The elements of the wavefunction


This page is a little vague and speculative. Written in 2011, I didn't work at it since. A previous attemtpt.

In Scientific American of August 1993 is an article named FTL? (Faster Than Light) written by Chiao, Kwiat and Steinberg. See also page 3 of THE COLLAPSE OF THE WAVEFUNCTION.

On page 43 they wrote about what one can call the building blocks of the wavefunction or what I would like to call the elements of the wavefunction: infinite long waves that are equal everywhere and the same forever, all over spacetime. If one superposes such a wave with a similar wave of a little longer wavelength and a wave of a little shorter wavelength, one obtains a pulselike object. When sufficient frequencies are added one obtains a real pulse or wave packet. So far well-known quantum mechanics from the article from Chiao, Kwiat and Steinberg.

Any wavefunction consists of (an infinite number of) such elements in superposition, call it a set of elements. In line with the assumptions of this site we state that each element has its own reality-experience and the different elements of one and the same particle don’t see each other.

Suppose a photon meets an electron at rest (at rest to us, the Outside Observers). Their constituent elements join. There is a set of elements not seeing each other, making up the electron. There is a set of elements not seeing each other making up the photon. And now there is a sum-set of elements not seeing each other constituting of all the elements of those two sets together.

Identical elements are indistinguishable. Do two identical elements merge into one element and the other element just disappear from the superposition? No, I don’t think so. They don’t see each other, so observed from one of the identical elements they are just kept separate, despite their equality. For us, the Outside Observers, the identical elements add up to one element of twice the amplitude.

Since all elements of the sum-set still don’t see each other, normally a reaction like a coupling doesn’t take place. In fact no reacties will ever take place. So how does it work then, in the universe?

Suppose, the sum-set of the elements of the photon and the electron at rest (call it sumset 1) is, at a certain moment, indistinguishable from the set of elements of an electron in one specific other state, without the photon (call that sumset 2). Then quantum mechanics demands these two possibilities to go into superposition. According to this site, when it comes to a decision the world splits in one world where the reaction has taken place and the sum-set now is the set of that one electron in its new state. And one world where the reaction has not taken place and where are still one electron at rest and a photon receding in some direction. There are two you’s but neither of you would notice. When it comes to a decisive measurement you will just find yourself back in one of the possibilities. This is all there is to the coupling of the photon and the electron. Thus, in fact, they don’t react. The state of the electron at rest with the photon is - or is not - replaced by the indistuinguishable new state of the electron alone.

Then there would be no point to acceleration. In our example the situation is at one and the same moment the electron at rest plus the photon and one electron with an impulse in a certain direction (and eventually a new phase). A decisive measurement chooses between those states and starting from an electron at rest you find yourself at once confronted with an electron with an impulse, without the electron ever having passed through the intermediate states.

Maybe this scenario is impossible with massless electrons. It all may just not fit. Then, maybe, the electron absorbs from a field just enough to supply its set of elements until it becomes indistinguishable from one specific other state. The electron is free NOT to absorb the missing elements - but then the reaction would not take place.

Is that field from which is absorbed, the Higgs field? In this storyline we suppose so. In QED the electron gets its restmass from the Higgsfield, otherwise the electron-photon-reactions cannot be renormalized. Does the electron absorb mass from the Higgsfield? Not necessarily. I think the electron absorbs elements from the Higgsfield that in the equations appear as mass. Then mass is not a property of a particle. It is the difference between states, the missing amount of elements to make those states indistinguishable, that in the equations appears as mass.

Assumed is the original sum-set as well as all other sum-sets do complement themselves at the moment of coupling with the necessary elements from the Higgs field:

sumset 1 + missing elements 1 = sumset 2 + missing elements 2

When the left part of the equation describes the arriving photon and “the-electron-standing-still (with respect to us) absorbing a Higgsparticle from a field standing still with respect to it (and to us)” then the right part of the equation describes “the-electron-with-a-velocity having absorbed a Higgsparticle from a field that moves with the opposite velocity (as observed from the moving electron)”. In fact it is still the same Higgsfield standing still to us, the Outside Observers.

One can add a same amount of missing elements left and right. New possible divisions will appear in the enlarged sumsets.

When sumset 1 is the electron at rest plus an electron neutrino, then in the right side of the equation sumset 2 might be a muon plus an muon neutrino. It looks as if the intermediate state, the W+ W- boson, has been skipped.

In the standard model the electron only reacts electromagnetic with the photon and weak with the W+ W- Z0 H0 particles. The electron has no other reactions. Here H0 is the Higgs particle. Since the neutrino’s turned out to have mass, the rule seems to hold: all particles with restmass react weak and all massless particles (the gluon and the photon) don’t. Therefore I took the freedom to classify the Higgs particle amongst the weak particles.

In principle it is possible that an electron in weak interaction with W+ W- Z0 H0 has a different mass than in electromagnetic interaction with the photon, because quite different elements of wavefunction have to be supplied there. There would be then a systematic mistake in weak calculations, made because no one considered two different masses for the electron at one and the same time.

Between two couplings the electron can be massless. If so, this doesn’t automatically mean it moves with lightspeed. If the indistinguishability of sumsets demands the resulting electron to be in this specific place and to have that specific impulse in that specific direction, then the massless electron will be so. The fact that the slightest disturbance would accelerate it to lightspeed doesn’t count. Such a disturbance isn’t there. In fact there are no disturbances, there only are indistinguishable sets of elements and choices made between them.

An electron that couples to a photon - absorbing or emitting, real or virtual - and thereafter has a different velocity, from where does it find its missing elements? It takes its missing elements from the Higgs field where they are available. And that is not necessary the Higgs field to which it is standing still. The Higgs particle has mass and so moves about with speed lower than c, eventually with zero speed. One can move with respect to it with any velocity. One can stand still with respect to it.

The Higgs field is a spin-0 field, a scalar-field; it only has a value and doesn’t have a transversal or longitudinal polarisation.

The vacuum is (or IN the vacuum there is) a superposition of all possible Higgs fields. According to quantum mechanics there is no other way. Here in this site we suppose all Higgs fields differ in state of motion only. Every possible state of motion is present there. They are pervading each other and don’t see each other and the whole earth is just another superposition to the fields.

Normally a field will Lorentz contract and therefore become denser when moving faster relative to it. But when all possible velocities are present and then one moves with respect to it, then your velocity will be added to every of the possible velocities and nothing will change. The field is still the field of all possible velocities. The Higgs field is velocity invariant.

As a consequence virtually all Higgs fields will have speeds very near to c, as observed from e.g. the earth. They will be accordingly massive. But that doesn’t matter - we don’t see them, they don’t see us. Our particles just pick the necessary elements out of their collective and that is all we will ever notice from the fields. Don’t feel bothered about so much unnecessary field. All those fields together are just such a small portion of the Sea of Possibilities.

Does it find its missing elements in one and the same Higgs field? Can it take elements from more than one field? The several Higgs fields are superposed. When absorbing from one field the electron enters the world of that field. When it subsequently absorbs the next missing element from another Higgs field it enters the world of that Higgs field. And so on. (I suppose this means it absorbs a Higgs particle from one field and then a second Higgs particle from a field moving with respect to it, and so on.) But stated like this, these are just separate subsequent couplings. When elements are taken simultaneously from different Higgs fields, it should be no problem. Then they just form one wavefunction.

Does the electron needs some consciousness to plan its route through the necessary Higgs fields? When it makes a mistake, can it give back the wrong elements to the Higgs field and restore the original superposition? I guess it doesn’t work like that. All possibilities, all possible routes, superpose and the most abundant then will turn out to be chosen.