Many Worlds

[Neutral Observer]

It works (out).

But are you, for example, assuming that there are no hidden variables, because it seems to me that MWI lives or dies on whether or not there are hidden variables.

 

[sjastro]

The mathematical frame work of quantum mechanics is built around Hilbert spaces using Bra-ket terminology of the form;
A|Ψ> = a|Ψ>.

A is the observable measuring the state defined by the vector space or wavefunction Ψ to produce a measurement a.
Where as physicists use interpretations the mathematical equivalent is picture.
There is the Heisenberg picture where the observable A is time dependent and the state or wavefunction Ψ is constant in time.
The Schrödinger picture has A as a constant in time and Ψ time dependent.
While both pictures appear to be mathematically different they are equivalent as they result in the same measurement a.

The Many Worlds interpretation has a leaning towards the Schrödinger picture, the Copenhagen interpretation does not discriminate.
As for these interpretations being considered different theories, this is debatable given the mathematical pictures are equivalent making the interpretations mathematically indistinguishable.
Other interpretations where the mathematics is not the same such as involving hidden variables can be considered different theories.

What the interpretations raise are interesting questions such as how is energy conserved in the Many Worlds interpretation.

 

[SelfSim]

The mathematical frame work of quantum mechanics is built around Hilbert spaces using Bra-ket terminology of the form;
A|Ψ> = a|Ψ>.

A is the observable measuring the state defined by the vector space or wavefunction Ψ to produce a measurement a.
Where as physicists use interpretations the mathematical equivalent is picture.
There is the Heisenberg picture where the observable A is time dependent and the state or wavefunction Ψ is constant in time.
The Schrödinger picture has A as a constant in time and Ψ time dependent.
While both pictures appear to be mathematically different they are equivalent as they result in the same measurement a.

The Many Worlds interpretation has a leaning towards the Schrödinger picture, the Copenhagen interpretation does not discriminate.
As for these interpretations being considered different theories, this is debatable given the mathematical pictures are equivalent making the interpretations mathematically indistinguishable.
Other interpretations where the mathematics is not the same such as involving hidden variables can be considered different theories.

What the interpretations raise are interesting questions such as how is energy conserved in the Many Worlds interpretation.

Re - Her video (and her final 'take'):

So Uranium, (or its thorium/alpha+Helium constituents), are regarded as 'physical' models and Energy is regarded as an 'abstracted' model(?) So then, the wavefunction is describing states (or attributes) of the abstractions(?)
I'm using my terms there (ie: they weren't hers).. only to help my own understanding of what I think she's saying.

I'm not quite clear on how she then concludes that Energy (the abstraction) is therefore what's 'real' there(?) Perhaps I missed something there?

Either way, the question about energy conservation in MWI is a good one.

 

[Neutral Observer]

Other interpretations where the mathematics is not the same such as involving hidden variables can be considered different theories.

What the interpretations raise are interesting questions such as how is energy conserved in the Many Worlds interpretation.

I'm surprised that I've never watched that video before. But it leaves me with one question, is the information about the state of the energy/object, contained within the energy/object itself, or is it actually contained within the environment?

 

[sjastro]

Re - Her video (and her final 'take'):

So Uranium, (or its thorium/alpha+Helium constituents), are regarded as 'physical' models and Energy is regarded as an 'abstracted' model(?) So then, the wavefunction is describing states (or attributes) of the abstractions(?)
I'm using my terms there (ie: they weren't hers).. only to help my own understanding of what I think she's saying.

I'm not quite clear on how she then concludes that Energy (the abstraction) is therefore what's 'real' there(?) Perhaps I missed something there?

Either way, the question about energy conservation in MWI is a good one.

In my previous post I quoted the general bra-ket equation A|Ψ> = a|Ψ>.
In quantum mechanics energy is a measured value E of the equation H|Ψ> = E|Ψ>.
H is the Hamiltonian operator which measures the energy of the state IΨ> = ∑ EₙΨₙ, the superposition of the energy states.
Her idea of using energy is based on this, the measured energy E is the real value, the superposition of the energy values is IΨ> = ∑ EₙΨₙ which is the abstraction.

I’m not sure why she concluded the video by being upset with this idea which admittedly is simplified but gets to the point.
Perhaps I’m biased towards her since she is an Aussie girl and more importantly a Victorian having done her BSc at Monash Uni before going on to do her PhD in Applied Maths at Cambridge!

 

[sjastro]

I'm surprised that I've never watched that video before. But it leaves me with one question, is the information about the state of the energy/object, contained within the energy/object itself, or is it actually contained within the environment?

In my response to @SelfSim , the video gives a simplified version based on the equation H|Ψ> = E|Ψ> where IΨ> = ∑ EₙΨₙ.

Things however can be more complicated as the “information” is not only contained in energy/object (E) and the environment (e) but also the test apparatus (a) where all three are in quantum coherence and entangled where the state or wavefunction is of the form IΨ> = ∑ EₙΨₙ [x] Ψₑ [x] Ψₐ where [x] is the tensor product operator and Ψₑ and Ψₐ are the states associated with the environment and apparatus respectively.
In this case the measurement or probability occurs when the state experiences decoherence.

Sabine Hossenfelder who likes to upset physicists gives a more detailed explanation.

 

[SelfSim]

In my previous post I quoted the general bra-ket equation A|Ψ> = a|Ψ>.
In quantum mechanics energy is a measured value E of the equation H|Ψ> = E|Ψ>.
H is the Hamiltonian operator which measures the energy of the state IΨ> = ∑ EₙΨₙ, the superposition of the energy states.
Her idea of using energy is based on this, the measured energy E is the real value, the superposition of the energy values is IΨ> = ∑ EₙΨₙ which is the abstraction.

Hmm .. thanks for that. I'll have to read up more on the energy operator and have a long think about it before going further.

.. and more importantly a Victorian

.. Oh .. (I'm very sorry to hear that!)

having done her BSc at Monash Uni before going on to do her PhD in Applied Maths at Cambridge!

She's also very good, clear communicator! I'm impressed.
Good discovery she is .. So we now have Mithuna Yoganathan (her), Sean Carroll and the maestro: Sabine Hossenfelder on particle physics!
Very cool.

 

[SelfSim]

.. Sabine Hossenfelder who likes to upset physicists gives a more detailed explanation.

Aarrggghh! That video brought back some very dim memories .. I'm rather shocked that I actually recall some of the math, albeit, in a vague sort of way!
Thanks again .. great stuff!

 

[stevevw]

The speculative many worlds idea has been around a long while now, and we've even discussed it here a few times at CF over the years.

It's good to realize though it's only one of many competing theories.

And that none of the competing theories have any unique supporting evidence, so that one can pick out which is correct, if any of them.

One might be correct, or none:

Here's a good listing of currently still in contention theories:

• 4Influential interpretations
  • 4.1Copenhagen interpretation
  • 4.2Many worlds
  • 4.3Quantum information theories
  • 4.4Relational quantum mechanics
  • 4.5QBism
  • 4.6Consistent histories
  • 4.7Ensemble interpretation
  • 4.8De Broglie–Bohm theory
  • 4.9Quantum Darwinism
  • 4.10Transactional interpretation
  • 4.11Objective-collapse theories
  • 4.12Von Neumann–Wigner interpretation
  • 4.13Quantum logic
  • 4.14Modal interpretations of quantum theory
  • 4.15Time-symmetric theories
  • 4.16Other interpretations

Interpretations of quantum mechanics - Wikipedia

en.wikipedia.org

So, it's very subjective to say which theory one likes or dislikes when we can't even rule any out, etc., but to me personally, my subjective reaction to many worlds is it seems a way to just avoid trying to figure out what's really going on. It's a kind of 'I give up' solution, it seems to me. Just my subjective reaction. But it also seems to make everything meaningless in a way: in one branch you choose to believe in God, in another you don't, etc. -- so that no real choices are truly made, etc., and everything is sorta meaningless, it seems to me, in that scenario.

Of course, whether we like something subjectively doesn't decide if it's correct.

But notice the other interesting competing theories!

What stands out for me as David Chalmers said that all interpretations are a little crazy in conventional terms which seems to say something generally about about our assumptions of fundamental reality.

 

[SelfSim]

In my response to @SelfSim , the video gives a simplified version based on the equation H|Ψ> = E|Ψ> where IΨ> = ∑ EₙΨₙ.

Things however can be more complicated as the “information” is not only contained in energy/object (E) and the environment (e) but also the test apparatus (a) where all three are in quantum coherence and entangled where the state or wavefunction is of the form IΨ> = ∑ EₙΨₙ [x] Ψₑ [x] Ψₐ where [x] is the tensor product operator and Ψₑ and Ψₐ are the states associated with the environment and apparatus respectively.
In this case the measurement or probability occurs when the state experiences decoherence.

Sabine Hossenfelder who likes to upset physicists gives a more detailed explanation.

She gives a really clear explanation of the math behind decoherence (I've watched it a couple of times now).
Some noteworthy points, (which I can relate to probably because of my own now distant background), which she supports with the math, and which also confirms, in different words, some of what you've said above:

i) At the 3:45 min mark: 'You never measure the superposition .. you only ever measure one or the other {of the basis vectors}'.

ii) At the 8:19 min mark: 'The reason this is called decoherence is because the random changes to the phase, destroys the ability of the state to make an interference pattern with itself'.

iii) At the 11:20 min mark: 'This is why decoherence only partially solves the measurement problem .. it tells you why we don't normally observe quantum effects for large objects .. it does not however tell you how it happens that a particle ends up in one, and only one, possible measurement outcome'.

The way the density matrix appears, is key for all decoherence related interpretations.

Good stuff!

 

[SelfSim]

What stands out for me as David Chalmers said that all interpretations are a little crazy in conventional terms which seems to say something generally about about our assumptions of fundamental reality.

Whereas proper science commences making no 'assumptions'.
Therefore science's 'fundamental' objective reality isn't based on assumptions, (in spite of what sooo many folk here seem to think).

 

[SelfSim]

She gives a really clear explanation of the math behind decoherence (I've watched it a couple of times now).
{etc}

Also noteworthy, is the survey she uses to argue that over half of Physicists don't understand the measurement problem:

Survey here:
Surveying the Attitudes of Physicists Concerning Foundational Issues of Quantum Mechanics:

Paper abstract:

Even though quantum mechanics has existed for almost 100 years, questions concerning the foundation and interpretation of the theory still remain. These issues have gathered more attention in recent years, but does this mean that physicists are more aware of foundational issues concerning quantum mechanics? A survey was sent out to 1234 physicists affiliated to 8 different universities. 149 responded to the questions, which both concerned foundational issues related to quantum mechanics, specifically, as well as questions concerning interpretations of physical theories in general. The answers to the survey revealed that foundational concepts in quantum mechanics are still a topic that only a minority of physicists are familiar with, although a clear majority of physicists find that interpretations of physical theories are important. The various questions, as well as how the respondents answered, are presented. The survey intends to give an overview of what the opinion of the physics community, in general, is concerning issues related to quantum mechanics.

Some of the key survey results:

 

[FrumiousBandersnatch]

Well, in the Schrodinger's Cat thought experiment for example, what if we simply take away the assumption that the decay of the radioactive particle is random, what happens to our many worlds then?

If, for the sake of argument, the radioactive decay was not a quantum event, there wouldn't be a superposition of potential outcomes, so there would only be one outcome possible, and the wavefunction wouldn't branch (or collapse), so the universe would remain unbranched in that respect (there would, of course, be many other branches happening with different quantum events/interactions).

Presumably, the relevant atom would decay after a constant period and the cat would be alive if you opened the box before that period expired and dead if you opened it afterwards.

No observer unaware of the decay period would notice any difference between the two scenarios.

 

[FrumiousBandersnatch]

What the interpretations raise are interesting questions such as how is energy conserved in the Many Worlds interpretation.

IIRC, Sean Carroll suggests that it's the universal wavefunction that's real and has whatever energy it has, and when a split occurs in it, the energy of those branches sums to the original total, i.e. the energy is split between them. From the POV of an observer 'duplicated' into the branches, nothing appears to change. The energy of each branch will, by now, be an infinitesimally small proportion of the total energy of the universal wavefunction, but apparently, from the POV of any individual branch, that doesn't matter...

I'm sure he could explain it better and explain exactly why it doesn't matter.

 

[SelfSim]

IIRC, Sean Carroll suggests that it's the universal wavefunction that's real and has whatever energy it has, and when a split occurs in it, the energy of those branches sums to the original total, i.e. the energy is split between them. From the POV of an observer 'duplicated' into the branches, nothing appears to change. The energy of each branch will, by now, be an infinitesimally small proportion of the total energy of the universal wavefunction, but apparently, from the POV of any individual branch, that doesn't matter...

I'm sure he could explain it better and explain exactly why it doesn't matter.

IOW there is no observer who could measure the energy of the universal wavefunction .. therefore its not objectively real after all.

 

[Neutral Observer]

Whereas proper science commences making no 'assumptions'.
Therefore science's 'fundamental' objective reality isn't based on assumptions, (in spite of what sooo many folk here seem to think).

Well then let me lay out my argument for why I think that MWI does indeed make assumptions, even if the Schrodinger equation is no more capable of making an assumption than 1+1=2.

The assumption is that there's no such thing as hidden variables. But as Sabine Hossenfelder argues in the following video that may not be true. (Starting at 8:15) There may indeed be hidden variables, in which case there's no such thing as a collapse of the wave function, and MWI is therefore a non-starter. The particle knew from the beginning which way it was going. And in the instances where we didn't measure it, the Many Worlds don't emerge because the wavefunction never collapses.

So it seems to me that MWI does indeed make an assumption, that there are no hidden variables.

 

[SelfSim]

Well then let me lay out my argument for why I think that MWI does indeed make assumptions, even if the Schrodinger equation is no more capable of making an assumption than 1+1=2.

The assumption is that there's no such thing as hidden variables. But as Sabine Hossenfelder argues in the following video that may not be true. (Starting at 8:15) There may indeed be hidden variables, in which case there's no such thing as a collapse of the wave function, and MWI is therefore a non-starter. The particle knew from the beginning which way it was going. And in the instances where we didn't measure it, the Many Worlds don't emerge because the wavefunction never collapses.
...
So it seems to me that MWI does indeed make assumptions, that there are no hidden variables.

So why do you think the question of hidden variables is an ongoing subject of quantum testing, then?
Its all about testing and, (hopefully), producing results that will inform us what's real in these quantum contexts.

Interpretations are hypotheticals .. not physical Laws or Theories.

 

[Neutral Observer]

So why do you think the question of hidden variables is an ongoing subject of quantum testing, then?

Because the existence of hidden variables is an assumption. It's not like one interpretation is making an assumption and the other isn't.

That's all that I was saying, that MWI is based on an assumption, but then again so is superdeterminism. Personally I like both interpretations. I can come up with really stupid ideas starting from either one. My ignorance and imagination know no bounds. But then that's obvious.

 

[SelfSim]

Because the existence of hidden variables is an assumption. It's not like one interpretation is making an assumption and the other isn't.

That's all that I was saying, that MWI is based on an assumption, but then again so is superdeterminism. Personally I like both interpretations. I can come up with really stupid ideas starting from either one. My ignorance and imagination know no bounds. But then that's obvious.

If you know all that, then you should know who/what you are arguing against.
So: who/what is it, that you're arguing against?

 

[Neutral Observer]

If you know all that, then you should know who/what you are arguing against.
So: who/what is it, that you're arguing against?

As far as I know I'm arguing against two of my favorite physicists, Hugh Everett and Sean Carroll. Of course my favorite is @Bradskii (aka Richard Feynman)

Or maybe I'm arguing against Bell. Heck who knows. But if I'm wrong I'd appreciate it if someone would show me where. I just hope that nobody objects if I refer to Sabine et al for my rebuttal.