Schrödinger's cat, pure or mixed state?

In summary: The usual description of Schrödinger's cat is that after being placed in the box, Schrödinger's cat is in a superposition state of being alive and dead, represented by two different pure states. However, it can also be described as a mixed state, where we have incomplete information about the exact state of the cat. This is less mysterious than claiming the cat is both alive and dead. This mixed state can also be created by loading a poison ampoule triggered by a randomly polarized photon, showing that the cat is in a mixed state along with the photon, photon-detector, and their environment. Ultimately, it is the combination of all these elements that is in a pure state, rather than just the
  • #1
Khashishi
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The usual description of Schrödinger's cat is that after being placed in the box, Schrödinger's cat in a superposition state of being alive and dead. Sometimes, I see this written as:
[itex]\mid \Psi \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle+\mid dead \rangle)[/itex]
This is representing a particular pure state which is distinctly different from
[itex]\mid \Psi' \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle-\mid dead \rangle)[/itex]
In some sense, these are different rotations of the alive-dead spinor.
But, should this be more properly treated as a density matrix?
[itex]\begin{bmatrix} 1/2 & 0 \\ 0 & 1/2 \end{bmatrix}[/itex]
That is, we have incomplete information about the Schrödinger's cat's exact state, which is significantly less mysterious than claiming the cat is alive+dead.

We could, for example, construct a Schrödinger box by loading an ampoule with poison, and triggering the poison with a photon detector which is behind a polarizer and a photon source. The photon source emits randomly polarized light. The photon polarization is in a mixed state, so the cat should be, too. Can we actually construct a pure state of cat actually be in a pure state of alive+dead?
 
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  • #2
You are right, Schrodinger cat is in the mixed state. The photon is also in the mixed state. But the cat, photon, photon-detector, and their environment TOGETHER are in a pure state.
 

FAQ: Schrödinger's cat, pure or mixed state?

What is Schrödinger's cat thought experiment?

Schrödinger's cat is a thought experiment in quantum mechanics proposed by physicist Erwin Schrödinger in 1935. It raises questions about the nature of reality and the role of the observer in quantum systems.

What is the pure state and mixed state in Schrödinger's cat experiment?

In Schrödinger's cat experiment, the pure state refers to the cat being either alive or dead with 100% certainty, while the mixed state refers to the cat being both alive and dead at the same time due to the principles of quantum superposition and entanglement.

How does the observer affect the state of the cat in Schrödinger's cat experiment?

In Schrödinger's cat experiment, the observer has a crucial role in determining the state of the cat. When the box is opened, the observer collapses the quantum wave function and forces the cat to be either alive or dead, ending the state of superposition and entanglement.

Is Schrödinger's cat experiment possible in reality?

No, Schrödinger's cat experiment is a thought experiment and cannot be replicated in reality. It serves as a theoretical illustration of the principles of quantum mechanics and is not meant to be taken literally.

What are the implications of Schrödinger's cat experiment?

Schrödinger's cat experiment raises philosophical questions about the nature of reality and the role of the observer in quantum systems. It also highlights the strange and counterintuitive properties of quantum mechanics, such as superposition and entanglement.

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