A molecule of O$_2$ and a molecule of my DNA are not identical. Therefore, some sort of restriction must be placed on the word "particle", but what sort of restrictions and why them, not others?

Perhaps the particles must be "of the same thing" e.g. two electron or two hydrogen atoms. Then again, two strands of DNA are not identical but still count as "same thing".

  • $\begingroup$ This post may be very helpful to you. If the math or quantum mechanics in that post are beyond what you can understand, let me know and I can write a more introductory type version of the ideas there. $\endgroup$ – DanielSank Jul 5 '17 at 20:04
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    $\begingroup$ Two particles are indistinguishable if they are excitations of the same field. $\endgroup$ – gautampk Jul 5 '17 at 20:09

Two identical particles are indistinguishable. Therefore, whether or not two free electrons (without specifying the spin state $m_s$) are considered to be identical particles depends on the environment:

  • If no B field exists, the two electrons are indistinguishable. Hence, they are considered identical.
  • However, if a B field exists and one of the electrons has $m_s = 1/2$ and one $-1/2$, then the two electrons are distinguishable. Hence, they are not identical.

The same logic applies to "two H-atoms". If one is in the ground-state while the other is in an excited state, the two atoms are not identical.

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  • $\begingroup$ This doesn't address the issue of DNA molecules. $\endgroup$ – DanielSank Jul 5 '17 at 19:59
  • $\begingroup$ I understand waht you're saying but my issue is with the word particle, not the word identical. what kinds of things count as particles and what things do not and why? Because I study biochem, not physics, I often encounter things that are not treated by a traditional QM course yet clearly the principle of QM should apply to these things. For example, QM usually talks about "small" things such as elementary particles like electrons or composite particles like protons or different kinds of atoms. How about "larger" , chemical, things like H2O, CO2, or DNA or protein? $\endgroup$ – Zeyuan Jul 5 '17 at 20:09
  • $\begingroup$ My idea is that when we enter the realm of chemistry and biochemistry, certain things such as identical particle does not seem to apply. So does it apply to those examples? If yes, how so? If no, why? $\endgroup$ – Zeyuan Jul 5 '17 at 20:11
  • $\begingroup$ @Zeyuan Size isn't really the important factor in whether or not something behaves quantum-mechanically. The most important factor is how much the thing in question interacts with other stuff. The more a thing interacts with its surroundings, the less quantum-mechanically it behaves. I realize that's not a particularly satisfying answer, but if you'd like to drop into the chat room, we can discuss more. $\endgroup$ – DanielSank Jul 5 '17 at 20:11
  • $\begingroup$ @Zeyuan Here is the chat room. Ping me with "@DanielSank" to get my attention. $\endgroup$ – DanielSank Jul 5 '17 at 20:57

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