Is the Schrödinger Equation True?

Any quantum particle can be used in the double slit experiment. It doesn't have to be photons. It's been done with electrons, neutrons, and even buckyballs (Carbon-60). So whatever is going on, it can't be as simple as "a field is created that photons respond to", because it's not only photons that show the pattern.

Think of heat transfer. Conduction, surfaces are in contact. Convection, a fluid medium is in contact. And radiation, what's that medium? How does heat from the sun warm the earth, with no medium in between?

If nature has a mind, it's not a good one. The medium for radiation is nature's ability to speed up and slow down it's clock. Just like an inflated tire will always find the leak, nature's always going to take the easiest way. Not having a mind, or having the worst mind possible, means you're going to do anything to take the easy route. This is special relativity. The tendency is to elevate spacetime to something mystical. Instead, you need to go lower, blur and know no distinction between frequency and intensity.

Coupled with the photoelectric effect of radiation hitting the entire object and not just a point of focus, and Brownian movements driving increasing entropy, meaning atoms exist but there's nothing really special on their boundary, you have a general principle. The object is in a bath of radiation particles acting everywhere. Brightness equates to an internal clock ticking fast. For every geometry with a specific boundary, there's a thermal topology just skimming the surface, that of infinite thermal dimensions. Hopefully that helps with Hilbert spaces.

Because this principle acts anywhere and everywhere, nature "goes to the tape" and will even change the record, everything around it faster than you can look at it, if that's the path of least effort.

How we get to atoms: Prior to Planck and Einstein, Newton's medium of radiation was just temperatures really close together. Under Newton's model, a closed closet full of cast iron pots and pans would end up with one burning bright hot, hot enough to swallow the sun, and everything else turning into black holes. Planck fixed this by saying if something is to exist, it has a capacity to absorb heat before it starts radiating it out. Using the speed of light, which goes back to Galileo, and the kinetic theory of gases which relates temperature to dimensionless probability, you have a limit on how small something to be. It's incredibly small, bringing the photon to a cosmic level if the Planck length is the size of a photon.

So particles aren't intuitive, not little grains of sand to build things out of. Anything with a discrete start and an end works even if it's purely thermal relating to an internal voltage on the medium of clock speed.

What makes an atom? They're always the same despite weight or lattice or grains. Any smaller means lightening's shooting out. Instead of counting what's inside or measuring all points of contact, just use that radiation topology to describe, or even define it completely. Likely nature is what does this.

Why this matters:

What if the holographic universe theory is right, and through technology we lower that distance to around the sun or even the earth?

What if string theory is right, and we increase the effective size of the string to the earth or the sun?

What would that look like?

Instruments inside the sun, whose orbit is a galactic one. If that is a matter wave that's following that orbit, and the other side of the interference pattern is the boundary of a black hole, that looks a lot like dark matter. Control that with another larger black hole, and another "data ground" to a therapeutic imaging machine, how could a tumor evade that? Dump more tech into that concept, get it big enough to microwave an incoming asteroid, humans are invincible on a cosmic scale.

Sure but I wasn't questioning my existence. Only yours and everybody and everything else's. Descartes still would need to believe in God in order to believe in you. It doesn't seem like a particularly good argument.

That would indeed by very unnatural. Fortunately that's nothing like what the Schrödinger equation says.

The basics of quantum mechanics are:

1. Any system can be described in a linear "state space", whose basis vectors (roughly speaking) are each possible arrangement of the things being described (every thing's location). However, all possible states include (complex) linear combinations of these. This is usually described as the "wave function", you can plug in any value for coördinates of all your things and get a number back out.

2. States in a closed system evolve according to the (time-dependent) Schrödinger equation, -i h-bar d/dt (state) = E(state). This is sometimes phrased as "energy is the generator of time translation" (note that this phrasing holds true in the Hamiltonion formulation of classical mechanics too, but with different, related meanings). Actually calculating this can be difficult, and you might need to do various tricks such as decomposing in a convenient basis.

No all-encompasing energy field binding and penetrating us needed, though the equation is non-local in the sense that it could depend on the entire world. (In fact, it's quasi-local in practice; energy is usually just a function of where things are (local), and how different that coefficient is on infinitesimally adjacent states (i.e. spacial derivatives of the wavefunction). But this does let changes propagate at any speed, including faster than light. Basic QM is not Einsteinian relativistic. It is perfectly Galilean relativistic in a very nice way though.)

3. If you measure a system, you're going to get results that are probabilistic with the probabilities proportional to the (absolute value of) the square of this wavefunction. After that, the state is reset to whay you measured, and evolution will proceed according to 2.

It's a lovely mysterious incantation, like the (worked-over by Heaviside) Maxwell equations. But (used much like Latin), they don't speak to any human beings except those that have the leisure and capacity to learn all that math ... and then to acquire a voluminous mental store of evidence to apply it to. Real truth is plain.

Newton's equations are approachable, closer to human experience and comprehension. Feynman's diagrams, perhaps a step in the right direction.

True? Science is not math; it has no proofs. A 'theory' is the expression of a model that's stood the test of time - but one piece of evidence can force it to be re-built. Science forces us to search for and adapt to the new. Feynman said, "When someone says ‘science teaches such and such’, he is using the word incorrectly. Science doesn’t teach it; experience teaches it."