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specdude
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Are electrons closed systems?
specdude said:Are electrons closed systems?
stevendaryl said:What does "closed system" mean? Do you mean in the sense of thermodynamics?
specdude said:Sorry actually I mean An isolated system. One which cannot exchange any heat, work, or matter with the surroundings.
stevendaryl said:Well, electrons are viewed as point-particles. "Heat" is something that only applies to a system of many particles. There is no way to make sense of the temperature, for instance, of a single electron.
stevendaryl said:Well, electrons are viewed as point-particles.
Jazzdude said:I find this answer rather misleading. First of all, the number of particles doesn't matter for a system to be statistically describable or in thermal equilibrium. It's the number of degrees of freedom that count, and the electron has infinitely many of them. In quantum theory you can easily construct a thermal system with just one electron and describe it with a density matrix. If the electron is bound you get an incoherent superposition of all bound energy states with the usual exp(-E_n/kT) weights where the temperature of the system *is* defined and given by T.
The second problem I have with your answer is the way you arrive at your conclusion from subscribing to a point particle ontology for the electron. When we usually say the electron is a "point particle", we don't imply that it has the configuration space of a single point (which you seemingly used to imply that it's not a thermal system), but that 1) there is no known inner structure and we can spatially constrain the electron state as accurately as we wish, at least theoretically, and 2) the interaction terms in QED are those of single points, not extended regions. That does in no way however imply a point particle ontology of any sorts, because these point shaped interactions are always in nontrivial superpositions for all valid quantum states. But even if you feel that the Bohmian ontology is the way to go, the conclusion is not that the electron has the thermal properties of a classical point particle, because it is still fully equivalent for statistical physics to viewing the electron as having all the degrees of freedom the wavefunction offers.
Cheers,
Jazz
stevendaryl said:Hmm. But if you are considering an isolated electron, then what does it mean to be in thermal equilibrium? What is the temperature of an isolated electron?
Could you please explain why?Jazzdude said:It's the number of degrees of freedom that count...
and the electron has infinitely many of them.
The second problem I have with your answer is the way you arrive at your conclusion from subscribing to a point particle ontology for the electron. When we usually say the electron is a "point particle", we don't imply that it has the configuration space of a single point
But even if you feel that the Bohmian ontology is the way to go, the conclusion is not that the electron has the thermal properties of a classical point particle, because it is still fully equivalent for statistical physics to viewing the electron as having all the degrees of freedom the wavefunction offers.
Jano L. said:The function ##\psi(\mathbf r)## is a concept that describes electron. Not all of its characteristics are also characteristics of the electron. For example, the function is complex-valued, but electron is not. Electron has mass, but ##\psi## function has not.
Similarly, the ##\psi## function may belong to Hilbert space with infinite basis, but electron does not. There is no necessity to project all characteristics of mathematical functions onto material bodies.
...of electrons. Yes! That's what I'm saying.bhobba said:Our theories are mathematical descriptions - ...
Jano L. said:Could you please explain why?
Sometimes some of us do mean that. Especially in non-relativistic theory. I am afraid there is no universal agreement on the meaning of point-like. It depends on context.
The function ##\psi(\mathbf r)## is a concept that describes electron. Not all of its characteristics are also characteristics of the electron. For example, the function is complex-valued, but electron is not. Electron has mass, but ##\psi## function has not.
Similarly, the ##\psi## function may belong to Hilbert space with infinite basis, but electron does not. There is no necessity to project all characteristics of mathematical functions onto material bodies.
Jazzdude said:It's the number of degrees of freedom that count, and the electron has infinitely many of them.
A closed system is one in which the total amount of matter and energy remains constant. This means that no matter or energy can enter or leave the system, and all interactions occur within the system itself.
Yes, electrons can be considered closed systems. They have a finite amount of energy and cannot gain or lose energy unless they interact with another particle. Within an atom, electrons are confined and cannot leave the system.
Electrons are considered closed systems because they follow the laws of conservation of energy and mass. They cannot gain or lose energy on their own and can only do so through interactions with other particles. This allows them to maintain a constant amount of energy and remain in a closed system.
Yes, external factors such as electric and magnetic fields can affect the behavior of electrons in a closed system. These fields can cause the electrons to move or change direction, but the total amount of energy within the system will remain constant.
Closed system electrons are confined within a specific space and cannot leave the system, while open system electrons are able to move freely and can enter or leave the system. Closed system electrons also follow the laws of conservation of energy and mass, while open system electrons may experience energy loss or gain from external factors.