Many Worlds

[Halbhh]

The problem with Bohmian mechanics is the concept of time.
Quantum field theories originated when physicists were able to combine special relativity where time is relative with quantum mechanics.
Bohmian mechanics relies on absolute time and Lorentzian relativity requiring the existence of an ether which was ruled out by the Michelson- Morley experiment.

On the subject of particles it was in classical physics where the point particle was introduced, where the mass and charge of a particle was concentrated into an infinitesimally small volume.
It made the mathematics considerably more simple.
For example the inverse square law for the gravitational force F between two objects is based on the equation F= Gm₁m₂/r² where m₁, m₂ are their point masses and F is a function of the distance variable r.
A more realistic equation is to consider the mass of the objects not their point masses expressed in terms of density ρ and volume v where m = ρv where the equation becomes F = Gρ₁v₁ρ₂v₂/r².
Problems arise for irregular sized objects where the volume v is not easily defined mathematically.

Ironically while point masses makes Newtonian gravity easier to handle, gravity messes up QFT which also assumes point masses.
A quantum theory of gravity is possible where particles are not point sized such as in String theory

Since you are approaching it all from the math side, one of the most interesting things to me at the moment might also be very interesting to you possibly, if you'd not already learned of it. It's very intriguing that 500 pages of algebra that QFT can lead to in order to calculate an outcome can it turns out be reduced into a single term, and how that's actually geometry...., so that one can approach it from the other side, without having to do all that algebra at all (suggesting it might be that QFT is just a step towards something more insightful)(....

It's so interesting to me about how it is a geometric thing.

A Jewel at the Heart of Quantum Physics | Quanta Magazine

Physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature.

www.quantamagazine.org

 

[sjastro]

Since you are approaching it all from the math side, one of the most interesting things to me at the moment might also be very interesting to you possibly, if you'd not already learned of it. It's very intriguing that 500 pages of algebra that QFT can lead to in order to calculate an outcome can it turns out be reduced into a single term, and how that's actually geometry...., so that one can approach it from the other side, without having to do all that algebra at all (suggesting it might be that QFT is just a step towards something more insightful)(....

It's so interesting to me about how it is a geometric thing.

A Jewel at the Heart of Quantum Physics | Quanta Magazine

Physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature.

www.quantamagazine.org

Thanks for the article but there are a couple of issues.
Firstly the end product, the calculation of the probability amplitudes is the same irrespective of whether Feynman diagrams or amplituhedrons are used.
This makes it difficult to assess if amplituhedrons are simply a useful calculation tool or represent a physical reality where space-time is considered emergent rather than fundamental as it is in QFT.
Secondly and perhaps more importantly amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle.
The LHC has failed to detect superparticles resulting in an increasing number of particle physicists abandoning or at least modifying the theory of supersymmetry.

The status of supersymmetry

Once the most popular framework for physics beyond the Standard Model, supersymmetry is facing a reckoning—but many researchers are not giving up on it yet.

www.symmetrymagazine.org

 

[Halbhh]

Thanks for the article but there are a couple of issues.
Firstly the end product, the calculation of the probability amplitudes is the same irrespective of whether Feynman diagrams or amplituhedrons are used.
This makes it difficult to assess if amplituhedrons are simply a useful calculation tool or represent a physical reality where space-time is considered emergent rather than fundamental as it is in QFT.
Secondly and perhaps more importantly amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle.
The LHC has failed to detect superparticles resulting in an increasing number of particle physicists abandoning or at least modifying the theory of supersymmetry.

The status of supersymmetry

Once the most popular framework for physics beyond the Standard Model, supersymmetry is facing a reckoning—but many researchers are not giving up on it yet.

www.symmetrymagazine.org

I wondered about whether we could make a firm statement like "amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle", as the description at the wiki is: "When the volume of the amplituhedron is calculated in the planar limit of N = 4 D = 4 supersymmetric Yang–Mills theory, it describes the scattering amplitudes of particles described by this theory.[1] The amplituhedron thus provides a more intuitive geometric model for calculations with highly abstract underlying principles", where the N = 4 D = 4 supersymmetric Yang–Mills "is a simplified toy theory based on Yang–Mills theory that does not describe the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories." -- so, is it going too far to say that it 'requires the existence of supersymmetry where each fermion and boson has a corresponding superparticle" in that for example what if the supersymmetry models turn out to be just some partial parallel to some (not yet found) more complete theory -- in that case we couldn't yet say what is the overall significance of amplituhedrons (for that matter, for me it's still pretty early and I want to read more and think more on it regardless, and that might take another month).

 

[SelfSim]

I wondered about whether we could make a firm statement like "amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle",

That's like wondering whether the invention of a wrench, (or a spanner), required the existence of nuts and bolts, or some deeper theory?!
(Angels dancing on the head of a pin ..)

 

[sjastro]

I wondered about whether we could make a firm statement like "amplituhedrons require the existence of supersymmetry where each fermion and boson has a corresponding superparticle", as the description at the wiki is: "When the volume of the amplituhedron is calculated in the planar limit of N = 4 D = 4 supersymmetric Yang–Mills theory, it describes the scattering amplitudes of particles described by this theory.[1] The amplituhedron thus provides a more intuitive geometric model for calculations with highly abstract underlying principles", where the N = 4 D = 4 supersymmetric Yang–Mills "is a simplified toy theory based on Yang–Mills theory that does not describe the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories." -- so, is it going too far to say that it 'requires the existence of supersymmetry where each fermion and boson has a corresponding superparticle" in that for example what if the supersymmetry models turn out to be just some partial parallel to some (not yet found) more complete theory -- in that case we couldn't yet say what is the overall significance of amplituhedrons (for that matter, for me it's still pretty early and I want to read more and think more on it regardless, and that might take another month).

In your very quotation the “….supersymmetric Yang-Mills theory…..” is an explicit statement for the requirement of supersymmetry in the study of amplituhedrons.
I suggest you watch this video I referred to in an earlier thread on symmetry paying particular attention to the UA(1) rotation and its application to conserved quantities such as the Dirac Lagrangian.

Yang-Mills theory is a generalization of this example where a SU(N) transformation is applied to a Yang-Mills Lagrangian.
For the Lagrangian to be conserved or symmetrical the resulting gauge fields are composed of massless bosons.
The theory is incomplete as W and Z bosons do have mass and is explained using spontaneous symmetry breaking and the Higgs field.

Where as in the Yang Mills theory the gauge fields are boson fields, in supersymmetric Yang-Mills theory there are both boson and fermion fields which are linked by the quantum mechanical supercharge operator Q which transforms fermions IF> into bosons |B> and vice versa according to the equations.

Q|F>= |B> and Q|B>= |F>.

As an example the fermion electron defined by the wavefunction |Ψₑ> has a corresponding bosonic superpartner the selectron |Ψₛₑ> and is defined by the transformation equation Q|Ψₑ> = |Ψₛₑ>.
There are four different types of supercharges Q hence N= 4 in four dimensional space D = 4 which defines the N = 4 D = 4 supersymmetric Yang–Mills theory.
Supersymmetry is very much a requirement for amplituhedrons.

 

[sjastro]

In a mathematical universe unlike the physical universe, the standard model of particle physics is a non abelian QFT and the Yang-Mills theory is one of the great unsolved problems in mathematics which forms part on the Millennium prize offering a US$1,000,000 reward for solving any one of the problems.

The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution.

The problem is phrased as follows:

Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R⁴ and has a mass gap Δ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975).

In this statement, a quantum Yang–Mills theory is a non-abelian quantum field theory similar to that underlying the Standard Model of particle physics; R⁴ is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory.

Therefore, the winner must prove that:
Yang–Mills theory exists and satisfies the standard of rigor that characterizes contemporary mathematical physics, in particular constructive quantum field theory, and

The mass of all particles of the force field predicted by the theory are strictly positive.

For example, in the case of G = SU(3)—the strong nuclear interaction—the winner must prove that glueballs have a lower mass bound, and thus cannot be arbitrarily light.

The general problem of determining the presence of a spectral gap in a system is known to be undecidable.

 

[Halbhh]

In your very quotation the “….supersymmetric Yang-Mills theory…..” is an explicit statement for the requirement of supersymmetry in the study of amplituhedrons.
I suggest you watch this video I referred to in an earlier thread on symmetry paying particular attention to the UA(1) rotation and its application to conserved quantities such as the Dirac Lagrangian.

Yang-Mills theory is a generalization of this example where a SU(N) transformation is applied to a Yang-Mills Lagrangian.
For the Lagrangian to be conserved or symmetrical the resulting gauge fields are composed of massless bosons.
The theory is incomplete as W and Z bosons do have mass and is explained using spontaneous symmetry breaking and the Higgs field.

Where as in the Yang Mills theory the gauge fields are boson fields, in supersymmetric Yang-Mills theory there are both boson and fermion fields which are linked by the quantum mechanical supercharge operator Q which transforms fermions IF> into bosons |B> and vice versa according to the equations.

Q|F>= |B> and Q|B>= |F>.

As an example the fermion electron defined by the wavefunction |Ψₑ> has a corresponding bosonic superpartner the selectron |Ψₛₑ> and is defined by the transformation equation Q|Ψₑ> = |Ψₛₑ>.
There are four different types of supercharges Q hence N= 4 in four dimensional space D = 4 which defines the N = 4 D = 4 supersymmetric Yang–Mills theory.
Supersymmetry is very much a requirement for amplituhedrons.

While what you lay out is interesting in its own way, the thing that is so interesting (at least to me!) is that:

It's very intriguing that 500 pages of algebra that QFT can lead to in order to calculate an outcome can it turns out be reduced into a single term, and how that's actually [like a] geometr[ical object]...., so that one can approach it from the other side, without having to do all that algebra at all (suggesting it might be that QFT is just a step towards something more insightful)(.... [more full wording in article]

What if we find out in time that a set of (mostly not yet known to us) geometric objects show (quickly and accurately!) the full structure of the (undiscovered correct general) physics, so that someday a general finished theory might turn out to be essentially geometric in some beautiful (elegant) comprehensive way.... (like maybe a set of objects that naturally are some family or some other such possibilities). See why it's so interesting to me?

 

[SelfSim]

While what you lay out is interesting in its own way, the thing that is so interesting (at least to me!) is that:

What if we find out in time that a set of (mostly not yet known to us) geometric objects show (quickly and accurately!) the full structure of the (undiscovered correct general) physics, so that someday a general finished theory might turn out to be essentially geometric in some beautiful (elegant) comprehensive way.... (like maybe a set of objects that naturally are some family or some other such possibilities). See why it's so interesting to me?

Truth-seeking! .. And not scientific thinking.
Back to ancient Platonic philosophical thinking it is for you!

 

[Halbhh]

Truth-seeking! .. And not scientific thinking.
Back to ancient Platonic philosophical thinking it is for you!

;-) I know right. (I thought of that when I wrote the above: the Perfect Forms) But it's still to be tested against reality: it would have to pass the test of correctly predicting things not yet seen, and do so reliably and consistently and accurately while many physicists are trying to find a place it fails.

 

[SelfSim]

.. But it's still to be tested against reality:

Science only tests against operationally defined models .. like Supersymmetric theories/hypotheses.

it would have to pass the test of correctly predicting things not yet seen and do so reliably and consistently and accurately,

producing verified observations consistent with theoretical predictions.

while many physicists are trying to find a place it fails.

Physicists have always lived with not knowing precisely where physical theories break down.
I don't see that as being a necessary criterion for defining objective reality.

 

[sjastro]

While what you lay out is interesting in its own way, the thing that is so interesting (at least to me!) is that:

What if we find out in time that a set of (mostly not yet known to us) geometric objects show (quickly and accurately!) the full structure of the (undiscovered correct general) physics, so that someday a general finished theory might turn out to be essentially geometric in some beautiful (elegant) comprehensive way.... (like maybe a set of objects that naturally are some family or some other such possibilities). See why it's so interesting to me?

Even if Feynman diagrams were replaced by amplituhedrons it will not simplify QFT.
Amplituhedrons won't impact on symmetries and the use of Lagrangian mechanics in QFT.
To illustrate this point the most profound equation in physics is not E = mc² but the incredibly complicated Lagrangian L for the standard model of particle physics.

 

[Halbhh]

Science only tests against operationally defined models .. like Supersymmetric theories/hypotheses.

producing verified observations consistent with theoretical predictions.
Physicists have always lived with not knowing precisely where physical theories break down.
I don't see that as being a necessary criterion for defining objective reality.

Physicists do often try to figure out a theory that can fit observed phenomena they don't yet have a theory for, but also at times they (sometimes) find a new theory that predicts things not yet ever observed or expected.

I don't really have a lot of spare time, so I'm will just suggest (the very very good habit) that you investigate that for yourself. You could of course start by not assuming physics can't find new theories that predict never before seen or expected phenomena.... and try to find out about instances where it has happened.

I actually don't feel I have time to search up just the best article to help fill this in for you, but this one looks like it may have some useful background, in that you can learn more about physics in a general way really fast in this kind of article, without much effort even: The 10 greatest predictions in physics – Physics World

 

[SelfSim]

(Physicists do often try to figure out a theory that can fit observed phenomena they don't yet have a theory for, but also at times they (sometimes) find a new theory that predicts things not yet ever observed or expected.

I don't really have a lot of spare time, so I'm will just suggest (the very very good habit) that you investigate that for yourself. You could of course start by not assuming physics can't find new theories that predict never before seen or expected phenomena.... and try to find out about instances where it has happened.

I actually don't feel I have time to search up just the best article to help fill this in for you, but this one looks like it may have some useful background, in that you can learn more about physics in a general way really fast in this kind of article, without much effort even: The 10 greatest predictions in physics – Physics World

The issue I'm having is with your descriptions of your observations of how Physics research proceeds .. they are just not consistent with the principles of the scientific method underpinning the physics.

For starters, you substitute theories when you mean hypotheses. This is confusing. Secondly, both are conceived by human scientifically thinking minds and not simply plucked out of some mysterious ethereal glow, which exists independently of the hard thinking efforts and therefore, work .. put in by scientists (who continually operationally define that .. such that it is no longer just some 'ethereal glow'). Your implied notion of a search for some undiscovered 'truths' behind how the universe works, is completely irrelevant as far as the demonstrable, practical value of a well accepted theory or working hypothesis, in making its predictions. If unobserved predictions were not regarded as fundamentally uncertain by physicists, there would be no imperatives for testing its models. There are also no 'correct' predictions .. only consistent ones.

In some threads this may not be a problem .. but in a SF thread about interpretations of QM, it is essential to get these basics clear .. given that interpretations are obviously choices, (in the light of the accepted uncertainty already inherent in the models). The same applies for the sub-topic you introduced on how to regard the concept of amplituhedrons in QFT.

Until your own interpretations of highly theoretical research topics reflect thinking changes on these fundamentals in science, I will continue to have issues with your descriptions of what research actually shows and as such, please don't include me in the group you believe accepts your sweeping generalisations on any of it.

 

[Ligurian]

I found the following video to be uniquely insightful on a subject that has long intrigued me, and I thought that it might intrigue others as well.

I realize that it's over half an hour long, and most people don't like watching anything much beyond five or ten

"Beyond five or ten" words, when it comes to math.

But "many worlds" is a theme I can buy into without knowing any math at all. The other planets and their life-forms don't have to match that which earthlings think habitable... thereby making other worlds in our image, so to speak.

 

[SelfSim]

... The other planets and their life-forms don't have to match that which earthlings think habitable... thereby making other worlds in our image, so to speak.

.. but other 'life-forms' have to resemble earth-life .. otherwise we wouldn't even recognise them as being 'life-forms' at all.
We don't know whether the term 'life' is even applicable outside of its earthly context.

 

[Halbhh]

The issue I'm having is with your descriptions of your observations of how Physics research proceeds .. they are just not consistent with the principles of the scientific method underpinning the physics.

For starters, you substitute theories when you mean hypotheses. This is confusing. Secondly, both are conceived by human scientifically thinking minds and not simply plucked out of some mysterious ethereal glow, which exists independently of the hard thinking efforts and therefore, work .. put in by scientists (who continually operationally define that .. such that it is no longer just some 'ethereal glow'). Your implied notion of a search for some undiscovered 'truths' behind how the universe works, is completely irrelevant as far as the demonstrable, practical value of a well accepted theory or working hypothesis, in making its predictions. If unobserved predictions were not regarded as fundamentally uncertain by physicists, there would be no imperatives for testing its models. There are also no 'correct' predictions .. only consistent ones.

In some threads this may not be a problem .. but in a SF thread about interpretations of QM, it is essential to get these basics clear .. given that interpretations are obviously choices, (in the light of the accepted uncertainty already inherent in the models). The same applies for the sub-topic you introduced on how to regard the concept of amplituhedrons in QFT.

Until your own interpretations of highly theoretical research topics reflect thinking changes on these fundamentals in science, I will continue to have issues with your descriptions of what research actually shows and as such, please don't include me in the group you believe accepts your sweeping generalisations on any of it.

Re "theories", there are 2 classes. Those without any unique supporting evidence and those that do have unique supporting evidence. An example of theories without any evidence are each of the competing interpretations of Quantum Mechanics, such as pilot wave theory or MWI.

An example of a theory with much supporting evidence is General Relativity. It is very well confirmed.

But it could be overthrown some day.

You can have whatever unique view of physics you like, but if you learn from me, you'll get a very mainstream view.

 

[Estrid]

Re "theories", there are 2 classes. Those without any unique supporting evidence and those that do have unique supporting evidence. An example of theories without any evidence are each of the competing interpretations of Quantum Mechanics, such as pilot wave theory or MWI.

An example of a theory with much supporting evidence is General Relativity. It is very well confirmed.

But it could be overthrown some day.

You can have whatever unique view of physics you like, but if you learn from me, you'll get a very mainstream view.

Did you think up your apparently unique
binary system of two types of theories?

 

[Halbhh]

Did you think up your apparently unique
binary system of two types of theories?

No, that's not mine. It's from Karl Popper as I understand.

 

[SelfSim]

No, that's not mine. It's from Karl Popper as I understand.

Cite references please.

 

[Halbhh]

Cite references please.

Ok.

" According to Popper, a theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can (and should) be scrutinised with decisive experiments."

Karl Popper - Wikipedia

en.wikipedia.org

as you can see me applying here with a some examples (notice all 3 underlined parts):

Re "theories", there are 2 classes. Those without any unique supporting evidence and those that do have unique supporting evidence. An example of theories without any evidence are each of the competing interpretations of Quantum Mechanics, such as pilot wave theory or MWI.

An example of a theory with much supporting evidence is General Relativity. It is very well confirmed.

But it could be overthrown some day.

You can have whatever unique view of physics you like, but if you learn from me, you'll get a very mainstream view.

This is for me things I learned decades ago now, and I hardly think any more to point it out. I tend to assume it and tend to expect most everyone assumes something similar already.