The statements are meaningless-and one way to see this is to replace electrons by helium 4 atoms in those statements. It's not true that the Pauli exclusion principle makes the statements it's associated with. This is, once more, explained in courses on the subject, so one should study them, though this explanation:  http://ejde.math.txstate.edu/conf-proc/04/w1/wightman.pdf  is, really, the most appropriate.

@ Stam Nicolis;;;;;

thank you my dear Stam Nicolis for saying statements are meaningless.

i am not getting your answer please elaborate.

you are saying; one way to see this is to replace electrons by helium 4 atoms in those statements. i am not getting about this...please elaborate.

thank you.

I suggest you to read the 1st chapter of https://www.amazon.com/Representation-Theory-Course-Graduate-Mathematics/dp/0387974954/ref=sr_1_1?ie=UTF8&qid=1476140832&sr=8-1&keywords=fulton+representation+of

Pauli principle is a combinatorial principle. Group theory is instrument used in combinatorics to get results. Pauli principle or modified Pauli principle comes as by product of the theory of representations of symmetric group. Nothing more to discuss.

@Arkady L. Kholodenko;;;;

thank you very much for giving me helpful suggestion.

this is the name I given to this particular modification and there is nothing more than this.

i can use another name for this new principle:  “identical particles (fermions, bosons) cannot occupy the same position”.

so i am requesting you to please answer only for this new principle. 

I can see that your mathematical level is low and that you are not willing to learn new things. The book I was recommending to you is ultimate source for any modification of  any existing (Pauli-like) rules.Because the combinatorics lies at the heart of Pauli principle as much as of any imaginable modification of this principle. Correctness of modification is contingent upon its compliance with the existing rules of group representation theory and combinatorics. Any discrete group is subgroup of symmetric group. This is rigorously proven result in mathematics.

@Arkady L. Kholodenko;;;;

yes my dear Arkady L. Kholodenko, i am of course willing to learn new things. any how i am respectfully thanking you to suggesting me to learn new things.

i am requesting you to elaborate;  my new principle: “identical particles (fermions, bosons) cannot occupy the same position”. is right or wrong?

if it is wrong please elaborate me.

This is your task if you want this result to be eventually published somewhere. I am just providing you with correct framework for talking publicly (and seriously) about such kind of topics

@Arkady L. Kholodenko;;;;

ya this is my published work in a journal: i am giving link below..

http://www.ghij.co.in/files/GPEP.pdf

i am respectfully thanking you for your valuable suggestions and support given to me up to now.

thank you my dear Arkady L. Kholodenko ....

International Journal of Gathering Hypothesis is not a journal which is indexed by the American Mathematical Society (Math Sci.Net database). I also  do not see this journal at the ADS database http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?return_req=no_params&author=Kholodenko,%20Arkady%20L.&db_key=PRE  where I am a regular contributor.  I do see, however,  that journal website claims that it is listed at the ADS database but I've checked this (ADS) database and was not able to find traces of this journal. While giving you an advise I had in mind ONLY journals listed in these databases

@Arkady L. Kholodenko;;;;

thank you ..

Somehow, teachers fail to mention that the Pauli principle formulated usual way applies only for the single-particle appeximation. 

Hence, the pain. Theoretical physicist who undertand this speak a different languare

@Igor Goliney;;;;

i am thanking you for your valuable response;

what i know is teacher never fails to mention something what is there in textbooks.

you know;

1) in past, teacher taught: earth is the center of our solar system.

2) in present, teacher teach us: sun is the center of our solar system.

earth or sun? experiment or evidence decide this.

according to me:

no scholar understand in different language but thinks the same thing in a different view as Einstein viewed.

as a theoretical physicist or a scientist we should not live in a dedicated circle. imagination is infinite. so, think without boundaries for the development of physics.

my dear Igor Goliney forget pauli and just give your valuable comment on my new view:

“identical particles (fermions, bosons) cannot occupy the same position”.

Dear s h s hussainsha,

You did not understand my remark about the teachers and what they forget to tell students.

As for your statement, it operates with the notion of the position of the particle which is not valid in quantum mechanics. The quantum mechanical systems are described with wave functions that extend through the whole space. These wave functions must be either symmetric or antisymmetric with respect to the change of notation. Otherwise everything would depend on our arbitrary chosen notation.

In the single-particle approximation that means that two identical fermions cannot have  the same one-particle wave functions, because the Slater determinant of them would be equal to zero. Hence, Pauli principle. 

The question about how do we know that the particles are indeed identical is much more interesting.

@ Igor Goliney.....

ya my dear Igor Goliney i too support your remark about the teachers (some) and what they forget to tell students.

as per my question;

the above information provided by you is absolutely correct.

1) i am requesting you to answer the following question:

in the single particle approximation two identical fermions occupy same position?

so please answer this question. so i can give elaboration (my view is valid in quantum mechanics)

2) this is the my intuition (In the single-particle approximation) why i given name as modified pauli principle. 

i am requesting you : is there any problem other than this which you mentioned in above answer?

thank you....

The generalization you are looking for is well-known. It is called The Spin-Statistics Theorem. It manifests whenever two particles (or multi-particle systems) are physically indistinguishable. The Pauli Exclusion Principle is a special case that applies to electrons. The simplest way to express it that fully captures all its implications is that, in their center of momentum frame, the two particles must have composite orbital (L) and spin (S) angular momentum such that L+S is an even integer.

An alternative, and more common, way to express it is to say that states of identical integer spin must be symmetrized and states of half-integer spin must be anti-symmetrized. But that is true only in an SU(2) (angular momentum) space. It is ambiguous in co-ordinate (position) space due to the 2pi rotation ambiguity in selecting a spin projection frame. 

@Mike York;;;;;

thank you my dear Mike York for your valuable response.

i want to clarify you one thing: " i am not swapping positions of any two particle".

if i say i am swapping, then your above answer is related (The Spin-Statistics Theorem) one.

i am requesting you, please once again read my new view and answer it.

my new view or proposal:

“identical particles (fermions, bosons) cannot occupy the same position”. If identical particles occupy the same position; they are entangled particles.

thank you.

Mike (York) I was saying exactly the same as you are saying but supported myself with the best mathematical source for completion of such a task. It is quite amazing (for me) that mathematicians had absolutely independently discovered all kinds of statistics used  in physics But they went far beyond of what physicists know and are willing to know.

State symmetrization or anti-symmetrization does not mean "swapping" except in the sense of  mathematical (non-physical) permutation.  In your paper (and in your question) you claim that 

“identical particles (fermions, bosons) cannot occupy the same position”

First you need to correct the word "position" to "state" because we are talking about quantum mechanics here. Then you say

"If identical particles occupy the same position; they are entangled particles."

which is in contradiction to your previous statement. This makes it very hard for anyone trying to grasp your ideas as they have to guess what you really intended to say.

As regards your paper it includes many other statements and concepts hat are too ambiguous (or contrary to usual usage) to to be useful. If you want any serious physicist to read and understand it it needs a major re-write that takes into account your audience.

That's how chemical bonds are formed. Two electrons occupy the same molecular orbital. The coordinate parts of their wave functions are the same. They differ by spins.

@ Igor Goliney.....

yep,Two electrons occupy the same molecular orbital. The coordinate parts of their wave functions are the same. They differ by spins.

my proposal is: if Two electrons occupy the same molecular orbital they are said to be entangled particles.

this is what i elaborated in this question:

“identical particles (fermions, bosons) cannot occupy the same position”. If identical particles occupy the same position; they are entangled particles.

thank you

@ Mike York;;;

my dear Mike York thank you for your valuable suggestions i am feeling lucky such a care giving to me.

my dear Mike York; is there any axiom in quantum physics  that says  you should pronounce only state not position?

what's wrong if i state position? 

in quantum mechanics, state is not obviously a single point in space. i think you know very well about this. in qm, quantum state some times constitute many points in space or group of particles.

this is the reason why i stated position despite of state.

you said: "If identical particles occupy the same position; they are entangled particles."

which is in contradiction to your previous statement. why it contradicts?

thanks a lot...

"state" is more general than "position" since a momentum state for example will not have a defined position. If you limit your argument to position when it can't be known -- as in discussion of atomic orbitals for instance -- you will likely end up with contradiction (as you did).

"cannot occupy the same position" contradicts the possibility "if they occupy the same position". 

@ Mike York;;;

of course state is a general than position.

but the problem is,

1) does Pauli principle hold good in multiple-particles approximation? 

my dear Mike York please answer this question

2) some times state constitute group of points in space or group many particles.

3) i want to include bosons also.

by considering these three problems i stated position rather than state.

my dear Mike York thats what i said : "if they occupy the same position".  they are entangled particles." in this way i remove contradiction.

and finally i am requesting you to answer this question:

"state" is more general than "position"

< does Pauli principle hold good in multiple-particles approximation? >

Pauli principle is for pairs of particles, not multi-particle states. You need to apply the spin-statistics theorem instead. Look at this paper:

https://arxiv.org/abs/quant-ph/9912057

As regards the contradictory statements, I assume from your response that the first sentence should then have read "cannot occupy the same position unless they are entangled." (This claim begs a lot of questions.) Physicists demand a logical argument. You need much greater clarity in what you write for them to see it.

@ Mike York;;;

i welcome you for your valuable suggestions...

my view is very clear that, identical particles cannot occupy same position unless they are entangled  and all entangled particles will be treated as; they are in same position.

still what questions This claim begs a lot ?

thank you

Except that is not what you wrote and why I had to drag it out of you.

What if particles have no defined position? E.g. if they are in a energy and angular momentum eigenstate? This is the situation that Pauli invented his rule for. What do you say about the Pauli rule then.

@ Mike York;;;

my dear Mike York good morning to you.

do you have proof:

1) particles have no defined positions cannot occupy same no defined positions?

2) particles have no defined positions can occupy same no defined positions?

do experiment or on logic basis tell me.. and you can adopt my view successfully to the above  questions. 

its true that: if they are in a energy and angular momentum eigenstate? Pauli invented his rule for..

due to angular momentum eigenstate I successfully applied my view. I think no need to elaborate here because you know about angular momentum.

thank you very much.....

still any questions or logical questions i respectfully welcome you.....

You have not addressed the issue:

What does " cannot occupy same position" mean if there is no defined position?

You should know that energy and angular momentum basis is incompatible with position basis. This is fundamental to QM. Definite energy and angular momentum implies indefinite position.

@ Mike York;;;

its true that, due to uncertainty principle if you know definite momentum implies indefinite position...

if there is no defined position: imagine two particles x and y....x has no definite position and y also have no definite position....x may be anywhere and y may be any where or they may exist all over space.

by adopting my view; if finding a particle x is having a probability of 1/4 at some point in space; at that point y does not exist. if exist, they are said to be entangled. in a similar if finding a particle y is having a probability of 1/8 at some point in space; at that point particle x does not exist. if exist, they are said to be entangled. 

this is the meaning of questions which i asked to you...

please may i know answer from your side: what is angular momentum and also represent in mathematical form. so i elaborate you very clearly....

thank you,,,,,

Consult any elementary textbook on QM. The Pauli principle you cited was introduced in terms of an atomic model in which electrons occupy states of definite angular momentum. You should definitely seek to understand  angular momentum states if you want to discuss the Pauli rule.

It also appears that you do not understand the concept of entanglement as I do not see how the way you use it connects to accepted usage. Which is probably because you apparently do not understand QM.

You may well have an alternative theory of the universe, but you seem to use terms in a way that disregards their accepted meanings. You would do better to invent your own terms in that case.

@Mike York;;;;;;

my dear Mike York thank very much........

i too applied my view in terms of an atomic model in which electrons occupy states of definite angular momentum...its absolutely right....

please you are missing one logic here its angular momentum.....there is a lot of difference between angular momentum and linear momentum...

i clearly explained you how to apply my view when you don't know definite position.

i feel very happy if you give proofs for your claim 'you do not understand the concept of entanglement '...

because you are like my physics and maths family member.....i welcome you and you have all rights to scold me, to hate me, etc..because we love each other.

thank you....

Sorry, I'm done.

@Mike York;;;;;;

yep, me to done......

@my dear unique scholars;;;;

its absolutely true that; in a single particle approximation Pauli principle is defined for energy and angular momentum.

the same statement i am modifying: identical particles cannot occupy same position.

skeptics says that:

1) Definite angular momentum implies indefinite position (according to uncertainty principle). Pauli principle is defined for angular momentum. then how you apply to  atomic model in which electrons occupy states of definite angular momentum?

2) What if particles have no defined position? 

my answers to skeptics for the above two questions:

1 answer: we have practical evidence that, Two electrons occupy the same molecular orbital. The coordinate parts of their wave functions are the same. They differ by spins.

     a) so how come to know The coordinate parts of their wave functions are the same?

     b) they don't know this (the following)?

            In the special case of a single particle approximation with no electric charge and no spin, the orbital angular momentum operator can be written in the position basis as a single vector equation:

 L= -i\h bar (r cross nabla )

2 answer: 

imagine two particles x and y....x has no definite position and y also have no definite position....x may be anywhere and y may be any where or they may exist all over space.

by adopting my view; if finding a particle x is having a probability of 1/4 at some point in space; at that point y does not exist. if exist, they are said to be entangled. in a similar if finding a particle y is having a probability of 1/8 at some point in space; at that point particle x does not exist. if exist, they are said to be entangled. 

some clever skeptics say after reading 2nd answer you do not understand the concept of entanglement :

if they understand that much clearly entanglement why can't they solve biggest problem of entanglement called as: as it violated the local realist view of causality?

my new view solves that problem :

to overcome this problem, i am proposing here a new principle

“identical particles (fermions, bosons) cannot occupy the same position”. If identical particles occupy the same position; they are entangled particles.

that is, Quantum Entanglement is the subject of assuming all particles are at same position though they are separated by large distance! 

my assumption is correct or wrong is decided by an experiment or evidence.

evidence: if entangled particles communicate instantaneously, my assumption is absolutely correct and causality problem also solved. 

if still anybody having doubts and questions please comment me for the development of physics...

thank you....