I would love to see this article, about 5-10 times longer. Dig one level deeper into what the notation means, how it relates to the zoo of fundamental particles, etc. Compare and contrast the sections dealing with different forces/particles. Talk something about the history of how this came out as a unification of models for gravity, electricity and magnetism, weak force, strong force.
The Deconstructed Standard Model Equation
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Re: The Deconstructed Standard Model Equation
#42"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…
Faddeev–Popov ghosts in particular are artifacts of covariant quantization in the path integral formalism. One way to think of them is as a kind of Jacobian determinant of the transformation to physical degrees of freedom.
Re: The Deconstructed Standard Model Equation
#43Earlier quoted context omitted.
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.
Took me years before thinking of variables that way and mathematical expressions are constraints over sets, formulas expressing relations of interests that way.
Re: The Deconstructed Standard Model Equation
#44Earlier quoted context omitted.
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 s…
Thank you for the thorough explanation!
I see your point with abstract expressions, but the connection I'm failing to make is - if they are completely abstract, then how can the equation be related to the physical world?
In essence, the equation defines the relations between some values - but if any or some of the values can be replaced by real measurements, then surely the relations between real measurements are not interchangeable?
Re: The Deconstructed Standard Model Equation
#45Earlier quoted context omitted.
>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 s…
Thank you for the thorough explanation! I see your point with abstract expressions, but the connection I'm failing to make is - if they are completely abstract, then how can the equation be related to the physical world? In essence, the equation defines the relations between some values - but if any or some of the values can be replaced by real measurements, then surely the relations between real measurements are not…
if they are completely abstract, then how can the equation be related to the physical world?
Math equations do not have to be related to anything in the physical world. It's just that humans have found that some patterns in nature seem to match some equations. Why or how math describes the real world is a deep philosophical question![1]
When G.H. Hardy[2] was exploring certain aspects of number theory and properties of prime numbers, it didn't have any relevance to the real world. 100 years later, we now use the math concepts in public key cryptography.
Does Isaac Newton's "F = ma" of "force = mass times acceleration" describe the "reality" of gravity and how planets move in the solar system? Well -- it does -- and it doesn't. It seemed to match reality well enough to find the planet Neptune -- purely by using math. But Newton's math equations didn't seem to match the "reality" of Mercury's orbit.
Then Einstein came up with another set of math equations that matched the "reality" of Mercury's shifting orbit.[3] But now today's physicists notice that Einstein's formulas don't match the "reality" of galaxies rotating faster than the his formulas predict. Today's physicists are trying to come up with another set of math equations to match that reality (or find the elusive "dark matter" so that Einstein's equations remain unchanged.)
(Einstein's equations do not make Newtons's equations obsolete. Newton's math (that doesn't perfectly match reality) is still good enough to guide Apollo rockets to the Moon and back. It's just not good enough to fully describe how Mercury wiggles around the Sun.)
Math is not reality. Math is its own topic that can stand apart from "physics" or "engineering". (Hence, math is the ultimate abstraction.) It's just sometimes convenient for humans to map some mathematics to some realities. It's often helpful for us to do that. Sometimes it backfires. Some Wall Street guys "mapped" math equations to model the financial behavior of mortgages and they turned out to be wrong.
Put another way: If math is used to model the physical world, it is only an approximation for it.
[1]https://www.google.com/search?q=the+unreasonable+effectivene...
[2]https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology#Cr...
[3]http://physics.stackexchange.com/questions/26408/what-did-ge...
Re: The Deconstructed Standard Model Equation
#46Earlier quoted context omitted.
Thank you for the thorough explanation! I see your point with abstract expressions, but the connection I'm failing to make is - if they are completely abstract, then how can the equation be related to the physical world? In essence, the equation defines the relations between some values - but if any or some of the values can be replaced by real measurements, then surely the relations between real measurements are not…
if they are completely abstract, then how can the equation be related to the physical world? Math equations do not have to be related to anything in the physical world. It's just that humans have found that some patterns in nature seem to match some equations. Why or how math describes the real world is a deep philosophical question![1] When G.H. Hardy[2] was exploring certain aspects of number theory and properties…
> Math equations do not have to be related to anything in the physical world.
Not to derail this into philosophy, but that position is conjecture. There are people who adopt a position where all mathematical concepts actually derive from physical structures, ie. a kind of mathematical physicalism. These people hold that the reduction of math to the physical may be obscure, like a reduction of economics to physics, but still real.
Re: The Deconstructed Standard Model Equation
#47Given 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…
This is rather poetic. There is no difference, mathematical notation is a natural language and initiated mathematicians will read it in sentence form.
Reading is a process of form recognition disconnect from vocalization. On the other hand, language seems to be mostly perceived as vocalisation, because that's the form it's learned from. As anecdotal evidence, tongue is an idiom for language and people have to make an actual effort to read without vocalizatio in order to increase reading-speed.
Note that your literal example does contain a lot more information about context. IE, you even omitted the quadratic equation itself. That shows exactly the problem that I thought the Parent would mean:
I prefer source code in a given language, that's actually compiled and maybe even proven correct, over terse mathematical notation that leaves a lot to context, intuition and shared information. Computability Theory gave rise to Computers, not the other way around.
Re: The Deconstructed Standard Model Equation
#48"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…
It doesn't really make sense to ask if the ghosts were predicted. They're mathematical artifacts of a particular computational formalism. There are other computational formalisms for QFT which don't feature ghosts, and which give the same answers for any observable quantities.
Re: The Deconstructed Standard Model Equation
#49Earlier quoted context omitted.
I, as a layman with basic college physics knowledge, and passing knowledge of the standard model, want to understand the meaning of those terms. Do you know how I can go about that? Ideally, with something a little less dense than a textbook.
I have a PhD in physics, though not particle physics. QFT was required, since the methods appear all over in condensed matter physics. Unfortunately, there is no real shortcut to being able to understand those terms except by studying one of the standard texts. And, physics being what it is, you can expect a pretty hard slog because the texts will assume you know first quantization back and forth. Add to that, it's n…
I was going to recommend the Griffiths book as well. The first two chapters are readable without any demanding mathematics. The latter ones require more work, but build up nicely.