I'd say that without extra dimensions you don't need a wave function.....what is the point of the collapsing wave and 'probabilistic' locations for particles if there are only three dimensions of space and time?

That's why I feel the wave function suggests extra dimensions......but then again. You have studied this far more than I have......though most physicists do believe in extra dimensions....string theory for example....old Professor Cox supports the 'many worlds' view.

I'm just tickling around the edges of the topic.....would be great to learn the maths for it.

Edited by Stirlingsays (03 Jan 2018 7.31pm)

'Who are you and how did you get in here? I'm a locksmith. And, I'm a locksmith.' (Leslie Nielsen)

You still need to look up the scientific meaning of the word "theory" because, if you had, you wouldn't continue to spout such nonsense.

We don't do possession; we do defense and attack. Everything else is just wa**ing with a football.

Oh really?

A well-confirmed type of explanation of nature, made in a way consistent with scientific method.

There ain't nothing well confirmed about our grasp of quantum physics or parallel universes or any related topic.

I'm not really sure how to answer this question, as I'm not sure why you intrinsically connect the notion of a wavefunction to how many dimensions you express it in.

The aforementioned 3D description of the Hydrogen atom is typically written in spherical polar coordinates (r, theta, phi). You could reduce this problem down to 2 dimensions, also in spherical coordinates (r, theta). When you "observe" the quantum state of the atom, you do so in the coordinate space you described the wavefunction in. If you have a 2D entity (like a disk), and embed this into a 3D space, you can still solve the wavefunction. But the 2D wavefunction does in no way imply the existence of the 3D space.

The "point" is the entire nature of fundamental science, and pretty much the nature of our reality, and indeed our very existence relies on it. Until observed, this Hydrogen atom exists in a superposition of states, separated and distinguished by quantised levels. Applying an "operator" to the eigenvectors (the "collection" of these states) yields an eigenvalue - this is the observation. A very common one is the Hamiltonian operator - this yields the energy (the eigenvector) of the system. At the fundamental level, this is the process by which all physical phenomena occur.

If you don't think there's any point of knowing the probabilistic location of particles in 3D space, I'd suggest you shut down your computer: those high-density circuits require consideration of quantum tunnelling of electrons through insulating layers.

You might also consider that our Sun relies on quantum tunneling for stellar fusion - the source of energy that permits our existence. We now understand, through calculating the quantum mechanical tunneling probability of a proton through the repulsive electromagnetic field, how two protons fuse to form deuterium (and in the process releasing energy).

I don't dispute there might well be extra dimensions: in science, a hypothesis must be falsifiable. Part of the problem with string theory is the lack of observables in experiments that could start discriminating between the "standard" model and those requiring extra dimensions.

If you were interested, the maths QM is built on is quite a mixed bag. Differential equations, calculus, vector calculus, matrix methods, complex numbers (essential for wave-based physics), coordinate transformation. Probably a tonne more stuff I've missed out :-)

I don't know what disciplinary rules apply to Schroedinger's cat or whether it exists or not, but mine has been advised that she will be turned into a Russian hat if she ever s***es in the shower again.

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The Ferret
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'Who are you and how did you get in here? I'm a locksmith. And, I'm a locksmith.' (Leslie Nielsen)