Ask HN: Good resources for studying physics from the “ground up”?
7 comments
Grad school.
It’s paradigmatic that physicists look at a problem and try to distill out the essence of it, you can see this at its best and its worse in The Feynman Lectures on Physics where Feynman seems to find a clever trick to make short work of a problem. He’d spent half a lifetime looking for this sort of trick and makes it look easy, one kind of student appreciates that, another kind thinks it is completely unreasonable to expect that they can pull a rabbit out of a hat on command.
There is a dark art of solving hard problems in physics that isn’t really taught outside of grad school, the problem of simulating the explosion of an atom bomb is one of those problems and so would be modeling the evolution of a star on the main sequence. In either one of those cases your main weapon is the partial differential equation and you aren’t going to find a closed-form solution but you are going to solve it numerically. People were solving problems like the above before they had computers, they did the numerical analysis by hand!
For a problem like that you start out using the technique of dimensional analysis that I learned in high school physics, at the outside of your calculation you’re going to have quantities with dimensions. You will have a handful of those and then many more parameters that are ratios (e.g. if you were modeling the planets in the solar system you would put in the radius of the Earth’s orbit in meters and put the rest of the planets in as ratios, notably you could double the size of the whole system and you could scale the time or gravitational constant accordingly and it would be “the same”)
With that in hand solving the inner problem is a long hard fight, it is not too different in principle from those cases where you can solve in closed form (say prove a spherical shell gravitates like a point on the outside but doesn’t gravitate on the outside) except you are going to use numerical solutions, approximations, and such. Actually you don’t learn very much about how to work at that level in classes in grad school, you learn it the hard way working on your PhD.
If there was something you should read to see how it is done, see “An introduction to the study of stellar structure” by Chandresakar and “Structure and Evolution of the Stars” by Schwarzchild. Those books were written before computers were ubiquitous so they show how you attack hard problems without getting bogged down in how you code it up in FORTRAN.
It’s paradigmatic that physicists look at a problem and try to distill out the essence of it, you can see this at its best and its worse in The Feynman Lectures on Physics where Feynman seems to find a clever trick to make short work of a problem. He’d spent half a lifetime looking for this sort of trick and makes it look easy, one kind of student appreciates that, another kind thinks it is completely unreasonable to expect that they can pull a rabbit out of a hat on command.
There is a dark art of solving hard problems in physics that isn’t really taught outside of grad school, the problem of simulating the explosion of an atom bomb is one of those problems and so would be modeling the evolution of a star on the main sequence. In either one of those cases your main weapon is the partial differential equation and you aren’t going to find a closed-form solution but you are going to solve it numerically. People were solving problems like the above before they had computers, they did the numerical analysis by hand!
For a problem like that you start out using the technique of dimensional analysis that I learned in high school physics, at the outside of your calculation you’re going to have quantities with dimensions. You will have a handful of those and then many more parameters that are ratios (e.g. if you were modeling the planets in the solar system you would put in the radius of the Earth’s orbit in meters and put the rest of the planets in as ratios, notably you could double the size of the whole system and you could scale the time or gravitational constant accordingly and it would be “the same”)
With that in hand solving the inner problem is a long hard fight, it is not too different in principle from those cases where you can solve in closed form (say prove a spherical shell gravitates like a point on the outside but doesn’t gravitate on the outside) except you are going to use numerical solutions, approximations, and such. Actually you don’t learn very much about how to work at that level in classes in grad school, you learn it the hard way working on your PhD.
If there was something you should read to see how it is done, see “An introduction to the study of stellar structure” by Chandresakar and “Structure and Evolution of the Stars” by Schwarzchild. Those books were written before computers were ubiquitous so they show how you attack hard problems without getting bogged down in how you code it up in FORTRAN.
Thank you for this very insightful answer! I've always been more interested in the structure of problems than in their specific detail, so your observations and recommendations seem right up my alley.
When it comes to mathematical foundations, do you believe that differential equations are the best approach to gain a grounded understanding of physics? Although I've been introduced to them, I lack a deeper, intuitive grasp. I'm curious if attaining such an understanding would markedly improve my comprehension of physical concepts.
When it comes to mathematical foundations, do you believe that differential equations are the best approach to gain a grounded understanding of physics? Although I've been introduced to them, I lack a deeper, intuitive grasp. I'm curious if attaining such an understanding would markedly improve my comprehension of physical concepts.
The idea of "understanding" is problematic in that we can't understand" everything but can get understandings about particular situation; certain sorts of problems are provably impossible to solve such as predicting the weather three years from now or being able to prove that any computer program either will or will not complete in finite problems.
You can understand that a problem is in such a class yet an insolvable problem always leaves the answer to that problem mysterious and knowingly "not understood".
Then there is the things nobody understands, like what dark matter is. People have all kinds of ideas, and the math is usually a lot simpler than the math for problems like "stars". What we're lacking is the experiment or observation that proves one thing or another. After that somebody gets the Nobel prize for furthering our understanding of the universe.
The line of understanding an area passes through solving problems, you prove what you understand through solving problems and discover gaps in what you understand to explore with by postulating more problems.
Differential equations turn up in undergrad physics at the third year level with electromagnetism and then with the theory of the hydrogen atom with the Schrodinger equation. It's a special case because of the spherical symmetry which lets it be solved exactly but it teaches you the other problems can have symmetry break in a way that gives an understanding about how the structure of the system effects the energy spectrum and other behaviors.
Differential equations might not be the ultimate nature of the universe and they do have that problem of not having a single strategy for solving all of them, many people think the differential equations course in undergrad math is disorganized and teaches a bunch of random methods but no unifying theory. They also behave can behave badly in like the Theory of General Relativity in which the singularities probably mean the theory is wrong or just misbehave in a computer.
If you're trying to answer harder problems (say how does air flow around a space shuttle that is reentering the atmosphere) it tends to come down to differential equations.
You can understand that a problem is in such a class yet an insolvable problem always leaves the answer to that problem mysterious and knowingly "not understood".
Then there is the things nobody understands, like what dark matter is. People have all kinds of ideas, and the math is usually a lot simpler than the math for problems like "stars". What we're lacking is the experiment or observation that proves one thing or another. After that somebody gets the Nobel prize for furthering our understanding of the universe.
The line of understanding an area passes through solving problems, you prove what you understand through solving problems and discover gaps in what you understand to explore with by postulating more problems.
Differential equations turn up in undergrad physics at the third year level with electromagnetism and then with the theory of the hydrogen atom with the Schrodinger equation. It's a special case because of the spherical symmetry which lets it be solved exactly but it teaches you the other problems can have symmetry break in a way that gives an understanding about how the structure of the system effects the energy spectrum and other behaviors.
Differential equations might not be the ultimate nature of the universe and they do have that problem of not having a single strategy for solving all of them, many people think the differential equations course in undergrad math is disorganized and teaches a bunch of random methods but no unifying theory. They also behave can behave badly in like the Theory of General Relativity in which the singularities probably mean the theory is wrong or just misbehave in a computer.
If you're trying to answer harder problems (say how does air flow around a space shuttle that is reentering the atmosphere) it tends to come down to differential equations.
I knew very little about Physics before I read a textbook about it on https://openstax.org. The math felt approachable too. Now, I feel like I can get the gist of some of the Physics-related articles that I see.
I am not sure I understand the question, but The Motion Mountain was quite a good textbook years ago. Available as free eBook: https://www.motionmountain.net/
There is a book "Physics for Mathematicians, Mechanics I", by Spivak, who wrote well-regarded books on differential geometry.
Physicist Gerard 't Hooft has a list of books by subfield of physics for self-study at https://webspace.science.uu.nl/~gadda001/goodtheorist/index.... .
Physicist Gerard 't Hooft has a list of books by subfield of physics for self-study at https://webspace.science.uu.nl/~gadda001/goodtheorist/index.... .
This is good
https://www.susanrigetti.com/physics
https://www.susanrigetti.com/physics
Additionally, most physics classes try to teach you "intuition" that is based on simplified models. This often results in a break-down of said intuition if some implicit assumptions made by the simplified model are not met - a failure mode that has caused me great frustration when trying to understand new concepts by using these intuitions.
So my question is: Is there a better way? Do resources like books, videos or websites exist that provide a structure for studying physics while minimizing the assumptions being made?
I realize that this is a challenging issue to address, given the sheer breadth and complexity of physics as a field. Nevertheless, I wonder if anyone has ventured to tackle this challenge?