Can QM be derived from Newton's Laws of motion

[jcsd]

Of course time is a dimension, it's just a game of semantics as the word 'dimension' has several meanings. It's not a spatial dimension though, even though you can have space and time as dimensions of spacetime.

Baryon number is only beleived to be a usually conserved quantity, IIRC there's no mechanism of conserving baryon number when speaking about situation like black holes without arbitarily violating gauge symmetry.

 

[Haelfix]

Baryon and lepton Number are explicitly broken in the standard model. The reasons for this is technical, and deal with topological field theory (it involves shifting the Dirac sea).

However the predicted value for the nonconservation of leptons, is something like 1 lepton violating process for some enormous quantity like 10^93 good ones.

Experimentally baryon number has never been seen to be violated, and the amount of data we have on that is incredible (literally trillions of data points).

Most people think however, that Baryon and Lepton number will be violated much more severly when we go to higher energy, as GUT processes will start to become important, and these often break the symmetry explicitly.

Still, these 'accidental' symmetries are good at most lab energies, and in most processes of interest

 

[Terry Giblin]

"Quantum electrons" not "wave-particle duality"

Replacing the electron gun, with an electron quantum tunnelling device, would not in any way change the result of the experiment.

Hence the question, "What is an electron?"

Because it should change our perception of the electron and photon.

"Wave-particle duality" Or different versions of the same fundermental "Quantum Electrons"

Terry Giblin

Id just add: don't get the impression that I mean classical physics doesn't involve induction. Taking the example of special relativity, Einstein inductively (of course Messrs Michelson, Morley et al deserve more than a little credit for this) derived the postulate that light travels the same speed in all inertial reference frames and then he deductively derived special relativity from previous classical theories. Special relativity is a classical theory.

Schroedinger inductively derived wave-particle duality (though the lionshare of the credit must go to Prince De Broglie for this), but he used induction again to derive his famous equaton (by first considering a classical wave equation then inductively making changes to it).

 

[zefram_c]

"Wave-particle duality" Or different versions of the same fundermental "Quantum Electrons" ?

I'm not sure I understand your question, but I'll try to answer since this seems to come from a common QM misconception. Thinking of quantum objects as having "wave/particle duality" may seem useful for teaching, but IMHO it confuses more than clarifies. I think it's much better to say that quantum mechanics describes quantum objects. These objects share some properties with classical particles, other properties with classical waves, but they are not "both at the same time" (that is in fact logically contradictory). In QM all electrons are quantum objects and so inherently indistinguishable - unless you have some definite position or momentum information.

Edit: Oh, and it is utterly impossible to derive QM from Newton's laws of motion, just as it is impossible to derive SR from Galilean invariance. QM converts Newton's 2nd law into statements about expectation values (Ehrenfest's thm). Newton's first law has nothing to do with the time evolution of a free wavefunction. Energy/momentum conservation carries over to QM.