Graduate Level Physics Courses: More Than Just Solving Equations?

[solomonics]

Hi all! My name is Mike.
I would like to new the recommended
course of study for someone who wanted
to know all there is to particle physics
through self study. I've done the derivatives
and beginning integration in calculus and
have just begun the first year physics text.
Could someone please guide me?

 

[Greg Bernhardt]

Go through the MIT open courses
http://ocw.mit.edu/courses/physics/

You'll need more advanced math too.
https://www.physicsforums.com/threads/math-required-for-particle-physics.86793/

 

[ZapperZ]

Hi all! My name is Mike.
I would like to new the recommended
course of study for someone who wanted
to know all there is to particle physics
through self study. I've done the derivatives
and beginning integration in calculus and
have just begun the first year physics text.
Could someone please guide me?

You can't just study particle physics without the proper foundational knowledge. You can study ABOUT particle physics, but to study it properly (i.e. know all there is to it), then you have to study to be a physicist first! This means a foundational knowledge at the undergraduate level in classical mechanics, classical electromagnetism, and quantum mechanics. THEN you proceed to more advanced knowledge in quantum field theory and quantum electrodynamics.

And to be able to do all of that, you will need an extensive knowledge of mathematics, significantly beyond just "derivatives and beginning integration".

You can't learn just a certain part of physics while ignoring others. You can't just pick up a particle physics textbook, or sit in a class, without already knowing classical E&M and QM, for example. That is why all upper level physics classes have prerequisites, and even then, these prerequisites are often the "bare minimum" that one should have and often still not sufficient to do well or to fully comprehend the upper level subject areas.

So since you asked for a recommendation for a course of study, my recommendation is to study to become a physicist at the undergraduate level first. That is the foundation you will need to study particle physics.

Zz.

 

[QuantumCurt]

ZapperZ pretty much covered it. I'm currently a physics undergrad, and actual particle physics textbooks still read like a mostly foreign language to me because I haven't yet studied the courses that lead up to that point. Physics isn't really the type of field where you can just learn about one given area. One could become an expert in the history of 16th century England without studying any other period of history. Physics doesn't work this way.

The math alone that is needed for particle physics is well past what you know, which seems to be roughly the equivalent of part of calculus 1.

The typical bare minimum physics sequence for an undergrad:

Freshman/Sophomore level (100 and 200 level courses) -
Physics I - Classical Mechanics w/ lab
Physics II - Electricity & Magnetism w/ lab
Physics III - Modern Physics (waves and oscillations, optics, thermodynamics, quantum physics, nuclear physics, atomic physics, elementary particles, and/or various other subjects) w/ lab
Calculus I
Calculus II
Calculus III
Ordinary Differential Equations
Linear Algebra

Junior/Senior level (300 and 400 level courses) -
Classical Mechanics (1-2 semesters)
Electricity & Magnetism (1-2 semesters)
Thermodynamics and Statistical Mechanics (1 semester)
Quantum Mechanics (2 semesters)
Upper level labs

More math! Specific courses will vary, but typically include at least some of the following -
Partial Differential Equations, Topology, Real Analysis, Complex Analysis, Tensor Analysis/Differential Geometry and others

That roughly sums up the undergraduate curriculum. We still haven't gotten to particle physics, aside from possibly having a cursory introduction to them in physics III during the sophomore year for a couple weeks.

Now let's head to graduate school

We'd typically start with the bare minimum required courses at the 500 level in the following -

Classical Mechanics (1 semester)
Electricity & Magnetism (1 semester)
Quantum Mechanics (2 semesters)

Many graduate students will take a semester or two of some type of Mathematical Methods of Physics course, or possibly some more advanced math courses that are relevant to the subjects they wish to pursue.

Then we specialize.

For particle physics, we'd next take some combination of -

General Field Theory
Quantum Field Theory
Subatomic Physics
Particle Physicstl;dr - Physics is very cumulative. The ability to work in a given field relies on the knowledge of numerous other areas of physics. Learning particle physics is a lofty goal. My ultimate academic goal at this point is to do my PhD in some area of particle physics. My interests lately have been narrowing down to neutrinos. I'm currently doing an honors project in my Physics III class on neutrino oscillations, but given my lack of knowledge of all of the physics I'll be learning over the next few years, the scope of the project has to remain pretty limited.

 

[jtbell]

A popular upper-level undergraduate textbook in particle physics is Griffiths's Introduction to Elementary Particles. In the preface, Griffiths notes that the students in his course "typically had under their belts a semester of electromagnetism (at the level of Lorrain and Corson) [or, I might add, Griffiths's own Introduction to Electrodynamics], a semester of quantum mechanics (at the level of Park), and a fairly strong background in special relativity."

Below that, most "introductory modern physics" textbooks for students who have taken a first-year course in classical mechanics and electromagnetism include a chapter or two on particle physics, but at a lower level.

 

[QuantumCurt]

My introductory physics textbook has a chapter on atomic physics, followed by a chapter on nuclear physics, and a chapter on elementary particle physics. The chapter on elementary particles is fairly simplified though. It introduces the standard model and discusses primarily the more qualitative aspects of the various parts of the standard model. The quantitative aspects of the chapter are very basic, and in no sense develop a full understanding of particle physics. It assumes that the student hasn't yet developed the necessary mathematical skills to really work with particle physics formally. It covers the basics of things like particle spin how the basic conservation laws work with elementary particles, and develops some of the basic ideas of the electroweak theory. These topics are all at a very simplified level, but I'm looking forward to ending this semester by covering these topics formally. It'll be great to finally get a little taste of some of the particle physics I'll be taking in far more depth later on.

 

[solomonics]

Thank you so much ZapperZ, QuantumCurt, jtbell, Greg Bernhardt for responding to my post. It is greatly
appreciated and I will definitely take to heart all of this guidance you were kind enough to leave me.
Mike

 

[IGU]

Now let's head to graduate school

We'd typically start with the bare minimum required courses at the 500 level in the following -

Classical Mechanics (1 semester)
Electricity & Magnetism (1 semester)
Quantum Mechanics (2 semesters)

Just for the fun of it, suppose you did a mathematics undergraduate degree and never came anywhere near physics except that you took all the mathematics you ever might need. Could you go for a graduate degree in physics starting with the graduate physics courses? Would it have to be theoretical physics since you had never done labs?

 

[QuantumCurt]

Not even close. One can't jump right onto graduate level physics regardless of their math background. Math is a big part of physics, but it's still math. It isn't physics.

And no, it wouldn't have to be theoretical (disregarding the feasibility of it). Undergraduate physics labs tend to just work to reinforce and confirm theory. It's the same physics though. People often seem to picture a much larger distinction between theoretical and experimental physics than actually exists between them.

 

[ZapperZ]

Just for the fun of it, suppose you did a mathematics undergraduate degree and never came anywhere near physics except that you took all the mathematics you ever might need. Could you go for a graduate degree in physics starting with the graduate physics courses? Would it have to be theoretical physics since you had never done labs?

That is like asking if one knows how to use a saw, a screw driver, a power drill, etc., can one then build a skyscrapper?

Zz.

 

[QuantumCurt]

That's an excellent analogy.

Similarly, one can own every single hand tool and power tool in the world...they have the necessary equipment to build a skyscraper, but they may not have the experience or the knowledge required to actually apply it.

One can know all the math in the world without knowing how to apply it to physics. The math involved in physics is solving the equation. The physics is setting the equation up and properly understanding what the equation means in a physical context. Someone with a math background does not know this. Physicists basically have to be good at math...however, I know plenty of people that are great at math and horrible with physics.

 

[IGU]

Sorry, I'm hearing claims that going straight to graduate level physics classes without any undergraduate physics (but lots of math) is silly or impossible or something, but no concrete example of what would be missing. Does a semester of graduate classical mechanics not teach classical mechanics, and graduate electricity and magnetism is not all the electricity and magnetism you need to know? Is the claim that there a significant pieces of these topics that are taught in undergrad and skipped over in the grad classes?

If so, what are these things that are missing from the grad classes? I'd like to understand why somebody with a BS in mathematics (and specifically all the mathematics needed for physics) would be unsuitable to be accepted into a Physics Ph.D. program without requiring remedial undergrad physics classes. This seems to me to be the assertion.

 

[ZapperZ]

Sorry, I'm hearing claims that going straight to graduate level physics classes without any undergraduate physics (but lots of math) is silly or impossible or something, but no concrete example of what would be missing. Does a semester of graduate classical mechanics not teach classical mechanics, and graduate electricity and magnetism is not all the electricity and magnetism you need to know? Is the claim that there a significant pieces of these topics that are taught in undergrad and skipped over in the grad classes?

Think about it. If graduate level courses of these subjects are nothing more than rehashing undergraduate material, what's the point in teaching these material? Do you honestly think that graduate level E&M and QM and CM are IDENTICAL to what we teach students at the undergraduate level? Seriously?

The Jackson's classic graduate level E&M text covers practically all of undergraduate electrostatics in his INTRODUCTION! By the time you start "Chapter 1", you are expected to know all of your undergraduate electrostatics!

If so, what are these things that are missing from the grad classes? I'd like to understand why somebody with a BS in mathematics (and specifically all the mathematics needed for physics) would be unsuitable to be accepted into a Physics Ph.D. program without requiring remedial undergrad physics classes. This seems to me to be the assertion.

Easy. Find someone like that, and do what I had suggested whenever someone asked me if someone with another major can go on to graduate school in physics:

https://www.physicsforums.com/threa...if-my-bachelors-degree-isnt-in-physics.64966/

Take a practice GRE Physics text, and then try to do well in a sample qualifying exam.

Each one of us can talk about this till we're blue, but that is as concrete of a test/experiment as anything. Those tests are what one normally expects an undergraduate physics major must know to go on to a physics graduate program.

Zz.

 

[QuantumCurt]

Because classes have prerequisites for a reason. Knowing all the math in the world doesn't prepare you for a graduate level class in physics. Math is but a small part of solving a physics problem. There is a great deal of...well...physics! People seem to often think that working a physics problem is like solving a math problem. Just "solve for x and substitute values." It's not. Once one is to the point that they're solving for a symbolic or numerical solution...one is no longer "doing physics." One is simply solving an equation.

There's a lot of math in chemistry. Would a math degree prepare a student for graduate school in chemistry?

Graduate level physics courses cover a lot of the same physics that is covered at the undergraduate level, but often in significantly different ways. It's not going to cover the basics. A graduate level classical mechanics course assumes that one is comfortable with drawing force diagrams, working with Newton's Laws, has a working knowledge of Conservation of Energy, and many more subjects. One is assumed to understand these things conceptually. Physics isn't just about solving equations. It's about understanding physics.

"Would it have to be theoretical physics since you had never done labs?"

This really pops out at me. Undergraduate physics labs are a necessary part of a physics education. They gave one experience with working with the types of data collection and laboratory methods used in physics. However, labs don't function as the component to "prepare the experimentalists." It compares experiment to theory. This is necessary for theorists and experimentalists alike. It's not as if one can "miss" the undergrad labs and still do physics...but -only- theory. Experiment leads to understanding of theory. I still remember one of my first undergraduate physics labs. We were using a force table and we had to use vectors to balance a system of weights and pulley's so they would stay balanced when we removed the pin that was holding them all in place. That lab helped me to understand what vectors ARE in a purely physical sense, rather than simply being a directed line segment on a graph. Mathematically, that's really all that a vector is. Physically, it is much more than that.

Is it hypothetically possible for someone to enroll in a graduate level physics class with no prior physics knowledge, and still do well? If that's only class that one is taking, and one sacrifices their sleep schedule to spend 18 hours a day getting caught up on undergraduate physics concepts...then sure.

Think of it this way...if you've never worked a problem involving Newton's Laws, what's going to be your first example? It's going to be a simple F=ma problem with a given mass and a given constant acceleration, and the goal of finding the force. Multiply the mass and acceleration together, and there you go. It's not going to be a problem in three dimensions involving drag forces, friction, multiple applied forces, etc.

This just honestly seems like a silly question.

 

[IGU]

Think about it. If graduate level courses of these subjects are nothing more than rehashing undergraduate material, what's the point in teaching these material? Do you honestly think that graduate level E&M and QM and CM are IDENTICAL to what we teach students at the undergraduate level? Seriously?

I think that undergraduate physics classes are taught to undergraduates. They are presumed when they are taught classical mechanics that they have a bit of calculus, almost no understanding of differential equations, and no understanding of PDEs. Thus you can't teach them much real physics at all. I am presuming that the graduate class teaches them the same stuff, but assuming they have the mathematical tools to understand it properly. Is that wrong?

The Jackson's classic graduate level E&M text covers practically all of undergraduate electrostatics in his INTRODUCTION! By the time you start "Chapter 1", you are expected to know all of your undergraduate electrostatics!

And this isn't an immature understanding informed by an inadequate knowledge of the necessary math, to be largely superseded by what you learn in Jackson? It actually requires that undergraduate understanding as a basis for what is learned?

Never having done any graduate physics myself, I know I don't understand. But back when I was taking the required introductory undergraduate physics at Caltech, I found that whenever I talked to graduate students (outside of class) about the physics I was learning and how it might apply to the research they were doing I was always told something like "Oh, don't take too seriously that crap they're teaching you; when you get to grad school you have to learn it again the right way. In this case, what that means is ..."

Because classes have prerequisites for a reason.

Do introductory graduate physics classes have prerequisites? Maybe a specific example would help.

Knowing all the math in the world doesn't prepare you for a graduate level class in physics. Math is but a small part of solving a physics problem. There is a great deal of...well...physics!

Yes, of course. So you are saying that an introductory graduate physics class is not going to teach me all the physics I need to solve physics problems. Okay.

People seem to often think that working a physics problem is like solving a math problem. Just "solve for x and substitute values." It's not. Once one is to the point that they're solving for a symbolic or numerical solution...one is no longer "doing physics." One is simply solving an equation.

Likewise, you seem to think that solving a math problem is just "solve for x and substitute values." It's not. An actual math problem looks more like "Here's a situation; try to understand it; prove some things about it and similar situations." That's math.

There's a lot of math in chemistry. Would a math degree prepare a student for graduate school in chemistry?

I don't know, but it seems quite a bit less likely than physics. Chemistry seems to involve far more arbitrary memorized information than physics. And the mathematical modeling seems much messier and uncertain.

Graduate level physics courses cover a lot of the same physics that is covered at the undergraduate level, but often in significantly different ways. It's not going to cover the basics. A graduate level classical mechanics course assumes that one is comfortable with drawing force diagrams, working with Newton's Laws, has a working knowledge of Conservation of Energy, and many more subjects. One is assumed to understand these things conceptually. Physics isn't just about solving equations. It's about understanding physics.

Sure. When you learn physics in high school without calculus it's about understanding physics too, but you don't have the right tools. Same thing for undergraduate physics, where you are beginning to have some useful tools, but still lack those with the necessary power. You mention understanding things conceptually -- perhaps I have been led wrong in believing statements to the effect that in modern theoretical physics you will find that physical intuition is not only insufficient but will actually mislead you.

It's apparent to me that I'm not communicating my questions very effectively, and I've effectively derailed this thread, so I'm going to stop now. My apologies.