Smolin: Lessons from Einstein's discovery....

[strangerep]

I'm reading Lee Smolin's paper: Lessons from Einstein’s 1915 discovery of general relativity

On p10, he writes:

Are there principles that can guide our ongoing search for a more complete understanding of the laws of nature?

One principle that seems reliable is background independence[6]. This says that the laws of nature should be statable in a form that does not rely on the specification of a fixed geometry of spacetime. Einstein’s theory of general relativity satisfies this principle, and it has been a useful heuristic for the search for quantum gravity. Background independence can be understood as expressing Leibniz’s principle of sufficient reason, which states that there should be a reason for every choice made in the formulation of the laws of nature[7]. This underlies the idea that space and time are aspects of relationships among dynamical degrees of freedom. One implication of this principle is that there can be no fundamental symmetries in the laws of nature. Every event in the history of the universe must be describable uniquely in terms of the relational degrees of freedom. This means that the closer we are to a fundamental theory, the fewer symmetries we should have. This may be why our search for larger and larger symmetries is no longer working. [...]

I don't follow why the restriction to relational degrees of freedom necessarily implies that as we get closer to a fundamental theory there should be fewer symmetries.

Any thoughts?

 

[atyy]

Because diffeomorphism invariance is the lack of symnmetries. When one compares GR and SR, both have diffeomorphism invariance, but SR additionally has global Lorentz invariance (let's take GR with a cosmological constant). So GR has less symmetry than SR.

 

[strangerep]

Yes,... but... I got the feeling Lee was alluding to something deeper.

Maybe I'm reading too much into it.

 

[atyy]

Yes,... but... I got the feeling Lee was alluding to something deeper.

Maybe I'm reading too much into it.

Maybe I'm reading too little into it.

I first encountered this argument of his in http://arxiv.org/abs/hep-th/0507235: "One way to formulate the argument against background spacetime is through a second principle of Leibniz, the identity of the indiscernible. This states that any two entities which share the same properties are to be identified. Leibniz argues that were this not the case, the first principle would be violated, as there would be a distinction between two entities in nature without a rational basis. If there is no experiment that could tell the difference between the state in which the universe is here, and the state in which it is translated 10 feel to the left, they cannot be distinguished. The principle says that they must then be identified. In modern terms, this is something like saying that a cosmological theory should not have global symmetries, for they generate motions and charges that could only be measured by an observer at infinity, who is hence not part of the universe. In fact, when we impose the condition that the universe is spatially compact without boundary, general relativity tells us there are no global spacetime symmetries ..."

There are many other passages expanding on that in the article.

 

[samalkhaiat]

I'm reading Lee Smolin's paper: Lessons from Einstein’s 1915 discovery of general relativity

On p10, he writes:

I don't follow why the restriction to relational degrees of freedom necessarily implies that as we get closer to a fundamental theory there should be fewer symmetries.

Any thoughts?

If the laws reveal no symmetries, they are as useless as Smolin’s ideas. For then any statement could be called “law of nature”.

 

[strangerep]

If the laws reveal no symmetries, they are as useless as Smolin’s ideas. [...]

Harsh words -- though I think I know what you mean. I often find Lee Smolin's papers to be like a meal in a Chinese restaurant: it seems tasty and interesting, but half an hour later I'm hungry again.

 

[martinbn]

I don't follow why the restriction to relational degrees of freedom necessarily implies that as we get closer to a fundamental theory there should be fewer symmetries.

Any thoughts?

Perhaps, if there are symmetries you can make a reduction and have a more fundamental description.

 

[atyy]

Harsh words -- though I think I know what you mean. I often find Lee Smolin's papers to be like a meal in a Chinese restaurant: it seems tasty and interesting, but half an hour later I'm hungry again.

High praise, if one believes a theory should make good predictions. "You will be hungry soon, order takeout now"

http://www.rinkworks.com/said/fortunes.shtml

 

[MacRudi]

Interesting, that he shows interest and like the idea in the holographic String Model of Susskind and Maldacena. On the physics forum, where he is writing too, there is an interesting idea of a holographic string model with backrunning time which should give dynamic spacetime in background and solved energyproblem which is not negative anymore he asked for. Maybe Smolin will publish next time a new Model. I'm looking forward to read it then.

 

[strangerep]

Perhaps, if there are symmetries you can make a reduction and have a more fundamental description.

Yes,... but (in principle) that's possible more generally.

But I think I see it now: restricting to relational degrees of freedom is analogous to (eg) decomposing the Kepler/Hydrogen problem into CoM dof's and relative dof's. The former are essentially "background", so we forget about them. The interesting physical features emerge by analysis of the latter.

 

[Ralph Dratman]

If the laws reveal no symmetries... then any statement could be called “law of nature”.

I assume by "any statement" you mean any demonstrated fact, not just some imaginative utterance. In other words, without any symmetries, a fact such as "the Moon is orbiting the Earth" might be called a natural law, removing the distinction between laws of nature and specific circumstances. But I do not think anyone has suggested that all symmetries were suddenly going to disappear, only that symmetries might no longer be the keystones of discovery they have been in the past.

 

[ShayanJ]

I don't follow why the restriction to relational degrees of freedom necessarily implies that as we get closer to a fundamental theory there should be fewer symmetries.

What I understand is that any symmetry a theory has, is actually a choice for that theory because we could make other theories for the same thing with other symmetries. Now if we accept that every choice in our theories should have a reason, any choice we make for the symmetry of our theory among a possible set of symmetries should have a reason, which means we're asking for an underlying theory. So it seems to me that Smolin is arguing that if our theories always have symmetries, we have to keep going down for ever and can never stop. So the fundamental theory has no symmetry.
But I don't think it follows. One caveat to the above argument is that maybe we can show that there is only one symmetry possible for the theories of a particular aspect of nature, or in this case, we can show that there is only one symmetry possible for any theory that is going to give us the current physics in some limit.
Also our theories do satisfy Leibniz's principle of sufficient reason even if they have symmetries: The sufficient reason can be that they correctly describe nature!

 

[Jimster41]

Crazy over-large Question that keeps bugging me: What kind of system design must display a mixture of symmetry and asymmetry? Why should a system with one have any of the other at all?

 

[jerromyjon]

Crazy over-large Question that keeps bugging me: What kind of system design must display a mixture of symmetry and asymmetry? Why should a system with one have any of the other at all?

Any entropic system has asymmetry... I think the symmetry belongs in the models, nothing in nature is perfectly symmetrical. The more symmetry the models "encompass" the less likely "other" symmetries present themselves...

 

[Dirk Pons]

Smolin may have a point. Our own work, which comes from a very different direction, indicates that both the asymmetrical leptogenesis and baryogenesis processes can be conceptually explained as consequences of a single deeper symmetry. That is the matter-antimatter species differentiation. That also explains asymmetries in decay rates.

I do wonder whether the 'symmetries' idea is overloaded. The basic concept is that some attribute of the system should be preserved when transformed about some dimension. Even if it is possible to represent this mathematically, we should still be prudent about which attributes, transformations, and dimensions to accept. Actual physics does not necessarily follow mathematical representation. There is generally a lack of critical evaluation of the validity of specific attributes, transformations, and dimensions for the proposed symmetries.

The *time* variable is a case in point. Mathematical treatments invariably consider it to be a dimension, yet empirical evidence overwhelmingly shows this not to be the case.Logically, we should therefore discard any mathematical symmetry that has a time dimension to it. That reduces the field considerably, since many symmetries have a temporal component. This may be uncomfortable from some, but is something we need to be open to considering. When something is not working, then it appropriate to go back and question the premises. Our own work suggests that time could be an emergent property of matter, rather than a dimension. This makes it much easier to explain the origins of the arrow of time and of irreversibility. So it can be fruitful, in an ontological way, to be sceptical of the idea that mathematical formalisms of symmetry are necessarily valid representations of actual physics.

 

[Ralph Dratman]

"Mathematical treatments invariably consider [time] to be a dimension, yet empirical evidence overwhelmingly shows this not to be the case."

This is a very interesting point. I want to make sure I understand you. You say that time is not a dimension. Is this because, for example, objects cannot be moved to an arbitrary coordinate in time, as they can in a spatial dimension? Or because the time coordinate must be multiplied by i before it can be manipulated like a spatial coordinate?

 

[strangerep]

[...] Mathematical treatments invariably consider [time] to be a dimension, yet empirical evidence overwhelmingly shows this not to be the case. Logically, we should therefore discard any mathematical symmetry that has a time dimension to it.

Perhaps, like Ralph above, I too do not understand you. Superficially, your words would rule out Lorentz boost transformations, as they mix space and time.

You refer to your "own work". Please give a reference to a arxiv paper, or (preferably) a paper published in a peer-reviewed journal. (Note that the PF rules are quite strong concerning unpublished personal theories.)

 

[Dirk Pons]

That's a useful clarification question. I propose the former.

I'm saying that empirical evidence, e.g.irreversibility, shows that time does not evidence symmetry. That includes the observation that 'objects cannot be moved to an arbitrary coordinate in time'. Consequently *time* cannot be considered to be a dimension about which it is valid to apply a symmetry transformation even when one exists mathematically. Alternatively, if we are to continue to rely on temporal symmetries, it will be necessary to understand how the mechanics of irreversibility arises, and why those symmetries are exempt therefrom.

I accept that relativity considers time to be a dimension, and has achieved significant theoretical advances with that premise. However relativity is also a theory of macroscopic interactions, and it is possible that assuming time to be a dimension is a sufficiently accurate premise at this scale, but not at others.

 

[Dirk Pons]

Please give a reference

[Links to references deleted]

Moderator's note: the references that were given here fall outside the scope of Acceptable Sources as set out in the PF rules.

 

[haushofer]

What I understand is that any symmetry a theory has, is actually a choice for that theory because we could make other theories for the same thing with other symmetries. Now if we accept that every choice in our theories should have a reason, any choice we make for the symmetry of our theory among a possible set of symmetries should have a reason, which means we're asking for an underlying theory. So it seems to me that Smolin is arguing that if our theories always have symmetries, we have to keep going down for ever and can never stop. So the fundamental theory has no symmetry.
But I don't think it follows. One caveat to the above argument is that maybe we can show that there is only one symmetry possible for the theories of a particular aspect of nature, or in this case, we can show that there is only one symmetry possible for any theory that is going to give us the current physics in some limit.
Also our theories do satisfy Leibniz's principle of sufficient reason even if they have symmetries: The sufficient reason can be that they correctly describe nature!

Yes,... but (in principle) that's possible more generally.

But I think I see it now: restricting to relational degrees of freedom is analogous to (eg) decomposing the Kepler/Hydrogen problem into CoM dof's and relative dof's. The former are essentially "background", so we forget about them. The interesting physical features emerge by analysis of the latter.

I must say I'm still not grasping this idea of Smolin. I have to think about it, but if someone would like to elaborate even more, I'd be happy to read it :P

 

[Dirk Pons]

As I understand it, Smolin's main point is not about symmetries per se, but rather about methodologies. He is saying that elegant qualitative explanations are more valuable than beautiful mathematics, that physics fails to progress when 'mathematics [is used] as a substitute for insight into nature' (p13).

'The point is not how beautiful the equations are, it is how minimal the assumptions needed and how elegant the explanations.' The symmetry methodology receives criticism for the proliferation of assumptions it requires, and the lack of explanatory power. Likewise particle supersymmetry and string theory are identified as having the same failings.

In summary: new physics will emerge by developing qualitative explanations based on intuitive insights from natural phenomena, rather than trying to extend existing mathematics. Explanations that are valuable are those that are efficient (fewer parameters, less tuning, and not involving extremely big or small numbers) and logically consistent with physical realism ('tell a coherent story'). It is necessary that the explanations come first, and the mathematics follows later as a subordinate activity to formalise and represent those insights.

 

[ShayanJ]

As I understand it, Smolin's main point is not about symmetries per se, but rather about methodologies. He is saying that elegant qualitative explanations are more valuable than beautiful mathematics, that physics fails to progress when 'mathematics [is used] as a substitute for insight into nature' (p13).

'The point is not how beautiful the equations are, it is how minimal the assumptions needed and how elegant the explanations.' The symmetry methodology receives criticism for the proliferation of assumptions it requires, and the lack of explanatory power. Likewise particle supersymmetry and string theory are identified as having the same failings.

In summary: new physics will emerge by developing qualitative explanations based on intuitive insights from natural phenomena, rather than trying to extend existing mathematics. Explanations that are valuable are those that are efficient (fewer parameters, less tuning, and not involving extremely big or small numbers) and logically consistent with physical realism ('tell a coherent story'). It is necessary that the explanations come first, and the mathematics follows later as a subordinate activity to formalise and represent those insights.

I think everybody agrees that this situation in theoretical high energy physics, our problems with QFT and QG, means something is wrong about our approach. But to say what that is, requires comparing different approaches and evaluating the amount of progress each is making. In the current situation where we clearly lack a fundamental understanding of our theories, I see no other way. So Smolin's argument seems strange to me because I don't know where it comes from!

 

[Dirk Pons]

requires comparing different approaches and evaluating the amount of progress each is making

That is ideal, but it presupposes that all candidate solutions are developed to the same degree of completeness, which is seldom the case. Also, it is possible that existing solutions are not capable of significant further gains, and that some very different solution is needed instead. This appears to be Smolin's perspective: he lacks confidence in existing mathematical methods to deliver the needed new insights.

 

[Demystifier]

I don't follow why the restriction to relational degrees of freedom necessarily implies that as we get closer to a fundamental theory there should be fewer symmetries.

Any thoughts?

I would not say that the former necessarily implies the latter, but it should not be difficult to see why the former suggests the latter. The relational degrees have less symmetry (compared to the usual diff invariant formulation of GR) and are supposed to be fundamental. This suggests (but not prove) that it might be a general rule that fundamental theory has less symmetry.

 

[Jimster41]

I find this paragraph pretty confusing - seems like he's suggesting something that is not background independent either?

"We also so far lack a formulation of the holographic principle which is consistent with the principle of background independence that grounds general relativity[14]. The boundary conditions that Maldacena’s form of the principle impose-that the spacetime be asymptotically AdS, imposes a fixed background and so breaks background independence. The negative cosmological constant and asymptotically AdS condition describe a subsystem placed in a box. We need instead a formulation of the holographic principle that applied to a closed universe with a positive cosmological constant, rather than a sub system of the universe in a box defined by a negative cosmological constant". p11

Is he saying that a theory that would work would have to describe both - a box containing a subsystem that appears to have negative cosmological constant and a closed system that appears to have positive cosmological constant?

At some point there is the problem of cosmogenisis... infinite regress etc. (his buddy Unger was all over this in their book) so isn't a fully and purely "closed-universe" a non-starter anyway?

 

[strangerep]

[...] The relational degrees have less symmetry (compared to the usual diff invariant formulation of GR) and are supposed to be fundamental. [...]

Yes -- that's pretty much the conclusion I reached in my subsequent post 10.

 

[Demystifier]

But I think I see it now: restricting to relational degrees of freedom is analogous to (eg) decomposing the Kepler/Hydrogen problem into CoM dof's and relative dof's. The former are essentially "background", so we forget about them. The interesting physical features emerge by analysis of the latter.

Thar's a great analogy!

 

[haushofer]

Could someone elaborate on what exactly are "relational degrees of freedom", compared to absolute degrees of freedom? Is it something like "distances between points on a manifold" vs "individual points on a manifold"?

 

[strangerep]

Could someone elaborate on what exactly are "relational degrees of freedom", compared to absolute degrees of freedom? Is it something like "distances between points on a manifold" vs "individual points on a manifold"?

I guess that's one example. E.g., relative velocity between 2 observers is physically significant, whereas absolute velocity is meaningless.

 

[Demystifier]

Is it something like "distances between points on a manifold" vs "individual points on a manifold"?

Yes, it's something like that.

 

[Jimster41]

Here's a quote from his book "The Singular Universe and the Reality of Time" written with with Roberto Unger Cambridge University Press 2015

"Relationalism offers a strategy that can take over at the point that reductionism fails. The properties of the elementary particles can be understood as arising from the dynamical network of interactions with other particles and fields. A property of a particle or event that is defined or explained only by reference to the network of relations it is embedded in can be called a relational property; its opposite, a property that is defined without reference to other events or particles, is called intrinsic. The ambition of a purist relational approach would be satisfied if all properties of elementary particles and events are relational." p380

He mentions a guy named Chew and collaborators from the 1960s "bootstrap approach" to understanding the observed hadrons as kind of pioneers of the view. I am just into the chapter on this now. He's working up from Liebniz' "principle of differential sufficient reason" and "principle of the identity of the indiscernible" - I'm struggling with it to be sure (and the whole chapter). It seems like a valiant but hopeless defense against infinite regress... I'm hoping it convinces me of some new way of ignoring that.

 

[Ralph Dratman]

Here's a quote from his book "The Singular Universe and the Reality of Time" written with with Roberto Unger Cambridge University Press 2015
"Relationalism offers a strategy that can take over at the point that reductionism fails." ... It seems like a valiant but hopeless defense against infinite regress.

I would say reductionism fails where there is intrinsic complexity that cannot be avoided or bypassed on the way to a theory. Then if you try to sum a quantity over terms that are more and more complicated, you may get an infinity that cannot be eliminated. Is that the idea?