# Settling Copenhagen Interpretation / Measurement in QM & Existence of Quantum Gravity

It is my understanding that there are many interpretations of observation/measurement in Quantum Mechanics (I am only familiar with the Copenhagen one).

The Schrodinger's Cat experiment forms a paradigm in terms of understanding the state of a quantum system before its observation. Sometimes the analogy is taken too far and interpreted in terms like "If you don't observe the moon isn't there / it could be or not be there" i.e. "If you don't observe it then the moon isn't necessarily there". Such an argument of course ignores the decoherence due to the size of moon. But consider the following where one could argue the existence of a quantum system in a definite state at the moment in time when it hasn't been observed.

TLDR - Modifying the cat experiment one could have two observers such that one is blind and the other is deaf. If the blind observer hears a meow then can't the deaf observer (who can only consult the blind observer) say that the cat is alive (also assume that this is a weird universe with only the two observers as supernatural beings floating in space and a mystery box)?

Detailed version - Suppose that I assume the existence of a quantum theory of gravity (just that it exists and not its particular form). Now, consider two sets of events A=$$\{A1=(x_{A1},t_{A1}) ; A2=(x_{A2},t_{A2})\}$$ and B=$$\{B1=(x_{B1},t_{B1}) ; B2=(x_{B2},t_{B2})\}$$ where

$$x_{A1} - x_{B1} = 0 \\ x_{A2} - x_{B2} = 0 \\ t_{A1} - t_{A2} = 0 \\ t_{B1} - t_{B2} = 0 \\ x_{A1} - x_{A2} = 10,000 \mathrm{\ light\ years} \\ t_{A1} - t_{B1} = 10,000 \mathrm{\ years}$$

Now, assume that there is a black hole merger at A2. Of course, A1 will not be able to detect it immediately and cannot make a statement whether the black hole (or the associated Hawking Radiation) exists or not and like the Cat experiment the existence of Black Hole at A2 is not guaranteed. But an observer at B1 can detect the merger thereby saying that even at the time of events A1 and A2 Black Holes existed.

Doesn't this settle the argument? I am sure there is some fallacy here otherwise people would have pointed this out ages ago.

Note : One could argue that I am making a logical fallacy here and I will reply that: Assume that you detect a merger at B1 and then the argument can be run backwards without any fallacy.

• Mixing a non-existent accepted theory of quantum gravity into the unproveable (one way or another) choice of interpretation of quantum theory does not sound like a good plan to me. The (awful) "Cat experiment" which has done so much to hopelessly confuse decades of students just isn't going to help here, IMO. My advice is to Run Away, as Monty Python would put it. :-) – StephenG Sep 16 '20 at 18:31
• @StephenG I agree but the motivation to ask this is to determine whether, just as a thought experiment, this would be enough to settle the issue? – self.grassmanian Sep 16 '20 at 19:44

## 1 Answer

I believe this is a badly drawn space-time diagram of the four events: $$\begin{array} & t\uparrow & B1(x_1,t_2) & B2(x_2,t_2) \\ & A1(x_1,t_1) & A2(x_2,t_1) \\ & & x\rightarrow \end{array}$$ Events A1 and A2 are at the same height, so they are at the same time. Likewise, events B1 and B2 are at the same height, so they are at the same time. Events A1 and B1 are at the same horizontal position, so they are at the same spatial location. Likewise for A2 and B2.

Looking at this, I'm not sure how B2 can detect that there was a black hole merger at A2 like you say. While it is at the same spatial location, it is time-separated from A2, so the gravitational waves from the merger at event A2 would have already left that spatial location, right?

• Apologies. I meant for it to be detected at B1. – self.grassmanian Sep 16 '20 at 19:41
• Oh okay! I suppose then I would say that, this is a false analogy. I think to be truly analogous to Schrodinger's cat, event A2 would be in a superposition of states "have merged" and "have not merged". Evolving the total state into the future with Schrodinger's equation won't change the fact that you will either measure "have merged" or "have not merged" and you don't know which it will be, just like it doesn't matter matter when you look in the box. You'll see either alive or dead, and you don't know which. (maybe this argument breaks because Schrodinger's eq isn't Lorentz invariant though). – UrsaCalli79 Sep 16 '20 at 21:09
• So the Cat experiment analogy is just meant to serve as TLDR. As for the future evolution it is already provided that a merger has been detected from gravitational waves. Now, the question is not whether they merged but whether they existed at the time $t_{A1}$ or $t_{A2}$. The thought experiment is meant to address a question like : If you don't "look" is a quantum system really there? The proposed resolution here is that it is possible to detect (in certain cases) future indications which can resolve for us whether the system existed in past or not & then universality takes care of the rest. – self.grassmanian Sep 17 '20 at 0:53
• I think a proper TLDR should aim to be analogous, but okay, never mind the cat. It just seems to me that if it's already provided that a merger happened, you automatically assume the black hole exists. It's as if you assume the gas has already been triggered and so the cat is dead (sorry to bring up the cat again). But isn't it the point that you don't know which one it is before the measurement? If it's provided that a merger has been detected, then the measurement has already been taken. So of course there is no mystery there of whether or not the black hole exists. – UrsaCalli79 Sep 17 '20 at 1:44
• Even if A1 cannot detect the merger, it is not the case that the quantum state at A2 is in a superposition. This is because you say that it is already provided that the merger happened. That is, if you say that, then some measurement has happened at A2 that already collapsed the state into "have merged". So then you're right in that in the future at B1, you can definitely know what happened in the past! – UrsaCalli79 Sep 17 '20 at 13:20