Wednesday, February 26, 2014

What is analogue gravity and what is it good for?

Image source: Redbubble

Gravity is an exceedingly weak force compared to the other known forces. It dominates at long distances just because, in contrast to the strong and electroweak force, it cannot be neutralized. When not neutralized however the other forces easily outplay gravity. The electrostatic repulsion between two electrons for example is about 40 orders of magnitude larger than their gravitational attraction: Just removing some electrons from the atoms making up your hair is sufficient for the repulsion to overcome the gravitational pull of the whole planet Earth.

That gravity is so weak also means its effects are difficult to measure, and its quantum effects are so difficult to measure that it was believed impossible for many decades. That belief is a troublesome one for scientists because a theory that cannot be tested is not science – in the best case it’s mathematics, in the worst case philosophy. Research on how to experimentally test quantum gravity, by indirect signals not involving the direct production of quanta of the gravitational field, is a recent development. It is interesting to see this area mature, accompanied by the conference series “Experimental Search for Quantum Gravity”.

Alongside the search for observable consequences of quantum gravity – often referred to as the ‘phenomenology’ of quantum gravity – the field of analogue gravity has recently seen a large increase in activity. Analogue gravity deals with the theory and experiment of condensed matter systems that resemble gravitational systems, yet can be realized in the laboratory. These systems are “analogues” for gravity.

If you take away one thing from this post it should be that, despite the name, analogue gravity does not actually mimic Einstein’s General Relativity. What it does mimic is a curved background space-time on which fields can propagate. The background however does not itself obey the equations of General Relativity; it obeys the equation of whatever fluid or material you’ve used. The background is instead set up to be similar to a known solution of Einstein’s field equations (at least that is presently the status).

If the fields propagating in this background are classical fields it’s an analogue to a completely classical gravitational system. If the fields are quantum fields, it’s an analogue to what is known as “semi-classical gravity”, in which gravity remains unquantized. Recall that the Hawking effect falls into the territory of semi-classical gravity and not quantum gravity, and you can see why such analogues are valuable. From the perspective of quantum gravity phenomenology, the latter case of quantized fields is arguably more interesting. It requires that the analogue system can have quantum states propagating on it. It is mostly phonons in Bose-Einstein condensates and in certain materials that have been used in the experiments so far.

The backgrounds that are most interesting are those modelling black hole inflation or the propagation of modes during inflation in the early universe. In both cases, the theory has left physicists with open questions, such as the relevance of very high (transplanckian) modes or the nature of quantum fluctuations in an expanding background. Analogue gravity models allow a different angle of attack to these problems. They are also a testing ground for how some proposed low-energy consequences of a fundamentally quantum space-time might come about and/or affect the quantum fields like deviations from Lorentz-invariance and space-time defects. It should be kept in mind though that global properties of space-time cannot strictly speaking ever be mimicked in the laboratory if space-time in these solutions is infinite. As we discussed recently for example, the event horizon of a black hole is a global property, it is defined as existing forever. This situation can only be approximately reproduced in the laboratory.

Another reason why analogue gravity, though it has been around for decades, is receiving much more attention now is that approaches to quantum gravity have diversified as string theory is slowly falling out of favor. Emergent and induced gravity models are often based on condensed-matter-like approaches  in which space-time is some kind of condensate. The big challenge is to reproduce the required symmetries and dynamics. Studying what is possible with existing materials and fluids in analogue gravity experiments certainly serves as both inspiration and motivation for emergent gravity.

While I am not a fan of emergent gravity approaches, I find the developments in analogue gravity interesting from an entirely different perspective. Consider that mathematics is not in fact a language able to describe all of nature. What would we do if we had reached its limits? We could take out maths as the middle-man and directly study systems that resemble more complicated or less accessible systems. That’s exactly what analogue gravity is all about.

I am sure that this research area will continue to flourish.

(If you really want to know all the details and references, this Living Review is a good starting point.)

42 comments:

Plato Hagel said...

I agree that analogues give thinking some impetus as a correlation to the quantum gravity issues at hand.

For ex:


“In microgravity, the fluids are almost stagnant, resembling solids. The absence of motion makes it easier to observe and mathematically describe what is occurring when the crystals are melted, and how the materials solidify to form a new crystal.”Sorry link now dead


Aleksander Ostrogorsky

Take special note of, "Working Inside the Box on the ISS (International Space Station)"

Notice current research on crystallography.

Best,

Plato Hagel said...

I disagree on the issues of string theory.

One is always looking for simplicity in a complex world, and such alignments of order can share the effect of, a vacuum lets say on speed of light absent of any medium.

Best,

hush said...

Sabine,
Just point to any physicist...point to anyone - I'm desperate - and have them tell the world what measurement does.

Nothing else matters. Nothing.

Or go on mutually indulging yourselves with entertaining questions that have no meaning until the definition of measurement is clear.

Plato Hagel said...

.....shhhhhhhhhhhthe definition of measurement is clear.

That's the point.:)

Zephir said...

/* ..gravity models are often based on condensed-matter-like approaches in which space-time is some kind of condensate... The background ... obeys the equation of whatever fluid or material you’ve used... */

I see, the aether... The only question remains, why you're censoring me from your blog, if you're admitting the relevance of this model?

/* consider that mathematics is not in fact a language able to describe all of nature. What would we do if we had reached its limits? */

I dunno.. Censor the people, who pointed to it first?

Uncle Al said...

The Equivalence Principle (EP) is true for all measurable observables: Eötvös experiments, Nordtvedt effect plus lunar laser ranging, pulsar binaries with solar stars, white dwarfs, pulsars. One absolutely discontinuous observable (outside Noether's theorems) can be calculated but not measured. Einstein-Cartan-Kibble-Sciama gravitation says it measurably violates the EP.

Gravitation theory beyond GR fails. Test the singular observable that causes failure while being consistent with all prior observations. The greatest obstacle to understanding reality is the illusion of knowledge.

N said...

Please forgive my laic approach, but since space- time is somewhat connected with distribution of mass, and as we (supposedy) know that the "quantum" of mass is the Planck mass, would it not be appropriate to loo gravity quanta at much higher energies?

Sabine Hossenfelder said...

Plato: "I disagree on the issues of string theory." It's an observation, not a judgement.

Sabine Hossenfelder said...

N,

The Planck mass is not the 'quantum of mass'. That's a big misunderstanding. There is no known 'quantum of mass'. This post explans what the Planck scale (Planck length and Planck mass) is. Best,

B.

Sabine Hossenfelder said...

Zephir,

How often do I have to tell you that the reason I am deleting your comments is, in most cases, not their content but their frequency. You're like some guy who sits in a seminar and talks loudly to himself and the other people can't understand what's going on at the blackboard. That's why I have asked you numerous times to tone it down, but you don't get it. So now you're allowed one comment per post and at least from my perspective that solves the problem. This has nothing to do with censorship, this is all about your lack of respect for other people.

Eujin said...

There was quite a controversy about whether the UBC group had deomstrated the Hawking effect in their analogue model. There was a paper about it recently from Unruh saying yes they did http://arxiv.org/abs/arXiv:1401.6612

If true, this is important, as it shows that the global property of the event horizon, as mentioned in the text, isn't really important for the Hawking effect.

Sabine Hossenfelder said...

Eujin,

Yes, I have followed this exchange.

Regarding the horizon: I don't really understand why this point has to be discussed at all. Particle production in time-dependent backgrounds doesn't need a horizon. You need a horizon for the strict thermality of the spectrum. Best,

B.

Eujin said...

The first line of Unruh's abstract;

"It is argued that Hawking radiation has indeed been measured and shown to posses a thermal spectrum, as predicted."

They claim to have a thermal spectrum, at least a Boltzmann distribution.

Do you mean that you need an infinite horizon that remains at the same temperature forever to have "strict thermality"? That would be a very formal requirement in my book.

Sabine Hossenfelder said...

Eujin,

Ok, to be more precise: You need the horizon to get a mixed state regardless of the initial state. The spectrum isn't the relevant aspect, the point is that it has to be uncorrelated. That's what you can't do without an actual event horizon. Anyway, in reality the distinction is somewhat academic, if you excuse the expression. It's a question of how precisely you can measure and how good is the statistics, etc etc. Best,

B.

Wes Hansen said...

Hey, alright Uncle Al; the hardest leave-taking is leaving "knowledge" for experience. That last is a slight modification of the great mystic's, Meister Eckhart's, saying, "The hardest leave-taking is leaving god for God." Not that I acknowledge the existence of the latter or the veracity of the former . . .

Sabine, I wholeheartedly disagree with you regarding mathematics! I feel the existence of Omega demonstrates that the set of all mathematics far exceeds the set of all "conventional reality." And the example that Max Tegmark uses to demonstrate the non-intrinsic existence of mathematics is the same argument Buddhists use to demonstrate the fallacious nature of all God arguments, interestingly enough. Every mystic, regardless of affiliation or lack thereof, has the same mystic experience, described as a state of Bliss; they enter a Bliss field. Most mystics, Brahmanic, Christian, etc., conclude that this Bliss field is the absolute creator deity or God. But Buddhist philosophers point out that if an absolute entity exists it must have intrinsic existence, it must exist unto itself, and Buddhists say if you spend enough time in meditative equipoise searching for this intrinsic existence all you find is the lack thereof – emptiness! This is because everything in existence, including the Bliss field, is of interdependent origin – truly emergent.

Now, believe me, I’ve spent a great deal of time meditating on this argument and if you truly understand it and its implications, there is no way you can argue that mathematics – Platonic forms – have no existence. I believe the practice of modeling DOES extract some mathematical substance from reality; the very fact of modeling REVEALS the inherent structure underlying conventional reality. This inherent structure, the mathematical substance being extracted, doesn’t have intrinsic existence but neither does anything else. Mathematical substance is a product of true emergence; to say that it doesn’t truly exist is to suggest, to me, that conventional reality is the result of “magic” or some absolute creator.

Mathematics is the study of pattern as is the study of science. Science recognizes a pattern in nature and uses structured logic, primarily Boolean logic and the Principle of Indifference (no "Quantum Logic" necessary, as Goyal/Knuth demonstrate), to distill those patterns down to their fundamental nature. The fact that this is even possible suggests to me that conventional reality, at its fundamental basis, is information-theoretic! I mean, do you not find it absolutely fascinating and mysterious, the fact that the wave/particle duality can be satisfactorily described as a function of the basis one chooses for the Hilbert space! And whether we observe a wave or a particle is a function of the basis for our observation, Ha, Ha, Ha . . . I just covered this topic in a short email to Kevin Knuth which I think I shall post here. If you find it off topic or irrelevant I’m sure you’ll simply delete . . .

Wes Hansen said...

The subject title of the email I sent to Kevin Knuth was, “the Grin without the Cat,” and this is what I mean when I say that to suggest mathematics doesn’t exist is to suggest reality is the result of “magic” or “divine creation," or, under the auspices of magic, has simply existed forever. To suggest that the cat exists but the grin doesn’t is clearly absurd but is it really absurd to say that the grin can emerge without, or prior to, or in conjunction with, the cat? To suggest that mathematics results due to the ability of humans, who evolved in a patterned environment, to recognize pattern is to implicitly suggest that, prior to humans, there was no logic, hence, no pattern. Now, I could very well be wrong since many people argue this very thing, but I, obviously, don’t think I’m wrong. The email (sorry, but it will require one long and one short post):

Charles Pierce initially distinguished three types of reasoning: hypothesis; deduction; induction. Deduction was in a category by itself in that it’s purely explicative; it manifests as your common algebra with its associated process calculus. Hypothesis and induction, on the other hand, are both ampliative in that they expand the boundaries of knowledge in probable and plausible ways.

In the early 1900’s Pierce refined his “foundations of inference” to abduction, deduction, and induction. According to Pierce, when novel facts emerge an explanation is desired and this “explanation must be such a proposition as would lead to the prediction of the observed facts, either as necessary consequences or at least as very probable under the circumstances. A hypothesis then has to be adopted which is likely in itself and renders the facts likely. This step of adopting a hypothesis as being suggested by the facts is what I call abduction. […] The first thing that will be done, as soon as a hypothesis has been adopted, will be to trace out its necessary and probable experimental consequences. This step is deduction. […] The next step is to test the hypothesis by making experiments and comparing the predictions drawn from the hypothesis with actual results […] that is alone properly entitled to be called induction.”

To me, this abduction step is the major hurdle to AI. I have a good deal of experience with creative problem solving; I’ve been granted one U.S. patent and have multiple U.S. and International patents pending. My inventions are, for the most part, mechatronic and, without exception, they were all inspired by a catalyst. I would see some technology already in use and realize I could use a novel variation of that technology to solve a novel problem; I would “abduce” a proven hypothesis to a novel situation; I would make an analogy. And essentially, in each case, the underlying structure of the technology remained relatively the same, only the context in which it was applied changed; this is the hallmark of analogy! This seems, to me, the essence of that which separates humans from computers, computers, for the most part, are currently unable to make these creative associations.

In his Pattern Theoretics, Ben Goertzel defines a pattern in an entity z as an ordered pair (x, y) whereby the entity x, a proper subset of z, when applied to the process y yields the entity z such that the structural complexity of x plus the structural complexity of y plus the structural complexity of applying x to y is less than the structural complexity of z. Structural complexity is defined as the set of all non-redundant pattern within an entity very much analogous to linear independence in vector algebra. Ideally, one wants to minimize the structural complexity of (x, y) which will maximize the compression of z and this is where your “Cox-Knuth Method” flexes its muscle. Essentially your “Cox-Knuth Method” is a robust procedure for generating mathematical structures representing deduction over abduction as defined by Pierce and what I find so enticing is the fact that your method, in the general sense, is invariant with regards to context!

Wes Hansen said...

Now I don’t know enough about your method to be certain but, having read most of your papers, it seems there must be a set of general deduction over abduction structures. Assuming that this is true then, computationally, a body of novel facts or, for that matter virtually any type of input, can be represented as a data set z and, of course, every data set z has a power set. Now every element of the power set of z, except z itself, represents a proper subset xi of z and every deduction over abduction structure in the set of all such general structures represents a distinct process yj. So then it becomes a straightforward search for the subset xi and process yj which most closely approximates data set z while minimizing the structural complexity of (xi, yj); the computer generates a logical analogy! If I could build such a system I would apply it to the study of mathematical structures in general via experimental and quasi-empirical mathematics. Anyway, I thought I would plant the seed in the collective mindstream; who knows, it could very well produce some tasty fruit!

Eric said...

Hi Sabine,
I think this is a category of physics that is ripe for the plucking. In fact, I think we can do better than just use macroscopic analogues to model gravity, though I think that is useful. A good way to organize one's thoughts is to categorize forces, including gravity, according to the level of organization of the underlying substance, whatever that is. This has deep resonances with what we observe in the macro world, but can also be used in the micro world if one chooses the appropriate analog force.

The obvious first choice for gravity is the electromagnetic field since its force carrier, the photon, is a long distance force carrier, just like the theoretical graviton for gravity. The phonon is the current best analog for the graviton. Again, using the electromagnetic field I think we can do better than phonons by using the overarching structure of the organizational level of the electromagnetic field as the man principle.

To be continued...

Eric said...

The degrees of freedom of the electromagnetic force in the macroscopic world is the Lorentz Force. What is unspoken, and unnoticed, is that the electromagnetic forces derived in the Lorentz Force equation come from an ORGANIZED electromagnetic field. In other words, previous accelerations of charges that have still left their effects are used to model the electromagnetic fields. Perhaps we can visualize that same field in its unorganized state, a state that has a very high entropy.

Perhaps we can still use the Lorentz Force equation but transform it in a way that it will now apply to a RANDOM electromagnetic field. Let's just try applying the first derivative to the equations of motion of charge in an ORGANIZED electromagnetic field used for the Lorentz Force equation and see if we can get qualitatively the right answers if applied to a RANDOM electromagnetic field. To see if this works qualitatively the degrees of freedom of massive subatomic particle, fermions, has to agree with the experimentally tested values for those degrees of freedom.

continuing...

L. Edgar Otto said...

Wes,
I certainly praise the depth of your comments.

By their fruits you shall know them
Not a sparrow falls that X does not know it as if to supply a landscape of meaning.
Apples start as pairs, one falls, the other grows. The mythical one that fell on Newton's head did not knock him out but upon awakening in the real positive solid world he saw at first an afterglow of stars and string theory.
For every ten thousand acorns that fall only one becomes a mighty oak.

Abduction seems to be a physical or phenomenal fact - but can apply to existing models or be generalized.
A coin can land on a flat abstract plane in more ways than heads, tails, or on edge.
"...Analogue Gravity does not mimic GR..."
Mach and some QM physicists were influenced by Buddhism.
As I mentioned elsewhere to you I too long used the metaphor of a Cheshire QM cat grin.
Some rats leaving a sinking string ship and climb aboard the SS QM gravity to claim her as their own as if their pirate flag not known long before they where a twinkle in there Mother's eye.

Deduction as more a scientific approach is not forbidden and all such logic as with geometry apply, stand or fall together. AI or consciousness is not restricted to barriers, no horizons or all horizons, what is singularity or not.

(Sorry Sabine, I had to respond although I technically cannot be said working in this loop. I did find your moebius band - strip in your last blogpost, a lazy 8 or infinity, sending me back to the books. After a bit of veritgo it suggested solutions long sought and clarified some problems)

I leave you with a metaphor, an open question as to if there is a higher level of discussion for all this. Try to balance or test on it with math or physics the extent of either as realms of ideas:

Imagine a box walls are all mirrors (5 sides are needed at least) and in it a single candle. You see an infinity of reflections fading in the endless (or not, that is the question).
In this box you are the center and observer. But neither light nor awareness can be assumed reflected or connected.
But take each image as an independent universe with independent observers of such boxes and so on..

It seems to me we cannot just say there are as many universes as ants and each can have its Brahmin. Nor that we can write it off as illusion or Nirvana as nothingness. There is at least one more level of thought and physics to which the great and encompassing Cosmic Year could be quite an inadequate conception.

Eric said...

The Lorentz Force equation in an organized electromagnetic field is

F = q(E + V X B)

If we transform those motions to the first derivative of the original the equation changes to

F = q(E + A X B)

I simplified the E side because in a truly random field everywhere is an inertial reference when moving at constant velocity. It wouldn't essentially change from the original equation.

What this says is that in empty space far from any gravitation object the forces would be equal in all directions on subatomic particles because the underlying
unorganized electromagnetic field
would be equal in all directions. Note that I'm including photons in this.

What this would imply is that even in an unorganized electromagnetic field the gravitational force still exists. What would account for this. It must be that the energy density of this unorganized "material" still can change and it accounts for the very weak force of gravity which still works at long range.

continuing...


For the electric force

Eric said...

The interesting part of this whole discussion is when you accelerate a subatomic massive particle. Photons are known to have their spin plane orthogonal to any acceleration. They have left and right circular polarization - that's it. So their degrees of freedom would agree with the fact that they do not have the Higgs. There spin plane does not bend into the direction of acceleration.

Fermions DO have the Higgs so when they are accelerated their spin plane DOES bend into the direction of the acceleration. And they will also deflect up or down as they bend into that direction according to the proven results of the SternGerlach magnets.

So if we try to equate this action to the magnetic part of the Lorentz Force equation it would mean that when you accelerate a particle with the Higgs you automatically invoke a magnetic field that would be orthogonal to the acceleration. Actually this seems to agree with the degrees of freedom all fermions.

But there is one more proven degree of freedom of fermions. This has to be the action of the Higgs changing the spin angular momentum of fermions as the particle cuts in into this INVOKED magnetic field. Fermions actually change angular momentum and this accounts for the increased energy of accelerated massive particles. Photons (aka gravitons) transfer between the random electromagnetic field when in the act of acceleration and that force also changes their angular momentum.

BTW, I think the new policy on Zephir is excellent. If people decided to just comment when they have something meaningful to say it would be a better world. I try to apply that to myself. It would be good Otto if you did likewise.

L. Edgar Otto said...

Eric,
Pardon my thought experiment.
There is s big difference between dimensionless and dimensions.
Also between meaningless and meaning free.
I would welcome being convinced by your view if I did not think it a logical but coincidental case. Maybe my mind is just a non linear stray voltage accelerator afterall, luck if the draw in some jumbled analog of cosmic rays and condensation spectra.
I find Cabali-Yau overly simplistic so can we make 3D analogs of fractal sets or not.?
I leave you with one of Wes's Cheshile Grins. )

Eric said...

Otto, yes you like to talk, and you do it very well. But I think rather than actually listening or absorbing info you are always thinking about what you are going to say next. I've found that many people are like you in that they enjoy being annoying and content free... either saying meaningless drivel or repeating the same thing over and over again, ad infinitum. That's why I no longer spend much time here.

Trolling, by any other name, would stink as bad. And if I enjoyed it then I would spend as much time here as you do.

L. Edgar Otto said...

Eric,
I do not know which you are. I am here quite by accident. I did not mean to interrupt the continuity of your posts.
Zephir 's problem I feel is not necessarily his concepts but unwarranted disrespect for Sabine 's indulgence. Sorry, if I have nothing to share with you. But make no mistake, with the honor to be here with care for foundations and frontiers one day you may see you walked among the gods.
In novels were characters take on a life of their own and nature does not allow such characterization of forces as the last word Nobel novels use big words.Who aspires to be spoken to as if we are children? Peace.

pete said...

Great article,

I have to agree with Wes (though I'll leave all of the mystical stuff and religious connotations out) when he talks about mathematics and its relationship with the world. I just don't see how the idea of mathematics being a "useful tool" holds any water when you see pure mathematical structures being used to predict particles years before they're discovered. In addition to this, we don't have free reign in mathematics to create anything we'd like and "construct" different theorems out of thin air. There is an inherent structure involved in the formal language of mathematics/logic, and these structures are present in the physical world.

I also want to stress that being a Platonist/mathematical realist should be totally divorced from notions of supernaturalism that some might associate with Platonic theory. It's not even about a world out there or a grand Theory of Forms; its simply the idea that mathematics has an objective existence independent of any humans thinking about it. This idea can be easily incorporated into a naturalistic philosophical outlook. Before one rejects that notion outright, I would take the time to really think long and hard about the so called 'concrete' or 'physical' objects that are held near and dear to so many of us.

I identify as a physicalist to this day, but I always realize that solid objects are actually made of 99.9999% empty space, with subatomic particles being made of 'mathematical point particles with no intrinsic structure' according to current theory. The theories of everything out there don't do much better, claiming them as 'vibrating strands of energy' whatever the hell that means. If things in the real world are so ephemeral, is the notion of abstract structures being present in the real world really that scary and absurd?

Sabine Hossenfelder said...

Wes,

You write:

"Sabine, I wholeheartedly disagree with you regarding mathematics! [...] I’ve spent a great deal of time meditating on this argument and if you truly understand it and its implications, there is no way you can argue that mathematics – Platonic forms – have no existence"

That is almost certainly true because "existence" is ill-defined. It is also not what I have said, you entirely misunderstood me. What I said was not that mathematical structures don't "exist" I said what if they're not sufficient? My problem with Tegmark's multi-level multiverse is not that he claims mathematics is real, but that he stops at mathematics. I don't know how we can possibly tell that mathematics is the ultimate and final language to describe reality. Best,

B.

Sabine Hossenfelder said...

Pete,

Please see my reply to Wes. You're talking past me. Best,

B.

DocG said...

Sabine: "I don't know how we can possibly tell that mathematics is the ultimate and final language to describe reality."

Let's underline that last phrase: "to describe reality."

Seems to me that what you (we) are talking about is not simply the description of reality but the representation of reality and one should clarify that as follows: the representation of reality in the abstract, and to the mind. So in this respect math could be understood as analogous to the paint and canvas artists have used to represent reality concretely, and to the eye.

In both senses math and (realist) art must be understood as media, not processes that are in themselves real. On the other hand, a noted Canadian once claimed that the "medium is the message," so . . .

Vincelovesfreefood said...
This comment has been removed by the author.
Vincelovesfreefood said...

I'm not a string theorist, but I highly doubt that string theory is falling out of favor. Thousands of people are still working on it.

And I'm not expert on analogue gravity, but studying analogue gravity makes as much sense to me as using the rubber sheet analogy to study general relativity in the solar system.

Wes Hansen said...

Sabine,

I apologize, I should have posted my comment to the Nature=Mathematics post. I became interested in the comment which links to said post:

“Consider that mathematics is not in fact a language able to describe all of nature. What would we do if we had reached its limits?”

You suggest that we can use simpler systems to model, hence, distill information about, more complex systems. But all we can ever hope to know about any system, regardless of complexity, is its regularities and the relations between said regularities and this IS mathematics. So then I follow the link to your Nature=Mathematics post and find:

“So where does that leave mathematics then? Mathematics is a tool that we use to improve on our models, it’s a technique that we force our thoughts through because it has proven to be incredibly useful. Nevertheless, the point I am trying to make is that this usefulness doesn’t mean a model actually extracts some mathematical “substance” from reality.”

And this is the argument that I find highly questionable to say the least. I thought I explained existence rather well; that was the whole point of the venture into Buddhist philosophy. But, to be more practical, if not as precise, consider the definition of George Ellis (http://arxiv.org/ftp/arxiv/papers/1212/1212.2275.pdf):

“Causation: The nature of causation is highly contested territory, and I will take a pragmatic view:

Definition 1 – Causal Effect: If making a change in a quantity X results in a reliable, demonstrable
change in a quantity Y in a given context, then X has a causal effect on Y.

Example: I press the key labelled “A” on my computer keyboard; the letter “A” appears on my
computer screen.

Existence: Given this understanding of causation, it implies a view on ontology (existence) as
follows: I assume that physical matter (comprised of electrons, protons, etc.) exists. Then the
following criterion for existence makes sense:

Definition 2 – Existence: If Y is a physical entity made up of ordinary matter, and X is some kind of
entity that has a demonstrable causal effect on Y as per Definition 1, then we must acknowledge that
X also exists (even if it is not made up of such matter).”

So now, assume, for the sake of debate, that Evolutionary Theory is a reasonably close approximation to that which takes place ontologically. Then Information Gathering and Utilization Systems (IGUSes) evolved the ability to gather and utilize information, which is to say, recognize pattern and make logical inferences about said patterns, because it confers upon them a survival advantage: why? I believe most evolutionists would say because the environment said IGUSes have evolved in is patterned and logical; IGUSes, self-aware logical patterns, i.e. mathematical systems, evolved in a mathematical environment with the ability to discover and explore mathematical structures because it gives them a survival advantage, said advantage due to the causal efficacy of said ability . . . or, perhaps, because the evolution of our mathematical universe demands it; ) And aside from a few people of questionable mental stability, I don’t think anyone would deny that mathematics has a demonstrable causal effect on physical entities.

Wes Hansen said...

Now the whole point of posting the email I sent to Kevin Knuth was to point out that mathematics, like science, is a PROCESS which includes an entity z, a proper subset of entity z called, purely for convenience, entity x, and a PROCESS y such that when entity x is applied to process y the entity z, or a reasonably close approximation thereof, results. I thoroughly understand what your post is fundamentally about but at the end of the day, studying simpler systems in order to gain an understanding of more complex systems is exactly what mathematics is about and any knowledge you have about the simple system is naturally codified in mathematics; you’re just making a logical analogy, as I pointed out.

I agree wholeheartedly with your critique of Max Tegmark’s MUH but I also agree with Tegmark that our universe is a mathematical structure. And in the world of reductionist science, guess what that means: mathematics is fundamental (see Murray Gell-Mann’s, “The Quark and the Jaguar,” pages 108-109).

“This is typical of mathematics, which is not so much about numbers as most people think – it is really about patterns. Sometimes numbers help, other times they get in the way. Many exercises in mathematics books are really asking you to find the pattern by solving a general problem (with letters) instead of a special problem (with numbers) . . . Mathematics expresses the pattern by symbols . . . “

- Dr. Gilbert Strang, MIT

Mathematics is the general case while science is the special case; hence, mathematics is more fundamental. And this is why I mentioned Omega; if mathematics has limits then Omega suggests that said limits are a function of the axioms utilized rather than of mathematics itself.

Finally, with regards to the relation thought has to reality: traditional materialists assume that Laws of Form pre-exist Laws of Thought; traditional idealists assume that Laws of Thought pre-exist Laws of Form; I, a non-traditional Idealist, assume that Laws of Thought and Laws of Form are of co-dependent origin such that reality itself emerges due to a bootstrap process involving both, the one feeds and feeds off of, the other – it takes two to play this game!

That said, thanks for responding to my comment . . .

Eric said...

Hi Sabine,
I'd like to illuminate one final point and I promise to shutup forever more on this blog. Non- neutral massive charges do not have linear paths through empty space. Whenever they are accelerated they deflect. This corresponds to the up-down degrees of freedom shown in the Stern-Gerlach apparatus. But a neutral massive particle made up of individual non-neutral individual massive particles will have a linear path through space (curved if its in curved space).

In other words those two up-down degrees of freedom are suppressed for the individual charged particles within the whole. But they still have an additional degree of freedom so that there is no information loss to the particle when accelerated - that degree of freedom represents a change in intrinsic angular momentum.

I promise to shut up forever about this now and assume you now have enough info to reject or contemplate this idea.

Best Wishes,
E

L. Edgar Otto said...

Wes,
Let us consider there is some sort if general background. (Martin Gardner used the term Phaneron).
We debate, discover, or impose some sort of understanding on it and even wonder if it is there regardless of how we think about it or ourselves.

If I map it as an invariant ordered coordinate system of crystalline pixel like regions where pixels may include issues of curvature I get a decidedly Euclidean concept of phaneron as Omega.
But each pixel may be an omega as a singularity point or a time like linear continuum.
Which absolute omega do you suggest, that which encompasses all that is phaneron as QM or that as GR?
Can we not imagine a combination?
Let us leave aside the usual issues of what makes up the phaneron, physics,math, logic, supernatural concepts, consciousness, whatever as we generalize to encounter evermore complex analogs of the same paradoxes.
What I simply find remarkable is that on this canvas by connecting the dots, counting them, filling in the colors, we can draw something as fundamental as an orthogon in any dimensional space.
If math as geometry alone were the start without an intelligible ordering can it intelligibly describe the phaneron?
We see better why some follow down to the models they do. But despite the wonderful gains in tech it us still a long way before our computers with or without memory, foresight, and issues of scale and energy can come full circle to outdo the thinkers with simple pencil and paper.

Sabine Hossenfelder said...

Vince,

You're confusing the value of a function with its derivative. Also, most of the string theorists are working on AdS/CFT, which might be many things but not an approach to quantum gravity. Best,

B.

Giotis said...

“…which might be many things but not an approach to quantum gravity”
It’s definitely an approach to QG. The theory in the bulk dual to the Conformal field theory must be a consistent theory of QG since the CFT is UV complete.
Did you know for example that you case use AdS/CFT to understand space-like singularities in the bulk beyond the SUGRA approximation?

L. Edgar Otto said...

Giotis,
That is simply a limited view.
Many more things in physics or math as intelligible (IFT) than by consistency.
Consider gluon and quark jets as influencing (TD just wrote on this). The bumps and anomalies vanish in a higher intelligible conception.
One can measure particles in a region of space and use statistical methods without a higher concept of gravity or what parallels may exist as to causality, which is over zero or infinity is excluded as a model of singularity and the theory be consistent.
One is tempted to conclude (in comments with JH) at a certain high energy as if a higher dimensional abstract atom pair production and thus protons can arise from pressures in empty space (a steady state model really) Such questions are still philosophic speculation. These consistent theories really need Sabine's
"Scientific Phenomenology" so as to.extend useful mathematics itself and to evaluate other abstract intelligible models.
I do not speak for her and cannot claim
I know nearly enough physics. But I do not read her as excluding any consistent model as many exclude hers. That perhaps should teach us something important. But keep inquiring that is worthy of scientific progress also. I am reminded of the builder of polytope 4D models that like tunneling thru a mountain from two directions the tunnels met as if in half blind digging the model fit together.

kashyap vasavada said...

Hi Bee: I am not sure how experiments or theory in condensed matter would help high energy physics.Suppose they find monopoles,axions,Majorana fermions or even black holes (as they may have found some of these as quasi-particles already)would it make any difference as to the existence of these as actual particles at high energies? I am not even sure if such efforts have helped in finding correct directions for theory.

pete said...

Thanks for the input Bee, didn't mean to talk past you!

I would definitely add that I can't really imagine anything not being amenable to mathematical description. Mathematics can be thought of more as the study of structure (as opposed to everything being built from numbers, which are simply fixed points in the structure of the natural numbers), which the universe clearly possesses. Even if you delve into chaos and randomness, these are still things that can be mathematically quantified.

At the risk of delving into metaphysics and philosophy when our focus here is more on the hard science, I would say that the universe, multiverse, and just existence in general is necessarily some sort of structure. That makes it amenable to mathematical treatment (hell maybe even 'mathematical' in and of itself.

Sabine Hossenfelder said...

Giotis,

As I've said several times before, when I say "quantum gravity" I mean "the theory of quantum gravity" which explains certain facts about nature, eg what happens to collapsing matter, what happened in the beginning of the universe, what happens to the gravitational field of electrons going through a double slit etc. What you mean when you say "quantum gravity" seems to be "a theory that has something with quantum and something with gravity". This might or might not address the problems I listed - in our universe. I will certainly agree that string theory is "a" theory of quantum gravity. I will not agree that it is "the" theory of quantum gravity that we are looking for because evidence for this is nil. Having said that, applications of AdS/CFT to certain strongly coupled systems are all well and fine and do something with quantum and something with gravity, but also do not address the problems I listed above. Best,

B.

Sabine Hossenfelder said...

kashyap,

I don't have much to say about that because I'm not sure either. But who knows, it seems quite possible to me that there will be a mutual inspiration and exchange of tools and techniques which might or might not turn out to lead to something. Best,

B.