There must be some smarter notation that captures the model with less verbosity?
Also, how on earth did various people put this together? Is there a good book about it?
The Deconstructed Standard Model Equation
31–40 of 58 posts
Re: The Deconstructed Standard Model Equation
#32Given the world we live in, right now, why does mathematics continue to insist on minified expressions? Given the option, most development teams would choose to read and write against verbose source code, rather than scrape obfuscated variables and method signatures out of a minified, transpiled, compressed package. So why do we continue this archaic practice of obscure, inscrutable symbols in mathematics? Cultural i…
>Given the world we live in, right now, why does mathematics continue to insist on minified expressions?
Because it is concise, precise, and widely accepted.
>Given the option, most development teams would choose to read and write against verbose source code, rather than scrape obfuscated variables and method signatures out of a minified, transpiled, compressed package.
What's your point? Source code is not the same thing as mathematics, not for the majority of software and not for the majority of mathematics as practiced by mathematicians. Verbosity makes sense when your domain involves concrete entities like "customers" and "widgets" and "thermal sensors." When your domain involves abstract entities like "ring homomorphisms" and "clopen sets" and "vector spaces," it doesn't. If you're writing a database, a name like "transaction_mutex" is more descriptive than "m." If you're universally quantifying over the domain of an arbitrary continuous function on the reals, "x" is about as descriptive -- and as conventional -- as any name you can come up with.
As an aside, I really wish we would dispense with the non-word "transpile." We have a word for translating a program from one language to another: compile.
>So why do we continue this archaic practice of obscure, inscrutable symbols in mathematics?
Because it works very well. I'm not sure what else to say. You spend maybe fifteen minutes learning about, say, the symbol "∂" when you're introduced to multivariate calculus, and then for the rest of time you have an extremely concise way of expressing a variety of combinations of partial derivatives that can be understood by anyone who has also been introduced to multivariate calculus.
Don't get me wrong, there are actual problems with mathematical notation -- overloading, "abuse of notation," and as often as not just plain omitting information -- but the use of non-ASCII symbols and short variable names are not among them.
Re: The Deconstructed Standard Model Equation
#33I've been banging my head on QFT and the Standard Model for enough time now that I can actually glimpse more or less what those terms actualy mean , as in , I can translate them into words. It's almost like learning a new language! Pretty awesome. Still, despite all this complexity, we still have several minor and major theoretical gaps to fill. Exciting times!
Can you recommend how to get started on this? Like beginner links or something? I'm currently just a physics noob, but have some of the basic concepts of quantum theory down. I would love to just have a basic grasp of that monstrous equation.
"Quantum Field Theory for the Gifted Amateur" by Stephen Blundell and Tom Lancaster.
It might be right for you if you know the basics of Quantum Mechanics and electromagnetism
Re: The Deconstructed Standard Model Equation
#34Given the world we live in, right now, why does mathematics continue to insist on minified expressions? Given the option, most development teams would choose to read and write against verbose source code, rather than scrape obfuscated variables and method signatures out of a minified, transpiled, compressed package. So why do we continue this archaic practice of obscure, inscrutable symbols in mathematics? Cultural i…
Your comment shows a common misunderstanding of what mathematicians are trying to do. Modern mathematical notation is not obfuscated, it is in fact making the object being described much easier to perceive for humans. Explaining the equation you see in English words is what every physics book does, however the equation itself represents a concept that is not human. It comes from an alien universe of symmetries and re…
While this might not be the OP's point, but for me the main problem are the one-character variable names. Generally computer code that just operates on cryptic one-letter variable names, is considered bad code. Yet equations almost always have one letter variables and the worst part of all, their meaning is almost never explained anywhere
Case in point, what are b, a and c? what is their meaning if I have to measure them, what is the device for measuring them or what quantity do they represent?
Re: The Deconstructed Standard Model Equation
#35There must be some smarter notation that captures the model with less verbosity? Also, how on earth did various people put this together? Is there a good book about it?
[deleted]
Re: The Deconstructed Standard Model Equation
#36There must be some smarter notation that captures the model with less verbosity? Also, how on earth did various people put this together? Is there a good book about it?
There is; the equation on the CERN mug in the photo is an example.
For example, the gluon Lagrangian (Section 1) may be more compactly written
-1/2 Tr F_{\mu\nu} F^{\mu\nu}
for a suitably defined F. Or further abbreviated to something like L_g.
It just depends on how much detail you need to expose.
Re: The Deconstructed Standard Model Equation
#37Earlier quoted context omitted.
Your comment shows a common misunderstanding of what mathematicians are trying to do. Modern mathematical notation is not obfuscated, it is in fact making the object being described much easier to perceive for humans. Explaining the equation you see in English words is what every physics book does, however the equation itself represents a concept that is not human. It comes from an alien universe of symmetries and re…
While this might not be the OP's point, but for me the main problem are the one-character variable names. Generally computer code that just operates on cryptic one-letter variable names, is considered bad code. Yet equations almost always have one letter variables and the worst part of all, their meaning is almost never explained anywhere Case in point, what are b, a and c? what is their meaning if I have to measure…
The point is that variables are evil and arbitrary. So you give them short names to signal that you could replace them with anything else, what matters is how they appear together. Additionally different subfields of mathematics and physics usually adopt naming conventions.
Re: The Deconstructed Standard Model Equation
#38"To clean up these redundancies, theorists use virtual particles they call ghosts.
This part of the equation describes how matter particles interact with Higgs ghosts, virtual artifacts from the Higgs field. [...] This last part of the equation includes more ghosts. These ones are called Faddeev-Popov ghosts, and they cancel out redundancies that occur in interactions through the weak force."
So the second half this equation is used to describe invisible things needed to cancel out wrong stuff from the first half? Sounds ad hoc to me, were these "ghosts" predicted by anyone beforehand? Even if not, as a model it can still be useful though.
Re: The Deconstructed Standard Model Equation
#39Earlier quoted context omitted.
Your comment shows a common misunderstanding of what mathematicians are trying to do. Modern mathematical notation is not obfuscated, it is in fact making the object being described much easier to perceive for humans. Explaining the equation you see in English words is what every physics book does, however the equation itself represents a concept that is not human. It comes from an alien universe of symmetries and re…
While this might not be the OP's point, but for me the main problem are the one-character variable names. Generally computer code that just operates on cryptic one-letter variable names, is considered bad code. Yet equations almost always have one letter variables and the worst part of all, their meaning is almost never explained anywhere Case in point, what are b, a and c? what is their meaning if I have to measure…
>Case in point, what are b, a and c? what is their _meaning_
The "b, a, and c" in the quadratic equation are abstractions. They are placeholders for any number. That math equation is purposely designed to not have any concrete meaning for a,b,c. Therefore, asking for their meaning does't make any sense.
I'll try an analogy. We can give provide analogous "computer equation" for taking the last four characters of a string:
s2 = Right(s1, 4);
If you further generalize the "computer equation" to be take the rightmost "x" amount of characters, you'd replace the "4" with "x" like this:
s2 = Right(s1, x);
The "x" is an abstraction/parameter/argument of any number. That number could be 4, or 40000. (You might be tempted to say, "but I know 'x' stands for the number of characters I want from the string!" If so, by analogy you can also say that "c" in the quadratic equation stands for the number that satisfies the equation when you know "x", "a", and "b" ... which just circles back to each 1-character variable not having a concrete "meaning."
The concrete meaning of "a,b,c" in the quadratic equation depends on whether the equation was modeling something in physics, or engineering, or finance.[1][2]
The concrete meaning of "s1" and "x" in the "computer equation" depends on whether you're parsing logs, decomposing dates, verifying credit card numbers, etc.
The analogy above could have been demonstrated with regex such as "(.+)(.{4})" ... which would trigger questions, *"why do programmers use 1-character symbols such as '.' and '+' instead of "anycharacterm_oneormoretimes_consideredasagroup_then_anycharacters_fourtimes_consideredasagroup" ... etc
tldr: computer programmers also deal with weird-looking "equations" but since they are used to them, they have the background knowledge to decipher them.
[1]https://www.mathsisfun.com/algebra/quadratic-equation-real-w...
[2]https://www.boundless.com/algebra/textbooks/boundless-algebr...
Re: The Deconstructed Standard Model Equation
#40Earlier quoted context omitted.
It's a Lagrangian, so this is the function nature tries to minimize. In common everyday systems, the Lagrangian is kinetic energy minus potential energy.
True, but with nitpick that it is the Lagrangian density so nature minimises its total over a region of 4-space. And with the more important nitpick that this Lagrangian is a quantum operator rather than a number. In some sense nature does try to minimise it even so, but I never got an intuitive grasp on what that sense is.
And with the more important nitpick that this Lagrangian is a quantum operator rather than a number.
I don't think that's true when dealing with the formulation in terms of path integrals as we do here...