What are some difficult concepts in physics that rely heavily on mathematics?

[TheDonk]

What things in physics have you found very hard to explain well without using math? I think it would be great to get a good list of those things here. Then maybe someone (or I) could hold a contest on explaining those things without math, judged by people who know the theory and people who don't.

 

[ceptimus]

Nice idea.

At the moment, I can't think of anything in classical physics that is difficult to explain without math, but anything to do with quantum mechanics is very tricky to explain without using mathematical concepts.

 

[russ_watters]

Interesting - I can't think of anything in classical physics that can be explained without math.

Explain how to find gravitational force of an object.
Explain how to find escape velocity.
Explain what an "orbit" is.

This will be a very useful exercise though...

 

[arildno]

Oh, really, Ceptimus?
To take one simple example, how would you explain the rotational instability in layman's terms known as Eulerian wobble without starting to speak of principal axes and the respective moments of inertia about them?
(Of course, a simple demonstration will suffice to justify what you're saying, but that's quite different..)

The intricacies of turbulent flow and multiple phase flow are also rather complex.

 

[Gokul43201]

To take one simple example, how would you explain the rotational instability in layman's terms known as Eulerian wobble without starting to speak of principal axes and the respective moments of inertia about them?

Just the example I would have picked.

 

[NeutronStar]

Oh, really, Ceptimus?
To take one simple example, how would you explain the rotational instability in layman's terms known as Eulerian wobble without starting to speak of principal axes and the respective moments of inertia about them?
(Of course, a simple demonstration will suffice to justify what you're saying, but that's quite different..)

Why couldn't you speak a principle axes or of respective moments of inertia about them in a non-mathematical way? Those concepts aren't mathematical in and of themselves. It's only when you bring in the specific quantitative relationships (i.e. formulae) that things start to get mathematical.

 

[Gokul43201]

Why couldn't you speak a principle axes or of respective moments of inertia about them in a non-mathematical way? Those concepts aren't mathematical in and of themselves. It's only when you bring in the specific quantitative relationships (i.e. formulae) that things start to get mathematical.

How would you explain (non-mathematically) why, in a cuboidal object you can sustain stable oscillations about the longest and shortest principal axes but not about the other ?

 

[russ_watters]

Why couldn't you speak a principle axes or of respective moments of inertia about them in a non-mathematical way? Those concepts aren't mathematical in and of themselves. It's only when you bring in the specific quantitative relationships (i.e. formulae) that things start to get mathematical.

Well then do it - start simply with explaining what an "axis" is without saying anything that sounds like geometry (catch: the word "axis" implies geometry...so good luck).

Then try to explain "moment of inertia" (or just inertia) without any math.

See, the problem is that any description, even if it contains no numbers, is a description of the math.

eg: inertia is resistance to acceleration. What's acceleration? Acceleration is change in speed with time. Guess what - that's a derivative and an equation! Oops, I just used calculus and algebra - and that's with a very un-descriptive explanation of inertia (it can't be used for anything without saying what the actual relationship is).

 

[NeutronStar]

How would you explain (non-mathematically) why, in a cuboidal object you can sustain stable oscillations about the longest and shortest principal axes but not about the other ?

I don't know how to explain it non-mathematically because I don't even know the mathematical explanation.

However, for me, to explain something in a non-mathematical way simply means to reduce the mathematical statements into their English translation.

While it may take quite a bit more to explain it that way (after all mathematics is indeed a short-hand language) I see no reason why it can't be explain in normal language. I would accept that referring intuitively to geometric figures and specific axes isn't necessarily stating things in terms of mathematics.

I think one of the biggest problems associated with the idea put forth in this thread is that everyone may have a different idea of what they mean by "non-mathematical" explanation

If you are going to claim that any reference to any geometric figure or axes is automatically using mathematical notions then I would say that, from that point of view, humans could hardly utter a sentence that didn't include some form of mathematical object or statement of quantitative relationship.

It would seem to me that someone who fully understands these oscillation restrictions in a cubiodal object could indeed explain them to a layman in a non-mathematical way. (i.e. In a way that doesn't rely directly on mathematical formula notation, but rather can be stated in a more intuitive geometric language.)

Don't forget, nobody gave any restrictions on how long or short the "explanation" needs to be. It might end up being a full chapter in a book to explain the meaning of a couple of equations. But it should be possible.

I personally believe that any mathematical statement can be translated into English.

In the case of QM sometimes the only translation possible is to simply say, "It's just a probability". Because, after all, even within mathematics that's all that's really being said. There simply isn't anything more to translate. Mathematicians don't understand what gives rise to these probabilities anymore than anyone else! They just work.

In the case of this oscillating cubiodal object, however, there probably is a comprehensible translation. Actually I would claim that if there is no possible translation then it probably isn't fully understood even by mathematicians. They just kind of accept the equations without fully understanding why they are true. That very well may be the case here. In that case, there's nothing to translate because even the mathematician don’t understand why the equations are saying what they are saying.

 

[EL]

I think this discussion is quite meaningless until "the Donk" explains what he means by "without using math"...

 

[ceptimus]

In a spinning object, the axis is the centre of spin - the part of the object that moves the least.

If you want to make a good flywheel, you have to put as much material as possible in the rim.

I can explain and demonstrate concepts like this to young children, who know no mathematics beyond simple counting. It's stretching things a bit far to call explanations like these mathematics. I think you are confusing quantitative explanations, where math is admittedly essential, with qualitative ones, where it often isn't.

 

[russ_watters]

However, for me, to explain something in a non-mathematical way simply means to reduce the mathematical statements into their English translation.

That's a different issue than the challenge in the original post. Saying "one plus one equals two" is the same as "1+1=2" and "force is proportional to acceleration" is the same as "f=ma". Using the words instead of the numbers or symbols doesn't mean its not still a mathematical statement.

 

[russ_watters]

I can explain and demonstrate concepts like this to young children, who know no mathematics beyond simple counting. It's stretching things a bit far to call explanations like these mathematics.

Why not? Teaching them math is exactly what you are doing. Learning any subject starts with defining the terms in it. However, while those descriptions are a good start, they don't help use the concepts until you start putting the numbers in. You cannot, for example, use your description of moment of inertia to construct a flywheel that you know will work (there is a thread around here somewhere on that very subject).

 

[ceptimus]

If I say, "It's more difficult to pick up a heavy object than a light one", am I making a mathematical statement?

How about, "It's further to the school than it is to the station" ?

 

[krab]

You guys are using different definitions of "without math". Russ is using it to mean "without using any concepts that are considered part of the domain of the subject of mathematics", and Ceptimus is using it as "without using any concept not understandable by someone not trained in mathematics". I'm with Ceptimus here, since Russ' definition becomes far too broad to be useful, and so would lead this thread nowhere.

 

[russ_watters]

If I say, "It's more difficult to pick up a heavy object than a light one", am I making a mathematical statement?

How about, "It's further to the school than it is to the station" ?

Yep: > (both cases).

You guys are using different definitions of "without math". Russ is using it to mean "without using any concepts that are considered part of the domain of the subject of mathematics", and Ceptimus is using it as "without using any concept not understandable by someone not trained in mathematics".

Pretty much, yeah. We may need a clarification from the thread starter.

I'm with Ceptimus here, since Russ' definition becomes far too broad to be useful, and so would lead this thread nowhere.

Well, that's my point: you can't do anything useful with physics without using math.

 

[TheDonk]

I'm glad to see so many responses! Sorry to not clarify sooner.
I do mean something closer to "without using any concept not understandable by someone not trained in mathematics".
All I mean is without writing equations or saying equations in english words that you instantly think of as an equation. Obviously this depends on the person but exceptable sentences are sentences that use the words: more than, stronger, faster, double, etc.

There may be times when using numbers is needed such as 'four dimensions' or 'twice as fast' but people who aren't familiar with math won't have trouble understanding it.

Example:
Gravity gets stronger as things get closer. In fact, when two things are twice as close, the gravity between them is four times as strong!

This example is debatable because it basically just gives an example of the effect of the equations. I think it is exceptable tho because it is very basic math and you can understand the effect without consciously grasping what the equation would be.

 

[Astronuc]

Looking at some previous examples:

"Explain how to find gravitational force of an object."

One could explain gravity, as a pull, as in it holds us down, or the analogy of Newton's apple. Or - "What goes up, must come down."

But finding the gravitational force (a quantity) requires math.


"Explain how to find escape velocity."

The speed at which an object needs to escape gravity or the pull of a planet, moon or star. (No math there - but a qualitative statement of a physical principle).


"Explain what an "orbit" is. "

An object traveling around another held in a continuous path by gravity. The simplest orbit is a circle. (a qualitative statement).


I think most of us have a qualitative understanding of many physical phenomenon well before we understand algebra, trig, and calculus. But at some point, math is necessary, e.g. to go beyond qualitative statements like hot/cold or heavy/light to quantitive statements like how hot (1000 K) or how cold (100 K), or how heavy (1000 kg or 1 g).

But to really understand the natural world, and in order to manipulate nature or at least make predictions, describe it quantitatively, and develop models requires math.