minus infinity on that "normal" time axis t.

So it is not certain that you have "before big bang".

This seems quite reasonable intuitively because hypothetical particle tend to occupy the whole universe as you move toward big bang (as universe shrinks).
 
  • #10
I found this on wikipedia:

If time were infinite, then as the universe continued in existence for another hour, the infinity of its age since creation at the end of that hour must be one hour greater than the infinity of its age since creation at the start of that hour. But since Aristotle holds that such treatments of infinity are impossible and ridiculous, the world cannot have existed for infinite time.
Indeed, such a treatment of infinity is ridiculous, but treatments exist in our head and not in the universe. The universe did exist for an infinite time, but us humans have chosen to begin counting from a certain point, which is why an infinite past is possible.

What do you say to this?
Speaking from a mathematical perspective...

I would say that the quote from Wikipedia is either wrong, or is taken out of context.

Aristotle's understanding of infinity was intuitive, and not based upon a self-consistent mathematical foundation as it is in modern (post-Cantor) mathematics. As a result, his reasoning was flawed.

There is nothing inconsistent with the existence of ordinalities greater then those of any finite natural number. In fact, the foundation of modern mathematics pretty much requires the existence of a Limit ordinal "w", which is the first transfinite number, i.e. smallest infinite ordinal...and is the order type of the Set of Natural Numbers (least upper bound). Because ordinal numbers are well-ordered, the immediate successor to "w" is the ordinal "w + 1".

So, a transfinite sequence of ordinals would be:

0,1,2,3...,w, w+1, w+2,...,wx2, wx2+1,...wx3,...w^2,...

Any of the uncountable ordinals after "w" could represent "an hour greater than the infinity of its age since creation at the start of that hour".
 
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  • #11
bcrowell
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I would like to ask why do you view general relativity as equal with big bang model?
As I understand general relativity with cosmological constant can have different solutions like big bang model or static universe model just as well.
Check out the Hawking singularity theorem: http://en.wikipedia.org/wiki/Singularity_theorems It guarantees that there was a big bang singularity based on certain observable facts that have been verified empirically. Those observable facts rule out static cosmologies.

Big bang can be just an artefact of chosen coordinate system. Say you can redefine some "normal" time axis t that way: t'=-1/t. On that new coordinate axis t' you will approach t'=0 as you move toward minus infinity on that "normal" time axis t.
This is incorrect. GR is very permissive about changes of coordinates, but they do have to be diffeomorphisms. Your example isn't a diffeomorphism. Singularities that can be removed by a change of variables are called removable singularities. The big bang isn't a removable singularity.
 
  • #12
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What direction is it north of the north pole?

True, this question has no answer. It is very hard to digest, but maybe that British physicist was right. I don't know his name, but he said : "just as we cannot expect a chimpanzee to understand quantum mechanics, our universe might be populated with aliens that are much superior to us in intellect and hence know it better". So with the human kind of thinking, I infer from here that this question, "what was there before the big bang", aka "what happened before the beginning", is meaningless and thus unanswerable. It "just began", I guess. Thanks for your time everyone :)
 
  • #13
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What direction is it north of the north pole?
South :wink:
 
  • #14
zonde
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Check out the Hawking singularity theorem: http://en.wikipedia.org/wiki/Singularity_theorems It guarantees that there was a big bang singularity based on certain observable facts that have been verified empirically.
Yes that is the point I was trying to make. That big bang model is result of certain interpretation of redshift and not exactly theoretical prediction of general relativity.

About singularity theorems - as I understand they basically prove that you can't extend geodesics by tying them in knots so to say. So they say that if universe is shrinking (in direction of past) then you can't avoid singularity at the end. And that's it.

Those observable facts rule out static cosmologies.
You can not exactly rule out some other approach. You can only show that your approach is better so far.
But big bang model is not exactly perfect at explaining observed facts.

This is incorrect. GR is very permissive about changes of coordinates, but they do have to be diffeomorphisms. Your example isn't a diffeomorphism. Singularities that can be removed by a change of variables are called removable singularities. The big bang isn't a removable singularity.
What exactly is incorrect? I am not saying that it is some big bang coordinate system.
It's more like static universe coordinate system. So instead of using cesium atom as universal reference for coordinate system (GR) it's possible to take some averaged cosmological distance as reference. Something like comoving coordinate system.
 
  • #15
bcrowell
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This is incorrect. GR is very permissive about changes of coordinates, but they do have to be diffeomorphisms. Your example isn't a diffeomorphism. Singularities that can be removed by a change of variables are called removable singularities. The big bang isn't a removable singularity.
What exactly is incorrect? I am not saying that it is some big bang coordinate system.
It's more like static universe coordinate system. So instead of using cesium atom as universal reference for coordinate system (GR) it's possible to take some averaged cosmological distance as reference. Something like comoving coordinate system.
It looks like there are some problems in your understanding of GR. If you post about your background in math and physics, I'd be happy to suggest what to read next to improve your understanding.
 
  • #16
zonde
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It looks like there are some problems in your understanding of GR. If you post about your background in math and physics, I'd be happy to suggest what to read next to improve your understanding.
But please identify these problems. Otherwise your offer is a bit meaningless.

Is it because I do not understand that introducing hyperbolic scaling factor can not remove or introduce big bang singularity?
Or maybe hyperbolic scaling factor is somehow "incorrect"?
 
  • #17
bcrowell
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Is it because I do not understand that introducing hyperbolic scaling factor can not remove or introduce big bang singularity?
Or maybe hyperbolic scaling factor is somehow "incorrect"?
Yes. In #11 I gave kind of a standard explanation of a standard topic, using standard terminology. It sounds like that wasn't understandable to you, so there are some gaps in your background. If you want help filling in those gaps, I'd be happy to help.
 
  • #18
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What direction is it north of the north pole?
I think if anything, this suggests time as being cyclical. Coordinates being relative, there is actually something north of the north pole.
 
  • #19
zonde
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Yes. In #11 I gave kind of a standard explanation of a standard topic, using standard terminology. It sounds like that wasn't understandable to you, so there are some gaps in your background. If you want help filling in those gaps, I'd be happy to help.
Well, yes. My response was meaningless. So I will try second time.

GR is very permissive about changes of coordinates, but they do have to be diffeomorphisms. Your example isn't a diffeomorphism.
For my example (t'=-1/t) to be diffeomorphism I should have specified that t' is defined in range from 0 to infinity excluding 0 point (big bang correspond to 0 point) but t is defined in range from minus infinity to 0 excluding 0 point.
Is this the reason for your objection?

Singularities that can be removed by a change of variables are called removable singularities. The big bang isn't a removable singularity.
Well, yes I am not sure that I know what are "variables" in standard terminology.
The thing related to "variables" is question about tunable parameters of GR. I suppose that tunable parameters are not considered "variables".
So you would consider any transformation that would try to convert one GR solution with certain tunable parameters into another GR solution with another set of tunable parameters as "incorrect". Is it right?
 
  • #20
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The universe is expanding with time. This statement is reasonably well supported by observation and is well accepted. For the purpose of my argument it will be considered an axiom.

The universe is a finite hypersphere, the 3 dimensions of space exist as the surface of this hypersphere. It makes sense to me and unless you can prove otherwise I will consider it an axiom.

A hypersphere is 4 dimensional but there is no need in my mind to invent a 4th spacial dimension. Time will do nicely. Our three spacial dimensions are the surface of the hypersphere, the past is towards the center and the future is towards the outside. This provides very neat answers to 2 fundamental questions...

1. What harpooned before the big bang is equivalent to asking what is below the center of the earth. Anyone can see it is a nonsensical question. In our every-day experience everything is supported by something below it, just like everything results from something that happened before. Your feet are supported by the floor. The floor is supported by joists. The joists are supported by the foundation. The foundation is supported by soil. etc until you get to the center of the earth. Similarly every event in our experience is caused by something before it.

Perhaps causality is something like the force of gravity. As you move towards the center of the earth the gravity you experience is less and therefore less support is required for a given mass. Perhaps as you move back in time you find that less and less cause is required for a given effect until at the beginning of time (center of the hypersphere) no cause is required. This theory would predict that there should still be some things that happen for little or no reason. We find when studying quantum mechanics that on a very small scale this seems to be true. Events have a calculable probability of happening but there is no apparent cause that leads to a given outcome.

2. This theory also explains why the universe expands. It does so because that is the very shape of the universe. Asking why the universe expands is like asking why the surface area of a sphere 2 meters in diameter is larger then the surface area of a sphere 1 meter in diameter. It is a fundamental property of spheres. The surface volume of a hypersphere with a radius of 14.7 billion years is greater then the surface volume of a hypersphere with a radius of 13.7 billion years.
 
  • #21
zonde
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The universe is expanding with time. This statement is reasonably well supported by observation and is well accepted. For the purpose of my argument it will be considered an axiom.
...
2. This theory also explains why the universe expands.
You can't explain axiom from within theory that is built using this axiom.
You can support axiom only by demonstrating usefulness of your theory in other directions.

This theory would predict that there should still be some things that happen for little or no reason.
This is kind of default state of affairs. The interesting part in science is when you can predict that things happen for particular reason.

We find when studying quantum mechanics that on a very small scale this seems to be true. Events have a calculable probability of happening but there is no apparent cause that leads to a given outcome.
Hmm, but we don't get very excited about random errors in classical measurements even if we can predict that they follow normal distribution probabilistically.
 
  • #22
Chronos
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A very Godelesque argument, IMO. Of course you cannot prove the context of an argument within an argument. But, this is not about proof, it is about evidence - evidence collected from disparate sources, in unconnected studies, that all points in the same direction. I consider that pursuasive.
 
  • #23
A very Godelesque argument, IMO. Of course you cannot prove the context of an argument within an argument. But, this is not about proof, it is about evidence - evidence collected from disparate sources, in unconnected studies, that all points in the same direction. I consider that pursuasive.
There is a lot to be said for being persuaded, but only in hindsight. Proof on the other hand, is something you can really hang your hat on. While this may not be about proof, and the points are persuasive, it may just be a paucity of points in a vast sea of them, or an error in your thinking.

This is in short, why being "persuaded" isn't really a scientific issue... even in the early stages of research. What you find persuasive in science, as opposed to merely indicative of a valid hypothesis, is literally meaningless to everyone but you, or me, or whoever is persuaded.

The fact that I AGREE with you here, doesn't change how deeply wrong your final statement is, in light of the eloquence of the former portion.
 
  • #24
zonde
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But, this is not about proof, it is about evidence - evidence collected from disparate sources, in unconnected studies, that all points in the same direction. I consider that pursuasive.
The thing with evidence is that it's not yes or no matter.
There is a lot that can be said about interpretation of evidence. And it is worth separate discussion.

But if we talk about axioms then I have to say that it makes sense to take certain interpretation of evidence as postulate and look where it will get you.
But in this case you should make falsifiable predictions i.e. you should tell using the theory what should not be observed. Or to say it another way you should reduce possibilities.
 
  • #25
The thing with evidence is that it's not yes or no matter.
There is a lot that can be said about interpretation of evidence. And it is worth separate discussion.

But if we talk about axioms then I have to say that it makes sense to take certain interpretation of evidence as postulate and look where it will get you.
But in this case you should make falsifiable predictions i.e. you should tell using the theory what should not be observed. Or to say it another way you should reduce possibilities.
Translation: Evidence is weighed, and don't forget Occam's Razor?
 

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