Of Particular Significance

Quantum Field Theory, String Theory, and Predictions (Part 2)

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 09/24/2013

[This post is a continuation of this one from Monday]

Coming to Terms

Before we continue, a little terminology — trivial, yet crucial and slightly subtle.

Think about the distinction between the words “humanity” and “a human” and “humans”; or “higher education”, “university” and “universities”; or “royalty”, “king” and “kings”. In each case, the three words refer to the general case, the specific case, and a group of specific cases.  Sometimes you even have to use context to figure out whether you’re dealing with the general case or a group, because “humans” or “kings” is sometimes used in place of “humanity” or “royalty”.

In a similar way:

  • The words “quantum field theory” (with no word in front) refers to the general case: the general type of equations that we use for particle physics and many other fields of study.
  • The words “a quantum field theory” refers to a particular case; an example of a set of equations drawn from the general case called “quantum field theory”.
  • The words “quantum field theories” refers to a group of particular cases: a set of examples, perhaps ones that share something in common. We might talk about “some quantum field theories”, or “all quantum field theories”, or “a few quantum field theories”.

Before I go on, I should probably point out that string theory/M theory is different, for a weird (and perhaps temporary) reason — it appears (currently) that there’s only one such theory that has fully consistent mathematics and contains a quantum version of Einstein’s theory of gravity.  That was figured out in the 1990s.

However, in that theory you need another, similar distinction. Let me postpone a proper definition until later, but roughly, a “string vacuum” is a particular way that string/M theory could manifest itself in a universe; if you changed the string vacuum that we’re in (says string theory), we’d end up with different particles and forces and somewhat different laws governing those particles and forces. Many such vacua would have particles and forces described by a quantum field theory, along with Einstein’s gravity; many (perhaps most) other vacua might not have this property.  And so, as before, we need to distinguish “string vacua in general”, “a string vacuum”, and “string vacua”, plural.

Now it’s time to talk about quantum field theory — the general case — in more detail.

Quantum Field Theory and Its Predictions

Does quantum field theory as a whole predict anything? In short, if you knew a universe had physics described by a quantum field theory, but you didn’t know which particular quantum field theory, what could you predict?

The answer is: almost nothing.

If you’ve been following this blog with care, or have read some books or articles about particle physics, you might well think: quantum field theories have fields; and fields have particles; so here’s a prediction: there should be some particles of some type.

Nope.  You’ve learned your lesson well — everything I’ve told you on this website suggests that it is true — but the conclusion is false. I’ve been white-lying to you this whole time, and I have to apologize for that. Quantum fields do often have particles. But many quantum field theories are scale-invariant. A scale-invariant thing looks and behaves more or less the same in a microscope no matter how strong a lens you use. The wikipedia article on scale invariance actually has a nice animation of a scale-invariant process. Another example of something scale-invariant is a fractal. And in a scale-invariant quantum field theory (except for one in which there are no forces at all), there are no particles. I’ve told you that particles are well-behaved ripples in fields… well, it’s true, but in a scale-invariant quantum field theory with at least one force, any such ripples die away and turn into several ripples, which die away and turn into several ripples, which die away and turn into several rippleswhich die away and turn into several ripples, which…

Click here to see an animation of a scale-invariant process, called the Wiener process. Animation from Wikimedia Commons (author Cyp). For more information, see http://en.wikipedia.org/wiki/File:Wiener_process_animated.gif

In short, no particles. This has been known for many decades (I’m actually not sure how far it goes back in the form I just described.) We observe this behavior in experiments — not in particle physics, where it isn’t relevant (at least currently), but in many solids, liquids, electrical conductors, magnets etc. that are undergoing “phase transitions”, such as melting, or spontaneous magnetization. In some cases we can also calculate this behavior, exactly or approximately. In some cases we can see this behavior emerge in computer simulations of real or imaginary materials. So we know there are many quantum field theories that don’t have particles.

[This might make you wonder if there are string/M theory vacua that don’t have strings. Good thinking… though actually there are other, unrelated ways to end up without strings… more on this later in the month.]

But If There Are Particles… A Prediction!

But here’s something important that we can predict. If we are studying a quantum field theory that does have particles (now we are talking not about all quantum field theories, but an interesting subset of them) then

  • the particles will come in types (in our world, electrons are examples of a type of particle, Higgs particles are an example of another, etc.); and
  • two particles of the same type will be identical in all their intrinsic properties. They will have the same electric charge, spin, mass [i.e. rest mass] etc.; if somebody swaps one for another, you won’t be able to tell the difference.  (In our world, all electrons are identical.)
  • Furthermore, in a world with three (or more) spatial dimensions in which Einstein’s special relativity is true, then particles of each type will be either fermions or bosons. (The Pauli Exclusion Principle, which determines all of atomic physics and chemistry, is a consequence of the facts that all electrons are identical and that electrons are fermions.)

Again, these are general prediction, not of quantum field theory as a whole, but of the subset of quantum field theories that have particles in the first place.  The Standard Model, the quantum field theory that seems to describe much of our world very well so far, is an example of one that has particles.

That these are the most important predictions of quantum field theory with particles was pointed out to me, when I was just out of graduate school 20 years ago, by none other than Freeman Dyson, who helped develop quantum field theory back in its infancy.

Moving Toward Particular Quantum Field Theories

Now, what about specific quantum field theories. What can we predict about them?

The answer, hardly surprising, is: it depends.

  • In some quantum field theories, we can predict an enormous amount, by doing some straightforward type of calculation.
  • In others, brute-force computer simulation of the quantum fields makes it possible to study the particles and forces described by that quantum field theory, and allows us to make some predictions.
  • In some quantum field theories, we can predict a smattering of things very well, using fancy math methods (for example, using fancy geometry, or supersymmetry, or string theory).
  • In still others… unfortunately, many of the most interesting… we have absolutely no idea what’s going on.  Sometimes we have the equations we’re supposed to use, but none of our methods for calculation work for those equations.  Occasionally we can make a good guess, but we can’t always check it.
  • In yet others, we don’t even know what the equations are that we should use to start studying them.  In fact, the existence of some of these theories was, until relatively recently, unknown. We didn’t even suspect they existed.  Maybe there are even more that we still don’t know about.

I’ll start describing these categories of quantum field theories in my ensuing posts.  Fortunately for particle physicists, the Standard Model is mostly in the first category, with a little leakage into the second.

The Standard Model: A Quantum Field Theory Of Particular Significance

Continued HERE.

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145 Responses

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  2. * I made this up. (Except for the stack of disks part. I added that just to tie it in to a concept I had already thought about.)

    * This is how I think about multidirectional space, string theory particle entanglement etc. Multi-dimensional space. (in excess of 3.) Look at the “shadow” of a 3 dimensional object and it will be a 2 dimensional representation of a 3d object .. 4 dimensional objects “shadow” would be a 3 dimensional representation of a 4d object. Think of existence being a bubble with everything existing on the membrane of soap. The first dimension as well as the extra dimensions could be perceived as membranes. You have “light” projecting from outside the bubble to inside. The projection inside the bubble is our perceived universe. This would also allow you to have multiple simultaneous universes occupying the same space by having different types of “light” projecting at different angles/frequency’s etc. (Perhaps it takes 3 lights to create our 3 dimensional space. Our arrangement of particles consists of those projections. This could explain why we can only perceive 3 directly.

    These projections from this membrane would represent different “Particles” that would have an intimate relationships with one another which would not be immediately apparent. (particle entanglement etc.)

    This would also explain string theory .. or at least my limited understanding of it. Why particles look like strings or loops from different perspectives. (vibrations of the membrane or membranes interacting with one another.) This “light” would also be the limit of how fast anything could move. If you were to travel the speed of light, which would essentially mean you have reached the membrane (the threshold between dimensions) you would have infinite mass/energy and occupy all space and time. From our perspective anyway. (And or you would “pop” out of our existence. Which might translate to the projection of your particles back into the bubble so you are not being destroyed but changing states.) (You would be projected into 3 dimensions and operate on a higher one) This projection could also be viewed during any point depending on which portion of the projected light you were looking at. (Referencing the wiki article where they describe it as a stack of disks representing the state of the universe at a given time.) Like the light we see from stars millions of years old. This concept would also explain the time differences when moving at speed. You change your location on that projection. Imagine you are on a highway .. with everyone else going a portion of light speed. You accelerate which goes into their future while the time passes to you at the same speed. You are in their future and your present. Every car on the road exists through their entire time line simultaneously. (As long as the car exists in time. This “car” is a collection of particles and or energy in a certain relationship. These particles/energy can’t be destroyed but their relationship can change into something not car like.) We just cannot perceive it. Otherwise if you were to take a flight and accelerate into the future nothing would be there. You could translate this up through more and more dimensions with each iteration being able to interact (and be in a relationship) with the others but not perceivable by us other than through inference.

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  5. I think you misunderstood the metaphor. A “suicide bomber” does not need to know anything except how to detonate his explosives. He (or she) hardly needs a brain. He can cause a lot of damage to his targets but does just as much or more to himself. And he does is all because of ideas someone else put into his mind. Einstein was not a “suicide bomber”.

  6. I follow Dr. Woit’s blog for years and I believe that he is essentialy right. Strings and related theories do make predictions, but they are untestable in the forseeable future (zero empirical support). Dr. Woit’s second objection (also right) is that strings dominated the field for decades to such an extent (and with a huge academic support) that a whole generation of clever theoretical physicists are now used into thinking in terms of string theory. This has impeded the growth of other possibly radically different ways of thought. I believe Dr. Woit has been vindicated by the recent LHC results and through the recognition by at least some string theorists that the field now has many troubles. Pr. Strassler’s blog is also wonderfull, but in my opinion he spends to much time lately trying to explain what string theory really is. I look forward to reading his more usual (instructive and excellent) articles.

    1. I wonder how you (and Woit) propose to achieve the aim of stopping the domination of particle research by string theorists? Fire Witten, Susskind, Maldacena, Polchinski and Co ? Forbid best students from choosing them as advisors (and force them to work with Peter Woit)? Stop public financing of research into string theory and forbid Russian billionaires from funding prizes that award millions of dollars to string theorists for research into “fundamental physics”? How else?

      And how are you going to achieve this growth of “other possibly radically different ways of thought”? Clearly your “leader” is incapable of producing any himself (you can search for his research papers on Google Scholar and check it for yourself). So who is going to do it for you? Established physicists who have been forbidden working on String Theory? Young physicists who have been banned from choosing thesis advisors of their choice? Fat chance.

      The entire anti-string movement is incoherent – it is based on the assumption that people who don’t know and don’t understand are the ones who know best and that their opinions should be counted in choosing the best directions of research. Fortunately this idea is so absurd that cannot possibly succeed (except in providing Peter Woit with a career and “fame” he could never have achieved by doing science). However, the disgraceful slanders against the character of some of the best of the world’s scientists involved in all this should be seriously annoyed to all others who seriously work on science for they can themselves become one day the next target. (On a personal note: for me it is almost equally irritating to observe so many who are clearly incapable of understanding serious mathematics or its deep relationship with physics being so conspicuously proud of this fact!)

      1. Not to forbid strings, but encourage other directions. Because other directions are discouraged. For example, I cannot continue my reformulation approach since it excludes renormalization. The latter is considered “an achievement” rather than a failure to formulate a theory correctly.

          1. In order to carry out my research program, I need funds. I cannot do it on my own. So, a research position/grant/etc. will do. However people say me: “first you finish your work, and the, we will see”. No way do get funds otherwise. And normally all oppose my subject – “reformulation” because they do not like my critics of renormalization. It is even difficult to publish something on this subject. It is discouraging and it is a kind of forbidding.

            Not only “mainstream” subjects (often too speculative) should be supported by academia and other sponsors, but other reasonable directions too.

      2. Well, I will not respond to your petty personal attacks against me and Dr. Woit. I shall tell a story. Once upon a time I read Brian Greene’s Elegant Universe and, behold, a wonderfull picture was opened before me, a cosmos of strings, branes, multiple dimensions and other amazing things. And I loved it deeply. But then I read Woit’s book and Smolin’s book and I began to become skeptical. Now I believe strings are the luminiferous aether theory of our days. And again a real genious, an Einstein, if you like, is needed to break the barriers. Witten and the others are very very very good, but not Einsteins. And that’s the problem.

        1. So does that mean that you blame Witten and the others for not being Einsteins or for pretending to be Einsteins when they are not? Or perhaps you think that only Einsteins should occupy themselves with theoretical physics and non-Einsteins should find something else to do? And how are Woit’s and Smolin’s books going to help us to find these new Einsteins?

          Come to think of it: if you read this whole thread carefully you will see that there are some posters who already believe themselves to be new Einsteins except that, unlike the real Einstein, they need “encouragement”. So perhaps a more constructive way for Peter to spend his time would be to try to provide some of it instead of running a training camp for suicide bombers in the “string wars”.

          1. P. Woit feels comfortable with renormalization, so he deletes my comments on it. And I do not believe I am “already a new Einstein”, you exaggerate here. I just want to carry out a research and do not find any support despite in former times it was a mainstream activity. Today generations of renormalizators win with their quantity, not with scientific arguments.

          2. All I wanted to say is that Woit’s and Smolin’s books opened the eyes of many people about the real status of strings as an unsuccessful theory. I admire Witten and the others for their brilliant cleverness (one that I obviously don’t have). But their attempts are now clearly a dead end. The new Einstein will turn up out of the blue. Historical Einstein was called “a lazy dog” by his teacher and no one expected him to revolutionize physics. He was not part of a training camp, but he was a suicide bomber!

  7. I think the main problem of physics is that prior to 1920’s theories were constructed to explain experiments but since the situation has changed. As experiments became more complicated the theory had to lead. While that was ok for a while, however, more and more extravagant theories had to be devised which forced even more complicated experiment (only one LHC) leading to a vicious cycle.

    All that culminated to String and brothers with no experiment only “Mathematical Consistency”.

    My conclusion is that the process and the results went astray long time ago and a mountain made of sand was built and it will crumble sooner or later to its base once the correct theory is found. The correct theory will be found much more quickly only by abandoning this faulty process and insist on a one that is less prone to institutional politics that has created such environment.

  8. Dear Dr.Strassler : Your blog is submerged under sub-blogs of all kinds , it is almost every one on the net wants to institute his own blog as a parasite to yours , Please , we need your precious posts….don’t waste your time it is very valuable ……thank you.

  9. “only one such theory that has “fully consistent mathematics”

    I’ve seen the phrase “mathematically consistent” used a number of times in QFT and string theory and now you’ve referred to it in M Theory. What does this fundamentally mean?

  10. I have not intended to actively participate in these discussions because I am (still) very ignorant of physics and very biased. But now that I have seen lots of others with exactly the same qualifications express very definite opinions, I have decided: why not me too?

    I am a mathematician working interested in topology and geometry. I have been aware for over 20 years of the usefulness of QFT and (more recently) String Theory in my work but until recently I was content to rely on my collaborators knowledge of these matters. Quite recently I decided to try to fill in these increasingly embarrassing gaps in my knowledge. Almost as soon as I started doing that I realised that these “applications” (perhaps “inspirations” would be a more accurate word) were even more mysterious and beautiful than I had ever expected. It is also only quite recently (within the last three years or so) that I discovered the “string wars”. Once the initial shock of discovering that the “social” side of physics was not quite like that of mathematics, I found myself naturally siding with the people who had discovered all these remarkable ideas rather than with their detractors. That is the reason why I would side with String Theory rather than Loop Quantum Gravity. Both have borrowed ideas from mathematics but only the former one gave anything back.
    Of course I am being somewhat facetious. I do think however that physical ideas provide such powerful intuitive insight in mathematics ought to be, in some sense true. They should be ideas about some sort of “reality” and contrary to the common opinion, this “reality” does not seem to be “purely mathematical”.

    But in the case of Dr. Peter Woit and his criticisms of String Theory I have a second, even stronger reason to be biased. As far as I am aware Dr. Woit’s criticisms of String Theory especially as the so called “Theory of Everything” are purely negative. Not only has Dr Woit not contributed anything substantial to the development of any alternative – but he has never been able to suggest any possible alternative. He seems to demand that such alternatives be found and insinuates that they would be found if the “vested interest” of “string theorists” did not suck out the blood out of non-string theoretic physics. But this sort of argument is not just a slander of the character of some of the most talented of modern physicists (who could easily succeed in almost any other area of physics or exact science) but it also seems to rely on a very doubtful premise. The idea that string theorists cover up the “failure” of their research project and surpress alternatives sounds to me absurd. First, string theory has already achieved enough for its leading contributors to be assured of a favourable mention in the history of both physics and mathematics. Secondly, it’s hard to imagine that if, for example, Edward Witten or Leonard Susskind or Juan Maldacena or many others became aware of a better alternative to String Theory as a Unified Theory, they would keep it secret lest revealing this fact would jeopardise their own scientific standing. Obviously the opposite would happen, except of course, in one highly unlikely situation. I have noticed that on every physics forum there seem to be several regular participants who believe that they themselves are already in the possession of the correct and, of course, very much simpler replacement for String Theory. Indeed, if this was the case, one would imagine that the credit would have to go to these so far unknown “new Einsteins”. But that does not seem to be the kind of thing Dr. Woit has had in mind.

    The basic point I am trying to make is that every major scientific theory will come out looking quite poor if subjected only to a barrage of criticism without any comparison with viable alternatives. This is true enough of theories in physics but even more so in other subjects, most notably the Theory of Evolution. It is only when compared with all the existing alternatives that these theories are seen as convincing in spite of numerous valid sounding criticism that can always be made of them. So, at least as far as I am concerned, until someone comes up with something better, String Theory’s position is as solid as that of the Theory of Evolution – there is no even slightly plausible alternative in sight.

    1. Regarding “String Theory’s position is as solid as that of the Theory of Evolution“:

      In my opinion this is a very unfortunate connection to make. It does not serve either side well and opens up avenues of attack for unwarranted criticism of both sides.

      On one hand (evolution) you have an extremely well established standard theory of its respective area of research with lots of empirical support. On the other hand you have a theory that is mathematically very interesting, valuable as a tool as Prof. Strassler points out, but that – as a fundamental theory for particle physics and quantum gravity – is highly speculative with (at this point and to my knowledge) zero empirical support.

      I know you said “as solid as”, and so strictly speaking you made only a claim about the degree of solidity, but this statement is far too likely to be understood as a claim of similar quality of both sides to leave it uncontradicted.

      1. M-Theory does, of course, have “lots of empirical support” from the parts of the theory, such as Quantum Mechanics, that it “unifies”. It also makes predictions independent of these parts – but these are at present impossible to verify. One can say many analogous things about The Theory of Evolution, which also has problems with “testability” and “falsifiability” (including the question of whether the most testable evolutionary theory – EVO DEVO – should be considered a part of Darwinian Evolution or rival theory) but this is a can of worms I did not want to open. I only mean to say that in the absence of viable rivals a self-consitent theory *supported by the evidence* (see above) is the best we have and can be justifiably considered the current “gold standard”.

        1. Absurd. Evolution is, because of its complexity, the best tested theory we have and the one that makes the most certain observations. We know for example that universal common ancestry applies with > 10^2000 times larger likelihood than multiple common ancestry due to the combinatorics of phylogeny.

          All you need to reject that observation is to find an example of a different common ancestor. All you need to reject evolution is to find examples where phylogenies are impossible (famously, a pre-cambrian rabbit).

          Also, evo-devo is by definition part of evolution, because biologists are defining theories additively – just add found mechanisms. No mystery there.

    2. “String Theory’s position is as solid as that of the Theory of Evolution – there is no even slightly plausible alternative in sight”.

      Perhaps Lucretius, but I doubt it. My suspicion is that 100 years from now the Theory of Evolution will still be going strong, but string theory – as a physics theory – will be long forgotten. Time will tell…

      You know, in this age of social media where everyone chimes in, it is all too easy to forget; the laws of physics are not established by consensus. Nor are they established because the math is judged to be pretty. Rather, theories are established because they conform to experiments. Fortunately, for those of us that are looking for a little insight into the real world, your statement that-

      “I do think however that physical ideas provide such powerful intuitive insight in mathematics ought to be, in some sense true.”

      – is not the criteria for acceptance of a physics theory.

      Unfortunately the days of testing theories by rolling balls down inclined planes, as Galileo did, are long gone. Experiments are expensive and budgets are limited. So the number and type of experiments performed are limited. Consequently only a relative few of the many proposed theories are ever tested experimentally. So which ones do get tested? Well naturally the most recently established theories relativity and quantum theory – the very pillars of 20th Century physics. And of course we probe the very small – particle physics, and the very large – astrophysics and cosmology. This is, I think, as it should be.

      As I understand it, String Theory and its more modern derivatives like M theory do not lend themselves to much experimental testing. (I say ‘to much’ rather than ‘any’ because I know that a version of M theory containing at least one “large (10^-6 m) extra dimension” predicted a great strengthening in gravity as well as a change from 1/r^2 to 1/r^3 at microscopic distances. However, this was found not to be the case). To my way of thinking any theory that cannot be verified experimentally now or in the near future is of very little use as a physics theory now or in the near future.

      So what I think some people are saying, and I agree, is that we should not give a theory, any theory, which does not lend itself to experimental confirmation the position of dominance that we have given to String Theory and its derivatives. By so doing we may inspire more thinking outside the box…

      1. I don’t understand what you mean by “we” in “we should not give a theory…the position of dominance that we have given to String Theory and its derivatives”. Who is this “we”? I certainly don’t remember being asked for my opinion on this issue. As far as I am aware there is no committee or any public or private institution that decided which theories should be given what “position” nor is it decided by a referendum or even a poll of people with PhD’s in physics.

        There is, of course, the Nobel Committee and Mr. Yuri Milner and others of that kind, but they are not in the habit of consulting the general public (and I don’t think they should be). In most areas of science (and certainly in mathematics) there is a fair degree of consensus about who the leading researchers are and (at least in a free society) they are left to judge by themselves what are the most promising and important directions of their research. Sometimes (more rarely than most of us) they turn out to be wrong but all we can demand of them is that they act in good faith and follow their own best judgement and conscience. It is the insinuation that the physicists who have been working on String Theory have somehow not been doing this that I find offensive in some of the writings of Dr. Woit’s and his followers.
        The issue of financing of scientific research, although not completely unrelated, is not really suitable for this discussion.

  11. Hi Matt,
    It always surprises and depresses me when people in your realm form rivalries. It doesn’t matter if it’s you and Woit, Hawking and Susskind, or whoever. Sure, for us minions it is dramatic and exciting, even enlightening for the more knowledgeable among us, but I keep wondering what would happen if you guys were collaborators instead. I mean, you are both pioneers and explorers, dealing with the great unknowns every day. And with science, even hard facts can only be considered tentative until better technology or someone with deeper insight comes along. So, why the angst? When someone cries out to the Universe “Matt is WRONG!!!”, just let the guy have his say, and then block any further posts from the troublemaker. It’s your blog, right? Besides, if he has never been wrong, then he might have some justification to complain. However, since he is as human as you, he’s probably made a few errors–maybe even errors that he still defends as facts–and is as vulnerable to attack as you are. Remember poor old Fred Hoyle? And everyone thought he walked on water…

    Anyway, I’m going to enjoy your promised articles.

    1. Note that Woit isn’t a practicing physicist, so any science collaboration is pretty much out of the question. In my view Woit is an anti-string ranter while Strassler goes overboard in being precise and saying nothing that could be wrong under any circumstances. Unless it’s about a string promoter making completely unfounded statements the two won’t see eye to eye.

      Although I think Strassler is giving this matter far more attention than it deserves, I’m really interested in reading the articles as well. A pretty decent silver lining as those go 🙂

  12. There are some phenomena that are scale invariant. Take for example anhilation and creation. This takes place in quantum fields with particles, in the life and death of organisms, stars,societies etc. Annhilation and creation gives reality a false infinite existence as the philosopher Hegel puts it. Therefore only information is carried from one generation to the next be it genetic, 4 momentum, knowledge etc

  13. Is there a basic conflict between string theory and particle-physics QFT when it comes to explaining the fundamental nature of particles? Because it seems that:
    1) In string theory, particles are fundamentally just vibrating strings, closed or open.
    2) In QFT, ‘particles’ are actually waves of the quantum fields, which due to their quantum nature have particle-like behaviour, ie: these waves carry energy and momentum in discrete sizes. In this view, there is no such thing as a particle at the fundamental level: a quantum field can manifest both wave-like and particle-like behavior.

    It seems the string theory description of a particle is closer to what we usually mean by the word ‘particle’, in that it is not the wave of a field.

  14. Am I right if I say that the strong force is SI as we can imagine an extended line of protonsneutrons…PN..PN.. Where the strong force will extend without dependence on distance !!?

  15. The minimum energy of a particle is obviously an example of something that is not scale invariant,and you clearly distinguish between this and scale-invariant. Please excuse my ignorance, but could you give me an example of a physical phenomenon that is (potentially) explained by a scale-invariant theory?

    From my perspective, classical descriptions of gravity sound awfully like an infinitely divisible effect,which would strike me as a property of an SI field.

  16. Does the general case/specific case/group of specific cases also occur in classical mechanics? For example, is Newton’s second law (and the associated concepts) just a specific theory of classic mechanics?

  17. “as far as i know this has only been proven for massive particles. noone knows why massless particles are restricted to half integer spin.”

    But they’re not. Did you mean to say integer spin here?

  18. oh, and one more thing (sorry for the nitpick):

    “Furthermore, in a world with three (or more) spatial dimensions in which Einstein’s special relativity is true, then particles of each type will be either fermions or bosons”

    as far as i know this has only been proven for massive particles. noone knows why massless particles are restricted to half integer spin.

    1. Well quite a bit is known-of course it’s quite technical, but the upshot is that it the spin-statistics theorem also holds for massless particles in (at least) 3+1 dimensions, thereby associating Fermi-Dirac statistics to particles with half-integer spin and Bose-Einstein statistics to particles with integer spin. One reference is “Causal fields and spin-statistics connection for massless particles in higher dimensions”, N. Ohta, Phys. Rev. D31 (1985) 442.

      1. i don’t contend that the spin-statistics theorem holds, i wanted to point out that for massless particles there is no fundamental reason to come in half-integer spin (the little group being Abelian). I confess my knowledge is from the mid 90’s and I would be thrilled to hear that the situation has changed meanwhile.

        1. Indeed-in fact it’s much older than the 90’s and goes back, at least, to Wigner, who studied the continuous spin representations of the two-dimensional Euclidean group. Complications seem to appear when one considers propagation of such fields and Abbott, for example, in Phys. Rev. D13 (1976) 2291 presents a calculation that indicates that such fields can’t propagate causally, so it would not be possible to identify them with physical particles. So that leaves the usual helcity representation for the massless particles in four spcetime dimensions.

        2. However these continuous spin representations do seem to hide some subtleties that haven’t fully been worked out, apparently. One must be quite careful as to what exactly are the assumptions on the equations of motion.

  19. you wrote:
    “Sometimes we have the equations we’re supposed to use, but none of our methods for calculation work for those equations.”
    Can you give an example of an equation whose solution which we don’t know how to calculate. I thought that computer simulations render just about every equation “possible to calculate”, albeit, the amount of time necessary for the calculation might be unreasonably long.

    1. >just about every equation “possible to calculate”,

      Actually, no. In complexity theory there is a class of problems called ‘undecideable’ which cannot be solved in the general sense. This is in contrast to the class of problems you mention which could be solved except that the universe won’t be around long enough.

      I’m very interested as a computer scientist in reading Matt’s explanation of these theories. Are they undecideable or intractable?

      1. Decidability has nothing to do with the physical computations of the kind discussed and in theory you may be able to calculate much (as long as you don’t need real numbers or can work with continuous fractions). But in practice the answer is no. And the problem is the scale required to get interesting results and the compromises you must make. Mathematical physics does not scale computationally, not because there is anything wrong with the mathematics but simply because the computations cannot scale.

        So you buy a nice big supercomputer (and several 10s of MegaWatts of energy for a period you can afford – failing which you move to a country where they build very large machines indifferent to the cost to run it (i.e., China). I’m thinking of large-scale complex analysis and/or statistical mechanics, Ising lattices, at this point appropriate renormalization is essential for practical purposes, As long as you can live with that …

        For no reason at all to do with the mathematics, your computation will not scale because computational efficiency (for all Turing models) decreases as your problem size increases. And there is no resolution to this matter (for reasons I don’t have time to go into here). And so you rapidly hit diminishing returns. Briefly, one computational problem is that Turing computation is a model of computable numbers and not a model of computable functors, you loose all structure in such calculations and have to reconstruct the lost structure in order to make sense of your results (clever data structures don’t help). In my terms, computational structures are impotent, while physical structures are not.

    1. Good question. That’s actually a grey area (one that my own research took us into.) I don’t think the answer is strictly known. We used to think the answer was yes, the number of types had to be finite…

  20. 1. Thanks a million. 2. I’ve recently read of fractional dimensions, using a fractal curve as an example; hmmmm. 3. Could some, but not all, of our dimensions be scale invariant?

    1. I always like giving the example of those nesting Russian dolls. I believe they’re called Matryoshka dolls. Of course fractals are another slightly more complicated example (that has to do with a larger but related group of symmetries)

  21. Now I’m a bit confused. Yesterday you said that a theory is a set of equations (along with a set of concepts). Today you talk about quantum field theories where you don’t know the equations, and you even make a distinction between theories that are known to exist but with unknown equations, and unknown theories that might exist. In what sense is a set of equations known to exist if no one knows what the equations are?

  22. Many comments to make but I only have time right now for one. I’ll return later after I’ve given these two posts a more careful read.

    As I understand your argument here, Quantum Field Theory is a theory of the continuum. A view I would share in general, if not in this particular case. Indeed, it is because I suspected that you held this view that I follow your postings.

    As I have read the literature, however, this does not appear to be a consensus view in QFT – not to mention, of course, the dissonance with the popular conception of the quantum world of elementary particles (reinforced socially by digital conceptions).

    I’d appreciate a clarification and (perhaps later) a critique over the Quantum Mechanics in general.

    1. Hmm. Not sure what you mean by “dissonance with popular conception… [etc.]”

      The consensus view in QFT is that questions about the ultimate structure of space-time, or indeed anything at much shorter distances than high-energy experiments currently probe, are always partially hidden from us by the way QFT works. One sees explicitly this in certain materials: there are phenomena well-described by a QFT, even though fundamentally the material is made from a discrete lattice of atoms. One sees this also in the history of hadrons; it took a long time for people to realize that they’d need something like quarks inside those hadrons. Why this “hiding” of short-distance physics takes place is well-understood, thanks especially to Wilson and Kadanoff; the jargon that goes with it is “Wilsonian renormalization”, and the notion of an “effective quantum field theory”, which is good enough to describe long-distance phenomena (and looks as though it is in the continuum) but cannot give you much insight into short-distance phenomena (and questions as to whether space and time are made from something discrete, or with some other odd structure.)

      Fortunately there are a few rare measurements that can get around this general rule. Unfortunately, none of them have turned up anything surprising, so far.

      1. The first issue for me in this account has to do with the existential and epistemological nature of the notion of space-time. You speak of it as an existential property of the world, rather than an epistemological one. As you are aware, no doubt, Einstein and as far as I am aware most relativists take the view, in my terms, that the notion of space-time is a convenient redundancy (ways of speaking about measures of material structure and dynamics).

        In other words, space-time is an epistemological device that cannot be considered to obtain existential status beyond its conception. So, from a purely mathematical point of view, to ask questions about the “ultimate structure of space-time” and whether space-time is discrete or not are “pseudo-problems.” They are not existential problems at all, they are epistemic questions.

        Pure mathematicians have their own questions concerning the discrete and the continuum, but these are not based upon the same premises at all (although they should inform mathematical physics). There is no uncertainty principle in pure mathematics and the questions reduce to questions concerning metrics and commensurable lengths. From this point of view Einstein’s result simply shows that there is no universal metric. Which, as I understand it (imperfectly perhaps), is exactly the problem that Wilsonian Renormalization is attempting to deal with. I doubt that you will find a pure mathematician that would consider the matter “well-understood.” Indeed, from my POV it is further “hand waving” – convenient as it may be.

        But if we must wave our hands, let us at least acknowledge the convenience and not confuse this with existential matters.

        My reference to “popular conception” it the prevalent view of your audience that the world is composed at bottom of discrete particles. I can interpret your account as saying that this is not the case but that elementary particles are discrete manifestations of an underlying continuum. And with this view I would agree. This would not be consistent with the QFT literature that I have read and may be further than you intended to go.

        Which reminds me. I’d like to see a sensible explanation of the epistemology surrounding the use of local covariance equations in QFT – which unlike the use of general covariance in relativity theory appears to profess no epistemological basis what-so-ever. It seems to me that such equations must, of necessity, resort to continuous universal fields to have any epistemic power (beyond utility).

        1. Perhaps I should point out for your readers that according to GR space-time is a purely mathematical way of speaking about the effect of gravitation. It is not the case, common pedagogy aside, that gravitation *is* the curvature of space-time.

          Einstein himself did not do a consistent job of making this clear (although he in fact stated it quite clearly). I think in part he did this for expedience in order to communicate his, at the time, difficult idea, and in part because he did not fully recognize the implications of what he was advocating.

          This seems evident in the field equations as they stand, and this led to the criticism that GR is “physically vacuous.”; a debate that has continued for far too long (see John Norton’s accounts).

          It is not BTW, but you need to restructure the field equations conceptually to make this clear and isolate space-time to its epistemic cause (as he intended).

          1. One of those “white lies” … It depends upon the principles of your theory of education.

            I happen to believe that teaching for vocational needs (often according to perceived needs in the marketplace) is a disservice to the public and an insult to the individual. Not to mention, socially oppressive … 🙂

            While teaching foundations and facts, “knowledge for its own sake,” no matter how intellectually challenging we may think it to be, is infinitely more interesting, has integrity, and is preferable to advocating what we assume to be easier abstractions.

            (This is why I educated my own 4 children at home). 🙂

          2. Mathematics can tell beautiful lies, Einstein certainly saw the forest, What I have learn from life is that if something seems to be unnecessary hard accomplish then I’m possibly doing something wrong. 😎

        2. I’m afraid some of your questions are deeper than I can go in this medium.

          However, I should emphasize that my quantum field theory discussion occurs in the imaginary world in which gravity doesn’t exist. What this reflects is that in most particle physics and condensed-matter contexts, gravity is a minor effect which need not be treated with quantum mechanics, and the nature of space and time, and the physics of extremely short distances where space might not be a continuum, can be ignored. Thus (just as we treat the earth as a perfect sphere, or even a point object, depending on what we’re doing, as an idealization) I am taking quantum field theory in the idealized context where most of the issues you raise do not need to be raised.

          Of course at some point, we must raise them. And then life gets more difficult.

          1. I know it is the common view, and I know it comes from the early focus on QM, but I believe it has now become counter productive.

            Modern physicists can no longer see the forest for the matchsticks. Someone needs to set afire.

            Things are often much simpler when you take a step back and look at the whole. Do not assume that the increases and diversity in mathematical complexity are a good thing. Mathematics can tell beautiful lies.

            1. Well, I don’t know if things are getting simpler or more complicated. There is no obvious way to measure complexity in this context; and often things get very complicated for a while until you understand them, at which point they become much simpler.

              And I don’t think there has ever been a time when people could see the forest while they were making their way through it in the dark.

              1. That’s only an imaginary forest! You can always come back and take another look at it 😉 What I have learn from life is that if something seems to be unnecessary hard accomplish then I’m possibly doing something wrong.

      2. The consensus view is wrong and you know why? Take, for example QED. This theory is incomplete – it does not have all the particles (or high energy excitations) that exist in nature. But is does not mean it does not have its own short-distance physics, which is smooth, not discrete. Hard photons, for example. They exist in nature and in QED. Now, any calculation at a given transferred energy E cannot excite those high energy modes of QED that have much higher threshold. So these excitations, right or wrong (incomplete), are physically inessential and technically they should not give catastrophes. If they give catastrophes in our calculations, it is our fault not to be able to formulate the theory reasonably. In a correct formulation there is no need in cutoff and renormalization. All what interaction may do is changing occupation numbers of the model particles rather than producing numerical catastrophes. Our not knowing all short distance excitations is not a pretext to keep catastrophes in place, that is my position. Catastrophes in our current formulation (principles!) is our failure and the effective theory ideology in QFT is our way to drug (fool) ourselves. In particular, the cutoff in QFT is a forced measure in a bad formulation and there is nothing physical in it.

    2. This reminds me of continuum mechanics and what laboussole said here about Weinberg and the radial and azimuthal conflict. You start by saying space (not spacetime) is an amorphous bulk, then you simplify it to a sheet, then you simplify it further to a stiff lattice. Then you focus on one horizontal lattice line and imagine it’s a guitar string. When you pluck it, then regardless of its length, your “pluck distance” is always the same. That relates to h. But when you do this you stretch the guitar string, and its length, and the stretch, and your ease, can all vary smoothly, just as photon E=hf energy can vary smoothly. Then if you choose not to pluck it, you can just stretch the guitar string smoothly. The more you pull the harder it is to stretch it further. That’s like the bag model. There is no pluck here, this is scale invariant. But this is not QED, this is QCD, and it not renormalizeable/>. Oh, and there’s our continuum again.

  23. I’ve always thought that “Quantum Field Theory” assumes special relativity as an axiom. I take as reference the book “The Quantum Theory of Fields” by Steven Weinberg, where Lorentz invariance is introduced at the very beginning. Also, S. Weinberg seems to assume 3+1 dimensions, but I’m not sure it holds throughout the book to be honest, it’s a pretty long one (3 volumes) and quite technical too.

    Nevertheless, wouldn’t it make sense to restrict “Quantum Field Theory” -in the general case if we follow your definition- to universes with 3+1 dimensions and where Lorentz invariance holds? I understand the power of imagination when it comes to other universes, but as far as I know more dimensions are still only fruitless speculations helping to maintain interest in string theory (sorry to be blunt,,and probably ignorant).

    On a side note, thank you for an excellent and very interesting blog.

    1. No, only *relativistic* quantum field theory makes that assumption. Condensed matter physicists regularly drop that assumption. And there are other applications where relativity is broken by the presence of a medium in which the physics is occurring.

      Actually, extra dimensions have nothing to do with string theory. [That’s a myth that both string-lovers and string-haters both seem to sustain.] Extra dimensions were considered long before string theory; Kaluza and Klein’s work on getting electromagnetic forces and gravity from a gravitational theory in 4 spatial dimensions goes back to 1921-1926, and Einstein spent much of his last 30 years thinking about it. And moreover, a great deal has in fact been learned about field theory (and probably will be learned in future about field theory) by thinking about field theories in 4 and 5 spatial dimensions and what happens when you bring them down to 3. Field theories in 2 and 1 spatial dimensions (with and without special relativity) have had enormous impact in the physics of materials. For example: have you heard of “graphene”? or “superconductors”? the list is long.

      So indeed, I think your worldview, when it comes to field theory, is too narrow. A good field theorist tries to learn it all (which is almost impossible, so big is the subject.)

      1. Honble Professor,
        if there is medium</b< "fundamental laws of physics might end up being probabilistic, as they are in quantum mechanics!" this is true – but… in <bvacuum (without mass-energy ?)

        Gaussian functions are widely used in statistics where they describe the normal distributions, in signal processing where they serve to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics where they are used to solve heat equations and diffusion equations and to define the Weierstrass transform.

        /However, I should emphasize that my quantum field theory discussion occurs in the imaginary world in which gravity doesn’t exist. What this reflects is that in most particle physics and condensed-matter contexts, gravity is a minor effect which need not be treated with quantum mechanics, and the nature of space and time, and the physics of extremely short distances where space might not be a continuum, can be ignored./

        /No, only *relativistic* quantum field theory makes that assumption. Condensed matter physicists regularly drop that assumption. And there are other applications where relativity is broken by the presence of a medium</b< in which the physics is occurring./

        /… and to define QM and GR as theories on the basis of mathematical consistency and predictivity alone risks cheapening their status or, by lumping them (by default) into the same category as speculative or toy theories that also meet your definition, unjustifiably increasing (by association) the stature of the speculative/toy theories as carrying verified “truth” about the physical world./- Marty Tysanner | September 23, 2013 at 8:49 PM.

  24. Matt: “… terminology — trivial, yet crucial and slightly subtle.”

    How true and important this statement is! In addition to the substance (the real beef) of physics, the importance of the subtlety of the *language* used in physics will rank even higher than the beef, as the *misleading* language will definitely bury that beef.

    There is definitely no problem for any reader to *understand* your usage of the term *prediction* in this article. But, I personally world like to use a different term (consequence) in its place. There is definitely *consequence* for “quantum field theory as a whole”, many different quantum field theor(ies). It is the same for “scale-invariant quantum field theory”, no particle as its consequence (prediction).

    There are many examples that models have tremendous amount of *consequences* while were viewed as no *prediction*. This has some dire consequences for the advancement in physics. I am sure that we will encounter some of those examples in due time.

  25. Matt,

    I just wanted to say thank you for doing this series. I’m a grad student in physical/statistical chemistry, and I’ve always been interested in higher physics like QFT but haven’t taken formal classes in anything above QM. It’s really nice to have resources that are above the laymen level but below the “pick up a textbook and try and understand it” level.

    Keep up the good work.

  26. Regarding my comments on both Unruh effect and Hawking radiation, what I meant is that in some mathematical formalization of quantum field theory, like axiomatic of algebraic, you can show that the thermal state is a general feature of even interacting field theories. One coul (and should) question if the mentioned formalisms are representative of what we woul like to call QFT, but at least that’s a step above field theories. Also there are some results concerning simple interacting QFT where we can show that an accelerated observer sees a thermal bath for the Minkowski vacuum, for instance in the case of Thirring model (sorry if I was a bit technical, the message is that we have strong indications that those results are valid for interacting field theories).

    I’m not sure what you meant by consistency of quantum field on curved spaces, at least for the case of the gravitational collapse resulting in a black hole things are very well established.

  27. Matt, just trying to expand on your list of QFT predictions, maybe not that notewhorty, but in 2 dimensions we have the possibility of fractional statistics, particles which are neither bosons nor fermions, that may be observed in the fractional quantum Hall effect.

    Also, was kind of surprised of seeing spin-statistics in the list but not the CPT theorem. After all the book was called “CPT, spin and statistics, and All That”.

    Last, but more curious (im my opinion), the Unruh effect and Hawking radiation can be shown for generic quantum field theories, so the fact that Black Holes radiate is a general prediction of field theory.

    1. You are certainly right that the prediction that all particles have antiparticles (which is the only consequence of the CPT theorem I can think of at the moment that I would want to explain in this article) is a prediction I should have included.

      I didn’t want to get into all of the beautiful and rich physics that is found once we go below 3 spatial dimensions (or we relax special relativity so that we can have 2d or 1d slices inside of 3 dimensions.) It’s just too much for me to do, and I’m not enough of an expert on that to do it well.

      The Unruh effect (that an accelerating observer observes particles being produced in her vicinity with a temperature proportional to her acceleration) is definitely a prediction of free quantum field theory. I have to think for a minute or two about what you’d say is observed in the general case, but yes, there is a general effect. Hawking radiation itself is a bit more subtle; you have to discuss whether and why quantum fields on curved spaces are consistent.

  28. Matt I note your comment “Not only can we see around us that the world isn’t scale-invariant…” and would like to push it further.

    I hope it’s fair to say that quantum field theories grew out of the quantum nature of light? We have h in E=hf and and p=h/λ, wherein h is the thing that underlies the quantum. Remember in Neil Turok’s address where referred to scale invariance and talked about waves having any wavelength? Well light waves don’t have any value of h. And the dimensionality of action can be expressed as momentum x distance. Take a look at some pictures of the electromagnetic spectrum. Yes they’re only pictures, but there’s something in those pictures that is invariant: the distance between the bottom of the waveform and the top. And have you seen any 611keV electrons at rest? Or how about 411keV? No, they’re 511keV.

    Maybe I’m jumping the gun here, but a scale-invariant quantum field theory sounds like a contradiction in terms. It sounds like a quantum field theory that has no quantum. One that pays inadequate attention to the evidence.

    1. As you’ve identified correctly, particles with mass are impossible in scale-invariant theories. But I already told you that these theories don’t have particles (or at best, if there are no forces around, they have massless ones). So there’s no contradiction.

      1. Maybe I’m missing something here Matt, but the world does have particles, and particles with mass. But if the world consisted only of photons, it would still have gravity, because any concentration of energy causes gravity. As you’ve said, virtual photons aren’t actual particles, they’re just “a disturbance in a field”. Gravitons are virtual particles too, the only field we’ve got here is the photon field, but there’s more than one way to skin Schrodinger’s cat. Re your reply to Cesar below, see this Baez page and see this: “Note: not the curvature of space, but of spacetime. The distinction is crucial”. You know that Ricci curvature is all about volume deviation. Draw a grid, but draw it so that the cells are flattened at the bottom but square at the top. But nevermind, no reply necessary, please just get on with your next blog entry. I’ll refer back to this if necessary.

      1. So then isn’t uncertainity a prediction of all QFT’s? Are there any non-QFT theories that do not require uncertainity?

          1. If all QFT’s predict uncertainity (although maybe uncertainity is not required for QFT) then that is something testable about all QFT’s.

          2. So what does a scale invariant universe look like under a microscope that resolves distances less then the Planck Length?

            1. In quantum theory, there are generally some basic quantities that you would have thought that you could measure simultaneously with arbitrary precision, but in fact you can’t.

              In quantum mechanics it is positions of particles and their velocities (strictly, their momenta) that you cannot simultaneously determine. Quantization is the statement that position and momentum are not to be treated merely as numbers, relative to one another, but as something more subtle. Position times momentum [in that order] isn’t the same, anymore, as momentum times position.

              In quantum field theory it is the field’s value and the change in the field’s value that you cannot simultaneously determine.

              This is true whether or not the theory is scale-invariant.

              However in some cases we do not know what the fields are and we cannot make this as simple or precise as I’ve just described it.

  29. “Furthermore, if we are in three (or more) spatial dimensions, Einstein’s special relativity is true, then particles of each type will be either fermions or bosons.”

    Can I ask for a clarification: Are you saying that in a QFT of 3+ spacial dimensions that is not scale-invariant, you will have SR, Fermions, and Bosons, or that it’s possible to have non-scale-invariant QFTs of 3+ spacial dimensions without SR, but in that case particles might not be categorized into Fermions and Bosons?

    1. I said that if you have SR and a QFT of 3 spatial dimensions, any particles will be fermions or bosons. [There may be some subtleties for massless particles.]

      Examples of theories in 3 spatial dimensions that don’t have SR and that have something more interesting than fermions and bosons are condensed-matter systems with “anyons”. Strictly speaking anyons are present in 2 spatial dimensions, but if I give up rotational invariance and translational invariance (which SR would forbid me from doing), I can get 2-dimensional sections inside a 3-dimensional system.

  30. Matt, I don’t see any evidence of you having told us “white lies” in the past. In prior posts, you’ve discussed the existence of fields that have no associated particle, and although you never specifically alluded to a QFT that is based exclusively on such fields, you never suggested it couldn’t, or doesn’t, happen. (PS: Do you ever go to IAS for talks or for their annual meeting? Would love to meet you.)

      1. I was planning on attending Dyson’s 90th too. Unfortunately I can’t make the opening day (Friday: Math and Physics). Will you be sticking around for the Astronomy session on Saturday?

  31. The sentence “Furthermore, if we are in three (or more) spatial dimensions, Einstein’s special relativity is true, then particles of each type will be either fermions or bosons” seems to be missing a word immediately before “Einstein’s”. It seems you must have meant either “… and Einstein’s special relativity is true, then …” or perhaps “… then Einstein’s special relativity is true, and …” but I don’t know which.

      1. Follow-up question: What would it imply if, in the world we inhabit, particles were found to exist that were neither fermions nor bosons?

  32. I mean that even ST have at its fundamental level some discrete entities corresponding to QFT particles , but If as you just said that at very short distances scale – invariant theories does apply then particles would be really just a macro-phenomena in our minds !!!???

    1. I think the distinction you make between “real” things and “phenomena of the mind” is in this form not useful in physics. If we can observe something consistently and repeatedly in several experiments then it is real in the physical sense.

      So particles are real, there is no question about that. And the reality of particles does not depend on how we explain or describe them now or in the future.

      In the same sense atoms, molecules, solids, liquids, bacteria, your computer, your hand, etc. are real. The sun is real, even though the concept of “the sun” as an “object” separate from its surroundings is an approximation. If you look closely at the sun, you don’t see a sharply bounded object but an immensely complex cloud of particles, and it is not possible to tell definitely which particle still belongs to the sun and which no longer. This does not make the sun less real in the physical sense. It makes it less fundamental, if you want – but what really is fundamental is hard to define and in some cases – I think – depends your point of view.

      1. You have to be careful here. When you say “real in the physical sense” you are still (traditionally) speaking of the mind, and all that you say is “true” (another mind concept). But this is different from the existential status of the something that you observe. A basic lesson from Fregean logic: both the morning star and the evening star are real by your definition.

        1. That’s why I wrote “real in the physical sense” as opposed to, for example, the philosophical sense.

          Even regarding the physical sense my comment does not tell the full story. I wrote “if we can observe something […] it is real […]”. The subtle point is that the act of observation depends in turn on our theory of the world. Because only by having a theory we can give structure and meaning to our stream of perceptions and thus interpret measurements. (Here I’m using the word “theory” in a wider sense than how it is used in Prof. Strassler’s article.)

          Heisenberg recounts in his autobiography “Der Teil und das Ganze” (highly recommended!) that Einstein pointed this out to him and that Einstein’s remark was one of the things that inspired Heisenberg to his breakthrough in Kopenhagen, where he formulated the uncertainty relations.

          Still, the simplified position taken in my original comment is very useful for scientific thinking, I believe, and it is a good starting point for getting rid of misleading notions of reality or non-reality.

          (Einstein’s remark as remembered by Heisenberg was: “Erst die Theorie entscheidet darüber, was man beobachten kann.”, which I find surprisingly hard to translate. It means about “Only the theory decides what one can observe” or “It’s not until you have a theory that you can decide what is observable.” Heisenberg’s autobiography is a wonderful book with a lot of deep thoughts and discussions about quantum mechanics. Unfortunately I don’t know whether it has been translated to English.)

          1. P.S. It seems there is an out-of-print English translation: Werner Heisenberg, “Physics and Beyond: Encounters and Conversations”, Harper & Row, 1972

          2. Oddly, I had Heisenberg’s Chicago lectures open on my desk as this note from you came in.

            My problem with what you said comes from an inability to distinguish what you speak of when you say “real in a physical sense” and what you may speak of as “real in a non-physical sense.” Reality is a way of speaking about apprehension, so the distinction you suggest confuses me. IOW, I do not understand a distinction between “reality” and “non-reality.” I think the distinction you are in fact looking for is between existence and reality.

            I think you also intend to say that the /interpretation/ of an “act of observation” /may/ depend upon our theory of the the world. Reality, simply says that it is what it is however we speak of it. And scientists really do not fit theory to evidence, they try hard to apprehend the world as close to reality as they can.

            Whereas, Einstein is saying that theory tells us where and how to look in the haystack of observations so that we may find needles.

            So, form my POV, the act of scientific observation does not depend upon our theory of the world. If it did we’d still be with Ptolemy. Rather, science is a process of inquiry in which we face the world with an open mind, we stand before the world as an “uncarved block.”

            If we can shutout the noise of convention and think for ourselves, being selective and critical of our intellectual authorities. We first probe the world (experiment), formulate ideas and intuitions (hypothesis and guessing) about the world long before we develop theory.

            A pure mathematician ignores the world and looks only upon the landscape of conceptions and pursues the science of necessary conclusions.

            In order to develop physical theory we need both.

            Pure mathematics is a good place to start because it cares nothing of “truth.” It is the job of logic (that I treat as a natural science) to build the bridge between pure mathematics and the physical sciences. It’s a long historical account (I am certain boring for this audience) just why mathematical logic does not, in fact, play that role today.

            Now, there are theories of logic and apprehension – treating logic as a natural science – that speak of these matters in physical, (now) biophysical, terms – and they do focus upon the bridge between Pure Mathematics and the Physical Sciences (as far back as Harvard mathematician Benjamin Peirce -1809-1880 – and his son Charles Sanders Peirce – 1839-1914). This is my field of research and study.

            This work naturally includes just how these theories inform ideas in physics and extreme-scale computation.

            I get drawn into cosmology and microscopic physics only in so far as it informs this work. I also have a special interest in Einstein because his epistemic contribution is profoundly important and underestimated. You would, perhaps, have expected his friend Goedel and the positivists strongly influenced by him others to catch the full implications – but Goedel says nothing about it and people like Riechenbach and Carnap pass it by with only cursory comment. Disappointing, because it is exactly what they were looking for.

          3. I meant something quite simple with “in the physical sense”: If you ask physicists “Are particles real? / Do particles exist?”, I think most of them would answer something like this: “We observe aspects of nature that we call ‘particles’ in many independent and reproducible experiments, so yes – particles are real / do exist.”

            This answer would not change if it turns out that particles can be understood as long range phenomena in a more fundamental theory, for example. Also there is no distinction between “existing” and “being real”, and it is understood that the answer above is actually more a definition of what we mean with “particles do exist” than an argument that particles do “exist” in some other sense.

            To back up my claim with a sample of n=1: Experimental physicist Tommaso Dorigo wrote in an article today ( http://www.science20.com/quantum_diaries_survivor/dzero_confirms_y4140_and_its_excitation-121198 ) about two new particle states both “strong reason to believe in their reality” and “I believe the matter is settled as regards the existence of these two states” (emphasis mine). The terms are used synonymously and both are based on observations.

            Regarding Einstein’s remark, I do not understand your interpretation. I really think Einstein meant that observation always depends on theory. To make this clearer, I’ll try to translate Einstein’s argument as recounted by Heisenberg:

            Only [Erst] the theory decides what one can observe. Look, observation is in general a very complicated course of events. The process that shall be observed causes some things to happen in our apparatus. As a consequence further processes happen in the apparatus, which at the end cause in a roundabout way the perception and the fixation of the result in our consciousness. Along all of this long path from the process until the fixation in our consciousness we need to know how nature works, we need to know the laws of nature at least in practice, if we want to claim that we have observed something. Only the theory, that is the knowledge of the laws of nature, allows us to conclude from our perception what the underlying process was.

            Einstein then went on to point out the difficulties in establishing a quantum theory while we still have to use our classical understanding of the world in order to talk about observations (a point still valid today). It is a wonderful exchange of ideas to which I surely cannot do justice in my translation.

  33. Matt. , this is very important for our physical world view , Is it possible that one day we may find that some scale-invariant QFT is a better one w.r.t reality ?

    1. No. Not only can we see around us that the world isn’t scale-invariant, but our lives depend on it. BUT — it is possible that at very short distances, the world becomes scale-invariant. So we might live in a world where the lack of scale-invariance is a property of long distance phenomena.

      This has been proposed as a possibility for quantum gravity itself.

      1. “…the world is not scale invariant…”

        Yes, but there are some subtleties here that must be emphasized. All critical phenomena are scale-invariant (or nearly scale invariant) and there are plenty of such phenomena at our scale of observation. Likewise, fractals exist at our scale of observation in various forms, from curves and surfaces, to Brownian motion, to percolation, to self-organized criticality, to the approach to turbulence in fluid mechanics and so on.

        1. Thank you: yes, there are scale-invariant phenomena in our world, and even in particle physics in certain contexts. All I meant was that the laws of particle physics are not as a whole scale-invariant.

      2. Actually the world is scale-invariant you just ignore all the provided evidence. Speaking about scale-invariance when there’s gonna be a blog post handling theories explaining the naturalness problem?

  34. You are very good in explaining all this sophisticated material.
    What about writing a book containing everything in the blog.
    It will be wonderful read for the ‘intermediary’ person.

    1. I think that’s not what you should ask. After all, electrons exist (old-style televisions wouldn’t have worked otherwise) but the way we think about them and the concepts that underlie the equations we use to describe them could change.

    1. I gave you several examples in other applications of quantum field theory to real world phenomena. It doesn’t apply currently to particle physics, but perhaps we will discover something in the future to which it applies.

    2. No matter what advances in physics you come up with, the Standard Model will remain a good description of physics upto the Higgs scale. Unless your new advances in physics enable easier calculation of phenomena upto this scale, the Standard Model is not going to be temporary, any more than Newton’s 3 laws of motion are temporary.

  35. But as you said here and in part 1 , the SM may well be of NO particular significance as — per part 1– we don’t know if the universe it describe is THE Real Universe we live in.

    1. You’re over-interpreting here. It certainly is our best working hypothesis for how particle physics works at the LHC and at all previous experiments, and in daily life — and that gives it very great, although possibly temporary, significance.

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A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC


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