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zerocold
2010-Jul-19, 09:49 PM
Simple, can somebody explain me the spin factor for a subatomic particle?, i understand is interpreted as some sort of rotational motion, but i don't understand , for exmple, some rules related with it, why, for example 2 neutrons can't occupy the same location?, while 2 photosn can, i understand this has to o with the spin value, any idea?

Thanks :)

Ken G
2010-Jul-20, 07:38 AM
You are asking about some of the deepest issues in quantum mechanics, so I'm not sure at what kind of detail you are looking for the answer. Spin is a fundamentally quantum mechanical attribute, there is no classical analog at all (picturing it as a point particle that is actually spinning is really only a piece of what is going on there, because a point particle could spin at any rate and still have zero angular momentum, whereas a quantum mechanical point particle with spin does have angular momentum). You asked in particular about the Pauli exclusion principle, so the way that works is, all particles with a half-integer spin are "fermions" and exhibit that principle, whereas all particles with integer spin are "bosons" and do not exhibit that principle. Neutrons, electrons, and protons all have spin 1/2, so are fermions, whereas photons have spin 1 and are bosons.

The reason for this has to do with some pretty deep stuff in relativistic quantum mechanics that connects the spin to the attributes of the wave function when you swap identical particles. If the spin is integer, swapping particles doesn't change the sign of the wave function, so both particles can be in the same state since swapping them is allowed to leave the wave function unchanged. But if the spin is half-integer, swapping the particles should change the sign of the wave function, but that can't happen if the two particles are in the same state, because swapping two particles in the same state doesn't do anything to the wave function. That's the Pauli exclusion principle-- two identical particles with half-integer spins cannot be in the same state. (However, if the spin is, say, 1/2, like for the neutron, then you can have an up or down spin state, so two neutrons can still be "in the same place", because they would still be in different states if one had spin up and the other spin down-- that's why helium is a non-interacting "noble gas", its two electrons can both be in the ground state if one has spin up and the other spin down, and two electrons in the ground state are hard to get to want to interact with anything else.)

CaptainToonces
2010-Jul-20, 07:50 AM
That's the Pauli exclusion principle-- two identical particles with half-integer spins cannot be in the same state. (However, if the spin is, say, 1/2, like for the neutron, then you can have an up or down spin state, so two neutrons can still be "in the same place", because they would still be in different states if one had spin up and the other spin down

When we consider this relating to two neutrons, let's say with the same spin direction, we say they cannot occupy the same location because of Pauli Exclusion. But what force prevents that? Is it still considered the Coulumbic force even though we are talking about two charge-less neutrons?

Ken G
2010-Jul-20, 01:55 PM
When we consider this relating to two neutrons, let's say with the same spin direction, we say they cannot occupy the same location because of Pauli Exclusion. But what force prevents that?
It's a force called "degeneracy pressure". But it would be safer to say that degeneracy pressure stems from Pauli exclusion than to say that the Pauli exclusion principle stems from degeneracy pressure. Ultimately, the "cause" results from the wave mechanics of quantum mechanics-- waves do whatever they are allowed to do, which is everything that does not experience destructive interference. That's why electrons don't fall into protons in a hydrogen atom, or why light makes a "double-slit diffraction pattern"-- they are doing everything that is not disallowed by destructive interference. There just aren't forces at work there, it's wave mechanics. Similarly, two neutrons (with the same spin) in the same state experience destructive interference between the wave function and its particle-swapped pair wave function, which must be just as valid a description of the reality (since the neutrons are indistinguishable). All that destructively interferes does not happen-- that's wave mechanics in a nutshell.

mugaliens
2010-Jul-21, 07:52 AM
Great thread! I'll keep my eyes open.

trinitree88
2010-Jul-21, 12:56 PM
Pauli invented a new degree of freedom for the electron which later became known as spin...SEE:http://en.wikipedia.org/wiki/Wolfgang_Pauli

SEE: http://en.wikipedia.org/wiki/Spin_(physics)

Mugs. Check ou the next link. Each electron gets a "mailing address" in the atom...(just like you like to receive your mail and not the neighbors")
The first part is the color on the chart ( the principle quantum number, n)
The second part is which "cluster"..on the chart... ones threes fives sevens of circles ( the sublevel type s,p,d, or f)
The third part is which circle in the "cluster" ...the orbital
The fourth part is that within each circle, or orbital two electrons are allowed, but to distinguish their energy discretely as unique, like your mailing address, Pauli invented a new quantum number which later became known as "spin". Grab an orange spinning with your right hand's fingers in the direction of the spin. if your thumb points up, it's spin up, if the spin reverses, the thumb points down, it's spin down. So it is with electrons. Fermi-Dirac statistics forbid two particles with half integer spins from having the same four quantum numbers, so when you pack them in, they resist, giving white dwarfs with nucleons packed degeneracy pressure. If the particles have integers or zero spin, they obey Bose-Einstein statistics which allow you to pack as many as you want in a given volume....(which is why intersecting laser beams don't interfere) Link:http://boomeria.org/chemlectures/goosechart.jpg

A similar structure of "mailing addresses" exists in the nucleus. Each nucleon gets a set of numbers, and just like particularly stable configurations of electrons cause chemical stability in the noble gases at 2,10,18,36,54,86...there are magic stability numbers in the nucleus causing radioactive decay stability...See magic numbers:http://en.wikipedia.org/wiki/Nuclear_shell_model

CaptainToonces
2010-Jul-21, 02:40 PM
Fermi-Dirac statistics forbid two particles with half integer spins from having the same four quantum numbers, so when you pack them in, they resist
But do they really "resist" according to a force that can be described with a function like inverse square of the distance, or is it instead that there is very very little chance of them both being in the same quantum state? Exact math is welcome.

Ken G
2010-Jul-21, 04:28 PM
But do they really "resist" according to a force that can be described with a function like inverse square of the distance, or is it instead that there is very very little chance of them both being in the same quantum state? Exact math is welcome.It's not a force, it's destructive interference. If you write a wave function for two independent particles, it looks like phi(1)*phi(2), where particle 1 and 2 are in the same state if phi is the same. But now, you have to make the function antisymmetric under swapping 1<-->2, because that is required of half-integer-spin particles (it has to do with relativity in ways I can't find a clear explanation). The antisymmetric form is phi(1)*phi(2) - phi(2)*phi(1) = 0. In effect, two identical fermions in the same state destructively interfere with the particle-swapped version of the same wavefunction, and since either version of the wavefunction is just as physically valid, the destructive interference is real. So "resisting" being in the same state is in the same sense that an X-ray "resists" diffracting around your broken arm-- destructive interference between all the equally valid ways the X-ray could move forces the X-rays to move in nice straight lines and produces a nice clear image of your broken arm. (Radio waves have much longer wavelengths, resulting in much poorer destructive interference, and hence they bend all around your bones and you could never see a radio image of your broken bone). It's all a matter of how wave mechanics works.

Note also that for bosons, the combined wavefunction is symmetric under swapping, so you can have phi(1)*phi(2) + phi(2)*phi(1) and the interference of two particles in the same state is constructive (I haven't bothered to normalize the resulting state). Wave mechanics allows what is constructively interfered, and disallows what is destructively interefered, there's no need for any "forces" to accomplish that (however, when you do put in a real force, like Coulombic attraction, the constructive interference between allowed "particle-swapped" states does alter the energy of the interaction, called "exchange energy.")

Grey
2010-Jul-21, 04:36 PM
But do they really "resist" according to a force that can be described with a function like inverse square of the distance, or is it instead that there is very very little chance of them both being in the same quantum state? Exact math is welcome.As far as we can tell, there is no chance at all that it can happen. But there's no "force" that prevents them from doing so, and certainly not one that has any kind of distance function. As Ken says, it's because the particle's behavior is consistent with wave mechanics. We don't really know why the universe is composed of half-integer-spin particles that are described by antisymmetric wave functions and integer-spin particles that have symmetric wave functions; that's just the way things seem to be.

Pursuant to the OP, "spin" is named that because it does have some things in common with classical angular momentum, but it's a good idea to remember that it's a decidedly quantum property, and trying to imagine it as a particle really spinning doesn't work very well.

chornedsnorkack
2010-Jul-21, 06:20 PM
How does the exact shape of Fermi hole, and Fermi heap, compare with hole caused by Coulomb repulsion?

While Pauli exclusion forbids two fermions from being in the same state, it does not end there. State could be ill defined, because particles can be free.

Pauli exclusion also bans two (identical, same-spin) fermions from occupying same vicinity of space. For example, consider an atom with 1s and 2s orbital filled with electrons of the same spin. Different "states", so both can be filled.

1s and 2s orbitals both have a cusp at the nucleus - this is where both electrons are most likely to be. But you are unlikely to find two electrons at the same time in the same small volume of space. 1s electron can be near the nucleus, but only when the 2s electron is at that time elsewhere in its electron cloud, and vice versa.

Exchange interaction causes Fermi hole. Averaged over time, it is less visible, because an electron causing Fermi hole in the distribution of the other electron is itself moving.

forrest noble
2010-Jul-21, 09:42 PM
The spin issue

...can somebody explain (to) me the spin factor for a subatomic particle?, i understand (it) is interpreted as some sort of rotational motion, but i don't understand , for example, some rules related with it, why, for example 2 neutrons can't occupy the same location?, while 2 photons can, i understand this has to do with the spin value, any idea?

Most practitioners in Physics consider spin as a characteristic of atomic particles rather than something that is happening so that the details do not have to be considered. On the other hand some physicists believe spin is a real condition of rotation on an axis. Although there are few other ideas out there concerning spin, there are a number of problems relating to actual axis spin if it were real. One is that some consider that electrons have no physical diameter but instead are a cloud of some kind. If they have a physical diameter their surfaces would seem to be traveling faster than the speed of light based upon some calculations. Another problem with atomic physical particle spin would be that the energy of spin would be an analog calculation meaning it could be divided into infinite parts. Quantum physicists do not accept energy values smaller than Plank's constant. An additional problem is that of half-spin or double spin. Concerning spin quantities such as half spin, what does it mean? One hypothesis is that the particle is wobbling on alternate axes showing its same face to an observer every other spin. If not this hypothesis then what does it mean to have 1/2 spin, a spin of 2, 1/3 etc.? These are some of the theoretical problems relating to particle spin as axial.

Photons were originally thought of as a packet of smaller particles, or entities of some kind. These packets were called quanta. One might consider packets being forced together or some such hypothesis as merging photons. Neutrons, on the other hand, degenerate into protons, electrons and neutrinos when attempts have been made to force them together. Charged particles cannot, so far, be forced together based upon same-charge repulsion forces and quantum rules which are based upon observations rather than some physical characteristic based upon physical theory. Bottom line is that present rules and mathematics are the determining factors in Quantum Mechanics and Particle Physics in their present forms and it doesn't matter much concerning these present guidelines whether there might be truly one kind or another of physical processes involved provided these rules are not violated.

ShinAce
2010-Jul-21, 10:42 PM
These are some of the theoretical problems relating to particle spin as axial.

One more.

If an electron really was spinning, how could that spin develop into a magnetic moment if the charge is evenly distributed within the electron. To think of the electron as made of little areas of charge cause even more problems than just accepting that a magnetic moment is a fundamental property of the particle. Let us not forget that there's a magnetic moment from the particle's 'spin' and another from its 'orbit'.

CaptainToonces
2010-Jul-22, 12:00 AM
It's not a force, it's destructive interference.
but how is the strength of this degeneracy pressure measured? This would be the same function that determines the radius of a neutron star given its mass (i think). It would also be a function that tells you if you fire an electron at a helium atom in a vacuum just how close in distance the electron may approach the atom before it may be turned away by destructive interference ignoring other effects.

Ken G
2010-Jul-22, 02:34 AM
but how is the strength of this degeneracy pressure measured? This would be the same function that determines the radius of a neutron star given its mass (i think).Yes, that's right. One way to think about pressure is it is the energy you must provide to make the volume of something decrease by a fixed amount (i.e., it is the energy per volume change you must provide to get that volume change). With normal gas pressure, you have to provide energy to do work against the force of pressure, but with degeneracy pressure, there really isn't a "force" there at all-- there's just a need to do work to get it to compress (which acts just like a force).

The reason there is a need to provide energy to get it to compress is that the neutrons (in a neutron star, say, or electrons in a white dwarf) are already "maximally compressed" in the sense that their wave functions are packed in with the other particles as much as the exclusion principle allows. To get them to compress more, you have to increase the curvature of the wave function, like you have to bend a rod to get it to fit in a box smaller than the length of the rod. Curvature in a wave function corresponds to kinetic energy of the particle, so to get it to curve more and fit in a smaller box requires that you add energy. That's what pressure means, adding kinetic energy to get something into a smaller box. However, the kinetic energy you add does not show up in the temperature, because temperature counts the energy in excess of the minimum possible required to have containment inside those little boxes. You can cool a white dwarf to "absolute zero", and it still has all the kinetic energy that the wave functions need to be as compressed as they are.

korjik
2010-Jul-22, 04:33 AM
Most practitioners in Physics consider spin as a characteristic of atomic particles rather than something that is happening so that the details do not have to be considered. On the other hand some physicists believe spin is a real condition of rotation on an axis. Although there are few other ideas, there are also a number of problems relating to actual axis spin. One is that some consider that electrons have no physical diameter but instead are a cloud of some kind. If they have a physical diameter their surfaces would seem to be traveling faster than the speed of light based upon some calculations. Another problem with atomic physical particle spin would be that the energy of spin would be an analog calculation meaning it could be divided into infinite parts. Quantum physicists do not accept energy values smaller than Plank's constant. An additional problem is that of half-spin or double spin. Concerning spin quantities such as half spin, what does it mean? One hypothesis is that the particle is wobbling on alternate axes showing its same face to an observer every other spin. If not this hypothesis then what does it mean to have 1/2 spin, a spin of 2, 1/3 etc.? These are some of the theoretical problems relating to particle spin as axial.

Photons were originally thought of as a packet of smaller particles, or entities of some kind. This packets were called quanta. One might consider packets being forced together or some such hypothesis as merging photons. Neutrons, on the other hand, degenerate into protons, electrons and neutrinos when attempts have been made to force them together. Charged particles cannot, so far, be forced together based upon same-charge repulsion forces and quantum rules which are based upon observations rather than some physical characteristic based upon physical theory. Bottom line is that present rules and mathematics are the determining factors in Quantum Mechanics and Particle Physics in their present forms and it doesn't matter much concerning these present guidelines whether there might be truly one kind or another of physical processes involved provided these rules are not violated.

When the post starts with 'Practitioners in Physics' you can be assured that everything that follows is wrong.

Everything in this post is wrong. Physicists actually learn what QM is, not just make assumptions and hand-waving statements that make it look like there is a problem in the understanding of a phenomena.

korjik
2010-Jul-22, 04:36 AM
How does the exact shape of Fermi hole, and Fermi heap, compare with hole caused by Coulomb repulsion?

While Pauli exclusion forbids two fermions from being in the same state, it does not end there. State could be ill defined, because particles can be free.

Pauli exclusion also bans two (identical, same-spin) fermions from occupying same vicinity of space. For example, consider an atom with 1s and 2s orbital filled with electrons of the same spin. Different "states", so both can be filled.

1s and 2s orbitals both have a cusp at the nucleus - this is where both electrons are most likely to be. But you are unlikely to find two electrons at the same time in the same small volume of space. 1s electron can be near the nucleus, but only when the 2s electron is at that time elsewhere in its electron cloud, and vice versa.

Exchange interaction causes Fermi hole. Averaged over time, it is less visible, because an electron causing Fermi hole in the distribution of the other electron is itself moving.

You have a misunderstanding of what an electron shell is. The electron isnt in a specific spot in the shell it is in all the shell. Well, at least it is until you measure it. For an atom that isnt being excited (the only way to measure it) the electrons dont have to worry about crowding one another because their locations arent defined well enough to make it a problem.

Ken G
2010-Jul-22, 04:52 AM
You have a misunderstanding of what an electron shell is. The electron isnt in a specific spot in the shell it is in all the shell.Actually, chornedsnorkack is making a valid point even if his words overly suggest a kind of known trajectory for the two particles (quantum mechanical prose is always a bit tricky, as the mathematics is never translated precisely)-- the antisymmetry of the combined two-particle wavefunction does not just mean that two electons cannot be in the same state, it also has affects on atoms and molecules with multiple electrons in them even when those electrons are not in the same state. This point is well taken: a "Fermi hole" appears when you have two electrons with the same spin, and then their joint wave function is not the same as two independent electron wave functions-- there is a tendency to find anticorrelation between the locations of the electrons when you locate both electrons. That is, you tend not to find them in the same vicinity of each other, and that's not because of their charge, it's because of their joint wave function. The additional fact that they do experience Coulombic repulsion means that this will be a lower energy state-- and this is why when you excite an n=1 electron in neutral helium to the n=2 level, it takes less energy to do that if the electron ends up with the same spin as the electron left behind in the n=1 shell.

Conversely, if the electron in the n=2 shell ends up with the opposite spin as the n=1 electron, then the spatial part of the joint wave function will tend to correlate the locations of both electrons-- they will tend to be found near each other moreso than two independent n=1 and n=2 orbitals normally would. Due to their Coulombic repulsion, this state has a slightly higher energy. All that is a consequence of the same kinds of considerations as the Pauli exclusion principle-- that's all chornedsnorkack was saying, there's even more to the issue of identical particles and joint wave functions.

mugaliens
2010-Jul-22, 06:52 AM
Neat stuff, Pete - thanks! I'm fairly well versed with electrons (both chemistry and physics), but hadn't heard of the similar concept with nucleons, probably because that gets into nuclear physics, which is beyond the typical sophomore level in either chem or phys in the school I attended. I think it's a class (or classes) in jr and/or sr years for both chem and phys.

Andrew D
2010-Jul-22, 07:13 AM
...the combined wavefunction is symmetric under swapping...\

What is the name of the transformation that represents the "swapping"?

CaptainToonces
2010-Jul-22, 07:17 AM
The reason there is a need to provide energy to get it to compress is that the neutrons (in a neutron star, say, or electrons in a white dwarf) are already "maximally compressed" in the sense that their wave functions are packed in with the other particles as much as the exclusion principle allows. To get them to compress more, you have to increase the curvature of the wave function, like you have to bend a rod to get it to fit in a box smaller than the length of the rod. Curvature in a wave function corresponds to kinetic energy of the particle, so to get it to curve more and fit in a smaller box requires that you add energy. That's what pressure means, adding kinetic energy to get something into a smaller box. However, the kinetic energy you add does not show up in the temperature, because temperature counts the energy in excess of the minimum possible required to have containment inside those little boxes. You can cool a white dwarf to "absolute zero", and it still has all the kinetic energy that the wave functions need to be as compressed as they are.

Forgive me if i failed to understand your answer, I am new to wave mechanics. But in my understanding kinetic energy doesn't really come into play here.

In the case of a white dwarf, the pressure (aka pauli exclusion, aka destructive interference) is an outward force holding up the star, not a compressing force. It's gravity that is the compressing force. At some point as the white dwarf is collapsing in on itself due to gravity, the strength of destructive interference becomes as strong as the gravitational force and the star stops collapsing at some radius x and is a stable white dwarf. If I add mass to this white dwarf, the strength of the gravitational force on it will increase, and eventually, overcome the strength of the destructive interference and the star will collapse further resulting in supernova or further degeneration into a neutron star, therefore there must be a quantifiable strength of this destructive interference, much like you can describe the strength of other forces using functions like "inverse square of the distance" just for example. So what is that function that describes the strength of the degeneracy pressure that holds up a white dwarf? In other words, how do i know what strength of gravity i need to overcome it?

Nereid
2010-Jul-22, 12:06 PM
Forgive me if i failed to understand your answer, I am new to wave mechanics. But in my understanding kinetic energy doesn't really come into play here.

In the case of a white dwarf, the pressure (aka pauli exclusion, aka destructive interference) is an outward force holding up the star, not a compressing force. It's gravity that is the compressing force. At some point as the white dwarf is collapsing in on itself due to gravity, the strength of destructive interference becomes as strong as the gravitational force and the star stops collapsing at some radius x and is a stable white dwarf. If I add mass to this white dwarf, the strength of the gravitational force on it will increase, and eventually, overcome the strength of the destructive interference and the star will collapse further resulting in supernova or further degeneration into a neutron star, therefore there must be a quantifiable strength of this destructive interference, much like you can describe the strength of other forces using functions like "inverse square of the distance" just for example. So what is that function that describes the strength of the degeneracy pressure that holds up a white dwarf? In other words, how do i know what strength of gravity i need to overcome it?
Just quickly ...

Think of the humble helium atom, or the neon atom, at very cold temperatures. The electrons, classically, are still zipping along quite nicely; in QM they occupy energy levels. The outer electrons in the neon atom at in higher energy levels than the inner ones.

Now try to squeeze a lot of neon atoms. They will form a solid, and the structure of the solid will, if in equilibrium, be one that minimises a certain energy measure.

Squeeze more and the electrons become liberated from the atoms, and become a Fermi sea. Being electrons, they can only populate the available energy states two at a time; being in equilibrium, they populate the energy states from the lowest levels up. Classically, the energy states correspond to electrons moving at different speeds; in QM they don't. Of course, the allowed energy states are much, much closer together than those of an isolated neon atom!

So why can't the electrons be squeezed into ever higher and higher (degenerate, Fermi) energy states, ad infinitum?

Because, classically, they begin to have 'speeds' that are relativitistic, the electrons gain mass* (even though they don't, in QM, move!), and at a certain point inverse beta decay becomes energetically favourable (just as it is in certain proton-rich radioactive nuclides, without being squeezed), the electrons in the highest energy states are 'lost', the degeneracy pressure falls, and a runaway reaction follows (just what sort of reaction depends on things like the elemental composition of the object).

* OK, this is a long way from being a good description, but how does one explain this stuff without being at least somewhat misleading?

Grey
2010-Jul-22, 02:51 PM
Forgive me if i failed to understand your answer, I am new to wave mechanics. But in my understanding kinetic energy doesn't really come into play here.

In the case of a white dwarf, the pressure (aka pauli exclusion, aka destructive interference) is an outward force holding up the star, not a compressing force. It's gravity that is the compressing force. At some point as the white dwarf is collapsing in on itself due to gravity, the strength of destructive interference becomes as strong as the gravitational force and the star stops collapsing at some radius x and is a stable white dwarf. If I add mass to this white dwarf, the strength of the gravitational force on it will increase, and eventually, overcome the strength of the destructive interference and the star will collapse further resulting in supernova or further degeneration into a neutron star, therefore there must be a quantifiable strength of this destructive interference, much like you can describe the strength of other forces using functions like "inverse square of the distance" just for example. So what is that function that describes the strength of the degeneracy pressure that holds up a white dwarf? In other words, how do i know what strength of gravity i need to overcome it?Take a look at the exchange interaction (http://en.wikipedia.org/wiki/Exchange_interaction). That's essentially looking at how this issue affects the expectation values of various quantities when the wavefunctions of particles overlap.

Nereid's got the right explanation for how to quantify when a white dwarf cannot be sustained. It's not so much that gravity overcomes the "force" of the electron degeneracy pressure. It's that as you add more and more electrons, the lowest available state has a higher and higher Fermi energy. Eventually, that Fermi energy is higher than the amount needed for the electron to combine with a proton, and form a neutron. When that starts happening, the object gets compressed, the Fermi energy increases, and more and more electrons undergo reverse beta decay. You can, though, model that degeneracy pressure as an actual pressure, or as a degeneracy energy. Here (http://www.sciencebits.com/StellarEquipartition) are a couple (http://nucleo.ces.clemson.edu/home/online_tools/polytrope/0.8/html/about_this_tool/tutorials/max_mass.shp.cgi) of examples of doing just that.

Ken G
2010-Jul-22, 03:40 PM
Let me clear up a couple points that could get confused. The degeneracy pressure I referred to above is not a compressive force, it is indeed an outward force, but it is really only a force in effect-- the "effect" referred to is quantified by asking how much kinetic energy you need to add to get a given drop in the total volume of the star (pressure can be thought of as energy added per volume drop, but the pressure isn't what adds the energy, it is gravity that does that, to clarify CaptainToonces' point).

As for what breaks down white dwarfs, what happens is that as you add mass to a white dwarf, the gravity strengthens, and so it is able to add more energy when the star contracts. As long as the gravity is able to add enough kinetic energy to increase the curvature of the electron wave functions, they can be fit in smaller boxes, and the electrons stay happy when gravity compresses them. However, if the electrons are not relativistic, they always reach a point, for any mass of the white dwarf, where they are no longer "willing" to be compressed-- they would need more kinetic energy to curve their wave functions (picture a bar being bent to put it in a box) than gravity is able to provide. So for any mass of white dwarf, there would be some minimum radius, and the radius gets smaller as the mass increases.

However, Nereid''s point is that eventually, the kinetic energy of the electrons approach 500 keV, and then the electrons start to go relativistic. As they get more relativistic, the kinetic energy you need to add to curve their wave functions enough to fit into smaller boxes is not as much as it would be nonrelativistically-- the "bar" gets easier to bend. If you keep adding mass to the white dwarf, the electrons get more and more relativistic, and when the mass gets to about 1.4 solar masses, they get so relativistic that gravity can always provide the needed energy to get them to compress any amount it wants. So it compresses them completely-- the white dwarf is completely crushed (and if it is in the core of a massive star at the time, this causes a core-collapse supernova).

As for the neutronization of the electrons, that's kind of a detail that does not have much to do with the crushing of the white dwarf-- instead, it has to do with the "last gasp" that 1.4 solar mass white dwarfs have to avoid being completely crushed to a point (a black hole). Neutrons have higher rest masses, so when electrons are neutronized, they go nonrelativistic, and return to their "harder to squish" mode, forcing gravity to provide more energy than it has available to get further crushing. However, the core is already the size of a city by this point, not the size of the Earth (as for a white dwarf), so the core collapse (and its supernova) has already happened. It's just a "last gasp" way to avoid a black hole-- to get the neutrons to go relativistic (and become "squishy" enough to compress to a point), you need a core mass like 3-4 solar masses, not 1.4.

trinitree88
2010-Jul-22, 03:48 PM
Neat stuff, Pete - thanks! I'm fairly well versed with electrons (both chemistry and physics), but hadn't heard of the similar concept with nucleons, probably because that gets into nuclear physics, which is beyond the typical sophomore level in either chem or phys in the school I attended. I think it's a class (or classes) in jr and/or sr years for both chem and phys.

Mugs. You're welcome. I think it actually helps when teaching the QM of electrons' states in the hydrogen atom, to extend it one step smaller, but more energetic into the magic numbers of the nuclei......then I wait for the student who thinks there might be another smaller structure. Yep. The nucleons themselves were found to exist in higher energy states, such as the delta. The delta decays to a proton, or neutron, and years after it's discovery, it was seen that the quarks in the proton may be bumped up (they circulate too) to higher energy levels from which they decay. This conceptualization carries over to other baryons/hyperons. From what we know, the levels stop there, hence the Standard Model with quarks and leptons. pete

SEE:http://en.wikipedia.org/wiki/Delta_baryon

SEE:http://en.wikipedia.org/wiki/Hyperon

SEE:http://en.wikipedia.org/wiki/Standard_Model

forrest noble
2010-Jul-22, 07:30 PM
korjik,

........ Physicists actually learn what QM is, not just make assumptions and hand-waving statements that make it look like there is a problem in the understanding of a phenomena.

Of course they don't make it look like there is a problem with their understanding of phenomena or that they really don't know what spin really is.

This is a quote from this link. http://en.wikipedia.org/wiki/Spin_(physics)

spin is a fundamental characteristic property of elementary particles............

My quote was
Most practitioners in Physics consider spin as a characteristic of atomic particles.......

The is a quote from a relevant link.

Nobody really knows what spin is, much beyond the fact that it is an attribute of an elementary particle.

Anybody can say, concerning a posting, that "everything in this post is wrong" as you did to mine just by making vague references. This is not what answering questions or providing information is all about. If you think statements are incorrect in a posting you need to be specific concerning your opinions and it is wise to always post links when making specific criticisms of specific statements, otherwise it is just he said, she said -- non-corroborated criticisms that may have no value.

Instead if you cannot find related links for what you believe to be true, you could ask if a link(s) be provided for a particular statement(s). The primary purpose Of Q & A is to provide accurate information to the questioner.

korjik
2010-Jul-22, 09:00 PM
korjik,

Of course they don't make it look like there is a problem with their understanding of phenomena or that they really don't know what spin really is.

This is a quote from this link. http://en.wikipedia.org/wiki/Spin_(physics)

My quote was

The is a quote from a relevant link.

Anybody can say concerning a posting that "everything in this post is wrong" as you did to mine just by making vague references. This is not what answering questions or providing information is all about. If you think statements are incorrect in a posting you need to be specific concerning your opinions and it is wise to always post links when making specific criticisms of specific statements, otherwise it is just he said, she said -- non-corroborated criticisms that may have no value.

Instead if you cannot find related links for what you believe to be true, you could ask if a link(s) be provided for a particular statement(s). The primary purpose Of Q & A is to provide accurate information to the questioner.

The primary purpose of Q&A is to provide accurate information to the questioner, not to allow you to confuse the issue with your extremely flawed understanding of physics. Trying to fix your misunderstandings is a pretty useless endeavour, and not really appropriate for this thread or Q&A in general. I am just unwilling to let stand when you make a post that will only confuse people and will leave a note that the post should be disregarded.

Swift
2010-Jul-22, 09:12 PM
Anybody can say concerning a posting that "everything in this post is wrong" as you did to mine just by making vague references. This is not what answering questions or providing information is all about. If you think statements are incorrect in a posting you need to be specific concerning your opinions and it is wise to always post links when making specific criticisms of specific statements, otherwise it is just he said, she said -- non-corroborated criticisms that may have no value.

Instead if you cannot find related links for what you believe to be true, you could ask if a link(s) be provided for a particular statement(s). The primary purpose Of Q & A is to provide accurate information to the questioner.

The primary purpose of Q&A is to provide accurate information to the questioner, not to allow you to confuse the issue with your extremely flawed understanding of physics. Trying to fix your misunderstandings is a pretty useless endeavour, and not really appropriate for this thread or Q&A in general. I am just unwilling to let stand when you make a post that will only confuse people and will leave a note that the post should be disregarded.
The primary purpose of Q&A is to provide accurate, mainstream information to the questioner. It is absolutely not about critiquing each others posts or to debate the primary purpose of Q&A. If you have a problem with someone else's post, you Report it.

forrest noble, if you want to address technical concerns brought up by another member, or to discuss the subtle problems of QM, then do so, but don't get into a debate about posting styles.

Now everyone, knock it off.

mugaliens
2010-Jul-23, 01:28 AM
Mugs. You're welcome. I think it actually helps when teaching the QM of electrons' states in the hydrogen atom, to extend it one step smaller, but more energetic into the magic numbers of the nuclei......then I wait for the student who thinks there might be another smaller structure. Yep. The nucleons themselves were found to exist in higher energy states, such as the delta. The delta decays to a proton, or neutron, and years after it's discovery, it was seen that the quarks in the proton may be bumped up (they circulate too) to higher energy levels from which they decay. This conceptualization carries over to other baryons/hyperons. From what we know, the levels stop there, hence the Standard Model with quarks and leptons. pete

SEE:http://en.wikipedia.org/wiki/Delta_baryon

SEE:http://en.wikipedia.org/wiki/Hyperon

SEE:http://en.wikipedia.org/wiki/Standard_Model

Curioser and curioser (http://en.wikipedia.org/wiki/File:Particle_overview.svg)... If we can split the nucleous, any chance we'll ever be able to split a nucleon, or are the requisite energies just way too high for it to ever have any practical application? And what of leptons and quarks - how much of a chance is there that they're not as fundamental as we think? What's the liklihood that at higher and higher energies we find there is no limit, that fermions are infinitiely divisible "knots" of bound energy? We may never recreate energies on the scale of Planck temperature (http://en.wikipedia.org/wiki/Planck_temperature)(1.4x1032 K), but I do believe that's a limit (or at least the TOE merging point between gravity and fermions). If so, fermions are not infinitely divisible.

Am I correct? Off target? Out to lunch?

Regardless, here's an interesting diversion (http://www.pbs.org/wgbh/nova/zero/hot.html).

EigenState
2010-Jul-23, 02:55 AM
Greetings,

I have spent close to 30 years investigating the manifestations of spin on such diverse physical phenomena as high resolution (Doppler-free) optical spectroscopy, magnetic resonance spectroscopy, hyperfine structure interactions, and both chemical dynamics and spin dynamics. Spin is simple. Spin is an intrinsic angular momentum. That is it! Spin is quantized. And as pointed out above by Ken G, spin has no, repeat no classical analog. If there is a problem, it is with having chosen to use the word "spin".

The value of any given spin quantum number is the value of the projection of that angular momentum onto some specified direction in 3-space. That projection can take on only discrete values in units of h-bar. Thus for the electron spin, values of ±½(h-bar).

Again, that is it! There is nothing more except for understanding the phuysical manifestations of spin angular momentum.

Best regards,
EigenState

forrest noble
2010-Jul-23, 03:37 AM
EigenState,

If there is a problem, it is with having chosen to use the word "spin".

The question then becomes if angular momentum does not refer to physical spin then what does that angular momentum actually refer to? You may be wrong if you believe there is ultimately no answer to this question. There are seemingly countless problems still remaining in quantum physics. As for now angular momentum is the correct answer concerning how spin should be interpreted, as you have stated.

grapes
2010-Jul-23, 03:47 AM
If an electron really was spinning, how could that spin develop into a magnetic moment if the charge is evenly distributed within the electron. To think of the electron as made of little areas of charge cause even more problems than just accepting that a magnetic moment is a fundamental property of the particle. Let us not forget that there's a magnetic moment from the particle's 'spin' and another from its 'orbit'.Part of the reason that the word "spin" was used, I suppose, because we're used to magnetic moment being produced from circular motion. I believe (correct me if I'm wrong haha) that most of what we observe as natural magnetism is a result of 'spin' rather than 'orbit'.

Geo Kaplan
2010-Jul-23, 04:09 AM
EigenState,

The question then becomes if angular momentum does not refer to physical spin then what does that angular momentum actually refer to? You may be wrong if you believe there is ultimately no answer to this question. There are seemingly countless problems still remaining in quantum physics. As for now angular momentum is the correct answer concerning how spin should be interpreted, as you have stated.

EigenState's viewpoint is precisely the mainstream view. Angular momentum does not require classical spinning any more than momentum requires mass. Just because these concepts historically derived from classical physics does not mean that they are forever bound to them. If your understanding differs from that of, er, "practitioners of physics", you should be asking questions in your own thread, not answering them.

forrest noble
2010-Jul-23, 04:34 AM
Geo Kaplan,

EigenState's viewpoint is precisely the mainstream view

This is exactly what I said if you wish to more closely read and understand what I said ".......angular momentum is the correct answer concerning how spin should be interpreted, as you have stated." Also see what Grapes stated in posting #31 which I believe is very relevant.

Geo Kaplan
2010-Jul-23, 05:02 AM
Geo Kaplan,

This is exactly what I said if you wish to more closely read and understand what I said ".......angular momentum is the correct answer concerning how spin should be interpreted, as you have stated." Also see what Grapes stated in posting #31 which I believe is very relevant.

Noted, but it got lost among the other dilutive verbiage of yours. I indeed read your posting closely, which is precisely why it was necessary to write what I wrote.

Len Moran
2010-Jul-23, 07:21 AM
I’m still working my way through the distinction between “intrinsic” properties and “measured” properties within quantum mechanics, so some confusion on my part will be obvious as far as my question is concerned here.

Is spin considered to be an intrinsic property of (say) an electron? I have previously thought of spin as being a measurable property, like the spin UP and spin DOWN measurable through the Stern Gerlach apparatus. But on reflection, if spin is intrinsic to the electron, then I suppose in terms of the Stern-Gerlach apparatus we are really measuring the manifestation of spin within a magnet, rather than the intrinsic property of spin that is associated with the electron outside of any measurement.

I have (I think erroneously now) been thinking of any property of an elementary particle as being part of a quantum state and always referenced to the observable (and in my opinion the observer). But spin seems to fall outside of that category as far as I can tell from this discussion and what I have subsequently read on Wiki.

Would this be correct, and if so, does this mean that the property of spin is not directly part of experimental physics? For example it seems that the spin of a photon differs to that of an electron, and clearly experimental physics can distinguish between a photon and electron in terms of attributes associated with those particles upon measurement and setup by an observer. But experimentally, can we perform any measurement that directly makes a distinction between a spin 1 and a spin 1/2?

In other words, I suppose what I am really asking throughout this post is, can the intrinsic spin of an elementary particle be directly measured (and hence would then be a property referenced to the observer rather than being an intrinsic property of the particle)? I think not, but if any one can clarify this for me I would be grateful.

Strange
2010-Jul-23, 09:59 AM
Spin is an intrinsic angular momentum. That is it! Spin is quantized. And as pointed out above by Ken G, spin has no, repeat no classical analog. If there is a problem, it is with having chosen to use the word "spin".

Just an idle observation prompted by this.

There is a desire (perhaps mainly among non-specialists) to try and relate things at the quantum level to our everyday experience. Clearly, this often fails (e.g. wave-particle "duality").

There are some properties of fundamental particles that do relate to our experience in the classical world in some way. There seem to be two classes. In some cases, they are familiar because we see the effects fairly directly; for example, we are familiar with charge from the "bulk" effects in classical electricity. Ditto mass.

On the other hand, we don't see the effects of spin at the macro level but, because we are famililar with angular momentum in the classical world, there is a natural tendency to interpret "spin" as, well, spin. (Hence the name, for better or worse.)

Then there are other quantities that have no analog in the "real" world, such as quark color.

It seems that people have more of a problem with things that look like they should be familiar but aren't (spin) than they do with things that either correspond to macro quantities (charge) or that have no real-world analog (color).

But ultimately they are all just inherent properties of these "particles"; they are what they are.

Geo Kaplan
2010-Jul-23, 10:59 AM
Just an idle observation prompted by this.

There is a desire (perhaps mainly among non-specialists) to try and relate things at the quantum level to our everyday experience. Clearly, this often fails (e.g. wave-particle "duality").

There are some properties of fundamental particles that do relate to our experience in the classical world in some way. There seem to be two classes. In some cases, they are familiar because we see the effects fairly directly; for example, we are familiar with charge from the "bulk" effects in classical electricity. Ditto mass.

On the other hand, we don't see the effects of spin at the macro level but, because we are famililar with angular momentum in the classical world, there is a natural tendency to interpret "spin" as, well, spin. (Hence the name, for better or worse.)

Then there are other quantities that have no analog in the "real" world, such as quark color.

It seems that people have more of a problem with things that look like they should be familiar but aren't (spin) than they do with things that either correspond to macro quantities (charge) or that have no real-world analog (color).

But ultimately they are all just inherent properties of these "particles"; they are what they are.

Exactly. In the particular case of the OP, the difficulty ultimately derives from the use of a familiar word -- spin -- to describe something totally unfamiliar. The natural inclination is to associate imagery from the macroscopic world with the word. Unfortunately, that doesn't work. Perhaps if Goudsmit and Uhlenbeck had called it "shnorgularity" instead, there would be less of a problem. But the word is what it is, and we have to live with the consequences.

EigenState
2010-Jul-23, 01:41 PM
Greetings,

I’m still working my way through the distinction between “intrinsic” properties and “measured” properties within quantum mechanics, so some confusion on my part will be obvious as far as my question is concerned here.

Is spin considered to be an intrinsic property of (say) an electron? I have previously thought of spin as being a measurable property, like the spin UP and spin DOWN measurable through the Stern Gerlach apparatus. But on reflection, if spin is intrinsic to the electron, then I suppose in terms of the Stern-Gerlach apparatus we are really measuring the manifestation of spin within a magnet, rather than the intrinsic property of spin that is associated with the electron outside of any measurement.

An "intrinsic" property is a fundamental, inherent property of a thing, such as the electron, and is independent of the amount or mass of the sample of things. Thus each and every electron has spin under any set of conditions.

What is measured is the particular manifestation of the projection of spin onto some direction in 3-space. Generally, that specific direction in 3-space is defined by an external, applied field as in the case of the Stern-Gerlach experiment. In atomic and molecular spectroscopy the manifestations of spin, electron and nuclear, result from the spin being quantized along the direction of the orbital angular momentum as one example.

I have (I think erroneously now) been thinking of any property of an elementary particle as being part of a quantum state and always referenced to the observable (and in my opinion the observer). But spin seems to fall outside of that category as far as I can tell from this discussion and what I have subsequently read on Wiki.

Spin is always there. The observable is the change in the projection of the angular momentum as quantized along some specified field direction.

But experimentally, can we perform any measurement that directly makes a distinction between a spin 1 and a spin 1/2?

Trivial experiment! Consider the Stern-Gerlach experiment. The original experiment utilized spin 1/2 particles and an inhomogeneous external magnetic field. The result was two distinct separated ensembles of silver atoms deposited on the detection screen: one for Sz = +1/2, one for Sz = -1/2. If they had utilized a spin 1 particle, there would have been three distinct separated deposits: one for Sz = +1, one for Sz = 0, and one for Sz = -1.

Best regards,
EigenState

Strange
2010-Jul-23, 01:48 PM
Exactly. In the particular case of the OP, the difficulty ultimately derives from the use of a familiar word -- spin -- to describe something totally unfamiliar.

And I was going to say, isn't it odd that this property has the dimensions of angular momentum (hence it being called spin). But, of course, that is only one interpretation of a value with those dimensions.

CaptainToonces
2010-Jul-23, 05:18 PM
Hi EigenState. Great to hear from someone with your level of experience!

Can you provide the formula that describes how the two electrons in a helium atom repel an incoming electron according to its distance away?

EigenState
2010-Jul-23, 06:30 PM
Greetings,

Can you provide the formula that describes how the two electrons in a helium atom repel an incoming electron according to its distance away?

That is a problem in collisional dynamics which is not my field. That said, I would approach it first by constructing the potential energy surface or wavefunction of whatever specific electronic state of He you wish to consider, and by treating the incoming free electron in terms of a Coulomb interaction with that potential energy surface. Obviously, one would need to include considerations of the kinetic energy of the incoming free electron and its trajectory relative to the He atom. There are different theories of electron-atom collisions that depend on the energy regime of the process. Such interactions would typically be characterized in terms of a collisional "cross section" which simply denotes some measure of the efficiency of the collisional process.

It also depends upon whether you want to treat elastic or inelastic collisions, or both of course. An elastic collision is defined as one in which there is no change in quantum state of the target atom. An inelastic collision is defined as one in which there is a change in quantum state of the target atom.

For some grater detail see: Introduction to the NIST Electron-Impact Cross Section Database (http://physics.nist.gov/PhysRefData/Ionization/intro.html).

Best regards,
EigenState

Ken G
2010-Jul-23, 09:14 PM
Can you provide the formula that describes how the two electrons in a helium atom repel an incoming electron according to its distance away?
I believe CaptainToonces is asking about degeneracy pressure here, not Coulombic repulsion. I'm trying to make the point that degeneracy pressure is not at all a force like Coulombic repulsion, so does not admit the same kind of language in describing it. Instead, it is an interference effect, that alters the probability of various things happening, based on the requirement that the multiple particle wave function be antisymmetric under exchange of identical half-integer-spin particles. Since it alters the probabilities of finding the electrons in various places in correlation with the places the other electrons are found (by an experiment that locates electrons, say), that also has energetic consequences due to the Coulombic interactions, but that's a separate effect from basic degeneracy pressure. Degeneracy pressure is a way to express the fact that it requires adding kinetic energy to particles to compress them further when their locations begin to interfere with each other, expressly to suppress that destructive interference in the multiple-particle wave function. Hence, it is not a "force" in the classical sense and cannot be written as a force on one electron as it approaches others. Indeed, it wouldn't exist at all if the approaching particle were not identical and interchangeable with the others, a property that is ignored in the language of standard classical forces.

EigenState
2010-Jul-23, 10:00 PM
Greetings,

My apologies. I certainly did misinterpret the question.

But now he has the opportunity to learn about both degeneracy pressure and atom-electron scattering.

Best regards,
EigenState

Ken G
2010-Jul-23, 10:49 PM
True enough, and that may even have been what he was asking. We've had a debate recently on how "prescient" our answerers should try to be when interpreting questions-- I prefer your approach, that any information is potentially important information, and the questioner does not always know what information they need to know when they ask the question.

slang
2010-Jul-23, 11:55 PM
[...] and the questioner does not always know what information they need to know when they ask the question.

Besides, the questioner may not be the only one reading this thread looking for answers, or for snippets of understanding.

Len Moran
2010-Jul-24, 01:12 AM
An "intrinsic" property is a fundamental, inherent property of a thing, such as the electron, and is independent of the amount or mass of the sample of things. Thus each and every electron has spin under any set of conditions.

Thank you for your reply - I wonder if I can just clarify this for myself. Is it the case that the intrinsic property of spin (as opposed to the projection of spin onto 3-space in terms of a measurement) is purely a mathematical property, rather than being a physical property?

I think of physical properties at the quantum level to be entirely referenced to observation, but presumably mathematical properties (in this case the intrinsic property of spin) have no such restrictions.

Any clarification would be appreciated.

EigenState
2010-Jul-24, 01:25 AM
Greetings,

...Is it the case that the intrinsic property of spin (as opposed to the projection of spin onto 3-space in terms of a measurement) is purely a mathematical property, rather than being a physical property?

Please allow me to push you intellectually on this point. If spin angular momentum, what most here have been referring to simply as spin (which I usually do myself), is a purely mathematical property, then how could the projection of that purely mathematical property onto some specified direction in 3-space be a physical, observable property?

I am not trying to be a semantic nitpicker here. I am trying to get you to think through this on your own. Think about it and we can follow up tomorrow.

Best regards,
EigenState

Ken G
2010-Jul-24, 04:02 AM
Is it the case that the intrinsic property of spin (as opposed to the projection of spin onto 3-space in terms of a measurement) is purely a mathematical property, rather than being a physical property? I think of physical properties at the quantum level to be entirely referenced to observation, but presumably mathematical properties (in this case the intrinsic property of spin) have no such restrictions.I think there are some deep questions here about what one means by "referenced to an observation", versus a "mathematical property." As I take your meaning, you would classify the wave function as a "mathematical property", whereas the experiments that wave functions can be used as tools to predict are "physical properties". So if someone asks you "is a wave function part of reality", you might say "it is not part of the observation itself, but it is part of the mathematical machinery for understanding the outcome." So I think your question could be stated, "is intrinsic spin more like the wave function, or more like the observable?" And I think that is kind of a tough question, because spin is an even more profound concept than a wave function. Spin can be thought of as a kind of high-order geometric behavior of a wave function under rotation.

Specifically, if you rotate the space occupied by a wave function of a spin 1/2 particle all the way around, 360 degrees, the wave function picks up a minus sign, and that has physical and observable ramifications, though the sign of the wave function is never itself directly observable. This is very deep and difficult stuff, related to the mathematical concept of a spinor (which I don't really understand myself at present), so one might be tempted to say that spin is even more mathematical than wave functions. But as has been mentioned, the components of spin are measurables, so correspond to operators in quantum mechanics (like Sz, with eigenvalues +1/2 or -1/2 for an electron in h-bar units). And there is a total spin operator, which normally appears squared, and is written
S2 = Sx2 + Sy2 + Sz2,
with eigenvalue s*(s+1) in h-bar-squared units, with s=1/2 for the electron. So we do have observables here that correspond to components of spin, and total spin, which makes it sound more like the kind of thing that wave functions predict, moreso than being a wavefunction itself. But I think if you ask a mathematical physicist what spin "is", you'll get an answer involving the spinor concept, which means a concept of the geometrical behavior under rotations of a complex-valued wave function.

Also, to really understand spin (and the origin of the Pauli exclusion principle), you apparently have to even treat this problem relativistically, and deal with what are called Dirac spinors, which have to do with geometric properties of the wave function in spacetime, not just space (which I view as an interesting overlap of relativity and quantum mechanics, normally considered ill-fitting, so I wish I understood this better). I won't begin to go there, because I don't have a clear understanding myself, but what I'm saying is, there is a very sophisticated mathematical machinery at work in the concept of spin, but it also gives rise to some directly observable properties, so it's not necessarily obvious which version one is talking about when one talks about "spin," the mathematical machinery (which most people, even physicists, never learn, frankly) or the observable consequences (which tends to be what physicists of typical education will mean by the term). So I'm going to cop out and say the answer to your question is "both", but defer you to someone who really understands spin to get a better answer.

Len Moran
2010-Jul-24, 11:14 AM
Greetings,

Please allow me to push you intellectually on this point. If spin angular momentum, what most here have been referring to simply as spin (which I usually do myself), is a purely mathematical property, then how could the projection of that purely mathematical property onto some specified direction in 3-space be a physical, observable property?

I am not trying to be a semantic nitpicker here. I am trying to get you to think through this on your own. Think about it and we can follow up tomorrow.

Best regards,
EigenState

Thanks for your continued interest in this question of mine.

I am basically uneasy over the context of the word “properties”, and I think Ken G sums my uneasiness up quite well when he says:

I think there are some deep questions here about what one means by "referenced to an observation", versus a "mathematical property." As I take your meaning, you would classify the wave function as a "mathematical property", whereas the experiments that wave functions can be used as tools to predict are "physical properties". So if someone asks you "is a wave function part of reality", you might say "it is not part of the observation itself, but it is part of the mathematical machinery for understanding the outcome." So I think your question could be stated, "is intrinsic spin more like the wave function, or more like the observable?" And I think that is kind of a tough question, because spin is an even more profound concept than a wave function. Spin can be thought of as a kind of high-order geometric behavior of a wave function under rotation.

My starting point for this is the notion of counterfactuality at the quantum level. I only state it here for completeness, you will obviously be quite familiar with this term and its breakdown at the quantum level.

I make a counterfactual reasoning when I say to myself: “By performing such and such an operation (for example going and seeing) I found that such and such a quantity has such and such a value. I consider this quantity would have this value, even if I had not performed the operation in question”. (From Bernard d'Espagnat, “On physics and Philosophy").

In terms of experimental physics, we can set the initial conditions and from that predict the outcome probabilities in terms of observations. What we observe is not assumed to be present prior to that observation, thus the properties are not intrinsic to whatever it is that exists in between the source and sink - they are (in part) a manifestation of the observer. The observation is all we get to access directly, and that observation I consider to essentially constitute empirical reality. Thus conterfactuality breaks down at the quantum level.

If we say that an electron has an intrinsic property of spin, then in this instance counterfactuality holds at the quantum level. Now this seems quite profound to me, for we are scientifically defining an electron as having a known property that exists in that form independently of any observer. But what is contained within this intrinsic property of spin that allows us to consider this property as “existing” at the quantum level in a form that transcends observer involvement rather in the way we consider a macroscopic property does?

I can readily understand how an abstract mathematical notion (which is what I consider a wavefunction to be) can predict outcomes, but those outcomes are always referenced to observation. So whilst it may be said that the mathematical notion of spin is connected to our observations, I would consider that the fundamental nature of what lay under that connection is outside of empirical reality and the scientific method. So whilst I don't think that a pure (in the sense of only being a property of the mind) mathematical property can project itself onto our macroscopic reality and produce an observable result, it is obviously the case some mathematics can be used in a manner that predicts those observational results. But I'm not sure that the predictive nature of that procedure can be taken as any kind of scientific proof that the mathematics in question are a direct and familiar representation of a physical property of spin (or any other aspect) that transcends human involvement. I think that (philosophically) there is bound to be a connection to nature as it exists outside of empirical reality, but the nature of that reality is not describable in any scientific manner when viewed from the philosophical perspective of open realism that I come from - the scientific method demands the exclusion of any effect that sentient beings have, but I would say that we have no scientific procedure in which to establish that such a scenario exists. Thus (importantly), I also consider physical realism to be a philosophical stance because there is no scientific evidence that we do have access to reality outside of our involvement through the use of mathematics. However if you were to suggest that, using the scientific method, we can properly describe an electron as having known and genuine intrinsic properties outside of any measurement, then that would certainly give me pause for thought.

Thus (from my perspective) any reference to spin as being an intrinsic property of an electron should not be thought of as giving scientific access to nature as it exists outside of sentient beings. I think it gives a philosophical access, but not a scientific one.

I don’t pretend to be clear on all of this myself, and the technical issues are well outside of my abilities – certainly the issues Ken G has raised in his post have raised the technical level to beyond anything that I can properly contemplate, but I do have a genuine personal interest in what the scientific method can tell as about nature as it exists outside of sentient beings. To what extent one can do this without the expertise in physics I’m not sure, but I do tend to pick up on physicists who deliberately take an interest in such matters. Bernard d’Espagnat is one of these, and so is Ken G on this forum. Certainly d’Espagnat, in his last book “On Physics and Philosophy” made available very profound thoughts on the nature of quantum mechanics in a manner that required little technical knowledge of the formalism.

So any clarification you are able to give to this aspect of intrinsic spin within the context I have described would be most welcome.

Len Moran
2010-Jul-24, 11:29 AM
I think there are some deep questions here about what one means by "referenced to an observation", versus a "mathematical property." As I take your meaning, you would classify the wave function as a "mathematical property", whereas the experiments that wave functions can be used as tools to predict are "physical properties". So if someone asks you "is a wave function part of reality", you might say "it is not part of the observation itself, but it is part of the mathematical machinery for understanding the outcome." So I think your question could be stated, "is intrinsic spin more like the wave function, or more like the observable?" And I think that is kind of a tough question, because spin is an even more profound concept than a wave function. Spin can be thought of as a kind of high-order geometric behavior of a wave function under rotation.

Thanks for this, I think the example you gave of the wavefunction sums up my thinking entirely. But you have included aspects here that as you say, go beyond the wavefunction. I am unsure whether all of this can be reduced to what I consider to be my "bed rock" of quantum mechanics, which is the simple but powerful notion of counterfactuality and its breakdown at the quantum level. It seems to me that if we can say an electron has an intrinsic spin then counterfactuality at the quantum level does not break down in this instance. And that seems (to me at any rate, and the level I come into this at) to be a pretty fundamental and very important thing to say because it implies that we can establish properties that have an existence in that form outside of any reference to sentient beings. And that statement leads to a scientific justification of physical realism, whereas I have always considered physical realism to be a philosophical stance.

As always, any clarification would be welcome.

Ken G
2010-Jul-24, 02:36 PM
I think the issues here go deeper than just quantum mechanics, they are endemic to science itself, and these kinds of questions existed even before there was any quantum mechanics. For example, we could ask, is time real, or did intelligence invent it? The way time works in relativity is quite a bit different than how it works in quantum mechanics, so we can say that what conceptual meaning we give the word "time" must be addressed in the context of a theory. Yet, time can also be measured, so when we ask "what is time", there is ambiguity about whether we are asking about the measurable or the theory we choose to understand the measurable. It is the same with "intrinsic properties" of particles, like spin, or rest mass. Even in relativity, there are "invariant" properties (like rest mass) that do not need to invoke any information about the observer, but the laws that invoke that property do need an observer to test those laws. That's the unique role of observation in any science, not just quantum mechanics-- science is always the study of the outcome of observations, yet our conceptual understanding of those outcomes is theoretical, not observational. Does something count as a "mathematical property" because it is part of a theory that gives it conceptual meaning, or is it a "physical property" because we can measure it, say rest mass or intrinsic spin, and always get the same answer connected with a given particle? I'm not sure that this distinction can be made in a uniform way-- do not ask if "mass" or "spin" is mathematical or physical, instead, say whether you are interested in the mathematical or physically measurable aspects of that property.

EigenState
2010-Jul-24, 05:07 PM
Greetings,

The two of you are getting deeply into philosophy now. Years ago while at Yale, a friend and colleague became infatuated with "Hidden Variables." Every time we had coffee together, that was all he would discuss. I came to realize that I could pursue either science or philosophy, but that I had neither the time nor the talent to pursue both. My career was already established so it was easy for me to decide to stick with science. I shall do the same here now.

In a different thread here at the forum, one mentioned above I believe, I was critical of the approach this forum takes to addressing questions. I believed, and still do believe, that the opportunity to learn is the vital objective and that the fundamentals of the philosophy under which science is done is important. I have always attempted to help my students hone their thinking skills--above all else to make their intellectual processes more objective and more independent. I stand by that approach. In my considered opinion, discussions such as this one serve that objective. The topic is complex in many ways and there are no simple answers, but that is no reason to sweep them under the rug.

In that other thread I mentioned that I had become so disheartened that I had asked for my membership to be closed. Obviously that did not happen, and I was lured back by a personal request for assistance on a matter of spectroscopy. Then I noticed the word "spin" and...well you know the rest on that. It is now time for me to depart.

Very best regards,
EigenState

Cougar
2010-Jul-24, 06:01 PM
...I believed, and still do believe, that the opportunity to learn is the vital objective and that the fundamentals of the philosophy under which science is done is important.

Very well put.

It is now time for me to depart.

Don't be ridiculous. :lol:

Ken G
2010-Jul-24, 06:16 PM
Obviously that did not happen, and I was lured back by a personal request for assistance on a matter of spectroscopy. Then I noticed the word "spin" and...well you know the rest on that. It is now time for me to depart.

You are correct that we've been discouraged to get into the philosophical issues of spin, in favor of treating that in a separate thread. I hope you won't be turned off by that attitude, but instead, join a thread like that if it opens. All I'm saying is, when someone asks in an OP (or as Len Moran is now doing) "what is spin", they need to also stipulate whether they are interested in the theoretical concept of spin, or the observational consequences of spin. The two are quite different, so it's not really getting philosophical to make that distinction, it's doing what you said it was-- honing our ability to understand a question before we can truly try to answer it. The problem is, the question evolves-- the OPer wants to know about the Pauli exclusion principle, but to understand that, one has to understand the asymmetry of the wave function when you swap identical particles. That naturally brings up the question of what angular momentum has to do with exchange properties, and that brings in the connection between spin and geometric aspects of the wave function, which is where the answer to the OP actually lies (and it's all in that mathematical/theoretical realm, not in the observational meaning of spin). How far does the OPer want to go down that road, and how far do other curious onlookers want to go? We could probably say the OP question has been answered (the Pauli exclusion principle involves destructive interference pursuant to the geometrical requirements of half-integer spin), and then say if anyone wants to go deeper into spin, perhaps even into the philosophical question of what is the difference between an observable attribute and a mathematical construct, they should probably start a new thread on those other questions.

One approach would be to ask zerocold if the original question has been answered, or if there is more interest in probing the theoretical/observational/philosophical aspects of spin. But as is often true, the OPer has not returned visibly to the thread, whereas many other people have entered their own questions. Why we can't just let the thread evolve to treat those is beyond me, but it is the stated intent of this part of the forum.

And by the way, I personally hope that you do stick around-- you have interesting knowledge that we all benefit from, and are very clear and polite in how you present it.

EigenState
2010-Jul-24, 08:50 PM
Greetings,

For the sake of clarity, I have no problems whatsoever with the evolution of this thread. On the contrary, I found it logical and intellectually satisfying. Nor do I have any problems with any of the contributors to this thread. I did not even mind being denounced as ridiculous by someone I do not know. I opted not to pursue the philosophical discussions not form lack of interest, but from lack of time. Such a discussion is something in which I would become immersed, and I simply do not have that luxury.

My decision not to participate in this forum was made some time ago. I violated that decision to help a member on a matter of spectroscopy after being contacted personally at a different forum, and further violated it by contributing to this thread. While I regret neither of those actions, I am imposing my prior decision upon myself.

Very best regards,
EigenState

Ken G
2010-Jul-25, 01:44 AM
I understand. In fact I spend too much time here myself! Happy trails.

zerocold
2010-Jul-25, 02:07 AM
Thank everybody for your replies :)

One more.

If an electron really was spinning, how could that spin develop into a magnetic moment if the charge is evenly distributed within the electron. To think of the electron as made of little areas of charge cause even more problems than just accepting that a magnetic moment is a fundamental property of the particle. Let us not forget that there's a magnetic moment from the particle's 'spin' and another from its 'orbit'.

Wonder if there is not a theory describing the electron with a toroidal shape cganging it orbit constantly.

Can this issue be solved interpreting the electron as a particle/wave orbiting an axis?

The X,Y,Z=0 location should not exist anyways, because the Planck limits, i think

How the super string theory interpret the spin?, probably as a rotating string?

he OPer has not returned visibly to the thread

Sometimes is better to be quiet and listen :)

Ken G
2010-Jul-25, 03:54 AM
Wonder if there is not a theory describing the electron with a toroidal shape cganging it orbit constantly.
Physicists generally try to come up with as concrete physical a model as possible, but no such model of electron spin has worked. So there is no model that gives electrons physical spatial attributes-- it is considered a "point particle." There can be situations where imagining it has various sizes and shapes might be a useful picture in that context (like giving it a "cross section" when it interacts with light, or a "deBroglie wavelength" when asking about how tightly they can be compressed, connecting once again with degeneracy pressure). But there's no physical model other than a point particle that works in every situation.

Thus, we find a kind of "new physics" here, where the objective is not to come up with more and more sophisticated physical analogies, but rather, where the whole concept of a physical analogy is dropped in favor of mathematical abstraction. Then, after the abstraction is built and it works, a physical analogy is retrofitted to the mathematics, as a kind of working model of the full theory that gets a decent answer in some situations but was never really the theory it is intended to convey.

So it is with spin, as it appears that we simply cannot apply macroscopic classical thinking to spin-- the electron is not like a tiny version of a geometric shape we could ever recognize-- understanding its behavior requires more profound mathematics (like the geometric properties of spinors). For one thing, when you measure its angular momentum around some axis, it never comes out zero. What normal "rotating shape" has no axis around which there is zero net angular momentum? And you can't say the act of measuring its angular momentum changes its shape, because you can entangle it with another particle and measure the spin of the other particle, thereby measuring the spin of the first particle from a location outside the causal sphere in which you could ever effect a physical change on that objects' attributes. In other words, spin is not even an attribute that is "owned" by the particle itself, but rather, it is associated with the particle by the system as a whole. It's just another case where we can't take a model of a tiny spinning classical object, no matter how small or how strangely shaped, too seriously-- it just won't work.

Can this issue be solved interpreting the electron as a particle/wave orbiting an axis?
That is how orbital angular momentum is often characterized, but not spin. The orbital angular momentum around some axis is also a geometric property of the wave function under rotation, but it has a more straightforward interpretation-- it has to do with the number of times the particle wave function will change sign as you rotate the space it is in by 360 degrees. It's a bit like spin, because if the angular momentum is 1/2 (in h-bar units), and you rotate through 360 degrees, the wave function changes sign, just like with spin 1/2. But for the rotation angles between 0 and 360, orbital angular momentum causes a proportionately intermediate change in the global phase of the wave function-- whereas I believe the spinor construct is more exquisitely complicated under such partial rotations. In other words, to get orbital angular momentum, all you need to include is the idea that a wave function has a phase that depends on rotation angle of the system, but to get spin angular momentum, you need to include even more mathematical sophistication than just a global phase.

How the super string theory interpret the spin?, probably as a rotating string?You like to ask easy questions, don't you? Personally, I have no idea! But you can bet it is an extremely sophisticated mathematical construct, that can be stripped of most of its meaning and described in some physically motivated terms that sound superficially informative but in actuality are nothing more than weak analogies. It tends to create the illusion that theories like string theory attempt to explain phenomena by constructing physical pictures and then building theories around them, when I think it would be fairer to say they construct mathematical theories and then build some physical analogy around them as a kind of poor-man's version that was never really the theory at all.

Sometimes is better to be quiet and listen.And good on ya for lurking and asking a followup question. As is often the case in Q&A, questioners' ability to ask simple-sounding yet profound questions vastly exceeds the answerers abilities to supply equally simple-sounding yet profound answers.

Len Moran
2010-Jul-25, 09:00 AM
I think the issues here go deeper than just quantum mechanics, they are endemic to science itself, and these kinds of questions existed even before there was any quantum mechanics

I obviously agree with this, at the heart of physics is the theory and the observation. Many tend to take the observation as being the final and definitive act of physics, so when they project back from this final definitive act of observation they take all the aspects of the theory as actually existing within physical reality.

But as soon as we take on board the inescapable philosophical conclusion that we may not be able to separate the observer from the observed, then that final definitive act of observation is seen not to be quite so definitive – the scientific procedure of that act is not to be questioned, but the interpretation of that act in relation to nature as it exists outside of the observer and observed is a philosophical quest.

Thus we have nature as it exists outside of the observer and observed, we have mathematical properties and we have observational properties. All these three aspects are connected with each other in some philosophical manner and this is why I wanted EigenState to comment on his statement:

“an intrinsic property is a fundamental, inherent property of a thing, such as the electron…..thus each and every electron has spin under any set of conditions”

The way that statement reads to me goes against what I have written above – it implies that we can scientifically impart fundamental intrinsic properties to a particle in the absence of being able to verify those properties as being physically meaningful outside of the observer and observed. But perhaps in my earlier post I was complicating things a little by bringing in quantum mechanics and the breakdown of counterfactuality to illustrate my problem with that statement – it just always seems more clear cut for me to invoke quantum mechanics, but consistently, your clarification shows the problem is endemic to science generally, and your conclusions really turn a quite confusing issue (for me) into really a very simple procedure:

do not ask if "mass" or "spin" is mathematical or physical, instead, say whether you are interested in the mathematical or physically measurable aspects of that property.

Just a quick comment on the Q&A policy -I realised after the event that I had departed from the current rules of Q&A when I interjected my question in tandem with the original question - I'm afraid I had completely forgotten about the change. But I think that mistake on my part illustrates the benefit to be gained by not being too ridged on this point. The clarification of spin provided by EigenState brought into play intrinsic properties - and I was puzzled over the context in which that term was used. That led onto an important distinction being made between mathematical properties and observed properties, which further led onto a brief introduction to some very advanced physics concerning the mathematics of spin. Strictly speaking the OP did not enquire about such aspects, but surely we have all benefited to some degree from my interlude. I could have opened a new thread instead of asking in this one, but the continuity involving the original question and participants would have been lost.

Ken G
2010-Jul-25, 02:56 PM
I think you have understood completely what I was trying to say, and I also agree with your last point, for what it's worth.

loglo
2010-Jul-31, 01:49 AM
The Force of Symmetry by Vincent Icke contains the best explanation of quantum spin I have read and neatly shows why it is called spin in the first place. Here is a Google books link to the appropriate chapter. (8.7 Spin and relativity) (http://books.google.com.au/books?id=usNi8cU8s3kC&pg=PA136&lpg=PA136&dq=icke+symmetry+spin&source=bl&ots=6fnuCVoQoI&sig=lnOxyifu8nKPenk-MNso_iedAqY&hl=en&ei=4H5TTPu1NZGlnQf_semVBA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBQQ6AEwAA#v=onepage&q&f=false)

Ken G
2010-Jul-31, 02:18 AM
That was quite insightful, though requires more familiarity with relativistic quantum mechanics than I possess. What I got from it was that the quantum-mechanical version of spin is what shows up when a particle's physical size becomes much less than its Compton wavelength. The Compton wavelength is the intersection of relativity and quantum mechanics-- the relativity is that all particles (except long-range force carriers like photons) have an energy associated with their rest mass, and the quantum mechanics is that having an energy means it has a momentum, and having a momentum means there is uncertainty in its location. Hence the Compton wavelength is the intrinsic limit on how well we can know where a particle is.

When the particle is much smaller than that, this lack of knowledge about its location introduces ambiguity in its orientation as well-- we can no longer talk about a classical meaning for orientation, and we thus lose the classical meaning of spin, or more correctly, we lose the classical decomposition of spin around its own axis, and orbital spin due to how its motion allows us to see the particle from different directions. This ambiguity in orientation means that the explicit and externally manifested degree of freedom of classical orientation submerges into an implicit, internal degree of freedom, and that's what spin "is", from a theory standpoint.

It is something distinctly quantum mechanical, with no classical analog because classically, one can always disentangle the apparent changes in orientation you see due to the motion of the object, and those you see because the object is actually spinning. Observers in different motion would all agree, classically, on the spinning part, they'd only disagree on the orbital part. Relativistically, they don't agree on either, so internal spin and external (orbital) spin become interwoven like how space and time are woven into spacetime. I get from that that quantum mechanical spin plays the role in talking about rotation that spacetime plays in talking about translational motion. Quantum mechanical spin is what happens to classical rotational spacetime when quantum uncertainty makes it impossible to know the orientation of a particle.

Further details would be needed to flesh this out, along with examples of how spin affects various types of questions. Spin is as spin does, and a good understanding requires working with it, but I accept this outline as a useful conceptual basis for saying what spin is from the theoretical standpoint. One question I still have: one might imagine nonrelativistic quantum mechanics being formulated prior to relativity. What if we still had not discovered relativity, would we not have spin in our nonrelativistic quantum mechanics? What would we then say is the answer to "what is spin"?

loglo
2010-Jul-31, 02:45 AM
I don't think my imagination is as good as yours. :) I suspect we would consider it as just another quantum number (which is the way it is treated) and not a reflection of a rotational symmetry.

Ken G
2010-Jul-31, 03:37 AM
Yes, perhaps a quantum number with no understandable origin-- until relativity comes along to help us get that origin. What's more, relativistic quantum mechanics is normally thought of as something of a "shotgun marriage", so I'll bet if you keep digging deeper into Icke's answer about spin being what you get when you stuff quantum mechanical uncertainty about orientation through the Lorentz symmetry, you will find a few cracks in the foundation there.

loglo
2010-Aug-01, 01:37 AM
Yes, perhaps a quantum number with no understandable origin-- until relativity comes along to help us get that origin. What's more, relativistic quantum mechanics is normally thought of as something of a "shotgun marriage", so I'll bet if you keep digging deeper into Icke's answer about spin being what you get when you stuff quantum mechanical uncertainty about orientation through the Lorentz symmetry, you will find a few cracks in the foundation there.

Undoubtedly, but that is ok, the foundations are in need of being replaced anyway.