How can a physical entity be infinite?

[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.

 

[stevendaryl]

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.

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.

 

[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.

 

[stevendaryl]

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.

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

 

[Chris Miller]

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.

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

 

[Paul Colby]

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

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

 

[Chris Miller]

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

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

 

[stevendaryl]

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

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

 

[Chris Miller]

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

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

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

 

[Stephen Tashi]

He informed me that nothing is zero. This is a fundamental truth. Experimentally things can only be consistent with zero.

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".

 

[Paul Colby]

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.

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.

 

[Stephen Tashi]

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.

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

 

[Paul Colby]

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

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.

 

[Stephen Tashi]

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.

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?

 

[Paul Colby]

Am I taking your statement out of context?

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?

 

[Stephen Tashi]

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?

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.

 

[Paul Colby]

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".

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.

 

[Chronos]

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

 

[Learner60]

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.

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

 

[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?

 

[Stephen Tashi]

in physics, infinity is synonymous to "not measurable".

That wouldn't distinguish between the intuitive notions of "infinitely large" and "infinitely small".

As soon as you have got a measurement value for some infinite property, the value is too small.

To distinguish between the notions of "infinitely large" and "infinitely small" we need somehow to get (or consider) measured values and then have some test or definition that tells us whether these values are too large or too small.

 

[Paul Colby]

Is the size of the universe measurable?

I would think a qualified "yes" would be in order. All conclusions obtained from measurements use some body of theory. A measurement of universe size could result in "the universe has infinite X based on theory Y consistent with observations Z"

 

[Gerhard Mueller]

That wouldn't distinguish between the intuitive notions of "infinitely large" and "infinitely small".

Infinitely small is not the problem. Size "Zero" would perfectly describe it. The problem is only to measure it.

 

[Gerhard Mueller]

A measurement of universe size could result in "the universe has infinite X

Sorry, but "infinite" is not allowed as measurement result.

 

[PeterDonis]

"infinite" is not allowed as measurement result.

That's why the response was a "qualified yes" instead of just "yes". Yes, it's impossible to directly measure the size of the universe if it is spatially infinite; but it is possible to get experimental support for a model which implies that the universe is spatially infinite. Our best current model of the universe is such a model.

 

[Stephen Tashi]

Infinitely small is not the problem. Size "Zero" would perfectly describe it.

For example, electric charge can be positive, negative, or zero. So , in the usual ordering of measurements of charge as real numbers, zero is not the "smallest" charge.

 

[Gerhard Mueller]

zero is not the "smallest" charge

If you just measure the value of a physical property, zero is the smallest result. Assigning negative values to another property is a special case and not fundamental. The problem to measure a potential inifinite length has nothing to do with the subtleness of very small or signed quantities.

 

[PeterDonis]

If you just measure the value of a physical property, zero is the smallest result.

This is obviously false; electric charge, which has already been pointed out, is a physical property and can have either sign.

Please bear in mind the PF rules about personal speculations.

 

[PeterDonis]

The problem to measure a potential inifinite length

Is irrelevant because our best current cosmological model, which says that the universe is spatially infinite, does not say that anyone can actually measure an infinite length. It just says that the universe being spatially infinite is implied by other things that we can measure.