what is the quantum theory?

[jamey2k9]

pretty dumb question but what exactly is the quantum theory

[Klaynos]

The answer to your question, is enormously broad, I think your best bet is to read something like this:

 

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

 

or

 

http://hyperphysics.phy-astr.gsu.edu/Hbase/quacon.html

 

And ask more specific questions about bits you don't understand.

[SkepticLance]

Quantum mechanics is a very broad topic, with enormous ramifications, and requires a lifetime of study to even begin to understand.

 

However, your question might be answered more simply. Quantum physics began with the understanding that light had a quantum nature as well as a wave nature. That is : under some circumstances, light appears to act like a stream of particles. The word 'quantum' refers to a discontinuity. This occurs when light appears to be particles rather than waves. Light particles (photons) can be envisaged like a stream of bullets from a machine gun. Since the particles are discrete, there are gaps between them. It is this 'gappy' nature that is described by the word 'quantum'.

 

Albert Einstein won the Nobel prize with his work on the photo-electric effect. He showed that, for light to push an electron free and generate an electric current, the light had to come in 'lumps'. Each 'lump' kicks out an electron. Thus, light is quantum. Of course, it is also a wave.

 

Of course, that was the mere beginning, and many other things in the world of the very small have now been shown to be quantum in nature. It is the ongoing study of how very small 'quantum' objects behave, and how we make use of their incredibly weird properties that is the scope of modern quantum physics.

[kleinwolf]

Matrix mechanics is also a geometrization of the axioms of probabilities :

 

(Axiom a) p(1)+...p(n)=1

 

(Axiom b) p(i)>=0....

 

(b)=>so we could write p(i)=a(i)^2, with a(i) a real number, or a(i)=¦b(i)|

 

hence (a) is just the squared norm of an n-dimensional [normalized] vector...this vector is the state-vector, or wave-function in infinite dimensional space

Edited February 9, 2009 by kleinwolf

[ajb]

Very loosely, quantum theory is the theory of the "small", things the size of atoms and smaller. Klaynos' links are a good place to start.

[fredrik]

Another possible condensed description of "quantum theory" from the conceptual side, is - in contrast to the prior dogma of realism in classicla physics - to see it as a "physical theory of measurement" and that in between measurements, all we have are expectations. But the deepest lesson from quantum theory is that, not only does the experimenter have only expectations on the physical systems in between obervations it acts upon, it really is the case that even parts of the system, say part of an atom, relates to other parts of the atom - by the same logic - ie. they interact with it's environment based on expectations.

 

Combine this with the idea of energy beeing transferred in quanta, we get quantized measurements/interactions as well, where we only can model our expectations on them happening. Which historically explain the stability of atoms.

 

So Quantum theory is a large concepctual lesson, and tells us something about how the world interacts with it's parts. The concept of interaction and information is central.

 

/Fredrik

[ajb]

I can tell you what we would like it to be, but unfortunately it does not appear to be so;

 

A functor from the category of symplectic manifolds (morphisms = symplectomorphisms) to the category of Hilbert spaces (morphisms = unitary operators).

 

There seems to be no such functor with all the necessary properties!

Edited February 18, 2009 by ajb

[fredrik]

I can tell you what we would like it to be, but unfortunately it does not appear to be so;

 

A functor from the category of symplectic manifolds (morphisms = symplectomorphisms) to the category of Hilbert spaces (morphisms = unitary operators).

 

There seems to be no such functor with all the necessary properties!

 

What would you say we are _now_ looking for in the light of this conclusion?

 

I for example think the utility of the abstraction of fixed hilbert spaces, to represent information is part of the problem. I think information must be allowed to be more dynamical, unless one insists sticking to a kind of birds view that encompasses everything, but then one is also sticking to a non-physical view.

 

I like to think that every physical perspective is a frogs view, this includes the development of theory and knowledge of physical law as well. I think these ideals makes the rigid hilbert space structures unsuitable as a tool.

 

I think we somehow need to understand the dynamics of the physical "frog-hilbert" spaces, and how these evolve but part rational selection but also part unpredictable feedback and evolution.

 

As you do mathematical physics, are you these days looking for some new structures, once it seems more and more clear that the old ideas from the origin of quantum theory won't solve everything?

 

/Fredrik

[ajb]

I should say that no such functor (with the right properties) is known, but no-one has formulated a "no-go theorem" stating that no such functor exists.

[fredrik]

I should say that no such functor (with the right properties) is known, but no-one has formulated a "no-go theorem" stating that no such functor exists.

 

Aside from the fact that it hasn't been proven that it is not possible, what are the motivation for asking this specific question?

 

As I understand it, that abstraction of quantizátion, and classical vs quantum worlds, seems to be the standard view. Do you really think that abstraction, will do also for the future generation of theories of TOE unification and new understanding on QG?

 

I personally have doubts in that, and only the lack of proof that it is not impossible seems insufficient motivation to support the question.

 

I guess I have a more philosophical angle than you, but I'm curious where your motivation to the more stronlgy mathematically abstracted quests comes from. As I see it, the physical and conceptual support is becomer weaker these days? do you disagree?

 

What I mean is that, perhaps an ultimate hilbert space with unitary evolution isn't the way our ultimate understanding will end up? It sure is still a possibility, but my confidence in that idea is dropping.

 

/Fredrik

[ajb]

Aside from the fact that it hasn't been proven that it is not possible, what are the motivation for asking this specific question?

 

The main issue is that (first) quantisation seems very ad hoc. It would be nice to have a very clear and well stated idea of exactly what quantisation is.

 

As I understand it, that abstraction of quantizátion, and classical vs quantum worlds, seems to be the standard view. Do you really think that abstraction, will do also for the future generation of theories of TOE unification and new understanding on QG?

 

Generally it seems that the average theoretical physicist will need to know more and more "pure mathematics" as time goes on. This is especially true in the fields of quantum gravity and TOE's.

 

I personally have doubts in that, and only the lack of proof that it is not impossible seems insufficient motivation to support the question.

 

It is an open question to formulate a well stated and posed no-go theorem. This is not the only motivation, but providing any light on this issue would help us understand quantisation. This has to be a good thing. Furthermore, if one can state it all in the fame work of category theory then it would be very neat.

 

I guess I have a more philosophical angle than you, but I'm curious where your motivation to the more stronlgy mathematically abstracted quests comes from. As I see it, the physical and conceptual support is becomer weaker these days? do you disagree?

 

I believe that one can get a deeper understanding of the natural world, and in particular via theoretical physics if one truly understands the mathematical frame works used. It also means things can be stated very clearly. However, I appreciate that for the most part physics is not mathematics.

 

What I mean is that, perhaps an ultimate hilbert space with unitary evolution isn't the way our ultimate understanding will end up? It sure is still a possibility, but my confidence in that idea is dropping.

/Fredrik

 

Very possibly. Maybe we need something else to incorporate gravity into a quantum theory. That said, as quantum theory has such a great standing any generalisations should include more standard quantum mechanics as some limit.

[fredrik]

Thanks for your comments ajb!

 

The main issue is that (first) quantisation seems very ad hoc. It would be nice to have a very clear and well stated idea of exactly what quantisation is.

 

Maybe we need something else to incorporate gravity into a quantum theory. That said, as quantum theory has such a great standing any generalisations should include more standard quantum mechanics as some limit.

 

I definitely share both these "quests" with you.

 

I guess I my personal guess is that even normal "first quantiztion" QM will be understood just as what you say in the latter note - as a limit. I do not think the structure of QM as it is known to be successful can be explained within itself. Maybe we need to think up different abstractions, where hilbert spaces and unitary transformations are understood and special, or limiting cases.

 

The major problem seems to be how to control the madness that presents itself when you allow non-unitary transformations and fuzzy hilbert spaces as you loose the solid reference. I think however that goes well with nature, there are not fixed references. But hopefully once we understand the origin of inertia in these terms, we can also see how stability and effective hilbert spaces can emerge and persist even while embedded in chaos.

 

/Fredrik

[north]

pretty dumb question but what exactly is the quantum theory

 

fundamentally

 

it is the understanding of the micro

[Klaynos]

fundamentally

 

it is the understanding of the micro

 

Micro implies 10^-6, which for most consideration can be treated classically. QM tends to only take over when you're sub micrometer.

 

Although if you consider things like microwave surface plasmons the length scales considered there are in the mm range.