Physicists who propose that symmetries are emergent?

[Suekdccia]

TL;DR Summary

Examples of physicist who propose that all symmetries (gauge, global…) from where laws are derived are emergent?

I know of some physicists (e.g Holger B Nielsen, Grigory Volovik or Edward Witten) who have proposed that all symmetries (Local gauge symmetries associated with forces and dynamics and global symmetries associated with conservation laws) are emergent rather than fundamental.

Are there any other well renowned physicists who also propose that all fundamental symmetries (and therefore, the laws of physics associated with them) are rather emergent?

 

[bobob]

I'm not certain of the exact context of those statements, but what they may be referring to are the symmetries remaining after a larger symmetry is broken. Symmetries imply that somethig is not observable. For example, every point on a sphere is equivalent, so there is no way to distinguish between a sphere and a sphere that has been rotated in any way. However if that symmetry is broken and you have prolate ellipsoid, you've broken the spherical symmetry such that rotations along one axis are distinguishable from rotations about the other two axes. In that sense, the ellipsoidal symmetry could be considered emergent.

 

[king vitamin]

The idea that quantum gravity implies no global symmetries is a rather widely-held belief, especially among string theorists. See for example this recent paper which made a huge splash by arguing that this is true within AdS/CFT: https://arxiv.org/abs/1810.05337. The first three citations on this paper also concern this conjecture.

 

[Fractal matter]

Summary:: Examples of physicist who propose that all symmetries (gauge, global…) from where laws are derived are emergent?

I know of some physicists (e.g Holger B Nielsen, Grigory Volovik or Edward Witten) who have proposed that all symmetries (Local gauge symmetries associated with forces and dynamics and global symmetries associated with conservation laws) are emergent rather than fundamental.

Are there any other well renowned physicists who also propose that all fundamental symmetries (and therefore, the laws of physics associated with them) are rather emergent?

I think Xiao-Gang Wen and Erik Verlinde also hold that view.

 

[Auto-Didact]

Are there any other well renowned physicists who also propose that all fundamental symmetries (and therefore, the laws of physics associated with them) are rather emergent?

Penrose has also argued for the view that symmetries are not fundamental.

 

[jake jot]

Penrose has also argued for the view that symmetries are not fundamental.

If symmetries are not fundamental. Does this imply the vacuum may not be Lorentz invariant? If so, does it imply new physics? Or will the vacuum not obeying Lorentz invariance means there is more degree of freedom for new physics?

 

[Fra]

If symmetries are not fundamental. Does this imply the vacuum may not be Lorentz invariant? If so, does it imply new physics? Or will the vacuum not obeying Lorentz invariance means there is more degree of freedom for new physics?

It is useful to note that different researchers use the word emergent for slightly different approaches. It generally means thay symmetries emerge as per some other parameters. It can be for observational scales (ie transforming the observing system in some way, either spatial scale or some other scale) or evolution stages which is not easily "parameterized" in the classical way (Smolin and evolution of law). These approaches are quite different, some are more radical than others.

Symmetry can be use in its detached mathematical physics meaning, and you can trow it around to find matematical possibilities but with risk loosing contact to physics and observational and processing foundations.

But from conceptual physical perspective symmetries refers to equivalence classes of hypothetical observers or more typically "observer frames". The transformations that generates the whole equivalence class, are supposed to generate all the possible observational perspectives. The classical poincare or lorentz transformaion are easy to grasp. But other transformatins are harder to see how it corresponds to different observer frames, because some transformations also include internal transformaions and even a mix of external and external. Here by tradition i would argue that most people loose track of what is going on(which is obvious from every single textbook I've read as well), and we reach the typical quantum confusion, and just accept to work with the mathematics that are proven to work.

If we by vacuum mean what's confined by the boundarys of a physical laboratory and if we by lorentz invariance mean the equivalence class of "classical laboratory frames" generated by lorentz transformations then i see no reason to expect or make sense of violations of this.

But if we are speculating about "vacuum" without clearly defined boundaries that are under the control of the lab frame, or if we are consider hypothetical Planck scale observer frames; then the prerequisites for construction the classes of observers is absent so it may be better to say that concept of lorentz invariance becomes undefined rather than argue that it is violated. Violation implies it is well defined AND violated. That IMO, makes no sense and I do not expect such strange things. The parameter here in which the "emergence" take place IMO refers to transforming the observer into new ways, that extent beyond "mechanical frames"

To talk about vacuum without a boundary in a classical laboratory, is as undefined to talk about quantum mechanics without a classical background with the measurement device, observer and computations take place. If we still want to do this, we are forced to reconstruct concepts without using the foundations we want to relax. In this case first has to define how spacetime itself emerges. Usually we think of spacetime as defined by relations between interacting parts (Rovellis attempts a reconstruction in this spirit in his QG book, but he is imo not radical enough, and the too uncritically brings in "QM" as a key; and the problem is that QM is dependeong on the classical BG in the first place; his construction is not convincing, old discussion).

/Fredrik

 

[jake jot]

It is useful to note that different researchers use the word emergent for slightly different approaches. It generally means thay symmetries emerge as per some other parameters. It can be for observational scales (ie transforming the observing system in some way, either spatial scale or some other scale) or evolution stages which is not easily "parameterized" in the classical way (Smolin and evolution of law). These approaches are quite different, some are more radical than others.

Symmetry can be use in its detached mathematical physics meaning, and you can trow it around to find matematical possibilities but with risk loosing contact to physics and observational and processing foundations.

But from conceptual physical perspective symmetries refers to equivalence classes of hypothetical observers or more typically "observer frames". The transformations that generates the whole equivalence class, are supposed to generate all the possible observational perspectives. The classical poincare or lorentz transformaion are easy to grasp. But other transformatins are harder to see how it corresponds to different observer frames, because some transformations also include internal transformaions and even a mix of external and external. Here by tradition i would argue that most people loose track of what is going on(which is obvious from every single textbook I've read as well), and we reach the typical quantum confusion, and just accept to work with the mathematics that are proven to work.

If we by vacuum mean what's confined by the boundarys of a physical laboratory and if we by lorentz invariance mean the equivalence class of "classical laboratory frames" generated by lorentz transformations then i see no reason to expect or make sense of violations of this.

But if we are speculating about "vacuum" without clearly defined boundaries that are under the control of the lab frame, or if we are consider hypothetical Planck scale observer frames; then the prerequisites for construction the classes of observers is absent so it may be better to say that concept of lorentz invariance becomes undefined rather than argue that it is violated. Violation implies it is well defined AND violated. That IMO, makes no sense and I do not expect such strange things. The parameter here in which the "emergence" take place IMO refers to transforming the observer into new ways, that extent beyond "mechanical frames"

To talk about vacuum without a boundary in a classical laboratory, is as undefined to talk about quantum mechanics without a classical background with the measurement device, observer and computations take place. If we still want to do this, we are forced to reconstruct concepts without using the foundations we want to relax. In this case first has to define how spacetime itself emerges. Usually we think of spacetime as defined by relations between interacting parts (Rovellis attempts a reconstruction in this spirit in his QG book, but he is imo not radical enough, and the too uncritically brings in "QM" as a key; and the problem is that QM is dependeong on the classical BG in the first place; his construction is not convincing, old discussion).

/Fredrik

By vacuum not obeying Lorentz invariance I meant ideas like Dirac Sea, Relativistic Aether, etc. where there is something in the vacuum generating the Lorentz Invariance as secondary effects. Also how do you define vacuum? as ground states or quantum fields or something existing behind spacetime? If the former. Then what do you refer to this description of what is behind spacetime or more fundamental than spacetime. Do you still call it vacuum?

This is from Rauscher complex spacetime. But before delving into this line where they just used spacetime as fundamental, even real complex spacetime. I want to know what term you called that which is behind spacetime? Something where spacetime and even quantum is emergent. I initially thought it could be referred to as vacuum. But your reply made me think it may not be the right word to use.

Many ideas could be radical but they may not be radical enough. The correct radicalness even to the extreme is something which should explain everything.

 

[bayakiv]

Summary:: Examples of physicist who propose that all symmetries (gauge, global…) from where laws are derived are emergent?

I know of some physicists (e.g Holger B Nielsen, Grigory Volovik or Edward Witten) who have proposed that all symmetries (Local gauge symmetries associated with forces and dynamics and global symmetries associated with conservation laws) are emergent rather than fundamental.

Are there any other well renowned physicists who also propose that all fundamental symmetries (and therefore, the laws of physics associated with them) are rather emergent?

I can only say that even ordinary people (not physicists) can think so, but this is not enough - a holistic concept is needed here, supported by mathematical conclusions. In other words, these questions should not be dealt with by physics, but by mathematical philosophy. Do you know a lot of physicists who are capable and willing to engage in mathematical philosophy?

 

[Fra]

By vacuum not obeying Lorentz invariance I meant ideas like Dirac Sea, Relativistic Aether, etc. where there is something in the vacuum generating the Lorentz Invariance as secondary effects,

Perhaps I didnt get the question?

But as you put it like this, it sounds like the kind of transient reasoning that appears when going from non-relativistic to realativistic QM?

Ie. you start out with quantizing the KG equation thinking its a boson, then find tha it gives strange results with the negative energy solutions, and then make a change of variables that mixes both internal and external degrees of freedom, in order to preserve a sensible spacetime properties of causality. Ie. at the level of textbook reasoning one is lead to "conclude" that quantizing the relativistic electron sort of by consistency predicts that there must be a particle with strange half integer spin, that has an antiparticle. To associate this with a kind of emergence and give it physical meaning may be possible, but it is strange and not the way textbooks I've seen introduces it, becauase attempting this can easily cause more confusion, and taking such reasoning to its logical extrapolations is an open question, not clear if it will work. The question is, if one is willing to make a physical interpretation of the relation between the KG equation and the dirac equations. It clearly mixes internal and eternal degress of freedom in a strange way. I personally always associated this to a change in observer structure, and that the internal structure of the "observing system" spontaneously transforms to one of the description. Ie. one can thinkg of it like this: suppse a physical system is set with the "initial conditions" of having wrong ideas of the lawas of nature? what would happen? One can argue that during certain circumstances there are two options, the observing systems has to learn (adapt and rerorganise its internal structure in order to survive) or get destabilised by the environment. This is ONE of the ideas of emergence. Where the laws emerges as "stable rules" among interacting parts. And the parts themselves also evolve. So laws of nature, and the properties of elementary particles may have evolved in harmony from an original disorder.

But this is just one extremeal idea of emergence.

There are other ideas based on more statistical, and observational scale or energy level emergences. For example, low energy laws "emerge" as energy drops. But in those ideas, there is usually an idea of reductionism where most things can be explained in terms of extremely fine tuned conditions and specifications of the high energy domain. The critique against that is that it is so fine tuned, that it seems unreasonable.

/Fredrik

 

[jake jot]

Perhaps I didnt get the question?

But as you put it like this, it sounds like the kind of transient reasoning that appears when going from non-relativistic to realativistic QM?

Ie. you start out with quantizing the KG equation thinking its a boson, then find tha it gives strange results with the negative energy solutions, and then make a change of variables that mixes both internal and external degrees of freedom, in order to preserve a sensible spacetime properties of causality. Ie. at the level of textbook reasoning one is lead to "conclude" that quantizing the relativistic electron sort of by consistency predicts that there must be a particle with strange half integer spin, that has an antiparticle. To associate this with a kind of emergence and give it physical meaning may be possible, but it is strange and not the way textbooks I've seen introduces it, becauase attempting this can easily cause more confusion, and taking such reasoning to its logical extrapolations is an open question, not clear if it will work. The question is, if one is willing to make a physical interpretation of the relation between the KG equation and the dirac equations. It clearly mixes internal and eternal degress of freedom in a strange way. I personally always associated this to a change in observer structure, and that the internal structure of the "observing system" spontaneously transforms to one of the description. Ie. one can thinkg of it like this: suppse a physical system is set with the "initial conditions" of having wrong ideas of the lawas of nature? what would happen? One can argue that during certain circumstances there are two options, the observing systems has to learn (adapt and rerorganise its internal structure in order to survive) or get destabilised by the environment. This is ONE of the ideas of emergence. Where the laws emerges as "stable rules" among interacting parts. And the parts themselves also evolve. So laws of nature, and the properties of elementary particles may have evolved in harmony from an original disorder.

But this is just one extremeal idea of emergence.

There are other ideas based on more statistical, and observational scale or energy level emergences. For example, low energy laws "emerge" as energy drops. But in those ideas, there is usually an idea of reductionism where most things can be explained in terms of extremely fine tuned conditions and specifications of the high energy domain. The critique against that is that it is so fine tuned, that it seems unreasonable.

/Fredrik

Thanks for the details, but my question is not that exactly fully. I'll explain it in words, so you can get it and try to share what my question is in the framework of theoretical physics.

It is not right to mention vacuum. As these are supposed to be ground states of quantum fields. So I don't want to mention vaccum. I can't use Aether either, even relativistic Aether as these are said to be superfluous.

In our physics, we have spacetime and matter. These were supposed to preexist so one can't ask what is behind spacetime and matter, or how these were emergent from? Or perhaps one can just mention Loop Quantum Gravity.

In the graphics in my previous message, there is mentioned a complex spacetime that is separate from normal spacetime. This means a possible dual physics where there is a barrier that separates the two. My question is that, if Lorentz Invariance is not fundamental, can we push the dual physics all the way to the origin of spacetime and matter? In a book "Physics Meets Philosophy at the Planck Scale" on quantum gravity. It was proposed the third avenue physicists were investigating which is spacetime and QM are emergent of an unknown third theory. So my question is, if Lorentz Invariance was not fundamental, does this third theory where spacetime and matter were emergent become more plausible?

 

[Fra]

These were supposed to preexist so one can't ask what is behind spacetime and matter, or how these were emergent from? Or perhaps one can just mention Loop Quantum Gravity.

My focus is not so much on the existential questions of "origin", but more to try to find a natural explanation to why the laws of physics are what they are and why he have 4D spacetime with the properties we know in thel low energy perspective.

In the graphics in my previous message, there is mentioned a complex spacetime that is separate from normal spacetime. This means a possible dual physics where there is a barrier that separates the two. My question is that, if Lorentz Invariance is not fundamental, can we push the dual physics all the way to the origin of spacetime and matter? In a book "Physics Meets Philosophy at the Planck Scale" on quantum gravity. It was proposed the third avenue physicists were investigating which is spacetime and QM are emergent of an unknown third theory. So my question is, if Lorentz Invariance was not fundamental, does this third theory where spacetime and matter were emergent become more plausible?

I am not aware of that book but that picture mainly represents various geometric theories, that try to generalize what has proven successfull to higher dimensions so as to try to include more of the fundamental forces. There were are many early attempts, to geometrize all of physics and include GR as well. But these attempts theselves is nothing what i call "emergence". They are still quite conservative or traditional methods.

The most advanced version along this line is string theory. Where 4D as we know it is a kind of effective "reduction" of a higher dimenstional space, and where the extra fancy transformations and geometric effects in the extra microstructure of the strings are supposes to encode the other forces to yield complete unification.

So if you want you can call it beeing emergent from a bigger space, but this reduction follows the logic of reductionism, and uses an even more complex picture, to explain something simpler, but in a non-natural way, requiring extreme fine tuning. The problem IMO with string theory except that it has not succeeded after lots of effort, is that it just pushes the same question back up into more complex spaces, without increasing any deeper insight of conceptual problems (beyond insight in the mathematical models themselves). One interesting part of string theory is that its full of dualities, much more complex and fancy than the original KG-Dirac duality, that with some imagination can be interpreted as observer-observer transformations in more abstract spaces, but the starting point for generating these dualities (ie the quantized string) is very ad hoc and i have never seen a string theorist elaborate this this way beyond historial pragmatic reasons of when ST was supposed to solve strong interaction when they thought particles appeared string like. As far as I know string theorists usually lable their own work as a conservative attempt to unify forces. With conservative probably refers to not messing up quantum mechanics too badly.

/Fredrik

 

[bayakiv]

So my question is, if Lorentz Invariance was not fundamental, does this third theory where spacetime and matter were emergent become more plausible?

The third theory will only inspire confidence if it makes plausible predictions, and until then (even if spacetime, classical and quantum mechanics are emerging within this theory) it will be a superfluous theory.

 

[robwilson]

I am not a physicist, but a reasonably well-known group-theorist who has spent ten years studying this question and related questions about what the symmetries of fundamental physics really are. My conclusions posted today on arxiv:2009.14613v5 can be interpreted either way, depending on what exactly you mean. There appears to be a symmetry group of order 24 that relates 12 fundamental bosons and 12 fundamental fermions to each other, that is clearly fundamental. Now if you pass to the classical limit, by taking large numbers of these particles, you end up in the group algebra, whose Wedderburn decomposition is a direct sum of matrix algebras. Do you regard these algebras as "fundamental" or "emergent"? I think I regard them as fundamental. Where the "emergent" properties arise is when you take a fundamental particle acting on the algebra by multiplication on one side, and a matrix group acting on the other side. This is putting a fundamental particle in a classical environment, and this is where you see all the symmetry-breaking, measurement problem issues, and things like that. At that level, the symmetries reduce to whatever symmetries the environment has, which in the real world will be none.

The really difficult question here is whether Lorentz symmetries are fundamental or emergent. The Lorentz *group* is fundamental in the sense I have just described, but then the question is what physical concept do you regard it as the symmetry group of? The algebra contains three distinct concepts, anyone of which you could reasonably define as spacetime, but with different symmetry groups. One of them has Lorentz symmetries, but the other two do not. The other two have a universal time coordinate, not a variable time coordinate. One of them has a rigid Euclidean space, the other has a stretchy Einsteinian space. The stretchy space can be used in the strong force to describe asymptotic freedom, and can be used in gravity to describe something similar to, but different from, curvature of spacetime. The amount of stretching defines the masses of the elementary particles. So if you ask me whether spacetime is fundamental or emergent, I cannot answer the question, because there are (at least in my model) three different concepts of spacetime: an absolute spacetime, a gravitational spacetime, and an electromagnetic spacetime. It is the tension between these three concepts that defines the concept of a force.

Of course, my model is new and speculative, but it makes lots of predictions, and it explains lots of things, so it should be easy to test.

 

[Auto-Didact]

If symmetries are not fundamental. Does this imply the vacuum may not be Lorentz invariant? If so, does it imply new physics? Or will the vacuum not obeying Lorentz invariance means there is more degree of freedom for new physics?

In physics, the breaking of symmetry is usually a consequence of some phase transition, but there are many phase transitions without symmetry breaking. From this point of view, symmetry breaking is seen as a secondary effect of phase transitions which would be more fundamental; important to note is that this is a standard viewpoint within the theory of PDE as well as in the theory of dynamical systems, but I digress.

Phase transitions in QFT involve the choice of a new vacuum state in which the state is said to tunnel from one vacuum to another; this idea is almost certainly an approximation since 1) states built up from one vacuum state cannot unitarily evolve from another vacuum state, because these states literally belong to different Hilbert spaces, and 2) this approximation requires the system to be taken as infinite, while it is finite.

In any case, Penrose lays out multiple mathematical possibilities why symmetry in fundamental physics, while obviously an extremely powerful idea, may have been applied inappropriately because of its very allure and perhaps prematurely. Among others:

• the possibility of non-uniform symmetry breaking i.e. different symmetry domains due to too rapid cooling
• cosmic topological defects, e.g. the possibility of gauge monopoles, cosmic strings or domain walls
• the inconsistency between universal symmetry breaking across space allowing a uniform identification of states from a $U(2)$-symmetric manifold and the very idea of gauge theory in terms of a connection on a fibre bundle with the $U(2)$-symmetric manifolds as fibres in which such a global identification is generally not possible.

 

[jake jot]

In physics, the breaking of symmetry is usually a consequence of some phase transition, but there are many phase transitions without symmetry breaking. From this point of view, symmetry breaking is seen as a secondary effect of phase transitions which would be more fundamental; important to note is that this is a standard viewpoint within the theory of PDE as well as in the theory of dynamical systems, but I digress.

Phase transitions in QFT involve the choice of a new vacuum state in which the state is said to tunnel from one vacuum to another; this idea is almost certainly an approximation since 1) states built up from one vacuum state cannot unitarily evolve from another vacuum state, because these states literally belong to different Hilbert spaces, and 2) this approximation requires the system to be taken as infinite, while it is finite.

In any case, Penrose lays out multiple mathematical possibilities why symmetry in fundamental physics, while obviously an extremely powerful idea, may have been applied inappropriately because of its very allure and perhaps prematurely. Among others:

• the possibility of non-uniform symmetry breaking i.e. different symmetry domains due to too rapid cooling
• cosmic topological defects, e.g. the possibility of gauge monopoles, cosmic strings or domain walls
• the inconsistency between universal symmetry breaking across space allowing a uniform identification of states from a $U(2)$-symmetric manifold and the very idea of gauge theory in terms of a connection on a fibre bundle with the $U(2)$-symmetric manifolds as fibres in which such a global identification is generally not possible.

I googled "penrose symmetry not fundamental cosmic topological defects, e.g. the possibility of gauge monopoles, cosmic strings or domain walls" but I only got hundreds of hits of the latter. No one article that linked Penrose. Can you please elaborate the context of "In any case, Penrose lays out multiple mathematical possibilities why symmetry in fundamental physics, while obviously an extremely powerful idea, may have been applied inappropriately because of its very allure and perhaps prematurely. Among others:".

Let's say there were cosmic strings, how does that relate to whether symmetry is fundamental or not? For example. If there were cosmic strings, symmetry (globally) is not fundamental? why?

 

[Auto-Didact]

I googled "penrose symmetry not fundamental cosmic topological defects, e.g. the possibility of gauge monopoles, cosmic strings or domain walls" but I only got hundreds of hits of the latter. No one article that linked Penrose. Can you please elaborate the context of "In any case, Penrose lays out multiple mathematical possibilities why symmetry in fundamental physics, while obviously an extremely powerful idea, may have been applied inappropriately because of its very allure and perhaps prematurely. Among others:".

Let's say there were cosmic strings, how does that relate to whether symmetry is fundamental or not? For example. If there were cosmic strings, symmetry (globally) is not fundamental? why?

This is a purely mathematical argument: given any topological manifold, any topological defects of this manifold would de facto constitute an obstruction to the existence of global symmetry breaking, i.e. the existence of any cosmic topological defects would mean that symmetry breaking can at best be an approximate and/or local phenomenon.

Both the universe and internal spaces such as the $U(2)$-symmetric manifold of electroweak theory are topological manifolds to which this mathematical argument would therefore automatically apply; whether or not there are cosmic topological defects is an open question in experimental physics.

 

[jake jot]

This is a purely mathematical argument: given any topological manifold, any topological defects of this manifold would de facto constitute an obstruction to the existence of global symmetry breaking, i.e. the existence of any cosmic topological defects would mean that symmetry breaking can at best be an approximate and/or local phenomenon.

Any reference or arvix paper about this? When I googled "penrose symmetry is emergent". All I got was about Penrose Tiling. Did Witten say the same thing?

Both the universe and internal spaces such as the $U(2)$-symmetric manifold of electroweak theory are topological manifolds to which this mathematical argument would therefore automatically apply; whether or not there are cosmic topological defects is an open question in experimental physics.

Who knows. It may exist in one way or another. Is this the major reason the giants in physics (Penrose, Witten) were thinking along the line of symmetry not fundamental?

 

[jake jot]

My focus is not so much on the existential questions of "origin", but more to try to find a natural explanation to why the laws of physics are what they are and why he have 4D spacetime with the properties we know in thel low energy perspective.

So the word "vacuum" must be reserved for QFT since it is the quantum state with the lowest possible energy.

"Vacuum" must not be used for Spacetime (TM) because Spacetime is separate from QFT?

If the constants of nature are arbitrary and the origin of quantum fields and spacetime are secondary to a separate primordial Superforce. Then it is separate from QFT and spacetime? Remember the third theory where QFT and Spacetime are emergence according to the book on quantum gravity. So you can't refer to it as vacuum? What does physics called it then? Or should this Superforce still follow the rule of QFT? But if QFT was derived from this Superforce. How can it use QFT? What words or concepts do those arxiv creative writers describe the arguments or categorize or distinguish them?

No this is not philosophy but logic and sigma 5 level thing.

I am not aware of that book but that picture mainly represents various geometric theories, that try to generalize what has proven successfull to higher dimensions so as to try to include more of the fundamental forces. There were are many early attempts, to geometrize all of physics and include GR as well. But these attempts theselves is nothing what i call "emergence". They are still quite conservative or traditional methods.

The most advanced version along this line is string theory. Where 4D as we know it is a kind of effective "reduction" of a higher dimenstional space, and where the extra fancy transformations and geometric effects in the extra microstructure of the strings are supposes to encode the other forces to yield complete unification.

So if you want you can call it beeing emergent from a bigger space, but this reduction follows the logic of reductionism, and uses an even more complex picture, to explain something simpler, but in a non-natural way, requiring extreme fine tuning. The problem IMO with string theory except that it has not succeeded after lots of effort, is that it just pushes the same question back up into more complex spaces, without increasing any deeper insight of conceptual problems (beyond insight in the mathematical models themselves). One interesting part of string theory is that its full of dualities, much more complex and fancy than the original KG-Dirac duality, that with some imagination can be interpreted as observer-observer transformations in more abstract spaces, but the starting point for generating these dualities (ie the quantized string) is very ad hoc and i have never seen a string theorist elaborate this this way beyond historial pragmatic reasons of when ST was supposed to solve strong interaction when they thought particles appeared string like. As far as I know string theorists usually lable their own work as a conservative attempt to unify forces. With conservative probably refers to not messing up quantum mechanics too badly.

/Fredrik

 

[Fra]

So the word "vacuum" must be reserved for QFT since it is the quantum state with the lowest possible energy.

"Vacuum" must not be used for Spacetime (TM) because Spacetime is separate from QFT?

Yes, spacetime is a pre-requisite for QFT as it stands.
The vacuum is the quantum description of classically "empty space" indexed by a classical spacetime. Without a solid classical background and spacetime it is difficult to justify the construction of quantum mechanics itself.

This is part of the problem.

If the constants of nature are arbitrary and the origin of quantum fields and spacetime are secondary to a separate primordial Superforce. Then it is separate from QFT and spacetime? Remember the third theory where QFT and Spacetime are emergence according to the book on quantum gravity. So you can't refer to it as vacuum? What does physics called it then? Or should this Superforce still follow the rule of QFT? But if QFT was derived from this Superforce. How can it use QFT? What words or concepts do those arxiv creative writers describe the arguments or categorize or distinguish them?

I still don't know which third theory is mentioned in your paper, but yes its possible to entertain speculative reconstructions where 4d spacetime is not a prerequisition. One idea is to consider higher dimensional worlds, where the 4D spacetime can emerge as an approximation. But this is just one idea. One can also picture NO continuous spaces at all, but instead start with more primary concepts, such as various relations or self-organisation in some large complexity continumm limie or low energy limit allows and emergence of 4D spacetime.

So if the question is wether there can be things more primary than 4D spacetime or vacuum then that is possible. But one must realize that once we thow out the classical references, we loose the ground on which QM is constructed. This is the difficult part. One can of course reconstruct QM mathematically without this ground, but then the physical basis is left out and we lost contact to reality and experiment.

/Fredrik

 

[Auto-Didact]

Any reference or arvix paper about this? When I googled "penrose symmetry is emergent". All I got was about Penrose Tiling. Did Witten say the same thing?

I heard this during one of his lectures and also directly from the horse's mouth. If I recall correctly, Penrose' critique of symmetry is also described in multiple chapters in his 1000+ page book as well as in his latest book.

Who knows. It may exist in one way or another.

As I said, it is an open experimental question, therefore can only be answered by experiment. Cosmologists, astronomers and astrophysicists are looking, but as always the jury is still out.

Is this the major reason the giants in physics (Penrose, Witten) were thinking along the line of symmetry not fundamental?

For Penrose, yes; he has gone on about this more at length in his latest book as well as in multiple talks if I recall correctly. Witten, I have no idea, but I doubt it given the flexibility of string theory.

It's really just the same centuries old argument between mathematicians about the primacy of geometry vs algebra but put in a more modern coat; in this case, what is more fundamental for physics: group theory or topology/analysis?

Penrose, being a geometer turned mathematical physicist, along with most relativists and dynamicists (myself included) tend to have a strong intuitive preference for geometric over algebraic arguments and therefore automatically tend to see topological & analytic arguments as more fundamental and algebraic arguments as more consequential.

On the other hand, most active theoretical physicists - especially those trained in particle theory after the 70s - have usually been trained in such a non-geometric manner as to have acclimatized themselves fully to linear algebraic, representation theoretic and group theoretic arguments.

This explains the preference of modern theoretical physicists for algebra over geometry, breaking with the geometric tradition in theoretical physics which lasted from Newton until Poincaré/Einstein and is carried on by mathematical physics and applied mathematics. This also explains the inability of theoretical physics to come up with a new theory, since monumentally large mathematical inventions usually requires a geometric intuition instead of a strict algebraic treatment, but that is a discussion for another thread.

 

[robwilson]

This explains the preference of modern theoretical physicists for algebra over geometry, breaking with the geometric tradition in theoretical physics which lasted from Newton until Poincaré/Einstein and is carried on by mathematical physics and applied mathematics. This also explains the inability of theoretical physics to come up with a new theory, since monumentally large mathematical inventions usually requires a geometric intuition instead of a strict algebraic treatment, but that is a discussion for another thread.

This also explains the inability of those who have a preference for "monumentally large mathematical inventions" to come up with a new theory. You can always model anything if your model is complicated enough. The trick is to see through the mass of experimental data to the simple core, and come up with a simple hypothesis that explains a lot. A complicated hypothesis that explains little is not of much use to anyone. An algebraic approach is more likely to find the simple hypothesis - although there is not much evidence that it has been found yet.

 

[bayakiv]

An algebraic approach is more likely to find the simple hypothesis - although there is not much evidence that it has been found yet.

And why not vice versa - from simple geometry and a simple dynamic principle to various solutions with algebraic properties of physical objects.

 

[robwilson]

The simple answer is that the universe is quantised, and individual elementary particles contain a finite amount of information. You cannot model that with geometry, you can only do it with algebra.

 

[Auto-Didact]

This also explains the inability of those who have a preference for "monumentally large mathematical inventions" to come up with a new theory. You can always model anything if your model is complicated enough. The trick is to see through the mass of experimental data to the simple core, and come up with a simple hypothesis that explains a lot. A complicated hypothesis that explains little is not of much use to anyone. An algebraic approach is more likely to find the simple hypothesis - although there is not much evidence that it has been found yet.

This is of course completely problem dependent. Sometimes a large ground up reworking is actually necessary, e.g. going from Newtonian gravity to GR. If such a complete revamp is in order to solve some problem, the clearest simplest hypothesis will never be sufficient. Many sciences to this day suffer severely from this - from economics to psychology - and in most cases (linear) algebra is often the crutch which keeps them handicapped, while making them feel as if nothing is wrong since "any model is better than no model".

The strength of algebra in science is more as a tool to be used by those who are trying to apply an already discovered theory i.e. a tool for doing applied physics and for creating/solving homework problems. Historically, at least in physics, algebra has been less useful as a tool for actually discovering new theories i.e. as the theoreticians go-to method for creating new theories, while geometry and its extension to analysis is and always has been the gift that just keeps on giving.

I should make clear that one isn't superior to the other; I even deeply believe in the underlying unity of both; however it is evident that the direct use case of both of these tools are just different. One should choose the tool which bests suits the problem that one is interested in; for actual ground-up revolutionary theorization in science, instead of mere theoretical tinkering within some already accepted theoretical framework, geometry seems to have an undeniable edge and there is literally centuries of scientific research into this matter to back this up. If you want to discuss this further, I suggest we start another thread.

 

[bayakiv]

You cannot model that with geometry, you can only do it with algebra.

geometry + dynamics = algebra

 

[robwilson]

If you want to discuss this further, I suggest we start another thread.

I'm new to this forum, so not sure how to do that.

 

[robwilson]

geometry + dynamics = algebra

No. That is not what algebra is. I write as a professional algebraist.

 

[bayakiv]

No. That is not what algebra is. I write as a professional algebraist.

Spiral linear vector fields form the algebra of complex numbers.

 

[robwilson]

First of all, complex numbers are not algebra, they are analysis. Second, do you really want to define the complex numbers as spiral linear vector fields? Mathematics is a lot simpler than physicists try to make it seem.

 

[Fra]

A complicated hypothesis that explains little is not of much use to anyone.

I symphatize with this! A construct that is more complex, or beeing based on an extremely a priori improbable conditions(ie. unnatural), has little explanatory value. It's merely a reformulation.

(BUT it may sometimes indirectly might lead forward. For example, if you like to think in terms of X, recasting it into X-abstractions may help you with insight. I think we all have our own pet abstractions. This is why reading some of the early work of founders of relativity and QM is interesting, it really gives us a inside view of how they were reasoning towards insight and results. This process is quite different from the purification process that mathematicians may later do, which may "clean things up", express things in a more compact language, but sometimes at the prices of covering up the tracks of the original construction an the physical justifications.)

What is deceptive, is that one can find such, often apparentely "timeless" and eternal "patterns" in special cases, and then get seduced and tempted to apply them outside their domain of justification, and this leads to fallacious reasoning. This insight might get totally lost if you detach the math from physics, refined it and come up with another way of putting it, where you have lost justification to physics and measurement.

This is the idea that Smolin also raised, that "the unreasonable effectiveness of mathematics is precisely because it is limited". For example, all the nice symmetry groups we have in particle physics, their domain of justification is for relatively speaking, events that take place in a small area under short times, and can be repeated by preparations and statistics in a lab, living in a solid classical spacetime. The beatiful symmetries and apparent truths observed here, does not necessarily apply to cosmological scales or cosmological times, or for that matter other assymmetric conditions between observer-observed, such as Planck scale events, or during big bang?

/Fredrik

 

[robwilson]

I symphatize with this! A construct that is more complex, or beeing based on an extremely a priori improbable conditions(ie. unnatural), has little explanatory value. It's merely a reformulation.

(BUT it may sometimes indirectly might lead forward. For example, if you like to think in terms of X, recasting it into X-abstractions may help you with insight. I think we all have our own pet abstractions. This is why reading some of the early work of founders of relativity and QM is interesting, it really gives us a inside view of how they were reasoning towards insight and results. This process is quite different from the purification process that mathematicians may later do, which may "clean things up", express things in a more compact language, but sometimes at the prices of covering up the tracks of the original construction an the physical justifications.)

What is deceptive, is that one can find such, often apparentely "timeless" and eternal "patterns" in special cases, and then get seduced and tempted to apply them outside their domain of justification, and this leads to fallacious reasoning. This insight might get totally lost if you detach the math from physics, refined it and come up with another way of putting it, where you have lost justification to physics and measurement.

This is the idea that Smolin also raised, that "the unreasonable effectiveness of mathematics is precisely because it is limited". For example, all the nice symmetry groups we have in particle physics, their domain of justification is for relatively speaking, events that take place in a small area under short times, and can be repeated by preparations and statistics in a lab, living in a solid classical spacetime. The beatiful symmetries and apparent truths observed here, does not necessarily apply to cosmological scales or cosmological times, or for that matter other assymmetric conditions between observer-observed, such as Planck scale events, or during big bang?

/Fredrik

All that is true. And it is true in pure mathematics too. Going back to the originators of the ideas is always instructive. I just feel that in the case of the standard model symmetries, the mathematical cleaning up process has not been done, and that is where I am trying to help. In the process of cleaning up, one sometimes finds errors, or at least one can iron out some inconsistencies, which is bound to be useful. And I am particularly interested in the question of why the symmetries have such limited domains of applicability - I think in some cases it may be because they have become too abstract, and divorced from experiment. The apparent asymmetry between observer and observed is also something that deserves more attention, in my view.

 

[Fra]

And I am particularly interested in the question of why the symmetries have such limited domains of applicability - I think in some cases it may be because they have become too abstract, and divorced from experiment. The apparent asymmetry between observer and observed is also something that deserves more attention, in my view.

Yes. Early on, one could understand which observer classes symmetries relates to. Ie poincare groip etc. Its then also easy to understand when and why it must hold.

But as structures that are not possible to understand classicaly that emerge as a result of combining relativity with QM, which get graudally worse the more interactions you look at, and you involve internal dof as well as mixing internal and spacetime symmetry in a way that is understood only mathematically and pragmatically, we start to get lost and rightfully get unsure about which symmetries to enforce from physical perspective.

I would argue that to do this, we need to acknowledge that an observer is more than its frame of reference in spacetime ;)

/Fredrik

 

[jake jot]

Yes, spacetime is a pre-requisite for QFT as it stands.
The vacuum is the quantum description of classically "empty space" indexed by a classical spacetime. Without a solid classical background and spacetime it is difficult to justify the construction of quantum mechanics itself.

This is part of the problem.I still don't know which third theory is mentioned in your paper, but yes its possible to entertain speculative reconstructions where 4d spacetime is not a prerequisition. One idea is to consider higher dimensional worlds, where the 4D spacetime can emerge as an approximation. But this is just one idea. One can also picture NO continuous spaces at all, but instead start with more primary concepts, such as various relations or self-organisation in some large complexity continumm limie or low energy limit allows and emergence of 4D spacetime.

So if the question is wether there can be things more primary than 4D spacetime or vacuum then that is possible. But one must realize that once we thow out the classical references, we loose the ground on which QM is constructed. This is the difficult part. One can of course reconstruct QM mathematically without this ground, but then the physical basis is left out and we lost contact to reality and experiment.

/Fredrik

About"But one must realize that once we throw out the classical references, we loose the ground on which QM is constructed. " What "classical references" were you referring too? What ground?

And instead of framing it as whether there can be things more primary than 4D spacetime or vacuum. Maybe the better words is something that may be parallel to 4d spacetime or vacuum. Meaning you don't just unit these two, but an ignored third stuff the universe is constructed of. This is semantically and theoretically sound statement, wrong?

 

[Auto-Didact]

You can always model anything if your model is complicated enough. The trick is to see through the mass of experimental data to the simple core, and come up with a simple hypothesis that explains a lot. A complicated hypothesis that explains little is not of much use to anyone.

This is a strawman argument. When arguing to use dynamics, topology, analysis or geometry as a tool I am specifically not arguing for complicated hypotheses over simple ones. Instead I am arguing for different perspectives which tend to have a completely different, often unconventional, foundation - i.e. unknown to most (not part of a standard curriculum).

Mathematical disciplines that are unknown to many tend also to be slightly intimidating to most, because it might seem to be more complicated than the simple alternative they already know, even if it is conceptually just as simple or even simpler than the more conventional alternative. An example of this is the exterior calculus and differential forms over standard "simpler" vector calculus and multivariable calculus learned in school.

Such "simpler" alternatives are easier in a specific context and purely perceived as generally being simpler due to them already being familiar and spoonfed from a young age, but they are in actuality not really conceptually or mathematically simpler, just different. From the broader mathematical viewpoint, they usually contain assumptions which prevent them from being directly applicable or generalizable to other theories, while the alternative formulations tend to have less or no such problems.

To paraphrase Feynman: "You can't make imperfections on a perfect thing, you need another perfect thing."

An algebraic approach is more likely to find the simple hypothesis - although there is not much evidence that it has been found yet.

This is simply not true in general, and in fact only becomes true once the correct framework has already been identified. But that is precisely the problem we are discussing: how does one identify the correct framework in the first place? What if this framework has not yet been discovered or invented? Algebra itself being non-specific i.e. framework independent is usually of little help in this identification and selection process, especially during the beginning stages.

Discovery of novel frameworks in mathematics is an experimental process of trial and error which requires intuition, not merely computation or deduction; that only comes later once everything has already been worked out. If one is in the beginning stages of creating new mathematical frameworks or generalizing older ones (e.g. the generalization of Euclidean to non-Euclidean geometry) one is typically necessarily unable to use algebra reliably because the correct framework upon which to do algebra simply has yet to be identified.