screen
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) ) ) ) ) radio wave
● ---->
M, Q <---- ●
M, Q
The radio wave will hit a screen far away, and we can determine the positions of individual photons.
We can calculate the shape of the radio wave classically, but we cannot calculate where the individual photons will hit the screen.
The process creates new particles. Is there a way to extend the de Broglie-Bohm model to this case?
Could this work: the photons "pre-exist" in the electric fields of the charges Q, and are "freed" in the scattering process? Then all the particles could have a hidden variable already at the outset of the experiment, and would sail in a deterministic way to the screen – just as in the double-slit experiment.
The outgoing photons have an uncountable number of possible momenta p. Even if we would have pre-existing photons in the field of Q, how would these obtain the required p?
Time asymmetry in the process
The initial configuration of two charges Q flying at each other is quite different from the final configuration where we have the wave function for the two charges Q plus many alternative configurations of photons. The entropy of the system grows, and there are more degrees of freedom in the final configuration.
What if there would be no growth of entropy? Then the initial and the final configurations should look similar. Maybe the number of the degrees of freedom does not grow any more?
What about inverting the direction of time? Then the degrees of freedom will shrink as time progresses.
Absorption of a photon by a hydrogen atom
An excited hydrogen atom can decay and send an individual photon. The atom can absorb the required momentum from the reaction as it launches the photon.
What about the reverse process? A wave function of the photon contains many cases in which the photon does not hit the atom at all. The photon passes the atom.
Can we somehow add more "worlds" in such a way that the the graph of possible worlds would look more time-symmetric?
In the case of a hydrogen atom absorbing a single photon, the degrees of freedom only shrink in the case of the absorption. In other cases, there is no change. A "wave function collapse" only happens in one branch of many-worlds.
Ignore photons and only consider (charged) particles which existed at the outset?
The de Broglie-Bohm approach might work if we only had undestructible particles. Let us have N such particles. Let us have a foliation of spacetime such that spacelike folios define "simultaneousness". Then we could replace the N particles with one particle moving in a space with 3 N spatial dimensions.
But we have a problem already with electrons: pair production and pair annihilation. There are no undestructible particles.
Give up determinism?
Albert Einstein said that God does not play dice. That is, the "next", measured, state of a physical system should follow deterministically from the "previous" state.
Since simultaneousness is not well defined in relativity, we maybe should say this: what happens at some point in time and space is determined by the light cone which precedes that point.
Why not require determinism also in the "initial" states of the particles? Why can the initial states be random? Does God play dice, after all?
Why is the time dimension different from spatial dimensions?
Defining a "branch" in many-worlds
Let us have a human living in spacetime. Most of the massive elementary particles in his brain survive for a long time. They are not annihilated. However, quite a few particles are replaced with other similar particles over his lifetime. How could we define the "branch" in many-worlds, in which he is living?
The brain consists mainly of electrons and of nuclei. These particles are, in most cases, conserved over 100 years.
Then we can apply the de Broglie-Bohm model to these particles, and obtain well defined "branches" of their configurations.
We do not try to define a branch in a more general sense: we do not define, e.g., which photons on Mars belong to his branch.
What if two photons collide and form an electron and a positron, and the electron subsequently is used as a new building block in his brain?
Could we simply accept a model in which the branch of this brain chooses "by random" the initial state of the electron, as it is integrated into the brain?
A new problem: which paths of separate particles are in the "same" branch of many-worlds?
Suppose that two electrons are created in pair productions, and these two electrons are integrated to the brain of the observer.
We can use the de Broglie-Bohm model to describe the paths of the two electrons. But what paths are in the "same" branch of many-worlds?
This might be the solution: we simply choose one de Broglie-Bohm path for each electron. Then the combination of those paths is taken to be in the "same" branch as the brain of the observer.
When a new particle is included into the brain, the brain performs a "quantum jump" to include a certain path of that particle.
Do we need precisely defined branches at all?
Definition of a branch does not change anything in the wave function. In the de Broglie-Bohm model, the path of a particle does not affect the wave function in any way.
However, picking a certain path may define the "real world".
Let us have an observer. Maybe he lives in the "real world", and the copies of him in other branches are just "empty" wave functions?
This does not sound natural. Why should a conscious observer always exist in the "real world" and not in the "empty" branches?
In the de Broglie-Bohm model, the empty branches do physically exist, too. They are just different branches of the wave function.
Maybe it is necessary to drop the concept of the "real world" and treat all the branches equal. This means that Schrödinger's cat is both dead and alive at the same time.
Do we have a reasonable definition of a "branch" now? A robot
Instead of an observer we may consider a computer or a robot which possesses a camera and other sensors. It also has arms for manipulating external objects.
Above we suggested that we can use the de Broglie-Bohm model to define a "branch" of many-worlds, such that an instance of the robot lives in that branch.
The robot will encounter various random (or pseudorandom) quantum phenomena, and adjust the contents of its memory accordingly. Its camera may register random photons hitting its CCD sensor.
The robot is an almost classical machine. It probably has relatively exactly definable states, and it in most cases functions deterministically.
Is the de Broglie-Bohm model an awkward way to define a branch in this case? Why not use a traditional Copenhagen model where the next state of the machine depends probabilistically on the previous state?
Assigning hidden variables is awkward?
The observing subject
Suppose that we have a reasonable way to define a branch for the robot. The computer in the robot, in that branch, will have a similar world-view as a human observer. It will remember its history. In almost every branch, the robot notices that physical processes in its history behaved according to the probabilistic rules of quantum mechanics.
According to Rene Descartes, cogito ergo sum. That is, I as an observing subject do exist.
My subject might be attached to one branch of a robot, my physical body, or it might "jump" from branch to branch. I would not notice anything if my subject jumps around the branches of many worlds.
It sounds strange if I alternate between different branches. I very much feel that I am in just one branch. This paradox is similar to another paradox about time. In what sense is now different from moments in the past or in the future?
*** WORK IN PROGRESS ***
