Questions related to the discernibility of many-body systems, its philosophical implications and its mathematical description.
Questions tagged [identical-particles]
403 questions
40
votes
9 answers
If electrons are identical and indistinguishable, how can we say current is the movement of electrons?
When we talk about current, we say electrons are "flowing" through a conductor. But if electrons are identical particles, how does it make sense to talk about them flowing?
To expand on that: imagine the simplest wire, just a 1-D chain of copper…
Mark Fugate
- 609
35
votes
4 answers
Are atoms unique?
Do atoms have any uniquely identifying characteristic besides their history?
For example, if we had detailed information about a specific carbon atom from one of Planck's fingerprints, and could time-travel to the cosmic event in which the atom…
Charles Burns
- 423
34
votes
5 answers
Are black holes indistinguishable?
In the standard model of particles it is understood that besides characteristics like momentum, spin, etc., two electrons are indistinguishable.
Are two black holes, in the same sense, indistinguishable given they have the same mass, momentum, etc.?
Marco
- 589
32
votes
11 answers
Theoretically, could there be different types of protons and electrons?
Me and my friend were arguing. I think there could theoretically be different types of protons, but he says not. He says that if you have a different type of proton, it isn't a proton, it's something else. That doesn't make sense to me! There are…
PaddiM8
- 457
29
votes
4 answers
How many of the molecules that you inhale in a breath did Caesar exhale in his dying breath, on average? - Does this question make physical sense?
There is a nice example of a Fermi estimation question where you ask: How many of the molecules which Julius Caesar (or Jesus, Muhammad, etc. — anyone who died a long time ago) exhaled in their dying breath do you inhale when breathing, on average.…
0x539
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27
votes
6 answers
Why doesn't the entropy increase when two similar gases mix with each other?
Entropy increases when two substances mix with each other.
For example, the entropy of mixing of two different gases are given by $$\Delta S= 2Nk\ln\frac{V_f}{V_i}\;.$$
But, the entropy doesn't increase when the two gases mixing are same.
This is…
user36790
26
votes
5 answers
Why are particles in Quantum Mechanics indistinguishable?
I'm currently reading about tensor products in Quantum Mechanics and composite systems and I've read that in Quantum Mechanics particles are indistinguishable while in Classical Mechanics that's not the case. This leads to the requirement that the…
Gold
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24
votes
4 answers
Why is every electron in the universe not entangled with every other electron?
According to the principles of identical particles, the wavefunction of a collection of fermions must be antisymmetric and such a state is entangled. Doesn't this mean that any given electron in the universe (which is a giant system) is entangled…
Solidification
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24
votes
4 answers
Why is the partition function divided by $(h^{3N} N!)$?
When computing partition functions for classical systems with $N$ particles with a given Hamiltonian $H$ I've seen some places writing it as
$$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$
where the integral is over the available phase space.…
Gold
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24
votes
2 answers
Are all electrons identical?
Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very slight degree? Is there a theory which proves…
Gsv
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23
votes
2 answers
How are anyons possible? (another version)
I know that this question has been submitted several times (especially see How are anyons possible?), even as a byproduct of other questions, since I did not find any completely satisfactory answers, here I submit another version of the question,…
Valter Moretti
- 80,330
23
votes
4 answers
How to justify "correct Boltzmann counting" (dividing by $N!$) without resorting to quantum mechanics?
Let a box of volume $V$ contain $N$ monatomic gas particles, with total energy $E$. By considering the "volume" of phase space consistent with our macro-observables ($E$, $V$, and $N$), the multiplicity of this macrostate is (from Ref.1)
$$
\Omega =…
eugenhu
- 555
22
votes
2 answers
Are protons and neutrons affected by the Pauli Exclusion Principle?
I'm very confused about the Pauli exclusion principle. Wikipedia states it as "two identical fermions cannot occupy the same quantum state in a quantum system". I understand this for electrons that for each energy level in an atom there are two…
shA3245699
- 335
20
votes
2 answers
Geometric quantization of identical particles
Background:
It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold $M^n = \frac{\mathbb{R}^{3n}-\Delta}{S_n}$, where…
David Bar Moshe
- 31,499
18
votes
5 answers
Is the $N$ factorial in the Partition function for $N$ indistinguishable particle an approximation?
I suspect that the $N$ factorial in the partition function for N indistinguishable particles
$$ Z = \frac{ Z_0^N } {N!} $$
is an approximation. Please someone correct me if I am wrong and why or why not. Thanks.
A simple case:
each particle has…
Chengjian
- 365