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As a supplement to this question, as to whether particles can be observers, let us suppose that the answer is yes. One could suppose a setup where particle $A$ is observing particle $B$, but what is to stop us switching viewpoints around here and supposing particle $B$ is observing particle $A$?

I find this is an intriguing possibility considering the importance of symmetry in Physics.

Question: Is there a symmetry of observed & observer in QM?

John Rennie
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Mozibur Ullah
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  • Observers are irrelevant to quantum mechanics. They are only relevant in interpretations that involve wave function collapse, which itself is unphysical. – my2cts Apr 12 '21 at 22:28
  • @my2cts: Observers are not irrelevant to QM. It's wrong to think that interpretations of QM are not QM; they manifestly are. This is why Bohr, Heisenberg and Einstein discussed the ontology of QM. It's also wrong to say that collapse is unphysical - it's only in Many Worlds and similar interpretations that the collapse postulate is said to be unphysical; there are many others where it is taken to be physical. – Mozibur Ullah Apr 12 '21 at 22:58
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    I couldn't disagree more. – my2cts Apr 12 '21 at 23:36
  • Same here. Anything beyond the minimal interpretation is philosophy, not science. It is fine for scientists to have philosophy, but that doesn’t make it science. – Dale Apr 12 '21 at 23:52
  • @my2cts: Well, you're disagreeing with Bohr, Heisenberg & Einstein. – Mozibur Ullah Apr 13 '21 at 00:40
  • @Dale: Rutherford, Lord Kelvin & Maxwell published some of their results in Philosophy Magazine. It's only in the modern era that physicists have become philosophically unaware. – Mozibur Ullah Apr 13 '21 at 00:42
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    @Mozibur Ullah I am not philosophically unaware, I am anti-philosophy in the context of science. Science has progressed substantially since the days of Rutherford, et al. Philosophy, not so much. – Dale Apr 13 '21 at 01:40
  • This question only makes sense if given a rigorous definition of what it means to be an observer and what it means to observe something -- as far as I know there aren't any. – Pedro Apr 13 '21 at 07:45
  • @MoziburUllah For over a century there are problems to reconcile philosophy and physics. The modern era that you mention started in 1905! – my2cts Apr 13 '21 at 09:23
  • @pedro: The question presupposes that these notions are to be made rigorous in some sense. Thats why I partly asked the question. Wigner by the way attempted such a rigorous definition. – Mozibur Ullah Apr 13 '21 at 22:28
  • @my2cts: There were problems to reconcile philosophy and physics much further back than that. Newton said he couldn't philosophically hold it teneble that gravity acted at a distance ... it took three hundred years before that particular puzzle was solved with GR. – Mozibur Ullah Apr 13 '21 at 22:30
  • @MoziburUllah However, the problems posed by special and general relativity and quantum mechanics have not been solved since over a century. Moreover, perhaps the gravity problem was solved by GR, but EM has the same issue. – my2cts Apr 13 '21 at 22:48
  • @my2cts: I'm pointing out that the philosophical problems posed by Newtons theory took 300 years to solve in order to show that the considerably more difficult philosophical problems of QM having not been solved after only a century doesn't seem so much of a surprise ... – Mozibur Ullah Apr 13 '21 at 23:24

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Particles don't observe each other, they simply interact according to the Hamiltonian (if they didn't quantum mechanics wouldn't be able to explain the hydrogen molecule, for instance).

If you have two macroscopic observers, and they try to observe each other they would both collapse individually (though their collective wave function might remain the same, depending on interpretation).
However, this effect is absolutely unnoticeable because most states are experimentally indistinguishable from thermal equilibrium (look into quantum equilibration to understand more on this).

So: yes, symmetry is preserved.

Malabarba
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I guess this sort of question depends heavily on the interpretation of QM you are "believing" in. However, IMO, measurement or observing is a undirected relation. Consider a two-dim. system with orthogonal states $| 0\rangle$ and $| 1\rangle$. The von Neumann "pre-measurement" will establish entanglement between you, the experimentalist observing the system, and the system itself: $(|0\rangle|\text{you measure 0}\rangle+|1\rangle|\text{you measure 1}\rangle)/\sqrt{2}$.

The Copenhagen interpretation would suggest that the state collapses into one of the two terms. In relative state interpretations, each term would correspond to a distinct reality or "world". But regardless what interpretation you choose, the measurement process is symmetric and it's meaningless to ask whether you measure the system or the system measures you. Note however, that I'm not aware to all interpretations of QM.

Jonas Greitemann
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Oops. Read only the title, so answered the question, if an observer can observe themselves. The actual question is meaningless because if one person observes the other, then the one who is observed is not the observer.

Answer to the question I (wrongly) inferred from the title:

Short answer: no.

Full answer: in a system that properly includes the observer, there are states that the observer cannot distinguish in principle. Thomas Breuer called it "subjective decoherence".

So, the observer can try to observe a system where he is properly included, but he will fail determining its quantum state. In other words, the quantum state of such system does not exist. The wavefunction is not well defined.

Anixx
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