Physics is too hard for physicists

[DrummingAtom]

"Physics is too hard for physicists"

What does this quote from Hilbert mean?

My Math professor said he can't stand how vectors are used in Physics. Being a first year student, I have no clue what this means yet. All of my friends at school are Math majors and have a certain distaste for Physics. When I ask them about it they usually give a vague answer that doesn't really make much sense but they know they don't like it.

As the levels get higher isn't Applied Math pretty much Theoretical Physics? What I mean by this is when the Physics gets more advanced isn't it just really the Math getting more complex?

I'm not trying to bash either discipline just trying to understand what I don't see right now. Thanks.

 

[fatra2]

Hi there,

There is room for interpretation in your comment. I don't know what the math people say about that, since I am a physicist. But from my point of view, mathematics are tools used to create models that try to explain real behaviors. Of course, we will use the vectors analysis, for example, in a way that is useful for our field of study. I never used vector analysis from a definition stand point, since I don't really need that. But what I need is a result from this analysis.

Anyway, I know that opinion may vary on this subject. Cheers

 

[Borek]

I'm not trying to bash either discipline

Could be that's your problem - you try to be open minded and honest, some of your friends are playing "pure math snob" card.

 

[Klockan3]

You know what I can't stand with the pure math snob's? Their utter lack of intuition. They see maths as just a set of axioms, that view is ignorant of how the history of maths actually played out. The structure isn't something in itself, all of maths are founded upon real world problems and then you extrapolate from there. Physics however is the subject where most of these real world problems comes from, most of maths is built upon the logic from physics. In my opinion you don't understand the maths if you don't understand why and how it was created from the beginning, which includes understanding why the physicists can use vectors like they do.

I still love pure maths however, I have taken more classes in it than most maths majors, but people who thinks that maths doesn't need the other disciplines are ignorant. Physics produce huge amounts of new interesting maths all the time, most of the legendary mathematicians worked mostly on problems close to physics etc.

Edit: Also you don't use vectors that differently in physics and maths, most who talks like that don't know what they are talking about. Everything in physics is mathematically rigorous up until certain parts of quantum field theory even if physicists in general don't invoke that rigor. The thing is that intuition of physicists have found a huge amount of maths that would be nearly impossible to find doing it the rigid mathematical way. Then the mathematicians can poke around trying to prove what the physicists already knows using mathematical rigor.

 

[DrummingAtom]

Could be that's your problem - you try to be open minded and honest, some of your friends are playing "pure math snob" card.

Haha, I think you're right. Pure math seems way different than physics. But is the applied math and theoretical physics line more blurred?

I see how the axiom way in math can be a hindrance to the creativity needed for physics. When the physics gets more advanced isn't it just really the math getting more complex?

 

[Jimmy Snyder]

I'm not sure if this is a good example, but in renormalization in QFT, when one infinity is subtracted from another to get 0, this surpasses what mathematics allows. The justification for it is that it gives the right answer. But the fact that it is good physics doesn't make it good math. Physicists are going to continue using the process without mathematical justification because there is no known alternative. At the same time they are going to look for some alternative, or wait for the mathematicians to come up with a mathematical justification.

 

[statdad]

Jimmy's comment is similar to my old experiences as an undergrad. I had a professor who, in the introductory (advanced calc no measure-theory) mathematical stat class, always made the remark "Ok, now we'll just pretend we're in the physics department and say since it works it's valid" whenever limit operations were interchanged (limits/integrals, etc.) No animosity intended by him.
I had physics professors comment on "now we will integrate over the whole universe - or, if you're a math major, a really big sphere" - in our E&M class. Again, there was no animosity present, simply a realization that approaches are different in different disciplines (and different according to the mathematical maturity of the student).
I would comment that the ribbing was gone in my graduate school career - except for the grief an analyst would give to an algebraist, or that which statisticians would give to analysts, or that everyone gave to the graph theorists.

 

[discrete*]

What does this quote from Hilbert mean?

My Math professor said he can't stand how vectors are used in Physics. Being a first year student, I have no clue what this means yet. All of my friends at school are Math majors and have a certain distaste for Physics. When I ask them about it they usually give a vague answer that doesn't really make much sense but they know they don't like it.

As the levels get higher isn't Applied Math pretty much Theoretical Physics? What I mean by this is when the Physics gets more advanced isn't it just really the Math getting more complex?

I'm not trying to bash either discipline just trying to understand what I don't see right now. Thanks.

I don't know what kind of mathematician your Professor is, but I've run into a few that had disdain for physics and applied maths in general. I think it's mostly playful, whereas they kind of jab insults and poke fun, not malicious.

Speaking for myself, I'm a student of pure mathematics and it's not that I look down on applied math (and physics), I respect it for what it is; but it's not pure math. Not saying it's better or worse, just that they're not the same, and for me it comes down to the approach of each subject. Physics and other applied disciplines tend toward the Platonic, whereas pure maths is more liberal in its philosophies -- maybe constructivist, maybe formalist etc.. You can research this topic quite a bit and draw your own conclusions.

 

[Mute]

I'm not sure if this is a good example, but in renormalization in QFT, when one infinity is subtracted from another to get 0, this surpasses what mathematics allows. The justification for it is that it gives the right answer. But the fact that it is good physics doesn't make it good math. Physicists are going to continue using the process without mathematical justification because there is no known alternative. At the same time they are going to look for some alternative, or wait for the mathematicians to come up with a mathematical justification.

Renormalization is a well defined procedure and not simply "subtracting infinities" as is popularly believed. The renormalization group procedure is on firm ground mathematically. The problem with the application of renormalization to high energy field theory is that we do not known the microscopic model that we are trying to coarse grain, and hence there is some sort of missing length/momentum scale that a microscopic model would provide. Hence the need to introduce various cutoffs, etc, to prevent integrals from diverging and doing all sorts of "trickery". If we knew the microscopic model, these scales we introduce would already be there and these quantities would not diverge. Renormalization in condensed matter models always starts with a defined microscopic (effective) hamiltonian, so the length scale is naturally provided (and the picture makes more intuitive sense when considering condensed matter systems).

(some further problems related to "subtracting infinities" result from taking continuum limits, which also results in the throwing away of this length scale, which results in infinities).