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Author Topic:   Introduction to Quantum Mechanics.
Son Goku
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Posts: 1075
From: Ireland
Joined: 07-16-2005


(1)
Message 16 of 32 (720819)
02-27-2014 5:41 PM
Reply to: Message 6 by RAZD
02-19-2014 2:08 PM


Good idea.
I think you should. I showed my Dad your old 2.1 version a while back and he really enjoyed it, it's a really nice "hammering home" of the evidence for an old earth.

Edited by Son Goku, : No reason given.


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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


(3)
Message 17 of 32 (720826)
02-27-2014 5:56 PM


Basic Plan.
So the idea is that the topics would be something like:

1. Derive quantum mechanics from looking at the Stern-Gerlach experiment. Basically that all the features of Quantum Mechanics (e.g. Complex numbers, probabilities) naturally follow from taking a serious look at how the spin of electrons is affected by a magnetic field.

2. Then, look into more depth at the framework we have derived. Deriving the uncertainty principle and entanglement for example.

3. Next, focus on the probabilistic aspects of Quantum Mechanics and their meaning. Proof of the Kochen-Specker theorem and other such results, which serve to prove how probability in quantum mechanics differs from normal statistics and probability.

4. Interpretations and Decoherence.

5. Quantum computing, as an application of the preceding four sections.

Edited by Son Goku, : Forgot to mention Decoherence.


Replies to this message:
 Message 18 by Dr Adequate, posted 02-27-2014 7:01 PM Son Goku has responded
 Message 19 by Taq, posted 02-27-2014 7:05 PM Son Goku has responded

  
Dr Adequate
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Posts: 15950
Joined: 07-20-2006
Member Rating: 4.6


Message 18 of 32 (720834)
02-27-2014 7:01 PM
Reply to: Message 17 by Son Goku
02-27-2014 5:56 PM


Re: Basic Plan.
I think there should be a section on how quantum mechanics means that Deepak Chopra is right about everything.
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Taq
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Posts: 7140
Joined: 03-06-2009
Member Rating: 3.9


Message 19 of 32 (720836)
02-27-2014 7:05 PM
Reply to: Message 17 by Son Goku
02-27-2014 5:56 PM


Re: Basic Plan.
1. Derive quantum mechanics from looking at the Stern-Gerlach experiment. Basically that all the features of Quantum Mechanics (e.g. Complex numbers, probabilities) naturally follow from taking a serious look at how the spin of electrons is affected by a magnetic field.

I think it would be absolutely awesome if you could explain what "spin" means with respect to QM. That is a concept that has never really clicked for me.


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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


(2)
Message 20 of 32 (720838)
02-27-2014 7:10 PM
Reply to: Message 18 by Dr Adequate
02-27-2014 7:01 PM


Re: Basic Plan.
If you listen to your heart, you already know he's right about everything. Except you can't listen with ears of flesh, but with the ears of love, the cochlea of understanding and the external auditory meatus of compassion.
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AZPaul3
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Posts: 3428
From: Phoenix
Joined: 11-06-2006


(1)
Message 21 of 32 (720845)
02-27-2014 8:45 PM
Reply to: Message 20 by Son Goku
02-27-2014 7:10 PM


Re: Basic Plan.
... and the brains of a dickhead.

Edited by AZPaul3, : No reason given.


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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


Message 22 of 32 (720890)
02-28-2014 8:28 AM
Reply to: Message 19 by Taq
02-27-2014 7:05 PM


Re: Basic Plan.
Well, talking about spin will be a big part of the notes, since it's the property of matter that displays all the features of quantum mechanics while still only involving simple mathematics.

I'll try an explanation now though, since I don't need the full notes to discuss it.

As you are aware particles have mass and charge, these are two numbers, one which determines how difficult it is to accelerate the particle and the other determines the strength of the electric field it produces.

Angular momentum, in quantum mechanics, in simply another number like this. You can think of it as determining the strength of the magnetic field an object generates. It is simply another "charge" like electric charge.

Some particles come with a certain amount of angular momentum, but you can also generate angular momentum from rotating around a fixed point.

Angular momentum is actually just a charge. You don't have to rotate to possess angular momentum, that's just one of the ways of obtaining it.

Think of energy. There is kinetic energy, mass energy, potential energy. They're all just different ways of possessing the same quantity, namely: Energy.

However in classical mechanics the only way to possess angular momentum is via the second method of rotating about a fixed point. Hence the conflation of angular momentum and rotations. Even the name is unfortunate, reflecting its historical origin. Angular momentum, implies that it is simply the analogue of momentum for rotations. It should really be called "external SU(2) charge", for reasons I'll explain in the notes.

So an electron isn't really spinning around or anything, it just possesses two charges:
Electric charge.
Angular momentum charge.

Since, unfortunately, in classical mechanics the second charge only comes from rotations, this leads to the mental picture of an electron rotating, however this is false. If you analyse the other effects of rotation (rotation causes things besides angular momentum) an electron doesn't display them, hence it is definitely not rotating.

In quantum mechanics, the angular momentum coming from rotations is called orbital angular momentum and angular momentum that the particle just naturally possesses is called spin angular momentum (again an unfortunate name as the particle doesn't really spin).


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Replies to this message:
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RAZD
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Posts: 18966
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 3.7


Message 23 of 32 (720892)
02-28-2014 8:53 AM
Reply to: Message 22 by Son Goku
02-28-2014 8:28 AM


spin
Is spin then more like a potential than a kinetic aspect?

In quantum mechanics, the angular momentum coming from rotations is called orbital angular momentum and angular momentum that the particle just naturally possesses is called spin angular momentum

I think of the electrical charge when in orbit causing a magnetic field being the kinetic aspect versus a non orbiting charge having the potential aspect.

?


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This message is a reply to:
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Dr Adequate
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Posts: 15950
Joined: 07-20-2006
Member Rating: 4.6


Message 24 of 32 (720909)
02-28-2014 11:13 AM
Reply to: Message 22 by Son Goku
02-28-2014 8:28 AM


Re: Basic Plan.
Even the name is unfortunate, reflecting its historical origin. [...] Since, unfortunately, in classical mechanics the second charge only comes from rotations, this leads to the mental picture of an electron rotating, however this is false.

So ... let's see if I've got this right. The reason for the name is that if the world was classical instead of quantum, then the Stern-Gerlach experiment would have been measuring how the particles spin. The results of this particular experiment were consistent with them actually, classically spinning, but only at a given rate. So people exclaimed "Ah, spin is quantized!" But really they weren't spinning at all, as has been shown by other experiments (which you allude to and I know nothing about.) It's just that their magnetic properties, not actually caused by them spinning, gave results consistent with the hypothesis that (a) they were spinning (b) the spin was quantized.


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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


(1)
Message 25 of 32 (720932)
02-28-2014 5:24 PM
Reply to: Message 24 by Dr Adequate
02-28-2014 11:13 AM


Re: Basic Plan.
The quantity was called spin because initially it was thought that this new angular momentum was coming from the electron spinning on its own axis.

The idea was that the electron was like the Earth, it had orbital angular momentum (motion around the Sun) and spin angular momentum (rotation about its own axis).

However when you really think about it (as people did almost immediately) this doesn't really make any sense, as the Earth's spin, is really just another form of orbital motion, simply the material of the Earth swinging around the main axis. Since the electron is fundamental, this doesn't really make any sense as the explanation of its "spin" value.

However, yes, assuming that the electron spun on its own axis with only certain fixed values possible was consistent with the Stern-Gerlach experiment. Or more accurately a quantum "indefinite" version of the Earth's spin was consistent with the Stern-Gerlach experiment. If this was true, spin would be just like momentum, i.e. it has a classical analogue and all quantum mechanics would do is to make it probabilistic.

However there are a few facts that show you that "spin" is not a quantum version of the Earth's axial rotation, as was initial thought (and which is the origin of the name). It is actually a quantum quantity that is not a random/indefinite version of any classical quantity.

The clearest example I can think of is that there is a simple expression relating angular momentum to the strength of a magnetic field and a second expression relating angular momentum to rotational velocity.

It turns out that the measured strength of an electron's field would imply a rotational speed exceeding the speed of light.

This would be problematic enough, however if this were true you could scatter other particles off an electron and in the scattering those particles would steal some of the electron's rotational energy and rotate themselves. Ultimately you could make the electron stop spinning, reduce the magnetic field to zero.

However in actual scattering experiments, nothing like this happens. The electron's magnetic field stays constant. So therefore there must simply be no rational energy to steal from. The "spin" angular momentum must in fact have nothing to do with spinning.

As I said, we know now that it is simply a charge, like electric charge.


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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


Message 26 of 32 (729470)
06-12-2014 9:44 AM
Reply to: Message 23 by RAZD
02-28-2014 8:53 AM


Re: spin
Sorry for the incredibly late reply!!

Yes, spin is more like a "potential aspect", in the sense you have defined it.

I'm much busier in work than I thought, but things a clearing up now and I hope to start this course soon.


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herebedragons
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Posts: 1413
From: Michigan
Joined: 11-22-2009
Member Rating: 3.0


Message 27 of 32 (729526)
06-13-2014 8:11 AM
Reply to: Message 22 by Son Goku
02-28-2014 8:28 AM


Re: Basic Plan.
Angular momentum is actually just a charge. You don't have to rotate to possess angular momentum, that's just one of the ways of obtaining it.

Was this known prior to quantum mechanics or was this realization a result of discoveries in QM?

HBD


Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca

"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.

Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.


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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


Message 28 of 32 (729575)
06-14-2014 9:05 AM
Reply to: Message 27 by herebedragons
06-13-2014 8:11 AM


Re: Basic Plan.
It was only discovered in Quantum Mechanics. It's not possible for classical particles, they can only generate angular momentum via orbital motion.
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Son Goku
Member
Posts: 1075
From: Ireland
Joined: 07-16-2005


Message 29 of 32 (742471)
11-20-2014 12:32 PM


First set of notes.
https://app.box.com/s/1f895jkhlekfv34ql4t9
Replies to this message:
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AZPaul3
Member
Posts: 3428
From: Phoenix
Joined: 11-06-2006


Message 30 of 32 (742554)
11-21-2014 5:36 PM
Reply to: Message 29 by Son Goku
11-20-2014 12:32 PM


Re: First set of notes.
https://app.box.com/s/1f895jkhlekfv34ql4t9 (Stern-Gerlach experiment)

OK. So, in the original experiment the beam was split spin-up/spin-down, all spin-down was blocked, the remaining beam of all spin-up was then split spin-left/spin-right, all spin-right was blocked and the remaining beam of (supposedly) only spin-up/spin-left was again tested for spin-up/down and found 50%-up, 50%-down.

It's like the quantum number for spin-up/down was reset during the spin-left/right test. (reset from "up" to "?", please excuse my layman's language)

In experiment "A" after the initial spin-up/down test the beam of (supposedly) all spin-up is split spin-left/right then brought back together and the second spin-up/down test yielded the same 50-50% result. Again it's like the quantum number for spin-up/down was reset. But, I note there is a detection of spin-left/right in the experiment "A" scenario.

In the "B" experiment this detection of spin-left/right is not made and the result of the second up/down test yields 100% "up". Even though the beam in the spin-left/right apparatus is split into separate spin-left and spin-right paths (since the equipment is exactly the same, functions just the same (minus the detector)) the quantum number ("up") from the first up/down test block was not reset by the left/right test block.

The only difference between the setup of the original and "A" experiments and the setup of the "B" experiment is that the original and "A" detect the left/right split while "B" does not.

This is a "Double Slit" experiment for electron spin, yes?

So in a layman's analogy (not totally accurate but close enough for some understanding) is saying ...

"When the spin-left/right paths are detected the quantum number for spin-up/down is reset to "?" thus allowing the second up/down test to spread the results among the quantum probabilities" ...

acceptable?

Edited by AZPaul3, : clearer, I hope


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