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I am not entirely sure what you are asking, but since you seem to be sincerely interested in understanding some of the fundamentals of Quantum Mechanics, I'll do my best to answer what I think you are asking.

The answer to why we don't consider a wave function to be a "real, deterministically evolving matter wave" is simply that such an interpretation isn't borne out in experimental data. There are an abundance of experiments which have validated and re-validated the Copenhagen Interpretation, so you will be hard-pressed to figure out a way to explain their results while rejecting one of the bedrock assumptions of their theory.

Another good reason to avoid thinking about the wave function itself as being a physically relevant quantity is that it is not real-valued. Schrödinger's Equation is not the Diffusion Equation no matter how similar they look. The solutions to SESchrödinger's Equation are implicitly complex-valued, so what's the fix: just throw out the compleximaginary part? Be careful: when you solve the Time-Dependent Schrödinger's Equation your energy eigenfunctions get multiplied by time dependent phases of the form $e^{-i\frac{E_n}{\hbar}t}$. What happens when the phase of the wave function is pure imaginary? Is the particle nowhere to be found?

Finally, your question may have been asked before by some very well-known physicists. Take a look at the EPR Paradox. The basic idea is that QMquantum mechanics implies entanglement, which seemingly violates causality: How can something I do to a particle here change another particle 1000 lightyears away? Well, experiments have actually show that the EPR Paradoxentanglement is true which ultimately resultedand, therefore, that quantum mechanics is non-local. This result culminated in Bell's Theorem.

The upshot Bell's Theorem is this: QMthat quantum mechaincs is necessarily non-local and probabilistic. No "hidden variable" theory can ever adequately explain its predictions. Take a look at the Quantum Eraser and Delayed-Choice Quantum Eraser experiments. They incorporate some fairly simple tweaks to get a sense of the weirdness of QMwell-known double-slit experiment that help to highlight just how counter-intuitive (but true!) quantum mechanics actually is. Both of those "eraser" experiments are not merely thought experiments, either: they were actually done.

I am not entirely sure what you are asking, but since you seem to be sincerely interested in understanding some of the fundamentals of Quantum Mechanics, I'll do my best to answer what I think you are asking.

The answer to why we don't consider a wave function to be a "real, deterministically evolving matter wave" is simply that such an interpretation isn't borne out in experimental data. There are an abundance of experiments which have validated and re-validated the Copenhagen Interpretation, so you will be hard-pressed to figure out a way to explain their results while rejecting one of the bedrock assumptions of their theory.

Another good reason to avoid thinking about the wave function itself as being a physically relevant quantity is that it is not real-valued. Schrödinger's Equation is not the Diffusion Equation no matter how similar they look. The solutions to SE are implicitly complex-valued, so what's the fix: just throw out the complex part? What happens when the phase of the wave function is pure imaginary? Is the particle nowhere to be found?

Finally, your question may have been asked before by some very well-known physicists. Take a look at the EPR Paradox. The basic idea is that QM implies entanglement, which seemingly violates causality: How can something I do to a particle here change another particle 1000 lightyears away? Well, experiments have actually show that the EPR Paradox is true which ultimately resulted in Bell's Theorem.

The upshot is this: QM is necessarily non-local and probabilistic. No "hidden variable" theory can ever adequately explain its predictions. Take a look at the Quantum Eraser and Delayed-Choice Quantum Eraser experiments to get a sense of the weirdness of QM. Both of those experiments are not merely thought experiments either: they were actually done.

I am not entirely sure what you are asking, but since you seem to be sincerely interested in understanding some of the fundamentals of Quantum Mechanics, I'll do my best to answer what I think you are asking.

The answer to why we don't consider a wave function to be a "real, deterministically evolving matter wave" is simply that such an interpretation isn't borne out in experimental data. There are an abundance of experiments which have validated and re-validated the Copenhagen Interpretation, so you will be hard-pressed to figure out a way to explain their results while rejecting one of the bedrock assumptions of their theory.

Another good reason to avoid thinking about the wave function itself as being physically relevant is that it is not real-valued. Schrödinger's Equation is not the Diffusion Equation no matter how similar they look. The solutions to Schrödinger's Equation are implicitly complex-valued, so what's the fix: just throw out the imaginary part? Be careful: when you solve the Time-Dependent Schrödinger's Equation your energy eigenfunctions get multiplied by time dependent phases of the form $e^{-i\frac{E_n}{\hbar}t}$. What happens when the phase of the wave function is pure imaginary? Is the particle nowhere to be found?

Finally, your question may have been asked before by some very well-known physicists. Take a look at the EPR Paradox. The basic idea is that quantum mechanics implies entanglement, which seemingly violates causality: How can something I do to a particle here change another particle 1000 lightyears away? Well, experiments have actually show that entanglement is true and, therefore, that quantum mechanics is non-local. This result culminated in Bell's Theorem.

The upshot Bell's Theorem is that quantum mechaincs is necessarily non-local and probabilistic. No "hidden variable" theory can ever adequately explain its predictions. Take a look at the Quantum Eraser and Delayed-Choice Quantum Eraser experiments. They incorporate some fairly simple tweaks to the well-known double-slit experiment that help to highlight just how counter-intuitive (but true!) quantum mechanics actually is. Both of those "eraser" experiments are not merely thought experiments, either: they were actually done.

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I am not entirely sure what you are asking, but since you seem to be sincerely interested in understanding some of the fundamentals of Quantum Mechanics, I'll do my best to answer what I think you are asking.

The answer to why we don't consider a wave function to be a "real, deterministically evolving matter wave" is simply that such an interpretation isn't borne out in experimental data. There are an abundance of experiments which have validated and re-validated the Copenhagen Interpretation, so you will be hard-pressed to figure out a way to explain their results while rejecting one of the bedrock assumptions of their theory.

Another good reason to avoid thinking about the wave function itself as being a physically relevant quantity is that it is not real-valued. Schrödinger's Equation is not the Diffusion Equation no matter how similar they look. The solutions to SE are implicitly complex-valued, so what's the fix: just throw out the complex part? What happens when the phase of the wave function is pure imaginary? Is the particle nowhere to be found?

Finally, your question may have been asked before by some very well-known physicists. Take a look at the EPR Paradox. The basic idea is that QM implies entanglement, which seemingly violates causality: How can something I do to a particle here change another particle 1000 lightyears away? Well, experiments have actually show that the EPR Paradox is true which ultimately resulted in Bell's Theorem.

The upshot is this: QM is necessarily non-local and probabilistic. No "hidden variable" theory can ever adequately explain its predictions. Take a look at the Quantum Eraser and Delayed-Choice Quantum Eraser experiments to get a sense of the weirdness of QM. Both of those experiments are not merely thought experiments either: they were actually done.