How many equations is the standard model composed of

[gamow99]

Roughly speaking General Relativity is summarized with one equation but 15 or so equations are packed within it. Sorry if that's wrong, but I'm not an expert or anything. (If I could get an answer to that questions I would appreciate it to). I saw once a physicist show me a finite list of how many equations the Standard Model is composed of as an argument that it must not be the whole story seeing as GR is so simple and so elegant and is only composed of one equation. So how many equations do you have to master if you want to learn the Standard Model of particle physics. I have found this page
http://blogs.discovermagazine.com/cosmicvariance/2006/11/23/thanksgiving/#.WZ_2-Xd94qI
and on it I can count 15 equations.

 

[gamow99]

Roughly speaking General Relativity is summarized with one equation but 15 or so equations are packed within it. Sorry if that's wrong, but I'm not an expert or anything. (If I could get an answer to that questions I would appreciate it to). I saw once a physicist show me a finite list of how many equations the Standard Model is composed of as an argument that it must not be the whole story seeing as GR is so simple and so elegant and is only composed of one equation. So how many equations do you have to master if you want to learn the Standard Model of particle physics. I have found this page
http://blogs.discovermagazine.com/cosmicvariance/2006/11/23/thanksgiving/#.WZ_2-Xd94qI
and on it I can count 15 equations.

I also found this page
https://www.sciencealert.com/this-is-what-the-standard-model-of-physics-actually-looks-like
but I only see one equation there.

 

[vanhees71]

To understand physics first of all you have to master concepts rather than equations. The equations are just the (so far only) adequate language to formulate physics in a concise way. Often the key to solve a physics problem is to find a clever way to write equations in a compact way. Sometimes physicists invent a whole new symbolism. One obvious example are Feynman diagrams, which are nowadays understood as very compact and intuitive to write down the equations for calculating S-matrix elements in quantum field theory. Feynman invented them in the late 1940ies, introducing them to his collegues in 1948 on the legendary Shelter Island Conference (see S. Schweber, QED and the Men who made it), in a completely intuitive way. It proved to be a great shortcut compared to the cumbersome method by Schwinger, who presented his version of QED on the same conference. To the surprise of the participants, Feynman and Schwinger agreed on their results, and shortly thereafter, Dyson showed that Feynman's diagrams can indeed be derived from perturbation theory of QED and that thus are just a clever notation for the complicated formulae Schwinger wrote down in his approach. Of coarse to do quantitative calculations you have to evaluate the Feynman diagrams and go through the cumbersome math after all (nowadays fortunately with help of computer-algebra systems), but to set up the scheme and to organize your calculation, such handy notations are the key. Also in the later development of QFT, most notably the renormalization theory the use of Feynman diagrams were again the key to success, organizing the counterterms making the final results finite to make sense of the entire formalism in a very intuitive way.

The same is true for the equations themselves. E.g., for the standard-model Lagrangian (containing the whole known properties of the fundamental particles, which are leptons, quarks, gauge, and (at least one) Higgs boson) starts in a quite short well-organized form, incorporating the very concepts behind the standard model (symmetry principles, local gauge symmetry, and all that), but to get the Feynman rules out, you need to go through some algebra, leading to very lengthy expressions, but you don't have a chance to understand anything from "mastering" these huge expressions to begin with. That's why I said, starting to learn theoretical physics, it's always important to get the concepts behind the equations first!

 

[gamow99]

Feynman invented them in the late 1940ies, introducing them to his collegues in 1948 on the legendary Shelter Island Conference (see S. Schweber, QED and the Men who made it), in a completely intuitive way. It proved to be a great shortcut compared to the cumbersome method by Schwinger, who presented his version of QED on the same conference. To the surprise of the participants, Feynman and Schwinger agreed on their results, and shortly thereafter, Dyson showed that Feynman's diagrams can indeed be derived from perturbation theory of QED and that thus are just a clever notation for the complicated formulae Schwinger wrote down in his approach.

That was one of my favorite episodes from the Gleick book on Feynman. I forget who it was, maybe Beta, told Feynman to make his lecture more mathematical so as to keep the audience quiet and well-behaved. When you make your lecture less mathematical they start getting too rowdy. I sometimes wonder if that's the best approach.

 

[mfb]

I don't think it makes sense to count equations.

Is 5=4+1 one equation? Does it become two if I also say 4=3+1? And 3=2+1?
What about 5=((2+1)+1)+1, the combination of all of them?

You can combine all 15 equations in your link to a single long equation. It just makes it less legible.

 

[gamow99]

I don't think it makes sense to count equations.

Is 5=4+1 one equation? Does it become two if I also say 4=3+1? And 3=2+1?
What about 5=((2+1)+1)+1, the combination of all of them?

You can combine all 15 equations in your link to a single long equation. It just makes it less legible.

I understand what you're saying, but you can at least come up with a definition of a basic versus a complex equation and using that rule determine what its consequences are. For example, it's hard to count the population of Chicago but if you at least come up with some boundary however imperfect you at least give the reader some information if you state how many people there are within that boundary

 

[mfb]

The population of Chicago is something you can count. "Equations in the SM" is not.

 

[Vanadium 50]

Suppose you have two equations, ax + b = 0 and cy + d = 0. That's clearly two equations, right? What if I write them as (ax +b)^2+(cy + d)^2 = 0. Now is it two equations or one? What if I multiplied it all out? This example shows that you cannot count the number of equations.

 

[gamow99]

Suppose you have two equations, ax + b = 0 and cy + d = 0. That's clearly two equations, right? What if I write them as (ax +b)^2+(cy + d)^2 = 0. Now is it two equations or one? What if I multiplied it all out? This example shows that you cannot count the number of equations.

What you have shown is that by one definition there are two and by another definition there are one. It's not that we cannot count equations it's that there are no wide conventions as to what counts as an equation or not. It's the same with the solar system. So by one definition of the solar system you could say that voyager has left the solar system and by another definition it has not. In this situation all you have to do is specify what definition you're using and you can then proceed to deduce consequences. The consequences still produce information in spite of the fact that there is a lack of a hard convention as when an equation is one or many.

 

[Vanadium 50]

What you have shown is that by one definition there are two and by another definition there are one. It's not that we cannot count equations it's that there are no wide conventions as to what counts as an equation or not.

Which makes it impossible to count, no? If we look at the same things and you say there are 3 of them and I say there are 5, how many are there?

 

[gamow99]

Which makes it impossible to count, no? If we look at the same things and you say there are 3 of them and I say there are 5, how many are there?

No. This gets into the distinction between a priori and a posteriori truths. So a billion has 9 zeroes is only true because we decide arbitrarily that that's how many a billion has and, as a matter of fact, no later than 1972 the British decided that a billion had 12 zeroes. It does not mean that it is impossible to count the zeroes on a billion, it only means that certain truths depend on arbitrary decisions on how to use language. That the Earth is 93 billion miles from the Sun at certain points in its orbit has been impossible to know at certain times in human history because that truth depends on the arbitrary decisions as to how language is used but it also depends on the behavior of material bodies during periods in spacetime. So what counts as one equation or two is merely true due to some arbitrary decisions made by humans. While it is true that these definitions have never been laid out in a hard manner unlike the definitions of certain numbers (natural, whole, rational, real), it is still true that a human can come up with a definition for what counts as one equation and what counts as two and using that definition they can prove that such and such a set of equations is consistent with such and such a definition and thereby provide real information to the reader. While it is also true that few people will care about this definition and are unlikely to repeat its use and their claims will be forgotten, it is also true that the person making that claim is being consistent.

 

[phyzguy]

You might be interested in Feynman Volume 2 Lecture 25, where he shows that all of the laws of physics can be reduced to one "Unworldliness equation", U=0. Here is a link.

 

[Vanadium 50]

No. This gets into the distinction between a priori and a posteriori truths

This has degenerated into philosophical mumbo-jumbo. It's not about physics anymore.

 

[gamow99]

You might be interested in Feynman Volume 2 Lecture 25, where he shows that all of the laws of physics can be reduced to one "Unworldliness equation", U=0. Here is a link.

Are you sure about that? I remember towards the end of the Gleick book around 1985, some historian asked him if he thought the laws of physics were somehow unified and Feynman asked him some rather hard questions and ultimately he ended the lecture and said it was a waste of time? Plus there is this famous quote

People say to me, 'are you looking for the ultimate laws of physics?' ...No I'm not; I'm just looking to find out more about the world. And if it turns out that there's a simple, ultimate law that explains everything, so be it; that would be very nice to discover. If it turns out it's like an onion with millions of layers, and we get sick and tired of looking at the layers, then that's the way it is. But whatever way it comes out ... Nature is going to come out the way she is.

 

[phyzguy]

Am I sure Feynman wrote that? Of course. It's in his lectures. Did you read the link I posted?

 

[ChrisVer]

Can you give me an example of a countable equation (i.e. one you can say it's only one) ?
if you want an important equation to learn, study the lagrangian formalism, since with that you can derive both eqs of the SM as well as GR.

 

[nikkkom]

The number of equations is meaningless metric.
Simplicity of equations is a better metric (Occam's razor principle), however it is fairly subjective and leads to quasi-philosophical arguments, not objective science.