Two Physics ? ?

[ajaysinghgoshiyal]

Been reading too much recently! How does Classical Physics possibly differ from Quantum Theory?

[TrappedLight]

Classical and non-classical theories are separated by the quantum effect known as the uncertainty principle.

[ajaysinghgoshiyal]

Is that as in Heisenberg? Or in Schrodinger what ever?

 

 

Who invented Quantum Theory? Any clue?

Edited September 30, 2013 by ajaysinghgoshiyal

[ajb]

Been reading too much recently! How does Classical Physics possibly differ from Quantum Theory?

You have asked a very general question here.

 

The basic and fundamental difference is that classical mechanics is based on commutative algebra/geometry as where quantum mechanics nessarily requires noncommutative structures.

[ajaysinghgoshiyal]

Yikes! Can you explain it to a lay man in simpler english?

[ajb]

Loosley, in classical mechanics the observables are functions on a commutative space. That is we have for any two functions fg =gf, under pointwise multiplication.

 

In quantum mechanics the observables corresponds to operators on particular vector spaces, and these will not in general commute. That is FG-GF is not zero. Much of the core ideas in quantum mechanics really come down to this lack of commutivity.

[studiot]

pretty well all new theory is an extension of what went before and usually reduces to it in simple everday cases.

Quantum mechanics is not exception.

 

 

The basic and fundamental difference is that classical mechanics is based on commutative algebra/geometry as where quantum mechanics nessarily requires noncommutative structures.

 

This is an interesting idea but have you considered the 'forbidden rotations' and axial vectors, both of which are available to classical mechanics?

 

The uncertainty principle also applies in classical mechanics.

 

Which brings me to a point.

 

The equation [math]{x^2} - 5x + 6 = 0[/math] is only true for two particular values of x. It is not true for all values of x.

 

This is very old and well known.

 

In physics we really want equations that are true for as many values of x as possible, preferably a continuous range of them.

 

So for instance Newton's second Law P = ma applies (in Newtonian mechanics) to any value of acceleration we choose, we can find a value of P that will provide this acceleration.

 

However more advanced classical physics has equations, often to do with energy, that are more like the quadratic I showed.

That is they are only true for certain values, but not all, and not even certain ranges.

 

This is the development (beginnings) of quantum theory out of classical theory.

The realisation that some quantities can only take specific values.

This is the origin of the word 'quantum', which means just that. The difference between two specific values.

 

We usually take the dividing line between classical and quantum as being centered on the year 1900, with overlap so that the boundary is between about 1890 and 1910.

 

That was the time when physical phenomena that required such mathematics was being examined. Subsequently effects, such as quantum tunneling, were discovered that have no counterpart in pre 1900 physics.

 

Thus was our knowledge of the physical world extended.

Edited October 1, 2013 by studiot

[timo]

In practice, the meaning of "Classical Physics" depends on the context. It is usually used in the conjunction of "classical physics and <some particular type of physics>". There, "classical physics" means "physics which is not <some particular type of physics>".

- In "classical physics and Quantum Mechanics", "classical physics" refers to all physics that is not Quantum mechanics. That can include relativistic physics.

- In "classical physics and relativistic physics", "classical physics" refers to all physics that does not take into account Relativity. This usually includes non-relativistic Quantum Mechanics.

- In this forum, "classical physics" means non-relativistic physics that is not Quantum Mechanics (and not "modern and theoretical" or "Astronomy" or "Cosmology" )

Edited October 1, 2013 by timo

[ajb]

This is an interesting idea but have you considered the 'forbidden rotations' and axial vectors, both of which are available to classical mechanics?

You are talking about the anticommutativity of the cross product. A little more generally you have the wedge product of differential forms and the wedge product of multivector fields. Both these are fundamental in classical mechanics and standard differential geometry. However, I would say that anticommutativity is not quite the same as the more general noncommutivity.

[Sensei]

Been reading too much recently! How does Classical Physics possibly differ from Quantum Theory?

 

Quantum physics is quantized.

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

 

In classic physics f.e. i=q/t

1 A = 1 C/1 s

Where i,q and t can be any value. And t>0.

 

In quantum physics 1 C is dividable by elementary charge 1.6*10^-19 C.

So you can only have 0 C, 1*1.6*10^-19 C, 2*1.6*10^-19 C, 3*1.6*10^-19 C etc.

 

Basically you cannot have half of electron, half of photon, half of proton etc. etc, or other fraction of particle.

[studiot]

 

In classic physics f.e. i=q/t

1 A = 1 C/1 s

Where i,q and t can be any value. And t>0.

 

In quantum physics 1 C is dividable by elementary charge 1.6*10^-19 C.

So you can only have 0 C, 1*1.6*10^-19 C, 2*1.6*10^-19 C, 3*1.6*10^-19 C etc.

 

Basically you cannot have half of electron, half of photon, half of proton etc. etc, or other fraction of particle.

 

 

Do you not think this classical?

 

It was first proposed by Democritus a few hundred years BC and revived by Dalton around 1800 AD. Various other 19th cent scientists confirmed the discrete nature of charge as well as matter, during the course of that century.

Edited October 4, 2013 by studiot

[decraig]

You have asked a very general question here.

 

The basic and fundamental difference is that classical mechanics is based on commutative algebra/geometry as where quantum mechanics nessarily requires noncommutative structures.

 

This is a very abstract way of looking at it. I would have said 'quantization', or "the uncertainty principle". I like your mathematical approach.

 

Is it possible to the tie this in with quantization?

 

You are talking about the anticommutativity of the cross product. A little more generally you have the wedge product of differential forms and the wedge product of multivector fields. Both these are fundamental in classical mechanics and standard differential geometry. However, I would say that anticommutativity is not quite the same as the more general noncommutivity.

 

Again, a very insightful comparison. I deal almost exclusively with anticommutative structures with real valued entries (for the most part). I would like to make some sort of contact with quantum mechanics. Do you have any idea that may bridge the gap between anticommutivity and noncommutivity?

Edited November 18, 2013 by decraig

[ajb]

Is it possible to the tie this in with quantization?

Yes. Dirac quantization is a clear example of the link between commutative and noncommutative structures. Classically we start with a phase space (x,p) which is a classical structure, but a little more than this it comes with a Poisson bracket which is a Lie bracket plus the Leibniz rule. We have on the coordinates {x,x}= {p,p}=0 and {x,p} =1 (or minus one depending on conventions). Dirac quantisation is basically the procedure of replacing the Poisson bracket with a commutator of operators on some Hilbert space. These operator algebras are noncommutative, [X,P] ~ h.

 

 

Again, a very insightful comparison. I deal almost exclusively with anticommutative structures with real valued entries (for the most part). I would like to make some sort of contact with quantum mechanics. Do you have any idea that may bridge the gap between anticommutivity and noncommutivity?

We have deformation of commutative structures into noncommutative ones, that may be close to what you are looking for. You should view anticommutativity as being almost the same as commutativity.