Can modern physics be understood qualitatively?

[FallenApple]

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?

 

[phinds]

There are instances where English just is not adequate for describing what's happening. An example of this that very frequently crops up is the concept of "virtual particle pairs" being an explanation for Hawking Radiation. You pretty much ALWAYS hear that explanation in pop-science but Hawking himself has specifically said that it is NOT a correct explanation and in fact was simply the best he was able to come up with to explain in English a concept that really can only be discussed properly with math.

 

[robphy]

One thing to consider is that many aspects of "modern physics" are not intuitively obvious
since they may occur at very small or very large scales, high speeds, or many particles (which may not behave like "everyday objects").

This famous lecture by Feynman seems appropriate here.

A fuller reference is below (with an interactive transcript).
This version on YouTube has the intro trimmed and gets right to the lecture.


A useful passage [at about 3m08s above, or 4m12s below]:

Again, electrons, when they were first discovered, behaved exactly like particles-- bullets-- very simple. Further research showed, from electron diffraction experiments and so on, that they behaved like waves. And as time went on, there was a growing confusion in the question of how the things really behaved-- waves or particles, particles or waves? But everything looked like both.

Now this growing confusion was resolved in 1925 or '26 with the advent of the correct equations for quantum mechanics. And now we know how the electrons and how light behave. But what can I call it? I can't say they behave like a particle wave, or they behave in typical quantum-mechanical manners. There isn't any word for it. If I say they behave like particles, I give the wrong impression-- if I say they behave like waves.

They behave in their own inimitable way.

Which, technically, could be called a "quantum-mechanical" way. They behave in a way that is like nothing that you have ever seen before.

[snip]

So it will be difficult. But the difficulty, really, is psychological and exists in the perpetual torment that results from your saying to yourself "But how can it be like that?" Which really is a reflection of an uncontrolled, but I say utterly vain, desire to see it in terms of some analogy with something familiar. I will not describe it in terms of an analogy with something familiar. I'll simply describe it.

For more info on this series of lectures:
http://www.cornell.edu/video/richard-feynman-messenger-lecture-6-probability-uncertainty-quantum-mechanical-view-nature

 

[dkotschessaa]

Do you see all the people without a math background asking questions about quantum physics based on watching Michio Kaku documentaries?

 

[robphy]

What got me to pursue degrees in physics is my frustration with pop science books trying explain relativity. They were good for attracting my interest... but not to fully understand or at least get a working knowledge from them. So pop books have a role to play.

 

[phinds]

What got me to pursue degrees in physics is my frustration with pop science books trying explain relativity. They were good for attracting my interest... but not to fully understand or at least get a working knowledge from them. So pop books have role to play.

Absolutely. I love pop-sci books and TV shows to sort of learn what the questions are, but I know better than to take them too seriously about what the answers are.

 

[Andy Resnick]

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.

This is a fallacy: 'Force' cannot be understood without it's precise (mathematical) definition; using words alone leads to mis-use ('force of impact'). The same can be said about many other words: stress and pressure are two obvious ones.

 

[FallenApple]

This is a fallacy: 'Force' cannot be understood without it's precise (mathematical) definition; using words alone leads to mis-use ('force of impact'). The same can be said about many other words: stress and pressure are two obvious ones.

Touche.

But still, the qualitative description captures some aspect of it. Just not completely.

 

[FallenApple]

Do you see all the people without a math background asking questions about quantum physics based on watching Michio Kaku documentaries?

Well, to be fair, my mind was blown after learning about the double slit experiment for the first time from popular science book. This was way back in high school.

Now, after reading some of the math behind it( basically vectors in hilbert spaces and Fourier series), things aren't really all that much more illuminating. But I've only recently started studying it, so maybe there's still more to see.

 

[dkotschessaa]

Well, to be fair, my mind was blown after learning about the double slit experiment for the first time from popular science book. This was way back in high school.

Now, after reading some of the math behind it( basically vectors in hilbert spaces and Fourier series), things aren't really all that much more illuminating. But I've only recently started studying it, so maybe there's still more to see.

Well, you start out having your mind blown and then there's a sort of illusion of competence that goes along with it. When you study the subject (any subject) formally in school you basically will get smacked in the face with how little you understand.

 

[phinds]

Well, you start out having your mind blown and then there's a sort of illusion of competence that goes along with it. When you study the subject (any subject) formally in school you basically will get smacked in the face with how little you understand.

Exactly. Personally, I persist in the illusion of competence despite being CONSTANTLY smacked in the face here on PF with obvious examples of my ignorance. I never let a little thing like not knowing what I am talking about get in the way of a good discussion.

 

[Aufbauwerk 2045]

Mathematics is just a type of shorthand. It has been described as a way of expressing the longest train of thought possible in the minimum number of symbols possible. Lanczos liked to test how well his students understood an equation by asking them to explain it in words. This may involve a rather long and at times convoluted train of thought, but it helps people think about what the equation means, as opposed to simply developing a facility for manipulating symbols according to a set of rules.

 

[phinds]

Mathematics is just a type of shorthand.

No, it is a language all its own. I understand what you mean but you are oversimplifying. Reread post #2.

 

[Andy Resnick]

Touche.

But still, the qualitative description captures some aspect of it. Just not completely.

Sure- there's a time and place for qualitative analysis. But in the hard sciences, it can't replace quantitative analysis.

 

[Aufbauwerk 2045]

No, it is a language all its own. I understand what you mean but you are oversimplifying. Reread post #2.

You mean I am oversimplifying about shorthand? Perhaps, but I don't have time to think about it now. I won't even say who I am quoting. Yes, NL etc. but in accord with one of my New Year's resolutions I am not going to drag in that old appeal to authority any more.

I'm getting fed up with words anyway. "Show me your equations." (mystery quote). I wonder how that fits in with this forum?

 

[FallenApple]

Sure- there's a time and place for qualitative analysis. But in the hard sciences, it can't replace quantitative analysis.

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

 

[ZapperZ]

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

But what does that have to do with the requirement that it must have a quantitative description? Setting up the Hamiltonian, even if one can't find the most general, closed-form solution for it is still extremely important. It is like setting up the force equation. It tells someone else what one is accounting for describing something. Without this, it is just hand-waving.

In addition, area of study such as Many-Body physics, often deals with situation where you can't have an analytical solution to each individual interactions. So we know how to deal with something like that.

I've said it a thousand times, and I'll say it again. Physics isn't just saying "What goes up must come down". It must also say "When and where it will come down"! A lot of people seem to forget that it is the quantitative aspect of it that makes it testable, and that experimental verification is central to any idea in physics for it to be considered to be accepted.

Zz.

 

[Dr. Courtney]

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

Not much. Chemistry and Physics are fundamentally quantitative sciences. They are all about making quantitative predictions about what will happen in quantitative experiments making accurate quantitative measurements.

There are some aspects of new theories that can be explained as qualitative differences from the older theories that they surpass. But if a student in incapable of using the new theory to make quantitative predictions, then they are just parroting qualitative descriptions without real understanding.

"Conceptual Physics" is an oxymoron.

 

[UsableThought]

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.

It may be worth pointing out that Aristotle (a) worked without math, using only words, b) and never bothered to check his descriptions of how nature operated. The connection is that he would have needed math to implement the measurements that he would have used to check those descriptions.

So you can strip the math out of a second-hand account, sure; but this leaves readers unable to verify even the simplest of assertions for themselves, including F = ma. So for all they really know, they could be reading total make-believe. Yes, we tend to trust authority because we must; e.g. like all humans, I don't have the time nor the expertise to verify the vast majority of descriptions of reality that I have encountered, from childhood on; but one of the things that makes science what it is is verifiability by others. Those outside the community of science (definitely including me, at present) who can read only pop science books can't verify that what we are reading about is actually science; we can only trust & hope.

Also, consider metaphor. It's frequently used to provide context for mathematical models; but appropriate metaphors must be chosen & inappropriate or misleading ones discarded; e.g. see the well-known video of Feynman explaining to an interviewer why rubber bands aren't an appropriate metaphor for magnetic attraction. Beyond that however, even the most useful metaphors (I am guessing here, but am pretty certain I'm right) have sharp limits beyond which they become inappropriate; only by knowing the math could you know what the metaphor helps make clear & what would be a misleading interpretation. Thus such metaphors wouldn't be much use to non-math readers.

So to me it seems that to "know" even a small bit of physics ("know" = prediction & control), rather than rely only on argument by authority, requires more than just verbal descriptions. Physics is made up of models & these models require both the math and the surrounding verbal/situational context. Take away either and you don't have a science. You can have a purely verbal description of the thing, but not the thing itself.

 

[ZapperZ]

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.

 

[Andy Resnick]

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

Sure- climate forecasting is one simple example.

The correct response to this problem is not to give up, it's to1) chip away using the tools that are available and 2) develop improved quantitative methods. Occasionally there's a major breakthrough, but more typically progress is slow and hard-won.

 

[spoirier]

I see you implicitly assuming a radical opposition between being mathematical (accurate) and being described in words without equations. I disagree with the idea of such an opposition. Indeed some of the math needs equations hard to understand for the majority, but I still see possibilities to express some exact math in words and "non-mathematical style" without too much difficulty as well, which unfortunately remains largely unexploited in usual physics teaching. And this widespread ignorance of the possible clean "exact math without equations" to explain things, is a mere particular case of the more general fact that much too often, physics teachers just repeat the same usual methods, lacking (or failing to use) the mathematical skills to rewrite their theories in cleaner and more appropriate mathematical forms. And math is full of rich concepts as well, far beyond issues of numerical values, so we shouldn't oppose the "conceptual" to the "mathematical" nor confuse "mathematical" with "numerical exactness", even if of course, it is very possible and widespread to present "conceptual approaches" which are mathematically wrong and nonsensical.
You can see for example how my presentation of Special Relativity is more conceptually correct and mathematically meaningful than usual courses precisely because I got rid of the numerically correct but conceptually inappropriate complicated formulas officially associated with this theory. And I even find good to develop the correctness of the mathematical conceptualization at the expense of the numerical correctness, by showing how relativity problems can be exactly solved by first assuming numerically incorrect negative values of c² and then deducing the numerically correct results by applying the formula on values of c² other than the ones by which we got it (using the analytic expansion as a function of c^-2).
It is also possible and clearer to explain just in words the least action principle (that is just the principle of equilibrium in a field of potential over the configuration space, when considering things in 4D), and deduce from it also just in words the conservation laws and the Liouville theorem. I also explained just in words (I admit it is not a full and rigorous explanation but...) how electromagnetism derives from a Lagrangian, and the sign issues around it.
For introducing quantum physics (just an introduction but) I also have a mathematical approach exactly formulated in the language of geometry, itself mainly expressed in words, with very few formulas.
On the other hand I find that we need formulas to express statistical physics (define entropy and explain its creation process), disagreeing with the usual "qualitative" approaches.

 

[ZapperZ]

I see you implicitly assuming a radical opposition between being mathematical (accurate) and being described in words without equations. I disagree with the idea of such an opposition. Indeed some of the math needs equations hard to understand for the majority, but I still see possibilities to express some exact math in words and "non-mathematical style" without too much difficulty as well, which unfortunately remains largely unexploited in usual physics teaching. And this widespread ignorance of the possible clean "exact math without equations" to explain things, is a mere particular case of the more general fact that much too often, physics teachers just repeat the same usual methods, lacking (or failing to use) the mathematical skills to rewrite their theories in cleaner and more appropriate mathematical forms. And math is full of rich concepts as well, far beyond issues of numerical values, so we shouldn't oppose the "conceptual" to the "mathematical" nor confuse "mathematical" with "numerical exactness", even if of course, it is very possible and widespread to present "conceptual approaches" which are mathematically wrong and nonsensical.
You can see for example how my presentation of Special Relativity is more conceptually correct and mathematically meaningful than usual courses precisely because I got rid of the numerically correct but conceptually inappropriate complicated formulas officially associated with this theory. And I even find good to develop the correctness of the mathematical conceptualization at the expense of the numerical correctness, by showing how relativity problems can be exactly solved by first assuming numerically incorrect negative values of c² and then deducing the numerically correct results by applying the formula on values of c² other than the ones by which we got it (using the analytic expansion as a function of c^-2).
It is also possible and clearer to explain just in words the least action principle (that is just the principle of equilibrium in a field of potential over the configuration space, when considering things in 4D), and deduce from it also just in words the conservation laws and the Liouville theorem. I also explained just in words (I admit it is not a full and rigorous explanation but...) how electromagnetism derives from a Lagrangian, and the sign issues around it.
For introducing quantum physics (just an introduction but) I also have a mathematical approach exactly formulated in the language of geometry, itself mainly expressed in words, with very few formulas.
On the other hand I find that we need formulas to express statistical physics (define entropy and explain its creation process), disagreeing with the usual "qualitative" approaches.

But you are forgetting one very crucial factor.

Just because you are able to explain all of these without using any math, how do you know that your message has been accurately received and understood by the type of audience that you intended this for? Did you do a thorough research on the effectiveness of your message? Have you investigated what people who have read your page understood what you were trying to convey?

We have seen way too many examples and cases, even in this forum, where non-scientists and students read one thing, and understood something else entirely! We have enough evidence where even how we arrange our words in describing something can trip someone into understanding it in a different way!

It is why we tell people here that simply asking something based on "I heard that..." or "I read that..." is not sufficient. We try to force people to cite their sources, and more often than not, when we find these source, they have misinterpreted what they read. This has occurred quite often!

So sure, even *I* can come up with a bunch of prose to describe many aspects of physics. But it doesn't mean that what I wrote and intended are what the reader will understand. You haven't shown any evidence that what you have written was accurately understood.

Zz.

 

[peroAlex]

Without reading other people's posts, I represent you my personal view on your question.

When you are trying to understand principles of relativity or quantum mechanics, it's almost impossible not to use additional explanation in terms of language. However, when we dig deeper into the matter, it becomes obvious that with basic definitions like this:

In quantum physics the two descriptions, particle and wave, are complementary. In some circumstances light behaves more like a a wave and less like a particle; in other circumstances, more like a particle and less like a wave. This means that wave and particle are two idealized extremes

-College Physics by Giambattista and Richardson

it is almost impossible to fully understand modern physics. Words are too vague, they cannot eloquently express what equations can. Even preliminary postulates of quantum mechanics (of today) are difficult to explain using words only, as definitions can become long, with lots of ambiguity in between the lines. Reading modern physics is not like reading a law book where interpretation of laws depends on your capability of language comprehension, here it takes strong mathematical background and extensive classical physics knowledge (although modern physics are sometimes the complete opposite or paradox to classical physics). And even then, you might struggle understanding certain aspects.

Unfortunately, it is impossible to simplify certain aspects of modern physics. You can give a dubious answer to Schrodinger Equation or uncertain answer to what is Uncertainty Principle actually about. But again, to understand such thing you need formulas.

 

[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.

It depends on whether you are learning physics (or math, for that matter) as a liberal art or as a trade.

 

[ZapperZ]

It depends on whether you are learning physics (or math, for that matter) as a liberal art or as a trade.

How would that matter on the LEVEL of understanding?

Zz.

 

[phinds]

It depends on whether you are learning physics (or math, for that matter) as a liberal art or as a trade.

I've never heart physics equated with liberal arts. How do you do that? What does it even MEAN to "learn physics as a liberal art" ?

 

[David Lewis]

You don't worry too much about doing something useful with it.

 

[FallenApple]

Well I think math does matter. But up to a point. Knowing the concepts of the math matters. But manual calculation of it is not that important for understanding.

If I am given a question, say a complicated oscillation question, I can think about the physics, set up the lagrangian, and at that point, the physics is done. The rest is just a formulaic calculation.

Probably at a certain point in human history, manual calculations and the solving of most equations can be done by sufficiently advanced calculator/AI and all we need to do is to come up with the setup.

 

[FallenApple]

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.

Well, it comes down to physical intuition as well. One doesn't need an equation to see why the two glass plates sticking together can't be due to gravity. I mean if it were, the first thing that would come to anyone's mind is that things would be sticky. Second, the Earth is just much bigger so it is clear that it would have a bigger pull on a plate more than the other plate, again physical insight, no equation needed here. Third, they can just dry the plate and watch it fall, concluding by logic that the water must have been the adhesive.The ancient greeks even knew why at an intuitive level and they didn't even have the right equation/theory.

But for more complex phenomina, I do agree that the math becomes much more important.

 

[ZapperZ]

You don't worry too much about doing something useful with it.

"Doing something useful" isn't really the issue of this thread, is it?

Zz.

 

[David Lewis]

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.

 

[ZapperZ]

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.

Unfortunately, you are going off in your own world.

The question is whether modern physics can be UNDERSTOOD qualitatively, without understanding the mathematics/quantitative aspect of it. This has nothing to do with what it is going to be used for, or if the person has the background for it.

Zz.

 

[phinds]

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.

Not doing it as a profession is no excuse of having a shoddy understanding of it PARTICULARLY if that shoddy understanding is mistakenly believed to be a decent understanding which I think it sometimes is.

 

[vela]

Not doing it as a profession is no excuse of having a shoddy understanding of it PARTICULARLY if that shoddy understanding is mistakenly believed to be a decent understanding which I think it sometimes is.

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. 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?