How isolated must a system be for it's wave function to be considered not collapsed?

Question

As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the person opening the box. Over time, I have come to realize that the Copenhagen interpretation actually is ambiguous and that "observer" cannot be so easily defined. Nonetheless, an objective collapse theory (which is what I was unknowingly assuming) still seems to me the simplest explanation of wave collapse phenomena.

I have read some of the objections cited in the Wikipedia article linked above, but it is still unclear to me why most physicists adopt the Copenhagen interpretation and reject objective collapse. For example, in this question on hidden observers, there was some discussion about the mechanism of wave collapse. It was suggested that perhaps the gravitational pull of a hidden observer would collapse the wave function. In response, it was pointed out that the gravitational pull would be negligible at the scales involved.

Okay, then imagine the following:

A hermetically sealed (i.e. isolated) box is balanced on a fulcrum. Inside the box is a radioactive isotope, a Geiger counter, and a trigger mechanism connected to a spring loaded with a mass on one side of the box. If the Geiger counter detects a decay, the trigger releases the spring and the mass shifts to the other side of the box. The shift in mass would, under observable conditions tilt the box on the fulcrum.

According to the interpretation of Schrodinger's cat that I often hear (the cat is in a superposition) it seems that the box should slowly tilt over as the wave function of the system evolves with the half-life of the isotope. I can't imagine that anyone thinks this is a realistic expectation.

I can see that people might object and say "But the contents of the box are interacting gravitationally with the outside system and observer so it is not really isolated!" Well, what of it? The same is true of the cat even if the interaction is less dramatic.

The question, then, is: How isolated must a system be for it's wave function to be considered not collapsed?

Answer 1

''How isolated must a system be for it's wave function to be considered not collapsed?''

Experimentally, a system whose collapse is observable must be so small that one can prepare it in a well-defined pure state. If this is not the case, one can only speculate about what happened, leaving much room to imagination.

This means that even when the carrier of the system is fairly big, the wave function collapsed models only extremely few degrees of freedom, and the real system considered is the one with these few degrees of freedom, not the bigger one.

For example, arXiv:1103.4081 discusses superposition and collapse of macroscopic objects. But prepared in a superposition is only a single degree of freedom, the distance; all other degrees of freedom are either uncontrolled (and hence presumably in a mixed state) or eliminated by extreme cooling. Thus the system measured is in effect a single quantum oscillator.

Now a typical quantum oscillator decoheres rapidly unless isolated, and a quantum oscillator of some size is hard to isolate. The experimental art consists in maintaining a superposition of two distances by isolating this particular degree of freedom from the environment. This isolation must be almost perfect, as otherwise decoherence effects responsible for the collapse set in extremely rapidly. (No special observer is needed. The environment does the observing by itself.)

''why most physicists [...] reject objective collapse.''

The main reason is that they want to maintain the simplicity of the traditional quantum mechanical foundations that are based on the assumption that the dynamics of quantum states is exactly linear, which seems to suffice for all applications. Objective collapse theories would require a tiny nonlinear modification of the basic laws, and spoil simplicity for (so far) uncheckable philosophy.

Note that ''no objective collapse'' doean't mean that collapse isn't observable (it is observed routinely), but only that the collapse is not due to decoherence (the approximation in which the collapse is derivable in terms of generally believed assumptions from statistical mechanics - needed already in classical physics) but to objective deviations from the Schroedinger equation. The latter has no observable basis, and hence is rejected by most physicists.

Answer 2

The minute you make the box able to change the surroundings, it ceases to be just a box; and becomes a measuring device.

How this happens can be easily visualised. Lets take an ideal geiger counter-atom setup in a similar box. It is wired outside to a display. Now, for obvious reasons, the atom wavefunction will be immediately collapsed. It will not slowly evolve. This is because you can observe the system using the display. We cannot argue that the geiger counter's wavefunction itself will be affected.

A more stark way of formulating your problem is by attaching the counter to a hammer. If, within the first xyz seconds, there is a decay, the hammer wil strike the box lid; opening it. If you are outside, and the box does not open in xyz secs, you will know that there were no decays, and will have collapsed the wavefunction WITHOUT opening the box. Here, the counter did not become a measuring device by affecting the surrounding; it did so by its ability to affect the surroundings.

Your box is again a measurement device, with the ability to affect the surroundings. Same thing happens, it immediately collapses the wavefunction.

Now to your original question: Anything that can affect the surroundings in a measurable way on the basis of whatever property is being measured counts as a measuring device for that property in the surroundings.

Now heres where everything goes crazy: I've specifically kept the weasel words 'in a measurable way' as QM observations are a fuzzy and conttoverersial topic. May be only conscious beings can make an observation. Maybe only beings who know the implication of their measurement can collapse the wavefunction (so a random person who sees the lever shift but doesn't know what the shift signifies won't collapse it). In the latter case, stuff like 'negligible effects' also create an issue, as the experimenter can't conscously register them and segregate them from 'noise', even though they might feel it.. For example, your geiger counter can emit a photon depending on the results. An experimenter can see the photon with his eyes (our sight is a photon phenomenon),but not register it. Im assuming that the experimenter doesn't have photon detectors.

From there onwards, it gets more philosophical. Which is IMHO why physicists have gone 'shut up and calculate' as @JohnRennie mentioned.

Answer 3

Well, this depends on the system inside the box and how long you want it remain in superposition state.

For example, D-Wave Systems creates the following conditions for their quantum computer:

• Electric magnets screening Earth's magnetic field, so to get at 1 nano tesla magnetic field across the processor, which is 50000 times less than the Earth's magnetic field.

• 200 sq feet refrigirator comsuming 7.5 kW electricity creates 20 millikelvin temperature for the processor's package and the board.

• 30Mhz filtering on any electric lines

source

Answer 4

The Schrodinger's cat is a though experiment modeled in such a way that it's as unrealistic as that common assumptions you see in physical questions, like assuming perfect vacuum. You can't get a perfect vacuum as you can't get a cat going its way through a poison bottle and get dead and alive without happening any decoherence in the middle, the Schrodinger's cat is just an unrealistic Zen Master of Quantum Collapsing Counterfeit's Cat (ZMQC³) as your box is a ZMQC²B.

What about looking at other experiments that shows more clearly the question about the measurement problem? Like the double-slit experiment which shows at which point by means of an observer (which implicitly refer to the thing, anything, that realizes a measurement, that interacts, not only conscious observers), the observed (the thing measured) comes out of its wave function as a quantized particle, and at which point not. The referred link also points out advances on non-perturbative detectors (which I must confess is new stuff to me, but as it's stated, doesn't contradict wave/particle duality and also relates with the objective collapse theories).

What seems clear is that, in the event of measurements/interactions ("observations"), quantum collapses ("spontaneous localization" as in the wikipedia article on objective collapse) will occur, and so, complex systems free from this measurements, that's, "isolated systems", are mostly unrealistic.

There's a good discussion related to this topic at this physics forum about Heisenberg views, which also seems more objective than the Copenhagen interpretation: www.physicsforums.com/showthread.php?t=492354

Quoting Heisenberg on "Physics and Philosophy":

"It applies to the physical, not the psychical act of observation, and we may say that the transition from the 'possible' to the 'actual' takes place as soon as the interaction of the object with the measuring device, and thereby with the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function."

Answer 5

quantum mechanics is inherently linear, this has consequences to superposition states, mainly multiple superpositions of a physical system cannot interact to each other.

Now, observation clearly breaks this, precisely because it is about different physical systems interacting with each other. In the particular case where one of the systems is the environment, it should be obvious that you cannot still have multiple superpositions not interacting to each other at the same time the environment is interact with both of them (or more precisely, a physical system coming from and returning to the heat bath). The reason for this should be clear: if they both stayed in superposition then they could interact to each other through the environment, hence breaking the quantum mechanics linearity.

This is why i think that measurement is inherently a non-linear process, because it breaks the linearity regime of quantum mechanics.

How is this possible? well, mainly because classical physical systems are non-linear, and quantum mechanics by correspondence should be non-linear in the classical limit. For instance, a physical object (like a geiger counter) will behave in extremely non-linear ways after an $\alpha$ or $\beta$ particle hits or doesn't hit. There will be gauge movements and electric currents in the case where it hits that cannot be simply modeled by anything as trivial as a linear superposition.

In more precise terms, a physical observer (again, like the geiger counter) is by design oriented to behave non-linearly across a range of eigenvalues in a very specific eigenbasis, while approximately linearly (i.e: non discriminating) in other non-conmuting eigenbasis. You cannot design an observer to behave non-linear in two nonconmuting eigenbasis at the same time. This is in essence the uncertainty principle