Does the cat collapse itself?

Christopher G

Using Quantum Mechanics is it possible to calculate the probability that conservation of energy does not hold
I guess you could, but the probability would be 0.

agentredlum

I guess you could, but the probability would be 0.
Great answer. Momentum is mv, kinetic energy is (1/2)mv^2 wouldnt HUP imply uncertainty in energy because of uncertainty in momentum? How can energy be conserved and still be uncertain?

Christopher G

Great answer. Momentum is mv, kinetic energy is (1/2)mv^2 wouldnt HUP imply uncertainty in energy because of uncertainty in momentum? How can energy be conserved and still be uncertain?
Well... you can't violate the expectation value for energy anyway!

agentredlum

Well... you can't violate the expectation value for energy anyway!
What do you mean by the expectation value for energy? Can you please elaborate?

Christopher G

What do you mean by the expectation value for energy? Can you please elaborate?
The average energy over a large number of measurements. The 'expected' energy.

==EDIT==
If you knew the energy of a system exactly, it would forever remain exactly that.
There is uncertainty in measuring energy however.

==EDIT2==
I totally see how this is confusing. But I'm definitely not equipped at the moment to explain it out in much detail (very tired, but I can't sleep... clowns). I'll do that tomorrow if this thread is not a poop-fest by then.

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agentredlum

Yeah, I just looked it up here.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html

I guess my question was fundamentally very simple on an intuitive level i was asking about a single measurement. I guess over many measurements uncertainties one way could balance out uncertainties the other way and you would get very close to the exact energy. Am i on the right track?

gamma5772

gamma5772 said:
It is experimental fact, as has been pointed out, that for microscopic objects, the Schrodinger cat experiment indicates that the cat (photon, electron, what have you) actually is in a superposition.
The Schrodinger cat experiment does not indicate that the cat is in superposition. Is is certainly not experimental fact that the cat is in superposition.

People seem to have a very difficult time understanding what the point of the experiment is. (Don't take this as offencive!) It simply serves to illustrate (as I have said too many times in this thread) the difference between the quantum world and the macroscopic world; When does a measurement take place? If you don't look at a far away planet is it's weather/clouds in a massive superposition of all possibilities until a human comes by to look at it? Unlikely (what's so special about a human?); so when does it collapse?
You seem to have misunderstood my point, both in the sentence you quoted, and in the my entire post. In the sentence quoted, the "cat" is not a cat at all -- it is a photon or electron -- experiments have been performed which indicate that the photon or electron is in a superposition (humor me when I say superposition since strictly speaking we don't know if the particle is in a superposition, we only know it behaves as if it were). The argument I presented IS the idea you have articulated so many times, that there is a difference between microscopic and macroscopic. That is premise 1, reproduced here for your reading convenience:
gamma5772 said:
P1. It violates experience and intuition to have a macroscopic object in a quantum superposition. ("I've never seen a cat in a superposition before!").
I, and the MWI, reject P1. We will discuss this in a second.

Decoherence (in the way that you mean it with 'many worlds') is an attempt to allow objects to remain in superposition 'post measurement' while still seemingly collapsing. This may be true, and the whole universe may be in superposition, but it would still have to behave effectively as if it wasn't. This is because we don't see objects in superposition. So if they are, it must be suppressed immensely (we don't ever see two cats).

More importantly, Discoherence has nothing to say about WHEN a measurement takes place. (when do the worlds split?)
I think you are misunderstanding decoherence and the MWI.

You state that decoherence and the MWI does not say anything about when a measurement takes place and hence when the world splits. Of course it doesn't and why should it? You ask, what is so special about humans; I ask, what is so special about measurements? What is a "measurement" if it's not an interaction we can model with quantum mechanics? If you want the theoretical outcome of a measurement, then model the interaction between your measuring device and system!

You also talk about worlds splitting as some kind of physical event. If it were a physical event, you're right, we'd want to know exactly when it occurs. It is not a physical event, though. It is a layer of interpretation to make things easier to talk about. I could talk about the cat experiment (as MWI would predict -- no collapse) without ever saying that the world splits. In fact, I will do just that.

gamma5772 said:
How would the cat experiment work? The cat would be in a quantum superposition of alive and dead (let's assume it is perfectly isolated from the outside world). When the scientist observes the cat, he would be in a superposition of observing an alive cat and observing a dead cat. When the scientist is recounting his experiment, he is in a superposition of publishing a paper saying he observed an alive cat, and of publishing a paper saying he observed a dead cat.
Now, here's a point of confusion which you bring up ("we don't ever see two cats") -- the cat is in a superposition, so why doesn't anyone see the cat as in a superposition? Well, the scientist saw the cat in a superposition, and look what happened to him! Now he's in a superposition too.

Keep in mind that although everything is in a superposition, it is entangled. Precisely, the state of the universe is
$$| \text{cat dead} \rangle | \text{scientist sees dead cat} \rangle + | \text{cat alive} \rangle | \text{scientist sees live cat} \rangle.$$
Does the scientist see a cat in a superposition now? Does he see 2 cats? No! The scientist that sees a dead cat sees a dead cat, and the scientist that sees a live cat sees a live cat. Now, you ask the scientist who sees a dead cat, "did you see the wavefunction collapse?" The scientist who sees a dead cat says, "yes." You ask the same question to the scientist who sees a live cat -- "yes" again. So although collapse has not occurred, experiments will look as if collapse has. It's certainly strange that the scientist is in a superposition ("I've never been in a superposition!"), but that's just argument ("I've never seen a cat in a superposition") jazzed up a little.

Delta Kilo

I pretty much agree with everything you said here. Just a couple of remarks:

The original argument only works if the cat in a box is isolated from the environment outside the box. But this is clearly impossible. When dealing with microscopic systems, we can prepare them in a known pure state by doing a measurement in a particular basis. This effectively "cleanses" the system from any entanglements it might have with other systems or the environment at large. But we can't do that to a cat (not unless we vapourize it entirely and beam through a Stern–Gerlach apparatus :)

Also |dead cat> and |live cat> are not pure states. There is a gazilion subtly different ways in which the cat can die of poison, and another gazillion ways in which it can stay alive if the vial remains unbroken. So the universe splits not just 2 ways but 2 gazillion ways. In half of those gazillion universes the cat is dead and it is alive in another half. If we look at another criteria instead of dead/alive, eg. which way the tail is pointing, we'll get a different split of these 2 gazillions. This is just to illustrate that the notion of 'split' in MWI is not very useful, and IMHO does more harm than good.

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