- #1
Whitefire
- 39
- 0
I have a question: can the mechanism behind Pauli's exclusion principle be considered a fundamental force, like gravitational, electromagnetic, nuclear weak or strong? Why?
Thx.
Thx.
No, it's a fundamental restriction on the states that are available. Calling it a force would be like saying there's some force that pushes a particle into states with integer angular momentum. Same thing - states with integer angular momentum simply happen to be the only ones available!Whitefire said:I have a question: can the mechanism behind Pauli's exclusion principle be considered a fundamental force, like gravitational, electromagnetic, nuclear weak or strong?
Whitefire said:I have a question: can the mechanism behind Pauli's exclusion principle be considered a fundamental force, like gravitational, electromagnetic, nuclear weak or strong? Why?
WannabeNewton said:No. Are you thinking of degeneracy pressure?
bhobba said:I suspect it may be, as I think Dyson first showed, that solidity is in fact a result of the Pauli Exclusion principle. Since many of the forces that occur in the everyday world are reaction forces due to this solidity in a sense it could be considered a fundamental force.
I don't agree with that view, but understand some may look at it that way.
Thanks
Bill
Bill_K said:No, it's a fundamental restriction on the states that are available.
HeavyMetal said:I've seen that question on here before a few times. It has come up relatively frequent. Interesting how everyone keeps coming to that conclusion!
fundamental restrictionon the states that are available
And forces are forces. You asked if the Pauli exclusion principle can be considered a force, and the answer is no, it cannot.Whitefire said:States are states. How the restriction happens is the mechanics I was asking about.Bill_K said:No, it's a fundamental restriction on the states that are available.
It's a build-in mechanism.Whitefire said:States are states. How the restriction happens is the mechanics I was asking about.
No, and thereforeJabbu said:Spin is just another name for magnetic dipole moment
NoIs magnetic force between two dipoles not part of derivation for Pauli exclusion principle?
Nugatory said:No, and therefore
No
When you say "move heat around," do you just mean heat transfer throughout the medium? Also, do states mandate particle behaviors, vice versa, or are they directly related?Ken G said:Yes, it stems from the uncertainty principle, if you like. The states always behave like that, but in a classical gas, the states are sparsely populated, so the particle behaviors are not constrained by what the states are doing, if you move around heat. In a degenerate gas, they are, so you have less freedom to move heat around. Yet either way, if you move no heat around, then both the classical and degenerate gases will have their particles follow the changes in their respective states, they follow the behavior of the state they are in-- the state that the particles in are "adiabatic invariants", so adiabatic compression of a degenerate gas is just like adiabatic compression of an ideal gas. Differences between "degeneracy pressure" and "ideal gas pressure" are often overstated.
Ken G said:Fermions have half-integer spin, but they don't have to have charge so they don't have to have a magnetic dipole moment.
Moreover, since electrons have charge, they experience electrostatic forces, but that also has nothing to do with the PEP.
Jabbu said:What other physical property there is to spin beside magnetic moment?
HeavyMetal said:Spin is a purely quantum mechanical property and there is no classical analogue.
HeavyMetal said:Anyone? Do paired neutrons repel each other, and if so, is this the basis of degeneracy pressure in neutron stars?
HeavyMetal said:So, because more than two bosons can occupy the same energy state, they demonstrate much lower pressure for the same number of particles as a fermion gas at any given temperature?
HeavyMetal said:If ##T = 0 K##, is the energy of a large number of bosons much lower than a group of fermions due to attraction?
I am not very familiar with the exchange interaction yet. It is something I've encountered but not used in my work. Is an exchange interaction similar to two potential wells that are next to each other, that gain just enough momentum to exchange? And as a result, the wavefunction becomes antisymmetric or stays symmetric depending on the nature of the particles?WannabeNewton said:Not at any temperature. If the temperature is high enough for the thermal wavelength to be much smaller than the spacing between gas particles then we pass over into Maxwell-Boltzmann statistics which doesn't distinguish between fermions and bosons. However at extremely low temperatures, i.e. ##T = 0##, we can say that for ideal Bose gas vs. ideal Fermi gas in the same volume the pressure of the latter is greater than that of the former. See below.
Yes but again it's not an attraction. It's just an exchange interaction. The bosons all like to clump together in the ground state because of Bose statistics. There is no attractive potential between the bosons in an ideal gas.
For a Bose gas of conserved particle number, and for a Fermi gas, the equation of state ##P = \frac{2}{3}\frac{E}{V}## still holds. For a photon gas, where particle number isn't conserved, we instead have ##P = \frac{1}{3}\frac{E}{V}##.
I mean adding heat, not just shifting the levels by slowly changing the volume. Adding heat shuffles the particles into new higher-energy states, whereas adiabatic compression simply moves all the levels up to higher energies but keeps the particles in the "same levels" as they shift up.HeavyMetal said:When you say "move heat around," do you just mean heat transfer throughout the medium? Also, do states mandate particle behaviors, vice versa, or are they directly related?
Good point, but that's because a neutron is not itself an elementary particle with zero charge, it is comprised of particles of positive and negative charges. In any event, the magnetic properties of the neutron have little or nothing to do with the pressure inside a neutron star.Jabbu said:Neutron has no charge and yet it has magnetic moment.
Sure, any chargeless fermion that is itself an elementary particle. Say, a neutrino.Can you name a particle with 1/2 spin which has no magnetic moment?
The quantum statistics that have to do with the Pauli exclusion principle and the way heat is partitioned among a set of fermions that are close to their ground state, like the electrons filling the levels in a molecule or atom. You don't think the electrons filling the shells of a noble gas atom have important magnetic effects do you? Yet, the level structure of that atom is completely ruled by the PEP.What other physical property there is to spin beside magnetic moment?
Not generally. For example, the helium atom has two electrons, and their electric repulsion is more important than their magnetic interactions. The PEP appears in how differently those electrons act if they have the same or opposite spins, and that's way more important than any magnetic effects.Wouldn't magnetic dipole force between two electrons overcome their electric repulsion if they came close enough together?
Be careful though, there exist a lot of misconceptions about pressure-- the pressure is a result of whatever reasons the system has internal kinetic energy, as usual. It's true that if you put the system in a low-temperature bath, it will still draw a lot of heat from that bath because degeneracy does require a lot of internal energy to fill all those states, and it's because of the PEP that this is true, but that's not the exchange interaction. The exchange interaction is different, it requires that the particles exert a force on each other, i.e., it comes from the potential energy in the Hamiltonian. Degeneracy pressure would normally neglect any forces between the particles, it applies for the quantum mechanical equivalent of an ideal gas.WannabeNewton said:So the pressure is really just a result of the exchange interaction between the fermions that forces the fermions to higher and higher energies above the ground state energy even at ##T = 0##, resulting in force exerted on the "walls" of the "container" of gas.
I don't want to seem picky, but the issue there is not whether the particles are conserved or not, it is how relativistic they are. Relativistic particles of all types have the 1/3 coefficient there, non-relativistic have the 2/3. But your main point is well taken-- pressure just comes from kinetic energy density, so if you want to understand what the pressure is, you have to understand the energy history. Too much can be made of the PEP in this context, it just depends on how you are tracking that energy history whether you care about the PEP at all.WannabeNewton said:For a Bose gas of conserved particle number, and for a Fermi gas, the equation of state ##P = \frac{2}{3}\frac{E}{V}## still holds. For a photon gas, where particle number isn't conserved, we instead have ##P = \frac{1}{3}\frac{E}{V}##.
Ken G said:In any event, the magnetic properties of the neutron have little or nothing to do with the pressure inside a neutron star.
You don't think the electrons filling the shells of a noble gas atom have important magnetic effects do you?
The PEP appears in how differently those electrons act if they have the same or opposite spins, and that's way more important than any magnetic effects.
It all depends on what you mean by "an interaction". If I have a hot gas in a box, and I open a door to the box, the gas comes shooting out. In a fluid description, we will say the gas accelerated out of the box. But there will not be any forces on that gas, so no "fundamental interactions" are involved in the acceleration of that gas-- it's just a bunch of particles that were carrying momentum and that's what they do when you open the door. This is the nature of pressure, so when one is talking about degeneracy pressure, this is what one is talking about-- not fundamental interactions.Jabbu said:The OP question is about Pauli exclusion principle being a consequence of some fundamental force, or not. I thought it is generally believed that every interaction is at its essence a consequence of one of the four fundamental forces, even though they can be expressed in different theories in terms of probabilities, curvatures, or virtual particles.
No, the PEP is talking about statistical mechanics, not forces between particles. The only type of force that the PEP directly gives you is the type you get when you look at a whole system and see how the internal kinetic energy E changes with volume V, so dE/dV. That is what we mean by pressure, but it's not a force between particles, it is a hypothetical change in energy of the particles when you hypothetically change V. You could effect that change in V using any fundamental force you like and it will make no difference-- you end up with the same dE/dV because that's a property of the system that has nothing to do with forces between the particles.I see here spin-orbit and spin-spin coupling are described as magnetic interactions. Is spin-spin coupling not the same effect PEP is talking about?
It involves the entire study of quantum mechanics, I'm not sure there is a shortcut. The key point is, in physics it's important to know when you need to worry about certain effects, like magnetic forces, and when you don't need to worry about them, like when you are using the PEP to understand the statistical properties of a bunch of fermions at very low temperature.And when this articles talks about relation between magnetism and mathematical formulation of quantum mechanics, in particular regarding spin and the Pauli principle, than what does it really mean and where can we see this "mathematical formulation"?
I think I presented an argument that the Pauli exclusion principle has nothing to do with any force or interaction; it is valid even for free particles w/o any interaction at all.Jabbu said:The OP question is about Pauli exclusion principle being a consequence of some fundamental force.
The spin-statistics-theorem demands to quantize spin-1/2 fields using the fermionic i.e. anti-commuting field operators. These operators guarantuee purely algebraically that the Pauli exclusion principle is satisfied. Everything else like interactions, atomic orbitals, pressure, macroscopic effects, ... comes on top of or can be derived from these fundamental rules.tom.stoer said:Introducing fermionic creation operators an electron with quantum numbers denoted by 'r' is described by a fock space state
[tex]|r\rangle = a_r^\dagger|0>[/tex]
where ##|0>## is the vacuum state. All states can be constructed that way. And all interactions can be expressed in terms of these creation (and annihilation) operators.
Now because of the Pauli principle (or the more fundamental spin-statistics theorem) we construct the creation operators such that the following holds
[tex]a_r^\dagger\,a_s^\dagger = -a_s^\dagger\,a_r^\dagger[/tex]
For ##r \neq s## this means that a state with two different fermions is anti-symmetric w.r.t. to interchange of to particles.
But for ##r = s## this means
[tex](a_s^\dagger)^2 = 0[/tex]
So we construct the mathematical formalism such that no two identical fermions can be described by the formalism
tom.stoer said:The spin-statistics-theorem derived from CPT demands to quantize spin-1/2 fields using the fermionic i.e. anti-commuting field operators. These operators guarantuee - as described above - that the Pauli exclusion principle is satisfied. Everything else like interactions, atomic orbitals, pressure, macroscopic effects, ... can be derived from these fundamental rules.
The best way to ensure accuracy on Wikipedia is to carefully evaluate the sources cited in the article. Look for reputable, peer-reviewed sources and cross-check information with other reliable sources. You can also check the article's edit history and discussion page for any potential biases or inaccuracies.
Wikipedia is not considered a reliable source for academic work, as anyone can edit the articles. However, it can be a useful starting point for research and can lead you to more reputable sources. Always verify information with other sources and use Wikipedia as a jumping-off point for further research.
Utilize the search bar and filters to narrow down your search and find relevant articles. You can also use the table of contents and headings within an article to quickly navigate to the specific information you need. Additionally, consider using external search engines, such as Google, to search within Wikipedia for more targeted results.
Anyone can contribute to Wikipedia by creating an account and editing articles. However, it is important to follow Wikipedia's guidelines and policies, such as citing reliable sources and maintaining a neutral point of view. You can also join WikiProjects related to your field of interest to collaborate with other editors and improve scientific articles on Wikipedia.
Wikipedia is not a primary source for breaking news or information. It is best to wait for information to be verified and published in reputable sources before using it for research or academic purposes. However, Wikipedia can be a useful source for background information on a topic and can lead you to more recent and reliable sources.