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Physics and Infinity.
==.
There is an opinion that science deals only with observable
universe. Then we have problem because modern physics
comes to situation when it meets unobservable world as
on the very small scales as on very big scales:
we cannot see quarks, virtual particles, gravitons
we cannot see dark energy- it is negative,
we cannot see dark mass- it neither emits nor reflects,
em waves- electron exist, but magneton- doesn’t: why?
Electron meets vacuum and we lost it- what is it destiny?
Some theories offer new spaces and particles which
no one can visualize.
Etc
It seems, to solve these problems we must understand the
unobservable world. In my opinion - the infinite world.
But, . . ‘ When you ask the theory questions, you have to be
very carful not to get infinite and inconsistent answer.’
/ ‘ The trouble with Physics’ page 55. Lee Smolin. /
Why?
Because there is a ‘scientific’ opinion- if the theory has
infinity it is wrong ( the scientist was mistaken).
It needs to escape from such solution ( using method
of renormalization ) and don’t think about it more.
Later, solving ‘infinity’ problem in such way we are
surprised that physics looks paradoxically.
#
Let us suppose that infinite world exists.
Then we can have materialistic (!) questions:
What are physical parameters of infinity?
How is possible to understand the infinity’s life?
How can we have concrete, finite, physical answers
from the infinity world?
What influence have infinite world on our Earth’s world?
P.S.
All answers must be received in the form of concrete
Physical laws and formulas!
Isn’t it a crazy project?
I think, Niels Bohr had waited for such project.
====.
Israel Sadovnik Socratus.
==================..

Before we start to think about infinity we have to be sure that we are making a clear distinction between mathematical infinities, like those of Cantor, and anything that might be considered to be a physical infinity. There are those who would argue that because, for example, -3 can exist as a mathematical concept, but you cannot find a physical -3, the same can be said of infinity. Personally, I feel that this does not hold up as a logical argument. All it does is deny the possibility of a physical infinity. How, then should we interpret an infinite cosmos? Surely, the most it can mean is that the cosmos is unbounded, and a little serious thought will reveal that this is very different from saying that it is infinite.

Once we have established what we mean when we use the term “infinite”, then we can start talking about its possible parameters.

I look forward to a lively discussion on this topic, but I think that unless we take it one step at a time we are likely to go round in circles.

1.
My opinion:
If the cosmos is unbounded . . . it is infinite.
2.
. . . for example, -3 can exist as a mathematical concept,
but you cannot find a physical -3,
/ Bill S./
===.
‘ What I mean is illustrated by the case of the number Three . . .
. . . . take the number Three. Don’t you think that it must
always be described not only by its own name but by that
of Odd, although Odd and Three are not the same thing? ‘
/ The last days of Socrates.
Plato. Page 164. /
==.
Can it be that ‘the number Three’ is a individual physical
particle which acts ‘ by its own name’ independently.
And ‘ by that of Odd’ means its interaction with other
numbers/ particles which can be explain mathematical.
‘The number Three’ is reason for ‘Odd’ – for math solution
======.
Socratus.

I have no problem accepting that something that is infinite is also unbounded, but I cannot accept that the synonymy is reciprocally valid. For example: our Universe might continue to expand for ever; in which case its expansion would be unbounded, but it could never become infinite. Of course there are those who would maintain that I am describing "infinite expansion", but I contend that this use of the term is one of the things that leads to confused thinking about the nature of infinity.

Another area in which confusion arises is that of mathematical infinities which include the ubiquitous "infinite series". Such concepts are infinite only in the minds of mathematicians.

The rest of your post will require some thought if I am to get my head round it.

Of course; but its name (what you might call its "threeness") and its oddness are characteristics of that concept which we call "three", which is a finite mathematical concept. I am not at all sure that I see the connection with infinity.

I cannot see that ‘the number Three’ is a "particle" of any sort, nor do I see how it could act independently. Perhaps, in pure mathematics, at might be possible to regard any number as an entity in its own right, but as a practical application a number must be a number of something in order to have any "reality".

Comment by earle:

On the subject of infinity, singularities, infinite density, etc:

Mathematicians: No problem. Infinite number of numbers.
Dirac delta (goes to infinity but doesn't stay there very long!)
Physicists: We don't like it but we can handle it.
Engineers: No way. "The pretty big bang".
Theologists: Whaaaaaa?? Goddiddit.
/ earle /
*

Let us take radiation .
The Kinetic Theory of Heat considered heat to be
the result of random motion of the numerous
individual particles. Since it would be impossible
to follow the motion of each single individual particle
participating in thermal motion,
the mathematical statistical method need be used.

So, the basis of Kinetic Theory of Heat is a single
individual particle, but the mathematical statistical
average value takes over a single individual particle.

Therefore Mr. Bill S. wrote ’ I cannot see that
‘the number Three’ is a "particle" of any sort ‘.
#
But Kinetic Theory of Heat ---> goes to Quantum Theory (!)
What do we know about a single individual particle which
takes participation in Quantum Theory?
Do we know its geometrical shape ?
Point? String? Sphere? Drop?
Do we know how it act?
We only can write the mathematical formula E=h*f
as a result of its individual electromagnetic vibration
(frequency).

Therefore Mr. Bill S. wrote ’. . . nor do I see how it
could act independently.’
#
We don’t know the particle, we know the result of its action.
The medal has two sides and we see only one of its side.
The particle and its waves not the same.
As Socrates said: ‘Odd and Three are not the same thing’
===.
I. S.

Comment by leonardomenderes :
#
Interestingly enough,
quantum pumps are used to control
and observe particles one by one now,
to achieve absolute zero.

Inside the working of Physics,
the waves and particles are coordinated
parts, not faces. A particle is waves
of moving energy trapped and stilled.
A wave is the energy free of
boundary conditions.

Sometimes the 'limits of my knowledge'
are projected to be 'the limits of all knowledge'.
But everyone has their boundary conditions.
Assume you are complete, and entropy
will come and gnaw on the defects.
What we know has a diffuse edge.
We need to know how to live with that,
to escape that personal desire for
simplicity that drives epistemic hegemony.
/ leonardomenderes /

Comment by Dr Infinity:

To my best knowledge, the first appearance of an
"infinity difficulty" in physics was the "ultraviolet catastrophy".
At that time, attempt to use known physics led systematically
to an infinite power being emit by a so-called "black body".

Did the physicist have any problem to deal with infinity: no.
Why was the "infinity result" unacceptable: simply because
it doesn't fit with experimental data.

Removing the infinity was -in the end- not difficult mathematically.
However this was, physically, a challenging new direction.
Because theory and observation didn't fit well,
theory had to be reshaped.
That's how science progresses.

Similarly, we have more and more observations pointing
to a finite world.
Why should physicists turn to infinity-mystics?

I don't know of any physical measurement lead to a real infinity,
except maybe supraconductivity. However, in the case of
supra-conductivity, "zero resitance" is a better representation
than "infinite conductivity". Resistance measures -or counts- and
amount of interactions. Such an amount is clearly finit,
or -even- zero for supraconductivity.
Conductivitymaybe inifite without physicist turing into monks.

I definitively know of only one striking infinite:
human study, that knows no limit.
/ Dr Infinity /

Also, according to Cantor, an infinite number of infinities; but they are all mathematical infinities which are totally different from the "real thing". Try counting to infinity, if you doubt that.


Lost here!


"...as long as it is only a mathematical infinity, which is as real as it gets."


Engineers never have to operate outside our familiar 4D, so why would they complicate things by introducing infinity?


Not forgetting the "omega point", of course.

Socratus, I follow your argument about the Kinetic Theory of Heat, but I fail to see how any of that implies that the number 3, or any other number, is a "particle", or anything more concrete than a mathematical concept. Perhaps I am missing something.



OK, but how is this a comment on whether or nor a number can be said to act independently.

I am neither a scientist, nor a philosopher so I need things to be fairly simple.

Comment by leonardomenderes:
Interesting, but as a comment on infinity it seems somewhat "off piste".

Comment by Dr Infinity:

No difficulty because it was a mathematical infinity, but it could have no place in experimental data, because that would need a physical infinity. No finite experiment could produce, or include, a physical infinity.


Of course observations point towards a finite world, that is what we appear to live in. If we lived in "Flatland", our observations would point towards a world with 2D of space, but that would not obviate a world of 3D of space elsewhere; or even such a world in which Flatland was embedded.


A physical measurement is essentially a finite concept used to evaluate a finite object or idea. It could never result in a physical infinity.


Dr Infinity does seem to have infinity mysteriously entangled with theology, perhaps this gives rise to a problem.


We are back to that confusion between unbounded and infinite. Human study may well be limitless (unbounded), but that does not make it infinite.

I don't know of any physical measurement lead to a real infinity,
except maybe supraconductivity.
/ Dr Infinity: /
====.
Oh, there are lots if you look for them.
<http://en.wikipedia.org/wiki/Ideal_gas_law>
The state of an amount of gas is determined by its pressure, volume, and
temperature. The modern form of the equation is:
where p is the absolute pressure of the gas; V is the volume; n is the
amount of substance; R is the gas constant; and T is the absolute
temperature.
n = pV/(RT)
At absolute zero kelvin, the amount of gas is infinite.
/ Androcles /
=================.

Bill S.
Socratus, I follow your argument about the
Kinetic Theory of Heat, but I fail to see how any of that
implies that the number 3, or any other number, is a "particle",
or anything more concrete than a mathematical concept.
Perhaps I am missing something.

Socratus;
We don’t know the particle, we know the result of its action.
The medal has two sides and we see only one of its side.
The particle and its waves not the same.

The Copenhagen’s interpretation of Quantum Mechanics is wrong.
#
Bill S. / #36344 - Yesterday at 10:39 AM /
I have no problem accepting that something that is infinite
is also unbounded, but
I cannot accept that the synonymy is reciprocally valid.

Socratus:
Infinite, unbounded, endless, never-ending ,unending,
perpetual, interminable, eternal, dateless, spaceless,
borderless . . .
- What do you read, Prince ?
- Words, words, words.
It is no matter how you call it.
The matter is:
How can Infinity have its Physical Edge ?

Particle or number, particle or wave, object or subject,
matter spirit, soul or smoke, spirit or gas . . . .

So, ‘ To be or not to be? that is the question.’
/ From Shakespeare with Love./

"To be or not to be? That is the question.
To be and not to be, that is the answer."
/ Marjorie Orr ./

#
Bill S.
OK, but how is this a comment on whether or nor
a number can be said to act independently.

Socratus:
In 1900 Planck said it is possible by spin ( h).
In 1924 Goudsmit and Uhlenbeck wrote
it is possible by spin ( h*=h/2pi.)
#
Bill S.
I am neither a scientist, nor a philosopher so
I need things to be fairly simple.

Socratus:
I am also ‘neither a scientist, nor a philosopher so
I need things to be fairly simple.’
======..
#
There are more things in heaven
and earth, Horatio, than are
dreamt of in your philosophy.

/ William Shakespeare,
Hamlet Prince of Denmark /

I know nothing except the fact of my ignorance.
/ Socrates /
===========.

Here I must disagree, strongly. The only way in which we can convey our ideas to others is through words. If the words we use mean different things to different people, how can we have any real communication? Exuberant verbosity is no substitute for understanding.

If you believe that "unbounded" and "infinite" are synonymous, and I do not; or if you find no distinction between mathematical and physical infinities, and I believe they are totally different, then our communication will always be fraught with pitfalls, which no amount of quotes from literature will rectify.



Does anyone claim that infinity has a physical edge? If so, that person is probably the only one who could answer your question.

"The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations." Wikipedia.

One of these limitations must be that any infinity derived from this equation would be a mathematical infinity. Another limitation is that this is an approximation. How do you approximate physical infinity?

General relativity has a problem with infinites because
inside a black hole the density of matter and the strength
of the gravitational field become infinite.
/ ‘ The trouble with Physics’ Page 5. Lee Smolin./

Perhaps you should have continued the quote a little further. "That appears to have also been the case very early in the history of the universe - at least, if we trust general relativity to describe its infancy."

My understanding is that GR breaks down towards the centre of a black hole. Does it not seem strange that we rely on GR for our description of precisely that area in which it breaks down. Recent computer simulations suggest that a singularity may not form at the centre of a BH.

Are we giving up with all these questions unanswered? Surely not.

Perhaps we should take one question at a time.

What are the physical parameters of infinity?

Here are some suggestions:
It has no beginning and no end.
It must always have been infinite.
It must encompass everything; therefore nothing can be add or taken away.
It cannot be divided or differentiated in any way; therefore every part is the entirety.
There is no passage of time, so everything that happens is happening "now".
Although there are infinite mathematical infinities, there can be only one physical infinity.
It has no dimensions, because dimensions are relevant to space and time which are features of our limited perception.