Physical implications of Kalām argument

Now here's a thought. Suppose that there is no end as such to the Universe, but that the quantum of time is able to increase in size without limit. Is it even logically possible to conceive of a situation in which an infinite time span could nonetheless contain only a finite number of time quanta? If there is such a thing as a supertask, in which an infinite series of operations is completed in a finite length of time, could there be such a thing as a subtask, in which a finite series of operations could not be completed in an infinite length of time?

I think there may be one or two rather insurmountable problems with that, but it's the only way I can see of having a finite universe with unbounded time unless time is cyclical.

Dave
 
Regarding the first axiom?, it is something I've had in my mind for quite sometime, I mean, existing a range of I think 10^80 atoms in the Universe that is more or less the upper limit of things that can exist of at least one atom, from there if you want to add subparticles... well maybe the number already includes it.. not sure.. the point being, there's a finite (but mind-boggling giant) number of things (at least of matter ) in the universe, maybe if you take probabilities into account.. that sort of thing can be infinite... but dunno.. sounds like cheating to me... can someone give an examplo of something physical and infinite in the Universe?
 
stup_id said:
Regarding the first axiom?, it is something I've had in my mind for quite sometime, I mean, existing a range of I think 10^80 atoms in the Universe that is more or less the upper limit of things that can exist of at least one atom, from there if you want to add subparticles... well maybe the number already includes it.. not sure.. the point being, there's a finite (but mind-boggling giant) number of things (at least of matter ) in the universe, maybe if you take probabilities into account.. that sort of thing can be infinite... but dunno.. sounds like cheating to me... can someone give an examplo of something physical and infinite in the Universe?
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That is not likely to be the number of partciles in the universe, just the observable universe?
 
Dave Rogers said:
Now here's a thought. Suppose that there is no end as such to the Universe, but that the quantum of time is able to increase in size without limit. Is it even logically possible to conceive of a situation in which an infinite time span could nonetheless contain only a finite number of time quanta? If there is such a thing as a supertask, in which an infinite series of operations is completed in a finite length of time, could there be such a thing as a subtask, in which a finite series of operations could not be completed in an infinite length of time?

I think there may be one or two rather insurmountable problems with that, but it's the only way I can see of having a finite universe with unbounded time unless time is cyclical.
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It's a cool idea, but I'm not really sure what it would mean for a quantum of time to "increase in size". Aren't quanta of time what time is measured in, in the first place? Seems like the effect would be indistinguishable from time just stopping at one moment, Thief of Time-style.
 
Dorfl said:
Last I checked, this thread was at 18 pages and still discussing whether #1 is well-founded or not. What I was curious about is just the physical implications it would have, if it were true.
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Regardless, the argument as stated in the original post is still question-begging from what I can see: its conclusion is one of its premises re-worded.

I'm not sure why a philosophy question would be in the science section, instead of the philosophy section.

There is an entire segment of philosophy inquiring whether mathematical concepts are reified.

See Wikipedia: [Philosophy of mathematics]

Also: [Reification (fallacy)]


It's hard to evaluate the quality of an argument that has imaginary premises. eg: "If my grandmother was a car, would she be a Datsun or a Chevy?"
 
Dorfl said:
2. Therefore, the universe cannot have existed forever.
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I think the weakness with this one is that they are treating time as a set of things, instead of what it is: a dimension. aka a direction. Like up, down, left, right, forward, backward, future, past.

Does 'right' end? Or could it go on forever? I can't see why not.

Even in a universe with finite objects, distance and time could extend without bound in all directions from any origin. Many coordinates in fourspace would have no events or objects.
 
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stup_id said:
Regarding the first axiom?, it is something I've had in my mind for quite sometime, I mean, existing a range of I think 10^80 atoms in the Universe that is more or less the upper limit of things that can exist of at least one atom, from there if you want to add subparticles... well maybe the number already includes it.. not sure.. the point being, there's a finite (but mind-boggling giant) number of things (at least of matter ) in the universe, maybe if you take probabilities into account.. that sort of thing can be infinite... but dunno.. sounds like cheating to me... can someone give an examplo of something physical and infinite in the Universe?
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Prime numbers?
 
blutoski said:
It's hard to evaluate the quality of an argument that has imaginary premises. eg: "If my grandmother was a car, would she be a Datsun or a Chevy?"
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But the point of this thread isn't to evaluate the argument, its to look at the implications of one of its premises and see if they match the real world.
 
blutoski said:
Regardless, the argument as stated in the original post is still question-begging from what I can see: its conclusion is one of its premises re-worded.

I'm not sure why a philosophy question would be in the science section, instead of the philosophy section.

There is an entire segment of philosophy inquiring whether mathematical concepts are reified.

See Wikipedia: [Philosophy of mathematics]

Also: [Reification (fallacy)]

It's hard to evaluate the quality of an argument that has imaginary premises. eg: "If my grandmother was a car, would she be a Datsun or a Chevy?"
Click to expand...
But I'm not asking a philosophical question. The entire point of the thread is what physical effects it would have if #1 were true. I don't give a rotten öre—I think this is called a "wooden nickel" in English—about the quality of the argument itself.
 
blutoski said:
I think the weakness with this one is that they are treating time as a set of things, instead of what it is: a dimension. aka a direction. Like up, down, left, right, forward, backward, future, past.

Does 'right' end? Or could it go on forever? I can't see why not.

Even in a universe with finite objects, distance and time could extend without bound in all directions from any origin. Many coordinates in fourspace would have no events or objects.
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I could be wrong but I was thinking of spacetime as a set of points. If it is, it would have to be quantized not to be uncountably infinite, and also bounded or closed in each direction, to avoid being infinite. That could be a naïve view of spacetime, though.
 
Dorfl said:
I could be wrong but I was thinking of spacetime as a set of points. If it is, it would have to be quantized not to be uncountably infinite, and also bounded or closed in each direction, to avoid being infinite. That could be a naïve view of spacetime, though.
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That might be true, although neither current theory nor any experimental evidence support it. And even in a universe like that, one can still construct infinite sets: the set of all ordered sets of points, for example.

In physics it's a fact that sufficiently fine-grained discretization is impossible to distinguish from a continuum... although things like black holes create surprising opportunities.
 
Dorfl said:
But I'm not asking a philosophical question. The entire point of the thread is what physical effects it would have if #1 were true. I don't give a rotten öre—I think this is called a "wooden nickel" in English—about the quality of the argument itself.
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#1 "No infinite set can exist in the physical world." is true without question. There are no infinite sets in the physical world. It is also true that there are no finite sets in the physical world. This is because sets are a mathematical concept, rather than a physical thing. There are no 'odd numbers' in watermelons, and no LaGrange Multipliers in the colour red, no numerators in moon rocks, no prime numbers in my pants.

So having accepted that #1 is true, I move to #2: "Therefore, the universe cannot have existed forever." The truth of this premise can be evaluated, but it is not related to the truth or falsehood of #1 in any way.

Alternatively, if you're planning to connect #1 to #2, you are engaged in a philosophical argument about the reification of mathematical concepts. Ergo, the two links I provided on the history of this debate.



Now, it's possible that I misunderstood premise #1, and perhaps it could be rephrased such that it is not using mathematical vocabulary. Perhaps it's merely saying that the universe cannot be infinite. If so: this is the same claim as #2 and redundant, and we're still examining #2 on its own merit.
 
Dorfl said:
I could be wrong but I was thinking of spacetime as a set of points.
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It could be represented as such. But that doesn't mean it is a set of points.


Dorfl said:
If it is, it would have to be quantized not to be uncountably infinite, and also bounded or closed in each direction, to avoid being infinite.
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Yes, it could be bounded to avoid being infinite. It could be unbounded to be infinite. I don't know how this answers a question about whether it is or is not actually infinite?
 
Roboramma said:
But the point of this thread isn't to evaluate the argument, its to look at the implications of one of its premises and see if they match the real world.
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Ah. So just one premise? Which premise are we evaluating? There's four there.
 
blutoski said:
#1 "No infinite set can exist in the physical world." is true without question. There are no infinite sets in the physical world. It is also true that there are no finite sets in the physical world. This is because sets are a mathematical concept, rather than a physical thing. There are no 'odd numbers' in watermelons, and no LaGrange Multipliers in the colour red, no numerators in moon rocks, no prime numbers in my pants.

So having accepted that #1 is true, I move to #2: "Therefore, the universe cannot have existed forever." The truth of this premise can be evaluated, but it is not related to the truth or falsehood of #1 in any way.

Alternatively, if you're planning to connect #1 to #2, you are engaged in a philosophical argument about the reification of mathematical concepts. Ergo, the two links I provided on the history of this debate.


Now, it's possible that I misunderstood premise #1, and perhaps it could be rephrased such that it is not using mathematical vocabulary. Perhaps it's merely saying that the universe cannot be infinite. If so: this is the same claim as #2 and redundant, and we're still examining #2 on its own merit.
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I may have stated #1 badly. Is it clearer if we restate it as "The universe cannot contain an infinite number of anything, whether elementary particles, points in spacetime or other objects", or does that make it too fuzzy?
 
sol invictus said:
That might be true, although neither current theory nor any experimental evidence support it. And even in a universe like that, one can still construct infinite sets: the set of all ordered sets of points, for example.
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Now I'm beginning to wish I had studied set theory properly yet. Is there any short version of how that is done, or some link that explains it in more detail?

In physics it's a fact that sufficiently fine-grained discretization is impossible to distinguish from a continuum... although things like black holes create surprising opportunities.
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That's annoyingly inconvenient... Is there no way that singularities could—even just in principle—be used to test if space is quantized on any level?
 
Yoink said:
The first.
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I thought Dorfl asked us to assume that #1 was true. I thought that was the one we weren't supposed to evaluate.

I'm getting mixed instructions: are we to evaluate the argument in terms of premise #1 being accepted as true, or are we allowed to evaluate the merits of #1 as a premise (given Dorfl's rewording in the most recent post).
 
blutoski said:
I thought Dorfl asked us to assume that #1 was true. I thought that was the one we weren't supposed to evaluate.

I'm getting mixed instructions: are we to evaluate the argument in terms of premise #1 being accepted as true, or are we allowed to evaluate the merits of #1 as a premise (given Dorfl's rewording in the most recent post).
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Just read the OP. Or, here, I'll cut and paste it for you:

What I wonder about is the physical implications that the premise #1 would have, if it were true. For example, it seems to imply that the universe is finite in both space and time—requiring a big crunch—and that space and time are both quantized.

Are there any other implications that #1 would have, and are they correct, as far as we know?
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Pretty straightforward, don't you think?
 
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