Theoretical physics has problems. That’s nothing new — if it wasn’t so, then we’d have nothing left to do. But especially in high energy physics and quantum gravity, progress has basically stalled since the development of the standard model in the mid 70s. Yes, we’ve discovered a new particle every now and then. Yes, we’ve collected loads of data. But the fundamental constituents of our theories, quantum field theory and Riemannian geometry, haven’t changed since that time.
Everybody has their own favorite explanation for why this is so and what can be done about it. One major factor is certainly that the low hanging fruits have been picked, and progress slows as we have to climb farther up the tree. Today, we have to invest billions of dollars into experiments that are testing new ranges of parameter space, build colliders, shoot telescopes into orbit, have superclusters flip their flops. The days in which history was made by watching your bathtub spill over are gone.
Another factor is arguably that the questions are getting technically harder while our brains haven’t changed all that much. Yes, now we have computers to help us, but these are, at least for now, chewing and digesting the food we feed them, not cooking their own.
Taken together, this means that return on investment must slow down as we learn more about nature. Not so surprising.
Still, it is a frustrating situation and this makes you wonder if not there are other reasons for lack of progress, reasons that we can do something about. Especially in a time when we really need a game changer, some breakthrough technology, clean energy, that warp drive, a transporter! Anything to get us off the road to Facebook, sorry, I meant self-destruction.
It is our lacking understanding of space, time, matter, and their quantum behavior that prevents us from better using what nature has given us. And it is this frustration that lead people inside and outside the community to argue we’re doing something wrong, that the social dynamics in the field is troubled, that we’ve lost our path, that we are not making progress because we keep working on unscientific theories.
Is that so?
It’s not like we haven’t tried to make headway on finding the quantum nature of space and time. The arxiv categories hep-th and gr-qc are full every day with supposedly new ideas. But so far, not a single one of the existing approaches towards quantum gravity has any evidence speaking for it.
To me the reason this has happened is obvious: We haven’t paid enough attention to experimentally testing quantum gravity. One cannot develop a scientific theory without experimental input. It’s never happened before and it will never happen. Without data, a theory isn’t science. Without experimental test, quantum gravity isn’t physics.
If you think that more attention is now being paid to quantum gravity phenomenology, you are mistaken. Yes, I’ve heard them too, the lip confessions by people who want to keep on dwelling on their fantasies. But the reality is there is no funding for quantum gravity phenomenology and there are no jobs either. On the rare occasions that I have seen quantum gravity phenomenology mentioned on a job posting, the position was filled with somebody working on the theory, I am tempted to say, working on mathematics rather than physics.
It is beyond me that funding agencies invest money into developing a theory of quantum gravity, but not into its experimental test. Yes, experimental tests of quantum gravity are farfetched. But if you think that you can’t test it, you shouldn’t put money into the theory either. And yes, that’s a community problem because funding agencies rely on experts’ opinion. And so the circle closes.
To make matters worse, philosopher Richard Dawid has recently argued that it is possible to assess the promise of a theory without experimental test whatsover, and that physicists should thus revise the scientific method by taking into account what he calls “non-empirical facts”. By this he seems to mean what we often loosely refer to as internal consistency: theoretical physics is math heavy and thus has a very stringent logic. This allows one to deduce a lot of, often surprising, consequences from very few assumptions. Clearly, these must be taken into account when assessing the usefulness or range-of-validity of a theory, and they are being taken into account. But the consequences are irrelevant to the use of the theory unless some aspects of them are observable, because what makes up the use of a scientific theory is its power to describe nature.
Dawid may be confused on this matter because physicists do, in practice, use empirical facts that we do not explicitly collect data on. For example, we discard theories that have an unstable vacuum, singularities, or complex-valued observables. Not because this is an internal inconsistency — it is not. You can deal with this mathematically just fine. We discard these because we have never observed any of that. We discard them because we don’t think they’ll describe what we see. This is not a non-empirical assessment.
A huge problem with the lack of empirical fact is that theories remain axiomatically underconstrained. In practice, physicists don’t always start with a set of axioms, but in principle this could be done. If you do not have any axioms you have no theory, so you need to select some. The whole point of physics is to select axioms to construct a theory that describes observation. This already tells you that the idea of a theory for everything will inevitably lead to what has now been called the “multiverse”. It is just a consequence of stripping away axioms until the theory becomes ambiguous.
Somewhere along the line many physicists have come to believe that it must be possible to formulate a theory without observational input, based on pure logic and some sense of aesthetics. They must believe their brains have a mystical connection to the universe and pure power of thought will tell them the laws of nature. But the only logical requirement to choose axioms for a theory is that the axioms not be in conflict with each other. You can thus never arrive at a theory that describes our universe without taking into account observations, period. The attempt to reduce axioms too much just leads to a whole “multiverse” of predictions, most of which don’t describe anything we will ever see.
(The only other option is to just use all of mathematics, as Tegmark argues. You might like or not like that; at least it’s logically coherent. But that’s a different story and shall be told another time.)
Now if you have a theory that contains more than one universe, you can still try to find out how likely it is that we find ourselves in a universe just like ours. The multiverse-defenders therefore also argue for a modification of the scientific method, one that takes into account probabilistic predictions. But we have nothing to gain from that. Calculating a probability in the multiverse is just another way of adding an axiom, in this case for the probability distribution. Nothing wrong with this, but you don’t have to change the scientific method to accommodate it.
In a Nature comment last month, George Ellis and Joe Silk argue that the trend of physicists to pursue untestable theories is worrisome. I agree with this, though I would have said the worrisome part is that physicists do not care enough about the testability — and apparently don’t need to care because they are getting published and paid regardless.
See, in practice the origin of the problem is senior researchers not teaching their students that physics is all about describing nature. Instead, the students are taught by example that you can publish and live from outright bizarre speculations as long as you wrap them into enough math. I cringe every time a string theorist starts talking about beauty and elegance. Whatever made them think that the human sense for beauty has any relevance for the fundamental laws of nature?
The scientific method is often quoted as a circle of formulating and testing of hypotheses, but I find this misleading. There isn’t any one scientific method. The only thing that matters is that you honestly assess the use of a theory to describe nature. If it’s useful, keep it. If not, try something else. This method doesn’t have to be changed, it has to be more consistently applied. You can’t assess the use of a scientific theory without comparing it to observation.
A theory might have other uses than describing nature. It might be pretty, artistic even. It might be thought-provoking. Yes, it might be beautiful and elegant. It might be too good to be true, it might be forever promising. If that’s what you are looking for that’s all fine by me. I am not arguing that these theories should not be pursued. Call them mathematics, art, or philosophy, but if they don’t describe nature don’t call them science.
This post first appeared Dec 17 on Starts With a Bang.
Your post arise big questions that I like very much.
ReplyDeleteWhen I'm reading most of the scientific articles, I feel a deep dissatisfaction feeling who is making my mind suffer.
The reason is that I do not find a true effort to accommodate all pieces in a single theory but a lot of article that pretend to explain this or that phenomenological observation.
You can't solve a point by introducing other problems or using another problematic point to explain it.
It is true that you need mathematics, but if you don't have a general view of you are going to do, you can move in the wrong direction.
In other words I'm strongly convinced that there are not missing pieces to formulate a quantum gravity theory.
There's only a great theory disorder that make us impossible to see the solution.
A lion, before to attack a herd of animals, is studying them accurately to find the weaker and easy to catch.
Which are the weaker points of the QFT and GR theory that needs to be cured in order to weld together our view?
What are the phenomenological aspects that has the worst interpretation?
If they exist, what is the easiest to be solved?
I don't think that when Einstein started to study the physics, he really wanted discover a new theory of gravity because he was not happy with the Newton's one.
ReplyDeleteIn fact he started with special relativity, because for him the law of nature had not to be constrained by a reference system.
As a consequence he was deeply unsatisfied by Newton's equation because the the speed of light was not constraining the gravity force.
That's what I understand, even if I could be wrong.
Well said, sir. Well said. Down with magical thinking...especially amongst physicists.
ReplyDeleteI don't like post-empirism...Without experiments...Could a truly unified and fundamental theory be trusted and verified through pure logic? I can only think about Gödel's theorems...Experiments in physics allow us to test precisely without the rules of any theory if it is right or not. More precisely, experiments can test if ideas are "consistent".
ReplyDeleteThere is nothing new about using consistency to develop theories. Think of how Einstein developed General Relativity. He wanted to reconcile gravitation and special relativity/electromagnetism. Consistency turned out to be sufficient to pin down general relativity.
ReplyDeleteImagine we lived in a world where our experimental skills were insufficient to distinguish general relativity from Newton's theory. In this world, any competent physicist would know that General Relativity is the best theory, because it englobes electromagnetism and special relativity. On ther other hand, there would probably be a cohort of people who would refuse to learn Riemannian geometry and GR, who would claim that the idea of a curved 4-dimensional spacetime is completely crazy. They would argue that there are no experimental checks that justify such wild speculations, and probably also claim that GR is definitely not science.
Now you can transpose this situation today with string theory, which is so far the only theory to successfully merge general relativity and quantum field theory. Sure we don't understand the theory completely, but there is ample evidence that it is even more constrained than GR was. This mean that we're not free to extend the theory as we want, there is only one way to do so and we have to find it. And that's what people have been doing. I don't see what is unscientific about that. This is no different than what Einstein did when developing GR.
Sure everybody would be happier if there was actually some experimental data pertaining to the quantum gravity regime, and that's why some people were over-excited about BICEP2. But until we do find one, the good news is that we can use consistency to make progress.
Sam:
ReplyDelete"Consistency turned out to be sufficient to pin down general relativity."
You are wrong, and the mistake in you thinking is exactly the mistake I have elaborated on in my post. Requiring consistency is *not* sufficient to derive general relativity. Einstein knew Maxwell's equations, which are evidence based, he knew Newton's theory of gravity, which is evidence based.
Yes, if you have sufficiently many axioms of a theory then you can use consistency to derive further consequences. You can derive general relativity from a handful of assumptions, that being locally Special Relativity, coupling to the stress-energy-tensor (this is central and a point that Einstein stumbled over repeatedly), reproducing the Newtonian limit.
But my point is that without connection to observation, consistency will never result in a useful theory. Best,
B.
Sam...The issue you mention is here, but in a quite dramatic way. General relativity is not different from tenso-scalar theories, modified gravity, or even supergravity or string theories, since GR can be recovered from those theories in certain limit. Ironically speaking, we have discovered the cosmological constant and that is killing a little bit string theory and superstring theories, since they have issues to explain its tiny value, BUT, it also kills (to some extent) QFT!!! Even worst, you have several classical theories like gravity with torsion and other variants of "extended" General Relativity. The departure from GR to a bigger theory is not observed, so with the exception of dark matter and dark energy, GR fits observations very well. Therefore, people assumes that GR is a very good approximation to low energy quantum gravity...Or it should, as far as we know. Beyond Standard Models theories have the same problems. I dislike the MSSM just because is too complicated, the SM fits observations EXTREMELY ok, it is consistent with all tests of the last 40 years or so, so it is solid. The problem is the same as that in "beyond General Relativty", SM deviations can be out of reach of current and near future colliders,...So, how can we advance in the experimental side without that post-empiricism non-empirical thing I don't like too much? For me, and I don't know if Sabine thinks similar, is...What kind or subclass of experiments can we guess that help us to really test quantum gravity theories at low energies or/and what are the best experiments can we make to go Beyond GR and Beyond SM? At low energies, BGR and BSM theories seems to be closely to GR and SM. Current experiments don't provide too much help, since they are providing even much solid evidence of current theories. Dark matter searches will become interesting in the next decade: we will approach the limit of neutral coherent neutrino scattering, so if we don't find dark matter, all the detectors will become neutrino detectors...And, we will need to transform them into directional detectors. Neutrino physics could, in principle, be a very interesting window to quantum gravity. Neutrino oscillations could detect effects from a minimal length in QG and neutrino Astronomy is just being born these days...We need to think harder in how to test quantum aspects of gravity.
ReplyDeleteMaybe there is scientific method but certainly there is no method for discovery: if there were we would not have "discovery" in our vocabulary.
ReplyDeleteCommunity of theoreticians has been definitely doing something wrong for last four decades: general relativistic space-time and GUTs - to not even mention super string models - are taken as dogmas. Besides this there is extreme specialisation -basically because it is easy to produce items to curriculum vitae by using method. It is also impossible to communicate alternative views because of "the only game in town" mentality: the rock stars of theoretical physics seem to have lost totally the touch to what is really happening.
The problem is not the lack of data. There exist a rich spectrum of anomalies within physics and if one gives up reductionistic dogma and takes seriously biology, neuroscience, and consciousness, theoretician has a marvellous pool of poorly understood phenomena giving strong guidelines. Quantum measurement theory itself would be a precious gift for a theoretician with real desire to understand rather than build career.
All this is however neglected and people waste their time to endless arguments about multiverse, blackholes, and what possibly happens in Planck length scale - a notion, which itself is an outcome of a mere dimensional argument applied to a parameter of a macroscopic theory of gravitation and feeding in Planck constant which is quantum notion and might make no sense! To my humble opinion fundamental length should not involve Planck constant in its definition!
Just single example about possible anomalies in solar system relevant to gravitation: Pioneer and Flyby anomalies. How many quantum gravity theoreticians take them seriously besides me ( http://matpitka.blogspot.fi/2014/12/pioneer-and-flyby-anomalies-as.html )?
Clarification: When I said "With the exception of dark matter and dark energy GR explains data very welll" I am saying not just GR via LCDM could not "describe" dark matter or dark energy, I mean, GR does not say what dark energy or dark matter ARE. Even people and experts, in my opinion, get confused in some cases with the meaning of the cosmological constant. I believe it is likely possible that cosmological constant (the bare value) is not the VACUUM energy. It is pretty close to it, according to cosmological data, but we don't know if it is a fundamental parameter, if it runs with energy, of if it locally varies. It is just and accident that Einstein realized that GR allowed for such a term in his field equations but it was neglected only after the discovery of the cosmic expansion. The drama of the CC is that if some kind of symmetry is involved with it, the breakdown is so soft that we are left with a ridiculous value. Plus, as I said, QFT predicts a huge vacuum energy, someway "equivalent" to a cosmological constant...So, QFT is WRONG in its prediction. If we don't find SUSY or something new in the LHC, we have a problem with the CC and the Higgs mass and its vacuum expectation value, it is about 50 orders of magnitude away. How can that be possible? What are we doing wrong with QFT or with cosmological measurements?
ReplyDelete"But my point is that without connection to observation, consistency will never result in a useful theory."
ReplyDeleteI'm totally agree, even if it does not strictly mean to make experiment.
Dark energy and dark matter are the biggest evidence we have, a trace to reconcile our theoretical vision with the Nature.
Let us step outside of the interesting question of why and how we believe certain things culturally that if there is physical evidence it is hidden from the public so as to protect our beliefs or encourage them for hidden purposes.
ReplyDeleteThe ideal example in our recent time is speculation on the idea of aliens with advanced or different technology among us.
Some of the concepts are consistent to a very elaborate level so as convincing as any potentially falsifiable pseudoscientific system, a parallel scientists think more fantasy than predictions of futuristic science fiction. Fantasy can be true to its own internal logic.
Can ideas explored in these areas as if future science fiction empirically realized as an accessible prediction, as technology such as faster than light space or time travel tell us something of what may be some say is retro-engineering?
The math or assumptions clearly defined or debunked in particular to observe nature in useful refinements.
Gods, angels, giants, ghosts, and aliens have been in our thoughts for a long time. It seems we enter a time of clearer superstitions that the next entry in the fine tuning of that sequence is that we are the aliens now capable of self engineering our genes and half afraid we become abducted by artificial intelligence as we evolve and design our logic.
Still, if the universe makes sense the right model in principle can clarify all these scientific questions we limited only to what we have not yet imagined.
Its no question that the social dynamics in the field is troubled.
ReplyDeleteThere are socially acceptable almost certainly wrong theories, which get published and promoted (untestable MWT, strings, variants on the above), while there is something called 'fringe science', done by those outside the social ring, which is more than ignored.
That double standard in the treatment of theories that are almost certainly wrong is the real problem.
Newton's gravity and Einstein's GR would have both been ignored by mainstream physics in today's world.
In Einstein's case, without GR its pretty obvious we would have had some wonderfully complicated QFT of gravity that would explain all observed gravity to within a small error. To challenge that with a classical field in 2015 would have been impossible, to say the least. Classical fields are a death sentence for any researcher today. GR would have no chance.
Physics through non official channels is surely very often exactly wrong, but that's not an argument against taking it more seriously, as there are some pretty laughable theories which are mainstream science.
Merely studying non-ordained physics is enough to get one thrown from the church. The followers know this and keep their heads down.
http://phys.org/news/2014-12-peer-breakthrough-manuscripts.html
”One major factor is certainly that the low hanging fruits have been picked”.
ReplyDeleteIMHO it's more like Standard Model physicists won’t stoop to pick them.
”It is our lacking understanding of space, time, matter, and their quantum behavior that prevents us from better using what nature has given us”.
Plus a lack of understanding of gravity and classical electromagnetism and how they relate to QED.
”And it is this frustration that lead people inside and outside the community to argue we’re doing something wrong... Is that so?”
Yes.
”It’s not like we haven’t tried to make headway on finding the quantum nature of space and time”
Who says space and time are quantized? Light is quantized. Photon energy is E=hf. The h is Planck’s constant of action. And for every action there is a reaction. Which is why a photon has a non-zero active gravitational mass. But it doesn’t approach you in steps.
"In a Nature comment last month, George Ellis and Joe Silk argue that the trend of physicists to pursue untestable theories is worrisome. I agree with this".
Me too. But I also think understanding is the initial issue for quantum gravity. Not experiment. That can come later.
The vacuum is postulated to be mirror symmetric toward both photons and matter. When vacuum is observed to be trace acentric toward matter, theory is parameterized, unendingly curve-fitting observation. General relativity does not contain Green's function.
ReplyDeleteOpposite shoes measurably violate the Equivalence Principle as enantiomorphic space group single crystals (geometric Eötvös experiment) and well-crafted racemic molecules' microwave rotation temperatures in vacuum. One cannot repair a problem while postulating the ansatz that causes the problem. LOOK.
For physics theories, the scientific method is clearly defined - it is called "deduction". The theory consists of arguments. Each of them has one or more premises and a conclusion. Each premise is either an initial statement (axiom, postulate) or a conclusion from some previous argument.
ReplyDeleteThe argument should be VALID, which means that if the premises were true the conclusion would have to be true. There can be no formal procedure allowing us to distinguish valid from invalid arguments, but if both the premises and the conclusion are clearly stated, the scientific community would easily reach a consensus. The problem is that the premises are often not stated at all, which explains the popularity of Feyerabend's "anything goes".
The experimental verification is indispensable but still the requirement for consistency is more important. I have tried to explain why in my comments to George Ellis and Joe Silk's paper in Nature.
Hello,
ReplyDeleteThe wording used today is unmasking:
all that "sellable" thoughts go as "theories", what else would you name the output of a school/institute/college in theoretical physics? :=(
I recommend to return in speech and writing to the classical terms:
- speculation (lets try something, but in private)
- hypothesis (eg. self consistent, not excluding any testability)
- theory (experimentally tested)
But before You do that in writing,
wait until You have tenure :=(
Wonderful essay - thanks!
ReplyDeleteThis hurt, though: "Whatever made them think that the human sense for beauty has any relevance for the fundamental laws of nature?"
I've long argued that in fact our notions of beauty - specifically of mathematical elegance - directly reflect the depth of our understanding. For example, Maxwell's original presentation of his field equations were by most ideas of elegance aesthetically inferior to more modern formulations. But to arrive at the more compact - and yes, elegant - formulations, we first had to recognize the rotational symmetry of space, the Lorentz symmetry of space-time, and the gauge symmetry of the E-M field - all of which reflect deeper understanding of the E-M field.
I firmly believe that what strikes us as "elegant" is a conciseness of expression that can be achieved only after we have recognized various symmetries or other aspects of the theory that allow complex formulations to be distilled down to a few fundamental expressions.
Now, just because I believe that successful fundamental theories will always be beautiful does not mean that all beautiful theories are correct! My hope is that beauty is a necessary but not sufficient criterion for a successful theory.
Maxwell predicted electromagnetic waves by making consistent the individual laws regarding the electric field and magnetic field that been discovered so far.
ReplyDeleteIf the demand for internal consistency was there from the start, could any progress regarding electricity and magnetism been made in the first place? (Also, what about the aether, which might have been a useful adjunct until it could finally be discarded?)
Dear Tom,
ReplyDeleteyou say a couple of things very interesting to me:
“Newton's gravity and Einstein's GR would have both been ignored by mainstream physics in today's world."
"To challenge that with a classical field in 2015 would have been impossible, to say the least. Classical fields are a death sentence for any researcher today. GR would have no chance.”
As far as I understand space-time is curved as a conseguence of the limited speed of light.
As said by johnduffied”Who says space and time are quantized? Light is quantized.”
So I would say other two things:
1- General relativity is already a “quantizied theory”. We cannot modify it without destroy the theory.
2- It is like that because we decided to describe the laws of physics in a general way, so doesn’t matter what is the reference system, we will get always the same results.
It is a matter of fact that our observation are made by a local point of view and when we observe our universe, we are at the "center" of our visible universe and it is not invariant.
The sun is orbiting around us, but it is not true, of course.
GR is a very mathematic way to see the things that is quite different from our observations.
GR warns us that what we observe have to be corrected in order to get the invariance, but nevertheless we see things in a different way.
For example, we see the star in wrong position due to the fact that mass bends the light.
So to understand it, I suppose that a complete map of what we see and what it is, is necessary.
Do we really have understood such a map at 100%?
So why not to study a classical field versus a GR field?
Of course, I absolutely agree. No scientific method no science. Call it something else. What really worries me is that, since the breakthroughs in the '70s, in physics we are left with nothing else. We are yet there to check theories of those years with nothing else in view. Meantime, entire careers, fame and glory, rich awards have been given generously. Sometime it has become difficult to get a paper published in a reputable journal just because some powerful group was there to rule. And some of these powerful groups were defending wrong theories obtaining funding and a lot of positions. This implies an undue delay in the scientific progress that does not seem to be the main concern anymore. It is not the truth what really matters now. Rather do a press conference and go in the media.
ReplyDeleteSo, what for the future? It is possible that a failure in supersymmetry could be the cause of a short circuit changing the history. Or maybe, we will be still here, forty years from now, repeating the same criticisms. The point is that this has become a cultural problem and it would be difficult to eradicate.
Arun:
ReplyDeleteYou're misunderstanding my point. I am not saying that demanding an inconsistent theory to be consistent cannot lead to a better theory. I am simply saying that if you only have the requirement of consistency, you will never arrive at a scientific theory. Nobody would ever have arrived at electrodynamics by sitting in a room thinking about consistent sets of axioms. If consistency is all you start from, you will inevitably be lead to an ambiguous theory, one that has a whole "landscape" of possibilities.
Now the theories that people today work on in quantum gravity arguably don't start from nothing at all, but still the point remains the same. If you rely only on consistency, you have no reason to expect that you arrive at a theory that actually describes nature. Best,
B.
I think the requirement of consistency should be obeyed from the very beginning. Here is Einstein informing the world that, although time dilation is symmetrical (either observer sees the other's clock running slow), it is still asymmetrical - the stationary clock runs faster than the moving one:
ReplyDeletehttp://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, A. Einstein, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."
Arun: what's that about the aether? It hasn't been discarded. See what Einstein said in 1920, see what Robert Laughlin said, and see the arXiv. It's a popscience myth that electromagnetic waves don't need a medium to propagate.
ReplyDeleteWell, thank goodness for the Standard Models - of cosmology and particles - and the questions they leave open, and need answering. Not to mention that we have examples that DO predict the Omega Minus - but for the wrong reasons. One might even wonder if Dirac got it precisely right, or did he get anti-matter right for the wrong reasons ? It has been a slog since before Newton, and I see no reason for that to change. Weinberg says there were some judgement calls, and he bet on the simple Higgs. Can someone explain precisely what is wrong with Georgi-Glashow SU(5) ? Or with supersymmetry ?
ReplyDeleteAnd 'consistency' with respect to what ? Someone told Feynman that Path Integrals are mathematical nonsense, then tHooft goes and uses them to deal with the SM ! Go figure. And what's up with Ghost Particles anyway ? The SM uses Dirac algebra - which can not even recover Peano's Axioms - it that a good enough tool ? Oh well, it would be easy if we knew how.
Excellent essay, Sabine.
ReplyDeleteJust today I went through Einstein's 'Brownian motion' paper with our 2nd years. I'm nostalgic for a time when you could extract, with no small effort, a formula connecting one observable to another, and then challenge experimentalists to test the prediction. I particularly like the way Einstein argues that if the experiments don't match the prediction, something is wrong with kinetic theory!
http://www.maths.usyd.edu.au/u/UG/SM/MATH3075/r/Einstein_1905.pdf
The demonstration of quantum gravity has its ideological caveat: it manifests just with phenomena, which were ignored and denied obstinately with mainstream physics (overunity, antigravity and scalar waves phenomena). Many of them are quite apparent and they manifest itself with macroscopic effects. They also violate the postulates of theories on which quantum gravity is based, so they also represent its falsification in certain extent..
ReplyDeleteBee and others,
ReplyDeleteSee this nice talk by Avi Loeb on guidelines for young researchers in astrophysics. (The same philosophy also applies to people working on theoretical physics)
http://online.kitp.ucsb.edu/online/colloq/loeb1/
He has also written about this
http://arxiv.org/abs/1305.5495
http://arxiv.org/abs/1405.2954
http://arxiv.org/abs/1207.3812
http://arxiv.org/abs/1108.5282
Hi Bee,
ReplyDeleteI can sympathize with your frustration for lack of evidence for any theory of quantum gravity. But as long as there is no alternative to string theory which points to a consistent road to unification of forces and possible extension of standard model, I think, we should not attack people who have faith that eventually it will have experimental verification. Of course no body is stopping any one from developing alternative models! Eventually the best theory will win! It has always happened in science before and will happen again undoubtedly in the present situation!
"... not a single one of the existing approaches towards quantum gravity has any evidence speaking for it.” Incorporate MOND into string theory.
ReplyDeleteConsider the problem of attempting to prove, under plausible physical hypotheses, that the Anderson-Campbell-Ekelund-Ellis-Jordan flyby anomaly formula is approximately equivalent to replacing the -1/2 in the standard form of Einstein’s field equations by -1/2 + dark-matter-compensation-constant.
"Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth" by Anderson et al., 2008
This is the way the situation looks before a really fundamental paradigm change.
ReplyDeleteWe have been studying abstractions and ignoring nature. For example, virtually no one reflects on the most fundamental property of the cosmos: nature is hierarchically organized. Very few question strict reductionism and absolute scale. Particle physicists and cosmologists will chase mythological WIMPs, magnetic monopoles, axions, etc. to the end of the rainbow.
So many assumptions are taken as fact and not questioned.
Nature stands ready to be understood by anyone who can "sees what everybody sees and think what nobody has thought."
Logic is a strange thing really. What is valid in one system (say Aristotle) is not valid by modern systems no matter how we arrange three propositions.
ReplyDeleteBut what if nature is inconsistent? Can we change that? Deny there may be somewhere a consistent unified theory that uniquely could have been developed free from experiment?
String theory as well as its quantum foundations break down when we ask what is the wave function of the universe? What is the totality if we imagine it one great string?
Bee.
ReplyDeleteI know why physics is stuck. But you will probably think I have completely lost it, or I am a cracpot, or you will be horrified at the implications. Essentially you guys trust Dirac Spinors. The problem is, while an electron can arrive left or right handed, it does not ever arrive as a positron because that would violate charge conservation. That was obvious getting the spectrum of hydrogen - just half is needed. So there are no Dirac Particles, only Pauli particles. Thus physicists have a defective understanding of algebra at its most elementary level. It is not that surprising.
The horror is that one does not want to give up the Lorentz Invariance of the wave equation. How to fix the Pauli equation to make it relativistic ? After all, Maxwell is. Same algebra.
Nature has to run on its own without human intervention. I think this is a lot better than simply requiring consistency with respect to, say, some nice supersymmetric algebra. The deeper issue is that the algebra really ought to recover Peano's axioms of ordinary arithmetic. It takes Octonions to do that. But now I see why Physics is stuck. Physicists can not make sense of Octonions. So they go for half baked measures.
I think that about sums it up.
Joel,
ReplyDeleteI agree with much of you view. But Dirac's
Nilpotent algebra can be thought of as a holographic limit. But particles seem to resist all we can do to slow their perpetual motion. To imagine the universe as one big hologram up to octonions is a consistent half picture too. So we might agree that something radically new is needed.
Why has there been no progress in so long? I was at the 2004 SLAC Summer Institute, where two of the presenters asked the same question: “What are we missing?” You were and still are missing two things. First, you have no viable spacetime model, and as far as I can tell, nobody is working on one. You won’t make progress until you discover what spacetime is made of, how it is structured, and how it works. Second, you refuse to treat consciousness as the real thing that it obviously is. Many a physicist has said something like, “That’s metaphysics, not physics, so I can’t be bothered with it.” Isn’t the history of the growth of physics congruent with the shrinking of the domain of philosophy and metaphysics? If you now draw an arbitrary line and say, “I will not cross this line because on the other side of it is metaphysics, not physics,” how can you expect to make progress? Boggles the mind.
ReplyDeleteShantanu:
ReplyDeleteThanks for the links to Loeb's lecture/papers! I read one or two of these papers and meant to mention them on my blog, but then forgot about it. He makes some good points there. Best,
B.
kashyap:
ReplyDelete"Of course no body is stopping any one from developing alternative models! "
That's like saying "Nobody is stopping you from travelling to Australia" to the homeless guy who sleeps in the subway.
Besides this, there is no reason to believe that quantum gravity necessarily must go along grand unification. The whole "no alternative" argument is entirely mislead. To me any model that makes testable predictions is better. Best,
B.
Well said Bee. I agree with every point you raise in your post especially about hiding speculations in dense mathematical formulations. I have term that I have coined regarding the decision one takes when confronted with a physical problem. I call it the "Einstein or Hilbert action". If one takes the Hilbert action, one uses abstract mathematics to try to get to the physics whereas if on takes the Einstein action one endeavors to understand the physics of the process via thought experiments etc. and subsequently seeks the appropriate mathematics to describe the physics. I prefer the Einstein action. It gives results that are falsifiable and in most cases a fairly accurate description of nature.
ReplyDelete1. John (johnduffield),
ReplyDeleteNo, it's not only a pop-science myth that electromagnetic waves don't need a medium to propagate.
As far as I know, in India as late as in 2002 (when I began pursuing my PhD in engg.), this erroneous idea was universally accepted---viz. that aether had been rejected out of the theory. I could cite awards-winning, and professionally honoured faculty (and not just science popularizers) from internationally renowned institutes in India, including from IISc Bangalore and IUCAA Pune. (They would also spend some time---if they had any at hand---about Occam's Razor, presuming that the listener would obviously not know about such things.)
And, even in 2015, after browsing just first page on a first Google search, here come up these two samples:
(i) On StackExchange
http://physics.stackexchange.com/questions/19670/why-dont-electromagnetic-waves-require-a-medium
(ii) A Harvard lecturer and text-book author's notes:
http://www.people.fas.harvard.edu/~djmorin/waves/electromagnetic.pdf
2. Every one:
As far the discussion on consistency and all goes, I think some clarification can be had via an introduction of the term: "ex post facto."
In particular, I think, it is not so bad an idea to first pursue only building a consistent theory, i.e., as a first step in a research program.
What is unambiguously bad is knowingly to build a theory that is basically ex post facto in nature.
3. Georg:
I appreciate your reply.
But I have always thought that the term hypothesis referred to a single new idea, as in contrast to a combination of several new and old ideas. I thought that the latter would have to be called something other than hypothesis, and the term "theory" seems a good fit.
A theory could turn out to be wrong later on. But that doesn't mean that until it is experimentally tested for every one of its imaginable consequences, it is not a theory. Higgs' would be an easy example.
BTW, a single idea could be far more valuable or consequential than several theories combined together. Avogadro's hypothesis vs. the phlogiston theory of heat, is an easy example. Similarly, the early fluid theories of electricity. Why, even Faraday's lines of force makes for a theory, in my understanding of the terms, not a hypothesis.
Of course, in the case of Avogadro's hypothesis, since it has held so well, they should have long, long ago changed the name to something like Avogadro's Principle. ... Just a curious historical accident, of nomenclature.
4. John, again:
Nice that you point out that the photon does not approach you (or a detector) in (discrete) steps, as if it were miraculously jumping over the finite chasms of space.
Once again, your position is, IMO, fully right, but then, there are a lot of people busy right now filling respectable peer-reviewed journals (and not just arxiv) with papers that being by assuming that space, time, or both are quantized. Not just as an abstract lattice model, but qua a fundamental theory of physical reality.
And, physics professors are busy being agnostic about the issue. (Ask any physics professor any question about the Planck scale, and then, follow a question regarding his opinion about this idea of quantization of space and/or time. They give you the same answer in popular talks, conferences, workshops, and class-rooms. In this respect, they are being consistent.)
Best,
--Ajit
[E&OE]
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ReplyDeleteBee:
ReplyDeleteIsn't it a hasty approach to believe that the "the low hanging fruits have been picked"? The consequent belief that "we have to climb farther up the tree" is also a risky one. When Copernicus and Gallileo came up with their low hanging fruit of an earth orbiting the sun, scientists of the era were busy with complicated models of hypothesized epicycles. No new experimental data needed for adopting the heliocentric model. As Matti Pitkanen argued above, "The problem is not the lack of data. There exist a rich spectrum of anomalies within physics".
In the situation theoretical physics presently confront, may be theorists should step down the tree and concentrate at reexamining, with pure thinking supported by the tons of existing experimental and observational data, the fundamental concepts we are stuck with. Attentive to the historical lesson given by the Copernican revolution theorists should, IMHO, put much more effort in recognizing our "heavens orbit earth" ways of thinking and our modern counterparts of epicycles, than in further climbing the tree while spending billions of dollars into new experiments that their results (if any) are at the risk of being interpreted erroneously due to historical picking of unripe low hanging fruits.
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ReplyDeleteThis comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteIt is entirely possible that the experimental data exist, but current theories are too primitive to derive postdictions for them. It is likely that the correct theory of QG would explain mass quantization, e.g. why m_p = 1836 m_e. After all, quantum theories often explain quantization of the associated charges, e.g. quantum angular momentum explains quantization of spin.
ReplyDeleteIMO what is missing in QG is locality. Of course, local observables in QG are only possible if QG has fewer gauge symmetries than classical gravity. So be it.
Thomas: Yes, agree with you. There is also the possibility that we are plainly missing evidence because we haven't suitably analyzed available data. People tend to think that if you have data it speaks for itself, but in reality it only speaks after you've suitably processed it and compared it to a null hypothesis. Best,
ReplyDeleteB.
A theory is an inconsistency if it contains incompatible statements. For instance, Newton's emission theory of light says that photons fall with the same acceleration as ordinary falling bodies - in the gravitational field of the Earth their acceleration has a single value: g. In contrast, in the relativistic literature the following accelerations for falling photons can be found (I could give references if necessary): 2g ; g ; 0 ; -g ; -2g.
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ReplyDeletePentcho:
ReplyDeleteIt is correct that a theory is inconsistent if it contains incompatible statement, but the example you use is not an inconsistency, it's an incompatibility with evidence.
An inconsistency exists for example between the Hamiltionan H \sim p^2 + V and Lorentz-invariance. Besides, since it has been mentioned before, resolving this inconsistency does not necessarily lead to the Dirac equation. There are other ways to do it. You need additional assumptions. Dirac eg used the requirement that the operator be linear. This just drives home my point that consistency isn't enough because it's not a unique requirement.
Best,
B.
There is a new idea in physics which has led to the creation of a plausible quantum theory of gravity. http://www.worldscientific.com/doi/abs/10.1142/S0219887815500425
ReplyDeleteIt is the only quantum theory of gravity that predicts the correct value of the cosmological constant eliminates singularities in GR, predicts galaxy rotation curves, derives the Baryonic Tully-Fisher Relation and calculates the baryonic mass of the universe.
Sabine:
ReplyDeleteYes this is not a genuine inconsistency insofar as the different values for the acceleration of falling photons are taught by today's authors while Einstein's 1915 theory gives a single value: (-2g).
I am not sure which evidence you mean when you say "incompatibility with evidence" so let me choose the most relevant one - the Pound-Rebka experiment. It can be shown that both the Newtonian prediction (g) and the Einsteinian prediction (-2g) are compatible with the experiment but (-2g) is absurd per se and has additional absurd implications.
Pentcho,
ReplyDeleteIf we can entertain intrinsic curvature we can imagine intrinsic curvature . It is absurd only insofar as time is asymmetric by this every other shift of count as a positive absolute value as a consequence of binary or ambiguity in arithmetic. Even three spaces over anticonsistency is evidently not necessarily anticompatible to our simplest extension into five space. The CC has the value it does naturally 5! In the next level subspace. It by maximum symmetry dividing a sphere into 120 regions exhausts reflections as if classically as the most parsimonious of theory's.
Imagine intrinsic linearity, that is
ReplyDelete"The unreasonable effectiveness of mathematics in the natural sciences" has received a lot of attention (google it for references if any are needed) which I am skeptical about. This post has tangentially supported my skepticism, because it supports my belief that mathematics can model anything we are capable of understanding (since, as I believe, math and thinking are the same thing - when you have three errands to do and decide which is the best order to do them in, you are doing math) - but that for every real (empirical) thing it models, it can also model an infinite amount of unreal things. At least, that is how I understand (and agree with) Dr. Hossenfelder's argument.
ReplyDeleteMathematics becomes theory through empirical testing. Euclid, Earth's surface, fail. SUSY, dark matter, quantum gravitation say "more mathematics!" More Euclid does not fix Euclid.
ReplyDeleteVertical wormhole in a gravitational potential. Bottom entry falls out the top exit into the bottom entry. An entered mass accelerates forever. Give it a charge, have it fall through a solenoid as generator. No wormholes. How much wormhole theory fixes that?
Stuart: Although I do not know much about your line of approach, I am quite curious to look at your paper. Unfortunately it is in a journal which
ReplyDeletemay not be readily available. Is there an online source? If I am not mistaken, we had a little exchange on Matt Strassler's blog.
http://arxiv.org/abs/1501.01919
ReplyDeleteThese are not paradoxes. Theory is OK locally but off by 120 orders of magnitude globally. Theory is wrong. The pendulum equation is not nearly
T = [2(pi)]sqrt(length/gravity)
except locally. Mathematics is necessary but not sufficient. All the fun is in the carefully excluded footnotes.
If internal consistency were sufficient then J. T. Graves would have been able, in principle, to derive the Standard Model in 1843. That was before anyone had electricity - or even sliced bread ! Clearly that is a kind of absurdity - like thinking that Hamilton could have derived the Pauli equation and predicted the Stern-Gerlach experimental results. He had the algebra, but knew nothing of electrons. Heck, he could have derived Maxwell too - same algebra.
ReplyDeleteThat is all to underscore what you say about observation and experiment and doing science. It simply can not be done by contemplating algebra in isolation from experiment.
The real problem is that while quaternion algebra deals with geometry - which we can check, the ugly fact is that Octonions define particles, and we can not inspect particles to verify whether they make octonionic sense. If we could, you could stick a fork in Physics, it would be done, or this idea would be falsified. That is the problem with Popper's idea - particles do not cooperate with any simple idea of falsification or verification. As Einstein Rings demonstrate, the same is true of geometry ! Subtle is the Lord !
And I saw the reference to the Pound-Rebka experiment. Praise MTW.
As to Max Tegmark's idea - I suspect it is a big example of what Quine called "bloated ontology", not that I intend any offense. But I haven't seen anything more bloated than the multiverse.
Joel,
ReplyDeleteThere is no doubt the ancient Aegyptians could have built Cadillacs if they had the technology and prototypes were not so expensive. Their kids played with wheels and axel cart toys when the adults rolled stones on logs. What toys today could advance technology? Algebra is said the hardest branch of mathematics but the trunk is the calculus and it seems most commenters do not know essential differences in its development. So how high is the low hanging fruit? Gauss wanted to leave the best if them, a few fruit and a shining diamond. In the tree top branches is where the fun begins both like palms growing from the top down or pine from the roots up. Usually apples bud into pairs and one falls off like half the nerve connections of a child adjusting to night terrors. Bloated ontology is a cop out philosophic term that in its do once post modern experiment tells us little of time balanced or moving. Seven manifolds if Riemann limited this way cannot see more in the seeds or pits of such fruit let alone predict them. The scientific method is sound but falling mysteriously from the tree we need a new method for anthropology.
Hi Bee,
ReplyDeleteYour article to me is a philosophical position that recognizes deduction to be used with induction.
This distinction is important.
To get too, any self evident position in the ascertainment of first principle, it is necessary to be able to make an intuitive leap with the mind. This is so that induction is used to keep to the very basics of the deductions that will allow the science to move forward.
L. Edgar:
ReplyDeleteyou mention Gauss - evidently he discovered Quaternion rotations before Hamilton, but never published.
Robert Hermann wrote a book on Spinors, Cayley numbers and Clifford Algebras,(MathSci Press) and had some very interesting remarks on the beauty of calculus and algebra together. That book is around here somewhere !
Science has under gone a perversion regarding empiricism making this aspect of the induction dogmatic. They have lost sight of the ability to be able to use that mind to theoretical push boundaries of thought. That is called Rationalism.
ReplyDeleteIt does require a logical exploration of truth regarding the theory made. If the basics of this journey has been true to the inductions made, at it's most basic principle, then the move forward in a inductive state is the science that seeks to understand the knowledge put forward.
Quantum Chromodynamics
ReplyDeleteI agree with Sabine. But even simple and reasonable "new" ideas encounter a severe resistance from the mainstream; that's another reason for the crisis.
ReplyDeleteL. Edgar
ReplyDeleteIs algebra the hardest branch ?
I'm a big fan of W.K. Clifford and he makes Clifford Algebra look like it could be taught in 4th grade. David Hestenes "SpaceTime Algebra" is a very interesting read on the subject. It includes the Reals, the Complex, and Quaternions and Complex Quaternions - the last being the same as Pauli Algebra. It includes Dirac algebra too. So
1 + x +y + z + xy + yz + zx + xyz
for a 3 space multivector. The x,y,z are just the pauli matrices ! Don't need any indices or greek letters. Pretty straightforward stuff.
Some seem to think that whether Octonions are important is a matter of opinion. Anyone who thinks so should read AA Albert's Studies in Modern Algeba. People worry about nonAssociativity, but don't worry about nonCommutativity much. If you want to define lots of analogs of a photon, you need things like
(oa)(bc) and o(a(bc))
the parens are illuminating - these are 'volume units' or pseudoscalars. (oa)(bc) is like a "cheshire tetrahedron" having just two of the six edges. Put in the remaining two and you get
oa + ob + oc ...
like a Maxwell E+B. Put the oscillators in a 3d cubic lattice and it sure looks like an ElectroMagnetic field .
an ao+bo+co looks a lot like a Pauli Spin Vector. Put that in the cube too - we can fit 2 tetrahedra in a cube. If there is a good reason to dot the B.S then it provides a term in the Pauli equation.
If I wasn't such a dunce I could have thought of that 5 years ago. A lattice is a cool way to put oscillators into 3 space in various ways.
too bad Clifford passed away at 33 years of age.
Clifford is the closest to my own view but his is not the deeper more finite groups in the picture. I think Einstein said that about algebra. I think arithmetic is deeper. What is the heart of algebra anyway but the distribution law?
ReplyDeleteI replied a comment on one of Bee's links yesterday which occurs to me may be. Posted here as well before all our cross link sharing gets lost in the sheffling.
ReplyDeleteVaibhav. What is equation 13?
Hocus Pocus could reduce to a deeper level of Helter Skelter "incompatiblity" on one hand and absolutely consistent magic on the other hand. The problem with the holographic principle is our core ideas as to what are degrees of freedom or for that matter how we can have different ratios of distance between different representations of the same span of a given space. Time not so much said to be an illusion and only surface a discrete measure of entropy. Various degree of freedom models are then partial illusions at least locally for what is there as material physicality over a few dimensions. Mathematics needs not be mysterious, unreasonable where it applies but without a consistent bigger picture it cannot be the deepest foundation nor free of consistent partial illusions. Some geometric shapes are almost possible but cannot be ultimately stable. Nevertheless new results from experiment suggest ways to warp space or bend light. These a much like mapping from a plane into a space which distorts say a perfect truncated octahedron into preferred directions which may or may not determine islands of higher atomic elements stability.
Uncle AI, you know of course if you turn a solenoid around it does not change the direction of the chirality.
ReplyDelete@kashyap vasavada
ReplyDeleteHere is a beta version of the latest paper.
http://www.academia.edu/8604226/The_Schwarzschild_Solution_to_the_Nexus_Graviton_Field
It is of course not as developed as the final paper since it does not include Black hole quantum phenomena and calculations of the baryonic mass content of the observable universe.
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ReplyDeleteRegarding the subject of quantum gravity, I explained many times here, that the subject of quantum gravity is just the everyday "classical" physics at the human observer scale with all its molecules, trees and bees (between others). This is because the quantum gravity is supposed to unify the quantum mechanics and general relativity theories at all dimensional scales - and the human observer scale sits just between the dimensional scales of quantum mechanics and general relativity. In this extent the experimental verification of quantum gravity is sorta trivial - we are facing them all the time...
ReplyDeleteEven if we would restrict the quantum gravity phenomena to the vacuum phenomena, we will face a wide spectrum of extradimensional fields and effects at the human observer scale. For example the Cassimir force cannot be excluded from quantum gravity effects, just because it has been recognized and named twenty years before the quantum gravity field itself. So that what the physicists are doing by now is sorta searching for light under candlestick. The extradimensional phenomena are all around us, because common world around us is heavily extradimensional.
Ajit: IMHO the "trouble with physics" is that physicists believe in popscience myths. They don't study the fundamentals, and spend years wasting their time on something that's "not even wrong". Then once they've dug themselves into a hole, they will not admit that they were wrong. So that's where they stay.
ReplyDeleteJohn (johnduffield),
ReplyDeleteUnfortunately, I have only browsed through Lee Smolin's book and not read it. I have not browsed through other similar books... Just no time at hand...
But yes, sometimes, I do wonder how such physicists (of the kind you mention) manage to get funding, and even manage to continue doing so... What makes that possible. And, a related question: Couldn't the money have been spent better? ... Then comes a closely related question: Would AT&T Labs, Westinghouse Electric, Siemens, etc. (all of an era long gone by now) have sponsored such ``research''?...
No, not all physicists are like them. The fact that this discussion occurs on a blog of a working physicist, itself tells you something about the fact there is a certain level of discomfort within the physicists community itself.
But, clearly, there are some broad systemic issues too, which are quite separate from any epistemological or philosophical issues that someone may face at a personal level---e.g. how irrational philosophies make physics (and mathematics) more difficult than it otherwise would be (for understanding, teaching or doing research).
Anyway, all this is too big a matter for me to even begin pondering at a detailed level (it could be science administrators' job), even though at a broad, philosophical level, I think I am fairly clear and comfortable about such issues. [Here, I have benefited a lot from Objectivist Epistemology; also check out Harry Binswanger and David Harriman's talks and books.]... In action, I usually just try to concentrate on what I want to do, my own research goals. And yes, in a way, I do feel lucky that I can work in engineering, and still manage to do something on the theoretical physics side, too.
Best,
--Ajit
[E&OE]