# Understanding light

1. Mar 26, 2008

### GRB 080319B

I have plethora of questions about light:

1.) I understand that light is created when the electrons in an atom jump to a higher level and fall back down to their ground state. When light is emitted, is it emitted orthogonal to the electron or at the angle of absorption? How is light emitted orthogonal to the nucleus when the electron jumps and falls back orthogonal to the nucleus? Isn't light emitted perpendicular to the direction that the electron jumps? Or are the electrons not orbiting parallel to the nucleus? Do photons/light waves propagate outward in all directions, e.g. a ripple in a pond, or unidirectionally?

2.) Is light from a reflective surface like a mirror really absorbed and re-emitted or is it just reflected? Is any energy lost in the process of re-emitting light, i.e. is some of the energy of the absorbed photon turned into heat, or is it a complete conversion? Is their any way to modulate the amount/wavelength of photons re-emitted? Do ionized atoms emit different wavelengths than their electrically neutral counterparts would? Does light in the form of photons/waves lose energy as it propagates through space and if so how?

3.) Light is described as being an electromagnetic wave, with electric and magnetic components. I understand these components come from electrons having magnetic and electric properties. How exactly do the magnetic and electric properties of electrons merge to form electromagnetic waves? Is the electric component caused by the electrons falling from higher energy levels? How is the magnetic component created? How does an electromagnetic wave contain both a magnetic and electric component within one wave? How do current, magnetic and electric fields affect light or produce it, and conversely, how does light affect said fields and current?

4.) I am familiar with seeing light shown like this: Lightwave
Is there any way to visualize light in 3D instead of 2D cross sections? Is light a standing wave and does it contain a definite beginning and end point on the wave (does it have a definite length, not wavelength)?
How does light get polarized in the first place, and into circular and elliptical angles? Does the amplitude and intensity of light correspond to the amplitude of the individual photon/wave or is it a property of the sum of the photons/waves of the light?

5.) I've also seen light shown as loops of electric lines of force: Loop
I am confused as to how the loop correalates to a wave and why it is expanding. Is the wave increasing in size and if so how?

I am struggling to visualize how all these processes are occurring to create light and would appreciate any help. Thank you.

2. Mar 26, 2008

### GRB 080319B

To re-phrase this question: Is light always emitted as a single photon/wave packet with a discrete wavelength or can it be emitted as a continuous wave, e.g. a sine curve.

Can light be generated from free electrons and if so can it be generated by a stream of electrons, e.g. electrons flowing through power cords? With reference to the double-slit experiment, how do the two light beams interact with each other to form the interference pattern? If the light is propagating in one direction through the slit, how does it end up expanding like a ripple and causing the interference pattern? Does this have to do with the angle that the photons are moving at relative to when they enter the slits? Also, I've heard that certain wavelengths are not allowed, and that only round numbers of wavelengths can be produced. Is this true, and if so, does it have to do with how the electrons are producing the light waves?

3. Mar 26, 2008

### jostpuur

These questions make sense only with the Bohr's model. Since Bohr's model is mostly false, I wouldn't waste time on trying to get answers to precisely these questions. Of course we could try to replace these with better questions though, about the same topic It is difficult to find good info about this. QED is a very advanced topic. I think... I'll say nothing else than that try to proceed with your studies towards more detailed understanding of basic quantum mechanics. Then you will get better picture of what you are trying to understand.

Since photons are electrically neutral, there is no other way for matter to interact with them, than absorbing and re-emitting.

When light is reflected of some surface, there is no energy loss for any particular photon. There is a phenomenon called Compton scattering, where an individual photons have their energies changed, but this needs X-rays to happen. Doesn't happen with visible light.

No. At least not in empty flat space time. Photons can lose energy in empty space as result of gravitational red shift though, but otherwise, no.

The classical wave emitting with oscillating charges is explained in good books about electromagnetism. You will need to understand multi-variable calculus first. Then you can understand Maxwell's equations, and rest of the task is solving some PDE problem.

This looks like Bohr's model again.

Notice one thing. When you see info about electromagnetic waves, they are usually waves of classical electromagnetic field. This is different thing than the photons, which you will need when dealing with atoms emitting light. Photons cannot be dealt with by classical fields, but you will need QED instead. Again, I'll say nothing else than that this is very advanced topic.

Individual photons don't have amplitudes of E and B fields. The electromagnetic field merges... hmhm.. somehow () ...from large number of photons. You will have to understand how to deal with quantum mechanical wave packets in harmonic oscillator (and something else too), in order to understand how classical electromagnetic field can arise from discrete photons. Very, very, advanced stuff!

And you will struggle for a long time!

My advice is this. Don't forget your questions, but don't get stuck on them too badly either. You need to learn about multi-variable calculus, PDE, Maxwell's equations, Schrödinger's equation first. Them come back to your old problems, and see if they look different.

The unfortunate fact is, that when you find information about these things, the chances are, that this topic is still too difficult even for the authors (as is the case with this post too). Some things, like misunderstandings with the Bohr's model, will probably get clearer soon when you learn quantum mechanics. However, there is always something with QED that doesn't seem to be making sense. It's not a very easy task to understand QED. Good luck on trying.

Last edited: Mar 26, 2008
4. Mar 26, 2008

### peter0302

LIght is not exclusively limited to the emission or absorptions of electrons is it? Aren't there other physical processes which generate photons? Collision of matter and antimatter for example?

5. Mar 26, 2008

### Staff: Mentor

Produce an oscillating electric current in an antenna and you get radio waves (lots of very low-energy photons).

Take a beam of high-energy electrons and bend it around a curved path (e.g. in an electron synchrotron) and you get synchrotron radiation. See for example the National Synchrotron Light Source.

6. Mar 27, 2008

### GRB 080319B

*suffers mental breakdown...
*recovers

Thank you for your insight. I know now where the discrepancies in my understanding of this topic are. Guess it's time to crack open those quantum mechanics and multi-variable calculus books!

Last edited: Mar 28, 2008
7. Mar 28, 2008

### erastotenes

In classical picture the oscillation of a charge without magnetic moment creates an electromagnetic wave that has of course both electric and magnetic components.

The magnetic component of electromagnetic wave is not caused by magnetic proporties of the oscillating charge but it is induced as a result of the change of the Electrig field in time according to the Maxwell equations.

8. Mar 28, 2008

### jostpuur

Or equivalently the magnetic component is produced by the moving charge. The "inducing"-terminology is confusing, but despite it, in the end, all electric and magnetic fields arise from charges.

9. Mar 28, 2008

### erastotenes

Yes but for the electromagnetic wave it is not the first term(you mention) but the second term on the right side in the following Maxwell equation that creates the magnetic part in the wave.

curl B = j + dE/dt . (B magnetic field, j electric current, E electric field)

The magnetic field and electric field in electromagnetic wave create each other according to the Maxwell equations leading to propagation of the wave. The charge plays only a role for starting the process.

10. Apr 8, 2008

### Usaf Moji

Hi Jostpuur, the question of how an electromagnetic field "merges" from a large number of photons is one which I am currently struggling with. Can you suggest a good book that discusses this? I have some undergrad in quantum physics (but not much) and a rudimentary knowledge of classical Maxwell waves, Schrodinger's equations (and the psi function therein), partial differential equations, multi-variable calculus, etc. I'm currently reading Feynman's QED, but find it too general and not very informative with respect to my interests. Conversely, I purchased a textbook called "Quantum Mechanics: An Accessible Introduction" by Robert Scherrer, but I find it gets bogged down in too much minutia without providing much info on the relationship between photons, classical EM waves, and wave packets.

11. Apr 8, 2008

### jostpuur

No. I don't have any sources on this myself. Usually, when you try to find information about this, you hear the usual arguments "that's not relevant, the scattering amplitudes are the observable quantities".

Somebody here, OOO or Demystifier probably, once recommended some book, which had something about wave functional approach to the KG field, but I don't remember what book it was anymore. Perhaps they can tell something. I'm myself currently too busy with other things, but I'm surely returning to QFT studies at some point again.

12. Apr 8, 2008

### jostpuur

You can, however, find information about constructing wave packets in harmonic oscillator, from some QM sources. I asked about them here wave packets that feel harmonic potential and got some useful info. Once you understand what wave packets are in a one dimensional harmonic oscillator, you can easily extend the construction to N-dimensional oscillator. The Klein-Gordon field is basically an infinite dimensional oscillator, so you can make a wave functional packet that describes the time evolution of the field, and the expectation value can be interpreted as the classical field. If the electromagnetic field was merely a four component Klein-Gordon field, then I think it would be simple to handle in the same manner, but unfortunately it is not merely a four component Klein-Gordon field, but instead there's the gauge condition issue. I'm not sure how to deal with the wave functionals of fields with gauge invariance.

13. Apr 8, 2008

### Usaf Moji

Thanks Jostpuur. Much of this is way over my head and education level, but the book "Quantum Theory" by David Bohm mentioned in that thread looks interesting. I think I'll get me a copy

14. Apr 9, 2008

### erastotenes

This is one of the most widespread misconceptions imo. Each photon has a polarization state and polarization state reflects the phase relation of E and B. Photons are not bulletlike entities. Quants emerge in the theory as the result of field quantization. The difference between quantized fields and classical fields is not that quanta are added in an ad hoc form to the field but the process of field quantization is just writing down E and B as opeartors instead of ordinary complex numbers. This process leads to discrete energy eigenstates of the field. In this picture n photons merely mean that the field is in the n'th energy eigenstate.

Another reason for this misconception is the widely spread statement: "what we experience as the static field is just the result of interaction with large number of virtual photons".

This may be true but this does not mean that "virtual photons are bulletlike entities so that large number of them lead to a classical pressure-like average that we experience as classical field" . On the contrary virtual photons are nothing but longitidunal and timelike propagating solutions of the covariant field equations. The integral over them gives the classic coulomb field. The integral is taken over electromagnetic field.

Thus field is primary and exists at the deepest level. Quanta emerge as a result of the quantization of the field. Quantization is not ad hoc injection of quanta into the theory but just writing down E and B as operators. This is at least how it is in quantized field theories.

Otherwise you could not explain in anyway how a plane radiowave (that is made up of large number of photons in the same direction) excerts a force (transfers momentum) on a charge in the antenna transversal to its propagation direction.

Last edited: Apr 9, 2008
15. Apr 9, 2008

### CaptainQuasar

[post=1556816]This post[/post] by rbj does not answer any of your particular questions but I think that you would find it interesting.

16. Apr 9, 2008

This Richard Feynman lecture (In New Zealand, 1978) courtesy of the Vega Science Trust brilliantly explains the basics of QED, the relation between light and matter, and gives great insights into how light appears to behave to us.
(There's 3 lectures, each lasting 1 and a half hours but they're all well worth watching).

http://www.vega.org.uk/video/subseries/8

17. Apr 9, 2008

### genneth

The classical field is best approximated by coherent states. These states are beefed up versions of what are called the same thing in the harmonic oscillator. In that case, you have a displace ground state wavefunction --- but that's actually not the interesting thing. Wikipedia has a fairly good page on coherent states, though I'm not sure if that only from the perspective of having understood most of it first. Once you understand them, look at the basic steps in quantisation of the EM field --- it's quite short and self-contained in most textbooks (the complications only start once you want to account for electrons too).

18. Apr 11, 2008

### reilly

GRB... Your questions are usually answered in 1. a course on classical E&M, 2.a course in QM, and then 3.a course in QFT. We're talking close to three years to get the answers you want, all of which then would be easily answered. Yes, your questions are basic, but somewhat hard to answer without considerable grounding in E&M. So, study for awhile; do your homework.
Regards,
Reilly Atkinson

19. Apr 12, 2008

### jostpuur

In case this seemed suspicious, I can clarify. There was no conflict between my post about Gaussian wave packets, and genneth's post about coherent states. The coherent states are Gaussian wave packets. But I'm slightly confused about this

Sure it is interesting! I don't see how else way could you understand what these coherent states are all about.

The solutions of one dimensional harmonic oscillator go like this. The Hamilton's operator is

$$H=-\frac{\hbar^2}{2m}\partial_x^2 + \frac{1}{2}kx^2$$

we define

$$\alpha := \frac{(mk)^{1/4}}{\sqrt{\hbar}}$$

and the energy eigenstates are given by

$$\psi_n(x) = \sqrt{\frac{\alpha}{\sqrt{\pi}2^n\; n!}} e^{-\alpha^2 x^2/2} H_n(\alpha x).$$

Now suppose we want to have a localized state at point $\Delta x\in\mathbb{R}$. The Gaussian wave packet

$$\psi(x) = \frac{\sqrt{\alpha}}{\pi^{1/4}} e^{-\alpha^2 (x-\Delta x)^2/2}$$

turns out be handy for this purpose. Modifying a little bit what variation explained in the thread wave packets that feel harmonic potential, we get a formula

$$\int\limits_{-\infty}^{\infty} H_n(\alpha x) e^{-\alpha^2 x^2 + A x} dx = \frac{\sqrt{\pi} A^n}{\alpha^{n+1}} e^{A^2/(4\alpha^2)}.$$

Using this, we can compute the components of the $\psi$ in $\psi_n$-basis.

$$\langle n|\psi\rangle = \int\limits_{-\infty}^{\infty} \psi_n^*(x)\psi(x)dx = \frac{\alpha}{\sqrt{\pi 2^n\; n!}} e^{-\alpha^2\Delta x^2/2} \int\limits_{-\infty}^{\infty} H_n(\alpha x) e^{-\alpha^2 x^2 + \alpha^2 \Delta x\; x} dx =\frac{\Delta x^n \alpha^n}{\sqrt{2^n\; n!}}$$

So we can write the state in eigenstate basis like this

$$|\psi\rangle = \sum_{n=0}^{\infty} \frac{\Delta x^n \alpha^n}{\sqrt{2^n\; n!}} |n\rangle$$

and this is just the coherent state, although $\alpha$ has now a different meaning than what it has in the Wikipedia's article http://en.wikipedia.org/wiki/Coherent_state. It could be there is a mistake somewhere in my calculation... the exponential term is missing... hmmhhmhh...

Last edited: Apr 12, 2008
20. Apr 12, 2008

### jostpuur

It could be that the mistake density keeps increasing exponentially now, but I'll try to press on anyway. The real Klein-Gordon field, in Fourier space is described by the Lagrange's function

$$L = \int\frac{d^3p}{(2\pi)^3}\big(\frac{1}{2}(\partial_0\phi_p)^2 - \frac{1}{2}(|p|^2 + m^2)\phi_p^2\big)$$

We can solve the canonical momenta

$$\Pi_p = \frac{\delta L}{\delta(\partial_0\phi_p)} = \frac{1}{(2\pi)^3}\partial_0\phi_p$$

and write the Hamilton's function for the same system

$$H \;=\; \int d^3p\; \Pi_p \partial_0\phi_p \;-\; L \;=\; \int d^3p\Big(\frac{(2\pi)^3}{2}\Pi^2_p \;+\; \frac{1}{2(2\pi)^3}(|p|^2 \;+\; m^2)\phi_p^2\Big)$$

In quantum theory, the system is described by a wave functional $\Psi(t,\phi)$, which satisfies the Schrödinger's equation

$$i\partial_t\Psi(t,\phi) \;=\; \int d^3p\;\Big(-\frac{(2\pi)^3}{2}\frac{\delta^2}{\delta\phi_p^2} \;+\; \frac{1}{2(\2pi)^3}(|p|^2 \;+\; m^2)\phi_p^2\Big)\Psi(t,\phi).$$

This is just an infinite dimensional harmonic oscillator, analogous, for example, to a Schrödinger's equation

$$i\partial_t\Psi(t,x_1,x_2,x_3) \;=\; \sum_{k=1}^3 \Big(-\frac{1}{2}\partial_k^2 \;+\; a_k x_k^2\Big)\Psi(t,x_1,x_2,x_3).$$

If one tries the separation attempt

$$\Psi(\phi) = \prod_{p\in\mathbb{R}^3} \Psi_p(\phi_p)$$

one sees that this solves the energy eigenvalue problem, if all components satisfy the one dimensional Schrödinger's equation for harmonic oscillator. So the energy eigenstates are characterized by mapping $n:\mathbb{R}^3\to\mathbb{N}$, $p\mapsto n_p$, and the solutions are something like

$$\Psi_n(\phi) \;\propto\; \exp\Big(\int d^3p\; \frac{1}{2}\sqrt{|p|^2 + m^2}\phi_p^2\Big) \prod_{p\in\mathbb{R}^3} H_{n_p}(\sqrt{|p|^2 + m^2}\phi_p)$$

Then suppose you have some classical field $\Delta\phi:\mathbb{R}^3\to\mathbb{R}$. It should be possible to construct a functional wave packet that is localized around this value. Basically you do the Gaussian wave packet for each component separately, so that the peak is at desired value, and then multiply them to form an infinite dimensional wave packet. If, for each $p$,

$$\Phi_p:\mathbb{R}\to\mathbb{C},\quad \phi_p\mapsto\Phi_p(\phi_p)$$

is peaked around some number $\Delta\phi_p$, then

$$\Phi:\mathbb{R}^{\mathbb{R}^3}\to\mathbb{C},\quad \Phi(\phi)=\prod_{p\in\mathbb{R}^3} \Phi_p(\phi_p)$$

should be peaked around the function $\Delta\phi:\mathbb{R}^3\to\mathbb{R}$, $p\mapsto\Delta\phi_p$.

Or at least this is how I've understood this All comments are welcome. I haven't been studying this from any reliable sources. More like half studying, half rediscovery. I think books usually prefer doing all this using highly abstract operators only, but this should be equivalent. Since the forum is full of physicists, conceptual mistakes in this post, if there are such, probably get corrected soon

Last edited: Apr 12, 2008