Doesn't Schrodinger's Cat start to decay?

[saddlestone-man]

TL;DR

If the cat is killed by the lethal gas, won't it start to decay and therefore when the box is opened it's possible to determine when the cat died.

In the experiment, if when the box is opened and the cat is dead, won't the cat's body have started to decay and therefore we could determine exactly when it had died.

This could have been a long time before we resolved the cat alive / cat dead question by opening the box. Therefore the state of decay shows that the alive/dead question was actually resolved long before we opened the box.

Or has the death of the cat somehow 'travelled back in time' from the instant we opened the box.

 

[PeroK]

This is one the essential points that doesn't get mentioned often. This is where the concept of decoherence comes in. To keep things simple, let's assume that the mechanism that kills the cat was only set to operate at one particular time. In other words, either the cat was killed at approx $t = 0$ or not.

To begin with you have a superposition of live and dead with little significant macroscopic difference. Now, as each of these branches evolves it diverges from the other. You have a huge number of superpositions associated with "live" cat that tend to a coherenet macroscopic system associated with a live cat; and a huge number of superpositions that tend towards a macroscopic dead cat.

The logic by which the two branches "decohere" follows a common QM theme where certain amplitudes tend to constructively interfere and others randomly destructively interfere. The result is that all the in-between states, that are in one sense just as valid as the two extreme states, have random amplitudes that effectively cancel each other out. Very quickly the probability of anything that is half-live and half-dead becomes vanishingly small.

The two extreme states, however, have a set of coherent amplitudes that constructively interfere and represent almost all the probability for the final state. This is how classical probabilities emerge from QM probability amplitudes for a sufficiently complex system - like a cat.

The QM/QED explanation for the behavior of light has a similar idea to explain diffraction, for example.

 

[Frodo]

That suggests a way (well, half a way) of traveling into the future. What happens if we wait a hundred years before opening the box and we find the cat is alive?

How has it survived 100 years when a cat's typical life span is less than twenty years?

Or is it saying that, in the "found alive" state, the cat aged normally and eventually died after consuming the food presumably left for it?

Also, isn't there a scientific view recently put forward that the wave function collapses of its own accord after a period of time if it is not interacted with. This gets over the problem of it needing sentience to collapse it.

 

[vanhees71]

This is an interesting question! Indeed there's a theorem that there cannot be an exactly exponential decay of a closed system due to unitarity. To derive the usual exponential-decay formula you must make an approximation (Wigner-Weisskopf approximation), which effectively treats the system as an "open system", which leads to decoherence.

For more details on the "no-go theorem", see J.J. Sakurai, Modern Quantum Mechanics, Revised Edition (I guess it's also in the newer 2nd edition edited by Napolitano). For the Wigner-Weisskopf approximation see, e.g., O. Nachtmann, Elementary Particle Physics.

 

[PeterDonis]

What happens if we wait a hundred years before opening the box

You can't. The box is not a magical box that keeps everything unchanged until you open it. The thought experiment only works if you open the box at a particular time after setting up the experiment, which time must be very short compared to the average lifetime of a cat.

 

[PeterDonis]

there's a theorem that there cannot be an exactly exponential decay of a closed system due to unitarity.

The radioactive atom inside the box is not a closed system. The complete box, including everything inside it, is considered to be a closed system for the duration of the experiment, but that total system has to include more than enough degrees of freedom to allow exponential decay of the radioactive atom to be a good approximation.

 

[phinds]

This gets over the problem of it needing sentience to collapse it.

There IS no need for sentience to collapse it. Sentience was an arbitrary point selected for the wave function collapse (I think by von Neumann) but it turned out that no sentience is required. For example, if the box is preprogrammed to open at a certain time and an electromechanical recording device "observes" the outcome, there is no need for a human to ever look at the recorded evidence.

 

[StevieTNZ]

There IS no need for sentience to collapse it. Sentience was an arbitrary point selected for the wave function collapse (I think by von Neumann) but it turned out that no sentience is required.

That is very misleading. As all interpretations, including consciousness cause collapse, supposedly give the same predictions, then all interpretations are wrong by your premise. Unless you have something to share we others don't know, that rules out requiring consciousness?

 

[PeterDonis]

isn't there a scientific view recently put forward that the wave function collapses of its own accord after a period of time if it is not interacted with. This gets over the problem of it needing sentience to collapse it.

"Collapse" is a matter of interpretation, and QM interpretations are off topic in this thread/forum. Discussions of QM interpretations belong in the interpretations subforum.

Unless you have something to share we others don't know, that rules out requiring consciousness?

Per the above, this is off topic for this thread/forum.

 

[PeterDonis]

The OP question has been answered, and this thread is closed.