Does Pauli Exclusion still make sense when the particle interpretation fails?

In summary, Pauli exclusion states that no two particles can occupy the same state and exchanging two particles results in a factor of -1, which is a basic fact about a spinor field due to anticommutation relations. However, in strongly curved space time, QFTs may not have an interpretation in terms of particles. This does not affect the Lorentz-transformation properties or quantum numbers of the fields, but it may make it difficult to define a natural set of basis modes for particles that would be recognized by all observers. Each observer can still define particles in their frame and relate them to particles defined by other observers through Bogolubov transformations.
  • #1
petergreat
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Pauli exclusion says no two particles should occupy the same state. Alternatively, it says that exchanging two particles generate a factor of -1. This is a basic fact about a spinor field, as a result of anticommutation relations. However, I hear that in strongly curved space time, QFTs have no interpretation in terms of particles. In this case, do the above two statement of Pauli eclusion fail to make sense, since both of them involve the concept of "particles"?
 
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  • #2
Well, your post itself says that "This is a basic fact about a spinor field", which doesn't seem to me to depend on the concept of particles. I know pretty much nothing about QFT in strongly curved spacetime, but I would be surprised if the Lorentz-transformation properties of the fields (which makes them spinors) or their quantum numbers (which define the states) were affected by the curvature.

I took a quick look at Carroll's section 9.4 on "Quantum Field Theory in Curved Spacetime"; he only considers scalar fields, but concludes (page 401), "We see that QFT in curved spacetime shares most of the basic features of QFT in flat spacetime; the crucial difference involves what we cannot do, namely decide on a natural set of basis modes that all inertial observers would identify as particles." Any given observer, however, is able to define "particles" in their frame, which can be related to the particles defined by other observers in different frames through Bogolubov transformations.
http://preposterousuniverse.com/spacetimeandgeometry/
 

1. What is the Pauli Exclusion Principle?

The Pauli Exclusion Principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This means that in a given system, two fermions cannot have the same set of quantum numbers, such as energy level, spin, and orbital angular momentum.

2. How does the Pauli Exclusion Principle relate to particle interpretation?

The particle interpretation of quantum mechanics assumes that particles are well-defined, point-like objects with definite properties such as position, momentum, and spin. The Pauli Exclusion Principle plays a key role in this interpretation by preventing two particles from occupying the same state, which would lead to ambiguities in their position and momentum.

3. Why does the particle interpretation fail in certain situations?

The particle interpretation fails in certain situations, such as in the case of particles in a confined space or at extremely high energies, because it does not fully account for the wave-like nature of particles. In these situations, the position and momentum of particles become uncertain and cannot be simultaneously well-defined.

4. Does the Pauli Exclusion Principle still apply in situations where the particle interpretation fails?

Yes, the Pauli Exclusion Principle still applies in situations where the particle interpretation fails. This is because the principle is a fundamental property of fermions and is not dependent on the particle interpretation.

5. What are the implications of the Pauli Exclusion Principle for understanding matter?

The Pauli Exclusion Principle has important implications for understanding the structure and behavior of matter. It explains why atoms have distinct energy levels and why elements have unique chemical properties. It also plays a crucial role in understanding the behavior of electrons in materials and is essential for many technological applications, such as transistors and computer memory.

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