November 2024 – Physics Notes

Source of Uncertainty Principle – Observation or Theory?

A Quoran asks: “Is the Uncertainty Principle in QM primarily a consequence of the mathematics involved (ie. derived from it) or of empirical evidence (which the mathematics has then been constructed to describe)?”

I answered “Both”.

The original idea of the uncertainty principle was motivated by the apparent empirical facts that in order to determine the position of an object very precisely it seems necessary to illuminate it with light of a very short wavelength, and that the empirically observed spectrum of black body radiation suggests that short wavelengths interact with matter not continuously but in discrete ‘quanta’ which transfer more and more momentum as the wavelengths get shorter. In the mathematical theories that were developed to describe these phenomena (but not so much motivated by the uncertainty principle itself) the uncertainty principle (and in fact a more general form of it) can be derived from the fact that measurements of position and momentum correspond to non-commuting operators on the Hilbert space that is used to represent states of the system.

Source: (1001) Alan Cooper’s answer to Is the Uncertainty Principle in QM primarily a consequence of the mathematics involved (ie. derived from it) or of empirical evidence (which the mathematics has then been constructed to describe)? – Quora

Schrödinger’s Cat

Why has Schrödinger’s Cat, the experiment, not actually been performed?

Basically because we have no way of putting a system as complex as a cat into a pure quantum state.

Schrödinger’s cat thought experiment was intended to challenge the idea that a system can have undetermined values of some observables in a way that does not just correspond to a lack of knowledge on our part. If the killing of the cat were the result of a purely classical source of uncertainty such as a coin toss we could just say that the cat is either truly alive or truly dead and we just don’t know which until we look. But quantum mechanics includes uncertainties of a kind that cannot be interpreted as just the result of incomplete information.

An example on a scale much smaller than that of a cat is if a single electron has a known value of its vertical spin component (up or down), and if we subsequently divert it by a device that sends it in different directions depending on its horizontal spin component, then there is a 50% chance of seeing it go in either of the two directions and it appears (from an analysis of the observed probabilities in various other directions) that there was no way of predicting the horizontal component (say from some other initial observations) before we actually measured it.

Schrödinger’s point was that there’s something weird about this business of not having a property until we measure it, and he used the cat as an extreme example. But in practice, if we are good enough detectives, there will always be evidence in the box telling us exactly when the cat died; and so, although there may have been some time before we knew the outcome, we never see anything that looks significantly different from what might have happened if the killing of the cat had been triggered by some classical probabilistic event (such as say the first double six in a series of dice throws).

In order to experience the weirdness of having a cat that is neither alive nor dead (sometimes referred to as being both at once) we would need to keep the system of cat and triggering nucleus (and everything else that they can interact with) in what is called a ‘pure’ quantum state, which requires having complete information about the quantum states of all its constituent elementary particles.

This is obviously impossible for a cat, but experiments have been done in which larger systems such as complex molecules are put into superposition states where something like the shape of the molecule (which perhaps seems more substantial to us than the spin of a single electron) does not have a value until we observe it. These will undoubtedly get larger and more impressively weird seeming as technology improves, but I am pretty sure that they will never reach the scale of an actual cat.

Source: (1001) Alan Cooper’s answer to Why has Schrödinger’s Cat, the experiment, not actually been performed? – Quora

Is Decoherence Reversible?

It depends on what you mean by the word “decoherence”.

The conventional use of “decoherence” to describe part of what happens in a measurement process refers to the interaction of a pure state of an experimental system (which may be a superposition of eigenstates of some observable) with a statistical mixed state of a complex environment (which includes some kind of measurement apparatus for that observable) such that, after the interaction, the relative state of the system is a statistical mixture of eigenstates of the observable, each of which is linked to some indicator state of the environmental apparatus. This is typically NOT reversible for thermodynamic reasons (basically due to the fact that the final state is not known in sufficient detail needed to determine the actions needed in order to reverse the process).

BUT, as another answer notes, if the word “decoherence” is being used to describe interaction of the system with an ancilliary system that is in a pure state, then after the interaction the combined system is still in a pure state and the unitary evolution of pure states is reversible.

Source: (1001) Alan Cooper’s answer to Is it possible to reverse quantum entanglement decoherence? – Quora

Watching Fall Into Black Hole

If we on Earth are now observing an object that we see as near a black hole and in free fall on a path that intersects the event horizon of that black hole, then what we are seeing will be extremely red shifted version of the object that is therefore both very dim and ageing very slowly. So the apparent (to us) progress of everything in the object’s frame (including its rate of fall) is very slow. As time (for us) progresses, we will see the object’s clocks and apparent rate of fall to get progressively slower as it also dims towards invisibility.

Source: (1001) Alan Cooper’s answer to An event horizon is a boundary beyond which events cannot affect an observer. What would we be witnessing if a spacecraft was to cross the event horizon of a black hole? The spacecraft disappearing, or eternally approaching the black hole? – Quora