Dear Colleagues,
1. It is known that the correspondence principle states that the behavior of systems described by quantum mechanics reproduces in a statistical way the classical mechanics in the limit of large quantum numbers, Bohr said that quantum mechanics does not produce classical mechanics in a similar way as classical mechanics arises as an approximation of special relativity at velocities very slow than light speed.
He argued that classical mechanics exists independently of quantum mechanics and cannot be derived from it.
2. For example in the case of "particle in box", if we examine the probability density for finding the particle when n growth (case of high energy) we found a sequence of peaks separated by a distance equal to half of De Broglie wavelength, so if the correspondence principle describes exactly the reality we need to accept that the motion in classical limit does not continue.
So first it is natural to assume that the motion (in classical world) is a sequence of appearances and disappearances events in space and time.
Then if we go back to the quantum world, and say okay, why the particle does not do the same for low energies too? I mean we can suppose too that it also disappears and appears as separate events in space and time, but of course, according to another law of motion(not the half of De Broglie wavelength), in fact I suggest this law in my theory:
Preprint The theory of disappearance and appearance
it is called "alike action principle" it is similar to the least action principle and can lead us simply to the path integral formulation.
What do you think?
Correspondence principle is more of a goal. The goal is to have a theory that corresponds to classical, quantum, and cosmological scales. A theory becomes more acceptable as the range of correspondence increases - or so the thought goes. This goal seems to be contrary to the outlandish suggestions.
Dear John Hodge,
This is the final goal to have a theory that corresponds to classical, quantum, and cosmological scales.
Anyway, we have some keys to think about it, the independence of quantum mechanics and classical mechanics is an important hint that tells us that the general law of motion must be broader than both quantum mechanics and classical mechanics, so from this point, the correspondence principle takes its importance because it is the bridge between quantum mechanics and classical mechanics.
God willing, I think if we found this law we can understand the foundations of quantum mechanics and resolve some important cosmological problems like vacuum catastrophe, dark energy, dark matter etc..
with best regards
The best approach to justify the complementary principle is the Ehrenfest theorem, but Bohr was right: it is not possible to approach classical mechanics as it is done in relativistic mechanics for v/c
Daniel Baldomir
True. But perhaps that is the problem for QM. Perhaps, QM should follow the walker drops.
Daniel Baldomir
Oil bath dropsthat bounce "bouncing drops", "walkers", Authors John WM Bush, E. Fort, Y. Coulder, Christian Borghesi.
Dear Daniel Baldomir,
Yes, I have quoted Max Jammer's words in my paper for reference #13.
What I mean is that the correspondence principle tells us that the motion (in the quantum world and classical world) is a sequence of appearances and disappearances events in space and time.
With best regards.
Dear Mazen,
What do you mean by appear and disappear? Notice that there are conservation laws as energy, momentum or electric charge that must be conserved locally.
Dear Daniel Baldomir,
1-I mean by "disappear" that the particle no longer exists (as it is), and I mean by "appear" that the particle exists again in the universe.
2- The theory is principally for the non-relativistic quantum mechanics, so in this case, the duration of disappearance is almost zero so we preserve the law of energy conservation.
3- In the relativist case I suggest in this paper:
Research Proposal Cosmological constant problems
that when the particle disappears, it back to the universe as energy distributed randomly throughout it, then after some time it returns as a normal particle, and this idea my resolve the cosmological constant problem.
With best regards.
Dear Mazen,
Quantum Mechanics says that for very short intervals of time the energy is not well determined, although it exists which is a quite different thing, and also it cannot be never zero. Therefore a particle cannot disappear and appear totally in our Universe, all that it can do is to transform it in others keeping the conservative quantities: energy, momentum, charge, flavour, color......
Dear Daniel Baldomir,
First sorry for my delay in reply,
Yes, as I told before, in my theory we didn't have any violation of energy conservation for the both cases, I mean the non-relativist case and the relativist case, and for this latest case, I suggest that when the particle disappears, it back to the universe as energy distributed randomly throughout it (as like you said "transform it in others keeping the conservative quantities.." ) before it re-appear again..
With best regards.
Dear Mazen,
There are basic things that I don't understand. The Universe is all and you cannot go ou and caming in following the present physical laws, for example energy is just related with the time translation symmetries and you need to explain how you do your transformations without breaking it. These are only basic considerations take into account.
Dear Daniel Baldomir,
mainly my theory is for non-relativistic case (I have some mini steps for the relativistic case), so in this case (I mean non-relativistic case), the duration between disappearance and appearance is almost zero so we have a spontaneous motion, so the conservation of energy still valid, and the same for momentum conservation etc..
You can imagine this using the path integral formulation, this formulation tells us that if the particle at time t1 is in position x1 so at time t2 the particle has multiple potential locations with different probabilities to found it, what I say that the particle disappears from position x1 (almost at time t2) then appear in x2 like spontaneous motion.
with best regards.
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