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I don't understand how and why the electric and magnetic fields oscillate in the electromagnetic radiation wave, and any way where do these fields originate from, for there are no charged particles in the wave (there are no particles in it at all). Till now I've taken this for granted that the electric and magnetic fields oscillate at 90° to each other but recently I'm trying to study quantum physics but due to this confusion I couldn't understand it.

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  • $\begingroup$ Related: physics.stackexchange.com/q/20331/2451 $\endgroup$
    – Qmechanic
    Aug 13 '14 at 10:49
  • $\begingroup$ "Why" is not a useful question in physics. Physics is all about "How does nature behave?". Maxwell's equations simply describe certain aspects of em waves, like free waves without charge carriers as they have been observed. That they don't mention particles, is a function of the chosen level of description (classical), not a function of nature. The same waves can be described in a particle picture in quantum electrodynamics, and you will get the same macroscopic predictions after averaging properly over all quanta. $\endgroup$
    – CuriousOne
    Aug 13 '14 at 20:00
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Part of the genius of Maxwell was to realise that it did not require the presence of currents or charges to generate a magnetic field. In analogy to the way that changes in magnetic field generating an electric field (or macroscopically we say that changes in the magnetic flux linked with an electric circuit can produce an EMF and hence a current), it turns out that changing electric fields can also produce magnetic fields.

Hence electromagnetic waves can propagate in a vacuum without the need for charges or currents - the changing electric field begets a time-dependent magnetic field and this changing magnetic field begets a time-dependent electric field, and so on.

You also ask where these waves/fields come from. Well yes they do require currents or charges to produce them in the first place. More specifically they require accelerating charges. For instance a good approximation to plane polarised electromagnetic waves can be produced using an antenna in which an A.C. current flows - the charge in the antenna will be accelerating and decelerating rather than moving with a steady velocity. Strictly speaking this produces spherical wavefronts, but at a large distance from the antenna they would appear to be plane waves.

Finally you ask whether you should learn about Maxwell's equations. Of course the answer is yes, but usually Maxwell's equations (in their so-called differential form, which is what is required for a full understanding of the generation and propagation of EM waves) are not encountered until year 2 of a typical (UK) undegraduate physics degree.

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  • $\begingroup$ this really sorts everything out but what do you mean when you say 'time -dependent' field and another thing i would like to clear up: I am just confused that once the EMR is emitted as it is simply energy or a wave carrying energy shouldn't it lose this energy to the surrounding particles e.g air particles and just 'disappear' (sorry for lack of a better word $\endgroup$
    – Sara
    Aug 13 '14 at 13:37
  • $\begingroup$ By time-dependent I mean that it is a function of time, i.e. it varies with time. As a wave propagates outwards, then the amplitude of the fields will decrease linearly with distance from the source. This ensures that there is no problem with energy conservation! EM waves can also lose energy if they propagate through a conducting medium. $\endgroup$
    – ProfRob
    Aug 13 '14 at 14:19
  • $\begingroup$ but EM waves from the sun travel extremely long distances but they do not lose their energy. How is that possible then? $\endgroup$
    – Sara
    Aug 13 '14 at 14:27
  • $\begingroup$ Yes they do. The flux (power per unit area) of EM waves from the Sun at the surface of the Earth is about 1400 W/m^2, but just above the surface of the Sun they carry 6.3 million W/m^2. The difference is a factor of ~46000, which is the ratio of the surface area of a sphere drawn around the Sun with radius at the distance of the Earth to that of a sphere at the Sun's surface. i.e flux*area = power is a conserved quantity. $\endgroup$
    – ProfRob
    Aug 13 '14 at 14:47
  • $\begingroup$ what form of energy is carried by EMR e.g the U.V rays and X-rays etc, i mean is it kinetic energy or potential or some other form $\endgroup$
    – Sara
    Aug 13 '14 at 14:58
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For a classical discussion on waves I would refer you to review the Wikipedia site on Maxwell's equations first and then also to discussion on the Continuity equation for the purpose of understanding conservation laws.

Now for the quantum part.

First we need to get you up to speed on what a field is. Simply put it is an abstraction used in physics to assign a value to each point in space and time (or spacetime for relativists).

This assigned values generally have four categorizations. The value can be:

  • a scalar (e.g. just a number)
  • a vector (e.g. an number with direction)
  • a tensor (e.g. a object that assign values to all directions and their correlations)
  • a spinor (e.g. a complex vector)

The electromagnetic field is actually the union of the electric field and the magnetic field. It is the first example of a gauge field. Gauge fields are the fundamental components of modern physics. As I have [reviewed previously](adapted from David McMahon)5:

If temperature is viewed as a field, then at each point in the room, the temperature takes on a definite value. So as you walk through a room, you might feel a change in temperature, which can be understood as the field changing its value.

An important additional concept is the idea that the values of the field are governed by some set of equations, and even though we can change the values of the field, the equations that govern them do not change. This is captured with the concept of gauge invariance which is interpreted to mean that the equations of a field do not change under certain transformations called gauge transformations.

Gauge transformations can be categorized as being one of two types, global and local. A global transformation does not depend on space or time. This is basically the same thing as saying that you can change the values of the the field $ \varphi $ in such a way that the change is exactly the same for every point in space and every moment of time instantaneously, or basically you add a constant everywhere for every time. Essentially, global transformations are generally undetectable since everything has changed everywhere for all time. This type of transformation leaves the underlying equations unchanged, but is generally uninteresting.

Local gauge transformations are transformations of the field that do depend on space and time. These type of transformations also have the property of obeying special relativity, meaning that transformations are not going to effect distant objects faster than the speed of light. In order to create local transformations that leave underlying equations invariant, we introduce an auxiliary field $ A_{\mu} $, or hidden field, that is called a gauge potential, which is also called a gauge field. The gauge field lets us define an object called the gauge covariant derivative $ D_{\mu} = \partial_{\mu} - iA_{\mu}$ which can act on a field $D_{\mu}\varphi = \partial_{\mu}\varphi - iA_{\mu}\varphi $ and leave the underlying equations governing the field unchanged (the $ i $ is used to tell us the gauge field is imaginary).

It can be argued that the combined electromagnetic field gains its waviness from the requirement that its Lagrangian (e.g. the equation that governs the fundamental relationship between the systems kinetic and potential energy) be Lorentz invariant (e.g. respect special relativity) under continuous transformations (e.g. a change in observational viewpoint of arbitrary precision).

Maxwell's discovery was that the electric and magnetic fields exchanged energy as a wave propagated in space. Solutions to the Lagrangian under the constraints of gauge invariance are in fact a type of simple harmonic oscillator.

With that understanding, we have to understand that in the context of quantum mechanics, every field actually does have a particle associated with it. In the case of the electromagnetic field, the particle is the photon.

In quantum mechanics, the "waviness" of the field is not actually manifested directly as an observable object. Instead the waves associated with the particle exist in an abstract Hilbert space which is an infinite vector of complex numbers. The wave encodes the probability amplitude (square root of probability) of detecting a photon at a given time in place. The manifestation of the wave is only observable when considering large numbers of particles. This is evident from the double slit experiment which shows the appearance of the wavy nature of underlying quantum field after the accumulation of multiple particle detections.

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There exists a very good formulation in this blog entry of Lubios Motl on how classical fields emerge from quantum theory, .

The link between the quantized photons and the classical field are the Maxwell equations , Classical solutions of the equations give rise to the classical fields. Used with the operator formalism the wavefunction describes a photon. The square of the wavefunction gives the probability of finding the photon at (x,yz,t). It carries not only the frequency nu of the classical field in its energy E=h*nu but also phases connected with the classical vector electromagnetic potential.

In a handwaving sense, the classical field is not chopped up into photons, but it emerges as a synergy of photons with appropriate phases and energy connected with the frequency. The phases ensure that the long range interference patterns seen and explained with classical waves are also the probability wave patterns that even single photons display through the double slit experiment.

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  • $\begingroup$ my physics course does not include Maxwell equations as its pretty basic(im doing alevels) but they seem to keep popping up everywhere. They seem pretty complex. Do you think should I still try to understand Maxwell's equations or just leave it be?plz give me advice $\endgroup$
    – Sara
    Aug 13 '14 at 12:24
  • $\begingroup$ @Sara Maxwell's equations are the the basic thing to properly understanding electromagnetism. You should get acquainted with them if you don't want to be limited by a layman description. $\endgroup$
    – Ruslan
    Aug 13 '14 at 12:39
  • $\begingroup$ Maxwell's equations are the mathematical formulation of all the electricity and magnetism laws intoi a coherent theory. Classical electricity and magnetism, together with classical mechanics is an indispensable course in a physicist's education, preceding quantum mechanics courses.The mathematical background needs differential equations, calculus, real functions and complex functions. I do not know whether these are down to A level level by now. In my time they were higher level college courses. Why are you doing premed if you are that interested in physics? $\endgroup$
    – anna v
    Aug 13 '14 at 13:05
  • $\begingroup$ everyone in my family's a doctor but ive considered changing my subjects. I just tried reading through Wikipedia's article on Maxwell's equation and couldn't understand a thing. Could you give me a brief description of it or something like that? $\endgroup$
    – Sara
    Aug 13 '14 at 13:21
  • $\begingroup$ No. The equations are a mathematical distilation of a lot of observations which had been formed into laws, like the bio savart law en.wikipedia.org/wiki/Biot%E2%80%93Savart_law , and the ampere law en.wikipedia.org/wiki/Amp%C3%A8re_law en.wikipedia.org/wiki/Electricity_and_magnetism . These laws themselves modeled observations. The M equations put everything in a mathematically elegant form with great predictive power. There are no shortcuts to elbow grease in physics, i.e. spending the hours in the necessary courses/ ( study hours even if self taught) $\endgroup$
    – anna v
    Aug 13 '14 at 13:29

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