# Frustrated by how physics is generally explained/taught

Andy Resnick
<snip> I would just like that there also exists this kind of alternative approach for many subfields of physics. And often it doesn't.
On the contrary, there is:

General introduction- https://www.amazon.com/dp/1107602602/?tag=pfamazon01-20
Fluid Mechanics- https://www.amazon.com/dp/0199679215/?tag=pfamazon01-20 (2 volumes)
Electromagnetism and optics- http://www.worldscientific.com/worldscibooks/10.1142/9251

These are just the few I have within reach. I'm sure if you search arXiv you can find monographs as well.

As to your question, why is Physics not generally taught that way, my unsatisfactory answer is that I'm not familiar enough with the math to plausibly teach the material. I can learn it (and I have been learning the material, after a fashion), but I'm not currently prepared to teach that way.

You would (or at least should) definitely appreciate this one: http://www.springer.com/us/book/9780387989921

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jtbell
Mentor
As to your question, why is Physics not generally taught that way, my unsatisfactory answer is that I'm not familiar enough with the math to plausibly teach the material.
Right, in order to teach such a course effectively, the instructor needs to be well-versed in both the physics and the math. I would wager that relatively few physicists have the deep math background that would be necessary.

Also, you need students who are prepared to take such a course. At least here in the US, I think relatively few physics students (either undergraduate or graduate) would have a suitable math background. How many math students at that level would also want to learn the physics?

chiro
What I was trying to ask is what sorts of structures and languages you were intending to use to convey the body of knowledge for science (in this case physics).

The thing is that without these elements, no one is going to understand what you really mean.

kith
I too don't really understand what exactly the OP is about. Since you are concerned with the teaching of physical concepts, maybe it would help to go into detail about a really basic example. Imagine you are in high school and want to teach a motivated class some physics. Can you give a tangible outline of what you would do? Which topic do you choose and how do you present it? Then we can contrast your ideas much better with more mainstream approaches.

Taking advances theories like GR as example doesn't make sense to me unless you think it would be best to start with the most advanced theory and derive the more basic theories which describe our everyday experience as special cases. But then again I would like to see an outline of how you would start teaching people who are not familiar with physics yet, so that there's a tangible thing to discuss.

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atyy
I think the OP just had bad introductory physics. I still remember my introduction to vectors, probably around 9th grade - "a vector is a magnitude and a direction" - which is the definition of the geometric quantity, not the coordinates. Also, the Feynman lectures stresses the difference between real physical quantities like a step of certain size in a certain direction which is invariant, compared to the set of three numbers which depend on the reference frame.

Thanks for the references Andy. Some of them look interesting. Unfortunately it is difficult to evaluate them as they are not free. Furthermore it seems that the first reference, while apparently very nice on the mathematical aspect, does not deal with classical mechanics but directly with einsteinian relativity and QM, what I won't call an introduction to physics.
These are just the few I have within reach. I'm sure if you search arXiv you can find monographs as well.
I'll try to deepen my research in that directions.

Imagine you are in high school and want to teach a motivated class some physics. Can you give a tangible outline of what you would do? Which topic do you choose and how do you present it? [...] I would like to see an outline of how you would start teaching people who are not familiar with physics yet, so that there's a tangible thing to discuss.
First let's make it clear that my question was moved in the teacher forums but my intention was more to focus on an epistemological rather than an strictly educational problem (what sort of language do/could/should we use to explain and understand physics). Anyway that's ok if it remains here. Second I'm not a physics teacher, I don't plan to become one and as it is probable we received education in different countries I'm not sure considering "what and how I would like to teach to high school students" would provide a relevant point of comparison. And last as I already said it I'm not trying to impose a better approach for teaching physics to the layman. I'm only asking for more numerous and more frequent alternative approaches.

What I was trying to ask is what sorts of structures and languages you were intending to use to convey the body of knowledge for science (in this case physics).
The thing is that without these elements, no one is going to understand what you really mean.
I too don't really understand what exactly the OP is about. Since you are concerned with the teaching of physical concepts, maybe it would help to go into detail about a really basic example. But then again I would like to see an outline of how you would start teaching people who are not familiar with physics yet, so that there's a tangible thing to discuss.
I had already mentioned this thread. Is this already too complex? Classical galilean physics can use it. To re-explain here I was suggesting that the physical concept of extensive property could be formally defined as a measure and could include many vector/tensor-valued quantities like momentum, angular momentum, inertia tensor, etc by opposition to an intensive property that could be defined as a field. To me this gives a very clear categorization of how quantities behave with respect to aggregation of systems. While fields are defined point by point, measures are defined locally and additively. Measures also naturally encompass discrete and continuous variants of the same notion. For example a mass measure can contain discrete masses, standard densities, linear mass densities and area mass densities at the same time. This categorization also naturally triggers the question of quantities that are neither extensive nor intensive and what could be their mathematical nature. This is an example of language and question that help me understand physics.

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chiro
You're going to have to define it in terms of numeric structures or sets.

The description you have given is way too vague and you will need to specify the constraints mathematically - again based on set structures or those synthesized by ordinary numbers (including complex numbers).

If you can't do this then it means you don't actually know what you are saying and trying to do - the only way to know what you are doing is to be precise about it.

You're going to have to define it in terms of numeric structures or sets.
What is "it" in this sentence?
The description you have given is way too vague and you will need to specify the constraints mathematically - again based on set structures or those synthesized by ordinary numbers (including complex numbers).
What does mean "to specify the constraints mathematically" here? From my point of view, you're the one a bit too vague. My purpose was not present an entire mathematical framework in this single post, just to give an idea of the language I'd like to find more often. But let's put it this way: let $\mathcal{A}$ a 3-dimensional euclidean affine space (3 dimensions are in fact not very satisfying: a 4D affine space would be better even for newtownian mechanics or even a 4D affine manifold, but let's put that point aside in this post). Its natural separated topology generates a single Borel $\sigma$-algebra $\sigma_\mathcal{A}$. A massic object in that space could be described as a finite measure $m$. We can equip it with a vector field $v$ (its speed) whose support is included in the support of $m$ and that takes values in $V$, the vector space associated to $\mathcal{A}$. We could of course discuss the regularity of $v$. I generally consider that a measurable piecewice-analytical function is enough to describe all situation of newtonian dynamics I know about but I would be delighted to be contradicted. Now you can define the integral/product:
$$p = v \cdot m = A \in \sigma_\mathcal{A} \mapsto \int_A v \cdot \textrm{d}m \in V$$
which is a vector-valued measure called momentum of our system...
Etc.

Is this still too vague for you?

chiro
It means you define the structures, algebras, relations, constraints and anything that reduces the uncertainty of what it is that you are trying to say.

A set has a very good definition which is why many mathematicians use them.

A number (from naturals to reals) also has a good definition.

Structures are in terms of sets and numbers with things synthesized from those quantities.

Sets have the set algebra (union and intersection) while numbers are based on arithmetic (including modulus) and things synthesized from these (like exponentiation as an example).

Forget all the high level stuff for the moment and get this stuff sorted first.

If you can produce all the information needed to represent what you are meant to convey then it will be easy to understand you.

Don't bother about buzz-words at the moment - use the language in mathematics as it exists and allow us to combine it so that we get an idea of what you are trying to say so that we can differentiate it from what already exists and then comment on the difference.

At the moment, you are too vague because you are not using the terms that are largely standardized. Start small if you need to and avoid buzz-words.

Also - realize symbols have no meaning unless they map to specific states of information. When you deal with mathematics you deal with constraint under consistency. You are going to have to highlight the constraint and how you make it consistent.

Finally - when you talk about spaces you should be telling us how you organize the information differently from what exists and why.

In physics things are organized with continuity and geometry because that is how humans sense this information in the real world. It doesn't have to be organized this way but it makes sense with visual and natural intuition being suitable. If you have an alternative then specify how you would organize it, why you would do so, what the advantages are with this new organization is and how you would make it all consistent and analytical.

The states will always be the same regardless of the approach since they map to exactly the same things - but the organization will be different and from what you are saying the thing you disagree with is how the information is organized and yet you haven't addressed these questions at all in any significant capacity.

Andy Resnick
Furthermore it seems that the first reference, while apparently very nice on the mathematical aspect, does not deal with classical mechanics but directly with einsteinian relativity and QM, what I won't call an introduction to physics.
That book ("Geometry of Physics") not an introduction to physics, it's an introduction to using algebraic geometry in physics.

Structures are in terms of sets and numbers with things synthesized from those quantities.
So what? Sure, if we're speaking about sets as defined by the usual set theory (ZFC) almost all usual mathematical objects, including numbers, can be described as sets. So your statement is trivially true.
Forget all the high level stuff for the moment and get this stuff sorted first.
Who decided that this stuff was higher level than set theory, number theory or real/complex analysis? You did?
Don't bother about buzz-words at the moment - use the language in mathematics as it exists and allow us to combine it so that we get an idea of what you are trying to say so that we can differentiate it from what already exists and then comment on the difference.
Buzz-words... mathematics as it exists... incredible ! If we take for example measure theory, its started in the late 19th century. It is a well established domain of mathematics and the foundation of the modern definition of integration.
In physics things are organized with continuity and geometry because that is how humans sense this information in the real world.
Well... affine space (that belongs to "high level stuff" I presume) is nothing more than the formal concept for the most usual geometric spaces ones considers when she informally speak about "line", "plane" or "3D space". You want geometry and continuity? Fine, read the definition of affine spaces. It's a good place to start.
The states will always be the same regardless of the approach since they map to exactly the same things - but the organization will be different and from what you are saying the thing you disagree with is how the information is organized and yet you haven't addressed these questions at all in any significant capacity.
Indeed it appears I haven't addressed these questions in a language you, Chiro, seem to understand, I grant you that. Let me make a last attempt: the language I'm expecting is precisely this kind of supposedly "high level buzz-words". Now I would suggest you to update your knowledge in mathematics (I told you: I'm not a teacher) rather than insinuating again and again I don't know what I'm talking about. But I have an idea that you won't be very receptive to such an advice.
That book ("Geometry of Physics") not an introduction to physics, it's an introduction to using algebraic geometry in physics.
I keep the reference. Thanks again.

George Jones
Staff Emeritus
Gold Member
To take a very simple example, I don't like the identification of the usual physical space with $\mathbb{R}^3$. It should simply be described as a set of points $\mathcal{A}$ ( = positions = places without spatial extensions). Assigning coordinates to positions is a pure computational issue. Now I can try to think about a structure on my set of points $\mathcal{A}$. As the notion of distance between positions seems to make sense I suppose there exist a distance function $d : \mathcal{A} \times \mathcal{A} \rightarrow \mathbb{R}^+$ with the usual axioms. There is obviously no priviledged point in $\mathcal{A}$, so I should not be able to speak about any center or origin. But it seems I can define things like lines and angles. So there must be a structure that can encode these notions
An affine space, with an inner product defined on the associated vector space?

Dale
Mentor
Closed for moderation

Edit: a recent slightly heated exchange has been removed and the thread is reopened.

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