I dont have idea about that but iam so interested

Hello Aparna,

Break all rules! Once you realize that physics and maths are all made up, by people like you, but Nature is still there to be found, still deeper, that you can find a better path, and help others, you may break the rules that someone else decided to make, a human, or a group of humans, and show the path of evolution. Imagine how much time and angst you can save, and someone else can find.

Cheers, Ed Gerck

If you feel that classical mechanics is totally flawed, which I disagree with entirely, then your proposal makes some sense.

But I have found that even though kids these days play with electronic toys from a very early age, it does not make them any more knowledgeable about what is going on inside. People not so interested in physics seem to understand mechanics better than E&M. Simply because they can see mechanical laws at work every single day.

The idea that F = ma is intuitively obvious to just about anyone. Not just that, it is very easy to show this with simple experiments. Easy, low tech. In high school, we even went riding up and down elevators, with just a scale and stopwatch, to demonstrate these laws of classical mechanics.

Whereas q = CV2, or the line integral of B dot dl = uoI, is just not out there for everyone to see.

Hello Manfredi,

F = ma is neither intuitively obvious nor correct. It actually fosters the wrong intuition, especially in special and general relativity, quantum theory, solid state physics, mechanics, or space. There are simpler ways to explain the magnetic field.

So, please suspend disbelief, and try to see a future without bothering about tension forces or the existence of a reaction to every action, equal, and instantaneous. Otherwise, it creates a bias we can avoid.

Cheers, Ed Gerck

F = ma is correct, at low speeds, Ed. I know you are on this crusade against classical physics, but the fact is, within its constraints, it works, it is used all the time, and it is very easy to understand and demonstrate. People like to hype up examples where it can't be used, like in certain functions related to GPS, but everything in education starts with what is easy to absorb, and then evolves to show that what was easy was incomplete.

It's still easier to teach arithmetic before teaching algebra, trig, and calculus. I've no problem with the idea that algebra should be taught in grade school, but that does not mean that arithmetic should NOT be taught in kindergarten.

Hello Manfredi,

There is no crusade of mine, the Cruz in it did not stand for that, the term was not used well at that time, and may offend people who suffered with it, including the Greeks. So, let us keep the conversion on-topic and, please, do not include ad hominen attacks.

Special Relativity begins at any speed, an object at rest in the palm of your hand can show large, easily measurable, relativistic effects. Look at how speed is defined, relative.

Algebra can, and has been taught before arithmetic, but that is off-topic here. It uses set theory, that even kids in kindergarten can easily learn, not even numbers.

Cheers, Ed Gerck

Come now, Ed, Let's not indulge in hyperbole.

When I measure a vehicle's length, guess what, that length stays the same, measured from outside, even at 150 mph. When people take a week long plane trip and return home, guess what, they do not return to the future. They do not find that everyone around them has aged beyond recognition.

Of course special relativity begins at any speed, but it is totally negligible at classical mechanics speeds. That's what it means when you start out with something easy to absorb, and then evolve to show that it was incomplete.

Hello Manfredi,

Please re-read my post, it tells you that an object at rest in the palm of your hand can show large, and I mean visible with the naked eye, easily measurable, relativistic effects. That is why it would de better to start with electromagnetism.

Cheers, Ed Gerck

Sorry, Ed, but that comment on how speed is defined has nothing to do with relativity. "Relative" addresses any number of effects, that have nothing at all to do with relativity. I can also say that Joe is taller than Mike, and not invoke relativity.

Just because speed relates time and distance, does not make special relativity effects significant at low speeds. What most people know is that when they travel, their watches remain synchronized. Even accurate ones, with quartz movements, remain synchronized.

Hyperbole is the art of exaggeration.

Hello Manfredi,

1. That comment on how speed is defined has everything to do with relativity, where I meant the only relativity I was talking about, the special relativity.

Speed is relative in relativity, you can be at rest in your frame, but you are not at rest to a passing or orbiting electron and, voila, a magnetic field appears to you, at rest in your frame.

2. That comment, saying that "an object at rest in the palm of your hand can show large, and I mean visible with the naked eye, easily measurable, relativistic effects" is confirmed. Macroscopicaly at rest, but not microscopically....

Same as above, and the magnetic field of relativistic (to you...) electrons may hold you, and your chair, or can be other relativistic effects, not just magnetism, affecting you, and you are still at rest on you chair, and that is why you are at rest.

These are not a matter of discussion in the 21st century, my friend. That is why it would be better to start with electromagnetism, people are receiving out of date education

Cheers, Ed Gerck

Should college students learn about electromagnetism before mechanics?

In fact this is a good perhaps philosophical question!!! I think nowadays, Science and Engineering have evolved a lot!! For sure the new vision is no longer the same as that before.

Earlier we could learn mechanics before electromagnetism because most machinery was at that time working only on mechanical principles and Horsepower.

However, since the discovery of magnetism produced from an electric circuit (a magnetic field due to a current flowing in a conductor), all machinery and equipments that involves movement and force require a simultaneous knowledge of electricity, mechanics and electromagnetism.

As an example, an Electrical Engineer student to understand the electrical motor behavior and operation is obliged to learn SIMULTANEOUSLY (and not one before or after the other) mechanics, electricity and magnetism. This is because the electrical machine itself involves these three disciplinary and the students should learn the basis of these disciplines before studying this machine.

If I want to go furthermore, it should be known that with the advance of science and technology, we are now talking of integrating several domains to study and analyze a single system. This can be viewed as 'modern mechanical engineering design' in the sense that the design of the mechanical system must be performed together with that of the electrical/electronic and computer control aspects that will comprise the complete system. In fact we are talking of the mechatronics engineering new domain.

.

In conclusion, in order to answer your question, nowadays students should have a multidisciplinary KNOWLEDGE including the essential basis of sciences, engineering and technology in order to study or produce a product or a system. These mechatronic systems include as an example: a CD or DVD player; a computer hard disc drive; a video cassette recorder (VCR); a fly-by-wire aircraft control system; and an anti-lock braking system (ABS). Each of these products is essentially mechanical in nature, but could not function without the integral design of the electrical and computer control systems that are critical to their operation.

Hello all,

From Carver Mead, of Caltech and well-known pioneer in the engineering behind Moore's law, comes the following words, in his EM book, Collective Electrodynamics:

"... an outgrowth of the industrial revolution; it was based on what was then called “the economy of scale.” The thinking went this way:

A 1000-horsepower engine costs only four times as much as a 100-horsepower engine. Therefore, the cost per horsepower becomes less as the engine is made larger. It is more cost effective to make a few large power plants than to make many small ones. Efficiency considerations favor the concentration of technology in a few large installations. The same must be true of computing. ...

But as I looked at the physics of the emerging technology, it didn’t work that way at all. ... Efficiency considerations thus favor the distribution of technology, rather than the concentration of technology. The economics of information technology are the reverse of those of mechanical technology."

So, counterexamples on intuition comes not only from learned, but incorrect, Newtonian mechanics, and not using special relativity in magnetism, but also from what was called "the economy of scale".

Cheers, Ed Gerck

Hello Anatas, Aparna, Bendiabdellah, and all,

First, there is, of course, no "right" answer to the queston. Different routes may be tried. Competition will solve it.

Today, though, 100% of the routes in higher education start with Newton mechanics first, which is an approach that we began to abandon 150+ years ago, before special relativity was even discovered. No modern paper can be found, or accepted for publication, that uses Newtonian mechanics. It is not to be found in a good toolbox for students, it will (not may) lead to errors in intuition and results.

The reasons are many, but we can try at least not have to carry the weight of history as we move on with science; history cannot inform or decide science, or humans, only nature should.

This thread is not about how to stay with what does not work, even at zero speed, but how we can find ways, acceptable, at least by some, for example as a metaphor, to avoid syllogisms (not used today, except in backward courses) when Boolean logic can be proven to work and it is easy.

Cheers, Ed Gerck

Interesting question, Useful answers.

Hello all,

To complement the information provided, the following text may be useful, protected by copyright as yet unpublished work by of a student, experiencing in vivo the problems mentioned in the question:

"In introductory electromagnetism classes in college-level instruction, one obtains Maxwell’s equations from the application of Coulomb’s Law, Faraday’s Law, special relativity, and other laws that should agree with empirical evidence [1]. The derivation of such equations relies upon trusting that framework to hold, through various laws and relationships.

In common words, the student expects the exposition to “make sense” as it is, not with a “deus et machina” approach in science!

However, one can not derive these equations neatly, with the fewest physical assumptions needed. There seem to be extra statements introduced, e.g., about special relativity, without justification, or just questionable, concurrently with the instruction.

This is not a fault of the professors in college, it is found to be caused mainly by historically valid, popular, but scientifically anachronic textbooks, that are, nonetheless, used in many top colleges and selective universities, such as top schools PCC and Caltech.

This work counters the belief that one can represent electrodynamics within Galilean space and time, and decisively show that the origin and nature of magnetism even of bodies at rest, at stand-still, can be explained only in the context of relativistic space-time.

...

Special relativity was discovered in 1905 by Albert Einstein [2] (using questionable, perfect mechanical rods and clocks), while Maxwell’s equations of electrodynamics were first published in 1865, before Einstein was even born in 1879 [3].

Thus, electrodynamics as proposed by Maxwell [3], is similar to writing English text but without the vowels — understandable, but missing important connections. In this case, connections that would arrive more than 40 years later.

Yet, when introducing magnetism in Chapters 29 and 30, Serway [1] does not mention special relativity at all. The reader is left with a deficient 19th century description, including nuclei and electrons in orbits, in a solenoid metaphor of the magnetic field, `a la Faraday.

To understand more deeply that there is no independence between the “magnetic field” and the “electric field,” it is also not useful [1] to consider extraneous objects such as atomic nuclei and other elements, when discussing later on the magnetic field of an electron in motion.

In particular, the notion of relativistic “length contraction” does not have to be used, which has questionable physical reality; it cannot be measured by all observers, and we show here that it is not necessary to be used as part of the proof. The principle is that unnecessary facts should be cleared from proofs.

Maxwell’s equations were already covariant with special relativity when discovered in 1864 (without using questionable mechanical rods and clocks), where the speed of the electromagnetic wave depends only on constants of the medium, and not on the relative motion between source and observer, as was customary with acoustic waves. This was, of course, unknown in its full importance at the time of Maxwell, albeit it was, 40 years later, postulated and explained by Einstein in special relativity.

Therefore, it is desirable to view electromagnetism as being already covariant with Special Relativity, not introduce the unnecessary presence of atomic nuclei, mechanically perfect rods, and clocks, not consider collective effects, and just admit the presence of one electron, as done in this work.

...

[1] J.W. Jewett and R.A. Serway. Physics for Scientists and Engineers with Modern Physics. Thomson Brooks/Cole, 2008.

[2] Albert Einstein. On the electrodynamics of moving bodies. Annalen der Physik, 322(10):891–921, 1905.

[3] James Clerk Maxwell. A dynamical theory of the electromagnetic field. 1865.

"

Cheers, Ed Gerck

Hello Manuel,

This is a useful discussion in RG, on higher education and science, I hope. It is off-topic to post your opinions on any other matter. You posted roughly the same opinion on another thread in RG, so I copy below roughly the same answer.

I never contested your position, but not for the reason you imagine and cite as mine. I never contested because you have a right to your opinion, which is all you present, even to deities, that you wrote in as existing.

Please correct your phrase on the point you incorrectly cite me. A simple request, no discussions, please. Whatever you do, even not correcting, is fine. I already pointed out the mistake.

If you want to participate effectively, please cite others correctly, respecting their copyright, and leave more time to your reply, your own last reply was standing 2 days without any reply, in cooperation, I'd think.

Also, it would be well if you leave more space for other views, maybe there is nothing wrong with the universe, it has been going on for almost 14 billion years without halting, which indicates that it is better than anything engineers or anyone else can create!

The imagination of the universe is bigger than that of humans, to cite Feynman.

Cheers, Ed Gerck

Hello Manuel,

You are discussing persons, not subjects, and one should not expect that in a scientific discussion.

Moreover, what do you think this thread is about? Not what you want, but a specific Question. Please read the Question and delete your posts that are off-topic.

Hello Manuel,

Your discussion continues to be off-topic, stop. Please do not try to define terms, in order to control the debate; it does not work. Consider participating more fairly, also with silence. Discussion may become even harder, otherwise.

Thank you for sharing this question.

In the advanced courses of classical field theories based on Landau & Lifshitz, it is natural to present a covariant description of mechanics and electromagnetism, including the Maxwell equations. The best example is a following course:

http://www.uio.no/studier/emner/matnat/fys/FYS3120/index-eng.html

It is difficult to follow the same approach at the elementary level; it will require new ideas similar to those introduced by R. Feynman in his famous course in physics. If we try to change the teaching methods at the basic level, we should also consider including the mechanics of a continuum. With this approach, it will be much less objectionable to teach electromagnetism before the standard course of classical mechanics.

The elementary course, which introduces the electromagnetism and mechanics of a continuum, should refer to the ideas of a discrete exterior calculus that is easy to teach and natural to our intuitions. This approach will introduce students to practical aspects of computational physics so common in most of engineering applications.

Hello all,

It is easy to deal with fantasy and nonsense posters in this thread:

1. One recognizes them, mostly, by talking about other posters, not about the subject. So, they are already off-topic.

2. They talk against known physics, such as special relativity; this is off-topic.

3. They add one or more of their own links, and call it referencing, but trying to get clicks while hiding self or fringe group advertising and false news, and repeat copying their own links under different titles, questions, etc.

4. When asked to stay on topic, they argue, instead of stopping.

5. When asked to correct their wrong citations by the authors themselves, they do not and continue to offend copyright.

If this happens, you can treat these messages as they are, ads, and skip them, reducing noise with known fantasy or nonsense posters.

Please be informed that, at any moment, all the answers and endorsements may be deleted here, instead of offering more free space for self-promotion, self or group advertisements and links, Google citations, lost time, incorrect notions, and copyright offenses, such as political, any form of personal attack, ad hominem arguments, etc., without another warning, to protect posters who obey RG rules of discussion.

In that case, there may be a memory of everyone's cogent responses preserved, copied and available as a Private Report at RG, possibly excluded all the fantasy and nonsense comments that caused the linting, under the sole and final decision of the question administration.

Cheers, Ed Gerck

I cannot imagine how this could be. Electromagnetism uses concepts of force and mass - all from mechanics. Mechanics is the field where math and physics were brought in the most tight union and however still mechanics didn't become part of mathematics. Nonlinearity is the key issue why mechanics still requires many measurements to check it's theories. Many things from the surrounding world which are intuitively common (like weather) however are still unsolved physical problems. Therefore I cannot imagine better introduction to non-linearity as through mechanics.

Hello Janusz, Ivan and all,

Thank you for valuable input, Janusz, and a link to the course in Norway. Thank you, Ivan, for motivating us to see solutions.

I try to respond to both, below, as Janusz is also a response. Non-linearity works beautifully in electromagnetism, including hysteresis, and collective effects, better than mechanics ever can, also in the lab.

The course Janusz linked in corresponds to the second year in my suggestion, after enough calculus and linear algebra, offering an unified view under Hamilton/Lagangian of mechanics and electromagnetism, suitable to add quantum mechanics next.

As to the first semester, mechanics could be held off (Calculus, elementary conservation laws, and Newtonian mechanics are supposedly covered in high school) and one could start with electromagnetism, special relativity, on a Calculus I level, which can be advanced concurrently.

This would allow students more time, also in a modern mechatronics curriculum for engineering, without outdated stuff.

Yes, this would have to be supported by new books, streamlined to actual science, maybe using an open platform with easy collaboration and no cost to students, like http://openstax.org :

"OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textbook was published in 2012, and our library since scaled to 29 books for college and AP courses used by hundreds of thousands of students. "

where one can even modify existing books, leveraging work already done, and/or start from scratch...

Cheers, Ed Gerck

Dear Ed,

As I remember-since there have passed many years from then- my problem was to understand the meaning of a 2nd order vector differential equation (Newton's second law) and not the rather naive flow diagrams for the EM laws (Gauss).

Actually I suggest:

• Extended teaching of Ordinary Differential Equations
• Vector Calculus before any EM or Mechanics course
• Linear Algebra before any Quantum Mechanics course

I don't think the problem is in the order of teaching, I think it is in the mathematical requirements, which are being taught in a limited extension, while Stokes Theorem is needed for example.

Hello Demetris,

Thank you. Electromagnetism (see posting above, with segment) can be taught based only on high school Calculus or concurrent Calculus I, and special relativity, with no Maxwell equations.

What you mention is taught only in Calculus III, and Ordinary Differential Equations is after that, so I see no problem from that side. Vector Calculus is not used in the course Janusz suggested from Oslo, because Hamiltonian or Lagrangian is used as a common basis in second year already, and that does not use vectors, so students have time to learn it. Linear Algebra should go before QM, but that is after the mechanics plus electromagnetism advanced (said above, see Oslo course), when gauge equivalence should be introduced.

The mathematical requirements, you are right, are even more important. But, they would be better served in the order above, with a course of relativistic electrodynamics first and no deprecated Newtonian mechanics course taking time in first year, avoiding the problem you mentioned.

Of course, different approaches may have to be used (e.g., in case students have no Calculus in high school).

Cheers, Ed Gerck

Dear Ed,

I agree on the Hamiltonian approach and that should be taught in early semesters. However as you realize ODE is again a requirement.

I don't agree on focusing in relativity, after all it has become a religious dogma during last century, it has so many friends and so many opponents that it cannot be defined as a broadly accepted theory, like Newton's old theory.

And, whatever approach you follow, you end up with Euler angles, so 3D Calculus is needed before Mechanics and Hamiltonian approaches.

In Greece situation has been improvement last years, they teach Linear Algebra from first year.

Hello Demetris,

Special relativity is confirmed by electromagnetism, easily. Without it, there is no magnetic field. This is part of the reason to advance electromagnetism. You can see the argument in previous comments.

Your other points may be a matter of choice, local practice.

Cheers, Ed Gerck

In mechanical engineering branch, No, but in other branches like electrical or communication engineering yes.

I agree with Dr. Ivanov. Perhaps following development path of theories can be a better and more coherent way of arranging the lessons

best

Hello Demetris and all,

In continuation to my last reply to you, it is a two-way proof, no matter where one starts from, electromagnetism or special relativity, the same result is obtained: the magnetic field exists, hence light as a consequence.

The very existence of light, that everyone can see, therefore also proves that special relativity is true, undeniable.

That is another reason to start logically , with electromagnetism, and not illogically with absolute time and space, using Newton mechanics.

Cheers, Ed Gerck

Interesting offer. But to answer this question, an experiment is needed that would show or refute your proposal as a hypothesis:)

Hello Mikhail,

Many people have followed, and could report if they want.

Some people learned electromagnetism on 4th grade, before mechanics, and later conservation laws as a a basis for both, before even hearing of Newtonian mechanics at all, which made the flaws in Newton's laws more apparent.Those people find the Newtonian concepts directly contradicting experiment.

Or, you can do it yourself, and learn, see for example,

https://medium.com/starts-with-a-bang/how-to-prove-einsteins-relativity-for-less-than-100-f5acfb5ea639

Or, try to swing around a stone on a rope, and see the difference between what Newton's laws predict versus reality, when you release both at the stone.

Cheers, Ed Gerck

Hello all,

Thank you for your participation so far, and hope for more contributions. We covered concrete suggestions, already, for example the course in Oslo, suggested by Janusz, my suggestion of electromagnetism without Maxwell's equations but special relativity instead, Bendiabdellah's suggestion of mechatronics, and others, some against a focus out of Newtonian mechanics first, even in college.

The separate thread, above, reserved for those who want to question special relativity, taken here for granted, is also going well. Let me report on it.

There, all answers have been helpful -- will help myself and readers to understand why special relativity is true in physics but not accepted by some. There are many reasons why not, albeit not in physics. I am curious of every answer, as we must all accept each other.

That question is not about Einstein or mistakes he did, which were too many to count, but why special relativity holds in physics, in all areas including an MRI of anyone's body, which MRI defines whether you will live or not, in some cases, and how to extend your life, but some people may object, not accept.

That is also a meta-question on collective effects, on a group interacting with another group, which can be viewed using physics of fluids (see my other questions and papers at RG, especially on the collective subjective, intersubjective, objective, and abstract effects and use of the scientific method), and also philosophically.

For example, using history as a social computation of interactions, computing an end state from a start state, using dialetics as a possible explanation of the struggle, Freud, Jung, eastern psychology, Vatican theology, Ismamism, atheism, economics, or quantum mechanics in trying all possible paths -- but, the end reality is the same. The MRI is still used, recognized by a medical doctor, or redone, payed for, people's lives are saved, clocks are synchronized properly, and time flows. Higher education, our goal here, should prepare better for that.

Special relativity (which had a better-concept-name as Einstein first proposed it, as a "Theory of Invariants", and Max Planck observed as his own physics weltanschauung in 1900) was not "turned ON" by Einstein. We have been living with it... for 13.772 billions of years.

Will, one day, special relativity be turned off? Will we not need to be concerned about it?

Yes, at any time today... when bodies are not used to carry intelligence, as in reference frame observer transfer that can be done by anyone today, all of a sudden going at 0.7c with an electron, and seeing NO magnetic field, from rest in a lab frame and seeing a magnetic component in an electromagnetic field, or, presumably but not proven experimentally, when time evolves after eons ... and there are not even black holes anymore, at the end of this universe.

Time seems to mark the existence of this universe. Will other universes, co-existing with this universe, exist? If... they do not have mass, if... intelligence is not only carried by a simple brain, or by silicon, nor by matter, such intelligence, presumably, would not be a prisoner of time.

But, this and no other thread in RG are the place to use words that are unacceptable by a scientific study, to proselytize by sock-puppets or cabal, to appear to win no matter the cost of experience, to assert how dumb Einstein was, that we should listen to the wise words of so-and-so, read these files, instead of losing time ...

Yes, we should strive to build collectively, to mine the gold of truth using fair, polite, on-topic, cogent public discussions. If that is not done, if those simple rules of debate are not followed, the loss is first, theirs.

To anyone who does not agree with this, you can continue to observe, or even join in, albeit in fair terms. Otherwise, life itself may become harder, even to all of us, life itself is a school.

Cheers, Ed Gerck

Hello all,

The quantum model of electromagnetism must follow special relativity! This is of fundamental importance.

Our lab is approaching electromagnetism from a new angle, based on proven identification methods from information theory, and collective effects.

Part of this new approach has been presented in a research draft, before quantum aspects are considered, and they show a much more simplified start point, highlighting the fundamental need for special relativity in the theory.

The draft is available at https://www.researchgate.net/publication/325934158_There_Must_Be_Light

Hello all: Physically, a non-inertial frame of reference should change but not shut-off length contraction, or time dilation, compared to what is calculated for inertial frames.

The expectation is that special relativity should apply to ARBITRARY motion, not just to inertial frames. This expectation also requires general relativity and quantum mechanics to obey special relativity.

The expectation has been realized by placing a spacetime description, e.g. Minkowsky, not the Lorentz transformation, as the basis of special relativity.

This brings more importance to begin studying special relativity early, in the first year of college if possoble. Share more on

https://www.researchgate.net/post/On_special_relativity_applied_to_accelerated_motion

This question is also about a movement to negate science, which is NOT billing itself as ANTI-SCIENCE, but as a legitimate refutation of science itself, and using its own methods of scientific discourse. It is similar to an auto-immune disease. One can see this in various groups at RG, especially the ones that refute special relativity, or claim to have improvements that are being ignored by science.

However, no one is blocking a person of genius. And, of course, it is legitimate to refute in science, but not what is plain to see, otherwise we would have a memoryless system, condemned to repeat the same errors, and where we seldom get to make new errors -- almost all the time being wasted in the old errors, that would have been discarded.

But special relativity is a good and robust ground, because it was not invented by any mortal but discovered in nature --- and we see it with modern time machines (aka, telescopes,) for bilions of years in the past, multiplying observations over what Einstein, Mikowski and Poincaré could use and relate to us, with effort.

I do not think you mean developed enm before mechanics. This requires

vector analysis.

Dont see much harm though in giving basic electricity and magnetism (Frances Kipp?) together with basic mechanics. These are compatible with a first Calculus.

Further ahead the student will learn the compatibility between SR in mechanics and in enm.

Further standart enm is classical, not quantum, you know that. SR is also classical.

Juan Weisz : Thanks. You are mislead by RG itself, which became a memoryless system (though, apparently, trying to cope with fantasy posters). Knowledge became collateral damage, trust and copyrights were not used.

Up there, please uncloak a message from Janusz Pudykiewicz that gives an example in Norway. Electromagnetism is also hown not to be Newtonian, time is not absolute, so Jackson does not apply. Of course, one may not agree, but a path has been shown already.

Pardon, but Im sure Jackson recognizes the bond between SR (and not Newton or Galilean) and electromagnetic theory.

Here I use the word classical to distinguish it from quantum.

The other distinction is between Newtonian and relativistic mechanics.

Juan Weisz :There is no correction on what I mentioned about your, maybe, well-known book, Jackson. I was talking about its truth condition, not truth value on "classical".

Jackson's electromagnetic theory exposition (irrelevant of name) uses time in not a SR way, not according to spacetime. It still has the Newton approach in it, which Mashoon explains and uses in his SR (see reference 4, op. cit.). It does not allow the "fusion" of space and time, time to become space, and vice versa. This is done in Burgess [2].

Also, one must not use a vector cross product, which product of vectors is not a vector. It is not a member of the same space. The space is not complete. It does not necessarily transform into the same quantity under coordinate change, it does not obey Galileo transformations, and Einstein in SR and GR. Jackson is choke-full of vector cross products.

Ed.

Yes , I know the definition of pseudo vector, but if you get into this

better find a substitute for the Lorenz force law, or the definition of torque in mechanics. These effects, the Lorenz force or torque are real in physics.

Maybe you can interprete the Lorenz transformation as giving a different

effect than your word fusion...but the math is still the same. It is not customary to describe this as a fusion(to be the same). The concept of space and time are different. IE. apples do not fuse with oranges.

You wont deny that he uses the Lorenz transformation? So far I think your argument is pure lingustics.

Juan Weisz : All this is solved using tensors, that are OK mathematically and physically. In SR and GR spacetime, tensors are used. The same mathematics we weed to use in EM. The E field has then the same units as the B field, there is only the EM field. Then gauge theory has an intrinsic meaning, of identity relationships.

Using the Lorentz transformations is not the litmus test for doing SR according to nature. In fact, if it comes before spacetime, it is incorrect. You can consult Burgess [2], he explains better. Again, it is not about the truth value of "classical".

I dont get it, if you object to how your pseudo vector transforms. then you could also object to how your tensor transforms, if it is an equivalent description.

Because all it is in practical terms, a vector that you need.

You do not necesarily improve with fancier math. In fact this might force all students to learn more difficult stuff, dont see the advantage.

You will become someone trying to explain Physics using the absolutely latest and highest mathematics available, so we should all resign and make way to mathematicians.

Juan Weisz : It is not a circular argument, nor linguist tricks. Copying from a current preprint in RG, where you can map the References back to the numbering system used in text of the discussion:

"CHOICE OF MATHEMATICS:

The treatment of SR in [1, Serway] considers the use of the Gibbs formalism in vector spaces, according to multivariable calculus (as studied in multivariable calculus). This uses the common version of Calculus Algebra, with scalar and vector products.

In this treatment, we will have to leave behind these concepts. A higher methodology is invited by Clifford’s multivectors, in what’s called STA, or Spacetime Algebra, used in SR. This, however, is not sufficient, so this work follows [3, Burgess] in working with tensor spaces. The reasons are summarized below, and they offer an easy on-ramp to GR [4, Taylor, Wheeler, 5-8, E. Gerck]:

1.1. DO NOT USE VECTOR CROSS PRODUCT: The 3D vector cross product is not a vector, but a tensor. This is well-known and the reason to invalidate its use in Maxwell's equations, and physics equations. This is both a physical and a mathematical reason, commented below.

1.2. CONTINUED ERROR: The vector cross product does not serve even a restricted purpose adequately, as it can create mistakes upon reference frame change, for example, simple mirroring, gives us wrong units in the SI MKS, worldwide, and this is all old news that have to be somehow continuously repeated, with a “life of its own,” as a misconception in even current college books at competitive US universities.

1.3. MATHEMATICAL REASON: The 3D vector cross product is not a closed operation in the set of 3D vector space, it produces a member that does not belong to the same set, the 3D vector space, although it may look like it in some cases.

1.4. PHYSICAL REASON: Both sides of an equation representing a physical relationship, such as A = B, must change equally when the frame of reference changes and the so-called inertial condition is obeyed, as already stated by Galileo, Newton, and Einstein, that the laws of physics are the same for all uniformly moving observers.

1.5. POLAR AND AXIAL VECTORS, PSEUDOSCALARS: If one writes an equation using a 3D vector cross product, such as A= B x C, the left and right side may transform differently if the coordinate frame of reference changes, while still inertial. In the past, this was accommodated, not solved, by considering spurious things such as polar and axial vectors, and pseudoscalars. This is solved using tensors, which maintain the form A = B under inertial reference change.

1.6. MULTIVECTORS ARE MATHEMATICALLY SOUND: In geometric algebras, or Clifford algebra, or Cl(n,1) algebras, or STA Hestenes algebra, multivectors solve the mathematical reason (1.3), creating a closed space in all operations. No geometric algebra operation is mathematically unsound.

1.7. MULTIVECTORS NOT PHYSICALLY SOUND: Multivectors do not solve the physical reason (1.4), but tensors do. This is another reason, besides lack of isomorphism with tensors and no use of time as a coordinate in spacetime, that invalidates the use of geometric algebras in equations of physics, including electromagnetism.

1.8. MULTIVECTORS DO NOT INCLUDE TIME AS A DIMENSION, THIS CAN NOT BE FILTERED: With multivectors, if one eliminates the physically wrong results, by requiring an additional step of “filtering” through, let us say, a Hamiltonian, this will not produce those results that are physically valid but were ignored in the first place, using just multivectors. A sequence of filters cannot filter less than the first filter, well-known in physics, math, and engineering. This appears, more easily to see, in non-euclidean spaces, as will be seen."

From (PDF) On Special Relativity Applied to Accelerated Motion, II (tutorial). Available from: https://www.researchgate.net/publication/328416821_On_Special_Relativity_Applied_to_Accelerated_Motion_II_tutorial

Traditionally in USA the physics with calculus for science and engineering was taught in three semesters.

1. Mechanics, heat, light (optics), and sound

2. Electromagnetism

3. Modern physics, particles, quantum mechanics, and atomic energy

Mechanics advanced content was taught in the engineering civil and mechanical departments as another three semesters for all engineering students.

4. Statics

5. Dynamics

6. Strength of materials

Electromagnetism was further developed in two more semesters of electrical engineering given to all engineering students.

7. Circuits, amplifiers, data, and communications

8. Power supplies, transformers, and transmission

The reason for the exquence was straight forward. A concept of forces, momentum, and energy are needed before attempting to teach electromagnetism.

Starting about in year 1970 some leading universities began to shorten the engineering programs that were seldom finished in four years, My first baccalaureate program was 169 semester hours including another two semesters of physics, and several other engineering courses that were not in my major field. Courses were eliminated, combined or pushed into the masters programs, causing me to decide on attending graduate school. My counselor went to teach in England while the changes were being made in USA.

The first physics course was revised to emphasize the mechanics content and renamed Mechanics and Heat. Sound and Optics were put into the second physics course and renamed Electromagnetism and Waves. The third physics course was dropped for most engineering students. The five engineering courses were reduced to one lecture each or less except for students in that major.

The courses and sequences were developed with considerable effort and time spent. To change them would require an enormous program of redevelopment.

I've been mentoring new engineering graduates for about 30 years and find they are well prepared to do routine work and things that can be found in magazines or books. The part that is lacking in education is the ability to bring seemingly unrelated things together into substantially new concepts and new inventions that can be constructed and tested.

For the present question mechanics before and after electromagnetism is helpful. Also electromagnetism before and after mechanics is helpful. Something is lost if the topics are compressed into one course each, and the order of teaching one or the other first must be chosen.

If you turn the vector product into a tensor, you do not get the right kind of

object for physical intuition, it just forces you to become more abstract.

Let me get this straight, you turn the cross product into a 2 tensor, or a one tensor

(the last is a vector)? In terms of matrices 3 by 3 or 1 by 3?

For an equation, you must have the same math object on both sides, so your equation involves 2 tensors only? Then how do you interprate your 2 tensor as a vector?

What I think you mean is that this operation involves a two tensor times a vector, giving a vector, which leaves you to say that the two initial vectors are not equivalently reperesented, which is rather acqward.

Juan Weisz : Abandon Gibbs vectors, that is what it says explicitly. Gibbs vectors never worked, even when one thought we all lived in 3D.

Some of us live in a 3D universe, others in a 4D universe. We can relay our experiences to each other, and even with all goodwill, our 3D or 4D experiences cannot be communicated to each other, a theorem in topology tells us.

We're a bit like a fish and a bycicle, from a German proverb, moving in different ecosystems.

Jerry Decker : Thanks for your input. A lot of time goes also to humanities classes, that people could just read about. So, the instruction goes into what could be reading time, for example, in mechanics at Newton level, and real classes could use Lagrangian for future courses. That way, the suggestion by Januzs, as in Norway, seems feasible. And would allow EM earlier.

Ed.

Now you want to do away with vectors themselvs...

An impossible task. Maybe 200 years from now they wont be used.

Now the prevailing view is that the electron theory was wrong. I am afraid that that is rather a simplistic view. It is now clear what in the electron theory was undoubtedly wrong – e.g. the electron is not a small sphere of charge. A completely wrong theory cannot make a number of correct predictions – e.g. the electron theory predicted that the electron mass increases with increasing velocity before the theory of relativity, yielding the correct velocity dependence, and that the relation between energy and mass is E = mc2. That is why it is maybe more appropriate to say that today “the state of the classical electron theory reminds one of a house under construction that was abandoned by its workmen upon receiving news of an approaching plague. The plague in this case, of course, was quantum theory. As a result, classical electron theory stands with many interesting unsolved or partially solved problems."

in P. Pearle, Classical Electron Models. In: Electromagnetism: Paths to Research, ed. by D. Teplitz (Plenum Press, New York 1982) pp. 211-295, p. 213; quoted in H. Minkowski, Space and Time: Minkowski's Papers on Relativity. 2012. Online at: http://rgs.vniims.ru/books/spacetime.pdf

Maybe you are right, electromagnetism and the quantum eventually have something to do with each other.

But as SR and the quantum, except in the case of the Dirac equation, have nothing to do with each other and seem to collide in philosophy, we do not have much to offer students with right now. In optics maybe , quantum optics.

I don't believe vectors will ever be eliminated, even if some other construction becomes more common. Vectors can be constructed and understood more easily than other proposed objects. Tensors do not replace vectors. Tensors supplement vectors. Quaternions have been recommended and have a purpose, but there is no compelling reason to eliminate vectors.

Quantum is in the direction of Dirac, Schrödinger is non-relativistic, thus false. Philosophy is not science, mostly subjective, rejects nature as the arbiter, a different ecosystem.

The course in Norway, above, a good example. Gibbs vectors didn't make it, not forward looking there. Students can focus on research, that will pull them to what works, even in industry. The book by Carver Mead, of Caltech, could also help in EM -- an electron can be a kilometer long. Collective effects.

The wave function may be a kilometer long.

the electron is the same as always. You confuse probability density of finding with the object itself.

Historically Gibbs vectors were an outstanding succes, read the history of math.

They displaced almost all other funny ideas.

Scrodinger is just the low speed approximation, very practical. Much more used than Dirac, due to some concerns with relativistic quantum theory.

The trend seems to be avoid both for quantum field theory, but this is still premature.

Juan Weisz and all: The wave function goes to infinity. I was not talking about that, but how to define the "length" of the electron -- it is not what Jackson says. Anyone doing superconductivity knows that the electron is not a small particle.

Gibbs vectors are not used in Lagrange or Hamilton methods, quantum mechanics, no real-world engineering, no real-world electromagnetism.

Gibbs vectors cannot be used in 4D. We live in 4D. If you think we don't live in 4D, don't take just my word for it -- rotate an object as slowly as you please, and make sure you do not have gimbal lock. You can not, unless you use quaternions. You should not have gimbal effect, just smooth Euler angles, if this world would be 3D.

But this all can wait -- students today need to get faster to EM that works in real-life. Some will, that is enough, the numbers will grow, by their very success.

Those who stay years in Gibbs vectors, Newtonian mechanics and non-quantum, non-spacetime SR in mechanics and EM in Jackson, will be included later, that's all -- nothing is truly lost. And their numbers can reduce too.

Ed

Still dont get you at all. The electron may have a radius, but not a length. The wave function may have a length.(as wave packet)

(do you claim both are the same thing?) I dont believe Jackson talks about a length for the electron. Its Classical Electrodynamics, not the quantum, in his book.

Cooper pairs, two bound electrons, behaving as a boson is relevant in superconductivity.(which sais nothing about the electron

itself). Electromagnetism is full of vectors, vector analisis is a must in this field. If you like vectors are also perhaps cartesian one tensors, so you may get away by using that term instead.

True that that the Lagrange and Hamiltonian theory use scalar densities. Maybe you can go around evading vectors for a while, I cannot.(what do you use instead to indicate a direction?)

4 vectors are alive and well in SR, nothing wrong with that. They exist in any dimension you like. In the infinite dimensional limit you treat functions as vectors to form Hilbert space. Just read about vector spaces. The inner product

of two functions in the quantum is analogous to that between two vectors.

Read Goldstein, Classical Mechanics about rotations. He does not use quaternions.(thats old fashioned!)

Well, your turn I guess

regards, juan

Juan: I could not make sense of your comments, traffic? For example, that 4-vectors exist in any dimension I like -- how about in two dimensions? This is also off topic here, which is about college students learning EM before mechanics, an option that some can have today.

Why not more students learning EM sooner? We are creating a society of historians, in science. We should trim the fat and go faster. Useless counterpoints will not help, just traffic. Stay in peace.

4 vectors are for space time, four dimensions.

Yes there are vectors also in two dimensions, Complex numbers can be considered such.

Sorry , I meant to say that you can have vectors in any dimension, constructing a vector space for it.

Whats the rush to learn ENM?

The reason I can see is that it takes time to learn about vector analysis, Stokes, Gauss, line integrals, divergence , curl, and all of that. I would not dream about doing this without vectors.

Its not trivial for students.

Juan: It is done today, in Norway, the US, and even online. Gibbs vectors are a poor base, ends in 3D, and not even there. Scientists are not so much into history, to study it too much. Lagrange and Hamiltonian methods used in EM and quantum to not use vectors. We need to advance education, there is more to learn. Vectors are already learned in high school.

Then you are asking students to learn the calculus of variations and Clasical field theory as in later chapters Goldstein?

Do not believe it too much. Tell me what books you use.That is not undergraduate stuff. At any rate the applications of this lie in Classical mechanics as well.

(principle of least action)

Again in vectors, you do not end up only in 3D. Maybe you do not understand the further developments of vector analysis.

Juan, please look earlier in this thread, for example posting with Norway example from Januzs.

My preference is to take the mechanics first to learn about energy and momentum, then take electromagnetics. In practice of sandwich studies (Co-Op) the students schedules get out of alignment with the catalog. The advisor approves courses out of sequence on a routine basis, sometimes concurrent courses, signed with a smile. The student copes with determined spirit, and later excels in the career that follows.

It is effective to take EM concurrently with SR, for example, as EM must be SR.

Indead, SR and EM are not the same, but EM is consistent with SR to a great degree, so that it is quite natural

to teach them a la par. EM at least in parallel with definitions and theorems of vector analysis, you cannot write normal form

Maxwell without this.

Jerry is giving us the normal sequence, first understand basic physical ideas. Students normally should take three ground level

physics: Mechnics, then heat and thermo with a bit of statistical mech, then modern physics. Later comes your stuff.

Expediency says to not use college subjects that are not used in research for more than 100 years. Let those subjects die in college. College students learned about vectors, Newtonian physics and calculus already in high school and AP courses. Physics and engineering in college can start with Thermodynamics and Calculus II. This can shave off one year of repetition, and wrong ideas. Remedial college students can have Newtonian physics and Calculus I, maybe also students in biology courses.

I see some very confused people on RG, presumably because they have dived into EM without knowning say the atom or

static electricity. Maybe they are the victims of your kind of system. I know that in Europe they have short University courses

assuming they have all the background from high school, but its good maybe to talk about the average student and not the brilliant ones.

Really I find some of the attempted research really dishartening, it does not serve if you just invent grandious terms which are supposed to be somwhat relevant. Not you, but some on RG. That way, imposible to distinguish ground breaking work from sheer rubish.

For a practical example of how to accelerate SR and GR in college education, please take a look at https://www.researchgate.net/post/Can_college_sophomores_develop_a_notion_of_general_relativity

CONCLUSION: Yes, college students should learn about electromagnetism before mechanics, rather than alternative non-covariant descriptions such as Newtonian mechanics.

First, vectors are a major hassle and consume too much time, considering their minor importance today. Rather than vectors (forces) in Newtonian physics with F = ma, students already can focus on the Euler-Lagrange equation, or Lagrangian, where one does not use vectors because the equations of motion are based in scalars (energy).

Further, in probably most physical situations, the Euler-Lagrange equation has been superior, for about 250 years, to using F = ma (even when F = ma is valid) especially where it is not, such as inside an atom or near a large mass, and electromagnetism is of more importance today.

More at Preprint New Physics with the Euler-Lagrange Equation: Going Beyond Newton

Ed.

Hope you are not about to try out your ideas on actual students, you want to throw them into the calculus of variations before vectors or simple derivatives. By the way vectors are vital in Maxwell, at least vector analysis is.

However I have seen some Russian authors base it all on principle of least action, but assume their students already have some certain background.