[Bill S]

Even in classical electromagnetism, if one can calculates the energy needed to assemble an electron, the result is infinite, yet electrons exist. The quantum self energy correction is also infinite although it can be rendered finite if we accept the fact that out theories are not valid up to infinite energies.

Is this not tantamount to saying that we cannot work with infinities unless we modify them in some way; in which case they are not infinite?

[alancalverd]

……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim? 

Interesting question. A hypothesis is scientifcally valid if it is (a) consistently predictive and (b) not disproved by experiment. It also has to be explanatory and consistent with previous observations. But a mathematical hypothesis is subject to absolute proof or disproof. So let's attempt an absolute proof. For any number a/b there exists a number a/(b+1) which is smaller and a/(b-1) which is larger. If b > a then a/b lies in the interval between 0 and 1. For any a there exists at least one  number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b. 

[yor_on]

Assume that for any point in a matrix there can be a defined distance. Then ask yourself how you can define it. By being 'inside' with it, measuring. 'Inside' is equivalent to the universe you're in, measuring on. Inside we need it, it's one of those things making macroscopic values work. It does not state what it should be from any thought up 'outside though. The simple solution to a outside is the idea of a universe as some physical entity, forming for example a sphere, or just a self enclosed barrier. If you instead define a 'outside' as being where distances won't hold anymore, then 'outside' can be thought of as a 'inside' too, but without arrow, and so without form.
=

Using that argument a distance becomes a sub division of another type of 'universe', where infinity loses its meaning, unless you want to define a infinity to anything lacking that arrow (clock). If you do, how will you treat the displacements between two 'ticks' on your clock? Also a question of discreteness.

[Bill S]

For any a there exists at least one  number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b.

"Mathematical ‘existence’ meant only logical self-consistency and this neither required nor needed physical existence to complete it.  If a mathematician could write down a set of non-contradictory axioms and rules for deducing true statements from them, then those statements would be said to ‘exist’.”  John Barrow.

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.

[Bill S]

Yor_on.  Your last post seemed to say something interesting; I just wish I knew what it was.   []

[alancalverd]

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.

Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.

[Bill S]

JohnDuffield is a major crackpot - Beware!!!!

If that's based on his posts in this thread, I guess I'm in danger of acquiring the same label.

Crackpots of the world unite,
Our limit is the skies;
Won’t they be pissed if we are right,
And win a Nobel Prize?

[JohnDuffield]

Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

Geddoutofit. The electron energy is 511keV. Not infinite. And you can diffract electrons. They aren't point particles. 

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.

What!? It doesn't follow that there's an infinite number of hadrons, they don't have infinite energy. And you don't have a clue what you're talking about.

[Bill S]

Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.

Absolutely!  These assertions are correct, but can exist only in the, presumably finite, minds of rational beings. 

A circular square centred on the bisector of the infinite side of a physically impossible triangle can exist in your mind, but, as you indicated, that does not make it a physical reality. 

[jeffreyH (OP)]

We pass through grass behush the bush to. Whish! A gull. Gulls. Far calls. Coming, far! End here. Us    then. Finn, again! Take. Bussoftlhee, mememormee! Till thous-endsthee. Lps. The keys to. Given! A way a lone a last a loved a long the


riverrun, past Eve and Adam's, from swerve of shore to bend of bay, brings us by a commodius vicus of recirculation back to Howth Castle and Environs.

[Bill S]

“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"

Then there's the Three quarks for Muster Mark!

And we're back to physics.

[chiralSPO]

Infinities are very useful mathematical concepts. We can never observe an infinity in the real world, but that does not necessarily mean that there isn't any physical infinity, it is just a restriction on our ability to observe and verify.

Infinitesimals are also very useful mathematically. I am not sure if quantization rules out any possibility of a physical infinitesimal, or just out ability to observe one.

A photon with zero energy would have an infinite wavelength. But again, even if it made sense for such a thing to exist, how could it be observed?

[jeffreyH (OP)]

“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"

Then there's the Three quarks for Muster Mark!

And we're back to physics.

You are a cut above the rest Bill.

[Bill S]

You are a cut above the rest Bill.

I could be a crackpot, though, couldn't I?   []

[jeffreyH (OP)]

You are a cut above the rest Bill.

I could be a crackpot, though, couldn't I?   []

I think we all have that potential.  []

[PmbPhy]

I think we all have that potential.  []

No. I don't believe that. It takes a particular personality for that.

[Bill S]

It takes a particular personality for that.

Would that be someone capable of original thought, like Copernicus, Newton or Wegener?

We are drifting away from the OP; does that mean we are running out of relevant things to say?

If that’s the case, perhaps we should ask Jeff if the original question has been answered.  To me, that is much more important than identifying crackpots.

[jeffreyH (OP)]

Well any jokes about crackpot potential aside I think some very interesting thoughts were expressed. All worth thinking about. It really isn't a question we can easily answer. We need to make sure we are thinking about how infinity relates to some of the functions we depend upon in the equations we use to describe nature. So no it wasn't answered but I didn't expect a concrete answer.

[Bill S]

I have long thought that with a thread like this, which contains a lot of interesting material it seems a shame that it often just fades out without any conclusion or summary.  I wondered about the value of a summary at some point by the OP, and whether this would be a good habit to cultivate. 

Although not the OP of this thread, I thought it might be worth summarising what I had gained from it.  I’m hardly past the first page, and I think I know why people don’t generally attempt this. []

[Bill S]

An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Surely a finite universe, which is all that exists, and is therefore expanding into nothing, is boundless, but finite.  This could not contain an infinite amount of matter.