Exploring the Many Worlds Interpretation of Quantum Theory

[Tanjore]

I have a question regarding the Many Worlds Interpretation(MWI) of quantum theory.

Is there any proposed thought experiment that can/does provide some kind of solid/good proof for the MWI?

I have an idea, an experiment and I am very curious about it's validity/soundness and the consequence if so.

Consider two hollow cones that are joined with each other at their bases. Let the inside surfaces of these cones be perfect/near perfect detectors (for gamma, X-rays or any kind of ionizing radiation). Let one of these surfaces be charged negatively and the other be charged positively. Now at the tip of the cone that is charged negatively (call it the electron cone) place a electron emitter and the tip of the cone charged positively (call it the positron cone) place a positron emitter (the cone surfaces are charged to prevent the particles from hitting their own cones). Now emit the two particles(the electron and the positron) at the same instance from their respective cones (maybe some time lag can be permitted). The electron and the positron would travel as waves right? If so then according to the MWI does it not mean that we would always see a collision of the particles (at every point but in each universe we would see it happen at some single point)? Aren't the two particles going to interact at every possible location inside the two cones because every possibility is realized in MWI? If we see gamma being produced for a certain number of e-p emissions from their respective cones (say a certain percentage of the total times we carry out the collisions) can we say that the MWI is true with some confidence and on the other hand if we do not see very many of the collisions and gamma being produced can we say that MWI is wrong with a certain confidence?

 

[Simon Bridge]

Is there any proposed thought experiment that can/does provide some kind of solid/good proof for the MWI?

No.

If we see gamma being produced for a certain number of e-p emissions from their respective cones (say a certain percentage of the total times we carry out the collisions) can we say that the MWI is true with some confidence and on the other hand if we do not see very many of the collisions and gamma being produced can we say that MWI is wrong with a certain confidence?

Neglecting the times that the particles are more strongly attracted to the opposite charged cones, or that your equipment described won't tell you where the annihilation occurs ... in each universe you only get one annihilation at one well-defined position. You realize that matter-antimatter reactions are very well studied right? Nothing inconsistent with there being just one universe has been observed ... though: some people have had it that quantum interference is evidence of other Universes ;) In the MWI the act of measurment sets which of the worlds you are in.

There's also some conceptual issues - eg. the particles do not travel as waves. What happens is that the probability of detecting a particle at a particular place follows a wave equation in the math. The "wave" is a probability. Similarly human heights have a probability distribution shaped like a bell that spreads out as you get older but that does not mean that your height is a bell shape.

 

[Tanjore]

Yes I know the experiment will not tell me where the particles will interact and I also know that the collision will happen at a well defined point inside the volume of the two cones. I also know that these are particles but where they would be found is defined by a wave equation.

My point was if I was to carry out the experiment and found that gamma rays were being produced say 80% of the times would it mean something?

the waves are considered to be real in the many worlds interpretation and the electron wave and the positron wave would overlap with each other producing a collision at every point they overlap according to MWI and creating an alternate path/universe with each collision so every time I carry out this experiment would I not see a collision? If so would it say anything about MWI? If there are very few collisions then would that say anything about MWI?

 

[Tanjore]

I am not a believer in MWI, just had an idea I believe can provide some useful lead to prove/disprove it, I want to know if I am right in thinking so.

 

[Simon Bridge]

I don't think the MWI makes makes any predictions about changing the probability of observing a gamma from annihilation.

It is unlikely that you will have come up with some definitive experiment, even in principle as a thought experiment, that would demonstrate the MWI one way or the other - especially considering how much effort has gone into this since it was mooted. But you shouldn't let that discourage you ... that's just the normal state of mind of a physicist :)

 

[Tanjore]

Simon, I am not a physicist, I am an engineer by profession and I just randomly read some deeper physics stuff (and) understand very little but that has never discouraged me ;)

Yes I know QM is probabilistic by nature but MWI says all possibilities are realized (where do probabilities come from in case of MWI?) I am not therefore talking about changing probabilities.

 

[mfb]

There's also some conceptual issues - eg. the particles do not travel as waves. What happens is that the probability of detecting a particle at a particular place follows a wave equation in the math. The "wave" is a probability.

You use probabilistic interpretations to describe MWI here, which does not work.

With MWI, both particle wave functions travel in the volume. Assuming that your setup is somehow perfect, they annihilate completely, emitting photons in a superposition of the whole possible annihilation volume. These photons now hit the detector and their position and time is measured - as this can give different measurement results which lead to a very different evolution of the whole system, you get multiple branches which measure the annihilation at different points. With perfect detectors, each branch measures a pair of photons.
If the setup is not perfect, you can get additional branches where the electrons hit the positive side and the positrons hit the negative side.With Copenhagen, both wave functions travel in the volume. Assuming that your setup is somehow perfect, they annihilate completely, emitting photons in a superposition of the whole possible annihilation volume.
At the point where those photon wave functions hit the detectors, the wave function collapses and a single pair of detected photons remains. With perfect detectors, you always measure a pair of photons.
If the setup is not perfect, you get the additional option to measure the electron at the positive side and the positron at the negative side.

As you can see, the experimental result is the same in both interpretations. You get a specific "annihilation point" with each repetition.

 

[Tanjore]

@ mfb:

By changing the diameter and length of the cones can we not see to it (if MWI is correct) that we get electron-positron collisions most of the times? and if MWI if not correct we will get these collisions very rarely.

I guess if we can keep the diameter to axial length ratio of the cones large enough we can have very few particles hitting the detectors without colliding with their antiparticles and producing gamma.

 

[Simon Bridge]

Why would you expect the positron and electron collision to be rare? They are attracted to each other after all, and you are shooting them at each other. For that matter, why would you expect a greater chance that the positron and electron would collide in the MWI than in CI? I mean - sure - if we could find some interaction which happens a lot in MWI and seldom in CI, and an experiment showed that they happened a lot, then MWI would be demonstrated ... the tricky part is in the details of how to set this up. Why would you expect to see something different in the experiment under discussion for the different interpretations?

AFAIK: both interpretations lead to the same prediction for your proposed experiment. However, I'm at a loss to explain to you why without knowing the reasoning you have followed.

 

[mfb]

How does the outcome depend on the geometry?
Annihilation always produces photons, which always hit the cones.

As the annihilation cross-section depends on the energy, slow particles should be better. This might give a significant annihilation probability.

 

[audioloop]

Testing Many-Worlds Quantum By Measuring Pattern Convergence Rates
Frank J. Tipler
http://arxiv.org/pdf/0809.4422v1

...Non-Many-Worlds quantum mechanics, based on the Born Interpretation of the wave function, gives only relative frequencies asymptotically as the number of observations goes to infinity. In actual measurements, the Born frequencies are seen to gradually build up as the number of measurements increases, but standard gives no way to compute the rate of convergence. The ManyWorlds Interpretation [6] allows such a computation: the MWI says the absolute difference between the observed distribution and the Born frequencies decreases inversely as the number N of measurements...

...Such a rate of convergence has long been suspected [7], but earlier proofs are known to be defective, and have not been stated in a way that allows an experimental test. I shall state the simple, easily testable formula here, and publish the proof elsewhere...

...An outline of the proof is as follows. Many-Worlds quantum mechanics asserts that before measurements, identical copies of the observer exist in parallel universes. Bayesian probability theory [8], applied to identical observers coupled to the wave function of the quantum system being observed, yields a Bayesian probability density (which in Bayesian theory is NOT a relative frequency density) equal to |ψ|² .Standard Bayesian analysis then yields the rate of convergence of the observations to |ψ| ²

[6] Hugh Everett, “Relative State Formulation of Quantum
Mechanics,” Rev. Mod. Phys. 29, 454–462 (1957).
[7] Bryce S. DeWitt and Neill Graham The Many-Wolrds Interpretation of Quantum Mechanics (Princeton University
Press, Princeton 1973), p. 185
[8] E. T. Jaynes Probability Theory: The Logic of Science
(Cambridge Univ. Press, Cambridge, 2003).

 

[mfb]

I cannot find a corresponding publication, and some claims look quite suspicious. Collapse interpretations have a meaningful way to compute how rapidly the observed frequencies approach the calculated values. In addition, I do not see where he uses the MWI at all. And "collect data first, determine bin size later" rings several alarm bells at the same time.

 

[audioloop]

who knows...
them have to push themselves to new frontiers.Page says that some cosmological observations might support MWI.

http://xxx.lanl.gov/pdf/gr-qc/0001001.pdf

Although many people have thought that the difference between the Copenhagen
and many-worlds versions of quantum theory was merely metaphysical, quantum cosmology may allow us to make a physical test to distinguish between them empirically.
The difference between the two versions shows up when the various components of the
wavefunction have different numbers of observers and observations. In the Copenhagen
version, a random observation is selected from the sample within the component that is
selected by wavefunction collapse, but in the many-worlds version, a random observation is selected from those in all components. Because of the difference in the samples, probable observations in one version can be very improbable in the other version.
---
and Plaga have a proposal too

http://xxx.lanl.gov/pdf/quant-ph/9510007.pdf

The many-worlds interpretation of quantum mechanics predicts the formation of
distinct parallel worlds as a result of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to this
interpretation. A procedure for “interworld” exchange of information and energy, using
only state of the art quantum optical equipment, is described. A single ion is isolated
from its environment in an ion trap. Then a quantum mechanical measurement with
two discrete outcomes is performed on another system, resulting in the formation of
two parallel worlds. Depending on the outcome of this measurement the ion is excited
from only one of the parallel worlds before the ion decoheres through its interaction
with the environment. A detection of this excitation in the other parallel world is direct evidence for the many-worlds interpretation. This method could have important
practical applications in physics and beyond.

 

[Tanjore]

@Simon: But we can never say with certainty where the particles are besides if the distances involved are large compared to particle size , say in meters then the attraction between them will be very small.

@mfb: If the diameter to axial length ratio is large would it not reduce the chance of particles (in case of those with high energy) colliding with their own respective cones.

 

[Simon Bridge]

@Simon: But we can never say with certainty where the particles are besides if the distances involved are large compared to particle size , say in meters then the attraction between them will be very small.

Excuse me but so what?

1. you have described a setup where the probability of an interaction with anything else is very small - doesn't that mean the probability of interaction with each other is very large?

2. your setup with the cones guarantees that their separation will, at least initially, decrease.

3. the particle's position does not need to be certain for them to interact ... they don't have to be in exactly the same place. This is not a "collision" like two balls bumping ... their mutual EM attraction, however small, allows them to measure each others position and they only need to get close enough.

Abstract the setup perhaps to just put a particle and it's antiparticle in an infinite square well - need not even be charged - we can make it as big as we like. We can rig them to be in an initial superposition so that one wavefunction is predominantly on one side and the other - the other side. This can be as tight as we like because we have a full set of basis states. Now let it evolve and keep track of the separation of the particles.

With the possible exception of the initial condition, there will almost always be times when the probability that the separation of the particles will be small enough for an annihilation is bigger than 0.