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Why is there a 'quantum' and 'classical' harmonic oscillator?

Hi,

Question is in the title - and can someone point me towards some rookie literature in the difference between quantum and classic physics as well as the harmonic oscillator.

I'd appreciate any help. If this question is elementary, please be kind, I'm a philosophy of science student not a physics one! :biggrin:

Reply 1

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Reply 2

TLK

Original post by bluemohito

Classic physics is based on Newtonian physics which is basically practical for daily life scenarios like calculating how long it takes a car to travel a certain distance at a realistic speed.

Quantum physics is used to describe the behavior of particles especially when travelling near the speed of light which is when stuff goes weird as well as Einsteins equations.

Reply 3

Freier._.lance

Original post by TLK

hi there. I believe you are confusing 'quantum' with 'special relativity'.

Reply 4

hdivider

This 'why' question is somewhat difficult to answer completely. One answer may be that in classical physics, measurement has no impact on the outcome of the measurement. A 1m rope will be measured to be of length 1m (within experimental error, which we can account for) no matter how many times you perform the measurement. But measuring the length of a 0.1 nanometre rope (call it a 'quantum rope') will give different results each time [1]. Quantum mechanics tells us that this discrepancy is not a result of our instruments being wrong, but rather it's because the quantum rope's length is inherently probabilistic - because the positions of the start and end points have an indeterminate value. Their values are 'calculated' by the act of measurement - in a sense, measurement 'forces' those points to make their minds up on a particular position.

So to at least partially answer your question: the classical harmonic oscillator is defined on variables whose values don't depend on their measurement, while a quantum oscillator is one that is defined on mathematical abstractions (e.g. operators) that allow you to calculate things like expectation values [2] of similar variables.

One point that might be relevant for philosophy: quantum mechanics has many different interpretations. Some of those would disagree with my two paragraphs above. But in the end, everyone agrees on the core mathematics. (Another thing: one nice bit of conceptual machinery that I've always liked is the correspondence principle [3]. Paraphrased and simplified it states that quantum mechanics turns into classical mechanics when you're looking at large physical systems - e.g. a dog as opposed to a carbon atom within that dog.)

This is an incomplete answer, since quantum mechanics has far more weirdness in it than just indeterminate quantities. =)

As for literature, for non-mathematical stuff on quantum mechanics I'd highly recommend Feynman's books. No one tops good old Feynman on this. Specifically, you might want to look at QED: The Strange Theory of Light and Matter. This talks about quantum electrodynamics - but it still includes quantum mechanics. It does frequently compare observations with what you'd expect from 'intuition' - i.e. the human brain's inherent heuristic understanding of classical mechanics. =)

[1] In special cases quantum mechanics can actually be deterministic - but to explain that I'd have to introduce a bit of maths. :wink: