Is Space-Time Finite or Infinite?

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In summary, if space-time is not infinitely divisible, then it cannot be infinite in extent. This proof uses the concept of smallest possible increment of space-time.
  • #1
laurence_white
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*note: I had this reviewed by a moderator before posting, so I hope you consider it appropriate to this forum.

Hypothetical proposition (of the form “if p, then q” – without asserting the truth of p or q):

If space-time S is not infinitely divisible, then space-time S cannot be infinite in extent.

Proof:

If space-time S is not infinitely divisible, then there exists a smallest possible increment of S, s. [The precise size of s does not matter; it only matters that it is finite.]

Since S is built from finite space-time components s, S requires an infinite amount of time (t∞) to become infinite in extent. [note that s is a space-time component, not simply a component of a geometric space.]

At any time t, we can assert that t∞ has not yet been reached (since t∞ is infinite).

Therefore, at any time t we can assert that space-time S is not infinite in extent.

Footnote: the number of dimensions of S (or equivalently, s) does not matter; it only matters that at least one is a time dimension.
 
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  • #2
the smallest unit idea is already firmly established by the concept of quanta and quantum observables- as well by causal set mathematics and computation: a non-discrete system has infinite information and thus infinite entropy and thus infinite instability NO causality- if you observe a causal universe with consistant physical laws your world is discrete

however your conjecture on infinite space is a non-starter- there is no model of cosmology which requires or suggeststhat the universe at the Big Bang was finite- this is often confused- some mistakenly think the BB implies a finite point in which the universe expanded- but the BBonly deals with the finite area we observe today- THAT is the tiny point- but there is no reason to think that the universe wasn't http://www.atlasoftheuniverse.com/bigbang.gif" [Broken]
 
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  • #3
i am familiar with commuting/non-commuting observables, Hermitians, etc. i don't accept your proposed counter-argument. an infinite space-time, by definition, cannot appear at once. remember: this is not a space; it is a space-time.

but i am pleased to see someone thoughtful respond. thank you for challenging my idea. i hope to hear from you again.

regards.
 
  • #4
Since S is built from finite space-time components s, S requires an infinite amount of time (t∞) to become infinite in extent.
Don't you need to prove that each s takes a positive time to be created/established/transversed? What if each (finite) s is "transversed" in "no time at all"? Then isn't t∞/0 = indeterminate?

Is this problem really different from any of Zeno's Paradoxes?
 

1. What is non-infinite space-time?

Non-infinite space-time refers to the concept that the universe has a finite size and age. It is the idea that the universe had a beginning and will eventually come to an end, rather than existing infinitely.

2. How is non-infinite space-time different from infinite space-time?

The main difference between non-infinite and infinite space-time is that in non-infinite space-time, the universe has a finite size and age, whereas in infinite space-time, the universe is considered to be infinite and eternal.

3. What evidence is there for the idea of non-infinite space-time?

There are several pieces of evidence that support the idea of non-infinite space-time, including the expansion of the universe, the cosmic microwave background radiation, and the observation of distant galaxies and their movement.

4. How does the concept of non-infinite space-time impact our understanding of the universe?

The concept of non-infinite space-time has significant implications for our understanding of the universe. It suggests that the universe had a beginning, which raises questions about what came before and how the universe will eventually end.

5. Is there any research being done on non-infinite space-time?

Yes, there is ongoing research being done on non-infinite space-time. Scientists are continually studying the expansion of the universe and looking for new evidence to support or challenge the idea of non-infinite space-time.

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