What are the axioms of physics?

[Johnny5]

Earlier in this category, I began a thread on Grand unification. I asked what kinds of things must the final supertheory of physics explain, and I got some nice answers. Some things there, I doubt I will ever understand. I am posting this thread here, because it seems the natural place for it.

 

I've been reading a lot of things going on in physics today. There are so many physicists coming from so many different angles at "who knows what." They cannot all have the right approach.

 

I've seen things on M-theory, which I have no clue about.

I've seen things on string theory, which I also have no clue about.

I've seen physicists poking fun at each other, for not having a clue about what each other is saying.

 

I have seen people quantizing space, using Planck length. I'm not sure they know what they are doing either, they still use the notion of continuity I think, but I can't say for sure because I don't know what they are doing.

 

I am looking at the whole problem epistemologically.

 

That means that there are certain rules one must follow in order to know something.

 

Aristotle had a lot of helpful information on this, believe it or not.

 

To his end, he focused on what he called axioms.

 

Two thousand years later, no one knows what he meant.

 

When I first seriously studied quantum mechanics, I became aware that there were five axioms for quantum mechanics. I still don't understand them, and doubt that they are necessary and sufficient to lead to the Schrodinger equation, which I did understand... at least to my own satisfaction anyway.

 

I have a question, which is hard to verbalize.

 

Let us suppose that there are N physicists in the world, trying to "unify physics." They all have different approaches, and theories, and none of them are where they want to be.

 

Let us extrapolate something from them all.

What is the portion of knowledge of physics, which the majority of them have in common?

 

In other words, what is their collective knowledge?

 

I don't want a list of ten million facts. The way Euclidean Geometry worked was this, you start out with five axioms, and some common notions, and then deduced a few hundred or so theorems. The Greeks were pretty confident that the five axioms led to all true statements about three dimensional space.

 

So what are the Axioms of physics?

 

I guess that's my question.

 

It seems to me, that once you choose a model, the axioms sort of just flow from having the right model, so what is the right model?

 

Or to put my whole question another way, suppose that I was a twenty fourth century student, about to begin learning physics, after physics had already been unified. What would be the main thing that I would have to learn?

 

I don't know if anyone here can actually answer this question, I just thought I would ask, at least to read what others have to say on the matter.

 

Thanks

 

PS: If I were going to answer my own question, I would start off like this:

 

Axiom I: Simultaneity is absolute.

Axiom II: Space is three dimensional.

Axiom III: Time is quantized.

Axiom IV: F= d(mv)/dt

Axiom V: The total inertial mass of the universe is conserved.

Axiom VI: The total electric charge of the universe isn't conserved.

Axiom VII: Quantum electrodynamics is correct.

Axiom VIII: (Conservation laws)

Axiom IX: p = hbar k

 

You get the idea. What would be added, what would be subtracted from the list which I gave?

[5614]

Axiom II: Space is three dimensional.

Isn't space 4 dimensional (time)?

 

Axiom X: p = hbar k

What does 'k' stand for?

[ydoaPs]

uh, simultaniality is NOT absolute.

[5614]

yeah he was having that debate in this thread here:

http://www.scienceforums.net/forums/showthread.php?t=9339&page=2&highlight=ladder+barn

where he argued against the proof from the ladder and barn 'paradox'... i should have mentioned it in my first post.

[ydoaPs]

well if he wants to throw out relativity (which is pretty much proven beyond a shadow of a doubt), then he can just make up whatever crap he wants. wait, he already does. example: photons=gravitons.

[Tom Mattson]

To start with, I'd say that general covariance and canonical quantization have to be ingredients of any candidate for a grand unification theory.

 

Axiom I: Simultaneity is absolute.

 

Axiom VII: The total electric charge of the universe isn't conserved.

 

Axiom VIII: Quantum electrodynamics is correct.

 

Axioms I and VII directly contradict Axiom VIII.

 

First' date=' QED is manifestly Lorentz covariant, which is not surprising seeing as it has SR [i']built into it[/i]. So simulteneity cannot be absolute if QED is correct. Second, conservation of charge follows from U(1) gauge symmetry, and U(1) just happens to be the gauge group of QED. So your Axiom I is a corollary to the negative of one of the axioms of QED, and your Axiom VII is the negative of a derivable result from QED.

 

Anyway, you don't need to know QFT to realize that there's no point in building a science from axioms that don't conform to experimental results.

[Martin]

Axiom X: p = hbar k

 

What does 'k' stand for?

 

k would stand for (angular format) wavenumber in that eqn.

 

that is the component of momentum p in the x direction is equal to hbar times the radians of phase the wave goes thru per unit distance in the x direction

 

it is closely analogous to saying that the energy E is equal to hbar omega

E = hbar w

 

where little omega (written w here because of font limitations) is the

(angular format) frequency-----the number of radians of phase the wave goes thru per unit time.

 

a lot of what Johnny says is legit and he is trying to think for himself, or so it seems to me anyway, so I say bravo and besides it livens up the board

[Martin]

Axiom I: Simultaneity is absolute.

Axiom II: Space is three dimensional.

Axiom III: Time is quantized.

 

I admit you are not asking for advice but I will give you some unasked which is (even tho it is a sign of intelligence and mental independence to challenge the idea that simultaneity is relative to the observer) EVEN THO all that, you should try to get thru the first 4 years of college mastering the mainstream models of nature and physical universe.

 

and also even tho they are not fully consistent. for example cosmology is based on a Friedman model (in turn based on Gen Rel) and in the Friedman model universe, now the prevailing consensus among working cosmologists, there is an idea of absolute time!

the consensus model cosmos is not Lorentz invariant, it does not globally have the symmetry of special relativity!

 

Even tho all this, you should not fight the system too much because it interferes with learning the received wisdoms of 20th century physics and also too much of of that can piss off the professor.

 

I personally tend to think that simultaneity is very much relative to the observer and that someday the Friedman model cosmology will be replaced with a quantized version where what you see depends on the observer. BUT i heartily applaud a highschoolage person who dares to consider the possibility that there could be an absolute clock somewhere. since it is a cliche that it is all relative it is refreshing to see someone go against that.

[Cadmus]

Isn't space 4 dimensional (time)?

In the dichotomy in which he is using the term space, any dimensions of time arte not counted as dimensions of space.

[Cadmus]

Axiom I: Simultaneity is absolute.

Axiom II: Space is three dimensional.

Axiom III: Time is quantized.

Axiom IV: F= d(mv)/dt

Axiom VI: The total inertial mass of the universe is conserved.

Axiom VII: The total electric charge of the universe isn't conserved.

Axiom VIII: Quantum electrodynamics is correct.

Axiom IX: (Conservation laws)

Axiom X: p = hbar k

Of all of your axioms, I consider that only number II is a true axiom. The others are far from fundamental, and do not constitute axioms. Furthermore, I strongly disagree with axiom II, and I am not alone. Many scientists do not consider that there are only 3 dimensions of space. However, for the purposes of any given model of physics, such as one that you might propose, it is fair to make it axiomatic that there are 3 dimensions of space. Euclidean geometry certainly does, and no matter how poor a model of reality Euclidean geometry is, it has certainly proven itself to be an extremely useful model of reality.

[Johnny5]

Isn't space 4 dimensional (time)?

 

What does 'k' stand for?

 

Time is not a spatial dimension. At most three mutally perpendicular infinite straight lines can meet at a point' date=' not four.

 

k is the wavenumber vector, I was trying to write this:

 

[math'] \vec P = \hbar \vec k [/math]

 

Here is a link which explains it:

 

Wavenumber vector

 

I'm busy looking for a better explanation, but in the meantime, here is an excellent site which seems devoted to waveform analysis:

 

Acoustic and vibration animations

 

Ok, I found what I want:

 

Wavenumber

 

Wavevector

[Tom Mattson]

Time is not a spatial dimension. At most three mutally perpendicular infinite straight lines can meet at a point' date=' not four.

[/quote']

 

That's only the case if you stipulate that you are working in R³ to begin with. So this argument against more than 3 spatial dimensions is circular, I'm afraid.

[Johnny5]

That's only the case if you stipulate that you are working in R^{3[/sup'] to begin with. So this argument against more than 3 spatial dimensions is circular, I'm afraid.}

 

 

^{The statement is true, so what's the difference?}

[5614]

well the point of it was that if you are working in R3 then the answer is different to say when I said 4th dimension was time.

[swansont]

The statement is true, so what's the difference?

 

It's true only because you assumed the answer to begin with.

[Tom Mattson]

The statement is true, so what's the difference?

 

It's true in R³. Basically, your argument amounts to this:

 

Time cannot be the 4th dimension because the universe is 3 dimensional.

 

Or more formally,

 

A

__________

Therefore A

[Johnny5]

To start with' date=' I'd say that general covariance and canonical quantization have to be ingredients of any candidate for a grand unification theory.

 

[/quote']

 

What does "general covariance" mean?

What does "canonical quantization" mean?

[Johnny5]

It's true in R³. Basically' date=' your argument amounts to this:

 

[i']Time cannot be the 4th dimension because the universe is 3 dimensional.[/i]

 

Or more formally,

 

A

__________

Therefore A

 

That argument (at most three...) wasn't mine, it was an ancient one. Seems fine to me.

 

How about this one:

 

If I were situated someplace, a rotation through 2 pi radians brings me looking where I was looking before. I think this basically proves space is three dimensional, since it would be true in any plane which I start the rotation in.

[Tom Mattson]

That argument (at most three...) wasn't mine' date=' it was an ancient one. Seems fine to me.

[/quote']

 

Once again: It's not fine because it's circular.

 

If I were situated someplace, a rotation through 2 pi radians brings me looking where I was looking before. I think this basically proves space is three dimensional, since it would be true in any plane which I start the rotation in.

 

That doesn't prove anything, because planes are subsets of Rⁿ for any natural number n. For instance you can have a 2D plane living in R⁶. What reason would you have to think that rotational invariance would be broken in that space?

[Tom Mattson]

What does "general covariance" mean?

 

General covariance indicates that the form of the theory is invariant under the most general Lorentz transformations' date=' just as General Relativity is. In other words, it should be frame-independent and background-independent. This gets back to what I was saying to J. C. MacSwell in the thread about the Cosmology Question (re: the relational view of space and time).

 

What does "canonical quantization" mean?

 

Canonical quantization is defined by the commutators anticommutators between dynamical observables, Bose fields, and Fermi fields.

[ydoaPs]

i am starting to think that johnny has a few formulas at hand and has no clue what they mean. not necesarily from this post, but most of his posts give me the impression. then he will just throw all known science away and make assumptions and use them as fact. man, you just can't do that.

[J.C.MacSwell]

 

If I were situated someplace' date=' a rotation through 2 pi radians brings me looking where I was looking before. I think this basically proves space is three dimensional, since it would be true in any plane which I start the rotation in[/b'].

 

A 2 dimensional guy made this argument the other day

 

If I were situated someplace, a rotation through 2 pi radians brings me looking where I was looking before. I think this basically proves space is two dimensional, since it would be true in the only plane which I know of.

 

It was a little more forgivable for him, afterall, he's only 2 dimensional.

[J.C.MacSwell]

General covariance indicates that the form of the theory is invariant under the most general Lorentz transformations' date=' just as General Relativity is. In other words, it should be frame-independent and background-independent. This gets back to what I was saying to J. C. MacSwell in the thread about the Cosmology Question (re: the relational view of space and time).

 

 

 

.[/quote']

 

Aether you believe in it or you don't.

[Tom Mattson]

Oh, that's just terrible!

[Cadmus]

It's true in R³. Basically' date=' your argument amounts to this:

 

[i']Time cannot be the 4th dimension because the universe is 3 dimensional.[/i]

 

Or more formally,

 

A

__________

Therefore A

I fail to understand how your argument supports the idea that time might be counted as the fourth dimension of space, as opposed to being a different sort of dimension, a dimension of time.