Undergrad Reconciling Determinism and Superposition in Quantum Theory

[Anonymous]

Hello all,
This my first time posting to this forum and am doing so to try and reconsile an issue I saw with quantum theory and determinism in my intro philosophy class. To my understanding, being a ce/eveg major, is that the law of superposition in laymen's states that certain properties cannot be known until one is observed ( cat in the box analogy) . My question lies more specifically what this means. Is this principle is saying. Is it saying that we as observing scientists and engineers cannot determine these properties past a certain point? Or that these properties do not exist necessarily exist in finite values until we observe them,meaning they essentially occupy multiple states simultaneously in the universe at the same time and takes on one only when observed? Basically is this saying it is scientifically indeterministic or metaphysically indeterministic ?

Thanks in advance

 

[PeroK]

Hello all,
This my first time posting to this forum and am doing so to try and reconsile an issue I saw with quantum theory and determinism in my intro philosophy class. To my understanding, being a ce/eveg major, is that the law of superposition in laymen's states that certain properties cannot be known until one is observed ( cat in the box analogy) . My question lies more specifically what this means. Is this principle is saying. Is it saying that we as observing scientists and engineers cannot determine these properties past a certain point? Or that these properties do not exist necessarily exist in finite values until we observe them,meaning they essentially occupy multiple states simultaneously in the universe at the same time and takes on one only when observed? Basically is this saying it is scientifically indeterministic or metaphysically indeterministic ?

Thanks in advance

According to the "Copenhagen" interpretation of QM, dynamic properties such as position, momentum, angular momentum, spin etc., do not have meaningful values until measured. The classic example is the spin of an electron. If you measure the spin in the z-direction, you always get one of the values $\pm \frac{\hbar}{2}$. The uncertainty is effectively the direction of the spin. It doesn't make any sense to ask "which way was it spinning before I measured it"? It only makes sense to say that a measurement of its spin returned + or -.

More generally, if you know the state of a quantum system, then its dynamic properties, when measured, may take specific values with specific probabilities. In the case of spin of an electron it's 50-50, but in the case of the angular momentum, say, you can have a wider range of possible values each with a given probability.

 

[lodbrok]

According to the "Copenhagen" interpretation of QM, dynamic properties such as position, momentum, angular momentum, spin etc., do not have meaningful values until measured. The classic example is the spin of an electron. If you measure the spin in the z-direction, you always get one of the values $\pm \frac{\hbar}{2}$. The uncertainty is effectively the direction of the spin. It doesn't make any sense to ask "which way was it spinning before I measured it"? It only makes sense to say that a measurement of its spin returned + or -.

More generally, if you know the state of a quantum system, then its dynamic properties, when measured, may take specific values with specific probabilities. In the case of spin of an electron it's 50-50, but in the case of the angular momentum, say, you can have a wider range of possible values each with a given probability.

The dimension of momentum includes $\Delta{x}$ and $\Delta{t}$, "instantaneous momentum" is imprecise language. Usually it is used to represent the concept that if momentum measured between $(x_0, t_0)$ and $(x_1, t_1)$ then we can say, loosely, that the momentum at space-time coordinates between $(x_0, t_0)$ and $(x_1, t_1)$ have that value. It is impossible to measure momentum at an instant because momentum is undefined for $\Delta{t}=0, \Delta{x}=0$. In positional space, a momentum measuring device must take into consideration a non-zero positional interval. Similarly, in momentum space, a position measuring device must take into consideration a non-zero momentum interval. Mathematically speaking, position and momentum are conjugate variables by definition, and $\psi({x})$ is the Fourier transform of $\psi({p})$. The uncertainty principle originates from the fact that one cannot simultaneously sharply localize a function and it's Fourier transform.

A similar analysis applies to spin directions $x, y, z$. The uncertainty principle has nothing to do with whether it makes sense to talk about "which way was it spinning before I measured it" it all has to do with the mathematical definition of what spin-$x$ means in relation to spin-$y$ and spin-$z$.

 

[DrChinese]

Is it saying that we as observing scientists and engineers cannot determine these properties past a certain point? Or that these properties do not exist necessarily exist in finite values until we observe them,meaning they essentially occupy multiple states simultaneously in the universe at the same time and takes on one only when observed? Basically is this saying it is scientifically indeterministic or metaphysically indeterministic ?

To some extent, the answer to this is interpretation dependent. For example, the Bohmian interpretation says properties are determinate but unknowable. However, the most common viewpoint is that there is no well-defined value for a property in a superposition unless and until it is measured.

 

[lodbrok]

My question lies more specifically what this means. Is this principle is saying. Is it saying that we as observing scientists and engineers cannot determine these properties past a certain point? Or that these properties do not exist necessarily exist in finite values until we observe them,meaning they essentially occupy multiple states simultaneously in the universe at the same time and takes on one only when observed? Basically is this saying it is scientifically indeterministic or metaphysically indeterministic ?

I would add that humans have invented concepts to describe what we observe. Normally those concepts "correspond" to actual entities that exist in the universe but are not themselves actual entities in the universe. However, some of those concepts are complementary to each other in the sense that they are not completely independent. Position and momentum are two of such. This is what "complementarity" is all about. Other examples include, energy and duration, spin on different axes, etc. Because these concepts were invented by humans to describe what was observed in the universe, it is wrong to ascribe all conflicts we observe between these concepts as conflicts existing in the universe as it could simply mean our descriptions/concepts are not fundamental. This is known as the "Mind Projection Fallacy". Yet we are bound by limits in those concepts, when we them to describe the world in the same way as we are bound by logic to avoid contradictions in our arguments.
In each case the solution is to revisit our definitions and be meticulous in being consistent. Once that is done, we can often answer questions about specific cases without resorting to unsubstantiated metaphysical claims that we really can't know anything about such as is common with different "interpretations" of Quantum Mechanics. I'm not saying "interpretations" are bad. In fact the role of interpretations should be to provide an ontology that allows the theory to make new predictions about yet unobserved phenomena to further refine the ontology towards obtaining as good a model about the universe as is possible.