Wave-particle duality/double slit experiment

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"Objects like electrons"? What does that mean? Exactly what kind of an "object" is an electron?

Does the existence of a "single formalism" (or mathematical description) imply that we really understand what is going on here? Do we yet understand what exactly the "wavefunction" is (if it is anything physical at all....)?


So we can completely explain quantum effects now on a qualitative basis? When did that occur?

Yeah...but aren't these predictions kind of ad hoc equations?

Can one derive the equations of matrix mechanics or Schroedinger's equation from first principles?
Thank you for your clear headed, honest, not bound by the party line comments.
More precisely

That isn't a valid requirement. A phase transition is a well-known phenomenon. In thermodynamics, a first order phase transition is an abrupt change, where one or more state variable can be discontinuous. In another example, a superconducting phase transition is where the resistivity also changes abruptly.

So your requirement that "nature tends to be more continuous rather than not" isn't necessarily valid. Maybe this is one more instance where nature isn't continuous.

I didn't mean by "jump to weirdness" simply being non-linear but more strictly the idea of mathematical discontinuity. The old delta epsilon argument: there is no point in time that we can get arbitrarily close to and find all the material of a phase transition in one state and then find all the material in another state. That would be a "step function" which does not exist in phase transition just very rapid change at a certain energy. Each molecule changes states individually which I could consider continuous but non-linear. Instantaneous phase change would be discontinuous. I haven't researched your other example yet but I think you will again concede that the resistance does not change instantaneously. Maybe resistivity is a little different, please inform, but I think atom by atom the change takes place not all atoms of the material changing at once at a threshold energy level.
Like i said i think its more of a moot point really because when you say 'jump to weirdness' or mathematical discontinuity you are applying your human intuition to a situation that might be counter intuitive and then getting annoyed when you get it wrong. Without knowing a complete laws of physics or 'backend code of the universe' if you like theres no way of knowing whats truely weird/incorrect. Obviously our current theories work pretty well and we can be assured that they will continue to provide correct data on the experiments they are related to. But for me science is like 20 questions. You can be thinking of an object and i can ask 19 questions to which the answer would be the same for both that object and something different, which i happen to be thinking of. If i stopped there id go away thinking about the wrong thing. If i asked the 20th question and got an answer which proved i wasnt thinking about the correct object then i have to rethink all the others two. In science the behaviour of stuff is the object and experiments are the questions. Theres nothing to say someone wont do an experiment tomorrow that completely turns everything on its head. Theres just no way you can say that for sure.

But now were getting nitpicky and off topic =)
Your are wrong and getting your concepts mixed up. The Particle-Wave duality is basically saying that light is made up of individual photons that act as waves when many photons are together. Sort of like a surfer on an ocean wave. The wave is the direction of motion and the surfer is considered the electron or photon.

Heisenberg's Uncertainty Principle basically says that you cannot ever measure both time and energy or location of an electron and it's momentum perfectly at the same time because the person doing the observation will "taint" or affect the true momentum (mass x velocity) and position of a photon or electron just by looking at it.

Quantum physics basically is somewhat disturbing because, unlike classical physics, scientists today cannot accurately predict where an electron will land or move next when it changes direction when after being hit by a photon. Scientists can only "guesstimate" using probability. Einstein had a problem with this because he refused to believe that God "liked to roll the dice" in cause and effect in science. However Niels Bohr, Max Born, Heisenberg and Wolfgang Pauli all said that Einstein was wrong and that atomic movements of particles is all random, and can never be predicted, only estimated - which to this day is the accepted fact.

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