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The thing that has always bothered me while taking my QFT course was the seemingly arbitrary nature of Lagrangians. For the Klein Gordon equation we just wrote down the simplest Lorentz invariant object and then went from there. For the Dirac Lagrangian we constructed some Lorentz invariant objects (in a different representation) and added them together. My colleagues always rationalized the Lagrangians we would construct as "the simplest possible non-trivial expressions" that we could construct using some mathematical objects (Dirac Spinors, complex scalars, 4-vectors, etc.) but that just hasn't sat well with me. Is the fact that we are effectively guessing Lagrangians indicative of some lack of understanding of the true nature (or framework) of the universe? Could these Lagrangians just be emergent phenomena of more fundamental theories?

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    $\begingroup$ Keep in mind that physics is descriptive. The meta rules for simplicity (Occam's razor) and beauty both suggest starting with a simple options and then discarding it in favor of a more complex one only if it doesn't meet the requirements (describing the world we actually live in). $\endgroup$
    – dmckee --- ex-moderator kitten
    Dec 29, 2016 at 23:28
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    $\begingroup$ In a way, I think that this guessing almost shows a great understanding of the "true nature of the Universe" because from what we have observed so far, so much of physics really is down to symmetry, and this is understood in more recent times more than ever. The Standard Model can be entirely recovered from basically the charges of fields under the symmetry groups. $\endgroup$
    – JamalS
    Dec 30, 2016 at 0:05
  • $\begingroup$ Thank you @JamalS, I think you are right. It really does boil down to symmetries at the heart of it all. $\endgroup$
    – I.E.P.
    Dec 30, 2016 at 1:56

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Is the fact that we are effectively guessing Lagrangians indicative of some lack of understanding of the true nature (or framework) of the universe?

I don't think we are guessing at Langrangians so much as weeding out the ones that don't work. The comments above say it better than I can, but as far as guessing goes, I think a fair assessment of, for example, Einstein's work in GR especially, demonstrated a fair amount of guessing, before he arrived at his final equation.

According to Hans Ohanian's book Einstein's Mistakes Einstein went through revision after revision, of both the structure and interpretation of the EFE, regularly telling his colleagues, to forget what I said two months ago, here's the newest version.

That guessing period has long been forgotten, in today's application and research using GR as an effective theory.

I cannot see that developing a Langrangian is any better or worse that guessing at the math underpinnings of any physical theory. After all, how much simpler could it be, bearing in mind what it describes?

I don't expect anybody, including yourself, thinks the Standard Model could be as straightforward as $F = ma $.

I am not trying to be glib here, I am just not sure what you expect instead of the equations currently in use.

If it's falsifiable, by later testing of the say, particle properties that emerge from it, and it cannot be simplified it further, then what more can we expect?

Could these Lagrangians just be emergent phenomena of more fundamental theories?

Now this is guessing, I am not sure that we will ever stop looking, or ever find, more fundamental theories but to turn this into a specific physics concept question rather than a personal opinion reply, I think you would need to be more specific.

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  • $\begingroup$ Thank you for the thoughtful comment. It is astounding to me that all of the comments here think that guessing implies a great understand of the universe. I mean, I guess we have a great understanding in the sense that we know how the universe acts and so we guess Lagrangians until we get the right answer? Ha. Your mentioning of the EFE is funny to me because that theory is by far the least arbitrary in its origin in my opinion. I suppose at the end of the day such pondering about how fundamental our physics is is useless, but it is fun nonetheless. $\endgroup$
    – I.E.P.
    Dec 30, 2016 at 1:52
  • $\begingroup$ No, you're wrong. Physicist try different thing (guess?), but there s also some reasoning behind it. You all make it sound like it's an experiment, try this, no oops try that, well have you seen a monkey do it? First, a lot of lagrangians were modifications of those that worked in classical theory, and they led to Hamiltonians which could then have us do the canonical quantizations. There was also an understanding of what different things meant,n kinetic terms, potential terms, mass terms, and the nonlinearities leading to self interactions.Then what is renormalizable. Read Preskill $\endgroup$
    – Bob Bee
    Dec 30, 2016 at 2:28
  • $\begingroup$ Where exactly did I indicate that there is no reasoning behind physics? Using Occam's razor and the fact that Lorentz invariance is important we "guess" the Klein Gordon action. It's not like I'm implying that monkeys could do it--it's just not a satisfactory derivation in my eyes. Let me give you an example of a satisfactory derivation: using well known classical physics we can write down the Lagrangian associated with the dynamics of an elastic medium; we then quantize the solutions for the displacement and identify phonons. This prescription is what is lacking in QFT. $\endgroup$
    – I.E.P.
    Dec 30, 2016 at 5:34
  • $\begingroup$ That are straight derivations. And we never guessed the Klein Gordon equations, note Diracs. It wasn't so simple before it was brought up, and described. Same for relativity. It's always a combination of intuition, logic, physical or other similarities, analyzing mathematical consistency, and much more. Comparing phonons and QFT is funny. I'm going to leave it at that, it's your opinion of the way some science works, but there is a lot of study of it and the way of science, or physics works, is not a topic in this site, it is not physics. Ask something specific. And physics is also not math. $\endgroup$
    – Bob Bee
    Dec 30, 2016 at 6:59
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    $\begingroup$ I can't really understand a lot of what you are saying due to poor english (don't mean to ad hominem there it's just true). Comparing phonons and qft is funny how? Phonons are a qft... I said that that prescription is lacking in other areas of the subject. If you read the original question you will see that I am asking if our lack of a systematic way to produce Lagrangians indicates that there is a more fundamental theory at work. Perhaps the answer to that is a matter of opinion, but I implore you to stop responding so pompously because it only distracts from an intellectual conversation. $\endgroup$
    – I.E.P.
    Dec 30, 2016 at 10:53

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