Can modern physics be understood qualitatively?

[phinds]

You're using some loaded words here. There are different levels of understanding, and I believe David's point is that the average person doesn't need to understand physics to the same level of sophistication as a physicist does.

Agreed

If musician has a qualitative understanding of a=F/m but can't solve the simple harmonic oscillator problem mathematically, do you consider that a shoddy understanding? Or is it good enough because the musician can better assess information and detect BS spouted by a charlatan?

We can get into a lot of anecdotal specifics but I think that's somewhat irrelevant. My point is that a lot of people, I think, don't realize what a poor understanding of science they have. I certainly don't think everyone should try for a professional's understanding of complex topics but personal confirmation bias tends to make people think they know something when they don't. I don't suggest that people not do the best they can, with a limited interest in the details, to gain knowledge, I just which more folks had a better understanding of how much the DON"T know.

 

[David Lewis]

Sometimes a physicist or mathematician will, instead of explaining what something is, give you the formula for calculating its value.

 

[ZapperZ]

Sometimes a physicist or mathematician will, instead of explaining what something is, give you the formula for calculating its value.

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

The naive and ignorant view here is that a "formula" or equation is nothing more than a plug-and-chug, which is clearly incorrect here. Plenty of equations in physics are the mathematical formalism of an idea or a concept. It is the same as a musician reading musical note - the sound plays in one's head when one "reads" those notes, rather than simply seeing it as a bunch of symbols.

There is no shortcut in being able to claim that one "understands" something in physics. It doesn't mean everyone should do it, and it doesn't mean everyone should have the same level of understanding as a physicist. But if one doesn't, then one only have a superficial understanding of it. This is not to be confused with the same level of understanding as a physicist.

There is a huge and distinct difference between seeing a cow, and seeing just the shadow of a cow. One cannot claim having seen a cow when one has seen only its shadow.

Zz.

 

[Nugatory]

Aren't there many situations where no analytical solutions can be found and costly to implement numerical solutions?

Yes, many. But if you want precise answers for these the sloppy hand waving qualitative descriptions are completely worthless and unhelpful won't tell you anything at any useful level of detail.

 

[Nugatory]

A well rounded, liberal education in hard sciences puts emphasis on qualitative understanding more than practical application because the student's intention is (presumably) not to do science as a profession.

A well rounded liberal education in hard sciences does not emphasize practical application, but it also does not short-change the rigorous math. Qualitative understanding means that you understand what the math is telling you; and a physics class that doesn't expect you to work with math that was well-understood three centuries ago is like an English Lit class that teaches Shakespeare out of the Cliffs notes (I'm a native English speaker - others should substitute their own language's literary equivalent).

 

[Khashishi]

Without doing the math, the best that one can do is memorize a bunch of physics facts. There's definitely some value in knowing physics facts, but math is necessary to learn new facts about novel situations. (For example, one could memorize that Moon has 1/6 the surface gravity of Earth because it's less massive. Now, what about the gravity on Mars? Well, if you didn't memorize that fact, then you'd be stuck. But if you can calculate it, then you can handle many more situations.)

So, is it adequate to just know a bunch of physics facts? Well, there are obvious disadvantages. You will have some difficulty in judging an authoritative source for your physics facts, and will lack the flexibility to solve new problems or build new things. I don't think it's good enough to qualify as "understanding" physics.

 

[Dr. Courtney]

A well rounded, liberal education in hard sciences puts emphasis on qualitative understanding more than practical application because the student's intention is (presumably) not to do science as a profession.

Making testable predictions is the heart of the scientific method. How many testable predictions are possible in modern physics based on purported qualitative understandings?

If you are not making testable predictions, you are not doing science. If students are not learning how the testable predictions of modern physics are made and then compared with the outcomes of experiments, then they are not really learning science. They are learning to believe things by authority of experts, which is something other than science, however warm and enlightened it might make them feel.

Real science cares more about why a model is true and can never be reduced to a set of facts regarding which models are true.

 

[sandy stone]

There seems to be an either/or thing going on here - either I devote years of my life getting a doctorate in physics, or I am feeling warm and enlightened, but fooling myself. There are those of us who will never be candidates for employment at CERN, as admirable as that may be, but who would still like to have some understanding of what goes on there, and what we hope to learn. I don't intend to calculate collision cross-sections, but I can still learn what they are, and get a reasonable idea of how they are calculated. Yes, I trust that the experts in the field probably are using the correct model, with known limitations, and I want to learn as much about that model as I can, out of sheer curiosity. Is that so bad?

 

[ZapperZ]

There seems to be an either/or thing going on here - either I devote years of my life getting a doctorate in physics, or I am feeling warm and enlightened, but fooling myself. There are those of us who will never be candidates for employment at CERN, as admirable as that may be, but who would still like to have some understanding of what goes on there, and what we hope to learn. I don't intend to calculate collision cross-sections, but I can still learn what they are, and get a reasonable idea of how they are calculated. Yes, I trust that the experts in the field probably are using the correct model, with known limitations, and I want to learn as much about that model as I can, out of sheer curiosity. Is that so bad?

But this isn't an argument against getting "... some understanding..." By all means, go and pursue that!

Instead, this is an argument against the idea that one can understand physics purely on a conceptual/qualitative basis. Claiming that one "understands", say, quantum mechanics means that if I asked you to find the Clebsch-Gordon coefficient of a 2-electron system, I shouldn't have to explain what this is. If you have read this thread from the beginning, I illustrated a very clear example of the case (and problem) of someone who only understood physics "conceptually", but yet tried to offer his own explanation to a problem. It wasn't pretty.

When I walk into the first day of an Intro Physics class, I tell my students that they all already have conceptual understanding of many aspects of the physics that they will encounter in that course. They already have the "Everything that goes up, must come down" concepts. But what we will do in the physics class is to now describe their conceptual understanding using mathematics. In other words, we will now find out "When and where it comes down!" This is the other required aspect of what we call "physics".

Zz.

 

[Khashishi]

We can't be experts in everything, but a little knowledge is way better than none.

If you are able to solve many simpler problems mathematically, you have a respect for the process that goes into solving the more complex problems, even if you cannot solve them yourself. You still need to accept some results on faith, but it's a different kind of faith than for someone who knows very little. You don't accept a result just because Steven Hawking said so, but because you know he has made a certain calculation to show it. And if Hawking has a hunch, and his graduate student goes through some calculations that show it cannot be, well, you better believe the graduate student, because you have a faith in the mathematics and the process, and not in authority figures. (Of course, in this instance, Hawking himself would accept the result of the math over his own hunch, because he respects the process.)

People with little to no understanding of the process tend to accept things based on authority, and then struggle when different authority figures clash.

 

[David Lewis]

A non-mathematical treatment will be easier to follow, and appeal to a wider audience. Some learn for the joy of understanding, not because the knowledge is good for something.

 

[Hlud]

I doubt you would get far in physics without much of a qualitative or quantitative description of what is happening. Physics is the marriage of the two.

I recall back to my own undergrad experience. Like a lot of undergrads (and high school classes) around the country, my professors didn't have us do much of a qualitative description of what is happening. They only had us do quantitative descriptions. I don't think i learned much of anything in my physics classes. I assume that a qualitative-only description of modern physics would be very similar.

One of my greatest endeavors is trying to reform high school physics education to balance out the qualitative and the quantitative.

 

[RogueOne]

All understanding is qualitative.

Understanding is qualitative. Quantification is for measurement of the ideas that are understood qualitatively, communication of ideas that are understood qualitatively, and precisely defining the ideas that are understood qualitatively.

Quantitative is to know, what qualitative is to understand.

 

[RogueOne]

A while ago, in this thread, a PF member who is no longer with us, used gravity to explain why two sheets of glass plates stick together. This member had a "conceptual understanding" of gravitational attraction, but lack any understanding of the quantitative aspect of it. He/she could not estimate the gravitational force between 2 typical glass plates, and whether the force from it is sufficient to provide such a "glue" to make them stick together. This is before considering that if the glass surfaces were wetted, the sticking is even stronger. Maybe gravity changes strength with added thin film of water.

This is a common occurrence. When people only think that they know the qualitative or conceptual aspect of something, but lack the quantitative or mathematical description of it, then they tend to use highly improbable or minuscule effects to explain very common observations. This is because they lack the ability to estimate the order-of-magnitude numbers associated with these effects. They are aware that two masses, such as glass plates, have gravitational field, but are not able to figure out the strength of the field and whether it can explain what has been observed. To be able to do the latter, the physics understanding must be accompanied by an underlying mathematical description.

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.

Zz.

What you described is actually a MISUNDERSTANDING, and we all are keenly aware that misunderstandings can occur qualitatively. All of the factors need to be identified qualitatively before determining how or where to represent them mathematically in an equation. Your example is equivalent to me posting an example of somebody making a mathematical error and using that as basis to say that physics cannot be quantified.

 

[ZapperZ]

What you described is actually a MISUNDERSTANDING, and we all are keenly aware that misunderstandings can occur qualitatively. All of the factors need to be identified qualitatively before determining how or where to represent them mathematically in an equation. Your example is equivalent to me posting an example of somebody making a mathematical error and using that as basis to say that physics cannot be quantified.

But a purely qualitative understanding CAN include such misunderstanding. It is because such a description is, by its nature, incomplete!

Saying two pieces of glasses have a gravitational attraction between them isn't wrong. Saying that this is the source of why they stick together is, because the qualitative understanding does not include any order-of-magnitude estimate of such attraction. It is not just a misunderstand, but rather it is an incomplete understanding of the phenomenon.

And that, by definition, is NOT an understanding of physics.

Zz.

 

[atyy]

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?

Can qualitative understanding be obtained without equations? Since you can understand F=ma qualitatively, then qualitative understanding includes equations.

 

[RogueOne]

Can qualitative understanding be obtained without equations? Since you can understand F=ma qualitatively, then qualitative understanding includes equations.

How was that equation obtained by humans in the first place? You think somebody arbitrarily decided to write "F=ma", and then they went on a search for what concept the equation quantified?

 

[RogueOne]

But a purely qualitative understanding CAN include such misunderstanding. It is because such a description is, by its nature, incomplete!

Saying two pieces of glasses have a gravitational attraction between them isn't wrong. Saying that this is the source of why they stick together is, because the qualitative understanding does not include any order-of-magnitude estimate of such attraction. It is not just a misunderstand, but rather it is an incomplete understanding of the phenomenon.

And that, by definition, is NOT an understanding of physics.

Zz.

We know that the attraction is not primarily caused by gravity. Everybody reading this thread knows that. Has an equation on this subject been mentioned here? Nope. Your post, ironically, is an appeal to our qualitative understanding on the factors at play between those to panes of glass.

When you don't have the whole picture, you can misunderstand something qualitatively. You can also make an equivalently profound mistake quantitatively by leaving out factors.

How does one identify which factors need to be included in the calculations? I'll answer that for everybody who hasn't done any physics outside of a textbook. The answer is qualitative reasoning and understanding. The calculations are there to communicate and precisely define the concepts.

 

[ZapperZ]

We know that the attraction is not primarily caused by gravity. Everybody reading this thread knows that. Has an equation on this subject been mentioned here? Nope. Your post, ironically, is an appeal to our qualitative understanding on the factors at play between those to panes of glass.

When you don't have the whole picture, you can misunderstand something qualitatively. You can also make an equivalently profound mistake quantitatively by leaving out factors.

How does one identify which factors need to be included in the calculations? I'll answer that for everybody who hasn't done any physics outside of a textbook. The answer is qualitative reasoning and understanding. The calculations are there to communicate and precisely define the concepts.

But how would you know if your calculations or qualitative reasoning is correct, or accurately reflects nature?

Just because one can say that the strength of an electric field drops as one moves away from the source charge doesn't mean one has a full understanding of the phenomenon. There is a difference between 1/r, 1/2², 1/r³,... and exp(-kr), etc... It is only via quantitative comparison of measured values at various r's can one distinguishes between one description versus another and pick out which one is valid.

So not only will one be unable to correctly describes a phenomenon completely and accurately, one will also be unable to distinguish which one is the right one simply based on a qualitative idea of it.

There is a difference in learning physics, and learning ABOUT physics. One should not fool oneself into thinking that the latter is the same as the former.

Zz.

 

[RogueOne]

But how would you know if your calculations or qualitative reasoning is correct, or accurately reflects nature?

Just because one can say that the strength of an electric field drops as one moves away from the source charge doesn't mean one has a full understanding of the phenomenon. There is a difference between 1/r, 1/2², 1/r³,... and exp(-kr), etc... It is only via quantitative comparison of measured values at various r's can one distinguishes between one description versus another and pick out which one is valid.

So not only will one be unable to correctly describes a phenomenon completely and accurately, one will also be unable to distinguish which one is the right one simply based on a qualitative idea of it.

There is a difference in learning physics, and learning ABOUT physics. One should not fool oneself into thinking that the latter is the same as the former.

Zz.

I have a different theory, but it is based on the same exact idea. Quantitative comparison of measured values only tells you the extent of the phenomena. So you've measured the voltage drop, but do you understand the root cause for that voltage drop? No. You've quantified results, but you have not discovered the mechanism that causes the change in the flow of electrons.

How can you understand an equation, beyond the step-by-step mathematical operations, without a conceptual/qualitative understanding of what the equation represents? How can you apply that equation to anything if you don't understand what factor it quantifies, or how that factor interacts with other factors? How can a learner place any value on a quantification process if he/she does not understand what they are actually quantifying?

Physics cannot be understood without doing it qualitatively. Knowledge comes quantitatively. Understanding comes qualitatively. You can know physics through purely quantitative means, having never qualitatively understood it, although that hardly makes you more useful than a calculator. The difference between knowing physics, and understanding physics, is qualitative.

 

[Khashishi]

Sure. Both are important. You can even think of doing the math as performing an experiment to test a qualitative prediction. That's called a thought experiment.

 

[ZapperZ]

I have a different theory, but it is based on the same exact idea. Quantitative comparison of measured values only tells you the extent of the phenomena. So you've measured the voltage drop, but do you understand the root cause for that voltage drop? No. You've quantified results, but you have not discovered the mechanism that causes the change in the flow of electrons.

How can you understand an equation, beyond the step-by-step mathematical operations, without a conceptual/qualitative understanding of what the equation represents? How can you apply that equation to anything if you don't understand what factor it quantifies, or how that factor interacts with other factors? How can a learner place any value on a quantification process if he/she does not understand what they are actually quantifying?

Physics cannot be understood without doing it qualitatively. Knowledge comes quantitatively. Understanding comes qualitatively.

You have this all wrong.

The ORIGINAL premise of this thread is the question on whether physics can be understood just qualitatively. If you have read my response, I've stated clearly that it has to be understood BOTH qualitatively and quantitatively.

Somehow, you've turned it around and seem to think that I'm arguing that the quantitative part is the only one that is needed. Where did I say that? What I've done is to stress the importance of the quantitative aspect, and the idea that physics just doesn't say what goes up must come down, it must ALSO (not instead) say when and where it comes down!

Can't physics be understood solely qualitatively? My answer is NO. This does not exclude qualitative understanding as part of understanding physics.

Is there any dispute on that?

Zz.

 

[FallenApple]

Can qualitative understanding be obtained without equations? Since you can understand F=ma qualitatively, then qualitative understanding includes equations.

Thats true. Having a strong gut feel for Newtons second law can allow one to understand the equation without even realizing it. And they can use that gut feel to derive an equation if they are also mathematically inclined.

However, it doesn't work the other way around. Understanding just the equation doesn't lead to an intuitive understanding. F=ma is merely a mathematical quantity equated to two other mathematical quantities being multiplied together. No physical insight there.

 

[Hlud]

Somehow, you've turned it around and seem to think that I'm arguing that the quantitative part is the only one that is needed. Where did I say that? What I've done is to stress the importance of the quantitative aspect, and the idea that physics just doesn't say what goes up must come down, it must ALSO (not instead) say when and where it comes down!

You are a little confusing in how you state your argument. From reading your posts, you use the term 'conceptual' and 'qualitative' interchangeably. I think a lot of people think that conceptual physics is just "physics, with no math." But, you also state that an equation is an embodiment of a concept. That really goes against your use of the word 'conceptual', doesn't it?

 

[ZapperZ]

You are a little confusing in how you state your argument. From reading your posts, you use the term 'conceptual' and 'qualitative' interchangeably. I think a lot of people think that conceptual physics is just "physics, with no math." But, you also state that an equation is an embodiment of a concept. That really goes against your use of the word 'conceptual', doesn't it?

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.

So my definition of a "concept" is the idea, theory, formulation, etc. in physics. Gauss's Law is a "concept". It has both qualitative and quantitative descriptions. To be able to fully understand it, you need BOTH. They each "feeds" the other.

Zz.

 

[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.