Could someone explain the Schrodinger's Cat experiment to me?

[Halcyon-on]

It is so because too few understand from where the CM determinism appears and how it is embedded in the theory. I repeat, experimentally any observation includes multi-photon exchange and only the average is deterministic. This average corresponds to the center of inertia of the observable body and the internal degrees of freedom are taken into account in making the average. In QED it is the same.

Ok, maybe I use the word determinism in another way. QM can be regarded as a statistical theory but which is not deterministic. With this I mean that in a proper statistical system you usually describe the macroscopic variables (temperature, pressure,...) but in principle you can even determine the position and the velocity of every particle of the classical statistical system and predict exactly with a simulation the evolution microscopically. In QM you can describe only statistically observables but you cannot but the uncertain principle forbids to know the exact value of an observable in a give measurement. In the Schrödinger cat case you can say that after a lifetime of the atom the cat will be dead at 50%, but you cannot say the exact moment when the cat die. In a statistical system, in principle, you can know the mechanism that kill the cat with all the accuracy that you want and predict with arbitrary precision when it will bang.

 

[Bob_for_short]

Ok, maybe I use the word determinism in another way. QM can be regarded as a statistical theory but which is not deterministic. With this I mean that in a proper statistical system you usually describe the macroscopic variables (temperature, pressure,...) but in principle you can even determine the position and the velocity of every particle of the classical statistical system and predict exactly with a simulation the evolution microscopically. In QM you can describe only statistically observables but you cannot but the uncertain principle forbids to know the exact value of an observable in a give measurement. In the Schrödinger cat case you can say that after a lifetime of the atom the cat will be dead at 50%, but you cannot say the exact moment when the cat die. In a statistical system, in principle, you can know the mechanism that kill the cat with all the accuracy that you want and predict with arbitrary precision when it will bang.

A classical statistical system looks as deterministic but it is not. I mean, any measurement is made with some precision, OK? So, even though you know the particle positions at t=0, they have some uncertainties. With time this makes predictions impossible.

Let us consider only one particle in an open space and let its initial coordinate is known exactly but the velocity has a small uncertainty delta_v. With time the particle position is determined with the precision delta_v*t which is growing with time. Now, if you consider this particle enclosed in a box, the uncertainty of its position in a closed space transforms in any possible position within the box. So you see, the determinism of CM and Classical Statistical mechanics should not be exagerated.

 

[Halcyon-on]

A classical statistical system looks as deterministic but it is not. I mean, any measurement is made with some precision, OK? So, even though you know the particle positions at t=0, they have some uncertainties. With time this makes predictions impossible.

Let us consider only one particle in an open space and let its initial coordinate is known exactly but the velocity has a small uncertainty delta_v. With time the particle position is determined with the precision delta_v*t which is growing with time. Now, if you consider this particle enclosed in a box, the uncertainty of its position in a closed space transforms in any possible position within the box. So you see, the determinism of CM and Classical Statistical mechanics should not be exagerated.

Ok. It is impossible to know exactly the initial condition even in a classical system, in a statistic system this leads to fact that only a statistical description makes practically sense. But the indetermination in QM is something different. The more you measure the velocity with accuracy the more you loose accuracy in the spatial measurements. So, once you fix exactly the coordinate the velocity of the particle is completely unknown, no matter how precise are your instruments. The indeterminism in QM is not a problem of experimental resolution, it is not a problem of your will to do good measurements, but it is a full impossibility to determine the value of an observable.

 

[Bob_for_short]

Ok. It is impossible to know exactly the initial condition even in a classical system, in a statistic system this leads to fact that only a statistical description makes practically sense. But the indetermination in QM is something different. The more you measure the velocity with accuracy the more you loose accuracy in the spatial measurements. So, once you fix exactly the coordinate the velocity of the particle is completely unknown, no matter how precise are your instruments. The indeterminism in QM is not a problem of experimental resolution, it is not a problem of your will to do good measurements, but it is a full impossibility to determine the value of an observable.

In QM there are "observables" that are always the same dispite spreading other "observables". For example, take a monochromatic light in a double-slit experiment. The photon frequencies are the same but positions change from one observation to another. The frequency is the energy, the position spread corresponds to the wave function. The wave function "measurement" needs many experiments. The energy, if it is an eigenvalue, does not need many. The momentum is reciprocal to the position, it is an argument of the wavefunction in the momentum space. In this respect making many measurements to find out the entire wave function does not differ from classical mechanical measurements that need many points for better accuracy (for determinism).

 

[Count Iblis]

I mean, any measurement is made with some precision, OK? So, even though you know the particle positions at t=0, they have some uncertainties. With time this makes predictions impossible.

This is not necessarily true. You cannot rule out discovering the exact laws of physics and the correct intitial coinditions. You then cannot rule out that a nontrivial mathematical theorem about the exact future state of the universe could be proven.

 

[Bob_for_short]

This is not necessarily true. You cannot rule out discovering the exact laws of physics and the correct intitial coinditions. ...

Yes, I can. In fact any system is many-particle one. As soon as it is so, it is impossible to reach the absolute accuracy. Take an electron, for example. It is in permanent interaction with the quantized electromagnetic field and there is no a threshold to excite soft photon modes. Thus it is not possible to know everything about the electron.

 

[kote]

Yes, I can. In fact any system is many-particle one. As soon as it is so, it is impossible to reach the absolute accuracy. Take an electron, for example. It is in permanent interaction with the quantized electromagnetic field and there is no a threshold to excite soft photon modes. Thus it is not possible to know everything about the electron.

You are arguing about the practicality of determining initial conditions which is entirely different from the logical possibility that definite initial conditions may exist. CI typically connects the two, but, as Bohm has shown us, QM itself does not necessitate this leap.

 

[Halcyon-on]

In QM there are "observables" that are always the same dispite spreading other "observables". For example, take a monochromatic light in a double-slit experiment. The photon frequencies are the same but positions change from one observation to another. The frequency is the energy, the position spread corresponds to the wave function. The wave function "measurement" needs many experiments. The energy, if it is an eigenvalue, does not need many. The momentum is reciprocal to the position, it is an argument of the wavefunction in the momentum space. In this respect making many measurements to find out the entire wave function does not differ from classical mechanical measurements that need many points for better accuracy (for determinism).

First comment: the energy is the conjugate variable of the time. To determine the energy and the frequency with great accuracy you must observe the wave for a long time, according to Heisenberg.

Second comment: even if you know exactly the wave function using QM you'll never know in which point after the doubleslit the photon will hit. You only know exactly the probabilities.

In a classical statistical theory, in principle, if you know exactly the initial conditions of the particles (suppose a sufficiently simple and not chaotic system), you can predict exactly the evolution also not statistically, particle by particle. This was the illuministic view of the physical world in XIX century, before the quantum revolution. A word made of perfect mechanisms and ball, completely determined by the initial condition.

 

[Bob_for_short]

You are arguing about the practicality of determining initial conditions which is entirely different from the logical possibility that definite initial conditions may exist. CI typically connects the two, but, as Bohm has shown us, QM itself does not necessitate this leap.

Logical possibility arises if we introduce some simplified notions for that. In particular, a sole but observable point-like particle which does not correspond to the experiment. It is our idealisation. It does corresponds to the center of inertia but does not include the internal degrees of freedom (multi-particle nature) of our body.

Ask yourself with what precision the Moon's position may be measured. With the size of the Moon because any point within it belongs to the Moon. But the average may have much less uncertainty.

In CM one often forgets about real sizes and reduces the physics to the center of inertia motion. No wonder such a simplification fails in certain cases.