As previously mentioned, I was recently at the FQXi conference on the Azores. FQXi, the "Foundational Questions Institute," has the mission "to catalyze, support, and disseminate research on questions at the foundations of physics and cosmology." I work at an institute whose research is "devoted to foundational issues in theoretical physics." Fundamental, foundational, basic – what do we mean with that? What should we expect from a fundamental theory? What are the foundational questions? This was one of the questions we discussed at the FQXi conference, and while several of the participants contributed, I don’t want to blame any of them for the following summary. So what is Fundamental?
A theory is fundamental if it cannot be derived from another, more complete, theory. More complete means the theory is applicable to a larger range. Note that a fundamental theory can be derivable from another theory if both are equivalent to each other (though one could plausibly argue then one should consider both the same theory).
Throughout history, the search and discovery of more fundamental theories in the natural sciences has lead to a tremendous amount of progress. That however is not a guarantee it will continue to be the path to progress. The issue is in the expression “cannot be derived” which could mean three different things:
Cannot be derived, version I: not possible in principle.
It might not be possible because it is not possible. Believers in reductionism think this is not the case for the laws of Nature we presently know: they should all follow from one most fundamental "Theory of Everything." While it is true that reductionism proved to be very useful and we thus have good reasons trying to continue it, there is no knowing the laws of Nature always allow a reduction. We would then be left with layers of theories that describe Nature on various scales that cannot ever be derived from each other, and thus have to be considered equally fundamental. While we presently don’t have evidence for this, it is a self-consistent point of view.
In the previous post on Emergence and Reductionism, I explained this is known as “strong emergence:” Emergent features on a higher level require a theory that cannot be derived from the underlying one. We previously discussed the paper “More really is different,” in which Gu et al offer an example for a system that does have emergent features, but it can be proved these are not derivable from the underlying theory. Granted, the system they consider isn’t particularly natural (see discussion on earlier post), but it gives you an impression of what this case means.
Cannot be derived, version II: not possible in practice
It might not be possible to derive emergent features from a more fundamental theory because of practical constraints. For example, it might take more computing power than we will ever have available, or more time than the lifetime of the universe to do it. It might take infinitely precise knowledge of initial conditions; it would make it necessary to measure parameters more precisely than we can plausibly expect ever; it would take a detector the size of the galaxy; etc etc.
Cannot be derived, version III: not yet possible
We might simply not have a derivation because
Okay, now what is fundamental?
The problem is that at any one time we might not know which of these 3 cases we are dealing with. The exception is if we had an actual proof for the impossibility of a derivation. (But then a proof is only as good as its assumption.) We are thus left with our assessment of the situation, which might change with better understanding of the theories we have. In some cases there is a pretty clear consensus on whether a law is fundamental, in other cases it might not be so clear.
Examples
- Take for example the Tully-Fisher relation. It relates the luminosity of a spiral galaxy with the 4th power of its rotational velocity. It is a useful heuristic relation, extracted from data, and has predictive power. There is no derivation of that relation; yet I doubt any physicist would argue it is a fundamental law. Instead, with increasing understanding of astrophysical processes, we will finally be able to derive it.
- Stefan came up with an interesting historical example, the Titius-Bode law according to which the distance of planets to the sun grows exponentially with their order in the sequence. The law works pretty well up to Uranus and fails with Neptune, but the far out planets were not known when the law was suggested. People once thought the planets' orbits are fixed by fundamental principles, but with better understanding about the gravitational interaction, the "law" was downgraded to a "rule," or possibly just a coincidence. Though with further knowledge about the dynamics relevant for the formation of solar systems the approximate validity of the relation might be an "emergent" feature one can expect to approximately be valid.
- Then there is of course the often discussed question whether it is in principle possible to derive all of biology, psychology, sociology and economics from physics and thus physics is the most fundamental of all sciences. Many physicists believe this to be the case. For that reason, one of my profs used to refer to physics as “the queen of sciences” (physics is a female noun in German). But we are far away from practically achieving such a derivation, and we thus do not actually know which of the three cases of “cannot be derived” we are dealing with. Already at the level of proteins things get murky, and we should be considering the option that indeed biology might be as fundamental as physics in the sense that it cannot be derived - cannot be derived in principle, not ever.
One of the reasons why the first case might apply even though reductionism has worked so well over a large range of scales is that in some areas of science the separation of scales might no longer work, and/or there might be no scale that can be used for separation. In physics typically the scale is energy, and we are used to neglect things that happen at energies much higher (wavelengths much smaller) than what we are probing. We know this is a safe procedure backed up by the framework of effective field theories. In contrast, a system like our societies does not simply have higher level organizations constituted out of smaller elements, such that these smaller elements define the "emergent" properties. Instead, these organizations also act back on the elements that they are built of and change their behaviour.
Coming back to physics, there are of course the questions that are hotly discussed at the front of research today, those asking what is fundamental in our present theories. Can the masses of particles in the Standard Model be derived from a more fundamental theory? Are space and time themselves emergent from an underlying theory (generally expected to marry quantum mechanics with general relativity). Is quantum mechanics fundamental, or can the quantization procedure and the measurement prescription be derived from a more complete theory?
I don’t know. But I really, really want to know.
Aside: Some weeks ago Clifford also wrote about the question what is fundamental, anyway? Since he sent me the link to make sure I don’t miss it, I can’t get away without mentioning it. Clifford is mostly concerned with people who use the label “more fundamental” to mean their work is more relevant. While that might happen, people using superlatives to claim their own work (life, opinion) is “more this” or “more that” than others’ is hardly remarkable, and certainly not specific to theoretical physics. The other point Clifford makes is that “Nature recycles good ideas,” meaning that the framework of fundamental theories can often also be found to be useful in non-fundamental areas - and the other way 'round. It is an interesting point, but it addresses more the question where one can find inspiration, not what is actually fundamental.
Bottomline
A theory is fundamental if it cannot be derived from a more complete theory, yet there are different reasons for why we may not be able to derive it: It might not be possible in principle, it might not be possible in practice, or we might not yet have the sufficient knowledge to do it. In general, we do not know which case we are dealing with. Misjudgement of the situation can waste a lot of time and hinder progress. If we wrongly believe a property is not fundamental, we risk searching forever for a more fundamental explanation that doesn't exist. On the other hand, if we believe something is fundamental even though it isn't, our understanding of Nature will remain limited. What is sure though is that understanding always starts with a question.
Hi Bee,
ReplyDeleteThanks for the link. I don't think you could have read my post too carefully, since you... er, fundamentally ;) ... misunderstood and somewhat trivialized the points I was making. The things you interpret as my points are really not my central points at all. Matters of "relevance" and "inspiration" take the matters at a rather too literal and/or superficial level. But, that happens... not to worry. Others can make their own interpretations by reading the source.
Best,
-cvj
Hi Bee, thanks, I'm fascinated by this idea. I think the "Turtles all the way down" story is very useful for considering what might be fundamental (for those who haven't heard the story, it is described here).
ReplyDeleteIf reality really is "Turtles all the way down" then we just get a series of endless "Why?" questions: "Why is the sky blue? Because molecules scatter light. Why do molecules scatter light? etc. etc. and you end up in infinite regression with nothing being truly fundamental.
However, some people suggest (Paul Davies) that there might be a "levitating Super Turtle" which supports the whole tower of turtles, the existence of which need not be explained by a "Why?" question, it is simply self-evident why it exists. That Super Turtle would then be fundamental.
However, personally I can't really see how a Super Turtle could ever exist. There will surely always be the potential to ask "Why?" and take things one level lower. In which case infinite regression is unavoidable and nothing is truly fundamental.
The only other way I can see of avoiding infinite regress is if the "Why"s loop round in a circular fashion, in which case you could endlessly circle the loop. But again in this case nothing is truly fundamental.
Hi Clifford,
ReplyDeleteYes, possibly I misunderstood. Sorry if you feel badly represented. I'll leave it as it is since, as you say, people can read for themselves. Cheers,
B.
Hi Andrew:
ReplyDeleteIndeed, I summarized a talk by Paul Davies here: Turtles all the way up :-)
B.
Hi Bee, thanks for that link to your earlier article. I strongly suspect the concept of something being "fundamental" is a human invention with no basis in physics. Should be an interesting discussion.
ReplyDeleteHi Andrew,
ReplyDeleteWell, we know there are some theories that are more fundamental than others, so the order relation certainly exists and is meaningful. Whether or not there exists something "most fundamental" is a different question though. Best,
B.
I remembered with this entry an article of G. Ellis about reductionism in Physics Today (2005). Also, as you mention, it could be well that is some more fundamental theory than QM and this is almost always just mentioned as an idea almost aside the relevant modern physics; it was nice at this respect the paper by 't hooft "The mathematical basis for deterministic QM" http://arxiv.org/abs/quant-ph/0604008 .
ReplyDeleteHi Bee: "we know there are some theories that are more fundamental than others"
ReplyDeleteI wouldn't say that one step further down an infinite road is actually "more fundamental". It's no nearer the destination. Infinity + 1 = infinity
I propose to amend the discussion of what is Fundamental with the notion of "fundamental equivalence". If, given two theories, each can be derived from the other, then they should be considered fundamentally equivalent. Neither is then more fundamental than the other.
ReplyDeleteIf properly applied, this notion has the potential to obviate most of the never-ending talk about which formulation of quantum mechanics is more fundamental. In reality... well, one can still dream. :-)
Dear Bee,
ReplyDeleteI see a problem with "derivable".
E.g., the properties of biological cells ultimately derive from chemistry and chemistry from quantum mechanics. So in that sense, the theory of one is derivable in principle from the other.
On the other hand, I doubt we can show, even in principle, that cells are necessary, given quantum mechanics, or that cells require quantum mechanics and are not possible with any other theory of mechanics.
So all we will be able to show is that QM is sufficient for cells to exist, but not that QM is necessary; and not that cells are required to exist if QM holds. So it is not much of a derivation, and so the theory of cells should be considered to be fundamental.
-Arun
Founding postulates are more fundamental than theory. Euclid and Newton were incomplete. Classical (GR) and quantum gravitation theories (string theory) assume the Equivalence Principle. Teleparallel theory in Weitzenböck spacetime does not. EP = True is GR; EP = False are explicit cases...
ReplyDelete...with one tested. The only allowed large amplitude EP violation is parity: left and right shoes. Quantum gravitation theories supplement Einstein-Hilbert action with an odd-parity Chern-Simons term. Take the hint.
Somebody should look. Yang and Lee thought the same about the Weak interaction - and for the same reason.
...with one untested. (sigh)
ReplyDeleteHello Bee
ReplyDeleteShould the question be restricted to physics? It seems to me (non-scientist) that reductionism cannot work even in principle for living/evolng entities per the well known arguments (emergence, agency etc). Do you and your readers in fact accept this tacitly? It would be interesting to hear from an expert on the living world, say a microbiologist
Hi Morris,
ReplyDeletehad you read what I wrote you'd have noticed I did not restrict the question to physics. I recommend you first read, then comment. Best,
B.
Hi Igor,
ReplyDeleteyes, I wrote essentially the same, didn't I? Best,
B.
Dear Arun,
ReplyDeleteI am afraid I don't quite understand. Without quantum mechanics, atoms wouldn't be stable and cells wouldn't exist at all, thus quantum mechanics is certainly necessary for cells to exist. It might possibly be you can find some other way to render atoms stable, and find some other theory in which cells can exist, but then I was saying the more fundamental theory should be more complete in the sense that it describes a larger range or phenomena. (Maybe I should have added it also shouldn't describe non-existing phenomena.) Thus, not any theory in which cells emerge will do. Best,
B.
Hello Bee
ReplyDeleteThanks for replying. I have in fact read your interesting post. My first note was too vague/diplomatic. Phrased in the radically opposite (but not in malice) direction the question becomes: What justification is there for considering that fundamentality in physics is relevant to say biology, or is this a dead or dying issue? This is a question and not an assertion and I would be interested what your readers think
Hi Morris,
ReplyDeleteWell, if you read it, you apparently didn't notice I replied to you question already. I said if you believe in reductionism then biology should follow from physics. Since reductionism has worked so dramatically well, it isn't surprising many people believe this to be the case. I also said that however we cannot know this is actually possible, for all we know we might be dealing with any of the three cases.
As to the question in how far it is "relevant," that's a different issue altogether. Even in physics, you can have more or less fundamental theories, but being more fundamental is in some limits irrelevant, thus you can use a less fundamental theory which is often easier to deal with. Best,
B.
Hi Bee,
ReplyDeleteA nice job of discussing the main points as to what is considered as fundamental theory. It’s also correct to point out that it could be nothing more then the fool’s gold of physics. For me however is to consider is that we still might not understand enough about what it is we are capturing to describe as being reality. Let me tell you what I mean by that.
If we first look at the ancient Greeks view of the world, they imagined it to be captured within the then known elements of nature, being air, water and fire; where to be able to explain the nature and actions of all of these would have been considered a having complete understanding of the physical world . A few millennia later, Newton readdresses all this by explaining what seemed then to be the central ingredients, being the motion of all bodies, including the recognition, description and action of gravity Then after only another two hundred years it was thought that with a few more tweaks, all that we know to be reality would be explained to be understood with these laws at the base. However, with the discovery that the world was also affected to be driven by the action of waves (Fresnell & Young), as well as by the action as expressed before, this all altered again. Then of course this brought us to our current place where all of we consider being the physical world is captured within SR/GR and quantum theory, which has divided our perspectives incompatibly between the very small and the very large.
This may seem a bit long winded ,yet what I’m really attempting to express is that I think we are caught up again in our own arrogance, in believing that we know what forms to be a complete description of what we are attempting to understand and codify, which we call simply reality. The evidence is already there of course that we don’t, with having the largest portion of matter to be something we didn’t expect to exist, not the least to admit to be uncertain as to what it is and with energy we find much the same. We’ve also found that our world which was once thought to be shaped and ruled by symmetry and simplicity is also defined by the the breaking of it for reasons not fully appreciated and with simplicity leading to complexity and order forming out of both random and chaos by a mechanism(s) yet unidentified.
So my (truly) humble opinion regarding our current state and position is to suggest we don’t as yet know enough about what forms to be reality to be able to offer solutions intended to explain it fundamentally. The truth being reality is what we are able to sense of it and science is not just to serve to increase our understanding of how it is like it is, yet also expands our senses to have us know what it is. We’ve gone from Ptolemy’s world, where his celestial spheres functioned only as its adornment, to a universe that is vast and expanding, where we and our island of consciousness represent to be a portion almost too small even to register as being perceptibly relevant within it. I therefore still believe it’s a little premature to talk about discovering meaningful and unshakable foundations before we more fully understand what they are required to support.
Best,
Phil
cvj:The tools we describe them with constitute quantum field theory, and we don’t need to declare whether or not the quantum fields and associated baggage (gauge symmetry, etc) are “out there” in Nature in some Platonic sense. Why bother? We are physicists and not philosophers. We need not (should not) confuse our tools with the things we are trying to describe with them. The same goes for string theory. If we find a place where string theory gives the best working description of the phenomena being studied and observed, why not just call it what it is? It is string theory that is being used, not “the tools of string theory”. There is no distinction.
ReplyDeleteI gather one might recognize where such an allusion can be made in my own perspective, while trying to orientate one back to what and where we place ourselves in this excursion to understand nature as it is.
The relationship and way the interconnectivity of the pursuit to understand encompasses different aspects of the sciences to know that the fundamental thing here is to know that such symmetricalness can be seen all the way down as "an intricate part of" in questing to see science in this whole new perspective.
It's cultured significantly from my perspective that such work takes on the assumptions of all that came before it, in order to progress to where work and theoretical perspective sits now.
Placement of the Einstein quote in the Azores post explains this understanding.
Best,
Best,
Dear Bee,
ReplyDeleteLet me try with a simpler example.
For a computer to exist all that is needed is switches with certain properties. The existence of such switches places no constraints on the underlying substrate; nor does our current fundamental theories have as a necessary consequence the existence of such switches.
-Arun
Dear Arun,
ReplyDeleteWhat you are saying is
a) An emergent theory can be consistent and if you don't aim for deeper understanding (make better experiments etc), you don't need a more fundamental theory. You can understand what your computer does without knowing QCD. If you use it as a fixed target in a particle collider you might need QCD.
b) While a theory can allow for the emergence of a specific feature, not all initial conditions might give rise to this feature, and we might wonder how common a particular scenario is. (I find it possible the emergence of computers or AI might be more generic than we understand today).
In either case, it could be "derivable in principle," thus I don't understand the problem. Best,
B.
hi Bee,
ReplyDeleteI'm not clear whether your "not possible in principle" version of "cannot be derived" includes incommensurability. I imagine you will respond that it does, but your discussion confines itself to reductionist reasons for us being unable to derive one theory from another. The mathematics of classical and QM Physics, for example, are differently axiomatic, shall we say. Similarly, the relationship of Special Relativity to Galilean relativity.
The question would be whether this gives you a 1a and 1b?
Hi Peter,
ReplyDeleteNot sure I understand the question. I didn't claim there is a complete order between any two theories in case that's what you mean. There are certainly theories that are not in any relation to each other, but I was talking about 'can (or cannot) be derived from a more complete theory,' where 'more complete' means it applies to more phenomena of Nature. You can of course have two theories that just describe other parts of nature. Not sure why you pick these examples in particular, as they don't fall in any of the 3 'cannot' cases. Best,
B.
What about fundamental concepts?
ReplyDeleteI can postulate a field as fundamental and fix all the parameters in a theory by the properties of this fundamental notion.
All the other concepts in the theory must be derived notions.
Or I can postulate the string as fundamental and everything else should be derived from it. Its length for example should fix the parameters in the theory etc.
Are you saying that there is a one to one correspondence between a fundamental theory and a fundamental concept?
Hi Giotis,
ReplyDeleteNo, I didn't say that. I didn't say anything about fundamental concepts at all. I think what you mean with that is what are the axioms of a theory (fundamental or not). Best,
B.
You talked about the concept of space-time though. Whether it is fundamental or not.
ReplyDeleteEach fundamental theory must have one and only one fundamental concept at its core or not?
Hi Giotis,
ReplyDeleteIndeed, I talked about space-time. You are right, that is an example for a concept rather than a theory. What I meant is General Relativity, a theory for the dynamics of space-time, that might be replaced by a more fundamental theory in which space-time is emergent. The concept itself however doesn't make a theory. Best,
B.
Ok. So the answer to my question:
ReplyDelete"Each fundamental theory must have one and only one fundamental concept at its core or not?"
is no, it doesan't have to?
Hi Giotis,
ReplyDeleteNo, it doesn't have to be only one concept. The fewer concepts though, the closer you get to the ideal of a 'unified' theory in which all follows from one simple prescription, and that certainly has a lot of appeal. Best,
B.
Yes, there should be some short of a correspondence between a fundamental theory and fundamental concepts.
ReplyDeleteHi Giotis,
ReplyDeleteFor the most part it’s still truth and beauty, which translates today as Occam’s Razor and Symmetry, Einstein’s take on the former was to say the following:
"The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience"
Best,
Phil
Phil, what's the time in Canada? Are you still blogging in the middle of the night:-)
ReplyDeleteHi Giotis,
ReplyDeleteIt’s just that I got up early as later on I have to test my knowledge of Newtonian physics with my control over a small sphere hit by a stick while walking over green spaces. The physics I understand well enough, it’s the hitting it as I’ve imagined I’ve never been able to master:-)
Best,
Phil
Bee: What I meant is General Relativity, a theory for the dynamics of space-time, that might be replaced by a more fundamental theory in which space-time is emergent.
ReplyDeleteIf what your are left with is a "frame of reference" and this is derived from a "fundamental theory" then I would say you are on the right track.:) I only say this "by example" and not by the hypothetical. Then examples of lets say "Penrose" seem to make there way into how we are perceiving the reality of the space time? Where are we observing from?
So if we are saying that the frame of reference is derived from some other state then one may say indeed that space time is emergent according too the theoretical implication string theory may have pushed forward in concepts for the future?
While for a lay person like myself, the complexity of the subject of string theory is a lesson in it's intricacy that Hooft gave by his own example does not invalidate the move toward that future based on the tools needed used in awareness resulting in complex and abstract notions in mathematics?
It's part of that journey now.
Brian Greene:Sure. One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory. So the question is, where are these extra dimensions? One suggestion is that they're all around us, but they're small relative to the dimensions that we directly see and therefore are more difficult to detect. The Elegant Universe
So to me while learning, this is a huge move in my own conceptual undertaking and such assumptions become elements fostering new perceptions with regard to that cross pollination. You are truly "grokking" the experience.
Best,
Deer Bee,
ReplyDeletehi Giotis,
concerning What about fundamental concepts?:
Finally I've managed to read also Clifford's post, and my impression is that he tires to make just this point.
With "fundamental" he denotes not only the "building blocks" or "fundamental entities" of a theory, but he uses the word also (if I get him right) to talk about "elementary" theoretical concepts, which then may apply to all kinds of systems, let them be fundamental in the "building block" sense or not. It is in this sense that he talks about "nature recycling a cool idea".
It may be even harder to define what makes a "fundamental concept" than a "fundamental entity", but I think it is a very interesting idea.
Cheers, Stefan
Dear Stefan, Giotis,
ReplyDeleteI don't think the idea of such a 'fundamental concept' makes much sense, since it a concept has no clear connection to its relevance in describing Nature, and thus an ordering of what is more or less fundamental is futile. In contrast, my definition for a 'more fundamental theory' has, via the range of phenomena it can describe.
The notion of 'recycling ideas' means not a concept is more fundamental than others, but that we should better speak of 'common concepts' in our (more or less fundamental) theories. Then however I would argue the most common concept is mathematics, and that isn't particularly useful knowledge, neither does it have any connection to how fundamental a theory is. Ergo, I think it is more useful and more insightful to speak of theories instead of concepts, of the science instead of its language. Best,
B.
Hi Stefan and Bee,
ReplyDeleteI can understand things only through examples. Sorry for that:-)
So an example of Clifford's "elementary theoretical concepts" could be quantization i.e. an underlying fundamental principle?
A fundamental concept (or entity) is what you postulate in your theory. Something you can't derive.
Here is how I imagine the correspondence between a theory and its fundamental concepts (or entities if you like) again with examples:
Old QM: point particles and fixed space-time are fundamental.
QFT: fields and fixed space-time.
GR: postulates the full dynamical metric (space-time as another field) as fundamental.
kaluza-klein: again the dynamical metric field is fundamental, but in 5D. It gives GR and EM in 4D.
String theory: strings, p-branes, M-branes, D-branes are the fundamental concepts. Everything else is a derived concept. No background independent formulation yet though.
AdS/CFT: The CFT on the boundary is fundamental.
Canonical QG theories (e.g. LQG): They just quantize the full dynamical metric. My understanding is that the metric as a field is again the fundamental endity and not the chunks of space-time.
I understand that Bee suggests that we should forget about the notion of the fundamental concept or entity and we should characterize only the theory itself as fundamental. I'm not sure how this works in practice though.
By Thor! Bee, yes, you did write about equivalence of theories. I must have missed it. In my defense, it only came up once, way at the beginning. Not enough redundancy to be idiot proof. :-)
ReplyDeleteHi Giotis,
ReplyDeleteI think we are talking somewhat past each other. What I mean with a theory is a set of axioms (together with an explanation what the quantities describe, as usual). The theory altogether does or doesn't have the power to describe Nature, and it might do so in a larger or smaller range of phenomena. If you however pick out only one axiom (eg things are strings) and call it "a concept" I don't know in which meaning it is more or less "fundamental" than other concepts, because there is no clear definition for what "more fundamental" means if you have no theory that connects you to Nature.
As I mentioned above, you could say a concept is more "common" than others. Eg you might say it is "more common" for a theory to be quantized than to be classical if you count dumbly 1,2,3 versus 1 in the Standard Model. But then I don't know if that's any meaningful measure.
About your examples: Please note that these don't give you a theory without further input (like a Lagrangian, an equation of motion, gauge groups, etc). You are using the word "fundamental" to mean it's an axiom in some theory, whereas I am talking about "fundamental" being about describing reality.
(Aside: Kaluza Klein with the metric as dynamical field does not give GR and EM in 4D, it only gives the free equations since spinors are missing.)
Best,
B.
I would personally be shocked to learn that there's something in "biology" that is uniquely "fundamental". It's complicated, but not magical, and I can't imagine that "new laws" are required to describe it in terms of those laws; just much more powerful computers. That said, if the computer has to be as complex as the system one is trying to simulate, I suppose for all practical purposes it's pointless to do that except as an ostentatious display of brute computational force. Better to simply study the natural system directly, then.
ReplyDeleteAnyhow, I tend to think of "biology" as a more qualitative state in a continuum of degrees of self-organization, which is a very hierarchical phenomenon that we see all the time in nature. Beyond it occupying perhaps the "highest" level (in terms of its thermodynamic properties, e.g. its "negentropy") in this hierarchy we've so far observed, I don't see anything special. That self-organization is ubiquitous is to me the strongest indicator that "biology" is far from "fundamental". Not that I don't love it!
Here's something that I suppose must be "fundamental" - what "works" strings in string theory. A "real string" like from a violin is made of constituent atoms, and we can predict the behavior of that string from laws about those constituents. But a "string" in ST is just as is, with no "components" I suppose (?) So what "runs the string" and makes it like it is, and do what it does? Do you imagine it's "made of math" and just expresses whatever conceptual essence you conceive it to have?
ReplyDeleteThat may be unavoidable, but brings up embarrassing questions like "why that brutal fact of existence, and not something else instead"? Without some yet more fundamental constituents, the strings are "fait accompli." Couldn't a mathematician (or God?) have constructed something else to get the ball rolling, which would behave differently etc?
Hi Neil,
ReplyDeleteYes it is kind of ironic, that for years physics has considered that part of the final explanation must show that reality comes with no strings attached, that the explanation being it is all strings for which it is required a reality to attach themselves to. So we are now asked to believe in a reality with both instruments and meaningful music, yet with having no composer or conductor or in other words foundations without a founder;-)
Best,
Phil
Hi Neil',
ReplyDeleteIf String Theory is the fundamental theory of everything then the point is there is no "more fundamental" description of a string. It isn't "made up" of anything, it just is. Period. That's exactly what it means to be fundamental (Davies' levitating super-turtle - it doesn't stand on anything). Your problem is that the analogy to strings on a violin is stuck in your head. Needless to say, the strings on the violin are not fundamental, and analogies aren't always useful. Best,
B.
And where we disagree then? I stated explicitly in my comment:
ReplyDelete"A fundamental concept (or entity) is what you postulate in your theory. Something you can't derive."
The issue is that I thought you were saying that it doesn't make sense to talk about fundamental concepts *within* the theory.
My argument was that any fundamental theory must have at least one fundamental concept at its core.
Thanks Bee,
ReplyDeleteActually I don't think fundamental "string" and violin strings are the same sort of thing, I was doing "comparison and contrast" to show the difference too. The difference is of the essence, it's the implications of the difference I care about.
Yes of course strings aren't like the macroscopic variety, my point is: what guide have you to picking what they are or "ought" to be like? That is the "problem" if problem it is.
Dear Bee,
ReplyDeleteMy last try for now. Your relationship "Theory A is derivable from Theory B" misses out that Theory B in general will not be an adequate explanation for the phenomena described by Theory B. Quantum mechanics has very little to say about von Neumann machines, for instance.
Best,
-Arun
Hi Stefan,
ReplyDeleteI managed to read Clifford's post. Indeed he is talking about the fundamental "ways of nature" if I may say, common in different regimes and not necessarily connected to a specific theory.
For what is worth, my opinion is that it is an interesting idea but too vague and I'm not sure if such a notion can be trusted at all.
I should have you know these are not real people in the dialogue below.
ReplyDeleteThe inventor of this Dialogue copied the format from my own dialogues to bring perspective to a place where it had not existed before.:)
Dialogue on the Foundations of String Theory
Sagredo: Yes, I see, although Poincare was not actually talking about mathematical transformations, he was specifically talking about physical laws and processes that would induce an effective metric, so that the postulated background geometry was unobservable, since we only observe the net effect of the background plus the physical processes. Your “string condensate” inducing an effective metric is precisely the kind of thing Poincare was talking about when he explained how both the effective dimensionality and the effective topology of space could be altered by suitable physical phenomena. Granted, Poincare talked in terms of a “switchboard” instead of “string condensates”, but his generic mechanism was actually more general than that of string theory, and included things like “string condensates” as a tiny subset. In general, he was talking about the same kind of things as you’ve described for string theory, and this is exactly the concept that at least one well-known string theorist strenuously argued was inconceivable ten years ago. I’m sure Poincare would be gratified to learn that string theorists have (re)discovered how to conceive of such things!
Best,:)
You have to know what Hooft meant when he talked about a "theoretical Physicist" and the skyscraper. It all had to be inclusive Uncle Al, and so too, objective recognition of what is postulated by, what transpired into the continuity of movement(now what is real), yet is not geometrically pinpointed(so Clifford throws up his hands as to what geometrically this means) seen.
ReplyDeleteMatthew Chalmers:In some ways, string theory looks like a victim of its own success. It did not seek to bridge the two pillars of modern physics – quantum mechanics and Einstein's general theory of relativity – while simultaneously unifying gravity with the three other basic forces in nature: electromagnetism, the strong and the weak forces. Rather, string theory began life in 1970 when particle physicists realized that a model of the strong force that had been proposed two years earlier to explain a plethora of experimentally observed hadrons was actually a theory of quantum-mechanical strings(bold added by me for emphasis)
Dear Arun,
ReplyDeleteI never said it has to be "adequate" or even useful to have a more fundamental theory. It certainly in most cases isn't. Eg even if we would manage to derive biology from quantum field theory, I doubt that would be particularly handy. Thus, yes, my definition doesn't take this into account at all. Best,
B.
Hi Neil,
ReplyDeleteWell, the guide is, as always, Nature. If a theory explains everything, then it explains everything, and no need to ask further. Best,
B.
Hi Giotis,
ReplyDeleteAnd where we disagree then?
Well, you can of course define whatever you like. What I am trying to tell you is that the notion of a "fundamental concept" is useless and meaningless by itself. Your definition only makes sense because you implicitly use the definition of a fundamental theory. But strip that away, take only your "concept" and try to explain why one should consider it fundamental, and you'll see why it is meaningless. Take the example Neil brought up, a string. Is a string a fundamental concept? Or isn't it? Well, in some cases it is, in others it isn't. So now what? An axiomatic theory always has "postulates" that cannot be derived within that theory. But that doesn't tell you whether these postulates are more or less fundamental in their power of describing Nature. Best,
B.
Yes of course Bee. How it could be otherwise? Theories is all we have in that respect. No contemporary experiment could proclaim an entity as fundamental only a theory can.
ReplyDelete.....he was specifically talking about physical laws and processes that would induce an effective metric
ReplyDeleteBee,
ReplyDeleteYou give the impression there isn't an a priori theoretical/conceptual reason (what would it be "based on" anyway ...) for imagining what fundamental constituents the universe starts with. But some thinkers have tried, and still believe there is an ultimate proto-theory (from logical consistency?) that could in principle tell us what's going to be there. That approach says we could (if clever enough) avoid the heuristic of asking "if we try to back-engineer this natural behavior, what fundamental theory will result."
If there are many worlds with different laws etc. the latter would be required, since you don't know in advance which one you were born into (except that it was "anthropically friendly" ;-).
Hi Neil',
ReplyDeleteI have no clue what you are trying to say. What do you mean with I'm leaving you with the impression "there isn't an a priori theoretical/conceptual reason for imagining what fundamental constituents the universe starts with." I'm not a neuroscientist, I don't know if there's a reason why humans try to find fundamental explanations for the world around them. I philosophized about that here, but no, I don't know.
In any case, I don't think humans will find the answer within themselves, the human brain is too insufficient to find an accurate and useful description of Nature without the guidance by experiment. Consistency and logic definitely isn't sufficient, since there are many "theories" that are consistent but are not fundamental theories of our universe, and there might be various consistent theories that agree on all observations that we currently have. If you're with Tegmark, then then the other theories possibly describe other universes, but as I've said many times before that's a pretty much useless point of view.
Best,
B.
Bee, thanks for "bearing with me." Well, you indeed acknowledge above and earlier that you think there is no intrinsic, logically a priori reason for the universe to have to be a certain way. I don't think there is either, other than IMHO very speculative anthropic design issues which aren't formally scientific.
ReplyDeleteBut I mention the distinction since there are people who have said, we might be able to explain "logically" why the universe had to be the way it is. No, not something about our minds, but some "Platonic" sort of logical necessity about existence. (But yes, we'd have to use our minds to find it, which is part of the problem.)
This idea seems to come up in the case of strings, when some theorists look for some "ultimately beautiful" proto-theory that "just has to be true" etc. No names remembered, but I know I've seen it.
BTW Bee you are a good and even inspiring and clever writer, but I wonder if deep subtleties about English (surely a second language for you) make it harder to appreciate some delicate framings. I feel misunderstood now and then, and maybe others too. (Not a put down - the well-intentioned are doing fine in this venue!) Yet I don't always frame well myself with my cumbersome yet telegraphic phrasing, part of the issue in quick comments I'm sure.
IMHO English is tricky but doesn't seem to be. (So it isn't IMHO so great for science and philosophy as backers think.) This could be an example of the "Sapir-Whorf hypothesis", which recently got more support in experiments about language differences and people's evaluations.
I've said about all I can right here. I ease off to other things ...
tx for your good work.
Hi Neil',
ReplyDeleteMore precisely what I was saying is that logic is necessary, but not sufficient, much like mathematics isn't a theory but a language.
I certainly miss a lot of subtleties of the English language (as I miss those of dozens of other languages presumably). The prime reason is that I have no chance to ever learn them since nobody ever corrects me. Thus, I've said it several times before, but please, please tell me if there's something funny with my English. In particular I easily get confused with prepositions (for or of? on or in? so or as? from or by?) The way I deal with it is that I'm not subtle. But then I'm not subtle in German either, so not a big stretch.
Speaking of not subtle. Yesterday, a Swedish guy asked if I'd answer a couple of questions for a survey. He first asked in Swedish and when I said I have no idea what he's talking about, he repeated in English. Since I had some minutes of time, I said "sure, go ahead," upon which he apologized and went away. My mistake or his?
Best,
B.
Bee,
ReplyDeleteThat Swedish guy surely made just the sort of mistake I was talking about. "Go ahead" in English means, to proceed with doing something (maybe from coach drivers etc. being told to "go on ahead", where ahead is the path in front of you.) But he must have heard the "go" which often means to go away (from the speaker saying that), and then thought "ahead" would be to keep moving forward. He didn't understand the "idiomatic phrase." Those phrases can mean differently from the expectations about the constituent words.
And yes, prepositions etc. are tricky. Half the time I'm not sure about "this" v. "that". English has a lot of irregularity and customary usage that you get from being around it, that you can't deduce from "logical expectation." Hey, that's kind of your idea of the universe, as something you have to discover like English. It's not a logically necessary product like what numbers must do once you start with them. Physics is like learning English, not like learning math.
Hi Neil',
ReplyDeleteThanks. I was wondering if I had used the expression wrongly for several years. This has happened in a couple of cases, very embarrassing if you finally figure it out. The issue with "customary usage that you get from being around" is non-trivial if you spend most of your time in an English speaking environment, but constituted mostly of people for whom English isn't first language either. One picks up a lot of mistakes and distributes others. I like to think learning a second languages is similar to how children learn speaking, just that one lacks somebody who corrects mistakes, which makes things much more complicated. The more common mistakes one can find in textbooks, but these are the typical ones native speakers make: I or me, then or than, it's or its, there or their - ironically, these are the mistakes you don't make as a non native speaker (because the problem doesn't exist in other languages). Either way, I guess next thing is I'll have to learn Swedish. Best,
B.
http://arunsmusings.blogspot.com/2009/07/fundamental-science.html
ReplyDeleteDear Bee,
ReplyDeleteThanks for taking the time to read my link. Please note that I am always attracted to physics precisely because of its fundamentalness as in your definition. Still, I think it needs to be kept in mind that the world could be different.
"Multiple realizations" is a philosophical idea, which may or may not be relevant to the real world. Only science can decide if it is relevant, so scientists should be aware of the possibility.
I was wondering, for instance, if superstring theory has hit the problem of multiple realizability. I don't think anyone has looked at the question of how many different ways the **same** low-energy world can be derived from different string-scale structures - the research has seemed to focus on how many different vacua are there or how to get a vacuum that is a good approximation to the standard model. But suppose one took some one - even unrealistic - vacuum and showed that it arises in superstring theory in multiple ways, that might both illustrate the philosophical principle of multiple realizability and also maybe, in the aftermath, point to a different direction for string theory research.
This latter is just Sunday afternoon speculation. Maybe some string theorist who reads your blog can quickly provide the answer.
Best,
-Arun
On the most fundamental level, it has been proven that Gnome quanta explain all aspects of physics, including string theory and quantum gravity.
ReplyDeleteSee here: uncyclopedia.wikia.com/wiki/Physics_doesn't_exist,_it's_all_about_Gnomes
Dear Arun,
ReplyDeletenow you have confused me
I don't think anyone has looked at the question of how many different ways the **same** low-energy world can be derived from different string-scale structures -
I thought the idea of "multiple realizations" was the other way 'round: same fundamental structure, different low-energy world (ashtray). There is certainly a degeneracy in the top-down direction, since it entails neglecting details. (That is essentially the reason why many models (think SUSY) are so unpredictive, you can go and add loads of particles - if only they are heavy enough it results in the same low-energy world.) I think the landscape scans do to some extend address this issue: take a random string-model and see if it will reproduce features a,b,c of the standard model. Best,
B.
"A theory is fundamental if it cannot be derived from a more complete theory,..."
ReplyDeleteWhile the theory of point sets is said to constitute the fundamental of mathematics, the whole building of mathematics seems to have worked quite well or even with less paradoxes without it. G. Cantor admitted having got his CH directly from god. Are arbitrarily stated axioms fundamental just because they cannot be derived? Has aleph_2 proven useful?
Dedekind banned the measure one (definitions 1 and 2 in book 7 of Euclid's Elements) from the definition of numbers when he equated his cuts/points as numbers.
Has this new foundation improved physics?
FQXi lets much room for fantasy that is based on theories. I doubt that this is the way to find out possible flaws in the very basics.