Yes it is.Electromagnetism is the first step toward a unification of the so called natural forces or interactions. In about 1984 ,Maxwell unified the electric force(now electric field E),as was discovered by Faraday(Fe= Kq2 q1/R^2), where K is constant,q1 and q2 ,interacting charges,with the magnetic force(now magnetic field B.Magnetic force given by Fm=C mM/R^2 .So Maxwell unified these two fields into one unified field called the electromagnetic field as a wave like field its components aer E and B perpendicular to each other. The energy is continous(not quantized),at that time with the classical mechanics and Lorence transformations,it was thought the theory of physics is completed,it can explain any natural phenomenon!!
But faced the new discoveries in 1900,quantization of energy(Black body radiations) and others such spectra quantization of atoms,and the discovery of a constant represent the boundary between classical physics and quantum physics,it is plank constan h=6.63X10^-34 Page on joule.sec.as h=0 we are in th realm of the classical physics, i.e. Classical physics is a limit to quantum physics as h approaches zer0.

It is taught in the framework of classical mechanics.

There’s a branch of quantum mechanics called quantum optics, where they deal with EM waves at very low intensity, where you can do experiments with only a handful of photons.

Quantum mechanics “quantizes” the wave, that is, deals with it as particles. I guess you know that quantum mechanics brought about the realization that everything can be described as waves or as particles. Quantum optics deals with EM waves as particles (photons). There are things there which are hard to visualize, like how a single photon can be polarized, or have orbital angular momentum - but they do.

The macroscopic world is still very accurately described by classical physics. Even when there is a more accurate theory at the quantum scale, in our lives, many processes appear which are well described by classical physics. So it is still of great interest to study the implications of classical theories - even though we know that they are not as accurate as others - we know that they are accurate enough to predict many things which appear at the classical scales… such as just about every property of light.

But in the case of electromagnetism, it holds at even smaller scales - by using quantum mechanics to quantize an atom, considering the electromagnetic interactions to be described by classical electromagnetism still provides very accurate predictions!

The whole point is… classical physics is still useful, even though we know that at certain scales it loses its accuracy. The scale where it works well is enormous, so why throw classical physics out, when it’s much simpler than quantum physics, and still can make extremely accurate predictions?

1

For classical mechanics, there is a huge base of certified science. Levers, Newton’s Laws of motion.

1a

The great missing piece is the ‘extra 1/r’ that keeps electrons in shells. The Bohr ‘orbital’ ‘angular momentum’ model fails for various reasons.

1b

For example, why is the Periodic Table 2, 8, 8, 18, 18, 32, 32? Why not 2, 4, 6? Why not 2, 8, 18, 32? That particular chain should have a classical mechanics reasoning for it.

1c

Gravity causation has not been solved. We know the behavior, but not the causation and how it fits with electromagnetism.

1d

What is mass? While we have a macro-world understanding, it become very difficult to understand at teh subatomic level. How does a photon have energy, but not mass.

1e

Thereby, Newton’s 2nd Law and its acceleration equals Force / mass (a=F/m) then become abandoned.

2

For electromagnetism, we are missing the causation for magnetism. We have the behaviors (Maxwell’s equations), but still not a direct link building to apply those remains missing. What makes that big at the equator flowing to north and south at each end.

3

Unfortunately, quantum theory does not quite solve those either. QM, QED, QCD, and QFT work by taking as given those assumptions, and are great and determining predictions for the set of behaviors.

4

I still believe these can get discovered and understood. Join the quest!

Much of the research in these two fields is toward recasting these fields in geometric language as this book suggests.

This book is a geometric formulation of classical mechanics.

Well as you know, classical electrodynamics is a pretty difficult subject. The basics are easy, but the more you study it the worse it gets, with runaway solutions and effects happening before their causes if you are not careful.

But it turns out, quantum field theory is much, much worse. Especially if you want to get to the point where you can get numerical answers out of it rather than just marveling about the concepts. Most physicists probably never master it.

The classical theory is just fine for most purposes. Back in the 1960s, E. T. Jaynes proposed that quantum field theory was not needed to explain the results of any conceivable experiment involving the electromagnetic field. It took several years for him to be proved wrong, because he is almost right.

When modeling experimental results, the important first step is to choose the correct tool for the job. Quantum field theory is the wrong tool in most cases.

According to the Correspondence principle, quantum mechanics must reduce to classical mechanics in the Classical limit. Thus, quantum mechanics should be seen not as a different theory entirely but as a generalization of classical mechanics to smaller scales.

This is similar to the requirement that special relativity reduces to classical mechanics at low velocities (relative to the speed of light) and general relativity reduces to Newtonian gravity for weak gravitational fields.

As a quantum system becomes larger, it experiences Quantum decoherence and gradually loses its quantum properties. Classical mechanics becomes a better and better approximation the larger the system is, until at some point the difference simply becomes unmeasurable.

It's unclear where exactly that point is. Obviously, subatomic particles must be described by quantum mechanics, while the dynamics of tennis balls may be described to an arbitrary degree of accuracy using classical mechanics. Objects as large as Buckminsterfullerene molecules ("buckyballs"), which are made from 60 carbon atoms, have been shown to have observable quantum properties.

However, it's important to clarify that quantum mechanics always applies, to any system of any size. In the classical limit it simply becomes unnecessary for any practical purpose. Similarly, general relativity always applies to any system of any size, but when you want to calculate the movement of a ball sliding down a ramp, you don't need to solve the Einstein field equations and/or the Schrödinger equation, you can simply use the equations of Newtonian gravity and Newtonian mechanics, which are much simpler and produce results that may be verified experimentally to a very high degree of accuracy.

Electromagnetism, electronics, and mechanics are all closely connected. Electromagnetism is the study of how electric and magnetic fields interact with each other and how they can be used to generate and control electric current and power. Electronics is the study of how electric circuit components, such as resistors and capacitors, interact with each other and how they can be used to create electrical systems. Finally, mechanics is the study of how forces and motion interact with each other and how they can be used to create and control machines.

The connection between these three fields is that each uses the others' principles to create useful devices and systems. For example, electromagnetism is used to create electric motors and generators, which are important components of many mechanical devices. Electronics is used to create circuits and systems that can control the operation of motors and other electromechanical components. Finally, mechanics is used to design and build machines such as cars, robots, and aircraft that can use the energy generated by electromechanical components.

The connection between electromagnetism, electronics, and mechanics can also be seen in the development of new technologies. For instance, the development of electric cars and other alternative energy technologies has been made possible by advances in all three fields. Similarly, the development of new robots and autonomous vehicles has been made possible by advances in all three fields. In short, the connection between electromagnetism, electronics, and mechanics is essential for the development of new technologies and devices.

They are called Maxwell's Equations, after James Clark Maxwell, who codified them in a unified framework. In simplest terms they say:

Gauss' Law- The net electric field leaving a closed area is proportional to the electric charge contained in that area.

Gauss' Law for Magnetism- The net magnetic field leaving a closed area is 0, because there are no isolated magnetic charges, called monopoles (as far as we know.)

Ampere's Law, as extended by Maxwell- Electric currents and changing electric fields create magnetic fields.

Faraday's Law- Changing magnetic fields create electric fields, as would a current of monopoles if such a thing existed.

In physics, it is often true that theories or theoretical paradigms with vastly, "qualitatively" different assumptions and "pictures to imagine what is going on" yield virtually indistinguishable predictions, and Newton's vs Einstein's physics is the simplest example of that.

According to Newton, for example, time was absolute. According to Einstein, time depends on the observer but time $t^{\prime }$ according to one observer is expressed as a function of time $t$ of another observer as

This approximation is good at low enough velocities,

$v\ll c$. You may see that the "times" only differ by a small number that depends on

$1/c^2$ which is 10^-17 in SI units (squared seconds over squared meters). They're different in principle but the difference is so small for achievable speeds that it is (almost) unmeasurable in practice.

Similar comments apply to many other phenomena and deviations. Newton would say that they're "strictly zero"; Einstein says that they are "nonzero" but their size is tiny, comparable to

$1/c^2$times a "finite" expression.

Analogous comments apply to classical physics vs quantum mechanics. Classical physics often says that something is strictly impossible, some quantities are zero, and so on. Quantum mechanics says that they are possible, nonzero, etc. but their numerical size is $\hslash$ times a "finite expression" which is again unmeasurably tiny for macroscopic objects.

In both cases and others, one may prove that the

$1/c\to 0$ or $\hslash \to 0$ limit of the more complete theory is exactly equivalent to the older theory. So (special or general) relativistic physics reduces to Newton's physics in the c→∞ limit, for example.

So, classical mechanics is valid even today, but at small speeds only.

Hope this helps.

Source : Did relativity make Newtonian mechanics obsolete?

Thanks for your A2A

Physics becomes classical when Newton's second problem is solved in a certain way. It implies that it is possible to “guess the forces causing it from the observation of a movement.” At the same time, the movement is understood as defined by Aristotle: movement, or change, or transformation.

In all cases of motion, classical physics assumes that the desired forces are unchanged and generate many motions that do not affect these forces. Under these assumptions, the kinematic equations (the equations of the Frenet line) can be solved in a general form, known in particular as the Second Newton Law.

The equations of electrodynamics also follow from the same kinematic equation, but under different conditions. In particular, it is well known that the movement of charges has a significant effect on electromagnetic interactions.

However, the most significant thing is that electromagnetic interactions cannot be represented in the form of Newton's Second Law. The reason is that mutual induction leads to the appearance of a dynamic impact, which has a component in the direction of binormal of the corresponding trajectory of movement.

As a result, the kinematic description of electrodynamics is quite classical, but dynamic is not.

Quantum mechanics is one and the same with that of classical mechanics! It is only our perception of classical mechanics that is the limiting factor in understanding the association between the passage of electrons, and quantum energy states and/or quantum entanglement.

Electrons exhibit dual properties; both as particles, and distribution of charge.

This implies that the position of an incoming electron is determined by the regional variations of electrical intensity between shells. Electric fields occupy physical regions of space; and the numbers of electrons with each shell determines the intensity within each shell.

Just as there is a pressure gradient within the air of the atmosphere, with higher altitudes compressing lower altitudes; so too is there gradual progressions of varying levels of electrical intensity of charge between consecutive shells of an atomic structure.

It may therefore be concluded that the volumetric distribution of a combination of all electric charges corresponds to the exact parameters of each shell. We have now revealed the specific dimensions associated to one or more atomic orbitals.

The next step is to explain why electrons are restricted to quantised energy states, which correspond precisely to the dimensions of each shell.

Orbiting electrons have a natural tendency of establishing circulating electric fields. The circulating motion establishes an energy efficiency that similar to that of a swirling tornado. Swirling energy efficiency resists change, enabling a tornado retains its shape. In the same manner, the energy efficiency of swirling electric fields retain their shape, and in the process resist change. This resistance to change has two fundamental properties, that not only restricts electrons to quantum energy states, but actually stops electrons from plummeting into the nucleus.

This implies that energised electrons resist what would otherwise be a gradual expansion of their orbiting circumferences, until such time that there is enough energy to break the energy efficient cycle; thereby defining the parameters of the combined swirling electric fields, which in turn correspond to the precise dimensions of each shell.

It may therefore be concluded that electrons are restricted to quantised energy states that correspond to the parameters of each shell.

If the SLA concept is credible for explaining electron quantum energy states; then there needs to be a justifiable explanation for the electron double slit experiment as well.

It has been stipulated that the failing of the present atomic model; is that electric fields having been totally neglected as active constituents of atomic structure. As it turns out; the same failure applies to electron double slit experiment as well.

Electrons exhibit properties which are electric in nature. This implies that moving electrons possess an associated moving electric field that expands outwards from an electron. Moving electric fields exhibit properties of a moving wavefront. The moving electrical wavefront is quite broad and therefore penetrates both slits at the same time; and more importantly possesses wave like properties which diffract when penetrating small openings.

It therefore becomes apparent that a moving electric field wavefront (magnetic field) that diffracts as it penetrates either of the small slits; has capacity to produce an interference pattern, when it interacts with its own individual electron; which penetrates any one of the two slits.

When an observer is placed at one of the slits; it interferes with that particular wavefront causing the circular diffracting waves to collapse and revert to straight waves. As a consequence; there is no diffraction, or resulting interference pattern; so electrons revert to properties as individual particles.

Quantum entanglement is not required to explain the weird behaviour that is taking place. It is simply physics doing what comes natural.

Electrons do not have an intellect to know when they are being observed; and the same applies to opposite spin electrons in the Stern-Gerlach experimental results; in which the act of observation is purported to make an electron take on one of the two spin states.

This is pulling a rabbit out of a hat reasoning that is based on nothing other than hypothetical uncertainties.

It therefore becomes apparent that Quantum mechanics and Quantum entanglement has no role to play in any of the above examples.

The SLA Atomic Structure research article can be downloaded free of charge from the International Journal of Science and Research.

Thank you once again for your time.

All ACCELERATING charged particles emit EM radiation - although things get a little murkier at the quantum level, and I would re-phrase to say that a charge “changing energy states” usually emits radiation (then there’s the Auger effect . . .).

Whether emission by an accelerating charge is oart of “classical mechanics” is debatable. Mechanics does not usually deal with electric or magnetic fields (although it deal with GRAVITY, which, since Einstein and certainly today is considered to involve a “field.)

I suspect that any attempt to divide physics into separable compartments is doomedto failure if pushed too hard. But university courses in “mechanics” do not usually deal with emission of radiation, SFAIK.

For Classical Mechanics, I strongly recommend the lecture notes of Dan Arovas at UCSD

I think this includes both terms of the course. I have looked through a few other texts, and none were better than these notes.

For electromagnetism…it’s just Maxwell’s equations. In my view, Wikipedia is fine for an introduction. D. Griffiths Electrodynamics is the standard undergraduate textbook, but all of the homework problems are “cute” and have special solution tricks that aren’t useful in real life. J. D. Jackson’s Classical Electromagnetism is the standard graduate text. It is dense, but good. It is all about picking the right “series expansion” to tackle a problem approximately. Exact cute solutions are not emphasized.

However, for lots of modern theoretical physics research and for casual interest, you really don’t need to learn much about classical electromagnetism beyond knowing Maxwell’s equations and Coulomb’s law. The reason is that most modern research falls into the categories of

(1) Condensed Matter and Atomic/Molecular/Optical physics, where we ignore most of Maxwell’s equations except for Coulomb’s law and consider materials directly in the context of quantum. This basically re-invents the theory of electromagnetism within materials (as opposed to in free space) taking quantum as given and working out the rest. We rarely worry about Maxwell’s equations.

(2) High Energy / Particle physics, where only quantum electrodynamics are needed, and for which Maxwell’s equations are sufficient. The contents of Jackson may be useful preparation for doing difficult calculations.

(3) Astrophysics, Cosmology, and Gravity research, where gravity is the most important interaction in general, but mostly you just need Maxwell’s equations and some knowledge of “radiative processes”.

Basically, you mostly only need Maxwell’s equations if you care about building antennae and waveguides and doing optical physics. Then it’s very important and I suggest Jackson for sure, although there’s probably books focused on optics that are more useful!

For quantum mechanics, I think the books by Shankar and Le Bellac are the best for an introduction. Both books teach quantum in the order I think is less confusing (not how it’s usually taught at universities, which is historically motivated and confusing IMO).

Sakurai is good for grad students who are somewhat familiar, as it is condensed and great to bring with you to an open-book exam. The homework problems in Sakurai are cool.

I also highly recommend this set of notes from John McGreevy (also UCSD)

As an aside, you’ve left out one of the most important subject, which is Statistical Mechanics. Once again, I recommend Dan Arovas’ notes

while I find most books are not that great. However, Mehran Kardar’s pair of textbooks, Statistical Physics of Particles and Statistical Physics of Fields are excellent as an introduction and very well written. They’re also good reference texts, although the homework problems aren’t my favorite.

For more advanced subjects, I also strongly recommend other lecture notes by these two. John McGreevy’s can be found here, and include General Relativity, Symmetry in Physics, Topology in Physics, Advanced Quantum Mechanics, Advanced Quantum Field Theory, Quantum Information, Renormalization Group, Special Topics In Quantum Field Theory (i.e., how to get QFTs from quantum mechanics, instead of just quantizing classical theories), and Quantum Phases of Matter. Dan Arovas has Superconductivity, Condensed Matter, the Quantum Hall Effect, and I’m sure more!

You can learn a TON of physics from the Books of Daniel and John!

Classical mechanics has everything made of bits. That means that you can take a thing and break it down into smaller bits. In principle there is no end to breaking the bits down.

Hang on! If we continue down that path then there would be an infinite amount of infinitely small bits.

That's sort of where classical physics becomes unstuck.

Now we can go to the beach and see waves. But because they are classical waves, we know that they are just made of bits.

But then light seemed to behave as a classical wave as well. So what are light bits?

We can build a mathematical model of waves. Waves are sort of a concept in the propagation of some influence. So let's forget about the bits for a moment and concentrate on the propagation of influence. Let's develop a wave theory. Maxwell did it for light. There are no bits in Maxwell's theory, there are sources and fields.

Similarly with water waves. They can be a thing in their own right. You can describe them mathematically without recourse to using bits. Afterall what really is a bit?

Now remember that bit problem; the infinite amount of infinitesimally tiny bits. Well it turns out that even the ancient Greeks had put a stop to that infinite regression. The concept of the atom is the concept of a smallest bit.

Now you really have to think deeply about what that actually means. The idea of bits is very intuitive. So much so that you might be tempted to think of an atom as a bit that you can't cut, or subdivide. But what the hell does that actually mean? What makes the nature of bits suddenly change?

So let's consider an electron as an actual example of a bit. If you think of an electron as some tiny ball, then you're falling back into the bit model of the universe. If it's a tiny ball, then why can't you cut it in half?

Remember that we also have a theory of waves, which is essentially a theory of how influence propagates from place to place. That's a different conceptual way of looking at the world. Yet it is pretty reasonable to ask about how something influences another thing. We're no longer thinking about cutting things into smaller bits, but about how one thing influences or affects another. It's a different, alternative, but actually very useful way of looking at the world. It's how things affect other things that makes the world interesting.

It just turns out that this alternative way of looking at the world still works when the bit model fails. At some point when bits no longer make any sense, the model of how things influence other things still holds. It doesn't ask what a bit is, but rather how it affects other bits. Turns out that that's a very useful thing to know.

So here's what we do: We throw out the bit model when it becomes silly, but we keep the wave model, because that's still useful. Sounds like we have the solution right there.

Uh oh… there is a problem. The wave model does a pretty good job at explaining observation at the microscopic level, but at the expense of bits having no defined position at all.

It turns out that waves describe the propagation of influence very well, but we need to understand how one point influences another point, and waves influence many points, which is essentially their property.

Therefore we need to bring back some concept of the bit, and that is that it is localised.

Thus quantum mechanics is a theory that tells us how one localised bit can influence another localised bit at some different location. It marries the localisation of the bit with the influence propagation of the wave.

What we have done is taken the two most essential concepts of wave theory and particle theory and merged them into a single theory that works remarkably well.

Thus quantum mechanics is a culmination of classical thought brought together in order to understand the world we observe by framing a way to understand its most fundamental parts.

We call it a new thought, but in reality it just keeping the parts that actually work from classical thought, and discarding the parts that don't work.

It seems like an interesting question, and one that I can only answer in part. The basic premise of quantum mechanics is that a particle (usually) does not have any definite state before it is observed; it exists as a waveform with multiple possible states until it is observed, at which point the waveform "collapses" into one of its possible states. This leads to all sorts of problems in trying to predict the outcome for experiments where we don't know exactly when they will happen - what we call uncertainty or indeterminacy.

This is where classical mechanics comes in. Classical mechanics does not have this regression effect, and describes the world as having a definite state before being observed; if you knew all the initial conditions of an experiment (such as its mass, velocity, direction of motion etc.), you could predict exactly what would happen to it no matter when it was observed.

It is common to think of the relationship between classical and quantum mechanics in this way: "Classical Mechanics" = "The Universe we experience""Quantum Mechanics" = "The underlying reality that gives rise to our universe.

The problem is that this gets things backwards. It's true that classical mechanics describes the world as we experience it, but quantum mechanics does not describe some "underlying reality" with which our universe collapses into when observed (as was first supposed).

Instead, quantum mechanics describes the universe as we experience it. Classical mechanics is just a good approximation for the behavior of macroscopic objects in our everyday lives.

The reason that the classical mechanics model breaks down for small objects is not because some special "quantum" physics takes over, but rather it's just a mathematical consequence of how our universe works.

I would suggest learning universal gravitation very thoroughly, and then drawing many parallels between it and electric force as you can find (there are many.)

Many people use the hydrodynamics analogy; much of the same math for water flows was reused by Maxwell to describe electric and magnetic fields. Beware of weaknesses in the water-in-pipes analogy for circuits, however. Double check each correspondence, because some do not hold, it is an imperfect analogy.

My mental picture of fields is the usual “field of arrows” like a field of tall grass, all blown outward from a positive charge as if from an explosion. It is imperfect (of course) because it isn’t three dimensional.

Absolutely track all of the units in all of your quantities meticulously. They can save you a great deal of confusion in mixing apples and orangutans.

Magnetism is harder to conceptualize. You might consider what a “gravitational dipole” would be mechanically, (think helium and lead), compare to an electric dipole, and compare that to a bar magnet.

Personally, I have always had a vague impression of magnetism as being a sort of “angular momentum” of electric charge. It helps my intuition in seeing which way currents will be induced.

I have always meant to sit down and work through all these analogies in more detail to learn their limits properly. Thanks for the reminder!

Good luck!

Put very simply, they are related in that both theories postulate that light is made of light-waves. Quantum theory is a more up to date version of classical theory regarding light. But neither theory is correct. In contemporary physics it is increasingly becoming apparent that light is entirely made of separate moving photons and nothing else at all.

All kinds of light (laser, electromagnetic radiation, white light, coloured light, x-rays, gammas rays, radio waves, invisible light, torch light, candle light, sun light, moon light, refracted light, ‘reflected’ light, etc) are all absolutely identical. All kinds of light without exception are made entirely of separate moving photons and nothing else at all. Each photon is nothing more than a tiny speck of oscillating electromagnetism, always moving in straight lines. All photons in the Universe, in all types of light and electromagnetic radiation, are totally identical to each other in every way.

The only difference (emphasis on ‘only’) between these various ‘kinds’ of light and EM radiation is the physical distance between the moving photons. If the distance is small it means a bigger concentration (a larger amount) of photons in a given light ray. The degree of the concentration of photons determines the degree of energy (the strength) of the light ray. For example, a laser has very concentrated photons with very short distances between the moving photons, hence a laser has high energy. The photons in laser light are identical to the photons in radio waves. The frequency of light is simply how frequent the photons appear in a given bunch of photons, i.e. the greater the concentration of photons the greater the frequency of photons.

Confidence in Newton's laws and Maxwell's equations is very high, and all available evidence points to them being essentially sound as classical theories. But physics is an experimental science, so it's not possible to tell if any of it is "finished," as a new experiment could always raise new questions.

There continues to be plenty of research investigating the consequences of those laws in areas such as turbulence in fluid flow, plasma physics, and chaotic dynamics, in which nonlinearities and other complications give rise to sometimes surprising phenomena. So far though, it doesn't appear there are any fundamentally new laws underlying them. And unless and until magnetic monopoles are experimentally observed, Maxwell's equations appear to be sound.

I assume you’re asking “Why don’t we just learn quantum theory and leave it at that?”

Classical mechanics describes the statistical behavior of “many quanta” systems with extreme accuracy and precision. While it is true that you could, in theory, study every system using quantum methods, and should get correct answers, this would be much more labor intensive and would fail to develop your intuition in as powerful a way.

You could equally well ask “Why must we learn to multiply, when we could achieve our goals by simply counting?” Yes, you could avoid the need to multiply by laboriously counting everything out, and you could likewise “divide by subtracting.” Looked at that way, the arithmetic tools of multiplication and division “aren’t really necessary.”

But they’re USEFUL because they save time and because they help us develop an “intuition about numbers” that serves us well in our work.

Another example is temperature. Why bother with noting the temperature of a gas, when we could “simply” consider the detailed position and velocity of each molecule, and everything would work out? Because it’s so much easier and because it “organizes” the molecular information in a helpful way.

Does this make sense to you?

See Matt Hodel's answer to Physics: Is there a definitive line that defines when the laws of Quantum Mechanics come into play?, copied below for convenience.

I'll give a much more simplistic (and not always trustworthy!) answer than the many great ones already posted, based on a technique that was stressed again and again in my introductory quantum class.

When you're faced with a complicated problem in physics, it is often very useful to get a heuristic feel for the system before trying to solve it exactly. Doing this helps give you an idea for what the answer should look like, and will help you realize when you've made a mistake if your expressions start to look nothing like what you heuristically expect.

One universally useful strategy for getting such a heuristic picture is using dimensional analysis. This is something all physicists do instinctually while solving problems. Check that the units of your answer are the same as the units for the quantity you're supposed to be calculating...if they don't match up, you made a mistake. There is another way to use dimensional analysis, though, before you've even started trying to solve the problem exactly.

Say you're trying to solve for the allowed energies of a particle in a box. If you treat the problem classically, you will (obviously) get a very different answer than if you treat the problem quantum mechanically, as it ought to be. We can rephrase your initial question as "What are the energy scales at which the quantum solution and the classical solution differ qualitatively to a significant degree?" Though this is still a relatively imprecise question, it will do for our purposes.

So here's what you do. You ask yourself what parameters are relevant to the system. For a classical treatment of the particle in a box, all we really have at our disposal are the mass $m$ and the length of the box $l$. We then ask how you can form an energy out of these parameters. Unfortunately in this case we're out of luck. Energies have units of

$\left[E\right]=M{L}^2{T}^{-2}$

(here the brackets [ ] around $E$ mean "the units of").

All we've got is a mass and a length. There's no way we can get a quantity with (time)^-2 in it's units from these parameters. This means that there is no typical energy of the system, which we interpret to mean that the particle can have any energy whatsoever in the classical treatment of the problem. Indeed, the actual solution is simply that the possible energies are $p^2/2m$ where the momentum $p$ can take on any value at all.

How about the quantum case? Well, we still have the mass $m$ and the length of the box $l$ as available parameters, but now since this is quantum mechanics, we also have the fundamental constant $\hslash$, called the reduced Plank's constant.

The units of $\hslash$ are

$\left[\hslash \right]=M{L}^2{T}^{-}1$.

As you can verify for yourself, we can combine these three parameters--$\hslash$, $m$, and $l$--to get a quantity with the units of energy by writing

$E_0=\frac{{\hslash }^2}{m{l}^2}$

where $E_0$ is interpreted as a "typical" energy of the problem. We can conclude upon heuristic grounds that the quantum effects of the system are only significant at energy scales near $E_0$.

Indeed, the exact quantum solution of the problem is that the quantized energy levels are

$E_n=\frac{{\hslash }^2}{2m{l}^2}{n}^2,n=0,1,2,\dots$.

Our guess for the ground state energy based on dimensional analysis was only off by a factor of 2! That's pretty darn good when all we care about is getting a sense of the order of magnitude of the answer.

Notice a fundamental difference between the classical and quantum solutions to the problem. Classically, the particle can have any energy at all. Quantum mechanically (or, as a professor of mine likes to jokingly say, "quantumly"), almost all energies aren't allowed! Only very special energies, of the form described above, are permitted for the particle to be in. It may seem like a miracle that the quantum solution reduces to the classical solution at energy scales that are large compared to $E_0$ (it must do so, or else the world wouldn't work the way we're used on the macroscopic level).

The answer is that, when you look at large energy scales (say, on the order of 10^60 * E0, which is the energy of a 1 gram ball moving with 1 Joule of energy in a 1 mm box), the spacing between energy states is pathetically small compared to the energy scale we're looking at.

Indeed, the difference between the n-th allowed energy and the (n-1)-th allowed energy is

$E_n-E_{n-1}=\frac{{\hslash }^2}{2m{l}^2}(n^2-(n-1{)}^2)$

$=\frac{{\hslash }^2}{2m{l}^2}(2n-1)$

which goes like $n$, as opposed to the n-th allowed energy, which goes like $n^2$. So their ratio goes like

$\frac{\Delta E}{E_n}\sim \frac{1}{n}$

where $\Delta E=E_n-E_{n-1}$.

As the energy scale (and therefore $n$) gets large, this relative spacing of energy levels goes to zero, and we recover the classical result that there is no spacing between allowed energy levels, i.e. all energies are allowed.

EDIT: More from the comments...regarding the particular example of the Hydrogen atom (an electron in a coulomb potential).

One way to think of it is that the Bohr radius,

$a_o=\frac{{\hslash }^2}{m{e}^2}$

is the only dimensionally correct "length" you can build out of the parameters of your system--an electron in the coulomb potential created by a proton.[1]

Note that I've implicitly assumed that the only relevant parameters are $\hslash$, $m$, and $e$. This is true as long as non-relativistic quantum mechanics is a good description of the system. This condition holds for most atoms, but if you want to see the "fine structure" of the energy spectrum, you need to include relativistic effects as well, and you have another parameter at your disposal: $c$, the speed of light.[2]

This introduces a problem. We can build a **dimensionless** quantity out these parameters!

$\alpha =\frac{e^2}{\hslash c}\sim 1/137$

This is bad because we can now build an infinite number of quantities that have the dimensions of length out of the parameters at our disposal. Just keep multiplying the length $a_o$ by the dimensionless quantity $\alpha$! Which one of these gives us the correct length scale?

Well, we already know $a_o$ is the right answer. Notice, however, that adding extra factors of $\alpha$ just decreases the length by a factor of roughly 1/137 each time. It turns out that the corrections to the non-relativistic approximation for the energy of this system (an atom) can be written in as a series of successive powers of the fine structure constant $\alpha$. So each length scale defines the scale at which a correction to the energy levels becomes relevant/"visible."

[1] the name "Bohr radius" applies to the specific case of Hydrogen, where the atomic number is 1. Other atoms have higher atomic number and thus will have a different characteristic length. This difference cannot be captured by dimensional analysis alone, however, since it only differs by a constant number which has no dimensions.

[2] in fact, relativistic effects are essential in getting the qualitative description of some atoms correct...in particular, without factoring in relativistic effects, we would expect mercury to be a solid.

In my opinion they are part of classical physics.

Maxwell proposed EM waves probably almost decade before quatum theory emerged. The need for quatum theory emerged from the failure of Maxwell’s Laws to predict blackbody radiation distribution or to explain the photoelectric effect.

The quantum ideas and apparent wave like proporties of small bodies apply to electrons/ neutrons - which are not the subject of Maxwells Laws.

I see quantum ideas as being more fundamental whilst the Electromagnetic radiation approach is a useful approximation. Almost exactly the same way in which Newtonian mechanics is a very useful approximation of relativistic mechanics.

There’s a lot of different issues here. Most importantly, the black body spectrum is ultimately more a property of light itself than of black bodies: it’s the state of maximum entropy for light (for a given energy density). Because it’s the state of maximum entropy it’s the state in which a particular batch of light has a well-defined temperature and can be in thermal equilibrium with an object (such as but not limited to a black body). The significance of a black body is merely that it slurps up any and all incoming light and re-emits new light with a maximum entropy spectrum corresponding to its own temperature in a single pass. If you have a closed cavity such as an oven, even one with very shiny walls, it will eventually also come to have a black body spectrum; it’ll just take more bounces. So you derive the black body spectrum by considering the entropy of the light in the cavity, and ignoring the walls except insofar as they have a well-defined temperature.

Thus any details of the coupling between the walls of the cavity and the light in the cavity (which would involve the Larmor formula or equivalent) are abstracted away. The argument just assumes that there’s enough coupling to bring things to thermal equilibrium eventually.

During the development of classical electromagnetism and Special Relativity (SR), only one subatomic particle was known (electron), the plum pudding atomic model was still in place, and the elementary quantum processes behind the emission, propagation, diffraction, interference and absorption of light weren’t well understood at all. Maxwell’s theory of classical electromagnetism was still based on a luminiferous ether, and he never conceived EM radiation as actual EM waves traveling through vacuum.

In the photoelectric effect, Einstein also addressed the units of light only as “light-quantum”, but never really implied that these are actual particles traveling through space. Yet, somehow the formalism of light became and remained as spatially traveling EM waves or photons through the vacuum of space. Even though SR had created an extremely successful theory around the absolute speed of electromagnetic (EM) radiation, and Quantum Mechanics (QM) had greatly improved the atomic model, the original formalism of EM radiation, being emitted as photons, traveling through vacuum as EM waves, just to be absorbed as particles again has basically remained unchanged until today.

To avoid contradicting one of the main postulates of SR, namely the negation of a universal medium as an absolute reference frame, all “post-SR” field theories, such as General Relativity (GR), Quantum Field Theory (QFT), and Quantum Electrodynamics (QED), refrained from endowing their corresponding fields with real physical properties and structure and only treated these fields as abstract mathematical constructs or described EM and gravitational processes with the abstract concept of spacetime. This limitation has been greatly hindering the completion of these theories, and consequently their unification has remained an elusive quest.

To fully understand all elementary quantum processes behind the emission and behavior of EM radiation, and expedite the completion and unification of QM, GR, QFT and QED, first a complete reconceptualization of the outdated EM and gravitational fields and EM radiation models is necessary.

Maxwell's equations are the laws of the electromagnetic field, endowed with scale independence, that is, the same laws are valid from the smallest conceivable order of size to the order of cosmic sizes.

Is that true?

If it were really true, electrodynamics would allow the formulation of quantum behavior. And there is no news about that. Or is there?

There is no academic news, nor anything published in academic media. The only thing available on the subject was published in spanish by a layman, without the slightest academic support, with the title James Clerk Maxwell Concimiento Prohibido. Searching for the title, it easily appears on the Internet.

yeah, obviously, all the that u need to find the motion of charged particle in the influence of electric field and magnetic field ., u can easily work out with the help of newtonian way. It’s called macroscopic theory or classical limit. if u want to work in the microscopic limit where u need to understand how particle change its position or momentum in the influence of electric field or magnetic field u can work out with Schrodinger equation.

So all the maxwell relation is really classical physics, and one interesting thing is all his equations is invariant under Lorentz transformation. So the thing is, electric and magnetic field is it self build under the impression of relativity. That’s really cool about classical physics.

All equally important. Without advanced math you are essentially illiterate in science, all you can do is talk about concepts and no hard calculations or estimates. A mathematically illiterate person can be a great physicist, faraday comes to mind (he was weak in partial differential equations, but his friend maxwell helped him there) but these days a physicist that does not know high level math is basically looking to teach high school physics for the rest of their career.

classical mechanics and classical electrodynamics are both considered core courses in an undergraduate curriculum in most schools. They are what you need before you can take quantum mechanics or statistical mechanics. If you are getting into gravitation, then having seen a linear version of the theory can really help when you do things like gravity waves, which are a current topic.

if you intend to get into particle theory, then of course you need more math, lots more math, group theory and topology at a minimum, and for GR, differential geometry is a must.

Quantum Physics or Classical physics or Relativistic physics, Physics is physics right?
It’s the laws of the nature, why are there separate set of laws?

Let’s start with the classical physics. As the name suggests, it is classical. The foundation for this were laid down by the scientists of 17th century like Galileo, Sir Newton, Kepler who unraveled the mysteries of forces, motion and eventually gravity.
This was quite a big deal, because before Newton, we really had no clue what force did and what was the cause of motion. Even today, unless you have taken a science course, there is good chance you don’t know what a force does.
Then came the laws of electromagnetism. The foundation for this were laid down by the scientists of the 19th century like Oersted, Micheal Faraday, Andre Ampere, the Scottish maestro James Clerk Maxwell. They were able to decipher the laws of electromagnetism.
Along with this and some other branches like, fluid mechanics, thermodynamics, this is pretty much what classical physics is all about.
In short classical physics is the rules that govern the things at a level that we see and interact with nature, everyday.

But by the end of the 19th century and the beginning of 20th century we realized, that somethings didn’t add up. In various parts of physics, especially electromagnetism, experiments were not matching with the predicted theoretical results. On more careful investigation we realized, that the classical physics start giving absolutely absurd and horrible results. Thus we realized that the physics was incomplete. There were hints of something horribly wrong with all our predictions of classical physics when we tried to apply it to tiny particles. Without getting into too much of details, the main problem was classical physics predicted that everything is smooth and continuous. That things can be infinitely divided. We soon realized that was not true. Things, like energy, cannot be indefinitely divided, but a minimum quanta exists. And energy can only come in integral multiples of these quanta. Thus the Quantum mechanics was born.

Quantum mechanics is the study of tiny particles, where everything has a minimum step size, a quanta. The step sizes are so small, that when we look at big things (macroscopic objects) these quanta play no role and we could assume that things are smooth, but at the microscopic level, these assumptions fail miserably.

Here is an analogy I like to give.

Think of a ramp and a staircase. If you have a ramp, you can stand wherever you want on the ramp, it’s continuous. But a staircase has a minimum step size and you can only stand at particular heights (integral multiples of step size)

Imagine a staircase that starts from your floor and leads to your ceiling. Imagine this staircase has 25000 stairs. How small would the steps be? I know right? So incredibly small. If you put a tennis ball on it, it would roll. If you put your kid on it, the kid will slide down, every experiment you do on this ‘stair case’ will confirm that it is a ramp. Because it behaves like a ramp. But only when you do careful experiments, with very very tiny objects, would you see the true nature of this stair case.
That’s how our universe is. Hope you can understand what is classical physics and quantum physics in this 25000 insane staircase analogy ;-)

Thanks for reading, have a good day