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I can't think of a single thing that could be infinite.

Because the universe is expanding, isn't it? But there is an ever-changing barrier, so why could there be anything infinite, both hypothetically and realistically?

Anixx
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    Judging by the nature of the answers/comments, I would say this question belongs on philosophy.SE – Michiel May 11 '13 at 11:05
  • That's the thing, that's not what I wanted this question to be about... :( –  May 11 '13 at 11:06
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    Maybe not, but the way you phrased the question (and I think even the question itself in general) asks for a pretty philosophical answer. could there be anything infinite can pretty much only be answered with thought experiments and philosophical arguments – Michiel May 11 '13 at 11:22
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    The question (v1) is not meaningful. Take a physical quantity $Q$ with the value $q$ and define a new physical quantity $f(Q)$, where the function has a pole in $q$. E.g. the conductivity of a superconductor is infinite, or e.g. tangent $\tan(90^{\circ})$ to a right angle is infinite. – Qmechanic May 11 '13 at 14:34
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    @Anixx: Philosophy-like tags are not allowed, cf. this meta Phys.SE post. – Qmechanic May 13 '13 at 09:32
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    @michielm That's ridiculous. Any answer from 'philosophy' wouldn't even come close to satisfactory. – user12345 May 13 '13 at 20:35
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    @user12345 indeed, their community is terrible. – Anixx May 14 '13 at 03:34
  • But there is an ever-changing barrier There is no "barrier." –  Jul 17 '13 at 14:17
  • For all we know the universe is flat within measurement error, and therefore it can very well be infinite. – Johannes Jul 17 '13 at 15:35
  • Expanding on Qmechanic's objection: According to our best experimental and theoretical knowledge (which, this being physics se, is always a necessary qualification), the parameter 1/(Number of tachyons in the universe) is infinite. If this seems like it is obviously violating the spirit of your question, well that is exactly the point. – Rococo Jan 04 '17 at 04:53

4 Answers4

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This is a philosophical question so here is a philosophical answer.

The scientific method in based on repeated observations and experiment. The whole science is just a collectivist instrument of acquiring knowledge. Being an instrument, it has its own limitations. Among them are:

  • The tools employed by science are built by humans. As such, all tools use finite number of atoms and other parts. The results of the measurements can contain only limited number of bits.

  • To satisfy the scientific method the result of a measurement should be communicated to other scientists in finite time via finite link.

This means that there is always a limit on the largest value that can be scientifically measured.

So the conclusion is: science (that is, physics) cannot establish existence of infinite quantities. There is nothing physically infinite. As such, existence or non-existence of infinite quantities is outside of the scope of science.

Anixx
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    That's obviously a correct statement. I don't understand how somebody can downvote this answer. Probably somebody clicking before thinking... not a very scientific attitude. – Yvan Velenik May 13 '13 at 18:39
  • @Anixx these two statements seem conflicting: 1)science (that is, physics) cannot establish existence of infinite quantities and 2) here is nothing physically infinite. How can you say there is nothing physically infinite when you said science cannot establish, etc? – good_ole_ray Jun 01 '13 at 20:38
  • @good_ole_ray it is obvious. physics cannot establish existence of infinite quantities => there is nothing physically infinite. – Anixx Jun 01 '13 at 23:24
  • @good_ole_ray For something to be physically infinite, physics should have a method to verify that it is infinite indeed, which is impossible with methods available to physics. – Anixx Jun 01 '13 at 23:30
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    @Anixx why can't something be infinite and still, physics cannot measure it. it is possible, no? – good_ole_ray Jun 02 '13 at 06:02
  • @good_ole_ray it is possible. – Anixx Jun 02 '13 at 08:55
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No (understandable/explainable) physical quantity could be infinite. "Infinity" is is physically very vague. When we say something is "infinite", it almost means we're throwing our hands up in despair that we can't explain something, or that quantity doesn't make sense in some particular framework. The whole point of physical quantities (observables) is to let us characterize physical phenomena. And a quantity which is infinite is pretty much useless for that purpose.

For starters, there are different kinds of infinities. The correct way to think about the concept of infinity is as a limit as something increasing, but without an upper bound. So it can grow arbitrarily large -- aka "infinity". So even if something is growing arbitrarily large, we can ask how fast it's growing and as compared to what other physical quantity (or some parameters). We can then replace the naively infinite physical quantity with this new quantity that tells us how fast it is going to infinity.

For all our progress in physics, we're still making effective theories to model phenomena in some particular regime. So in some cases, it might well be that our effective theories don't make sense beyond some values of the parameters. So we'll have to "cut off" the validity of our theory in some regime of the parameters and claim that beyond that, some better theory must take over.

Ultimately, the guiding principle is that nature can never behave badly enough to make some physical quantity infinite. If you see a physical quantity becoming arbitrarily large (ie without bound), then you're doing something wrong -- either considering the wrong quantity, or using a framework beyond it's regime of validity.

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Siva
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  • My answer is a little abstract, and if you'd like some concrete examples for the things I say, let me know. – Siva May 11 '13 at 17:03
  • No, this was a good answer. Since I'm new to this, I can't up vote. –  May 11 '13 at 23:58
  • It is extremely antiscientific to say what this answer says, namely, to tell to the nature how should it be, how discrete it should be, how finite it must be, especially after we know that Universe and fields are infinite. Thank you for deleting this argument. It is indicative that these dictators, denying modern theories, send us to the philosophy area. – Val May 12 '13 at 12:56
  • (1) The answer says nothing about the universe being discrete. (2) Even if the universe is infinite, the region to which we are causally connected and can say anything meaningful about, is finite. (3) It doesn't make any sense to say fields are infinite -- Field theory forms a very good effective model for solid state physics, which actually sits on a lattice. So to define a "good" field theory, you only need to separate those scales and you don't actually need an infinite number of points or field values. – Siva May 12 '13 at 18:50
  • What about fields? Is there anything stopping a photon from travelling infinitely far? – user12345 May 13 '13 at 17:52
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How about space? I understand a standard assumption in cosmology is that the universe is spatially infinite in extent.

Of course whether it actually is - is an entirely separate question.

For how can you measure something to be infinite? It maybe that some parameter is inversely related to that something. And you could measure that value to be zero.

In Philosophy Aristotle stated that Infinities can never be actual but only potential.

Mozibur Ullah
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    We don't know if space is physically infinite. It appears flat but the topology of the universe may be finite. – Brandon Enright May 13 '13 at 18:01
  • @BrandonEnright:Yes, I know. Thats why I said it was a standard assumption. I'm sure that there are other theories in which its not taken to be infinite. – Mozibur Ullah May 13 '13 at 18:36
  • I read somewhere that space is not infinite - because then temperature would drop to 0K throughout the universe and observing celestial bodies so close to each other would be rare. We'd hardly have galaxies since everything would be so far apart. – mikhailcazi Jul 17 '13 at 13:06
  • @mikhailcazi: sure if space was infinite, and an infinite amount of time has passed then then the temperature will drop to exactly zero. However if only a finite amount of time has passed it cannot be exactly zero; since space is large (i.e. approximately infinite in the appropriate sense!) & a large but finite amount of time has passed since the big bang - the average temperature should only be slightly above absolute zero. – Mozibur Ullah Jul 17 '13 at 13:12
  • Physical space has a well defined border, the particle horizon. Everything beyond that is non-observable, so physically does not exist. – Anixx Jan 08 '15 at 13:33
  • I've retracted this answer - as thinking about it - space, at least in the Big Bang cosmology is finite; as it must be given that a finite amount of time has passed since the Big Bang and space expanded from a point. – Mozibur Ullah Jan 08 '15 at 17:27
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Here is a list of actual infinities in physics, mentioning

  1. Real Numbers. For instance, a set of all possible distances, this is a set with infinite cardinality, and thus actually infinite. Even the same distance, from infinitude of possible observers, is infinitely large or distance between relatively moving objects has infinity of values, taken at infinite moments of time.
  2. Fields
  3. The singularity (infinite density)
  4. Uniform cosmology (size and amount of matter in the Universe) "This is not a potential infinite, because the infinite set exists entirely in this universe, not in some possible universe."
Val
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    These are infinities in our models of reality. Whether there exists anything actually infinite in Nature will belong forever to the realm of philosophy not physics (how would you devise an experiment to check the infinity of anything?). – Yvan Velenik May 11 '13 at 10:56
  • Aren't the models actually exist? If something actually exist in the Universe and infinities exist in this something, doesn't that imply that intinities actually exist by pure logic? Don't you add this your very profound comment about filosofy to every answer, regarding physical reality, in the world? – Val May 11 '13 at 10:59
  • With all due respect, I think this answer is wrong. Have a look at my answer for an explanation. – Siva May 11 '13 at 17:05
  • @michielm, Here are 4 points claimed to be infinite. There is no surface length among them. Stop arguing by straw man argument. – Val May 12 '13 at 09:45
  • You are right, my argument didn't connect to your answer. My apologies. Still, I have to agree with Yvan Velenik and @Siva on this one – Michiel May 12 '13 at 10:48
  • @YvanVelenik I agree that 1,3, and 4 are nonsensical, but what about 2 (fields)? Is there anything stopping a photon from travelling infinitely far? – user12345 May 13 '13 at 17:51
  • @user12345: I am only saying that such a statement is meaningless from an operational point of view (in that sense it's not science, but philosophy). Again, how would you test this hypothesis? – Yvan Velenik May 13 '13 at 18:36
  • It is our physical theory. How do you test it? – Val May 13 '13 at 20:08
  • BTW, how can anybody, who can simply look into infinity, http://en.wikipedia.org/wiki/Infinity_focus, say that it does not exist? – Val May 13 '13 at 20:10
  • @YvanVelenik Why is it not a scientific statement to say "there is no physical law that we know of that would prevent a photon from travelling infinitely far"? – user12345 May 13 '13 at 20:27
  • @Val To your first comment: Yes, it's a physical theory. Clearly, it would not be useful, or even testable. I'm not saying the concept of infinity is a physical one, just that I can't see a reason why it couldn't be physical. To your second comment: that is in no way a proof. – user12345 May 13 '13 at 20:33
  • @user12345: Again, your statement "there is no physical law that we know of that would prevent a photon from travelling infinitely far" is about our current theories (it is a statement about a property of the set of physical laws we currently use to model physical reality), it is not about Nature. The only scientifically meaningful statements are those that can (at least in principle) be tested in experiments. Yours cannot. – Yvan Velenik May 14 '13 at 06:55
  • @YvanVelenik Yes, my last comment said exactly that. To discuss further, we'd have to stray into the philosophy of science... and let's not. – user12345 May 14 '13 at 09:16