Can modern physics be understood qualitatively?

[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."