# Why Pauli's Exclusion Principle?

TriTertButoxy
Hi. I'm a sophomore undergrad studying chemistry at Rice University. I recently took quantum mechanics... and I now realize I should have gone into physics rather than chemistry. Ok. Whatever.

Bosons are particles with integer spins (helium-4 atoms). Fermions are particles with half-odd integer spins (electrons). I can't think of a non-(God-made-it-so) reason for why every fermion in a given system must have a unique set of quantum numbers (Pauli's Exclusion Principle). This rule simply doesn't apply to bosons. While this phenomena in nature is the very reason we observe such diverse chemistry among the chemical elements, could it be that the exclusion principle is simply an axiom of nature?

If not, I'm really, really dying for a good expanation.

Spin_Network
[/I]
TriTertButoxy said:
Hi. I'm a sophomore undergrad studying chemistry at Rice University. I recently took quantum mechanics... and I now realize I should have gone into physics rather than chemistry. Ok. Whatever.

Bosons are particles with integer spins (helium-4 atoms). Fermions are particles with half-odd integer spins (electrons). I can't think of a non-(God-made-it-so) reason for why every fermion in a given system must have a unique set of quantum numbers (Pauli's Exclusion Principle). This rule simply doesn't apply to bosons. While this phenomena in nature is the very reason we observe such diverse chemistry among the chemical elements, could it be that the exclusion principle is simply an axiom of nature?

If not, I'm really, really dying for a good expanation.

In a Nutshell Proton Decay! ..in an ElectronShell Virtual-Decay

To get to the bottom of things you have to start from the top

If one starts from topDOWN principles, then the Electron Spin, prevents tables and chairs from penetrating the floor they stand upon.

The 'Space-Quantization', or by the same person who coined this effect, Pauli Exclusion Principle, is generated from Electron Spin Angular Momentum.

Quantum Ranging?..Whilst moving in a certain direction, say along the Mendelev Table?..one has to know which way is up, and which way is down?, with respect to Atomic Structure, things have to know along which 'Path', Gravity wants to send its signals!

Photons comminicate this fact to Neigbouring matter , without this communication, jumping off a Table to the floor would be rather boring immpossibility!

The Uniqueness of the Quantum Numbers is contained by Geometric Paths, Triangles are Different to Spheres for specific reasons, not axiomic, if a Table was a perfect Orb/sphere, it could not be balanced upon a Perfect Triangluar Floor, the specific shape induce's movement, over-distance at specific rates.

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da_willem
If you keep asking why to a question, sooner or later you will come to a question that is (yet) unanswerable. As this is quite a fundamental question, you will come to this pretty fast.

Maybe you already know this but I'll explain where the Pauli principle comes from, in which I will assume you know what a wavefunction is.

If you have two distinguishable particles a and b (a proton and an electron for example) with wavefunctions $\psi _a (\vec{r}_1)$ and $\psi _b (\vec{r}_2)$ the combined wavefunction will be the product of these two

$$\psi(\vec{r}_1, \vec{r}_2)=\psi _a (\vec{r}_1) \psi _b (\vec{r}_2)$$

This is in accord with your intuition when you view the wavefunctions (actually their modulus squared) as a probablility density function. Where $| \psi _a (\vec{r}_1)| ^2$ gives the probablility (density) to find particle a at position $\vec{r}_1$ and $| \psi _b (\vec{r}_2)| ^2$ gives the probablility (density) to find particle a at position $\vec{r}_2$

$| \psi(\vec{r}_1, \vec{r}_2) |^2 = |\psi _a (\vec{r}_1)|^2 |\psi _b (\vec{r}_2)|^2[/tex] gives the probablility (density) to find particle a at position 1 and particle b at position 2. No surprises here, this is just the multiplication of probabalities. More interesting is to look at two indistinguishable particles a and b, two electrons for example. There is no way to distinguish one electron from another, they have no differing characteristics. In this case the combined wavefunction should be such that, and this is important, you can't tell which particle is in which state! The combined wavefunction can be either $$\psi _+ (\vec{r}_1, \vec{r}_2)=\psi _a (\vec{r}_1) \psi _b (\vec{r}_2)+ \psi _b (\vec{r}_1) \psi _a (\vec{r}_a)$$ or $$\psi _- (\vec{r}_1, \vec{r}_2)=\psi _a (\vec{r}_1) \psi _b (\vec{r}_2)-\psi _b (\vec{r}_1) \psi _a (\vec{r}_a)$$ (here I have omitted the normalisation constants) In both cases you can't tell if it's particle a at position 1 and b at two or the other way around, so quantum mechanics allows in this way for fundamentally indistinguishable particles. Particles that combine with the plus sign are called Bosons and those who combine with the minus sign are called Fermions. It turns out that Bosons always have half-integer spin and Fermions have integer spin. This can be proven, but it takes some advanced relativistic quantum mechanics, and even then there are still some people (Feynman for example) who doubt the validity of this proof. Now with this all in mnd the Pauli principle naturally follows. For two particles to be indistinguishable, they must have the same quantum numbers. In the case of Fermions the wavefunction $$\psi _- (\vec{r}_1, \vec{r}_2)=\psi _a (\vec{r}_1) \psi _b (\vec{r}_2)-\psi _b (\vec{r}_1) \psi _a (\vec{r}_a)$$ will be zero for [itex]\vec{r}_1=\vec{r}_2$. This means the probability two find two (the same) Fermions with the same quantum numbers at the same place is zero: The Pauli Exclusion Principle. The probability to find these two particles ever closer is ever smaller, resulting in a so-called 'exchange-force' between the particles.

Note that the probability to find two indistinguishable Bosons at the same place is 2 times as large as if they were distinguishable (if you like you can verify this yourself). This accounts for the fact that Bosons like to be near each other, which can be seen in a laser for example.

Maybe you already knew this and your question really was why do Fermions combine with the plus sign and Bosons with the minus sign, but to that there is, at an elementary level, yet no simple answer.

TriTertButoxy

da_willem
You're welcome, and that makes two of us. It is pretty humerous though...

εllipse
TriTertButoxy said:
could it be that the exclusion principle is simply an axiom of nature?
I thought that a principle was an axiom and therefore wasn't derivable .. ? Is this incorrect?

Homework Helper
No. A principle is a postulate/ axiom.

Daniel.

da_willem
εllipse said:
I thought that a principle was an axiom and therefore wasn't derivable .. ? Is this incorrect?

I don't know if that holds in general, but the relation between spin and (anti)symmetry of the wavefunction is an axiom in nonrelativistic quantummechanics...

Homework Helper
da_willem said:
I don't know if that holds in general, but the relation between spin and (anti)symmetry of the wavefunction is an axiom in nonrelativistic quantummechanics...

Sort of. It's not in the axiomatical strucure for sure. In terms of nonrel. QM it is merely a SPECULATION.

Daniel.

Staff Emeritus
Gold Member
Dearly Missed
dextercioby said:
Sort of. It's not in the axiomatical strucure for sure. In terms of nonrel. QM it is merely a SPECULATION.

Daniel.

I don't understand your "SPECULATION" and your wink. Don't you believe the spin-statistics theorem holds for nonrel QM? In spite of Feynmann's demurral, it's well derived from the Wightman axioms in QFT.

Nicky
I don't understand your "SPECULATION" and your wink. Don't you believe the spin-statistics theorem holds for nonrel QM? In spite of Feynmann's demurral, it's well derived from the Wightman axioms in QFT.

Even in QFT, I thought that the commutation rules for fermion and boson fields were taken as axioms. The spin statistics theorem just explains why fermions are spin n+1/2 and bosons are spin n, not why fermions and bosons exist. Please correct me if I am mistaken, I've only just started learning QFT.

Homework Helper
I don't understand your "SPECULATION" and your wink. Don't you believe the spin-statistics theorem holds for nonrel QM? In spite of Feynmann's demurral, it's well derived from the Wightman axioms in QFT.

Ok. I've said pretty clearly that in the terms of norelativistic quantum mechanics, ascribing a whatsover connection between spin & statistics would be a simple speculation, because there's no way one would begin with the 6-th postulate (the symmetrization one) and end up with the boson-->integer spin & fermion-->semiinteger spin.

Daniel.

metacristi
TriTertButoxy said:
I can't think of a non-(God-made-it-so) reason for why every fermion in a given system must have a unique set of quantum numbers (Pauli's Exclusion Principle). This rule simply doesn't apply to bosons. While this phenomena in nature is the very reason we observe such diverse chemistry among the chemical elements, could it be that the exclusion principle is simply an axiom of nature?

Such questions show why the philosophy of science is indispensable for the scientific quest, the roots of science lie in philosophy. Science without philosophy of science is blind, despite its obvious pragmatic 'success' (which by no means amount to say with certitude that science approach us to the Truth).

Returning at your question yes you could see that postulate as a sort of axiom. However the great difference to the situation in mathematics is that it is always considered corrigible (in a nontrivial way going till its rejection from science if further research prove it sterile), that is accepted only on a provisional status. We are far from having some (known as) true first premises from which, together with a theory of good observations (empiricism), to answer (by deduction), step by step, all possible questions about Nature, the dream of Aristotle.

At the basis of scientific methodology a very important role plays the so called hypothetico-deductive method (deductive nomological): from a set of premises considered true (at least provisionally) we obtain a set of novel predictions (some of them corroborated/'confirmed' in the case of accepted scientific theories). But this does not imply that a scientific hypothesis should answer all the 'why' questions (implying causality) in order to qualify at the status of scientific theory. Not at all, a descriptive account/phenomenological account is enough.

So that in the set of premises are accepted also postulates (such as Einstein's postulates in SR and GR or Pauli's exclusion principle etc) as much as they are useful for the theory using them, helping the theory to give a more accurate description of the world at the observational level. The mechanism is like this: those postulates toghether with other accepted premises produce more (as many as possible) novel testable predictions at the observational level accesible to us + accomodate some known facts (at least some novel predictions confirmed experimentally).

The great observational success of GR for example fully justify the use of such postulates even if they (the postulates in the premises of GR) are not directly testable experimentally (testable in isolation). This fully entitle us to grant a fallible epistemological privilege to those postulates even if they are not required with necessity by observed facts (that is they are accepted provisionally as being part of science, accepted as corrigible). Pauli's Exclusion Principle proved fruitful and empirically evolving long ago-in 1928 Sommerfeld and Bloch explained using it the properties of electrons of conductions in metals, it explains the repartition of electrons in the Periodic System etc-it fully deserves its place in science at least currently. This notwithstanding that we deal with unobservables in the case of Pauli's principle, not amenable to direct empirical observations (we have only indirect ones at the direct observational level + confidence via the great coherence with the other (still) accepted parts of science; the fact that it is 'in line' with the standard formalism of QM does not amount per se to a direct confirmation, the standard formalism is at its turn provisionally accepted, and anyway gives only a descriptional view not a causal one).

Some go way further (such postulates are forever inside science being approximately true) but I don't think that the current situation enable such a stronger conclusion, both the foundationist and coherentist theories of truth/justification have (still) important problems; I'd argue that scientific knowledge is merely justified belief not justified true belief, fallibilism (in a non trivial way) should never be dropped especially in physics where the problems of underdetermination and theory ladenness are very important (in the light of the lessons of the history of science too).

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mikeyork
TriTertButoxy said:
I can't think of a non-(God-made-it-so) reason for why every fermion in a given system must have a unique set of quantum numbers (Pauli's Exclusion Principle). This rule simply doesn't apply to bosons. While this phenomena in nature is the very reason we observe such diverse chemistry among the chemical elements, could it be that the exclusion principle is simply an axiom of nature?
No. Such an axiom isn't necessary. All you need to know is basic quantum mechanics -- in particular the necessity of choosing a unique state vector for a unique state description, if you want to compute interference effects -- plus a rule (a very obvious one) that says particle permutation is not observable (because particle ordering is an artifact of how the observer describes multi-particle states).

In particular, forget all the stuff that says that fermions and bosons obey a different type of quantum mechanics. Because that is putting the cart before the horse. Rather, it is the same QM that tells us they have a different statistical behavior in large ensembles. And forget all the stuff that says wavefunctions must be anti-symmetric for fermions. Because it isn't true, except in a special case (the usual, but not explicitly stated case) that a particular order-dependent (anti-symmetric) method of choosing the spin quantization frames is used.

In fact there is a single general exclusion rule that works for all particles, regardless of spin and which follows from the uniqueness and permutation unobservability I described above. It just happens that for spin half particles in a particular frame of reference it can be expressed as the Pauli principle. (An additional important factor in understanding this is that, for fermions, state vectors for state descriptions that are related by a 2pi rotation of their spin quantization frame differ by a minus sign. In other words to define unique state vectors, you must specify the relative orientation of the spin quantization frames. It is not sufficient to specify only the three axes in each case.)

A word of warning: Most physicists do not understand this yet. The conventional wisdom is still that either an additional axiom (The Symmetrization Postulate) is necessary (see da_willem's post, for example) or that it can be proved in Quantum Field Theory as a consequence of "(Relativistic) Local Causality". So if you try to argue the common sense description I have given without really understanding the math (see below) then you will get into deep water with people who (incorrectly) think they know better and to whom you won't be able to provide a convincing answer.
If not, I'm really, really dying for a good expanation.

Here it is:

http://xxx.lanl.gov/abs/quant-ph/0006101

mikeyork
da_willem said:
More interesting is to look at two indistinguishable particles a and b, two electrons for example. There is no way to distinguish one electron from another, they have no differing characteristics. In this case the combined wavefunction should be such that, and this is important, you can't tell which particle is in which state!

The combined wavefunction can be either

$$\psi _+ (\vec{r}_1, \vec{r}_2)=\psi _a (\vec{r}_1) \psi _b (\vec{r}_2)+ \psi _b (\vec{r}_1) \psi _a (\vec{r}_a)$$

or

$$\psi _- (\vec{r}_1, \vec{r}_2)=\psi _a (\vec{r}_1) \psi _b (\vec{r}_2)-\psi _b (\vec{r}_1) \psi _a (\vec{r}_a)$$

(here I have omitted the normalisation constants)
In both cases you can't tell if it's particle a at position 1 and b at two or the other way around, so quantum mechanics allows in this way for fundamentally indistinguishable particles.
So far you have given a good explanation of the conventional wisdom. As a follow-up to my last post, however, I'll point out a little problem with what you have written.

First off, you haven't defined the frame of reference for spin quantization. No matter, we'll assume you are using a canonical frame (the same frame in which you measure both position vectors) -- in which case the spin quantization frame is the same (in the sense of having the same axes) for both particles. However, since you are using 3-vectors instead of polar co-ordinates, we don't know the relative orientation of the two position vectors. If we do a 2pi rotation on one particle's frame of reference, but not the other, then we will change the wavefunctions for a half-integer spin particle by a factor -1, even though the frame axes end up to be the same. Using your notation, there is no way to distinguish the new wavefunctions from those that haven't been rotated. In other words, your single-particle wavefunctions are not unique (they are ambiguous up to a sign). Therefore, the sign of superposition will also be ambiguous since you cannot rule out the possibility of a 2pi rotation on one particle's spin quantization frame when you do the exchange. (Without uniquely defined relative orientations of frames, you don't have uniquely defined wavefunctions and so you don't have a unique definition of exchange.)

In fact it should be obvious that if you choose relative orientations of spin quantization frames so that one particle's frame gets rotated by 2pi by the exchange then your "anti-symmetric" wavefunction becomes a "symmetric" wavefunction in your ambiguous notation.

It turns out that when you set up a method for defining spin quantization frames in an order independent way then you can always get symmetric wavefunctions, regardless of spin. The conventional anti-symmetry is actually due to an implicit (but not obvious) geometrical asymmetry in choosing a canonical frame. (The details of this are in my paper referenced in my previous post.) Note that the observable properties are the same, regardless of which choice is made, because the inclusion or exclusion of an additional order-dependent phase cancels itself out when you examine the allowed physical quantum numbers that result from the interference due to the superposition.

Particles that combine with the plus sign are called Bosons and those who combine with the minus sign are called Fermions.
Unfortunately, this conventional notion is convention dependent. As I have pointed out, one can always choose fermion states (obeying Fermi-Dirac statistics) that are superposed with a plus sign.

Staff Emeritus
mikeyork said:
A word of warning: Most physicists do not understand this yet. The conventional wisdom is still that either an additional axiom (The Symmetrization Postulate) is necessary (see da_willem's post, for example) or that it can be proved in Quantum Field Theory as a consequence of "(Relativistic) Local Causality". So if you try to argue the common sense description I have given without really understanding the math (see below) then you will get into deep water with people who (incorrectly) think they know better and to whom you won't be able to provide a convincing answer.

This is because most physicists pay attention to work that has appeared in peer-reviewed journals. Scanning your paper, it appears that you cited yourself from papers you wrote that only appeared in the e-print archive. Can you please cite which peer-reviewed journals they have appeared in?

However, most importantly, can you show which experimental observations so far have proven that your theory is more valid than the "conventional wisdom", especially where there is an explicit effect due to a different "frame of reference of spin quantization"?

Zz.

mikeyork
ZapperZ said:
Scanning your paper, it appears that you cited yourself from papers you wrote that only appeared in the e-print archive.
There was a crunch of space in the published conference proceedings. So I had to truncate either the paper or the references. I also had to leave out the appendix (that appears in the e-print). The first reference in that paper contains a comprehensive list of references to all papers using a similar (but incomplete) argument to mine published before 2000.
Can you please cite which peer-reviewed journals they have appeared in?
The conference paper was published in the proceedings. I see no point in publishing it again.

I made two earlier submissions to refereed journals that were rejected. Once because it was too long (it was indeed very long) and once because, according to the referee, "everyone knows" that fermion wavefunctions must be anti-symmetric, when the whole point of my paper was that this wasn't always true and isn't a good way to look at things.

After the 2000 conference I started a newer paper that would flesh out my conference paper and include more details on many-particle systems, intending to submit it to a refereed journal, but my job (in math finance theory) has kept me from finishing it.

I also think that forums such as this provide a much better opportunity for discussion than refereed journals. Referees can simply refuse to discuss the matter and often do. In a public forum such as this there is more incentive to engage in serious debate.

However, most importantly, can you show which experimental observations so far have proven that your theory is more valid than the "conventional wisdom"
Indeed this is a lot more important. But for two-particle states, the claimed observable results are identical and cannot be used to discriminate. However, it is simply a matter of logic. The conventional view is self-contradictory since it claims a unique exchange phase for wavefunctions that are not themselves unique. This logical hole, was previously not noticed, or ignored. In fact I don't believe the 2pi rotation sign change for fermions was fully realized until some time after the symmetrization rules had become established wisdom. Everyone knew how to calculate in order to get the correct answer, so that is what they did. What I have done is to fill this hole.

For states of more than two identical particles, the observable rules for all such pairs are, again, the same. The critical area lies with composite bosons. Are they "true" bosons or does complete antisymmetrization of their constituents give different observable effects? This is a pretty complex issue, and the first questions about it date back to the 1920s and diatomic molecules. To my knowledge, all the data shows that they behave as "true" bosons as my theory predicts until the bosonic states are broken up by interaction. Plainly if the composite bosons are no longer in their identifying eigenstates (because of interaction) then my rules concerning composite eigenstates no longer hold. However, to my knowledge, scattering data such as alpha-alpha or d-d gives an unequivocal yes to my description of these composite systems as true bosons. I don't know what the anti-symmetrization argument predicts in terms of observable data, but as far as I can see, it should give different predictions (as I believe I have proved in my appendix). However, some people hold that it gives the same answer, which I do not understand and cannot verify as I have never seen the argument in sufficient detail.
, especially where there is an explicit effect due to a different "frame of reference of spin quantization"?
I don't know what you are referring to here. Choice of spin quantization frame is arbitrary and has no observable effect. Any observable difference lies with states of three or more identical particles and differs according to whether or not complete anti-symmetrization holds (conventional view) or whether composite eigenstate rules obtain (my view) and whether there is a difference (as far as I can see there must be).

If you really want to get to the bottom of this, I suggest you do more than just "scan" my paper.

Staff Emeritus
mikeyork said:
The conference paper was published in the proceedings. I see no point in publishing it again.

I made two earlier submissions to refereed journals that were rejected. Once because it was too long (it was indeed very long) and once because, according to the referee, "everyone knows" that fermion wavefunctions must be anti-symmetric, when the whole point of my paper was that this wasn't always true and isn't a good way to look at things.

After the 2000 conference I started a newer paper that would flesh out my conference paper and include more details on many-particle systems, intending to submit it to a refereed journal, but my job (in math finance theory) has kept me from finishing it.

I also think that forums such as this provide a much better opportunity for discussion than refereed journals. Referees can simply refuse to discuss the matter and often do. In a public forum such as this there is more incentive to engage in serious debate.

So in other words, none of what you are claiming is part of mainstream physics AND has never appeared in a peer-reviewed journal. If that is the case, you may want to read our guidelines FIRST about "discussing" such things. This forum is unlike others.

Indeed this is a lot more important. But for two-particle states, the claimed observable results are identical and cannot be used to discriminate.

For states of more than two identical particles, the observable rules for all such pairs are, again, the same.

To my knowledge, all the data shows that they behave as "true" bosons as my theory predicts until the bosonic states are broken up by interaction.

However, to my knowledge, scattering data such as alpha-alpha or d-d gives an unequivocal yes to my description of these composite systems as true bosons.

I don't know what the anti-symmetrization argument predicts in terms of observable data, but as far as I can see, it should give different predictions (as I believe I have proved in my appendix). However, some people hold that it gives the same answer, which I do not understand and cannot verify as I have never seen the argument in sufficient detail.

This is VERY confusing. You are claiming that (i) there's no difference between yours and conventional theory and/or (ii) there is in some cases. Can you please make the EXACT citation to the particular experimental data that support your claim but not the conventional idea?

Other than that, I would request that, until you reread our forum guidelines, that you refrain from using your idea as an explanation to the issue at hand. You will understand that the validity of your idea has to be established FIRST, and that can only be done in peer-reviewed journals and by experts in the field. If you wish to use this forum to "work out" your idea, I would then refer you to the new Independent Research forum to submit your work. It no longer belongs in the main PF physics section.

Zz.

metacristi
mikeyork said:
No. Such an axiom isn't necessary.

Unfortunately what you pointed out does not really offer the 'why' answer the OP was asking. You provide a formal description but this does not really amount to answer the 'why' question inside the standard formalism of QM, that is without interpretational elements (the assumptions made are questionable; others here tried entirely from inside the standard formalism but the solution offered is only descriptive not causal). As a digression here, descriptive formal explanations are distinct from explanations implying understanding, meaning either a normative/causal theoretical argument or a deduction from direct experience, not the case here for we deal with unobservables; anyway we have a big problem with the empirical base even at the level of observables, science 'is erected on a swamp', to quote Popper, everything is corrigible, we can only interpret experiments we do not deduce truths from observations.

The standard formalism of QM, the only one which really makes testable predictions, is descriptive in nature, none of its proposed ontologies, interpretations, really have the edge, we deal with a strong underdetermination here, not to mention theory ladenness (this despite the arguments of many leading physicists-some of them hinting a very poor understanding of modern philosophy of science-that only the current main views are acceptable the rest being 'dead ends' forever).

Feynman mentions that Pauli tried to base his principle on QFT and Relativity but this is questionable. So its safer to follow the advice of the same Feynman (in the 3rd volume of his lectures) that the anti symmetry of the wavefunction(s) for fermions (and subsequently Pauli's principle) is a fundamental principle of how nature works.

I'd argue that in this state of research, that is for the moment at least, we have to be contended to consider Pauli's assumption a fundamental principle of nature, provisionally accepted inside sicence. Which, of course, by no means amounts to say that this will ever be the case, maybe we could deduce it, from 'deeper' assumptions by showing that one of the intepretations is really superior. What if it would be a hidden variables approach, realistic in nature, even if we will have to drop the invariance of laws in all frames, after all Brans-Dicke hypothesis is a serious contender to GR even now...

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mikeyork -- Virtually all of chemistry depends critically on the standard anti-symmetric electron wavefunctions, not to mention superconductivity, and particle theory, and most everything else. Do you find different results in atomic or any physics? -- relative to the standard approach.

Regards,
Reilly Atkinson

mikeyork
ZapperZ said:
So in other words, none of what you are claiming is part of mainstream physics AND has never appeared in a peer-reviewed journal. If that is the case, you may want to read our guidelines FIRST about "discussing" such things. This forum is unlike others.
On the contrary, a large part of my paper, including the part which draws so much heat here (the critique of the antisymmetrization forumulation of the spin-statistics theorem) has been published in refereed journals by several other authors (see the references I have already pointed you to that appeared before 2000). This is the part that shows how to derive the conventional anti-symmetric wavefunctions from symmetric wavefunctions as a consequence of a relative 2pi rotation on one particle's spin quantization frame. (Michael Berry, for instance, uses configuration space.) This part of the proof is widely accepted and understood by experts in the field, including those who prefer field theory proofs. It just hasn't percolated through to the wider community yet which is why people erupt in astonishment when I point it out in forums like this. However all these published and refereed proofs suffer from another problem, which is to provide a convincing argument as to why the symmetric wavefunctions must be symmetric in the first place and the arguments they have presented have been rightly criticised in other refereed and published papers. The only part that is unique to my paper and not yet published in a refereed journal is the part that resolves this issue.

This is VERY confusing. You are claiming that (i) there's no difference between yours and conventional theory and/or (ii) there is in some cases.
If I had claimed that, then I would understand your confusion. And I notice that you snip parts of what you quote from me that add to this confusion. Read what I wrote again (not your edited version) and you will see that I have said that for two-particle systems, there is no observable distinction, but that many particle systems such as bosons that are fermion composites there is an open question that has not been resolved because, although I claim the "complete anti-symmetrization" rule is incompatible with my (observed) bosonic exclusion rules, others (private conversations) have claimed they are the same but have not provided the details.
Can you please make the EXACT citation to the particular experimental data that support your claim but not the conventional idea?
The issue was first raised in the context of experimental data by Ehrenfest & Oppenheimer (Phys Rev 37, 333, 1931) and was raised again by Tino (http://xxx.lanl.gov/abs/quant-ph/9907028) a few years ago. Most people think the jury is still out. As regards alpha-alpha and d-d scattering, you will find this discussed in standard texts on particle scattering. As far as I know, no one has ever questioned the notion that the bosonic exclusion rules (usually described as symmetrization) apply. The experimental evidence lies in the angular distribution. Those who believe that the consituent fermions must be anti-symmetrized will, as far as I can see, have a hard time with this, but, as I said, those with whom I have communicated claim that there is no contradiction, but haven't provided the argument.

mikeyork
reilly said:
mikeyork -- Virtually all of chemistry depends critically on the standard anti-symmetric electron wavefunctions, not to mention superconductivity, and particle theory, and most everything else.
Not true. It depends on the exclusion rules which specify which states are allowed. Despite common belief, these exclusion rules are NOT synonymous with anti-symmetrization. This has already been fully explained in my posts (and numerous refereed publications by other authors).
Do you find different results in atomic or any physics? -- relative to the standard approach.
See my response to ZapperZ.

Staff Emeritus
mikeyork said:
On the contrary, a large part of my paper, including the part which draws so much heat here (the critique of the antisymmetrization forumulation of the spin-statistics theorem) has been published in refereed journals by several other authors (see the references I have already pointed you to that appeared before 2000).

Hang on. I'm not asking about the physics, nor am I asking for things that were published by "other authors". I'm asking specifically if you have published this topic in a peer-reviewed journal. You kept refering to your "papers", but they were all e-print archive papers or conference proceedings. At SOME point, your work HAS to be evaluated by your peers, people who has the expertise in THAT field of study. This is what I am asking for.

If I had claimed that, then I would understand your confusion. And I notice that you snip parts of what you quote from me that add to this confusion. Read what I wrote again (not your edited version) and you will see that I have said that for two-particle systems, there is no observable distinction, but that many particle systems such as bosons that are fermion composites there is an open question that has not been resolved because, although I claim the "complete anti-symmetrization" rule is incompatible with my (observed) bosonic exclusion rules, others (private conversations) have claimed they are the same but have not provided the details.

And I AM asking for this "multiparticle system" that you claim are "open questions". As a condensed matter physicists, I work with "mutiparticle system" BY DEFINITION. ALL of them, be it the BCS ground state, the ferromagnetic and antiferromagnetic ground state in quantum magnetism, etc. ALL are antisymmetrized in the working hamiltonian. I am asking for specific experimental evidence, not just "open questions", where the conventional theory and your theory DEVIATES and point to yours as being correct.

The issue was first raised in the context of experimental data by Ehrenfest & Oppenheimer (Phys Rev 37, 333, 1931) and was raised again by Tino (http://xxx.lanl.gov/abs/quant-ph/9907028) a few years ago. Most people think the jury is still out. As regards alpha-alpha and d-d scattering, you will find this discussed in standard texts on particle scattering. As far as I know, no one has ever questioned the notion that the bosonic exclusion rules (usually described as symmetrization) apply. The experimental evidence lies in the angular distribution. Those who believe that the consituent fermions must be anti-symmetrized will, as far as I can see, have a hard time with this, but, as I said, those with whom I have communicated claim that there is no contradiction, but haven't provided the argument.

The tino paper is not an experimental paper. The STRONGEST it can say is that "It is shown that in a strict sense these experiments cannot test the validity of the symmetrization postulate". Even if this is correct, it says nothing about the validity (or invalidity) of the symmetrization principle, and it certainly says nothing about the validity of yours.

There have been TONS of experimental evidence recently on many-body spin interactions. 1D Haldane spin chains, 2D Mott insulators, Fermionic gas condensates, etc.. etc. Are there nothing in this wealth of experimental data that point to the inadequacies of the conventional theory and correctly described by yours?

Zz.

mikeyork
ZapperZ said:
Not in your previous post, which I responded to, where you wrote

"none of what you are claiming is part of mainstream physics AND has never appeared in a peer-reviewed journal"

I was simply pointing out that your statement isn't true. Most of what I am claiming and which engenders such opposition from people such as yourself, is indeed part of mainstream physics and has appeared in peer-reviewed journals. It just hasn't filtered through to non-experts in the field yet.

It's difficult to have a rational discussion if you keep shifting the ground.
At SOME point, your work HAS to be evaluated by your peers, people who has the expertise in THAT field of study. This is what I am asking for.
I would very much like that too, but it hasn't been forthcoming.

At the Spin2000 conference, Sudarshan (who, as a co-author with Duck of a book on it, is considered an expert in the field) was actually very warmly receptive to (and appreciative of) my paper even though I knew that he (previously, at least) held a contradictory view-point. At the end of the conference, I asked him to critique it for me, but unfortunately he never did so (I think he was very ill and underwent heart surgery).

Berry, on the other hand, has been very sympathetic to my point of view and has urged me to re-submit it, but I just haven't had the time. If I was in a full-time physics job, I would not hesitate to do this. As things stand, and without knowing that my paper would be refereed by someone who actually understood the field (which wasn't true in the past), inviting people to read and critique what I have already published in the conference proceedings and prior e-prints is a lot easier for me.

When people express puzzlement or mystification at the origins of the spin-statistics theorem and whether or not it requires a new axiom from QM, it just doesn't seem reasonable to me not to share what I know even if it isn't yet widely understood by others. The number of physicists working on the theorem and that understand that there are issues with the antisymmetrization formulation can be counted on the fingers of two hands, but includes some very eminent theoreticians.
I am asking for specific experimental evidence, not just "open questions", where the conventional theory and your theory DEVIATES and point to yours as being correct
I have already answered this to the best of my ability, but I'll do so again. It seems to me that any system of two bosons that are fermion composites that behaves as true bosons (like an alpha-alpha system) is verification in my favor, because, as far as I can see, antisymmetrization of the constituent fermions violates this (and the proof is in my paper). No one has ever provided any grounds to contradict my proof or claimed that the data show otherwise.
There have been TONS of experimental evidence recently on many-body spin interactions. 1D Haldane spin chains, 2D Mott insulators, Fermionic gas condensates, etc.. etc. Are there nothing in this wealth of experimental data that point to the inadequacies of the conventional theory and correctly described by yours?
I am afraid I don't know this field well enough. I would love to look at this, as you suggest, but without a great deal of help I have neither the expertise nor the time.

Staff Emeritus
mikeyork said:
Not in your previous post, which I responded to, where you wrote

"none of what you are claiming is part of mainstream physics AND has never appeared in a peer-reviewed journal"

I was simply pointing out that your statement isn't true. Most of what I am claiming and which engenders such opposition from people such as yourself, is indeed part of mainstream physics and has appeared in peer-reviewed journals. It just hasn't filtered through to non-experts in the field yet.

It's difficult to have a rational discussion if you keep shifting the ground.

No, because if you look what you quote AND couple that with what I said later about YOUR work being evaluated, I clearly have indicated that it is YOUR work that is in question. Furthermore, if such ideas have been published, then when you make references to them, it is imperative that you cited the published work, and not your unpublished papers.

I'm also puzzled. If such work ALREADy have been published, then what else is there to say? Aren't you kinda LATE in trying to publish this? However, if you are trying to convey that there's MORE to it and that you're pushing a new idea (after all, if you have nothing new to offer, your paper will never be accepted), then THAT idea hasn't been published yet and is NOT part of any "established" nor accepted physics.

I have already answered this to the best of my ability, but I'll do so again. It seems to me that any system of two bosons that are fermion composites that behaves as true bosons (like an alpha-alpha system) is verification in my favor, because, as far as I can see, antisymmetrization of the constituent fermions violates this (and the proof is in my paper). No one has ever provided any grounds to contradict my proof or claimed that the data show otherwise.

1. Cite the EXACT experimental work that you are claiming to support your theory but not the conventional one.

2. Write a comment to that journal citing this.

3. Wait till it is accepted.

4. After (3) has occured, then you can claim that your theory has at least been considered to be valid. This is how ALL of us have to go through to make sure our ideas are heard AND evaluated to be valid. Airing them on a public forum on the internet does NOTHING towards that end.

I am afraid I don't know this field well enough. I would love to look at this, as you suggest, but without a great deal of help I have neither the expertise nor the time.

Same here! I have never seen anything done just on the 'net that has ever added anything significant to the body of knowledge of physics. Have you? It is why I put very little emphasis on things that JUST appear on here but never in a peer-reviewed journal. I have other things to read and consider that have a greater likelyhood to make a difference and an impact. Also, I would think that if I'm claiming something "universal" that trumps conventional idea, then I would think that I would want to be up-to-date on all the experimental results relevant to my theory. Claiming ignorance of such a large body of evidence is simply never good enough. I've seen people being eaten alive at conferences when they are not aware of such things.

Zz.

mikeyork
ZapperZ said:
I'm also puzzled. If such work ALREADy have been published, then what else is there to say? Aren't you kinda LATE in trying to publish this?
Actually no. My first papers on this were Rome University pre-prints in 1975 and pre-dated the first peer-reviewed publication (Broyles, 1976). Although he doesn't cite my pre-print (presumably because it was not published in a refereed journal) his proof is very similar, but incomplete.
However, if you are trying to convey that there's MORE to it and that you're pushing a new idea (after all, if you have nothing new to offer, your paper will never be accepted), then THAT idea hasn't been published yet and is NOT part of any "established" nor accepted physics.
Yes, there is more to it than has appeared in any peer-reviwed publication, as I have already explained:

"However all these published and refereed proofs suffer from another problem, which is to provide a convincing argument as to why the symmetric wavefunctions must be symmetric in the first place and the arguments they have presented have been rightly criticised in other refereed and published papers. The only part that is unique to my paper and not yet published in a refereed journal is the part that resolves this issue."

although I should have added that incompatibility with simultaneous complete antisymmetrization of many-fermion systems is also new to my paper.

Staff Emeritus
Then you have a huge mountain of evidence to overcome, or to suffer through. Everything from the Deborah Jin's fermionic condensates to the Mott insulator to the BCS ground state started OUT with the antisymmetric Hamiltonian.... and were successful!

Zz.

mikeyork
ZapperZ said:
Then you have a huge mountain of evidence to overcome, or to suffer through. Everything from the Deborah Jin's fermionic condensates to the Mott insulator to the BCS ground state started OUT with the antisymmetric Hamiltonian.... and were successful!
I can't say anything about that without seeing the detailed math in such an "antisymmetric Hamiltonian". Can you indicate references freely available on the 'net, as I don't have easy access to a library?

Staff Emeritus
mikeyork said:
I can't say anything about that without seeing the detailed math in such an "antisymmetric Hamiltonian". Can you indicate references freely available on the 'net, as I don't have easy access to a library?

Er... the field theoretic method to the BCS theory is, to say the least, widely known and should be available on the 'net. The rest are all copyrighted papers. But I don't get it. The Deborah Jin's paper last year created such a big brouhaha. Don't tell me you didn't hear about it!

Secondly, here's something I do not comprehend. Considering that you consider multi-particle system as being a strong candidate to prove you right, why aren't you more familiar with condensed matter/many-body physics? I mean, anyone who had to go through G.D. Mahan's text, for example would have seen multiple times the Hamiltonian for fermions with creation/destruction operators [c,c*] being anticommuting to preserve the asymmetry. We're talking about this being on Page 18 of a 700 page text here! This Hamiltonian in its various forms are used repeatedly throughout the text in many physical systems, even in the form for the BCS Hamiltonian!

All these SHOULD be known to anyone doing anything in multiparticle system of any kind! Condensed matter system should be the FIRST place anyone looks for the "poster child" of many-particle physics since by is VERY nature, this is what it studies! So I don't understand why the experimental listing that I just mentioned appears to be "new" to you.

Zz.

mikeyork
ZapperZ said:
Er... the field theoretic method to the BCS theory is, to say the least, widely known and should be available on the 'net. The rest are all copyrighted papers. But I don't get it. The Deborah Jin's paper last year created such a big brouhaha. Don't tell me you didn't hear about it!
No I didn't. I don't have time to keep in touch with the majority of what happens in physics. Since I left full-time reseach in 1977 (until when I worked in S-matrix theory) I have had little time for any physics except for infrequent forays to keep up to date with developments around the spin-statistics theorem.
Secondly, here's something I do not comprehend. Considering that you consider multi-particle system as being a strong candidate to prove you right, why aren't you more familiar with condensed matter/many-body physics?
Because I never studied those areas. My realization of the incompatibility with full simultaneous anti-symmetrization came as an afterthought that I haven't had the opportunity to develop further. There is a limit to the number of problems a single person who can only devote occasional time to it can handle at the level of up-to-date research, while holding down a job in a completely different field and I chose to focus on the areas that I thought most fruitful given my personal resources.
I mean, anyone who had to go through G.D. Mahan's text, for example would have seen multiple times the Hamiltonian for fermions with creation/destruction operators [c,c*] being anticommuting to preserve the asymmetry. We're talking about this being on Page 18 of a 700 page text here! This Hamiltonian in its various forms are used repeatedly throughout the text in many physical systems, even in the form for the BCS Hamiltonian!
Anti-commutation of creation-annihilation operators is equivalent to pair-wise fermion exclusion rules as long as the state vectors that are created obey the usual order-dependent conditions for the choice of spin frames. For more than three particles it is possible to make those choices for (say) the first pair and for the third particle with respect to the second particle and so on, but (unless I have made an error that I have not yet discovered) it is not possible to make this choice simultaneously for all possible pairs (because there are insufficient degrees of freedom).

In creation operator terms, I intuit that it is like saying that yes the application of any subsequent creation operator will obey a specific commutation relation with its preceding operator, given a specific ordering, but that it can't be guaranteed to give the same commutation relation with all others (i.e. given a different ordering) unless a possible additional spin frame rotation is factored in when the operators are commuted. My suspicion is that this is what happens in the usual full anti-symmetrization, but because the (crucial) relative orientations of spin quantization frames are not made explicit, it is hidden. How this affects any given computation will differ from case to case and is not clear to me what the consequences will be.

Because there is so much field theory developed around full anti-symmetrization, those with whom I have discussed the matter insist that the physical equivalence must hold, just as in the two-particle case, but can't identify my error. It may well be that in those computations which have been fully developed, the hidden phase factors come out in the wash, just like the two-particle case, but my intuition says not. I chose instead to focus on the issue of bosons as fermion composites as being the easiest area to understand -- since no field theory is involved.

Unfortunately, as you can see, this is getting into areas that I haven't yet fully explored. For all these reasons, I have been careful to qualify everything I have said about what my formulation predicts in the many-particle context as having an unresolved area.

Although it grieves me to say it, it will probably take someone with greater skills in field theory than I have to apply my fully symmetrized formulation to creation-annihilation operators in the many-body case before the differences, if indeed they exist as I believe they must, are fully identified in field theoretic computations. Nevertheless I am willing to look at any references you provide to see if I can identify any areas that give any answers.

metacristi
Seen from a purely philosophical perspective the interesting fact is that irrespective of which system of axioms has really the edge (mykeyork's or the orthodox one, remain to be seen) the question 'why' Pauli's principle is not really answered. No more than 'why' Heisenberg's Uncertainty principle, though it can be argued that it can be deduced formally from the standard formalism of QM (even this can be safely contested, see Popper's critique, valid for the deduction of Pauli's Principle too, for, upon Born's interpretation of the wave function, we are allowed to talk only at a statistical level not for singular cases).

But let's assume that at the level of pure formal description they might be seen as resulting as formal deductions from some sets of axioms. Unfortunately for really answering the 'why' question we need a causal deduction of Pauli's Principle and this requires an interpretation of the formalism proved as being superior at least to all existing alternatives. The purely descriptional deduction of Pauli's Principle from a formalism can be seen at most as showing the high coherence of it with the system of axioms from which it is purely formally deduced, in a purely descriptional way, nothing more.

Now Mike York's solution has elements of interpretation incorporated, it's not really only 'plain QM' (for ex. the assumption of completeness is clearly part of the interpretation) but it is too sketchy at this point to count as a causal deduction of Pauli's principle. Even if he would eventually provide one his solution should prove to be at least theoretically progressive, being capable to accomodate more facts than its alternatives but in a sizeable way. One or two extra accomodations of facts (if it can really provide this, personally I'm skeptical) does not makes it really superior. This is why, for example, the capacity to handle spin till 11th decimal place of quantum electrodynamics (still) does not make it really superior to a relativized Bohm's research program, I don't think the hidden variables path is a 'dead end'-as some, for example on motl's site/blog, emphatically claim. The fact that Lorentz invariance is dropped is not at a all a problem coherence with previous accepted scientfic knowledge is not neccessarily a sign of truth.

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Staff Emeritus
mikeyork said:
No I didn't. I don't have time to keep in touch with the majority of what happens in physics. Since I left full-time reseach in 1977 (until when I worked in S-matrix theory) I have had little time for any physics except for infrequent forays to keep up to date with developments around the spin-statistics theorem.

Then may I be so bold to advice you that till you are up to date on all the latest results, that you refrain from advertizing your theory on here till you are SURE that it is valid AND that it has been evualuated in peer-reviewed journals? Using your unverified theory as an explanation to a question on here is not only misleading, it is against PF guidelines.

Anti-commutation of creation-annihilation operators is equivalent to pair-wise fermion exclusion rules as long as the state vectors that are created obey the usual order-dependent conditions for the choice of spin frames. For more than three particles it is possible to make those choices for (say) the first pair and for the third particle with respect to the second particle and so on, but (unless I have made an error that I have not yet discovered) it is not possible to make this choice simultaneously for all possible pairs (because there are insufficient degrees of freedom).

In creation operator terms, I intuit that it is like saying that yes the application of any subsequent creation operator will obey a specific commutation relation with its preceding operator, given a specific ordering, but that it can't be guaranteed to give the same commutation relation with all others (i.e. given a different ordering) unless a possible additional spin frame rotation is factored in when the operators are commuted. My suspicion is that this is what happens in the usual full anti-symmetrization, but because the (crucial) relative orientations of spin quantization frames are not made explicit, it is hidden. How this affects any given computation will differ from case to case and is not clear to me what the consequences will be.

Because there is so much field theory developed around full anti-symmetrization, those with whom I have discussed the matter insist that the physical equivalence must hold, just as in the two-particle case, but can't identify my error. It may well be that in those computations which have been fully developed, the hidden phase factors come out in the wash, just like the two-particle case, but my intuition says not. I chose instead to focus on the issue of bosons as fermion composites as being the easiest area to understand -- since no field theory is involved.

Unfortunately, as you can see, this is getting into areas that I haven't yet fully explored. For all these reasons, I have been careful to qualify everything I have said about what my formulation predicts in the many-particle context as having an unresolved area.

Although it grieves me to say it, it will probably take someone with greater skills in field theory than I have to apply my fully symmetrized formulation to creation-annihilation operators in the many-body case before the differences, if indeed they exist as I believe they must, are fully identified in field theoretic computations. Nevertheless I am willing to look at any references you provide to see if I can identify any areas that give any answers.

Then I would say that till you can rederive an equivalent to the BCS ground state from YOUR theory and get back all the physical values that it did that match the experimental observation, I would put a serious question mark to its validity.

Zz.

mikeyork
ZapperZ said:
Then may I be so bold to advice you that till you are up to date on all the latest results, that you refrain from advertizing your theory on here till you are SURE that it is valid AND that it has been evualuated in peer-reviewed journals? Using your unverified theory as an explanation to a question on here is not only misleading, it is against PF guidelines.
Once more you go too far by not distinguishing the part that has indeed been evaluated in peer-reviewed journals concerning the inadequacy of the usual antisymmetrization formulation if not accompanied by the qualifications regarding the ambiguities and choices of spin-quantization frames. The more this error is perpetuated, the more physics suffers. It also seems unnecessarily perverse to me to point out the problem without also mentioning the solution.

As regards the many-particle issue, I only mentioned this in response to (a) repeated demands from you that I cite areas where experiment can distinguish my formulation from the usual one and (b) because the issues around the antisymmetrization formulation introduce unresolved questions about its use in many-particle field theory computations. It is you that keeps hammering on about this. In responding to you, I have also always been quite clear to mention the unresolved areas.

Then I would say that till you can rederive an equivalent to the BCS ground state from YOUR theory and get back all the physical values that it did that match the experimental observation, I would put a serious question mark to its validity.
Actually, when I awoke this morning I remembered there was a caveat regarding my many-particle proof. The caveat effectively concerns a condition in my proof that possibly can be relaxed. This is the condition that rotation phases induced by permutations cannot depend on the states of particles not involved in the permutation and is obviously where the question mark lies. The relevance can be seen as follows:

Consider a 3-particle state. One can antisymmetrize pair [1,2] by the usual order-dependent choice of relative orientation of the spin quantization frames (SQF). Likewise one can antisymmetrize pair [2,3] in the same way. However, one is not then free to antisymmetrize pair [1,3] in the same way, because the relative orientations of the SQFs is already specified. This is the basis of my proof forbidding full anti-symmetrization.

However, it turns out that it is still possible to antisymmetrize [1,3] by introducing an additional exchange phase factor for this pair only that involves the relative orientations of [1,2] and [2,3]. (One can always introduce additional order-dependent phases and consequent exchange signs, as long as one keeps track of them.) This seemed crazy to me at the time (and in terms of the usual field-theoretic antisymmetrization formulation as a property of only the exchanged pair it is indeed crazy) so I ruled it out. However, it does suggest that simultaneous full antisymmetrization is possible using a highly complex and artificial order-dependency that employs additional order-dependent phases to those that come purely from choosing relative SQFs for the exchanged particles. And for four or more particles the majority of pairwise relative orientations become special cases that depend on unexchanged particles, rather than the simple order-dependency condition that holds for the two-particle case and involves only those two particles. The final exchange phase, being always a simple minus sign hides the complex order-dependency required in the individual state descriptions.

I will have to think about this more, but I am realizing that my condition concerning non-involvement of non-exchanged particles in defining the order dependence between any exchanged pair may not be reasonable after all and this may be a source of error in my claim that full antisymmetrization is not possible.

None of this discussion places any question mark, however, over the derivation of the two-particle exclusion rules -- which is what my original contribution to this thread was about.

Staff Emeritus
mikeyork said:
Once more you go too far by not distinguishing the part that has indeed been evaluated in peer-reviewed journals concerning the inadequacy of the usual antisymmetrization formulation if not accompanied by the qualifications regarding the ambiguities and choices of spin-quantization frames. The more this error is perpetuated, the more physics suffers. It also seems unnecessarily perverse to me to point out the problem without also mentioning the solution.

As regards the many-particle issue, I only mentioned this in response to (a) repeated demands from you that I cite areas where experiment can distinguish my formulation from the usual one and (b) because the issues around the antisymmetrization formulation introduce unresolved questions about its use in many-particle field theory computations. It is you that keeps hammering on about this. In responding to you, I have also always been quite clear to mention the unresolved areas.

But you haven't! In fact, I was the one who pointed out several examples in condensed matter in which, not only is there no such thing as being "unresolved", but CLEAR antisymmetrization were used to describe those phenomena! (Mott insulator, BCS ground state, let's include He3 superfluidity in it too). And these ARE NOT just "two particle" systems, but a many-particle system where you claim that "conventional theory" and your theory should deviate. Yet, the conventional theory works VERY well here. On the other hand, there's nothing from your end to make the same level of success. In fact, it appears that till I brought it up, you were not even AWARE of such phenomena.

So let's see... on one hand, conventional theory HAS produced a consistent many-body description of a great deal of phenomena. On the other hand, you claim they haven't (very strange when you were not aware of these phenomena till yesterday when I brought them up), and instead your class of theory can (I believe you still haven't come up with something similar to the BCS ground state).

I'm sorry, but no matter how well and gorgeous your theory is, until it can make an agreement with experimental observation, I don't buy it. Start with one of THE most tested and verified phenomena of all time: the many-body phenomena of superconductivity. Produce a rival to the BCS theory. Till you can show this, you will understand that your claim that many-particle antisymmetrization is an "unresolved" question.

Zz.

mikeyork
ZapperZ

I am tired of this silly game where you consistently misrepresent whatever I write in the worst possible way you can find and jump to the most aggressive but inaccuratel conclusions. Even when I correct this you continue to repeat the same misrepresentations which you justify from selected partial readings of what I write. I presume this gives you some sort of perverted pleasure. I would have preferred a respectful dialogue, but I guess it's not to be found with you.

In the meantime, I suggest you get up to date on the origins of the spin-statistics connection and the Pauli rule if you intend to contribute to a thread about it.