Many Worlds

[FrumiousBandersnatch]

My opinion and that’s all it is the measurement problem is solved by decoherence as quantum mechanical probabilities are converted into classical probabilities of the macroscopic world.
Of course this puts me in the 50% of people who don’t know what they are talking about according to Sabine Hossenfelder.

Yes, me too... I couldn't see why she thought decoherence wasn't a reasonable explanation.

 

[Neutral Observer]

Where as in Lagrangian mechanics the shortest path is a unique solution this is not the case in quantum mechanics.
There could be an infinite number of pathways all of which follow the principle of least action and does not include purely random pathways.
The pathways are probability amplitudes which need to be summed to find the optimized path.
The summing process results in both destructive and constructive interference of the probability amplitudes from which the optimized path is obtained.

Thanks again, but... another question... concerning the probabilities.

Specifically, how does quantum mechanics determine them?

For example, if I take a very simple case of flipping a coin. At first glance one might think that it's fairly easy to determine the probabilities, it's 50 percent heads and 50 percent tails. All things being equal both outcomes are equally likely. In MWI you'd end up with lots of variations of realities, but always with 50 percent of them heads and 50 percent of them tails. But let's say that there's a 1 percent chance that the coin ends up on its side. Now the probabilities don't seem to work, because there are immensely more ways that the coin can end up on its side than heads and tails combined. This is due to the fact that heads/tails only have 360 degrees of freedom around the vertical axis, whereas landing on its side includes 360 degrees of freedom around both the horizontal and vertical axes. So there are a lot more ways that it can end up on its side, and if they all actually occur every time that you flip the coin, as per MWI, then landing on its side would seem to be the most probable outcome, because it has the most ways in which it can occur.

It wouldn't seem to matter that in our macro world things such as gravity will strongly favor the coin ending up heads/tails rather than on its side, because as I understand it in QM every outcome that can happen will happen, and since there are a lot more ways in which the coin can end up on its side there should be a lot more worlds in which it does so.

So in cases such as flipping a coin how does QM determine the probabilities?

 

[SelfSim]

..

But let's say that there's a 1 percent chance that the coin ends up on its side. Now the probabilities don't seem to work, because there are immensely more ways that the coin can end up on its side than heads and tails combined. This is due to the fact that heads/tails only have 360 degrees of freedom around the vertical axis, whereas landing on its side includes 360 degrees of freedom around both the horizontal and vertical axes.

I'm not sure I get that(?)
The outcomes are surely constrained by the axis of rotation rather than a statically, (arbitrarily), selected set of axes(?)
The axis of rotation would have to do with the initial conditions establishing the rotation?

I could understand it if it were a combined coin flip and coin spin exercise .. but just a flip?

Seems more like an issue related to system definition to me?

 

[Neutral Observer]

I'm not sure I get that(?)
The outcomes are surely constrained by the axis of rotation rather than a statically, (arbitrarily), selected set of axes(?)
The axis of rotation would have to do with the initial conditions establishing the rotation?

I could understand it if it were a combined coin flip and coin spin exercise .. but just a flip?

Any coin that ends up either heads up or heads down is restricted to resting on that single horizontal plane. A tabletop for example. The coin is either heads up or heads down, those are the only two possibilities. However it can be rotated in all 360 degrees of that plane. So it can end up oriented to the east, or to the west, or in any of the 360 degrees of that horizontal plane.

On the other hand a coin that comes to rest on its side can be rotated on two planes. The horizontal plane and the vertical plane. The coin can have the top of the head at the bottom, or at the top, or anywhere on the 360 degrees of that vertical plane. It's face can also be rotated such that it faces to the east or to the west on the horizontal plane. An additional 360 degrees of freedom.

Therefore the coin that comes to rest on its side has a lot more possible outcomes, and per QM, if every possible outcome is realized every time you flip the coin then there should be a lot more realities in which the coin is on its side compared to when it's either heads or tails. Thus what we should see is that the coin comes to rest on its side more often than it comes to rest heads or tails.

At least that's my reasoning. If every possible outcome is realized every time that you flip the coin, then there should be more realities with the coin on its side than with either heads or tails. Since there are more of them, probability would seem to dictate that whenever we flip a coin it should be more likely to come to rest on its side.

 

[Neutral Observer]

Seems more like an issue related to system definition to me?

Exactly!!!! There are variables which will serve to dictate the final outcome, so long as you can define them precisely enough. In QM however, you often can't define them precisely enough.

 

[Neutral Observer]

I'm not sure I get that(?)

Just to try to clarify where I'm going with this, let's consider the double slit experiment. If you fire a particle through the slits there's a certain probability associated with every point on the screen as to where that particle could possibly end up... but why?

Let's say that there's a statistically high probability that the particle is going to end up in the center of the screen, and a statistically infinitesimal probability that it's going to end up waaaayyyy off to the side.

As I understand QM, or at least MWI, every single possibility is going to be realized every time that you fire a particle. Thus no one outcome will end up being realized any more often than any other outcome. They'll all be realized, every time.

How therefore does QM account for probability if every outcome is realized every time? The probability for any of them is always 100%.

 

[SelfSim]

Any coin that ends up either heads up or heads down is restricted to resting on that single horizontal plane. A tabletop for example. The coin is either heads up or heads down, those are the only two possibilities. However it can be rotated in all 360 degrees of that plane. So it can end up oriented to the east, or to the west, or in any of the 360 degrees of that horizontal plane.

On the other hand a coin that comes to rest on its side can be rotated on two planes. The horizontal plane and the vertical plane. The coin can have the top of the head at the bottom, or at the top, or anywhere on the 360 degrees of that vertical plane. It's face can also be rotated such that it faces to the east or to the west on the horizontal plane. An additional 360 degrees of freedom.

Therefore the coin that comes to rest on its side has a lot more possible outcomes, and per QM, if every possible outcome is realized every time you flip the coin then there should be a lot more realities in which the coin is on its side compared to when it's either heads or tails. Thus what we should see is that the coin comes to rest on its side more often than it comes to rest heads or tails.

At least that's my reasoning. If every possible outcome is realized every time that you flip the coin, then there should be more realities with the coin on its side than with either heads or tails. Since there are more of them, probability would seem to dictate that whenever we flip a coin it should be more likely to come to rest on its side.

Ok .. so before the toss, the experimenter has selected a coin, ensured that the coin is not biased, ensured that the toss is not biased, ensured that the surface its going to land on is horizontal, ensured that its possible for the coin to land on its side, decided to ignore unusual gravitational influences (the toss isn't happening near a black hole, etc), ignored the effects of wind, temperature, pressures, etc, etc ..

There are a lot of experimenter controls going on there, so I think the experimenter's choices, therefore, also bias how he/she/it envisages the 'possible outcomes', prior to the excution of the toss/flip. Therefore the probabilities should reflect that .. or ignore it, depending on the specific purpose of the experiment, no?

 

[SelfSim]

Just to try to clarify where I'm going with this, let's consider the double slit experiment. If you fire a particle through the slits there's a certain probability associated with every point on the screen as to where that particle could possibly end up... but why?

Let's say that there's a statistically high probability that the particle is going to end up in the center of the screen, and a statistically infinitesimal probability that it's going to end up waaaayyyy off to the side.

Its an experimenter choice to recognise that .. and a decision as to whether, or not, to ignore it, (should it occur).

As I understand QM, or at least MWI, every single possibility is going to be realized every time that you fire a particle. Thus no one outcome will end up being realized any more often than any other outcome. They'll all be realized, every time.

How therefore does QM account for probability if every outcome is realized every time? The probability for any of them is always 100%.

Is it of practical use to realise that 100% probabilty?

 

[Hans Blaster]

Co-incidentally, I read just the other day that they've nailed down the mass for a neutrino of ~0.8ev .. which (obviously) means they're sub luminal, which is interesting. {Edit/correction: that is- February 2022 upper limit of the effective electron neutrino mass, mν < 0.8 eV c–2 at 90% CL)

I guess I missed this new upper limit on neutrino mass.

While neutrinos are subluminal (given that they have mass) they are very relativistic. Typical energies for neutrinos are ~ MeV, so the relativistic "gamma" ( total energy, E = gamma * m c^2 for particles with non-zero rest mass m) is very large. Gamma ~ 1 million. Which gives a velocity about 1 part in a trillion of the speed of light slower than the speed of light.

 

[SelfSim]

I guess I missed this new upper limit on neutrino mass.

While neutrinos are subluminal (given that they have mass) they are very relativistic. Typical energies for neutrinos are ~ MeV, so the relativistic "gamma" ( total energy, E = gamma * m c^2 for particles with non-zero rest mass m) is very large. Gamma ~ 1 million. Which gives a velocity about 1 part in a trillion of the speed of light slower than the speed of light.

Interesting .. (thanks for that .. a handy metric!)
Playing around with these things just keeps producing more interesting ideas .. which can then be turned towards both practical use (for science) and for movie scripts ... (I dread the pseudoscientific consequences though .. )

 

[sjastro]

Thanks again, but... another question... concerning the probabilities.

Specifically, how does quantum mechanics determine them?

For example, if I take a very simple case of flipping a coin. At first glance one might think that it's fairly easy to determine the probabilities, it's 50 percent heads and 50 percent tails. All things being equal both outcomes are equally likely. In MWI you'd end up with lots of variations of realities, but always with 50 percent of them heads and 50 percent of them tails. But let's say that there's a 1 percent chance that the coin ends up on its side. Now the probabilities don't seem to work, because there are immensely more ways that the coin can end up on its side than heads and tails combined. This is due to the fact that heads/tails only have 360 degrees of freedom around the vertical axis, whereas landing on its side includes 360 degrees of freedom around both the horizontal and vertical axes. So there are a lot more ways that it can end up on its side, and if they all actually occur every time that you flip the coin, as per MWI, then landing on its side would seem to be the most probable outcome, because it has the most ways in which it can occur.

It wouldn't seem to matter that in our macro world things such as gravity will strongly favor the coin ending up heads/tails rather than on its side, because as I understand it in QM every outcome that can happen will happen, and since there are a lot more ways in which the coin can end up on its side there should be a lot more worlds in which it does so.

The problem with your argument is assigning an equal weight to each universe.
Let’s look at a simplified example of your coin toss where there are three possibilities heads, tails or the coin lands on its edge.

According to MWI our entangled universe branches off into a universe where one of the three possible outcomes occurs.
It is unlikely a coin toss will branch off into a universe where it lands on its edge as there are considerably fewer universes where this happens and is based on the experience of coin tossing which indicates this is an extremely rare occurrence.
Even if there are an infinite number of universes where the coin lands on its edge there is the issue of transfinite mathematics which states there are infinite sets of different sizes.
For example the set of integers is an infinitely large set as is the set of positive integers yet intuitively there are “twice” as many numbers in the set of integers.
Hence the number of universes where the coin lands on its edge is smaller than the number of universes where a heads or tails is tossed despite being an infinitely large number.

This raises the issue of defining probabilities in MWI.
More realistically is to assign a weight factor for universes where a heads or tails occurs is much more highly weighted than for universes where the coin lands on its edge.

So in cases such as flipping a coin how does QM determine the probabilities?

Let’s consider the equation A|aₖ> = λₖ|aₖ>.

A is the mathematical operator which performs a measurement on the eigenvector |aₖ> and gives the eigenvalue λₖ.
If |aₖ> is in a superimposed state |Ψ> where

|Ψ> = α₁|a₁> + α₂|a₂> + α₃|a₃> + ……. + αₙ|aₙ>
α₁,α₂,α₃,….. αₙ are the probability amplitudes, are not physically real and are complex numbers in the form α = x + yi where x and y are real and i = √-1.

The probability P of obtaining the measurement λₖ is defined by the equation.
P(λₖ) = |<aₖ|Ψ>|² = |aₖ|²

Once again Sabine Hossenfelder can provide more details in this video.

 

[Hans Blaster]

Can't help but wonder whether neutrino behaviour might turn out to be the exception standing independently from current understanding of QM particle behaviours (ie: that QM is largely based around) .. (?) I mean they sort of stand close to the 'border' of particle and wavelike, eh? Never heard of neutrinos in the same breath as the two slit or entanglement contexts. Mind you, that's probably my own ignorance of what's going on in neutrino research ..

Neutrinos are interesting vis a vis QM as they are always superposition/composite states. This is because the mass eigenstates of neutrinos that propagate are not the same as the flavor eigenstates that interact with the weak force. A neutrino born as an electron neutrino is a composite of the "1", "2", and "3" mass eigenstates (yes, the names are that dull). Because the flavor and mass eigenstates do not align, the probability of detecting the neutrino as electron, mu, or tau flavor changes as it propagates.

 

[SelfSim]

Neutrinos are interesting vis a vis QM as they are always superposition/composite states. This is because the mass eigenstates of neutrinos that propagate are not the same as the flavor eigenstates that interact with the weak force. A neutrino born as an electron neutrino is a composite of the "1", "2", and "3" mass eigenstates (yes, the names are that dull). Because the flavor and mass eigenstates do not align, the probability of detecting the neutrino as electron, mu, or tau flavor changes as it propagates.

Hmm .. you've gotten me reading up on neutrino Oscillation following your post there. (The 'Theory' section of that link explains more).

Thanks for your pointer there .. Its nice to have a thread (for once) which actually prods a deeper understanding of the real science .. (ie: as opposed to the usual 'other stuff').

 

[Halbhh]

A physicist came up with an excellent analogy about hidden variables.
It's like putting sand on a laboratory orbital shaker, you observe the sand shaking but it's the vibrating plate concealed by the sand which causes the sand to shake.
The vibrating plate is the hidden variable but is beyond observation.
While hidden variables might solve the measurement problem it creates another problem of not being falsifiable as they are experimentally indistinguishable from standard quantum mechanics.

'Hidden variables' I've always understood to say not yet found possible new physics with new variables. E.g.: perhaps there is for example deterministic new physics we might discover, so the previously 'hidden' variables would become revealed then. And then be falsifiable in principle or someday by some practical new way of measurement possibly. One of several attractive qualities of the Pilot Wave theory is eventually being testable. (and already experiments have been made to try to test the general concept of a pilot wave, as I linked earlier, where they didn't replicate a vibrating oil pan pilot wave action previously seemingly seen by chance in one device. So while Pilot Wave is a not yet supported theory (like the rest), it also seems still alive as another possibility.)

 

[Halbhh]

I guess I missed this new upper limit on neutrino mass.

While neutrinos are subluminal (given that they have mass) they are very relativistic. Typical energies for neutrinos are ~ MeV, so the relativistic "gamma" ( total energy, E = gamma * m c^2 for particles with non-zero rest mass m) is very large. Gamma ~ 1 million. Which gives a velocity about 1 part in a trillion of the speed of light slower than the speed of light.

Yes, for those already known kinds. Many experiments are ongoing because of open questions, including whether there might be additional types.

We can't yet rule out slower neutrinos even, I think (we'd have to figure out a way to detect something so extremely non interacting with known particles though, when the energy is also so low for example).

 

[FrumiousBandersnatch]

For example, if I take a very simple case of flipping a coin. At first glance one might think that it's fairly easy to determine the probabilities, it's 50 percent heads and 50 percent tails. All things being equal both outcomes are equally likely. In MWI you'd end up with lots of variations of realities, but always with 50 percent of them heads and 50 percent of them tails. But let's say that there's a 1 percent chance that the coin ends up on its side. Now the probabilities don't seem to work, because there are immensely more ways that the coin can end up on its side than heads and tails combined. This is due to the fact that heads/tails only have 360 degrees of freedom around the vertical axis, whereas landing on its side includes 360 degrees of freedom around both the horizontal and vertical axes. So there are a lot more ways that it can end up on its side, and if they all actually occur every time that you flip the coin, as per MWI, then landing on its side would seem to be the most probable outcome, because it has the most ways in which it can occur.

It's not just a question just of the number of possible outcomes, but also of the probability of each outcome. The vast majority of ways the coin can land are metastable and will decay to head or tails. A tiny fraction of landings will be on the edge and stable, and in that tiny fraction, there is a wide variety of possible orientations.

 

[FrumiousBandersnatch]

Just to try to clarify where I'm going with this, let's consider the double slit experiment. If you fire a particle through the slits there's a certain probability associated with every point on the screen as to where that particle could possibly end up... but why?

Let's say that there's a statistically high probability that the particle is going to end up in the center of the screen, and a statistically infinitesimal probability that it's going to end up waaaayyyy off to the side.

As I understand QM, or at least MWI, every single possibility is going to be realized every time that you fire a particle. Thus no one outcome will end up being realized any more often than any other outcome. They'll all be realized, every time.

How therefore does QM account for probability if every outcome is realized every time? The probability for any of them is always 100%.

Sean Carroll published a detailed explanation of how probabilities arise in MW - see Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. 'Self-locating uncertainty' is the situation an observer finds themselves in after a quantum measurement is made but before they know the result, i.e. before they know which branch they're on.

 

[SelfSim]

Sean Carroll published a detailed explanation of how probabilities arise in MW - see Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. 'Self-locating uncertainty' is the situation an observer finds themselves in after a quantum measurement is made but before they know the result, i.e. before they know which branch they're on.

Dare I repost what they say in the introduction(?) .. @stevevw and pseudoscientists will love this!:

We propose a general principle, the Epistemic Separability Principle (ESP), which captures the idea that predictions made by local agents should be independent of their environment. Given ESP, we show that there is a unique rational way for such an agent to assign a credence to each of the quantum worlds they might be in. These credences are precisely the ones recommended by the Born rule. The probabilities are fundamentally subjective in the sense that that they are not written into the laws—as they are in spontaneous collapse theories—but instead capture the degrees of belief of a rational agent; however, they are objective in the sense that a rational agent must assign Born rule probabilities (if ESP is correct).

Firstly, I don't see how 'a rational agent' is in any way independent from their model of the 'environment'.
Secondly, the concept of a 'rational agent' quantifying beliefs, now somehow qualifies as 'objective' for the purpose of creating a so-called: 'correct(!?) Principle', in Carroll's view, eh?
I presume all this as being an untestable philosophical principle .. in order to keep MWI alive, then?

Sorry Sean .. can't see this as meeting Physics' standards for 'objective', or a 'physical principle'.

(Confession: I haven't progressed beyond the introduction yet) .

 

[sjastro]

'Hidden variables' I've always understood to say not yet found possible new physics with new variables. E.g.: perhaps there is for example deterministic new physics we might discover, so the previously 'hidden' variables would become revealed then. And then be falsifiable in principle or someday by some practical new way of measurement possibly. One of several attractive qualities of the Pilot Wave theory is eventually being testable. (and already experiments have been made to try to test the general concept of a pilot wave, as I linked earlier, where they didn't replicate a vibrating oil pan pilot wave action previously seemingly seen by chance in one device. So while Pilot Wave is a not yet supported theory (like the rest), it also seems still alive as another possibility.)

Paradoxically while Pilot Wave theory is the most realistic of the interpretations, mathematically it is more complicated than the Copenhagen and Many Worlds which are based on equivalent mathematics.
While the pilot wave wavefunction Ψ evolves according to the Schrödinger equation;

There is an extra equation, the so called guiding equation;

Q is the potential of the quantum force and is proportional to the curvature of the amplitude of the wavefunction.
It is a component of the total potential Ṽ = V + Q.

Many physicists dislike the mathematical complications introduced by Pilot Wave theory particularly the quantum force which sounds like it comes out of Star Wars.

 

[Halbhh]

Paradoxically while Pilot Wave theory is the most realistic of the interpretations, mathematically it is more complicated than the Copenhagen and Many Worlds which are based on equivalent mathematics.
While the pilot wave wavefunction Ψ evolves according to the Schrödinger equation;

View attachment 325427

There is an extra equation, the so called guiding equation;

View attachment 325428

Q is the potential of the quantum force and is proportional to the curvature of the amplitude of the wavefunction.
It is a component of the total potential Ṽ = V + Q.

Many physicists dislike the mathematical complications introduced by Pilot Wave theory particularly the quantum force which sounds like it comes out of Star Wars.

Heh, I was just looking to see if there are more recent pilot wave experiments (which I'll do more later), and I see Hossenfelder offers her opinions, which might be interesting or provocative to watch ;-). Anyway, I'll look for more recent experiments and try to get more about where we are at if there are any useful updates, but it may take a while since I'm stealing time right now from a home improvement project I want to get done ideally before christmas.