In my last post I raised a question about the pros and cons of common sense. I left it as a wide-open question, as I was curious to see how readers would react.

Many aspects of common sense affect how we relate to other people, and it’s clear they have considerable value. But the intuitions we have for nature, though sometimes useful, are mostly wrong. These conceptual errors pose obstacles for students who are learning science for the first time.

It’s also interesting that once these students learn first chemistry and then Newtonian-era physics, they gain new intuitions for the natural world, a sort of classical-physics common sense. Much of this newfound common sense also turns out to be wrong: it badly misrepresents how the cosmos really works. This is a difficulty not only for students but also for many adults. If you’ve read about or even taken a class in basic astronomy or physics, it can then be challenging to make sense of twentieth-century physics, where Newtonian intuition can fail badly.

Let’s take just one example. Any child who has tried to move a heavy box by sliding it along a floor knows that if you want to keep it moving at a constant speed, you have to keep pushing it; and the heavier the box, the harder you have to push it. It also seems harder to push it at a high speed than at a low speed. For this reason, the natural expectation of any reasonable person who hasn’t taken a physics course is that the amount of force required to push the box grows with the **speed** *v* at which you want to push it and with the **weight** *W* of the box.

Such a person might then imagine, incorrectly, that this is true for any object in any circumstance, at least on Earth. It’s common sense.

Misconceptions of this sort *(which arise from not recognizing the crucial role of friction) *were typical for centuries, even among highly intelligent, thoughtful scholars. * *It wasn’t until Isaac Newton that the veils were entirely lifted, with his laws of motion, of which the second reads * F = m a*. This equation implies

- that no force at all is required to make an object move at a fixed speed and direction,
- that the force
required to change the speed or direction of an object is proportional to its*F***mass***m*(not its weight) and the object’s**acceleration**(not its speed,) and**a** - the direction of the object’s acceleration is the same as the direction of the force applied to the object.

And yet no sooner has a student spent months learning and internalizing this law, developing a detailed intuition for it, than it is undermined by the 20th century, first by Einstein’s relativity and then by quantum physics. That’s unfortunate for people who take only one year of physics, because those advanced subjects are either not covered, or are covered in a cursory way that does not allow for a new intuition to take hold. Worse, incoherent statements about these topics are not uncommon in first-year textbooks.

In Einstein’s theory of motion, the analogue of * F = m a* is a much more complex equation, as you can find in the 2nd, 4th and 5th sections of https://en.wikipedia.org/wiki/Acceleration_(special_relativity) . Worse, the intuition for what is meant by force and acceleration in this context are not straightforward. Textbooks and courses rarely consider them with care.

Not realizing this, people often apply the following incorrect logic:

- Einstein claimed that no object can move faster than the cosmic speed limit
(also known as the speed of light);**c** - Therefore, the closer an object’s speed to
, the more difficult it must be to accelerate it (and therefore the more force must be applied to do so, for the same acceleration); otherwise its speed could easily be made to exceed**c**;**c** - And so, an object’s mass must grow with its speed, so that a fixed force produces less and less acceleration.
- In fact, as its speed reaches
, the object’s mass must become infinite to assure that that the acceleration correspondingly becomes zero; otherwise it could accelerate past**c**.**c**

This sounds perfectly reasonable, but it is somewhere between misleading and inconsistent. It is an effort to retain Newton’s law, and Newtonian common sense, in the context of Einstein’s relativity. But it’s simply not true that * F = m a*, where

*and*

**F****point in the same direction in three-dimensional space; it is only approximately true at low speeds. In Einstein’s terms, you can write a generalization of**

*a**, but then both force and acceleration have to be generalized to point in*

**F**= m**a****dimensions (i.e. both in space and in time) and the mass**

*four**m*has to be the object’s

*, a constant*

**rest mass****which does not depend on the object’s speed**. If you try to maintain your Newtonian intuition, defining

**and**

*F***as before (in terms of three-dimensional quantities) and defining mass**

*a**m*to increase with speed, ambiguities arise which cannot be resolved. Among other things, the object cannot be assigned a definite mass;

*any definition you choose will have to depend on the direction in which the force is applied relative to the object’s direction of motion*.

What happens to * F = m a* in quantum physics? Even the idea of such an equation assumes that objects have trajectories — paths across space on which objects travel as time goes by. But what we learned from quantum physics is that real objects in the real world do not, in fact, have trajectories. It’s a long story to see what happens to Newton’s law in that context. (For a glimpse, see https://www.physnet.org/modules/pdf_modules/m248.pdf, but that’s just the beginning.)

In short, not only does our common sense intuition from **before** first-year physics have to be discarded, so does the intuition built up **during** first-year physics! This is a serious challenge for students, teachers and writers. And it raises an interesting question: would it be better, both for those who will someday take a first-year physics class and for those who never will, to try to convey some preliminary, qualitative intuition for how the world really works? Only later would we then teach Newton’s physics for what it is: not as a set of ancestral truths, but merely as an approximation that served (and still serves) as a temporary bridge between ordinary common sense and the universe’s underlying reality.

1) really looking forward to the release of your new book

2) I thought it was understood, in todays world, that “relativistic mass” was an antiquated term, and by definition what physicist call “mass” is the rest energy of an object. By that definition, “rest energy”….doesn’t that automatically imply that mass is reference frame invariant?

1) Great! 2) “antiquated” is too strong. Particle physicists do not use “relativistic mass”, but science journalists, some astronomers, and non-expert scientists and first-year physics teachers often do: for instance, https://bigthink.com/hard-science/speed-of-light/, or https://www.energy.gov/science/doe-explainsrelativity , or https://galileoandeinstein.phys.virginia.edu/lectures/mass_increase.html , or https://cosmosmagazine.com/science/physics/luminous-space-cow-relativity/ — just google “mass increases with speed” and you’ll find hundreds of hits. Also, note that “gravitational mass” (which is neither rest mass nor relativistic mass) is widely used by astronomers and gravitational theorists, which is why the internet can’t agree whether photons have mass or not. In fact, they have zero rest mass and non-zero gravitational mass.

Would it be correct to say that photons have non-zero gravitational mass, because they have energy? If I remember correctly, space time curvature is a function of energy density?

Yes; all objects have energy, and all have non-zero gravitational mass as a result of that.

Dr. Strassler:

Along those lines, from a pedagogical point of view, we are taught in high school, that momentum is M*V. Ok, then we learn, in “basic relativity” that momentum is actually M*V*gamma. Then we learn that photons have a momentum based on wavelength, and photons can transfer their momentum to physical objects! then we learn that gravitational waves….ripples in Spacetime also carry momentum. So, while mass x velocity may be one manifestation of momentum, it’s not the only manifestation. So, with that said…..what really is momentum? In a more fundamental sense, Is it the ability to exert a force over time in a direction?

No, momentum is more fundamental than force; it is better to define force in terms of changes of momentum rather than the other way around. There are many contexts in which force can be hard to define, but momentum is more generally meaningful.

Momentum is **that quantity which is conserved because the laws of nature are the same everywhere in space.** In the same way, energy is **that quantity which is conserved because the laws of nature are the same everywhere in time.** These definitions are unambiguous (and are clearly defined, using a theorem of Emmy Noether) and they work as long as spacetime itself is not too complicated. If it is complicated, and we need the full power of general relativity, then these statements are only true locally, in small regions of space and time, and one needs more sophistication to understand what happens across larger regions.

Dr. Strassler:

Along the lines of reference frames, I had seen some comments / you tube videos stating that the cosmic microwave background, can be viewed as an absolute frame, in other words your velocity relative to the CMBR can be thought of as an absolute velocity? Isn’t this just a choice of reference frame? In other words, in relativity, no one frame is more correct than the other.

If I was in space, with a velocity relative to some star, I can’t say that I’m moving thru space, the only thing I can positively say, is that I have a velocity relative to that star. In one reference frame, I can be stationary with the star moving towards me, and in another reference frame the star can be stationary with me moving towards it…..there is no way to tell who is really moving, the only thing I can say is that I have a velocity relative to that star.

Does he CMBR change that?

How the world “really” works does not really apply to everyday life, at least with the current approach we have some hope of connecting theory to what we can actually show the students.

I respectfully disagree. How the world “really” works absolutely applies to everyday life, in all sorts of hidden ways that we simply gloss over in first-year physics class as though they don’t matter. Of course we should teach first-year physics as we do; I’m not suggesting we abandon it. But what benefit is gained by permanently obscuring what everyday life is actually about, and how the objects around us (and our own bodies) actually work?

I just noticed one thing in Matt’s reply above that I think pedagogically and socially important. ” Of course we should teach first-year physics as we do.” Well, I’m reading that as “how we did 50 years ago when I took it”. It was devastating!

I expected to be a physics major.The course was classical mechanics, the whole course. And it was excruciatingly boring. The highlight was measring the difference in gravitational potential between the bottom row of the auditorium and the top with a portable gravity meter (which the prof had invented.) There was nothing at all unexpected. Nothing!

I had taken two six week high school summer courses of higher math (mainly number theory and what is now called algebraic geometry) at UT Austin and found them unexpected and wonderful. But when I went to college my roommate (who eventually graduated #1 in our class … he had gone to the best high school in Guatemala!) was so much better than I that I discounted math as my major. I settled on chemistry because the class covered numerous topics reasonably well including stat thermo and a bit of QM. One prof was doing scattering experiments on molecules that were very physicsy and interesting [aligning CH3I molecules so all the I’s pointed north or south at the flick of a switch and seeing which end reacted with potassium]. So I decided specifically on the most physicsy parts of chemistry. That’s my story … and several friends had similar experiences.

I think that freshman courses should be samplers, covering at least some things that are not even touched on in AP high school courses. With a prof well attuned to the ideas, such courses can in fact give real hints to what “really happens”.

I’ll never forget that prof I mentioned explaining to me how QM allowed him to make all the (gas phase) methyl iodides have their I’s pointing north, but why only a few percent of the original ones could be so aligned, the rest being thrown away. At the end he did say it was hand-wavy.

Professor, reading your blog is a joy! You clearly are a dedicated teacher. Loved your bit dismantling common sense. Ironically, that is what I love about physics, it demands the student remain mentally flexible.

Looking forward to the book! Growing up in two cultures, I’m very aware of how a perspective of common sense shifts radically with your “first principles” assumptions. Japanese mentality is comfortable with something having two (or more) aspects, without reconciling how it can be both, or which is dominant, or which is real and which is the illusion. If you tell a Japanese person “an electron is both a particle and a wave” (ignoring the finer implications of the statement), they will tend to accept that as fact simply because it was stated to be fact, and move on to the next lesson, whereas in the west that statement requires much elaboration, analogy, and debate. On the other hand, if a new idea doesn’t fit into one of your preconceived categories, in the west, we’ll tend to quickly move on and assume that must belong to a new category, while the Japanese will doggedly fight to make it fit one of the available molds. These are gross generalities, of course, but I see it every day, and can trace most of back to cultural common sense-isms taught at an early age. In the LEAST, kids should be told that their science fair styrofoam beryllium atom (for example) is a great simplification, and on some level incorrect, so they leave the door to flexibility open in their heads. The problem is when you think you’ve learned a thing and you’re “done”. Every analogy is only a bad placeholder until you synthesize a (hopefully) better one. I’ve found many better ones in your blog.

Darren, I think this is particularly well-put. Your point about Japanese vs Western-European culture is a fascinating one. And I agree that the problem is often that we tell kids “this is how it is” instead of “this is a good but approximate way to think about it.” It would already go a long way if we changed that approach.

Common sense is a very necessary social thing, but it has no place in physics.

All of “us”, people like you and me, (a chemistry professor who taught quantum mechanics, including one course that covered relativistic electronic structure, which we needed to explain an experiment I did,

the reactive scattering of H + Br2 or H+I2) “lie to children”. I, for example, pretended until the last day of the

class that its OK to just replace Hartree-Fock with Dirac-Fock and go from there. It gives the right answer, but its a lie.

Even the “greats” lie. I sat in on a first-year grad quantum mechanics (not field theory, which at the time he was barely starting to get right for the strong force) by Sheldon Glashow. He made a big deal of “motivating” everything. It was mostly shameless lies! Lots of us, after an hour of thinking, could find loopholes in his logic.

I suspect that when he closed those in his field theory course, he lied about something else.

But in fact, to do otherwise is hopeless. Education is a series of nested jeweled eggs.

I guess I’m suggesting we could lie differently. I.e., it’s one thing to lie and say nothing; it’s another to say: I’m lying, and here’s where you could go learn about what I’m lying about and why I’m lying at this moment. And also it depends on the level of the student. You were advanced — you knew little lies were being told. Beginning students taking a first (and often last) physics class have no idea, and will go off into the world with too strong a belief in what they’ve been told, and too little understanding of how deep the layers are that lie beneath.

Sheldon Glashow was always a great liar — one of my favorites! One of the first big-time physicists I ever heard speak, back in my teen years; I still have my notes. And I asked him what the Higgs field is all about. He lied. But he told me he was lying! So I knew I hadn’t gotten the real story.

Energy DISTRIBUTION is the monopole source of all polarities.

SPACE is everywhere all the time, instantaneously and simultaneously, as the primary energy distribution mechanism.

FORCE is focused energy distribution and is always ON. There are 0 static non-moving parts to this universe.

Matter, mass, force and information are simply effects of energy distribution with timelines.

True lies?

Could be. Or maybe false truths.

“would it be better, both for those who will someday take a first-year physics class and for those who never will, to try to convey some preliminary, qualitative intuition for how the world really works?”

Yes, I find this teaching approach essential as modern society continues to evolve and develop. For example: Before you enrolled on your undergraduate physics course, were you already aware that an electron was a well defined disturbance in an electron field like the photon for the electromagnetic field?

I’m somewhat mystified as to why I knew about the particle-wave duality of the electron from the popular books I read on the subject, yet I saw this as far more controversial than the photon being a chunk of EM energy/momentum in the EM field. Perhaps the writers saw the Higgs field as irrelevant here? I’ve read elsewhere that Dirac was more comfortable with the electron, rather than the electron field, interacting with the EM field, but I don’t know how credible the source on this was.

Your blog has profoundly turned upside down, in a positive way, how I now view electrons in electric circuits: a disturbance of the electron field, given mass by the Higgs field. As time goes on, this will become increasingly mainstream within the minds of EE undergraduate students from the popular science books they read.

Even basic mechanics using just Newton’s laws can be very difficult to understand in itself, such as in the ‘inelastic’ collision of two canon balls conserving momentum and energy. There’s a lot of material science going on here to adequately explain how the masses reverse the motion of one another. And this requires interacting point masses as a model to help build up an adequate macro model.

I wasn’t aware, not even while taking quantum mechanics, that electrons were ripples in an electron field. I did know about particle-wave duality, but it was all confused, because the distinction between electrons-as-waves and wave functions of physical states was never made clear. In fact it still isn’t made clear in most contexts. I haven’t even done a good enough job of it on this website yet, though I do need to.

I do think it is useful to start by understanding by what things are (to the best we understand them, of course) and then proceed to understand why they can be viewed more simply. Everyone knows that the Earth is a giant pile of rock and has a complex surface and a complex interior, and the fact that we can often treat our planet as a sphere or a point is worth discussing *before* we start actually treating it as a sphere or a point. The fact that waves can often be treated as particles is actually covered in freshman physics under the guise of “geometric optics”. So it is hardly a big step to say that electrons are waves too — strange ones, since they are in a sense particulate, rather than continuous-seeming like water waves — and yet in many circumstances we can treat them as though they were idealized points traveling on trajectories.

“the distinction between electrons-as-waves and wave functions of physical states was never made clear. In fact it still isn’t made clear in most contexts.”

Yes, that’s a crucial point for me but I had no idea how world class professional physicists saw this distinction. There’s a well known philosopher of science who claims that:

“Every presentation of any quantum ‘theory’ uses a ‘wave function’ to describe the physical state of a system. This is as true in QFT or quantum gravity as it is in basic quantum mechanics.”

If true, I find this surprising because I thought QM and its wave function is a particular case of a QFT which doesn’t need a wave function generally to define it. I wonder how physicists like Bohm, Everett and Bell would reassess their concerns about QM from the viewpoint of QFT as understood today?

My guess is that their concerns would disappear, knowing that the wave function of a quantum system is a computational device to considerably simplify a QFT problem; similar to the way macroscopic properties such as conductivity, permittivity and permeability of matter is used in Maxwell’s equations to simplify what would otherwise would be a far more difficult problem to solve using the more general microscopic Maxwell’s equations.

On my table I have a cup: how permanent is it?

My senses tell me it’s permanent, yet the QFT picture tells me, if I understand it correctly, that it’s not exactly the same as it was moments ago. Does the Higgs field maintain its existence?

Your questions are too many and the answers too complex for me to really address them in an answer to a comment. Picking one: a wave function can apply to any system, including a Quantum Field Theory or even a Quantum Gravity theory. The philosopher of science is correct on this one. The wave function may be a function of an infinite number of variables, and therefore essentially useless for any practical pupose; but it does exist. The only reason we often see wave functions appearing in Quantum Mechanics is that they prove useful for solving problems. In quantum field theory we generally need other methods, but that’s not because wave functions don’t exist.

In pre-quantum field theory we have a field which (at any moment in time) is a function of space. In quantum field theory, we have a wave function which is **a function of a function of space** (often called a “functional”, for what it is worth.) For every function F(x), there is a number Psi(F(x)) whose square is the probability of finding the field equal to F(x).

This is to be distinguished from, say, electrons, which are individually given by **functions of space** in quantum field theory; the field theory allows you to have many of them in three-dimensional space, and for that number to potentially change. This is different from Quantum Mechanics where electrons are treated as objects **at positions in space**, the number of them is fixed, and the wave function is a function of all of their positions — that is, if there are three electrons, then the wave function is a function of nine dimensions: Psi(x1,y1,z1,x2,y2,z3,x3,y3,z3).

How you obtain Quantum Mechanics of electrons from the quantum field theory of electrons is subtle and one of my main goals this year is to find a nice way to explain it on this blog.

A last point: a cup is made of fluctuating objects; nothing within it is the same from moment to moment. (This has nothing to do with the Higgs field — it’s just the nature of quantum fields to be always in flux, and that’s even true for classical objects at finite temperature.) But its macroscopic properties hardly change, and so, in that limited sense, as a macroscopic object, averaging over its microscopic properties, it is (quasi)-permanent.

“How you obtain Quantum Mechanics of electrons from the quantum field theory of electrons is subtle and one of my main goals this year is to find a nice way to explain it on this blog.”

Great, I’ll use it to help me answer for myself how this then goes on to provide more modern answers to the concerns of Einstein, Bell, Everett, Bohm etc about interpreting QM in their era; assuming this isn’t part of your goal. Your answer above emphasizing that QFT is founded upon probability has already helped me see intuitively that they were highly likely misguided by their then common sense view of the world.

Re “how I now view electrons in electric circuits: a disturbance of the electron field, given mass by the Higgs field.” That is mixing cases.

Free electrons have masses given by the Higgs field, AFAIU.

But in material systems bonds and conduction of valence electrons modify what we see as bond and valence electrons as well as their effective masses given by their environment. That is why a metal or semiconductor conduction electron is much “hotter” than its crystal environment and why the collective movement of them is “much” slower than c (well, some, at 2/3 c at times). It is in general better to think of these entities as “quasi-particles” – of electrons and sometimes their lack described as “holes” – even if it is a misnomer. Here too an intuition formed in other situations do not much apply.

Writing some letters and symbols and making hand waving descriptions about the meaning of each letter and symbol and how they may correspond to the real world is already outside the realm where the phrase “common sense” has much useful applicability.

When a first order approximation which successfully models 99% of cases in the real world is insufficient to model the other 1%, that shouldn’t be confounding or unexpected, and is also outside the realm where the phrase “common sense” has much useful applicability.

Common sense may be applicable to some aspects of those things, like it may be applicable to anything. If the letters and symbols and handwaving seem to contradict common sense, that sounds to me like a problem with them, not with common sense.

I admit I didn’t entirely understand your message; it wasn’t clear when you were referring to pre-physics common sense and when you were referring to Newtonian-based common sense. For instance, you say: “When a first order approximation which successfully models 99% of cases in the real world is insufficient to model the other 1%”, are you referring to ordinary common sense, or to Newtonian physics?

Either way, I have some questions about how you come up with “99%”, which I find amazingly high — but I’d like to understand your reasoning before I give you my counterproposal for what that number should be.

Note also that “Writing some letters and symbols and making hand waving descriptions about the meaning of each letter and symbol ” is not what I would recommend, in most cases. Explanations come first; then one might choose (or not) summarize one’s understanding in a simple equation. Doing it the other way round is a way of mystifying simple things; it makes it easy for those who already understand what’s going on, but not for anyone else.

“would it be better, both for those who will someday take a first-year physics class and for those who never will, to try to convey some preliminary, qualitative intuition for how the world really works?”

I think my other thread wasn’t staying with your basic Newton’s law example and the aims of your site, so I’ve created another one here. My answer to your question is: “It would be helpful, given your professional background and teaching abilities”.

Over the years dabbling in teaching myself classical mechanics, two texts have stood out for me: Mechanics: Volume 1 – L D Landau, E.M. Lifshitz and Morin’s Introduction to Classical Mechanics: With Problems and Solutions. The first text, originally aimed at Russian graduates, uses the Principle of Least Action from the start, whereas the latter text is aimed at Harvard physics undergraduates who are introduced to Newton’s laws at the beginning via statics, The Principle of Least Action in the middle and Special Relativity towards the end. I gave up on the first text as my main one because it was far too difficult and fast paced for me to deal with, covering in one page what takes others a few pages to a chapter. But now, older and wiser, I appreciate with awe how quickly the first text focused with a laser-like precision on what mattered to get graduates up to speed.

I definitely would have benefited from knowing how the Principle of Least Action lies at the foundations of classical mechanics and theoretical physics generally, at a popular science level. But few authors would have been able to do this in a way I could have understand at the beginning; requiring someone from a professional background with a genuine interest in learning from the feedback of their audience. Likewise with other topics in theoretical physics generally such as particle physics and field theory etc.

Matt, at what level do you want to keep discussions and questions on your site at?

In the past, I’ve assumed that you’ll have an audience ranging from interested public to professional physicists so that questions and discussions within this range should be OK, where it’s left to you to decide in the comments.

The physics courses I have taken has in general mentioned the provisional nature of the material up front, but infuriatingly rarely tried to sketch the current picture of “how the world really works”*. It isn’t merely annoying that they do not, it would improve guidance if they do.

*I hasten to add that I think QFT is a robust picture so we can take that as how the world really works.

And of course the basic courses reiterate the iterative nature of science and its progress.

Professor Strassler,

Only recently I have discovered your blog, which I think of great interest also for those – like myself – who are not Physicists nor students of physics, belonging, as they do, to the middle-cultured man of the street, so to say. My personal approach is of a philosophical type. I am especially interested in the notions of space and time in their general implication for our (philosophical) view of reality.

You argue that we have to “dismantle common sense”. Right. Understanding “common sense” as the equivalent of “empirical intuition”, that is, what our senses show us as the reality surrounding us, you demonstrate, with a very clear exemple, “where Newtonian intuition can fail badly”.

But how far is this “dismantling” supposed to extend? To the point of stating that “real objects in the real world do not, in fact have trajectories”, also when they undoubtedly appear to have trajectories, and very precise ones at times (cannon balls, bullets, missiles, football balls, etc)? I must admit that this is difficult to accept.

But you specify that objects do not have trajectories according to “quantum physics”. Should we conclude, then, that the realm of quanta is regulated by laws that are different from those regulating the realm of macrophysics and, furthermore, that it is not possible to unify the two realms under the same law?

Thank you for your attention.

Paolo Pasqualucci

I’m fond of the ‘lies to children’ approach. There’s always too much to lay on people all at once, so you have to do things in steps. At each step new things must be learned and old things unlearned. This is a pain, so it pays to keep in mind that you ARE being lied to. This works for spherical cows in a vacuum, later on you may learn how it works with actual cows. After all, do we not still USE Newtonian physics, even to launch our rockets?

I’ve not seen more abject failures of science education as when something is counched in too many qualifications. Often people do not realize the appeal to accuracy and shades of gray and only see a fool who has no idea really what they’re talking about. ‘Four dimensional vector? Listen to this man, he admits Newton is wrong and is making stuff up. There’s no intuition at all and that’s why gravity is a lie and the Earth is flat.’ People NEED intuition, even when it can be wrong. Our minds are susceptible to it for a reason.

Continuous evolution of a wave function interspersed with discontinuous collapse thereof is hard to reconcile with common sense. Trajectories between collapses are considered indeterminate. If collapse is a Feynman vertex, is the existence of particles between vertices determinate, or is the only definite thing the combination of the particles at the vertex?

“…would it be better, both for those who will someday take a first-year physics class and for those who never will, to try to convey some preliminary, qualitative intuition for how the world really works? Only later would we then teach Newton’s physics for what it is: not as a set of ancestral truths, but merely as an approximation that served (and still serves) as a temporary bridge between ordinary common sense and the universe’s underlying reality.”

I struggled with this question for many years as a high school physics teacher. The solution I found is somewhat different than what you are suggesting. I’m finishing a textbook that puts my solution into practice.

As is common, the course’s first semester is mechanics. We follow an historical approach with a modern perspective, which means telling the story of how mechanics developed, but using modern notation and vocabulary. Students do not learn F = ma, and we hardly talk about acceleration at all. Instead, they learn conservation of momentum. (We use p_i + F∆t = p_f, where p_i and p_f are the system’s initial and final momentum, and F is the net external force.) There are three reasons for taking this approach.

1. It is historically accurate. Newton stated his third law in terms of force and momentum, not acceleration.

2. Conservation of momentum is much easier for students to understand and use in calculations.

3. Unlike F = ma, conservation of momentum survives in the 20th century.

Students learn Newton’s momentum formula, p = mv, and they are warned that this formula will not survive in the 20th century, but is an excellent approximation below for velocities below ~10^7 m/s.

Third quarter is 19th century physics. Fourth quarter starts with relativity. We do not present Lorentz transformations. Instead, we base our treatment on Minkowski’s 1908 lecture “Time and Space,” which gives a geometric view of special relativity. Students learn

1. We live in 4 dimensions. The fourth is time.

2. The constant c is a conversion factor for converting between traditional space and time units (e.g. between meters and seconds).

3. Minkowski’s magnitude formula for the magnitude on any 4D vector.

Momentum is now a four dimensional vector, whose components are E, p_x, p_y, and p_z. The magnitude on the momentum 4-vector is the mass, and Minkowski’s magnitude formula in this case is

m^2 = E^2 – p^2

Since the momentum 4-vector is tangent to the object’s world line, we can use similar triangles to see that dx/dt = p/E, or v = p/E. This is the relativistic formula relating momentum and velocity, replacing Newton’s p = mv. This formula can be inverted to get p = gamma mv. However, since students are already experienced using momentum and energy, we never actually need to do that.

Notice that there is no trouble with the case m = 0, which gives E = |p|, and v = 1 (more precisely, the unit vector in the direction of p). We never talk about relativist mass, and don’t even talk about rest mass or rest energy, since those are just mass in our treatment.

Then we introduce quantum mechanics by following the story of the photon’s discovery. First, the photon was just a quanta of energy, and students learn that Plank’s constant, h, is a conversion factor for converting between energy and frequency, E = hf. Then they learn about Compton’s experiments showing that the photon actually has momentum, too, which means h is also a conversion factor between momentum and 1/wavelength, p = h/L, where L is wavelength.

Now we see that light is both a wave (19th century) and a particle. So we follow De Broglie in suggesting that other particles are also waves. We do a bunch of particle physics, including relativistic collisions and decays.

I should note that this is an algebra based course, and it is a graduation requirement at the school. Every student in the high school must pass this course to graduate. 70-90 students have taken this course each year as I have developed it, so there has been a great deal of refinement over the last 8 years. Students who do not like science, do not like math, and do not want to be in this class have consistently mastered all of these ideas.

Before finding this solution, I tried to teach “how the world really works” with Newton later. It didn’t work for me and my students. However, there is an excellent book using this approach for a calculus based course: “Matter & Interactions” by Chabay and Sherwood. I taught calculus based physics with this text for many years. Their bold approach gave me the confidence to try my own ideas in the algebra based physics course. Students who complete the algebra based course and continue to the calculus based AP course find it very easy to go from my approach to Matter & Interactions.

Nice piece, though it reminded me of an example that illustrates that these issues can be subtle. I had a physics professor who gave an example of how, contrary to the common trope that Aristotle’s laws of motion were wrong, that Aristotle was actually correct in assessing the motion of a falling body in a fluid (constant terminal velocity which is reached pretty quickly for most things dropped in water) as that was the experimental situation he chose. Certainly Galileo’s choice of an inclined plane was a more clever choice for trying to characterize gravitational acceleration in a vacuum, but Aristotle was absolutely correct about the limited situation he chose to examine (and though wrong in trying to generalize his findings, he was a step further along in the “common sense” he developed than that developed by trying to push a heavy object along the surface of the earth).

“We live in 4 dimensions. The fourth is time”.

(From the comment by Gavin Pholemus)

The notion embodied in this statement is considered today as a fact, practically a law of nature. Space and time are so intertwined that you have to refer to them as an intrinsic unit: “space-time”. But is this notion to be considered as absolute or relative? That is: to be applied every time you mention time or space or relatively to a certain viewpoint only?

Let’s consider the phenomenon of growth and decay: birth, youth, maturity, old age, decadence, death. This process, involving the whole of nature, seems to take place in time only: we become old because our organism has changed in time only. Space has nothing to do with the whole process. It is the repetition of our vital interior processes in time that wears them out while the space where they take place (our body) remains always the same.

So here the notion of “space-time” seems impossible to apply: the cause of ageing is the passing of Time, considered independently.

Paolo Pasqualucci

Hi Doc, about common sense text:

I greatly admire your honorable theoretical physical position and your incredible knowledge about and your extreme mathematics, and to give it us this subject, about pure mathematics, but I am sorry for the mistakes of many journalists around the world by addressing a 99% mathematical matter About such, where no scientist, mathematician or level programmer with credibility, that today admits the existence of any Artificial Inteligence, AI, now it is fashion in every press and every journalist uninformed it for everything, a lack that does everything, to washing, cook and iron clothes … in the aberrations for all publications, if not, we review this (in lay language), even knowing that it is not your fields area but it on your extreme mathematics:

We start the subject (I questioning you about, because I am a little of this field, but to see if you confirm my possession about) first, in the example of CHATGPT, that it only form phrases using a probabilistic model. In fact, the basis of ChatgPT text generation is the conditional probability, which is calculated based on a large amount of training data. During training, ChatgPT language model learns to calculate the conditional probability of a word being the next word in a sequence of words. This calculation is based on the history of the previous words in the sequence. Therefore, there are no artificial intelligence anywhere in the world, nor in the US, Europe, Japan, China, etc. All false journalistic advertising. Why? Because simply, non renowned institute, organ, company, etc., worldwide is able to admit or informs that it have AI there, as it can been processed in billions, by knowledgeable people and denounce it for falsehoods, as the chatgpt itself confesses from many errors about, That alone absolutely denies the existence of some AI, all lies, falsehood and simulation AI and journalists write in great letters that being there AI. It just doesn’t exist, agree? How many times I have seen reports in newspapers, TV, fake web of AI, on cancer search, diagnoses, tourism, investments, etc., to be there AI, all by fake-journalists that often non diploma has.

SO THE REALITY:

But explaining in a “popular” way (confirm it please) of why it will still take about 100 years or more for the true AI been to exist: AI needs born in a programming, computer language and none, absolutely none one can allow it today. Lets take for example the mother of all languages, her tool, the C language (and her variations/derivatives, visual C, C ++, C#, etc.), which is nothing more than the “screwdriver”, “pliers”, etc ff the languages that ended up practically creating all, even the latest, say a javaScript if it is a car engine, so why will use the pliers, keys to reassemble this engine from scratch? But C can create a plane turbine on this example, if you want it, then a mother for everything. Ai turns out that like a little train in a closed circuit, in a circle, that this will never get out of the tracks, always inside and obeying it. The programming is absolutely this circle, NOTHINF ESCAPES FROM IT, a routine, sub-routine, etc., ever, since the size it has, like Windows 10/11, very gigant, at many GB memory, perhaps the largest program in the world, maybe never, never It will be an AI, despite “millions” of itself powers, capacities, security, warnings, etc., that it looking thinking, solves a lot, in programs, memory, HD, web, etc. But it will always be, eternally (giant) in a closed circuit, and always obeying its immense list of orders, program (yes, orders, obedient), a puppy that obeys everything, therefor unlike a mere dog, cat, yes With AI, even minimal but allows them to escape from this closed circuit of the train, falls out, chooses for you, goes somewhere else, does what they want, smells, bite, destroys, etc, go to the street, runs away with someone else, Makes pee and coconut over the circuit train, etc. This is freedom, this is AI, choices in itself, not confined and obeying a routine, program, etc, absolute freedom, only then will existing AI. So you ask yourself, since when is there an AI on train circuit? At someone following the tracks strictly? Never. Because programming is exactly the rails, determine where you go. There is no computer that disobeys the rails, on everything written on the program, a prison, a prisoner inside, cloistered everything written, without any choice, never get out of programming and do what you want. The chatgpt is just that, but giant, with a thousand INTERNAL options, searching and searches, an true Google search , that’s all, no invented word or phrase, created since zero, as if someone searched Wikipedia to take it to teacher, but never lies that everything came out of his head. Only that ChaptGPT makes billions of comparisons in a second to choose the best text that gives you the best answer, and there may be 999 millions found of good answers in this billions, but chose the one that gave you, in mathematical comparisons, statistical that is your closest Question, but never leaving the train circuit, the rails that has been programmed. Then can you call it AI? A thousand times better, an thousand times better, that a cat that refused some ration, or scratched you, because it really thought. Such an animal os that, is millions of times more rational than the best computer program in the world, than the largest and fastest computer, than ChaptgPT, Windows 11, etc. There will only be AI the day that chips in 3D processors emerges, 3 -dimensional processing, just like neurons, communicating in it spaces, around itself, without limits, and not as 2D as today, still with independent freedoms and processors, not Depending one on the other to respond, analyzes, interpret, process, etc, very different way from today, light years ahead, perhaps at light/photons and non -electronic/digital processors like today, photonic system, perhaps 100 years from now or More and with totally different language, never in a process electronic line, a line in line waiting one for another to finish it, to start the orher, the line contained in the program, in written language, if someone has seen one of many lines, one below on the other, with loop, deviations, subroutines, jumping conditions (if, then, etc.), etc. This totally makes the AI unfeasible. Therefore, as said, a mere dog or kitten that changes its idea in something it would do, it goes beyond millions of times and “reasoning” ability of the most advanced computer, or programming language or program already done.

Your mathematical knowledge gives you this clarity very well, you know that mathematically today is impossible such a real AI existence, or in physical, on this itselfs mathematics or physics (engineering, etc.) that they would never allow it (thats talks about itself digital life, this is AI). Then gives a such of lapse to admit the AI existence.

Note: Computing are absolutely the mathematics domains.

Perhaps some day you write us about it on your the extreme mathematical capacity, because someone needs to break this myth.

Sorry for a large and a lot of text mistakes.

PS: people said, that the true AI would necessarily descend from human intelligence and therefore it would have to have behavior, profile, personality, where there would not been intelligence without personalities, that is to be cold, rude, without a minimal emotion, then if one day go to exists AI, would have to Build it with some kind of personality, as every human has, such answering questions as ChatGPT do, but then one could choose from the list, a type of profile, personality, such as an doctor answering, or a lawyer, physical, engineer, etc, of course, with only 10% of a personality, because it gets all in decades coexistence with family, friends, etc, and then choosing in chat an joyful profile, serious, grinning, playful, etc., That is, absolutely different from the cold chatgpt, an more human profile and therefore with real intelligence, even it refusing to answer an question if it want, but never give a long answer, as all people refuse, ordering him to serach the question, like an human profile . Do you agree that? thanks.

The future of AI will be the physical of AI and not the biology, says neurons, says electric current.