Can modern physics be understood qualitatively?

[Hlud]

I've taught an undergraduate class called "Conceptual Physics" for non-STEM majors. Conceptual physics isn't "physics, with no math". It is "physics with not a lot of math". So already there are varying definitions of the word depending on the context.

Well, that's my point. I think we need to abandon that idea, that conceptual physics is for people who don't have the math skills to do 'real' physics. Conceptual physics should be done at all levels of physics.

I can flip through pretty much any solutions manual for any high school or early college textbook and this is what i will see: questions that are 99% answered qualitatively, in words, and problems that are 99% answered quantitatively, with math. Sometimes you get the bold person who writes, "I am now going to use trig to solve this," every other problem. That ain't conceptual. Unfortunately, i don't have the best definition for what is. I recall most of my tests throughout college (and i know i am in the overwhelming majority) and it was pretty much entirely math based, as well.

The only effort i have seen to tackle this problem is on the AP test with their Qualitative/Quantitative problems. AP scores for Physics I and II (not C, which is much more math intensive, ironically) are the lowest for all AP exams. The only reason i can explain these awfully high failure rates is due to the amount of students who just don't understand what they are doing, because they are almost never asked to.

 

[ZapperZ]

Well, that's my point. I think we need to abandon that idea, that conceptual physics is for people who don't have the math skills to do 'real' physics. Conceptual physics should be done at all levels of physics.

I can flip through pretty much any solutions manual for any high school or early college textbook and this is what i will see: questions that are 99% answered qualitatively, in words, and problems that are 99% answered quantitatively, with math. Sometimes you get the bold person who writes, "I am now going to use trig to solve this," every other problem. That ain't conceptual. Unfortunately, i don't have the best definition for what is. I recall most of my tests throughout college (and i know i am in the overwhelming majority) and it was pretty much entirely math based, as well.

The only effort i have seen to tackle this problem is on the AP test with their Qualitative/Quantitative problems. AP scores for Physics I and II (not C, which is much more math intensive, ironically) are the lowest for all AP exams. The only reason i can explain these awfully high failure rates is due to the amount of students who just don't understand what they are doing, because they are almost never asked to.

Let's not confuse teaching and educational practices and effectiveness with the original question of this thread.

Can physics be understood purely qualitatively? No, if this "understanding" means a full, complete understanding. Can there be a superficial understanding of physics from just qualitative understanding? Sure! Does an understanding of physics involve both quantitative and qualitative aspect? Notwithstanding the "shut up and calculate" philosophy, my answer is yes.

Zz.

 

[Hlud]

Let's not confuse teaching and educational practices and effectiveness with the original question of this thread.

Sorry. It's a pet peeve of mine when people horribly misuse the term 'conceptual physics'.

 

[dkotschessaa]

The above conversation implies that a real qualitative understanding implies quantitative understanding. So putting the big q words aside the question is really whether physics can be understood without math. Or, to what extent is it possible to understand physics without math. The answer is clearly that you just can't have a deep understanding because you will be missing details and answers to basic questions such as, well, "Why?"

There is also a basic toolbox of critical thinking skills that is learned in formal science and math that will probably be missing in a non-quantitative setting. Understanding a physics problem involves following a line of reasoning which has both mathematical and non-mathematical steps associated with it, but even those non-mathematical steps require rigour. Without math you are missing a lot of details and subtleties.

BTW this might be obvious but I want to point out that knowing math doesn't automatically grant you a backstage pass to understanding physics, either. It possibly gets you a front row seat. But physics is difficult precisely because it involves applying rigorous mathematics and reasoning to actual physical situations, which is a different (but related) skill set than solving math problems.

-Dave K

 

[dkotschessaa]

Sorry. It's a pet peeve of mine when people horribly misuse the term 'conceptual physics'.

I think you'll need to get over it, as the term is not well defined enough to get picky about.

 

[Hlud]

I think you'll need to get over it, as the term is not well defined enough to get picky about.

It's not the term. It's the idea that many think that physics is just doing algebra, but with physics equations (at least in my realm of high school). They relegate conceptual physics to those who don't have the algebra skills. Yet, in a lot of these 'conceptual physics' courses, the teachers just do the same thing, but with easier algebra.

Physics education is in an awful state, in my opinion, for that reason.

 

[David Lewis]

The goals and motivations of each physics student are unique. With formal technical training and education, the student usually wants to acquire marketable skills and be able to provide valuable service to future employers.

 

[dkotschessaa]

It's not the term. It's the idea that many think that physics is just doing algebra, but with physics equations (at least in my realm of high school). They relegate conceptual physics to those who don't have the algebra skills. Yet, in a lot of these 'conceptual physics' courses, the teachers just do the same thing, but with easier algebra.

Physics education is in an awful state, in my opinion, for that reason.

I see. I guess I don't know know what a conceptual physics course looks like. I know there is such a thing as high school physics, and I'm assuming that they use algebra but not much if any calculus.

What I can relate this to is pop-sci books and documentaries and such. Documentaries for certain try to avoid any math (unless it's cool looking equations floating around to give it an intellectual flavor).

Pop sci books also have an unwritten rule about putting actual equations in books. Stephen Hawking in his Brief History of Time wrote:

Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, $E=mc^2$ . I hope that this will not scare off half of my potential readers.​

I think we all agree that there is definitely a place for easier (non calculus based) or conceptual (non math based) physics... It's fascinating, intellectually stimulating, and it can potentially inspire someone to go further. The problem of course is mistaking this for any kind of deep understanding.

BTW we could have this conversation about math itself! There are documentaries and even plenty of math books written with little or no actual equations in them. I couldn't get enough of these books as an undergraduate math major. I was able to think about math in a non-hardcore way while lying in bed or on the beach or whatever. They kind of supplemented and gave a context for the real work I had to do.

-Dave K

 

[zwierz]

I know that people can understand F=ma with just words.

this equation hides all the miracles of classical mechanics, dynamical chaos for example.
So what do you mean "understand"?

 

[yolo420wildebeast]

I'm curious on just how much modern physics can be understood qualitatively, without equations.

I know that people can understand F=ma with just words. For example, the acceleration an object experiences is directly proportional to overall force pushing or pulling on the object. The more force the more acceleration and vice versa. Of course, this ignores the fact that its a differential equation, but that's a minor detail compared to the overarching concept.

Why can't a similar approach be taken with more modern physics? I've heard that lots of the popular science books for layman dumb it down so much as to be inaccurate. Why? Could it be that the equations have so many parameters and mathematical concepts that expaining them would be impossible? If that is the case, then why even read the books then? If the rubber sheet analogy is wrong, when what is the point? Is it because it's wrong but just not so terribly wrong what knowing it is better than not knowing anything about it at all?

I would argue that there are a lot of equations that can be qualitatively understood and if you can understand the equation that way then you can understand the physics that way.

 

[Hlud]

I think we all agree that there is definitely a place for easier (non calculus based) or conceptual (non math based) physics... It's fascinating, intellectually stimulating, and it can potentially inspire someone to go further. The problem of course is mistaking this for any kind of deep understanding.

I think this is the problem. You say that conceptual physics is non-math based. There are physics concepts that include math. Trying to go a little back to the original topic, i remember taking a test in a Relativity class (undergraduate level). There was like three problems, and all of them required me to derive equations previously derived in class. None of the problems really cared if i knew what the equation meant. Most of my physics classes were like this (and looking at problems in textbooks, leads me to believe that most classes around the world are like this).

Now, there was definitely an implied understanding. (And i was working at nights through college). Nevertheless, i think that a purely quantitative understanding is just as good as a purely quantitative understanding of modern physics, or any part of physics. Physics is the marriage of the two. A conceptual physics course, in my opinion, would reflect this, and be offered at any level of physics. I don't know how this would look for modern physics (because i don't think i learned much in my modern physics courses), but i am trying to develop true conceptual physics courses for my regular and AP classes.

 

[WWCY]

I'm curious on just how much modern physics can be understood qualitatively, without equations.

I know that people can understand F=ma with just words.

One of the many purposes of physics is solving physical problems. With just that intuition alone, you're not going to be able to:

1. Calculate tension of ropes holding a box and explain how different angles of suspension cause said ropes to have different tension.
2. Calculate the velocity at which a car must travel on a frictionless banked curve to not slip
3. Derive a friction coefficient with any sort of given variables.

Essentially, you're not going to be able to solve any sort of meaningful, complex physics problems. All you can do without doing the mathematical work is rattle on about how an object accelerates when it experiences a net force. If you can't apply your "knowledge" on a novel problem, you have not understood physics. What you have done, was simply memorise a bit of trivia for your weekly pub quiz.

F=ma is merely a mathematical quantity equated to two other mathematical quantities being multiplied together. No physical insight there.

I doubt anyone has ever said that the quantitative side of physics is the only important side of physics. Where did you pull this from?

 

[dkotschessaa]

I think this is the problem. You say that conceptual physics is non-math based.

Not really. Again there is no definition for "conceptual physics." Pop-sci books and shows avoid mathematics like the plague. Perhaps this should be called "science communicator" physics. I think it has it's place, like sort of as a marketing tool for science.

There are physics concepts that include math.

You mean like...all of them? :)

Trying to go a little back to the original topic, i remember taking a test in a Relativity class (undergraduate level). There was like three problems, and all of them required me to derive equations previously derived in class. None of the problems really cared if i knew what the equation meant. Most of my physics classes were like this (and looking at problems in textbooks, leads me to believe that most classes around the world are like this).

Now, there was definitely an implied understanding. (And i was working at nights through college). Nevertheless, i think that a purely quantitative understanding is just as good as a purely quantitative understanding of modern physics, or any part of physics. Physics is the marriage of the two. A conceptual physics course, in my opinion, would reflect this, and be offered at any level of physics. I don't know how this would look for modern physics (because i don't think i learned much in my modern physics courses), but i am trying to develop true conceptual physics courses for my regular and AP classes.

I'm having a hard time figuring out what you think things should look like by your posts. What do you mean by "A conceptual physics course..offered at any level of physics." What would a statics class look like? A class in relativity? QM?

-Dave K

 

[Hlud]

Not really. Again there is no definition for "conceptual physics." Pop-sci books and shows avoid mathematics like the plague. Perhaps this should be called "science communicator" physics. I think it has it's place, like sort of as a marketing tool for science.

I fully agree with you here. Science fiction also is known for garnering interest in the sciences.

I'm having a hard time figuring out what you think things should look like by your posts. What do you mean by "A conceptual physics course..offered at any level of physics." What would a statics class look like? A class in relativity? QM?

Unfortunately, i don't have a detailed response for you. When i first started teaching, i knew something was wrong with how we present physics to our students because our students were struggling with rather basic topics. A few of our students who were building a circuit for an after school club were struggling with what a resistor does, despite doing well on the circuits exam in their AP Physics 1 class. I am the first one to admit that i struggled a lot coming out of college with "What does it mean?" type questions.

I think all non-lab based physics classes, for the most part, should be conceptual. The best i can do to explain what this means is to give examples for my level of experience, in high school. A lot of problems with ramps, would look as follows: "A block of mass m is h up a smooth ramp of angle ϑ. What is the speed of the block as it leaves the ramp?" These problems might get 'tricky' and have the block go up the ramp first.

A better problem would look as follows: "A block is placed at the top of a smooth ramp, curved inwards. An identical block is placed at the top of a smooth ramp, curved outwards. Which block will reach the bottom of its ramp first; which block will be moving faster upon reaching the bottom of its ramp?" Another example was seen on the AP exam a few years back: "Trial 1 - A block is placed on the top of a smooth ramp. The ramp is free to move on a smooth table. The block is released. Trial 2 - A block is placed on the top of the same ramp, but the ramp is no longer free to move. Which trial will the block be moving faster upon reaching the bottom of the ramp?"

I know some classes might do the former example in class, as a demonstration, but very few have the students participate in the explanation (as in a lab, rather than a demo) and are responsible for the information on the test. These kind of questions, in my opinion, are harder to develop, but require much higher thinking than the first example type of questions.

 

[Julian Baker]

As a teacher one must know that getting the concept correct is the first step to scientific rigour. The concept is the first thing we must get our pupils to understand, and (IMHO) that is best done in physics by building on the pupils real world experience.
How many of your students have attempted to attack projectile problems mathematically without first separating the horizontal and vertical planes?
One can only apply mathematics to the off-centre collision of balls if one first understands that there can be no tangential force at the contact point.
Interference between waves is best shown by first drawing a picture of the waves that you know from the seaside.
You can explain satellite motion wholly incorrectly with reasonably straightforward maths, but the principle that gravity is the only force acting on the satellite is best understood by whirling that conker around on a string.
Yes, the correct concepts come first, the mathematics define where and when.
.

 

[David Lewis]

I can give you the Schrodinger equation. It is a "formula". Do you think this is something to be used to "calculate its value"?

That's an exception. Normally, the math is a representational model that corresponds to reality, but in this case, math is the reality.

 

[dkotschessaa]

That's an exception. Normally, the math is a representational model that corresponds to reality, but in this case, math is the reality.

You cannot make the case that the Schrodinger equation is not a mathematical model.

EDIT:

To add to this - I have a B.A. and almost master's in math. In theory I have everything I need to understand this equation - but I don't have a background in physics. So I don't know the motivation for the equation. There's a whole story there and a a history that I don't have.

I would have an easier time than someone without a math background trying to go back and learn, but no, just looking at an equation doesn't solve all your problems either.

-Dave K

 

[ZapperZ]

That's an exception. Normally, the math is a representational model that corresponds to reality, but in this case, math is the reality.

I don't even know what that means. You're speaking in tongues.

Or maybe that has been your strategy from the very beginning, because this appears to consistently be your MO.

Zz.

 

[gleem]

“When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts advanced to the stage of science.”
― William Thomson, 1st Baron Kelvin

Physics is the study of how thing happen (processes) and in particular the relationships among the various interacting entities of our universe which are characterized mathematically. Physics is applied math. If it were not for mathematicians ( and remember Newton was also a mathematician), like Fourier, Lagrange, Sturm, Liouville, Cayley physicists would not have the "tools" to express their ideas.

These "Conceptual Physics " courses I am led to believe have been instituted to "help" non scientist gain an appreciation of physics and its contribution to our wonderful technology. (of course they could also be for the filling of seats) I am also led to believe, that these people will be informed enough and understand enough to manage our technology for themselves and/or the country.

Dumbing down is what you get when you try to teach physics ignoring the mathematical underpinnings. You fail to arouse an appreciation of the methods of physics. when you avoid mathematics.

This type of course may go more to dividing the scientific community from the non scientific for we are telling them that they do not have the ability nor do we care about their truly understanding what and how we do what we do.

 

[David Lewis]

"Without the mathematics, at best, one can only claim a superficial understanding of physics. One cannot claim to have a useful, usable understanding of physics." - ZapperZ

Useful and usable implies using your knowledge to solve practical problems. There's a place for that, but due to lack of resources, some courses are designed to help students get good grades on the test, instead of understanding anything.

 

[sshai45]

I read this stuff and to me it seems you need both, not just one xor the other. If you just have maths alone, then imo you end up just memorizing formulas and not really knowing what they mean. You can memorize them but it's rather difficult to then use that to solve problems. To solve problems you also need a conceptual / qualitative _scaffolding_ on which to _place_ the formulas so you can understand what formula to use when.

 

[dkotschessaa]

I read this stuff and to me it seems you need both, not just one xor the other. If you just have maths alone, then imo you end up just memorizing formulas and not really knowing what they mean. You can memorize them but it's rather difficult to then use that to solve problems. To solve problems you also need a conceptual / qualitative _scaffolding_ on which to _place_ the formulas so you can understand what formula to use when.

Learning math isn't "memorizing formulas."