# B How can a physical entity be infinite?

1. Dec 29, 2016

### Chris Miller

Just googled, "Is the universe infinite?" and got this: "The surface of the torus is spatially flat, like the piece of paper, but finite. However, with expansion, it is possible that even if the universe just has a very large volume now, it will reach infinite volume in the infinite future."

This is just word play. There is no point in the future that an infinite amount of time will have elapsed.

∑ x=i/∞
i=1

Does x approach 1 or 0? Theoretically/philosophically I can see where ∞/∞=1, but i/∞ = 0 for any tangible/integral value of i.

2. Dec 29, 2016

### stevendaryl

Staff Emeritus
What they are saying is that the volume is finite, but unbounded.

If you have a function $V(t)$ giving the volume of the universe as a function of time, then what they're saying is that:

$lim_{t \rightarrow \infty} V(t) = \infty$

which is another way of saying:

$\forall x \exists t: V(t) > x$

There is no upper bound on how big it will get.

3. Dec 29, 2016

### Paul Colby

Physics is the interplay between theory/models and observation/measurement. Can an infinite thing be measured as infinite? Certainly not in any direct way since all measurements are finite.

[added] There was a discussion I had with my thesis advisor which really stuck with me as a life lesson. I made the claim that something was identically zero. He informed me that nothing is zero. This is a fundamental truth. Experimentally things can only be consistent with zero.

4. Dec 29, 2016

### stevendaryl

Staff Emeritus
Saying that a quantity is infinite is just a matter of saying that it is larger than any finite value.

5. Dec 29, 2016

### Chris Miller

Thanks Paul. Interesting. I figured that no material entity could be infinite, but never considered 0. Neither infinite nor non existence are possible.

6. Dec 29, 2016

### Paul Colby

Need I ask how many measurements would it take to verify this?

7. Dec 29, 2016

### Chris Miller

Thanks, I understand. Any value may be incremented. "Unbounded" might be a better word.

8. Dec 29, 2016

### stevendaryl

Staff Emeritus
You can't verify that something is infinite. That would be a theoretical prediction of some theory.

9. Dec 29, 2016

### Chris Miller

Thanks Steven, this clears up the cosmological assertion that the universe "is infinite" nicely for me.

10. Dec 29, 2016

### Stephen Tashi

Another way to put that, but perhaps not what your advisor meant, is that numerical (physical) units are used in referring to some property of a thing. A numerical unit is not, itself, a physical object. For example, there cannot actually be a "2 kg mass sitting on an inclined plane". There can be a tea cup or a circular saw sitting on an inclined plane and that physical object may have the property of "2 kg mass".

11. Dec 29, 2016

### Paul Colby

For me it meant that the contamination background I was asserting was "zero" was in fact some small value that I should estimate and quote. The larger issue is the meaning of something being verified in science is that it is true within the measurement error and to some finite confidence bound. It has nothing to do with units used.

12. Dec 29, 2016

### Stephen Tashi

With respect to this thread, that raises the interesting question of whether all properties studied by science must correspond to some unit of measurement.

13. Dec 29, 2016

### Paul Colby

What is the unit of a branching ratio? Last I checked these are dimensionless and only known (verified) to finite accuracy. I don't get your point at all.

14. Dec 29, 2016

### Stephen Tashi

I'm just taking what you said literally: "the meaning of something being verified in science is that it is true within the measurement error and to some finite confidence bound." If something has a "measurement error", I presume there is some unit of measurement for it. Am I taking your statement out of context?

15. Dec 29, 2016

### Paul Colby

Not exactly.

A dimensionless quantity, say the ratio of reaction A product to reaction B products (aka a branching ratio), is a dimensionless number with a statistical error obtained from its measurement. These are studied all the time in high energy physics and compared with model predictions. In light of this I don't see how one can claim all things measured have units and further that this is related to measurement errors?

16. Dec 29, 2016

### Stephen Tashi

Ok - my question is whether all properties of things studied in physics have some associated numerical "measure" - whether the measure has a "unit" or whether the measure is "dimensionless".

Since you just mentioned a dimensionless quantity having a measurement error ( "A dimensionless quantity, say the ratio of reaction A product to reaction B products (aka a branching ratio), is a dimensionless number with a statistical error obtained from its measurement.") then I assume we agree that dimensionless quantities are included in those properties that have numerical measurements.

17. Dec 29, 2016

### Paul Colby

This is all sounding too philosophical for my tastes. In experimental physics we measure things. This involves numerical values and estimating associated errors. Experiments are not done at random (well, usually) and must be carefully designed for the intended purpose which is (usually) aimed at answering a question.

18. Dec 30, 2016

### Chronos

One might argue indefinite integrals cannot be trusted beyond the extent they can be renormalized.

19. Dec 31, 2016

### Learner60

Infinity is really an idea..meaning some entity..frequently mathematical, has NO END. ex natural numbers..proof? X+1....+1 +1 ad infinitum.

20. Jan 3, 2017

### Gerhard Mueller

Hi,
in physics, infinity is synonymous to "not measurable". As soon as you have got a measurement value for some infinite property, the value is too small. Therefor the question is: Is the size of the universe measurable?