# Quantum mechanics observer one dies

As far as I understand quantum mechanics, Schrödinger's cat is dead and alive when you don't watch, i.e. it is in superposition. Only after you look into the box the cat becomes dead or alive. Suppose that there are two observers in a room and the first observer looks into the box. They see the cat is dead and are about to shout the result to the second observer who is sitting behind the computer and cannot see the cat, but get a heart attack and die just before they shout. My question is, is the cat again in superposition for the second observer?

• Essentially this exact question is addressed in Sidney Coleman's entertaining and interesting lecture "Quantum Mechanics in Your Face." See pages 8-10 of arxiv.org/abs/2011.12671. The lecture is also on youtube, youtube.com/watch?v=EtyNMlXN-sw – Andrew Jan 16 at 23:11
• Schrodinger's cat illustrates the illogic and problems that occur when there is a hidden assumption that one of these situations applies: 1) there is no reality until it is observed; 2) all possible outcomes can exist simultaneously until an object is observed. If there is no observation of the particular situation, there is no information to confirm or refute either of these assumptions. – David White Jan 17 at 3:08

The thought experiment is known as Wigner's friend and it is a demonstration that quantum mechanical description of a situation depends on the choice of observer.

From the point of view of the first observer - call her Alice - the superposition collapses when she opens the box since in this description this is the point at which a measurement is performed.

From the point of view of the second observer - call him Bob - no measurement actually takes place. Instead, Alice becomes entangled with the cat in the box.

Mathematically, the description from Alice's perspective proceeds as follows

1. Cat is in the state $$|\psi\rangle = |D\rangle + |A\rangle$$ where $$|D\rangle$$ denotes the dead state of the cat and $$|A\rangle$$ denotes the alive state of the cat and where we neglect normalization.
2. Measurement collapses $$|\psi\rangle$$ into $$|D\rangle$$.

On the other hand, the description from Bob's perspective is

1. Cat is in the state $$|\psi\rangle = |D\rangle + |A\rangle$$, neglecing normalization.
2. Alice interacts with the cat. The composite system consisting of Alice and the cat becomes entangled in the state $$|\phi\rangle = |D\rangle|D'\rangle + |A\rangle|A'\rangle$$ where $$|D'\rangle$$ denotes the state of Alice having seen the cat dead and $$|A'\rangle$$ denotes the state of Alice having seen the cat alive.

Note that if Alice had not had a heart attack and managed to shout the result of her observation to Bob, then the second description would continue as

1. Measurement collapses $$|\phi\rangle$$ to $$|D\rangle|D'\rangle$$.

The key fact to understand is that in any application of quantum mechanics we designate - usually implicitly - certain system as the observer. An interaction of the observer with another system constitutes a measurement. This invokes the measurement postulate by which the state of the system collapses. On the other hand, interactions that do not involve the system designated as observer do not invoke the measurement postulate and do not lead to state collapse.

Note that while this is the description offered by quantum theory, we do not really know whether there are certain limits, e.g. of size or mass, beyond which it no longer applies.

Something that's not generally known about the Schrödinger's Cat thought experiment is that Schrödinger was actually making fun of the whole idea -- mostly because he didn't understand it. Sure, later in life, he would become a respected quantum physicist, but the cat in the box thing was intended to be a ridicule.

What he didn't understand at the time is that the detector that releases the poison or not is what makes the "observation". You don't have to have a brain to make an observation (in the quantum mechanical sense), any effect that produces a change at a macro level is an observation. So, the cat is actually always either 100% alive or 100% dead, with no superposition.

To address your further questions, once a wavefunction is collapsed, it stays collapsed. Once the detector has observed that the radioactive material did or didn't decay, that's what everyone else will also observe, whether they're another detector, a human, a dog, or a spider.

• thanks all for taking the effory to reply. much appreciated. – Mart Jan 17 at 0:08

The cat is no longer in a superposition. It is now in a definite state.

The observation was already made whether or not this information reaches observer 2. Whether or not observer 2 knows, the system is in a definite state after the observation is made.

When observer 1 opens the box, the wave function collapses, and the system is in one of its two possible eigenstates with probability equal to one. Reduction to a single eigenstate upon collapse is due to the interaction with the macroscopic world and is not contingent upon human consciousness or cognition.

The system is initially in a superposition of two possible states

$$\psi_{cat} \rightarrow \frac{1}{\sqrt{2}} ( \mid \uparrow \rangle + \mid \downarrow \rangle )$$

where the states $$\mid \uparrow \rangle$$ or $$\mid \downarrow \rangle$$ can represent either plights of the cat. When an observation, or an interaction, occurs between the external macroscopic world and the detector, the system drops into either state $$\mid \uparrow \rangle$$ or $$\mid \downarrow \rangle$$ with probability one.

More information on this is detailed in what is known as the observer effect. Once this system has been observed, or measured, one knows its current state and this prevents it from evolving into one of its other states.

It is also interesting and important to note that this phenomena and how it happens has many interpretations. And from this article

An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics "corresponds" to reality.

• So what if there is an observer3 which is a dog. He sniffles around and looks under the box. He sees the cat is dead. Is it also definite? Following question if a spider would be observer3 and crawls under the box and observer1 and 2 dont know a spider went under the box. Thanks for replying in advance. – Mart Jan 16 at 23:25
• Any interaction at all that collapses the wave function. That is,any interaction with the external world. It has nothing to do with human perception. This is a common misconception. – joseph h Jan 16 at 23:44
• You cannot prove that it is not due to human consciousness though so why are you making that claim? – Stijn Boshoven Jan 16 at 23:53
• Yes you can prove it. There are infinitely many quantum interactions happening throughout the universe right now. Are you saying that all these processes should not happen because no one is there to observe them? Is that your claim? – joseph h Jan 17 at 0:04
• @StijnBoshoven Are you claiming that every process happening right now in your computer components and transistors are because you are directly observing these processes? – user280085 Jan 17 at 2:57