If you know one thing about theoretical physics, it's Albert Einstein's name. While Einstein was inspired and guided by his contemporaries, both in theory as well as in experiment, his achievements are remarkable examples for the power of pure thought combined with mathematics. Einstein is not the only example; Dirac's equation that describes relativistic particles with spin 1/2 is another case where an axiomatic approach lead to predictions that were later confirmed by experiment, leaving us in awe of genius and the beauty of equations.

In the history of science these examples are however rare, and it is exactly because of their rarity that they impress us. An axiomatic approach towards the reconciliation of general relativity and quantum mechanics will, I am sure, if pursued vigorously, eventually lead to success. But the question remains if pure thought is sufficient to find the right starting point, for there might be more than one, some of which leading to theories incompatible with observations. And an axiomatic top-down approach brings with it a heavy load of developing mathematical tools along the way, detours to insight that can take a long time. In the history of science, physicists have often taken the freedom to go ahead and write down phenomenological models that were indeed not justified by any solid basis. And while rightfully met with skepticism, again and again they have been successful with it, thereby helping along the development of more and more fundamental theories.

The above mentioned example of Dirac's equation an instructive one. In the non-relativistic limit, Dirac's equation in the presence of an electromagnetic field reduces to the Pauli-equation which describes the coupling of electrons to electromagnetic fields with a gyromagnetic ratio of 2. It was derived by Dirac from his equation in 1928, but already in 1925 two Dutch graduate students, Samuel Goudsmit and Georg Uhlenbeg, had used a phenomenological model to describe the structure of atoms and the response of ions to magnetic fields. Their model did not make much sense since, classically, the gyromagnetic ratio should be one. Naturally, many physicists were not convinced by the model and Pauli even advised the students not to publish it. Yet, it described experiments well and Dirac's later derivation of their model from his equation served to document the validity of Dirac's theory.

Another example is Pauli's exclusion principle, according to which no two fermions can occupy the same state. It was postulated and used since 1925, among other things to explain the Zeeman effect. Yet it was not until the development of quantum field theory and an understanding of the properties of multi-particle states in 1940 that a derivation was achieved.

Coulomb's law, Ampere's law and Biot-Savart's law can be derived from Maxwell's equations, but they were known and in use long before that, significantly contributing to the development of the full theory of electrodynamics. Fermi's theory we know today is an approximation of the electroweak gauge theory, but was in use long before that, teaching us lessons in renormalizability. The Rahleigh-Jeans law and Wien's law for the spectrum of thermal radiation were combined in Planck's law. In 1900, Planck constructed a derivation for this radiation spectrum based on the, back then unfounded, assumption that the energy of photons is quantized and proportional to the frequency. It predated Einstein's explanation for the photoelectric effect by 5 years. The constant of proportionality that Planck introduced is now called Planck's constant and it was the starting shot for quantum mechanics.

Due to the difficulty to analytically describe the formation of bound states in Quantum Chromodynamics (QCD is asymptotically free, ie it's easier to deal with it the higher the energy) still today most of the models used are phenomenological and many predate the development of QCD. There is for example the the Nambu-Jona-Lasinio model, the Gell-Mann-Levy model or the String-Lund model, all of which have significantly contributed to our understanding of the structure of elementary matter.

One could at this point speculate which present day phenomenological models will turn out to have lead the way towards the now searched-for theory describing the fundamentals of space and time. It springs to mind String cosmology and Loop Quantum Cosmology, searches for deviations from Lorentz-invariance, extra dimensions, or signatures of space-time discreteness. The models currently in use are not derived from a fundamental theory. Instead, they aim to incorporate and allow tests for specific features the fundamental theory might have, like additional dimensions or modified Lorentz-invariance. But these models, even if they turn out to be incompatible with experiment, are guides on our search for the correct theory. Guides that, after 75 years, we have good use for.

One could at this point speculate which present day phenomenological models will turn out to have lead the way towards the now searched-for theory describing the fundamentals of space and time. It springs to mind String cosmology and Loop Quantum Cosmology, searches for deviations from Lorentz-invariance, extra dimensions, or signatures of space-time discreteness. The models currently in use are not derived from a fundamental theory. Instead, they aim to incorporate and allow tests for specific features the fundamental theory might have, like additional dimensions or modified Lorentz-invariance. But these models, even if they turn out to be incompatible with experiment, are guides on our search for the correct theory. Guides that, after 75 years, we have good use for.

In one of his books, TRtQG I think it was, Lee Smolin predicted, optimistically as he noted, that we'd have a theory of QG in 2012.

ReplyDeleteIn your professional opinion, are we on track to achieve such a theory next year, and if not, when?

Btw, very nicely and well-written article, thanks. I was getting frustrated with the lack of progress in QG of late, and this re-kindled my interest.

Depends on who you ask. Most string theorists would probably argue that we already have a theory of qg. The question remains though if that theory actually describes the the real world around us (the qg realm of General Relativity, not QFT in flat space via Ads/CFT).

ReplyDeleteCan't recall what Lee wrote in his book, but you see there's some professional pressure for researchers to be optimistic. Do you really expect somebody who works on QG to walk around and say, well, give it another 75 years and then ask my grandson? So you should take everything biased people say with a grain of sand.

Having said that, I think we'll see light in a decade, and the fog will clear out in 2 decades.

Hi Bee,

ReplyDeleteAn interesting piece which sheds light on the value of the phenomenological approach to physics in respects to how it aids physicists to extending our insights. I totally agree with what you’ve said and would also point out those such developmental approaches should not only be appreciated , yet more importantly not forgotten. That is because at times some become so enamoured with the beauty of existing theories as to forget what they were inspired to have explained.

I’ve always found this to have been best expressed by someone I find as one of the greatest modern phenomenologists, J.S. Bell, when in his paper on how to teach special relativity he reminded that “the longer road sometimes gives more familiarity with the country.” That being when one has difficulty in finding your way it’s always good to be able to retrace the path from which they came to have become being lost; such as to be able see where one might have taken a wrong turn in the road or simply taken something as being true which simply isn’t justifiable.

“The approach of Einstein differs from that of Lorentz in two major ways. There is a difference of philosophy , and a difference of style.The difference of philosophy is this. Since it is experimentally impossible to say which of the two uniformly moving system is really at rest, Einstein declares the notions ‘really resting’ and ‘really moving’ as meaningless. For him only the relative motion of two or more uniformly moving objects is real . Lorentz, on the other hand, preferred the view that there is indeed a state of rest, defined by the ‘aether’, even though the laws of physics conspire to prevent us from identifying it experimentally. The facts of physics do not oblige us to accept one philosophy rather then the other. And we need not accept Lorentz’s philosophy to accept a Lorentzian pedagory. Its special merit is to drive home the lesson that the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simpler to work in a single frame rather than hurry after each moving object in turn.

The difference of style is that instead of inferring the experience of moving observers from known and conjectural laws of physics, Einstein starts from the hypothesis that the laws will look the same for all observers in uniform motion. This permits a very concise and elegant formulation of the theory, as so often happens when one big assumption can be made to cover several less big ones. There is no intention here to make any reservation whatsoever about the power and precision of Einstein’s approach. But in my opinion there is something to be said for taking students along the road made by Fitzgerald, Lamour, Lorentz and Poincare. The longer road sometimes gives more familiarity with the country.”

-J.S. Bell “How to teach special relativity”-Progress in Scientific Culture, Vol. 1, No. 2, summer 1976

Best,

Phil

ReplyDeleteIn 1900, Planck constructed a derivation for this radiation spectrum based on the, back then unfounded, assumption that the energy of photons is quantized and proportional to the frequency.Actually, Planck's initial postulate referred only to a quantization of energy of the oscillators (electrons) of the (black body) cavity walls, interacting with a classical electromagnetic field inside the cavity. It was Einstein who proposed that the energy of photons was quantized as well, explaining therefore the photoelectric effect.

Best,

Christine

ReplyDeleteenergy of photons was quantizedI mean, of course, the energy of the electromagnetic field was quantized, later called photons.

Best,

Christine

ReplyDeleteBee:But the question remains if pure thought is sufficient to find the right starting point, for there might be more than one, some of which leading to theories incompatible with observations.I am glad you are returning to the subject of QG too. What motivation are your inclination for such a search, and you may have your reasons, as I have mine.

Showing biography of pure thought are the examples of Dirac and Einstein as you point out, "are the example."

Dirac and Einstein because of the thought experiments and visualizations that were matching up with the mathematics.For me such generalizations I lean toward on those mathematically professed to help in the development of "the concepts" which can lead to pure thought.

Why I listen very carefully to what our younger co-harts are saying. Those with many years in the trade.

The expression of phenomenology is of course the eventual consequence leading toward the falsifying the theory. It is a good position to be in after all the hype and the reality recognition, so that one could say they are indeed dealing with the reality.

Bee:It was derived by Dirac from his equation in 1928, but already in 1925 two Dutch graduate students, Samuel Goudsmit and Georg Uhlenbeg,Yet, it is okay to develop the theory that might some day match up with the occasion as you pointed out and lead by Dirac.

Best,

Hi Christine,

ReplyDeleteThanks for the correction! Best,

B.

Bee....the subject of QG with regard to the phenomenology of course.

ReplyDeleteWhat correspondences phenomenology wise do you have to show in the QG area?

Best,

Hi Phil,

ReplyDeleteI have to admit that when I was a student I greatly preferred a deductive way in teaching, ie just writing down the axioms and see what follows. I suppose that's because I started out from mathematics and it just came more naturally. It was only over the course of time that I found that while it underlines the elegance of the theory, it isn't too helpful for doing research because it leaves out all the arguments and pitfalls along the way. Thus, I now see the value of my prof proceeding along the historical development - taking students along the road - though eventually I didn't learn after his lecture notes because I found them too cluttered. Best,

B.

Hi Plato,

ReplyDeleteNot sure I understand the question. What do you mean with "correspondences"? Best,

B.

ReplyDeleteBee:Not sure I understand the question. What do you mean with "correspondences"?Some of the phenomenological approaches to testing QG?

Best,

Hi Plato,

ReplyDeleteWell, basically it's what we discussed on last year's workshop, sorry for being repetitive. There's since been progress on the Causal Sets stuff, at least is what I see on the arXiv, inching closer to pheno there, and there's new data from the LHC making large extra dimensions increasingly improbable. (Should probably write a post on that, but have a problem of time.) There was also a review article on String Cosmology on the arXiv the other day, which is very nice, and more details on the tensor modes in Loop Quantum Cosmology that are relevant to connect to experiment (but for what I can tell nothing strikingly new there). I haven't heard anything new with regards to the gamma ray bursts, which is funny because I was expecting news already last year. Not sure what takes them so long to analyze the data they must have by now. Well, yes, that's a brief status update. Best,

B.

PS: Though not pheno, this might be of interest as well

ah thanks Bee,

ReplyDeleteWhile looking through your blog posts

ABSTRACTS - Experimental Search for Quantum Gravity

Abstracts - Perimeter Institute for Theoretical Physics

Cosmic particle collisions are of interest to me in relation to ICECUBE, about faster then light medium of expressions. There is some interest for me about "the location" of these collisions.

The QGP relation and expressions as too, information transfers. Do not know if my thinking is sound.:)

Best,

This comment has been removed by the author.

ReplyDeleteWhat is Alain Connes and his crew up to in France. Any progress there?

ReplyDelete"Anytime someone mentions 'The Universe', we must all stand up and bow."

... Alain Connes

Sounds like my kind of guy. Thanks to Lee Smolin in one of his books for turning me onto that one.

Yes, a very good post, Bee. It sounds like your orientation is slowly changing from a bottom up to a top down orientation. That may be my more optimistic interpretation of your post because that is my own preference. One takes what is useful from the past and builds on it for bottom up work. One uses more visualization from observation of phenomena for the top down approach. The tricky part in taking a bottom up approach is knowing what is useful from the past. That is usually not obvious but people seem to treat it as if it was obvious. Big mistake.

ReplyDelete

ReplyDeleteAn axiomatic approach towards the reconciliation of general relativity and quantum mechanics will, I am sure, if pursued vigorously, eventually lead to success.Newtonian cannot be GR and QM. An axiomatic system cannot exceed it weakest axioms. Perturbation treatments - string/M-theory - are particularly defective for excluding new symmetries. Teleparallel gravitation, Einsteinet al., specifically falsifyies quantum gravitation for its misrepresenting angular momentum. Rigorous derivation from error is still wrong.There is no measurable observable whose presence or contrast violates the Equivalence Principle (BRST invariance dependencies in string theory), weak field plus relativistic and quantum regimes. Validated spacetime models are geometric and continuous, gravitation acting on fermionic mass assuming they it is bosonic. Photons do not test fermionic mass interactions. The proper test of spacetime is chemically and macroscopically identical, opposite geometric parity atomic mass distribution test masses. Geometric parity can be observed and calculated but not measured. Chiroptical probes (specific rotation, ORD, CD, Flack parameter) detect but d not measure atomic mass distribution.

Ohysics has

neverobserved gravitation versus spatial odd-parity fermion distributions. This is where teleparallel gravitation and GR are disjoint with high amplitude: 99.97+% active mass in total test mass (relative nuclear positions in space).http://www.mazepath.com/uncleal/erotor1.jpg

an empirical falsfication of quantum gravitation. Somebody should look.

True story.

ReplyDeleteThere was a rhinoceros kept in a circular pen at a zoo. It walked around the perimeter incessantly.

People felt bad for it, so they dramatically increased the size of the pen.

The rhinoceros walked around the same old small circle incessantly.

If you want to get somewhere, you have to break out of the cage.

"The models currently in use are not derived from a fundamental theory. Instead, they aim to incorporate and allow tests for specific features the fundamental theory might have, like additional dimensions"

ReplyDeleteWhy is that? In one of the most popular model of inflation in String theory the inflaton in 4D is the position of a D3 brane falling in a warped throat of a Calabi-Yau with an anti-D3 brane at its tip. Isn't this a derivation from the fundamental theory?

Hi Giotis,

ReplyDeleteNo, it's not a derivation from a fundamental theory. It's some brane model for inflation that's currently popular. It for certain doesn't follow from string theory, it just uses ingredients from. There are several other scenarios for string cosmology that are equally well motivated (or not motivated, depending on your perspective). Best,

B.

Hi Bee,

ReplyDeleteThus, I now see the value of my prof proceeding along the historical development - taking students along the road - though eventually I didn't learn after his lecture notes because I found them too clutteredIt then could be argued that what is called genius is simply someone who has the historic journey become simpler ;-)

"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"-Albert Einstein

Best,

Phil

Hi Phil,

ReplyDeleteTED Talk-Leonard Susskind: My friend Richard Feynman

Listening to this talk with regard to Susskind's opinion about his friend Dick, he too would have thought about, "

irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience."Pure thought(what does this linguistic representation actually mean) would have to lead you there and be most understandable as to leaving no doubt as to what has been derived.

I have often wondered where Feynman actually deduced his diagrams from and for me I think seeing how Dirac worked, this was suffice to me to actually see how "i" in for matrices was derived.

This again is my opinion. I am searching for answers.

For me it was about where one set them self in terms of their observation of the place "this simplicity" might have been realized.

Coxeter might have said circle when looking at a round table from above, while standing to the side, he would say ellipse

Best,

Bee said,"Quantum gravity has the potential to revolutionize our understanding of space, time, and matter and with it redefine our own place in the world."

ReplyDeleteI feel sorry for the people wmiho have accepted this premise. Quantum Mechanics and its progeny have its problems which have been voiced by many of those who first conceived Quantum Mechanics. General Relativity on conceptual and observational grounds has even more problems. In order for General Relativity to have some semblance of validity, dark matter has to be directly detected in the laboratory. Otherwise, it just like the putative aether idea. like General Relativity will spiral into a unrecoverable tailspin is dark matter is not detected. Furthermore, some believable clue has to be articulated as to what causes the fact of cosmic acceleration.

Quantum Gravity is an attempt to marry two failing theories and expect that marriage produce valid, believable and useful thoery. After Einstein spent a good amount of is life trying to do this he said,

"I consider it quite possible that physics cannot be based on the field concept, i. e., on continuous structures. In that case nothing remains of my entire castle in the air gravitation theory included, [and of] the rest of modern physics.

- Einstein in a 1954 letter to Besso, quoted from: Subtle is the Lord, Abraham Pais, page 467"

To expect something good come out of marrying two bad theories is about as sad as expending the billions that have already been spent looking for the dark matter particle and measuring and remeasuring cosmic acceleration. http://vixra.org/abs/0907.0018

Hi Igor,

ReplyDeleteYes, that is of course entirely true. (Though there is some possibility we're already seeing some phenomenology, just haven't recognized it for what it is.) That is certainly responsible for the large number and variety of different models. However, the situation today is in experimental terms very different from how it was a century ago. Today, one has to invest a lot more effort into studying a new parameter range. It isn't so surprising then that it's the models coming first, pointing out interesting directions to look at before the experiments are conducted. Back then, people were basically stumbling about new and unexplained effects. Not so anymore. Best,

B.

Nothing worse then having to quote oneself in order to press the point. Carry on with life indeed as if nothing missed.:)

ReplyDeletePure thought(what does this linguistic representation actually mean) would have to lead you there and be most understandable as to leaving no doubt as to what has been derived.Algorithmically, the HTML language is representative of the order in which we might represent an idea....as is done mathematically...that it is conceptually enriched(

put a cloud around it) that by such representation it would include historical understandings. These encapsulated by that rhetorical past is "inclusive."You just take that for granted/assumption as long as the interpretation actually speaks to the historical development and proceeds forward toward an phenomenological order.

Most had to go through the historical development in order to understand where we are today. For the layman in my "seeing choice of method of production" toward falsifying, the choice of structure of phenomenological order is displayed as to demonstrate the thinking's involved scientifically that demonstrates the logic of approach toward a culmination of models of apprehension.

This display's the approach for myself. Might it be an example then of the whole development toward phenomenological order?

Best,

Osborne Reynolds' Sub-Mechanics of the Universe and An Inversion of Ideas as to the Structure of the Universe unites quantuum and gravity.

ReplyDeleteSee my articles on Scribd.com.

Bruce Lamar Rosenberg

LHC Sound is always an interesting way to look at things?:)

ReplyDeleteHi Bee,

ReplyDelete"It for certain doesn't follow from string theory, it just uses ingredients from.

In what sense?

The model I'm talking about (known as KKLMMT) like the majority of the stringy inflationary models are constructed in the strict context of IIB string compactifications. Maybe you have in mind brane models of Randall-Sundrum type which are indeed toy models inspired by string theory but with no underlying theory.

"There are several other scenarios for string cosmology that are equally well motivated"

I guess you have in mind String GAS cosmology which is an alternative to inflation.

Yes of course. This is the well known "problem" of String theory i.e. its inability to produce *unique* predictions for the 4D world. Indeed there are many 4D worlds or cosmologies which could be derived from String theory but that doesn't mean that the specific models don't follow from the fundamental theory. In the end you will peak the one that solves the theoretical problems and fits the observational data.

Or maybe you mean that the various models seems too contrived and don't follow naturally from the theory without some degree of fine-tuning? Well again this is a well known characteristic of String phenomenology. That's why the multiverse paradigm has emerged as you know. But even in a multiverse you must find a vacuum/model that fits exactly *all* the observational data of this world. Again this dosen't mean that the models don't follow from the fundamental theory (at least from its low energy approximation).

Hi Giotis,

ReplyDeleteYes, the string/brane gas is one of the models. There's also the ekpyrotic one. That a model is 'constructed in the context of' is exactly what I mean with it's a model that 'uses ingredients of' but doesn't follow from the theory. The mere fact that there are different models with different predictions tells you that. Best,

B.