Re: Why quantization?

Igor Khavkine wrote:

On 2006-08-20, Peritas <galoislie@xxxxxxxxx> wrote:

Quantum mechanics is the physicist's tool (and a good one at that!) for
describing what's going on. The crux of my original question is that
i'm trying to think of what makes nature behave in the way it does such
that quantum mechanics works so well. Based on your response, it looks
as though the wave nature of matter is indeed the reason particles
become quantized provided sufficient confinement.

So this leads to the next question. Why is de Broglie correct? From
my limited knowledge and understanding, that's just the way things are.
In other words, wave-particle duality is a fact that stands by itself.
Is this indeed the case? Or am I missing (or forgetting) some more
fundamental concept that naturally leads to matter waves?

Sadly, there can be no scientifically satisfactory answer to this
question. Given a theoretical hypothesis, it is a reasonable scientific
question to ask *whether* it fits all available data. Once the last
question has been answered in the positive, it is less reasonable to ask
*why* the given hypothesis works. That is simply because there could be
several hypotheses that fit the data equally well and the question
"Why?" presupposes that one of them is the correct one and the other
ones are not. But in the absence of more data, it may be impossible to
tell.


Ah but there can be one way to break the tie between two theories that fit
the data equally well. The Occams Razor test. Which every theory needs
the fewest postulates to explain the most phenomena is the better of two
otherwise equal theories or hypotheses.


But here's an example. We know that Newton's laws of motion work
extremely well in everyday situations.

An example of a better theory by the Occams Razor test would be Hamiltonian
Dynamics. Which is derived from the one principle of least action.
Instead of the three laws of motion.

However, for objects travelling
close to the speed of light, relativistic dynamical laws have to be used
instead of the Newtonian ones. So, *given* that relativistic dynamics
*does* reproduce all experimental observations, it makes sense to ask
*why* Newtonian dynamics works so well in everyday life. And the answer
is that Newton's laws coincide with the approximation to relativistic
dynamics for velocities much smaller than the speed of light.

On the other hand, quantum mechanics enjoys the status of not being in
contradiction with any experiment, at the moment. Hence, the "Why?"
questions as to its validity have to be reserved until a more general
theory is *needed* and *has* been formulated.


Lastly it is worth noting that Hamiltons principle of least action plays a
role in both relativistic and quantum mechanics. Which makes it very
fundamental in deed.

Hamiltons principle of least action says: Natural processes evolve on the
path from point a to point b that will minimize the action integral
A=integral[kinetic energy - potential energy]dt (a,b). This brings me to
the original question. Why E=hv? h and \hbar are units of action. The
smallest possible units of action. So all processes in nature will be
expressed in terms of this fundamental unit of action. Though these units
are not all that convenient for everyday use.


Hope this helps.

Igor
:-)

--
"....a good profession as long as you don't earn a living at it." A.E
www.geocities.com/hontasfx

.

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