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Rigidness (Pauli exclusion principle)

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Marko

Thu Aug 16 2007, 02:00AM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Hello guys

This is one other thing that has been harassing me. Upon Pauli principle, no two Fermions can occupy a same quantum state at same time. The problem is, I pretty much failed to understand what a 'quantum state' really is.

I tried to visualize this in several ways. In atom, electrons are present as wavefunctions with their orbitals being boundary surfaces with highest probability for electrons to be found.

Principal and azimuthal quantum numbers somehow ''define'' the shape of orbital directly from planck's constant.

Now what really causes electron (and other leptons) to form into really odd 'atmosphere' around the charged nucleus in the way it does? What force is restraining it in this shape?

Now completely other thing, extreme pressures within white dwarf cores. Atoms are clumped together but refuse to 'merge' or form any kind of mess because this odd force, which now becomes very real, acts upon them.

Problem is, there is no really such an interaction in standard model which could do this. How are then electrons interacting in this case? At what ''distance (if it means anything) electrons 'stall' and halt the compression of matter?

The 'force' also still owns it's final magnitude before it is broken and atoms are destroyed, turning into neutrons with higher degeneracy pressure.

Or something else, what is with free electrons which may find themselves completely outside of atoms? What is their 'quantum state'?

For some reason I always naturally assumed that 'rigidness' of all everyday matter comes from electrostatic forces, electromagnetic interaction between electrons. To what point is that correct, if at all?

Now if some other particle is considered; all fermions obey Pauli principle.

What is with atomic nucleus. Like all things, protons and neutrons should have quantum states as well..

In past I naively imagined that nucleus owes it's stability due to 'balance' between strong and electrostatic force. Obviously, things are much more complex than that.

It's ''OK'' for protons, but uncharged neutrons should appear as ghosts to them and collapse themselves into black hole through that naive assumption.

Since force between nucleons is actually residual 'color force' acting between quarks this understanding may be flawed, but the point it;

From the neutron star example from above neutrons have their own degeneracy pressure as well, they can 'settle' on each other and somehow form a stable nucleus.

What now determines the point where the mysterious force 'acts', and the way it does, like it shapes electron orbitals? Quantum numbers again? I only know them for electrons, and at this point I'm completely lost

Even quarks inside nucleons, although I can't say much about that, obey Pauli principle, and are eventually clumped into some kind of dimensional structure, defying the strong force between them.

Related to this, one important thing: Proton is , for example, said to have a 'diameter' , 1.5Ã—10âˆ’15m. What does now this mean? I thought it would work exactly the same as if it was a dimensionless point. Or that is again Pauli principle, the boundary between two protons can't be 'crushed' without getting destroyed?

And, I guess, it is again defined by Planck's constant?

From the other side, I fail to find senseful implementation of neutron diameter with quantum mechanics where all particles are wave-like with their frequency proportional with kinetic energy.

Now for last, take this to something even more different: neutrinos poorly interact with themselves and almost anything else, only through weak and gravitational interaction, yet they are fermions and are 'rigid'.

If a neutrino was suspended on a hypothetical string and a bunch of other neutrinos are fired at it, they can ping upon the hanging neutrino and transfer momentum and information without really interacting by any of four interactions. (Excuse my ignorance at this point).

Now how does that resolve? Partly, I think, because the pinged neutrino must 'use' another interaction to transfer information to another kind of matter?

Bosons, interaction carrier particles, from far other side do not suffer from Pauli principle and are completely different sort of thing. I hoped all this will also give me truer distinction between *matter* and *energy*, in general.

Steve Conner

Thu Aug 16 2007, 09:32AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Quantum mechanics doesn't make sense in any intuitive way. I don't know anyone who understands what a quantum state "really" is, beyond some vague hand-waving explanation that involves a cat in a box. So if you feel completely lost, you understand it better than you think.

Bjørn

Thu Aug 16 2007, 11:29AM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

You probably have to take up advanced math to be able to get a proper feeling of how the different bits fit together and makes sense in a framework. A lot of this makes much more sense as equations since it often contradicts the reality you observe.

Marko

Thu Aug 16 2007, 07:39PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Quantum mechanics doesn't make sense in any intuitive way. I don't know anyone who understands what a quantum state "really" is, beyond some vague hand-waving explanation that involves a cat in a box. So if you feel completely lost, you understand it better than you think.

I just *knew* that I'll receive such a reply.

I don't think quantum mechanics is more special than anything else. General relativity may be very confusing and counterintuitive to someone.

I don't know what to say and not repeat something from the first post, I just tought my questions, although lot of them, were simple and clear enough.

I just hoped to raise some interest in subject..

Carbon_Rod

Fri Aug 17 2007, 12:39AM

Registered Member #65 Joined: Thu Feb 09 2006, 06:43AM
Location:
Posts: 1155

Sorry I don't recall the expanded equations off the top of my head (but iirc the symbol Psi expands to some ugly probability equation that can only be proven for less than 3 shells.)

Sadly I only memorized the quantum fill orders for the periodic table along with some exceptions. <hides shameful heuristic... Grin...>

I will have a look for my old text when I get some free time if you like,
Cheers

Simon

Fri Aug 17 2007, 06:15AM

Registered Member #32 Joined: Sat Feb 04 2006, 08:58AM
Location: Australia
Posts: 549

The theory of QM works in a fundamentally different way to mechanics at school.

A ball ends up on the ground because gravity pulls it down there.

Electronic orbitals have those shapes because after looking at all the rules of QM and what makes sense for an electron around a nucleus, we threw out a whole lot of possible shapes and narrowed them down to just a few.

Marko

Fri Aug 17 2007, 01:16PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Hopelessly throwing a bunch of equations in front of me won't help me in any way, so don't bother.

Cynicaly I could say that due to pauli principle there must be, apart from fundamental four, at least as much new interactions as there are fermions.

Electron is not spinning around the nucleus like in Bohr model. So some kind of force must be there to prevent them collapsing onto the nucleus, and there is no such one in standard model.

Some kind of force is also repelling other atoms and electrons.
Some kind of force is preventing nucleons from collapsing into a black hole from their strong interaction.
Some kind of force is preventing quarks from collapsing into black hole from their strong interaction.

What in a world is this force? Or am I just confusing 'interaction' and 'force'?

Now I thought, Isn't at least some of it simply due to repulsion between charged particles?
Still atoms are holding their shape due to degeneracy pressure, and now I wonder, about the chair I'm sitting on, to what extent am I sitting on degeneracy pressure?

I always thought indirectly about general rigidness/stiffness of matter, that it's delusional and that all must be coming from physical interactions.
Now QM has it's revenge in a fascinating way.

Is *that* what, naively said, really distinguishes matter and energy on fundamental level?

Bjørn

Fri Aug 17 2007, 02:16PM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

The term you are looking for is called degeneracy pressure. When the particles are compressed the incertainty of position will go down, according to Heisenberg the uncertainty of momentum must go up and that is the cause of the "force".

I have to say once again that almost all of this is the result of very clever people manipulating very complex equations for decades until they found something that looked good. The equations were checked against experiments and the bad ones thrown out. It is not chear how these equations relate to reality except that they can predict an impressive number of observations. So trying to understand it without math will require a number of large leaps of faith.

Some people like Hawkins say that that the relationship with reality is insignificant since no one can say what reality is anyway. Other people like Penrose say that if we don't know how reality originate from these equations we are going to miss valuable insight.

Some of the ideas and equations are complete fairy tales that hopefully will be replaced by something more sensible some time in the future.

Simon

Sat Aug 18 2007, 04:05AM

Registered Member #32 Joined: Sat Feb 04 2006, 08:58AM
Location: Australia
Posts: 549

Marko wrote ...

Electron is not spinning around the nucleus like in Bohr model. So some kind of force must be there to prevent them collapsing onto the nucleus, and there is no such one in standard model.

The electron isn't spinning like some solid ball on a string but it's still got angular momentum. It's like something's spinning, just not in a crisp, localised way.

Marko

Sat Aug 18 2007, 12:06PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

The electron isn't spinning like some solid ball on a string but it's still got angular momentum. It's like something's spinning, just not in a crisp, localised way.

That question may have been straying from the thread a bit, but hey, simon gives some clue here.

But how does it translate to other situations, and pauli principle in general?

I completely agree with what bjorn said; lowering the uncertainty in position increases uncertainty in momentum which on average becomes very large.

But why do neutrons care, anyway? They have no charge, and only attractive strong force between them. Why can they come in 'contact' after all, why aren't they transparent like ghosts to each other in that case?

Why even fundamental particles like electron and quark behave so?

If magnetic quantum number defines orbital momentum and keeps electron in place, what keeps another electron from falling into the same orbital?

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