how small is the smallest thing before it's nothing

Originally posted by RJHinds
How about Wightman axioms?

http://en.wikipedia.org/wiki/Wightman_axioms

The particulars of quantum field theory are determined by observation and data. The theory itself is a mathematical system known as a field: a set of objects that obey certain "field axioms" involving two binary operations and a relation. The Wightman axioms are no more a part of physics, really, than the field axioms. They're additional assumptions about the field featured in quantum field theory that enable one to prove mathematical propositions about the field in a rigorous fashion. The validity of the Wightman axioms are not really dependent on particular properties of the universe. Here's one:

For each test function f, there exists a set of operators which, together with their adjoints, are defined on a dense subset of the Hilbert state space containing the vacuum. The fields A are operator-valued tempered distributions. The Hilbert state space is spanned by the field polynomials acting on the vacuum (cyclicity condition).

The axiom is stating something about the existence of purely mathematical entities called operators, not anything that is physical. We're delving deep into the enchanted forest of theoretical (i.e. mathematical) physics.

You might do better claiming that the statement "Physical laws are invariant across space" is a physical axiom. Most physicists probably take it for granted, but then again many might say it's "just a theory" that has held up without fail under repeated observation.

Originally posted by Soothfast
The particulars of quantum field theory are determined by observation and data. The theory itself is a mathematical system known as a field: a set of objects that obey certain "field axioms" involving two binary operations and a relation. The Wightman axioms are no more a part of physics, really, than the field axioms. They're additional assumptions abo ght say it's "just a theory" that has held up without fail under repeated observation.

The article starts off with the following statement:

In physics the Wightman axioms are an attempt at a mathematically rigorous formulation of quantum field theory.

So it matters not what you think, because axioms are defintely used as a part of physics. The wightman axioms are in physics, not mathematics. Sorry buddy, you are the one that is wrong.

More use of Axioms in Physics

Electrogravity Axioms:

http://electrogravityphysics.com/electromagnetic-nature-gravity/

Physical Axioms Applied to Circuit Elements By Mark W. Ingalls

Abstract - When an electric current flows in a circuit of inductors, capacitors and resistors there is a precise analogy with a moving mechanical system of masses, springs and frictional forces. This analogy may be extended to include the distributed parameters of a single component. An analysis of capacitors, inductors and resistors based on these axioms is presented.

Physical axioms provide a bridge from clearly understood mechanical phenomena to more abstract electrical phenomena. Application of the axioms has correctly predicted the behavior of a number of circuit elements over a wide frequency range. Moreover, this point of view has led to new designs. With the computational power available today it is no longer necessary to represent complex behavior with rational function. By correctly applying the axioms, the engineer is enabled to use this power to its full effect.


Now are you convinced of my superior knowledge of Physics?

Originally posted by RJHinds
The article starts off with the following statement:

[b]In physics the Wightman axioms are an attempt at a mathematically rigorous formulation of quantum field theory.

So it matters not what you think, because axioms are defintely used as a part of physics. The wightman axioms are in physics, not mathematics. Sorry buddy, you are the one that is wrong.[/b]

In the same article it says, further down, that the Standard Model rests on no mathematically rigorous foundations. Maybe it's possible to axiomatize it, maybe it isn't. Does that mean the Standard Model is not physics?

On mundane scales of measure (not too big, not too small) Euclidean geometry can be used to model all sorts of physical situations. Are you going to tell me that the five axioms of Euclidean geometry are a part of physics? Really? Just because the axioms seem to coincide with the observable universe of the ancients doesn't make them physics. The ancients observed the universe, came up with a body of knowledge about points, lines, planes and so on, and then eventually somebody axiomatized that body of knowledge in order to make it possible to do rigorous proofs of things within the mathematical system that eventually came to be known as Euclidean geometry.

But the axiom that "Given any straight line segment, there exists a circle having the segment as radius and one endpoint as center" is no more physics than "For each test function f, there exists a set of operators which, together with their adjoints, are defined on a dense subset of the Hilbert state space..."

Originally posted by RJHinds
More use of Axioms in Physics

Electrogravity Axioms:

http://electrogravityphysics.com/electromagnetic-nature-gravity/

Physical [b]Axioms Applied to Circuit Elements By Mark W. Ingalls

Abstract - When an electric current flows in a circuit of inductors, capacitors and resistors there is a precise analogy with a moving mechanical system of mass ...[text shortened]... rectly applying the axioms, the engineer is enabled to use this power to its full effect.[/b]

If you want to call your unproven assumptions about the physical universe "axioms" (rather than hypotheses) that's your look-out, but it's a word physicists have no business using. And that goes for "theorem," too.

Returning to my original point: All physics is mathematics. I stand by that, and it means physicists will be using axioms and theorems in their work. But they are mathematical entities, not physical. There is no "theorem of gravity," for instance, or "second axiom of thermodynamics." Not generally. Theorems and axioms tend to relate to mathematical concepts, not physical ones. Yes, with the Internet you can find obscure corners of research where these words are used in some capacity (usually still mathematical, though). But in the main physicists speak of laws, theories and hypotheses, and mathematicians speak of axioms, theorems, and conjectures. You understand that much, yes?

I watched a program on discovery channel where they were actually splitting electrons, which were previously thought to be fundamental particles. It's a while back and I think they said they were made up of two other particles, but don't quote me on it. However, they were being split.

Nice website for understanding the basics of the really small. I first found this website roughly 10 years ago when it actually looked a lot better - less chaotic - than now. But still it gives a nice overview of what the universe's supposedly made of.

http://www.particleadventure.org/index.html

And a 2009 (i think) BBC documentary asking the question "How long is a piece of string". Lightweight science, but very entertaining and informative.

YouTube

Originally posted by Soothfast
If you want to call your unproven assumptions about the physical universe "axioms" (rather than hypotheses) that's your look-out, but it's a word physicists have no business using. And that goes for "theorem," too.

Returning to my original point: All physics is mathematics. I stand by that, and it means physicists will be using axioms and theorems in ...[text shortened]... ematicians speak of axioms, theorems, and conjectures. You understand that much, yes?

One needs to know more than mathematics to design and build a television or even repair one. A mathematician can't do anything, but put numbers and symbols on paper. So the answer is NO - PHYSICS IS NOT MATHEMATICS.

Originally posted by RJHinds
One needs to know more than mathematics to design and build a television or even repair one. A mathematician can't do anything, but put numbers and symbols on paper. So the answer is NO - PHYSICS IS NOT MATHEMATICS.

Physicists don't built televisions, you bemusing yo-yo. And usually folks called technicians or engineers help put together their experiments.

Originally posted by Soothfast
Physicists don't built televisions, you bemusing yo-yo. And usually folks called technicians or engineers help put together their experiments.

When I went to college studying to be an Electrical Engineer, I was required to take many types of Mathematics courses and I took courses in Physics for students of science and engineering. And I can tell you that Physics was not part of Mathematics. Yes, I used the mathematics I learned in Physics, but I had to do my own experiments in the labs, because I had to understand how it works and if it worked. Theory and practice do not always agree. Electricity, Magnetism and electronics are taught in Physics not in a Mathematics course. So you are full of BS.

Originally posted by RJHinds
When I went to college studying to be an Electrical Engineer, I was required to take many types of Mathematics courses and I took courses in Physics for students of science and engineering. And I can tell you that Physics was not part of Mathematics. Yes, I used the mathematics I learned in Physics, but I had to do my own experiments in the labs, because I ...[text shortened]... etism and electronics are taught in Physics not in a Mathematics course. So you are full of BS.

I don't think you understand what I mean when I say "physics is mathematics".

Originally posted by Soothfast
I don't think you understand what I mean when I say "physics is mathematics".

I don't think he understands what you say at all.

I don't think he understands.

Originally posted by Soothfast
I don't think you understand what I mean when I say "physics is mathematics".

Maybe so.

Originally posted by RJHinds
Maybe so.

Well then, you could read up on the mathematics of physics and how deeply they are entwined but that would presuppose you would be interested in actually learning about science since it might just shake your fundamentalist right wing christian young earther blues.