Four or Five fundamental forces

[DaTario]

Hi all

In Paul Tipler's book on modern physics (with Ralph LLewelyn) I read an explanation for the formation and stability of a molecule, which is based on Pauli's exclusion principle. This principle was responsible for a term in the energy equation, which yields also (naturally) a term in the force equation.

Is this quantum force an independent interaction or is it possible to decompose this exchange interaction in terms of gravitational, eletromagnetic, weak and strong nuclear force?

Best wishes

DaTario

 

[olgranpappy]

The "exchange interaction" is due to requirement that the many-body wave-function of a system of electrons be total antisymmetric with respect to particle interchange. In terms of single-particle wave-function this means that the electron "fill up" single particle states and no more than one eloectron can be in the same state. People do not usually consider exchange to be another type of force since it is just due to the symmetry of the wavefunction. And no it can't be decomposed into gravitation, electromagnetic, etc.

 

[DaTario]

If it cannot be thought of as combination of the four fundamental interactions, and if it is responsible (at least in part) to something important and relevant as the stability of molecules, I see no choice other than consider exchange interaction as one of the fundamentals.

Best wishes

DaTario

 

[peter0302]

Perhaps it is not considered a fundamental force because it acts instantaneously across the entire system (i.e. it has an infinite speed) and because iif there were an associated boson mediating the force it would have to have inifnite energy.

Otherwise I too wonder why it wouldn't be considered a force...

 

[danime]

Hi all

In Paul Tipler's book on modern physics (with Ralph LLewelyn) I read an explanation for the formation and stability of a molecule, which is based on Pauli's exclusion principle. This principle was responsible for a term in the energy equation, which yields also (naturally) a term in the force equation.

Is this quantum force an independent interaction or is it possible to decompose this exchange interaction in terms of gravitational, eletromagnetic, weak and strong nuclear force?

Best wishes

DaTario

The book is somehow wrong or you had not understanded it. The exclusion principle is not a force, but an effect of the anti-simmetry of the fermion wavefunction. There's a term in the energy due to the anti-simmetry, but the force in the term is one of the four fundamental forces. The term is due the exclusion principle, but the force in question is one of the four basic interactions.

 

[DaTario]

The book is somehow wrong or you had not understanded it. The exclusion principle is not a force, but an effect of the anti-simmetry of the fermion wavefunction. There's a term in the energy due to the anti-simmetry, but the force in the term is one of the four fundamental forces. The term is due the exclusion principle, but the force in question is one of the four basic interactions.

Tipler says the energy term associated with exclusion principle has the form U_{ex} = \frac{A}{r^n} where A and n are to be determined based on the experimental data of the specific elements which constitutes the molecule, and r is the distance from the nucleus. The term would be responsible for the repulsion, otherwise the coulomb attraction would imply the crashing of both nuclei.

There seems to exist, therefore, a force term (which in the case of K Cl is of the form A/r^{10} according to a solved exercise) implied by quantum mechanics. It still seems plausible to ask if this force can or cannot be derived from anyone of the four fundamental interactions.

Learning from Casimir effect, we may think of this force as eletromagnetic, in nature, but originated from quantum fluctuations (the r{-10} dependence reminds me the casimir term)

But no clue on how to estabilish this result.

Best wishes

DaTario

P.S. in no place we can read in the book that coulomb repulsion between protons take part in this process.

 

[danime]

The force is electromagnetic In fact it's the coulomb force. Many people thinks ferromagnetism is due to magnetic force. It's impossible once magnetic force can do no work and ferromagnetism can do work. In fact ferromagnetism is due to the coulomb force in the exchange energy term.

 

[blechman]

I think danime has it right: if you set the charge of the particle to zero, then there is no force, exchange or otherwise! So there you go. The force is EM.

What about the centrifugal barrier in ordinary mechanics? You know there is a term in the effective potential that goes like L^2/(2mr^2) in three dimensions, and a similar term appears in the quantum Hamiltonian. What "fundamental" force do you associate with this term? It comes from the "centrifugal force" but we would never consider such a force "fundamental" - as a matter of fact, some people would claim that it isn't even a FORCE in the rigorous sense. It is strictly a consequence of the non-inertial nature of the reference frame.

I think you can make an analogy here. The "exchange FORCE" is not a "force" in the rigorous sense, but is a consequence of the quantum-mechanical nature of matter's electromagnetic interactions, in the same way that the centrifugal "force" is a consequence of the reference frame.

 

[danime]

Descartes said "In trascendental matters be transcendentally clear".

There's no such thing as exchange force. There's a term in the hamiltonian due to the electromangnetic interaction that lowers the total energy when identical particles are in such state, which depends on the hamiltonian in question.

 

[danime]

As an example we can cite the ferromagnetism.

Once the electrons are fermions their total wave-function must be antisymmetric. When you construct the hamiltonian for say more than one electron interacting through coulomb force there are negative cross terms. If the terms are non null the total energy will be less so the nature prefers to make this terms non null. But the only way this terms can be non null is if the spins are parallel, once anti-parallel spin wave functions are orthogonal. This creates an effect contrary to the coulomb repulsion once the more the wave-functions overlap in the space the more effective is the exchange term.

It's a brief description of the ferromagnetic effect. There other things as domains, anisotropies, etc... But that have nothing to do with what we are dealling.

 

[DaTario]

What about the centrifugal barrier in ordinary mechanics? You know there is a term in the effective potential that goes like L^2/(2mr^2) in three dimensions, and a similar term appears in the quantum Hamiltonian. What "fundamental" force do you associate with this term? It comes from the "centrifugal force" but we would never consider such a force "fundamental" - as a matter of fact, some people would claim that it isn't even a FORCE in the rigorous sense. It is strictly a consequence of the non-inertial nature of the reference frame.

I think you can make an analogy here. The "exchange FORCE" is not a "force" in the rigorous sense, but is a consequence of the quantum-mechanical nature of matter's electromagnetic interactions, in the same way that the centrifugal "force" is a consequence of the reference frame.

I appreciate your mentioning the smilarities beween cantrifugal force and this exchange force. I would say that in the former case, the inertial contribution has a form which perfectly matches what we consider and expect of a force, while in the case of the exchange force, what we have in hands is a statement that poses restrictions on the probability of being at some specific portion of space. This geometrical and probabilistic nature of the exchange term is what puzzles me the most, for we are not used to force terms with this appearance.

Besides, it seems that you both agree that exchange force is the electrical force plus quantum fluctuation effects. Note that you don't mention the quantum mystery of the magic numbers 2, 8, 18, that represent the electronic capacity of each quantum level in the atomic structure. The exclusion principle as I know it, is an "ad hoc" term in quantum theory. It does not appear as consequence of the Shroedinger equation (correct me if I am wrong...).

Hoping we can see some light on this subject,

DaTario

 

[danime]

I appreciate your mentioning the similarities between centrifugal force and this exchange force. I would say that in the former case, the inertial contribution has a form which perfectly matches what we consider and expect of a force, while in the case of the exchange force, what we have in hands is a statement that poses restrictions on the probability of being at some specific portion of space. This geometrical and probabilistic nature of the exchange term is what puzzles me the most, for we are not used to force terms with this appearance.

The similarities are only superficial. Centrifugal force is just an inertial effect and depends on the frame of reference. The exchange term do not depends on it. It's as real as the fact that exists solids, which is a quantum effect due to the exclusion principle too.

Besides, it seems that you both agree that exchange force is the electrical force plus quantum fluctuation effects.

No quantum fluctuations here. Just fermionic wave-functions plus electrical force.

Note that you don't mention the quantum mystery of the magic numbers 2, 8, 18, that represent the electronic capacity of each quantum level in the atomic structure. The exclusion principle as I know it, is an "ad hoc" term in quantum theory. It does not appear as consequence of the Shroedinger equation (correct me if I am wrong...).

Correcting: Exclusion principle is not "ad hoc". It's a due to the fact that elementary particles are really identical, so exchanging identical particles cannot modify the probability of something to happen. Once the probability is the modulus of the wavefunction (a complex number), the exchanging may multiply the wavefunction by 1 or -1. When the factor is 1 we are talking about bosons, when -1 fermions. This alone produces the exclusion principle in fermions and the tendency to have many particles in the same state in bosons (ex: laser beams).

 

[danime]

Besides, it seems that you both agree that exchange force is the electrical force plus quantum fluctuation effects. Note that you don't mention the quantum mystery of the magic numbers 2, 8, 18, that represent the electronic capacity of each quantum level in the atomic structure. The exclusion principle as I know it, is an "ad hoc" term in quantum theory. It does not appear as consequence of the Shroedinger equation (correct me if I am wrong...).
DaTario

By the way this numbers are not magic. They are consequence of the exclusion principle and the solution of the schroedinger equation for the coulomb potential.

 

[peter0302]

By the way this numbers are not magic. They are consequence of the exclusion principle and the solution of the schroedinger equation for the coulomb potential.

Many physicists call them "magic numbers."

This geometrical and probabilistic nature of the exchange term is what puzzles me the most, for we are not used to force terms with this appearance

Not sure why you would say this. All force terms are geometrical and probabilistic. The electromagnetic force, for example, and the probability "sphere" of a single bound electron, look very similar. In fact, I would think you could recharacterize the magnitude of the force as the probability of a single quantized interaction (i.e. a photon exchange). The probability then decreases with the square of the distance. The quantum exchange "force" behaves similarly, with the exception that it doesn't depend on the distance.

Again, the only substantive difference I see between the quantum exchange interaction and the four fundamental forces is that the former is non-local.

 

[danime]

Many physicists call them "magic numbers."

It means nothing. Every physicist knows where they come from.

Not sure why you would say this. All force terms are geometrical and probabilistic.

Another meaningless statement.

The electromagnetic force, for example, and the probability "sphere" of a single bound electron, look very similar. In fact, I would think you could recharacterize the magnitude of the force as the probability of a single quantized interaction (i.e. a photon exchange). The probability then decreases with the square of the distance.

It's not how it works...

The quantum exchange "force" behaves similarly, with the exception that it doesn't depend on the distance.

The exchange "force" depends of the distance once it depends on the overlapping of the wavefunctions.

Again, the only substantive difference I see between the quantum exchange interaction and the four fundamental forces is that the former is non-local.

The substantive difference between the exchange interaction and the four fundamental forces is that the former are not a fundamental force, being an effect of the four fundamental forces

 

[peter0302]

It means nothing. Every physicist knows where they come from.

Now you're just being pedantic.

It's not how it works...

Why don't you illuminate us then?

The exchange "force" depends of the distance once it depends on the overlapping of the wavefunctions.

And then when it is triggered, it acts instantaneously across the entire system, i.e., non-locally.

 

[danime]

Now you're just being pedantic.

Sorry if I sounded pedantic. It's a matter of the first course in quantum mechanics in every university.

Why don't you illuminate us then?

It's not the probability that falls with square of the distance, but the potential. The probability has to do with the mean values whose calculate using operator acting on the wave-function, which has to do with state of the particle.

And then when it is triggered, it acts instantaneously across the entire system, i.e., non-locally.

Certainly, but it have never to do with what I said. You spoke about the time evolution of the state and I spoke about the spatial spread of the wave-function.


Do you want to have some guiding in studying quantum mechanics?

 

[danime]

Finally the topic was "Four or Five fundamental forces". By now four because even if you consider the exchange force as a real force It's not fundamental because it requires the electromagnetic interaction which is fundamental itself.

 

[blechman]

Let me try again. I tried previously to use the centrifugal barrier to give some intuition about the exchange force, but that didn't pan out. Let me try this one - the analogy is MUCH more appropriate:

What about the "6-12 potential" that appears in many branches of physics? This is an interaction that exists between molecules in a diatomic gas, for example. In reality: this is nothing more than the "leading order" effects of the quantum mechanical system and the electromagnetic interactions. We don't consider the "7-13-force" to be anything special - it is nothing more than an EFFECTIVE (macroscopic) interaction between the molecules. In fact, the 6-12 potential can be derived from the fundamental Coulomb interaction between the molecules and their constituents, INCLUDING things like the "exchange force".

And there are other examples as well. Infinitely many of them, in fact!

In summary: the "exchange interaction" is NOT a special force - it is part of the quantum realization of the fundamental force (in this case, E&M). It's almost misleading to call it a force at all!

 

[peter0302]

Do you want to have some guiding in studying quantum mechanics?

Tempting, but no thanks.

 

[DaTario]

By the way this numbers are not magic. They are consequence of the exclusion principle and the solution of the schroedinger equation for the coulomb potential.

Thank you. I could have avoid this error. In fact these numbers arise from justified requirements put on the solutions of the diferential equations that are produced in solving the SE by separation of variables.

Just to bring to this debate well known authorities, Eisberg and Resnick refer to this question clearly distinguishing exchange force (exclusion principle) and repulsion between nucleus in the same context, namely, the stability of a diatomic molecule.

Exchange interaction, as far as I know, cannot be reproduced by classical stochastic electrodynamics, being quantum in essence.


best wishes

 

[DaTario]

Another fact to join here. I have read in Eisberg Resnick that electromagnetic attraction and repulsion TOGETHER with exclusion principle act to produce molecular stability.

It seems that these authors do understand Pauli exclusion principle as something other than electromag.

best wishes

 

[Haelfix]

The exclusion principle is a consequence of the spin statistics theorem. This in turn is fundamentally due to quantum mechanics, the existence of identical and nonidentical particles and Lorentz invariance (of various quantities). It is not a force!

 

[DaTario]

The exclusion principle is a consequence of the spin statistics theorem. This in turn is fundamentally due to quantum mechanics, the existence of identical and nonidentical particles and Lorentz invariance (of various quantities). It is not a force!

I would like to produce with you together something which is more than sentences with exclamations marks. You must agree that this principle imposes restrictions to the positioning of the pair of electrons under consideration here.
Therefore it works like a force. Suppose a mass is attatched to a spring andit is also under the influence of a random force. Statistically, this two forces imply probabilistic restrictions on the mass positioning.
I know the randomic force is not even necessary in this argument, but I put it here to suggest the existence, in Pauli's principle, of some randomness (my belief).

best wishes,

DaTario

 

[peter0302]

There's a difference between a force increasing or reducing the probability of a particle being somewhere, and a principle that prevents absolutely a particle from being somewhere. It's the Pauli _Exclusion_ Principle, not the Pauli _Repulsion_ Principle. I think that's one of the important things that distinguish this from a "force."

 

[DaTario]

There's a difference between a force increasing or reducing the probability of a particle being somewhere, and a principle that prevents absolutely a particle from being somewhere. It's the Pauli _Exclusion_ Principle, not the Pauli _Repulsion_ Principle. I think that's one of the important things that distinguish this from a "force."

In part I agree. Coulombian repulsion prevents absolutely a charged particle to be at r = 0 (other charge's position) (charges of same sign).

I think your argument should not be considered a demonstration of your statement.
In think we need something different. Why the force does not imposes probabilistic restrictions on position?

best wishes

DaTario

 

[Haelfix]

Datario, as I just explained the spin statistics theorem is a consequence of various kinematic properties of the system (for instance lorentz invariance and so forth). It makes no allusion to a potential term or the functional form of the lagrangian (other than it must be a lorentz scalar). Ergo, it is not a force. It does no work on a system.

The confusion arises b/c in many body systems, people talk about say degeneracy pressure and things like that, indicating the difficulty to squeeze a bunch of electrons inside an enclosed volume. On one hand you will have coulomb like terms, on the other you have something that is intrinsically QM representing exclusion principle like pressure effects. But this is misleading, its an effective term that is really generated b/c the system under consideration isn't exact but merely modeled and emergent. Ultimately those terms are generated by the combination of many different processes including spin interactions and so forth. At a fundamental level, it is still not a force.

There are many analogies that I can think off. For instance, selection rules in atomic physics. These are restrictions and constraints on a many body system, but the reason they arise is hidden and one might be tempted to call them a force as well.

 

[DaTario]

Quoting and commenting separetly parts of your last post.

Ergo, it is not a force. It does no work on a system.

I know you know, but force does not have nacessarily to do work on a system.

Ultimately those terms are generated by the combination of many different processes including spin interactions and so forth. At a fundamental level, it is still not a force.

when you say that it include spin interactions it seems that you are yourself convinced
that it is a force.

Finally, even if you succeed in proving that PEP may be expressed in terms of a selection rule for transitions between position eigenvalues, it will not deny the possibility of its being interpreted as a force.

I agree that we know almost nothing about accelerative properties related to PEP, but it is physically simple to imagine a sort of collider implying two Hydrogen atoms to get very close and its electronic wave functions put to overlap. We know that this process for instance can not be treated adiabatically and it must be very difficult to dsolve in deed. But once PEP is valid statement, it will have implications on the decrease of the velocity of both atoms when they get too close. Force interpretation follows.

best wishes

DaTario

 

[peter0302]

The repulsion of atoms has more to do with the coloumb force than the PEP though no?

How does a black hole get around the PEP? Does the matter actually break down into photons or other bosons?

 

[DaTario]

If one considers PEP as electromagnetic interaction together with quantum fluctuations, things seems to quiet, but in this argument, there is no allusion to identical particles. Two different particles will also interact electromagnetically and will also suffer quantum fluctuations. I see no necessity of the equality of identities claim to provide PEP with a E&M + QM descrption. And at the end, this description will be incomplete, as identical particles are part of PEP.


Best wishes

DaTario

 

[Dmitry67]

I would say, there are 4 *fundametal interactions* and 5 *force sources*
Pauli ep is not an interaction but it behaives exactly like a force in some cases, for example, it is responsible for the stability of the white dwarfs and neutron star.

If you don't agress that Pauli e.p. is not a force, please fill the void in the following sentence:

In the while drarfs the gravitational force is compensated by ... that is why these objects do not collapse.

 

[tim_lou]

the so called 5th force is actually included in other forces already. The coulomb potential is in fact only an approximation. The actual physics comes from QED and when one goes beyond the first order approximation, one gets a spin dependent potential. So in fact, just by electromagnetism, the "coulomb" force is dependent on the spin of the two particles that are interacting.

Saying the Pauli exclusion principle is a force is wrong because if the QED interaction term is gone, then there will be no interactions. Two particles will never scattering/ or annihilate with one another. In fact, in this hypothetical world, there can never two particles having the same spin and momentum (the math just does not permit this from happening).

As for Dmitry67's sentence, if you really want to avoid using degeneracy pressure, you can say the gravitational force is compensated by spin dependent interactions from QED. You may complain that neutrons have zero net charge, however, there is still electromagnetic interaction (since the constituent quarks have charge).

 

[DaTario]

I would say, there are 4 *fundametal interactions* and 5 *force sources*
Pauli ep is not an interaction but it behaives exactly like a force in some cases, for example, it is responsible for the stability of the white dwarfs and neutron star.

If you don't agress that Pauli e.p. is not a force, please fill the void in the following sentence:

In the while drarfs the gravitational force is compensated by ... that is why these objects do not collapse.

It is easy not to get satisfied with your proposal of separating interactions from forces. These two concepts are entagled. Fundamental interaction and fundamental force seems to be the same thing.

Best wishes,

DaTario

 

[Dmitry67]

You may complain that neutrons have zero net charge, however, there is still electromagnetic interaction (since the constituent quarks have charge).

What about the neutrino?
They are fermions, right? So the pauli's principle is applicable to them too?
Should we also claim that "there is still electromagnetic interaction" between the neutrinos?
:)

 

[tim_lou]

The neutrinos interact via weak interaction. Similar "repulsion" effects will result if you take that into account. The reason why I mentioned QED only is because it is the one that I am familiar with. However, not knowing much about weak interaction, I do not know if the massive bound states (like neutron) can arise. If no bound state exists, the question of degeneracy pressure simply isn't valid.

The pauli exclusion principle essentially comes from the creation operator being anti-commuting, it is a feature of the free theory. This property is universal in any interaction (in the interaction picture) be it QCD, QED, or other things.

Ideas like pauli exclusion principle appear often in statistical mechanics. It is a general universal feature regardless of how complicated the interaction is. Similar to how a system tends toward maximum multiplicity. If the exclusion principle is a fundamental force, then I would say The tendency toward maximum entropy is another fundamental force, phase transitions would be another force... that just doesn't work, they are merely universal behaviors of more fundamental forces. A bound state of neutrons and/or a "hypothetical" bound state of neutrino all follow the pauli exclusion principle but fundamentally, they come from different interactions. Just because their behaviors look the same doesn't mean they come from the same interactions.