Does lack of rigour cause problems in Physics?

[Albertrichardp]

Does physics need rigour?My problem lies with the fact that if a physicist makes a mathematical error he may not be able to identify it due to his lack of understanding of the rigourous mechanism which the mathematician is aware of.

 

[Albertrichardp]

Can you please give me specific problems?Thanks.Comments appreciated.

 

[BvU]

Hello AR, welcome to PF !

Most of the errors physicists make are not related to what you describe. Sometimes rigourousness is certainly required, and then physicists (especially theoretical physicists) turn out to be pretty good mathematicians too. There isn't such a deep gap between the two disciplines.

Having said that, I must admit that casual treatment of differentials is common practice in physics, because the relationships normally aren't as pathological as the ones mathematicians can concoct

 

[UncertaintyAjay]

Physicists are generally very very good at math I believe. Feynman who was a physicist won the Putnam Prize which is a maths exam, but then again- that was Feynman, so...

 

[rumborak]

Yeah, that's way too much of a blanket statement for having a genuine discussion. Without any specifics, the answer is "physics usually is very proficient in its use of mathematics ".

 

[BvU]

After all, folks like Newton and Leibnitz had to invent important chunks of mathematics before being able to proceed with their physics ...

 

[UncertaintyAjay]

Also, with math being so rigorous, its very abstract. You can't do that with physics because you need to make deductions about the real world from the math you do in physics. I believe Feynman says something similar in the Feynman Lectures ( and yes I'm a colossal fan) when he says that physics isn't only about being able to do calculations bit about being able to reason things out from the math.

 

[UncertaintyAjay]

After all, folks like Newton and Leibnitz had to invent important chunks of mathematics before being able to proceed with their physics ...

Touché. You wouldn't have calculus without physicists. Vive les physicists! Though mathematicians are cool too. I want to double major in both so...

 

[BvU]

Hehe, turns out Leibnitz was mostly a mathematician. Didn't know too much about the chap, so I googled him up -- no wonder Newton is much more famous !

 

[nasu]

I think you may refer to the "practice" of physicist to use some mathematical tools without going to the lengths of proofing that the tools work in that specific case or even "abusing" notation in ways will make a mathematician scream.:)
Even Newton's calculus was not a mathematically rigorous construction. But it worked very well for his purposes.

Part of the problem (or absence of a problem actually) is that the functions and other mathematical objects that model actual phenomena are "nice", they naturally satisfy all the conditions that the mathematician will first prove. But the physicist will just assume that nature take care of it and goes ahead.:)