Is there a way to detect the collapse in wave function of entangled particles instantaneously? [closed]

Question

Is there a machine or instrument which will notify us instantly when the wave-function has collapsed if we have access to only one of the entangled particles? Note that the wave function collapse will be triggered by observing the particle which we do not have. Or in other words is there a way to identify (instantaneously) if the entangled pair of a particle has been observed and the wave function has collapsed.

Answer 1

The collapse of the wave function is a concept within the interpretation of quantum mechanics. There are also interpretations of quantum mechanics that do not contain the mechanism of quantum collapse. An example is the Many Worlds interpretation. Unfortunately, there is no known way to perform experiments to determine which interpretation (or type of interpretation) is correct.

Hence, if you perform an experiment and draw conclusions about the collapse of the wave function, then these conclusions are contingent on the interpretation within which you are considering the experimental results. From a strictly scientific perspective we cannot say anything about the collapse of the wave function. We cannot even know whether the collapse of the wave function is really a physical process or just a figment of our imagination.

Answer 2

The early form of the Copenhagen interpretation contained the misconception that the wave function is somehow a physical attribute of a particle, encapsulated in the notion of "wave-particle duality". This was never accepted by Heisenberg and was shown false in the mathematical formulation of quantum mechanics given by Dirac and Von Neumann. The wave function is more correctly called a probability amplitude. It is a statement of probability for the result of measurement, not a physical attribute of a particle.

So when Alice observes particle A, Alice gains information about particle B. Consequently Alice's wave function for particle B "collapses", i.e. Alice's assessment of probabilities for particle B changes. Bill, who observes particle B, knows nothing of Alice's measurement, and Bill's wave function for particle B is not changed. There is no observation Bill can carry out which will tell him anything about Alice's measurement, or even whether she has done a measurement.

Only later, when Alice and Bill bring their results together, do they find a correlation. Nonetheless, neither Alice nor Bill's observation has any direct affect on the observation of the other. All they can say is that there is no classical explanation for the correlation.

Answer 3

Every time an interaction happens , the former wave function describing the system is made invalid and a new one arises from the new boundary conditions.

Look at this one event of a $K^-$ proton interaction.

At the point of interaction, the wavefunction describing the system of a $K^-$ proton , $Ψ$ which allows to compute the probability for the interaction to happen equal to $Ψ^*Ψ$ (the only measurable effect of $Ψ$) a new $Ψ$ describing the exit of four particles is defined automatically, the previous one is not longer valid, i.e. it collapses.

Is there a way to detect the collapse in wave function of entangled particles instantaneously (at the same moment the wave-function collapses)?

The K and the proton were entangled at the moment of interacting, but this is quantum mechanics, which is only deterministic on probability distributions, not mathematical functions. This means that there exists an uncertainty interval, the envelope given by the Heisenberg uncertainty principle , in the case of your question the time energy one:

\begin{align} \Delta x\Delta p&>\frac{\hbar}{2}\\ \Delta E\Delta t&>\frac{\hbar}{2} \end{align}

so there is no possibility of talking of instantaneous observations.