No more Infinities?

[skwinty]

Returning to the issues raised in a previous thread regarding infinite mass in zero volume, the argument that the equations raising the infinities, should be renormalised to remove the infinities.

If I understand Einsteins theories of gravity correctly, then black holes fall into this theory. Under further investigation into this issue, I came across this mathematics lesson.
Now, I am not a mathematician, but it strikes me that Einsteins Theory of Gravity cannot be renormalised. See attached PDF.

Looking forward to any comments and further discussion with regards to this hypothesis.

[Dujon]

I got a bit lost in the terminology, Steve. The general gist though seems to be somewhat like the hare vs tortoise, where it can be shown that the hare will never catch the tortoise because whenever the hare reaches the tortoise's last known position said tortoise has moved.

Of course, at least in quantum theory, the tortoise could be anywhere - possibly hoisting the trophy - when you're not looking.

[xelasnave]

Math is not my strong point and I dont feel qualified to comment... however that has never stopped me before..
All I would like to say is this...
It seems so much comes from an extrapolation of an observed trend...the Universe is expanding.. extrapolate this and we get...therefore at some point it must have expanded from a single point...long stretch in my view but thats the one we are ruled by...
and so lets look at an infinity...and ask this simple question... how can one arrive at an infinity with a finiteinput???
A black hole has "infinite" gravity...how so??? what was once outside as a finite accumulation of matter and therefore a finite amount of gravity thru some mysterious extrapolation no reasides in a region that now has infinite gravity (and time if you think about it)... you can not grow an infinite fruit from a finite seed.. no matter how many times you doudle and redouble and double again the finite it can never grow to infinite...

so how can we have parcels of infinite everywhere when we are contained within a finite Universe .. an if you build it via the big bang it can only ever be finite..big but finite.


and so I say simply this infinities of gravity and time are built using finite inputs...this is impossible.
alex

[bindibadgi]

Isn't the infinity we're talking about here the density of the black hole singularity, not its gravity?

I must say, however, that I also find infinities quite off-putting.

[xelasnave]

I am not sure really but time and gravity presumably are part of the mix...
but as I say one can ask... how can any proportion of something be called infinite if contained in a finite body ... the infinities can not be built from finite building blocks...

This is new thinking from my part but the logic seems fair.

alex:):):):)

[skwinty]

The point of infinity is very specific. Not a hairs breadth on either side.
Use your calculator and calculate the tangent of 89.9999999999999999999999 degrees and 90.99999999999999999999999 degrees and you will get a very large number. Not infinite but very large.
Infinity only occurs at exactly 90 degrees.

Now the density of the singularity approaches infinity rapidly but never really gets there, its like the frog in the middle of the pond who jumps half the remaining distance, he never gets out the water.

The issue I have is that the mathematicians like to get rid of infinities in their equations via renormalisation. This then makes the infinity dissappear.
However, the confusion I have is that some theories/equations are unrenormalisable. So, in some cases you cant get rid of the infinity in the equations.
General Relativity is one of these.
But still the mathematicians apply renormalisation to these and I would like to know why?:P

Now, it is beyond reason to expect infinite mass density in zero volume, but for all intensive purposes it gets pretty darn close. Current calculations show that the density of a neutron star would yield 100 million tons per cm3.
Infinity being N+1 we could hypothetically carry on forever:thumbsup:

[xelasnave]

Does this help??
http://www.pha.jhu.edu/~blechman/papers/renormalization/node1.html

alex

[xelasnave]

Steve said...

However, the confusion I have is that some theories/equations are unrenormalisable.

Some wont fit the bill and presumably outside the opperation I think.

alex

[xelasnave]

I read the following at another site.....http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/renormalisation.htm

renormalizable theories, rather than being "fundamental" are merely those theories which survive the scaling down from the fundamental scale to the "laboratory scale. Non-renormalizable theories get wiped out in the process of taking this limit."

alex

[skwinty]

Thanks for the links
Will check them out when time allows:thumbsup:

[sjastro]

Mathematicians don't renormalise, theoretical physicists do.

General Relativity as a stand alone theory in fact doesn't require renormalization.

The problem with Quantum field theory as opposed to QM is that in order to predict the interaction between particles or particles with electromagnetic fields etc, theoretical physicists have to rely on Perturbation theory. http://en.wikipedia.org/wiki/Perturbation_theory_%28quantum_mech anics%29
In simplest terms this means you allow the basic QM operators to deviate (perturb) under the influence of an external field.

The solutions to these Quantum field equations are expressed as a mathematical series. The series can be infinite for having an infinite number of terms, one or more of the coefficients are infinite, or both. Renormalization occurs if one is able plug back certain physical constants back into mathematical series and reorganize the series so that the infinite terms cancel out and/or truncate the number of terms in the series.

Getting back to GR, from a QM viewpoint, GR cannot be renormalized because as a gravity field theory the mathematical series is infinite. It would require an infinite number of steps to renormalize the series.

Regards

Steven

[skwinty]

Hi Steven
Thanks for the explanation.
I can understand renormalisation from a quantum field/mechanics point, but not in general relativity.
I have come across papers where the general relativity equations are being renormalised and this is what I dont understand.
I will find the relevant paper and review it again to make sure I understood it correctly.:thumbsup:

[sjastro]

While quantum gravity cannot be renormalised there is a method where only low energy scales are considered. This reduces the equations to a finite number of parameters which in turn leads back to GR.


Regards

Steven

[Doug]

What though is infinite or infinity. I'm getting to old to cope with maths much beyond 2+2=4, but it seems to me that in the forgoing discussions infinite/infinity is being understood in terms of a numeric value. As was pointed out to Alex some little time ago infinite refers only to potential, not actuality. This is why we can have a finite universe of matter contained in a volume of infinite potential.
Doug

[skwinty]

Of course infinity does not relate to a number, if it did it would be finite.
The issue is when an equation relating to conditions in a black hole relates to infinite density in zero volume then the laws of physics and the theory break down. Now, if you say that renormalising an equation removes the infinity from the result and so makes the equation valid isnt that a cheat?

If you calculate the density of a neutron star you dont get an infinite result but you may approach infinity assymptotically.ie you never get there!
If you look at a cutoff point in an equation that leads to infinity, where do you make the cutoff? 10^10??? 10^500??

Now, if there was no Hawking radiation around a black hole then the density would approach infinity although would never get there.

[Doug]

Which comes back to the only definition of infinity I ever heard:
'Undefinable'

cheers,
Doug

[sjastro]

An apt description considering that mathematicians struggled with the concept of infinitely in set theory in the late 19th century.

For example the set natural of natural numbers and set of integers are infinite sets, yet the set of integers contains twice as many numbers.

Steven
http://users.westconnect.com.au/~sjastro/small (http://users.westconnect.com.au/%7Esjastro/small)

[renormalised]

Hi guys, I'm back (from an enforced exile not of my making). Right now, this discussion is a little beyond me as my brain ain't working properly due to the flu. I'd have to apply myself to wiping out the infinitely frustrating sniffles and gagging cough and then I'd still feel like I've been hit by a runaway truck:eyepop::P:D

[AGarvin]

Been a long time since I've done calculus, so correct me if I'm wrong:

When talking infinity, it's not the function that is infinite, as in f(x) = 1/x where x=0, as this is technically undefined, but it's the limit (lim x-> infinity) that tends to infinity as x approaches 0.

Andrew.

[sjastro]

Correct.

For f(x)=1/x
Lim x-> 0, f(x) -> Infinity.
Lim x-> Infinity, f(x) -> 0

In set theory things get really bizarre as mathematicians refer to concepts as countable infinite sets and uncountable infinite sets.:shrug:.

Regards

Steven

[xelasnave]

I caught a radio show re the "new" math of infinity.
Interesting points but obvious..you can not double anything to infinity, no matter how large a portion you remove from infinity it still remains infinity...and that folk in the math infinity business had a tendency to go crazy:eyepop:???

alex:):):)

[dannat]

in maths is there really infinity?

0.999999 recurring = x 10x = 9.999999

10-1x = 9.999999 - 0.999999 = 9 = 9x 9x/9 = 1

hence divide and x = 1,no such thing as infinite decimals :P

[avandonk]

I think you will find that the Universe solves this conundrum quite simply by having an inderterminate quantum 'foaminess' at an incredibly short scale so that infinities do not and cannot occur. There is no such thing as ZERO in temperature or any other scalar quantity.

We are just scratching the surface of the possible knowledge.

We can only infer the existence of black holes and nowhere do we need infinities to predict them.

Bert

[xelasnave]

So I will take that as I take everything else...that I am on the right track:lol::lol::lol:
What got me thinking is some of the wild unsupported stuff one comes across...I would like a higher level of reason than that stuff and I am not sure if that is a big ask.
Thanks Bert
alex:):):)

[renormalised]

I think you'll find that despite that indeterminate nature at the quantum scale of things, that many aspects of quantum theory are shot through full of infinities. That's why the equations of state in these theories are renormalised.... to get rid of (or at least reduce) the infinities.