The collapse phrase seems strange to me. The semantics imply that a function is some type of object. Bridges sometimes collapse. A card player's house made of cards often collapses. The wave function is analogous to a table of probabilities. It provides probabilities for various possible Quantum Level events. When dice are thrown, nobody says: The phrase used is: What is the origin/intent of the collapse phrase?
Could it be that the wave function represents the uncertainty in knowledge of the system? Example: A criminal escapes from prison, steals a car. After an hour, (driving at legal speeds to avoid attention), he would be in an area within a radius of 60 mi. A sighting at a location 30 mi. distant, collapses the wf, and generates a new one centered on that location.
Belief, like fear or love, is a force to be understood as we understand the theory of relativity, and principles of uncertainty. Phenomena that determine the course of our lives.These forces that often remake time and space, they can shape and alter who we imagine ourselves to be, begin long before we are born, and continue after we perish. Our lives and our choices, like quantum trajectories, are understood moment to moment, at each point of intersection, each encounter, suggest a new potential direction. [Cloud Atlas]
Science only makes models of reality. There is never a claim that any model fully represents reality. As science advances the models get better, but they may never be perfect. That does not bother science. There are plenty of concepts used every day in science that are of doubtful reality but which work when accounting for and predicting phenomena. Newton's theory of gravitation and the "arrow-pushing" used in organic chemistry are just two common examples. A discussion about the nature of reality is something that belongs in the Philosophy section. Science is pragmatic and uses what works.
There you go again trying to dictate what people should be allowed to discuss. Isn't there some chemistry forum somewhere where you'd be happier? Or perhaps a medieval theocracy?
correct, science has decided that there can be multiple real. real is only seen as a physical state by most humans with perception only.
Dinosaur, I'm not sure of the origin, but here's a thought. Suppose that an electron is in a superposition of two states - spin up and spin down. Its wavefunction might look something like this: \(|\psi>=|up>+|down>\) Then, when you make a measurement, it reduces to either \(|\psi>=|up>\) or \(|\psi>=|down>\). As you can see, the function has "collapsed" so that the function after the measurement is simpler and shorter than the one before it. In general, a wavefunction is a superposition of many measurable states (eigenstates). But when a measurement is made, it always collapses to just one of those. That is, the wavefunction always gets shorter and simpler when the "collapse" happens.
I have read the various replies & the collapse phrase still does not seem semantically valid. The wave function provides probability data relating to possible results of some quantum process. Correct, I assume? A table of dice throw probabilities provide analogous probability data relating to dice throws. Correct, I assume? Nobody ever says the dice probabilities collapsed to snake eyes, box cars, or some other result. They merely say the shooter rolled box cars or whatever. Why the strange semantics for quantum processes? What is the origin of the semantics? As mentioned in a previous post: Objects like bridges & houses built of cards collapse. The collapse phrase implies that the wave function is a real object rather than a function. Is the implication a valid one?
Indirectly, yes. But the wavefunction does more than that. It actually contains everything that can be known about the quantum state in question. Yes, but that is a statistical matter. It ignores the mechanics of what happens when you throw the dice and looks just at the distribution of outcomes. You could actually argue, however, that the quantum situation is similar in that we don't know the mechanics of the collapse process - all we know is that it occurs. Dice are fundamentally deterministic. In principle, if you knew exactly how the dice were held when they were thrown, where they were in relation to the table, how fast they were thrown, and so on, then you could calculate what number would come up. The same is not true for quantum dice, where all that can be known is the distribution of possible measurement outcomes. Another crucial difference is that classical dice can't ever exist in a superposition of states. They are in a given state (which changes over time) before, during and after the throw. But before you throw quantum dice (e.g. measure the spin of the electron in my example above) the electron actually is in a state of having both spin-up and spin-down at the same time. How can we tell the difference between a classical state that is merely undetermined and a quantum state that is a superposition? The answer is that experimental outcomes are possible in the quantum case that are impossible for classical objects. This is because superposed states can interfere with each other in various ways, and evolve in different ways from classical states. The canonical example of that is the two-slit experiment with light (or electrons, or atoms, or whatever), where an interference pattern is observed on the screen that is doing the measuring. Such a pattern cannot be explained using a classical model of the particles. What is an electron? What is a photon? If the wavefunction contains all the information that can be known about the state of an electron, then it seems valid to talk about the electron's wavefunction almost interchangeably with the electron itself. The wavefunction is as real as the electron itself, because it contains all the same information. You might also wonder whether the wavefunction only describes what we can know and not all that there is. You might think there are "hidden variables" in an electron that tell it how to behave (deterministically) to produce the measured quantum outcomes predicted by the wavefunction. However, a number of experiments suggest that hidden variables cannot exist in quantum systems. The wavefunction is all there is.
The reply was within the context of "wave function collapse". It's still being debated, along with the "measurement problem". There are a few theories developed to explain quantum phenomena, but no winner.
From James R Post #14: Calling dice throws deterministic is based on the notion that a die is a classical solid object. Actually, a die is mostly empty space & interacts with other objects via electromagnetic effects (primarily repulsion between the electron clouds surrounding atoms & molecules). The Heisenberg Uncertainty Principle & the probabilistic laws of Quantum Theory belie the notion that dice throws are deterministic. I stand by my remarks in a previous Post (paraphrase, not an exact quote).
I understand now that boundaries between noise and sound are conventions. All boundaries are conventions, waiting to be transcended. One may transcend any convention, if only one can first conceive of doing so. [Cloud Atlas]
Good stuff. See weak measurement work by Jeff Lundeen et al and in particular the semi-technical explanation: "With weak measurements, it’s possible to learn something about the wavefunction without completely destroying it. As the measurement becomes very weak, you learn very little about the wavefunction, but leave it largely unchanged. This is the technique that we’ve used in our experiment. We have developed a methodology for measuring the wavefunction directly, by repeating many weak measurements on a group of systems that have been prepared with identical wavefunctions. By repeating the measurements, the knowledge of the wavefunction accumulates to the point where high precision can be restored. So what does this mean? We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory."
I see what you mean, but I think I'm with James on this, inasmuch as QM wave-particles behave like both waves and particles, depending on the circumstances, so I don't see there is much to be gained by trying to determine that one representation is "real" whereas the other is only a mathematical function. I've always taken the word "collapse", applied to wavefunctions, to be analogous to the collapse of a wave when it reaches the seashore, albeit slightly metaphorical language in that no one suggests the process of collapse can be analysed in the same way as a wave crashing onto a beach. Personally, I picture the wave as real, while bearing in mind that any interactions resulting in measurements can only give quantised values, corresponding to "whole" particles, at specific locations, with specific energies. But that may be because chemists spend a lot of time thinking about electrons in atomic and molecular orbitals, which are wavelike structures.
IMHO a better analogy is the optical Fourier transform, see Steven Lehar's website: Please Register or Log in to view the hidden image! Also see Aephraim Steinberg's website re weak measurement, and note the depiction of the photon going through both slits. When you detect the photon at one of the slits, the wavefunction is temporarily focussed or "collapsed" into a dot that goes through that slit only. Then when you detect it at the screen, the wavefunction is again collapsed into a dot. You don't need any multiverses or anything mystical to explain the double-slit experiment.
