Is Wave Theory the Key to Understanding All Physical Phenomena?

[Demystifier]

Easy. MWI can break symmetry in symmetrical way.

Say, initial state is symmetric: 0:0
In MWI 2 branches can appear: -1:1 and 1:-1

It's easy to say so. But can you show by mathematics that such branches really appear? Can you point to a reference where it is shown?

 

[Dale]

However in order to reproduce the predictions of standard qm de-Broglie-Bohm needs the quantum equilibrium hypothesis, which states that if for some variable $$\rho (q,t_0)=\left|\psi(q,t_0)^2\right|$$ is valid, then $$\rho (q,t)=\left|\psi(q,t)^2\right|$$ is also valid. If one assumes this hypothesis, the predictions of standard qm and Bohmian mechanics are the same. However one guy called Valentini assumes that this equilibrium situation is just the limiting case of a more general theory, which can also treat nonequilibrium cases

Thanks Cthugha, this was very useful. I have seen this happen before where an interpretation (deBroglie-Bohm) is really just an interpretation with no experimental distinctions, but it provides a different viewpoint that allows a new theory (Valentini) to be developed later. Something similar happened with relativity where Einstein's special relativity was just an alternative interpretation of Lorentz's aether theory, but it provided a geometric viewpoint that lead a new theory of general relativity.

 

[sokrates]

Sokrates, who are you quoting when you say "the position of an electron is determined to extreme precisions..."? I googled the whole phrase and it doesn't appear anywhere on the Internet except in your post.

Conway, I do not "quote" people for everything I say... What I am saying is a very, very basic thing about quantum mechanics, and you are trying to challenge it by looking for exact matches of my posts in google?

You do not see my phrase anywhere in the internet, because you have brought this argument to the point of exhaustion.

You are obviously not aware of the position operator x , and that when you "measure" the position along one coordinate axis, you "collapse" the wavefunction and it becomes A DELTA function, and etc...

Both theory and experiments are in perfect agreement in this case, so please.. before typing anything else, go check those wikipedia articles I listed for you above.

 

[Dmitry67]

It's easy to say so. But can you show by mathematics that such branches really appear? Can you point to a reference where it is shown?

just a standard decoherence stuff.
look at it this way: everythere in CI you get something random, in MWI you get a branch.
every 'random' event in CI 'injects' new information into system making it more complex.
The same in MWI

 

[sokrates]

No I can't. Can you give me a single experiment that favours any interpretation of QM ?

As I understand it, there's nothing predicted to be different so experimental evidence
is irrelevant.

So, I am naively asking: Why should I believe in the objective existing entities of both the wavefunction and the particle?

Why would I take BM any more seriously than another crazy interpretation where all the predictions are tuned to match exactly to those of standard QM?

If BM is a challenging theory - a theory that supposedly "solves" some of the problems (if you are not solving any problems of standard QM, why even bother?) it has to be favorable over CI, or it has to be testable, right?

So this is the point I am not getting: You are defending BM by saying it EXACTLY matches CI... But if BM is to REPLACE CI - how can you even benchmark your theory by CI?

 

[eoghan]

And why do they move according to their wave? An electric charge, for example, moves according to an electric field; and in this case?

I can ask you: why does a free particle classically move in a straight direction? This is a postulate, there isn't a reason. So it's nonsense asking why a particle moves according to a wave: it's just a postulate.

 

[sokrates]

But I did read the Wikipedia article and I didn't see anything about electrons. I even went back and searched for the word "electron" and it said "phrase not found". Isn't the quantum eraser experiment done with photons?

Photons electrons, protons or buckyball molecules.

Everything has this wave-particle duality.

Don't narrow-mindedly search for exact matches, try to look for generalized themes.

 

[Dmitry67]

Well, CI is not well defined: why the most fundamental notion in CI is a "measurement" or an "observer" both are not clearly defined.

 

[sokrates]

I think unless an experimental distinction between interpretations is identified, favoring one over the other is not positive science.

It becomes a philosophical issue at that point, if they are not different in reality, CI is as clean as MWI ( same goes for BM ), so interpretations must find a way to make things experimentally different.

But paradoxically all interpretations are trying to tune themselves to the predictions of CI and then they claim they must replace CI. Of course there's no new prediction, because everything was arranged nicely to match CI (because it WORKS extremely well) and you end up with this very elegant theory albeit it is not testable... So anything can be made to fly using this scheme. That's why we have so many so-called "interpretations" all predicting the same things.

 

[lightarrow]

I can ask you: why does a free particle classically move in a straight direction? This is a postulate, there isn't a reason.

Not exactly, even if quite. The postulate is space homogeneity.

So it's nonsense asking why a particle moves according to a wave: it's just a postulate.

Then I can postulate that particles goes in the screen after the slits exactly in the way we see the interference picture. Wouldn't it be simpler?

 

[Hurkyl]

It becomes a philosophical issue at that point,

Not purely. There is pedagogical merit in having different interpretations -- and don't forget that theory building is an important part of science.

 

[Count Iblis]

CI interpretation is, strictly speaking, self contradictory. The wavefunction of a closed system should evolve in a unitary way until observed by an external observer. However, the closed system could itself contain an observer. In that case, the CI would predict that the state of the closed system does not evolve in a unitary way.

So, what Dmitry says is correct: The CI is not well defined. But the difference between CI and MWI can be probed experimentally by trying to find devations from unitary time evolution. CI predicts that closed systems can change in non-unitary ways, MWI predicts that this can never happen.

 

[sokrates]

Not purely. There is pedagogical merit in having different interpretations -- and don't forget that theory building is an important part of science.

I agree.

But shouldn't the new proposals at least make an effort to suggest experiments to probe the differences?

 

[zenith8]

And why do they move according to their wave? An electric charge, for example, moves according to an electric field; and in this case?

Because it is a repository of 'energy' which can be given up to and retrieved from the particle, just like in the case of the electromagnetic field.

I refer you to the response I gave in a recent thread to someone asking 'what is a pilot wave', which I quote in full below:

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In non-relativistic quantum mechanics the pilot wave, or wave field, is a real field objectively existing in 3d space that is represented mathematically by the 3N-dimensional wave function of Schroedinger theory. It is a time-dependent distribution of energy (or more strictly energy-momentum) in space.

So now you tell me that you don't know what energy is. Well, it doesn't seem to bother most physicists, but let's just say that energy is something which:

(1) is conserved.

(2) exists in different forms

(3) can be stored

(4) can be transferred through space or from one material body to another

(5) can be transformed into other forms of energy

Now in the de Broglie-Bohm interpretation of QM or pilot-wave theory - which is what you're referring to - electrons (say) exist as particles in addition to the pilot wave. Because the wave field is a repository of energy it can exert a force on the particles (the so-called 'quantum force'). Like all such a fields it has a potential energy function (Bohm's 'quantum potential' Q) and the force is given simply by $$-\nabla Q$$ .

Remember that in general, potential energy is a property of fields, and the potential function Q represents the potential energy available to the particle at a specific position in the wave field.

Depending on the prevailing circumstances, some (or all) of a particle's energy-momentum can be transferred and temporarily stored in its wave field. Once stored in the field, energy-momentum can be returned to the particle if circumstances change, and its kinetic energy will then increase (it will accelerate). This has the interesting consequence that the motion of a quantum particle need not be in a straight line even if there no external field present.

For example, if the pilot-wave passes an obstacle (such as a couple of slits) then its form will change (it will develop an interference pattern in this case) and energy will be transferred to and from the particle traveling through it according to the usual equations; the electron trajectory will then deviate from its classical (Newtonian path). It will end up getting guided into places where there is constructive interference in the pilot wave, and so after multiple experiments we see an 'interference pattern' developing in the positions of particle detections on a screen placed on the other side of the slits.

Even though Feynman (and God knows how many textbook writers like, say, Landau and Lifschitz) said no-one knew how to do this in terms of electrons following trajectories. They were just wrong.

So to summarize the properties of the pilot wave and the quantum potential:

(1) the pilot wave exhibits the usual wave properties (e.g. reflection, transmission, diffraction, interference etc.) and obeys the principle of linear superposition. The whole experimental field of 'matter wave optics' depends on this being the case, thus indicating unequivocally that the wave field objectively exists (in order for it to act in such a manner, and be acted upon).

(2) Since the Schroedinger equation is homogeneous, the pilot wave is not a radiated field and there is no source term for the field.

(3) The environment surrounding a quantum particle (in part) determines the shape of the pilot wave..

(4) The pilot wave is the repository of potential energy in a quantum system.

(5) The pilot wave acts on the quantum particle similar to an external field and receives or imparts energy and momentum to the particle.

(6) The quantum potential represents a portion of the energy contained in the pilot wave and is the amount of potential energy available to the particle at its specific position in the pilot wave field.

(7) The magnitude of the quantum potential is independent of the intensity of the pilot wave.

(8) Non-local connections between particles in a many-particle quantum system are facilitated through the operation of the quantum potential.

If you want to know what it is at a deeper level than that, then the answer is that nobody knows. But that doesn't stop you from asking or trying to find out (though don't tell ZapperZ - it'll be our little secret..).

 

[zenith8]

Hi Zenith8,

I know next to nothing about BM and I am interested in the structure of the atom according to BM. Charged particles that travel through space give off energy. You said the electron is supposed to be both a wave and a particle at the same time. So, why don't the electrons fall into the nucleus if they are traveling continuously around the nucleus?

Hi Wavejumper,

That's a good question (unusual around here whenever de Broglie-Bohm gets a mention..!) which as far as I know has not been properly addressed in the literature. It is also difficult to answer in a simple way, since a complete answer would require knowledge of the full high-energy QED, rather than boring old Schroedinger theory which is what this thread is largely about.

Before I give my partial answer to it, let me briefly address a couple of points. These are both related to the fact that this yet another case of a somewhat "unfair attack" on de Broglie-Bohm theory, in the sense that the question exists in standard QM as well, but people never worry about it there. This is because Uncle Bohr has convinced them if they can't see something they don't need to worry about it (rather like Zaphod Beeblebrox's 'peril-sensitive sunglasses' in HHGTTG, which turn totally black when you see anything that might alarm you). Generally, de Broglie-Bohm theory seems to make people worry about things they don't usually worry about. This is of course because it's so much clearer than orthodox QM.

Anyway, my two points:

(1) In the case of, say, two-slit interference, one could ask similar questions in standard quantum theory. After all, there is a potential present, the particles do not move freely, and the "acceleration operator" should have a non-zero mean whenever the electron wave packet overlaps with the screen. This should imply a non-zero mean for the quantised EM field. It's probably the case that standard "nonrelativistic QED" predicts a small EM radiation from the system, which no one usually bothers to study, and which probably makes no real difference to discussion about "which path" etc. There are presumably semi-classical arguments to the effect that the radiation doesn't contain precise enough info for us to tell which hole the electron went through -- though I don't recall anyone ever discussing this. (Basically, instead of shining a light on the electrons to see where they go, we can let them shine radiated light directly at us.)

(2) It's completely unjustified to assume that deBB charged particles will couple to the electromagnetic field in the same way that classical particles do, so there's no particular reason to believe "semiclassical" expectations about their rate of radiation. On the other hand, there will be an interaction with the electromagnetic field, and if one wants to know the effect of a deBB charged particle on the EM field one should ask deBB theory what the answer is (rather than asking classical theory).

OK, so how do we do this?

Rather than working with full high-energy QED, it might be good to look at this in a de Broglie-Bohm version of what is sometimes called "nonrelativistic QED" -- the theory of a nonrelativistic (say spinless for simplicity) charged particle coupled to the quantised EM field. I have in mind the theory commonly used in quantum optics. As far as I know, no one has ever studied a pilot-wave version of it, but it should be simple enough to set up. It would suffice for a start to look at a single atom interacting with the quantised electric field via the standard dipole interaction d dot E, where d = (charge) times the position operator X of the electron with respect to the nucleus, and E is the electric field operator. The wave functional would be a function of x and t and a functional of E. In this model, for an entangled state of x and E, the guidance equations will imply that the motions of x and E are coupled. It will be certainly be true that, for a given psi, the time evolution of the deBB E field will depend on the electron trajectory x(t). This dependence will, in general, be quite unlike in classical physics, and in most circumstances won't look much like standard "radiation". The dependence will generally be highly wave-functional-dependent; there won't be a simple general relation between E and the motion of x.

One could investigate the above model, and see what happens - again, asking deBB theory to tell us what happens in deBB theory.

For example, in standard quantum theory, excited atomic states do radiate and this occurs via interaction with the quantised EM field (simple wave mechanics doesn't really explain why atomic states spontaneously decay). One could see how that works in the deBB version. One might expect to find that the radiation is being produced by acceleration of the trajectories, as the semi-classical picture would have it, but I doubt that's true except maybe in special cases (e.g. semiclassical Rydberg atoms). My guess would be that if one starts with, say, a hydrogen atom in the first excited state, then the EM radiation produced by the decay will depend very much on the initial wave functional, and won't be given by any simple function of the electron motion alone (unlike in the classical case).

I don't have much of an intuition of what the answers might look like, as I've never really thought about this or worked on it. It might be interesting to study this.

In case you don't know, in nonrelativistic QED there's a whole literature (from the 60s to the 80s) about the two points of view regarding why an excited atomic state decays. One view, usually given in the books, is that spontaneous emission is caused by EM vacuum fluctuations. Another, equivalent view says it is caused by "radiation reaction", that is, the back reaction on the electron from the radiation it radiates. I vaguely recall that one can make either view true by an appropriate choice of operator ordering, but I'm not sure if this is uncontroversial. I'm talking purely standard QM here- one wonders how all this might look from a pilot-wave perspective.

As I said before, good question!

 

[zenith8]

Hi Mentz114 and zenith8, you two are confusing me:This is what I had understood previously, that it was an interpretation of QM, not a separate theory. But zenith8 disagrees:So which is correct? Does it make different experimentally testable predictions from standard QM (therefore being a different theory) or does it make the same experimentally testable predictions (therefore being a different interpretation).

Hi Dale,

Um, with all respect to Mentz114, I am correct. As I have outlined in endless previous threads, once you postulate the separate existence of particles and waves then it is clear that the former do not logically have to be distributed as the square of the latter.

It is therefore somewhat of a puzzle to realize why they are, until you realize that any distribution of particles being guided by a wave undergoing Schroedinger evolution according to the deBB prescription will become distributed in the course of time according to the square of that wave, and thereafter will remain so distributed.

A nice visual illustration of this is given by the numerical simulations of Valentini and Westman; the relevant pictures are shown in lecture 5 of Towler's http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" - see slides 26 onwards.

As someone else said, Valentini has devoted extensive effort to understanding whether there could be any observable consequences when the particles are 'not in equilibrium'. His papers on the subject are very illuminating. A particularly interesting consequence is his 'signal nonlocality' where he points out that the existence of non-equilibrium distributions should allow one to signal faster than light. Oh yes. See the relevant section of the Further Reading page of the above lecture course.

 

[berkeman]

Thread locked pending Moderation and cleanup.

 

[Doc Al]

Moderator's Note: I'm reopening this thread (after deleting a few off-topic posts). Please keep it about the physics.