# What is light?

1. Aug 1, 2005

### LeonhardEuler

I have only taken an introductory course on QM so far, and a lot of it doesn't make sense to me. One thing that confuses me is what light is. In classical physics it was a wave consisting of oscilating electric and magnetic fields. In QM, I keep hearing about "wave-particle duality". My question is this: when light is a wave, what is it a wave in.

Here is why this confuses me: Correct me if I'm wrong, but I don't think it makes sense to speak of a "force" in QM, at least not one resembling a classical force because there really is no position in QM, so there can't be a second time derivative of position, and what I always (incorrectly?) took as the definition of force was $\sum\vec{F}=m\vec{a}$. If there is no force there can be no force field. If there is no force field, then there is no wave in the force field. Usually in QM equations you have a "potential" instead of a force. I was thinking maybe light was a wave in electric and magnetic potential, but then I remembered Faraday's and Ampere's law. $\oint\vec{E}\cdot ds$ and $\oint\vec{B}\cdot ds$ are not necessarily zero around closed loops, so you can't speak of a potential without speaking about a particular path! And yet, light must clearly have some electromagnetic nature because it can push charges around in a circuit, for example in a radio (I'm using the word "light" in a more general sense than visible light). So what is light a wave in, if not $\vec{E}$ and $\vec{B}$ fields. And if it is not a wave in these how does it move charges. And if it is a wave in these, how does it get around the force problem? Thank you for reading all this!

2. Aug 1, 2005

### EddieZ

I'll take a crack at this, but I'm sure you'll get some better answers soon ;)

The question of what is light a wave in is a good question. First I'll adress the classical view. The electric and magnetic fields of a light wave are what is waving so to speak. If you look at a picture of an electromagnetic wave, you will see a depiction of two sine waves, out of phase with each other, one for the magnetic field and one for the electric field. The plane of oscillation of each of the waves at each point is always perpendicular. What is actually happening is that there is an oscillation of energy between the electric field and the magnetic field. At the point in the trajectory where the magnetic field is at a maximum the electric field is zero (essentially), and when the electric field is at a peak, the magnetic field is zero. In between these points, the electric field is waning while the magnetic field is increasing (and so on). So, the energy in the electromagnetic field is bouncing back and forth between being fully expressed in a magnetic field and an electric field, and as each works its way through a cycle, it generates the other, and this process repeats itself at whatever the frequency of the wave (light) is.

I'll invite somone more knowledgable to comment on how the magnetic and electric potentials fit in to the process.

Regarding the wave-particle duality, I'm sure there are a number of threads on that in this forum already, so I won't expand on it here, unless someone would like to.

3. Aug 1, 2005

### neurocomp2003

what is a E & B field =]

4. Aug 1, 2005

### Pengwuino

Electrical and Magnetic fields

5. Aug 1, 2005

### neurocomp2003

mmm ok so if i typed it out you would have replied E and B fields?

6. Aug 1, 2005

### Pengwuino

yes. I think M already has a designation... I think thats why we use B.

7. Aug 1, 2005

### CarlB

It's true that quantum mechanics deals with a different representation of the object, one that doesn't require a particular position. But even with classical mechanics objects that are described without a specific position can nevertheless have forces applied to them. For example, a gas doesn't have a particular position, but gases exert forces have masses and can have forces exerted upon them.

First, for scalars, one can take the gradient of the potentials used in QM to get a force. However, this is not done for the same reason that the corresponding classical situation also uses potential energy instead of forces. It's an easier problem to solve with potential energy, especially if you can write the potential energy as a scalar. That is, the force is a vector so it is naturally more complicated to work with than a scalar.

For the case of photons, one can analyze a problem in several different ways. Since my education is in elementary particles, I naturally prefer to analyze photons as elementary particles. In the elementary particle point of view, there is no electricity and magnetism, just elementary particle interactions.

In elementary particles, light takes the form of photons. These are excitations of the vacuum that are like any other particle. Forces are conveyed between particles by the exchange of other particles. In the case of electrons interacting by E&M, the force is mediated by the exchange of photons. Uh, photons can also have forces applied to them, for example by the exchange of electron / positron pairs or the like.

As an example of the simplicity of the elementary particle version of physics, as opposed to the condensed matter method of dealing with E&M, consider the Aharonov-Bohm effect. In QM, this is a mysterious thing wherein an electron is influenced even though it travels only in regions with zero magnetic and electric fields. The electron's wave function is modified and that changes its interference with itself. A big mystery and a subtle part of QM.

Looked at from the elementary particle interaction point of view, the electron travels through regions that are stuffed to near overflowing with photons, they just happen to cancel their interactions in a way that eliminates classical effects but leaves quantum effects. [Classically, we say that the magnetic field is "shielded", but that does not mean that no photons are exchanged in the elementary particle sense. Photons are excitations of the electric and magnetic potentials, not the E&M fields themselves. Instead, "shielded" only means that the photons are arranged so that there is no net classical effect. In the A-B effect, the E&M fields are shielded, but their potentials are not.] The quantum effect, naturally, changes the phase of the electron and hence the Aharonov-Bohm effect. No mystery at all.

Carl

8. Aug 2, 2005

### Nicky

My opinion is that you have hit upon one aspect of the so-called "macro-objectification problem", which is still an active area of debate and research in physics. Macroscopic objects have a definite position, thus we can easily speak of forces and the E and B fields of the Maxwell equations. However, microsopic systems don't have definite position, only wavefunctions. In the wavefunction picture, the E or B you observe depends on how the system is measured, so it is hard to talk about the physical reality of E or B independent of the measurement.

The unsolved problem is, how do you choose which systems are microscopic and which are macroscopic? That choice is left rather fuzzy in the standard quantum mechanics formalism, though it has been good enough so far to produce calculations that agree amazingly well with experiment. Maybe that is because most of the things we know how to study with current technology are either very microscopic (molecules, atoms, particles) or very macroscopic (metal spheres, insulating cylinders, etc.)

Here is one review of the macro-objectification problem that I am trying to read: arXiv:quant-ph/0302164

Caveat: I am still learning quantum mechanics, so the above views may be quite naive. Those of you who are more experience in the field, please correct any gross misunderstandings.

9. Aug 2, 2005

### neurocomp2003

what are fields? mathematical object or have physicality?

10. Aug 2, 2005

### εllipse

The other replies haven't specifically addressed this, so I thought I would. The wave in a wave-particle duality is a wave of prabability. According to the Copenhagen interpretation, when a photon isn't being measured it exists as a wave, and when it is measured it is a particle. The wave determines the probability of where the photon could be at any given time. In this interpretation, there isn't a physical material (or field) that "waves". What waves is the probability of where the photon will be when observed.

11. Aug 2, 2005

### nabodit

is that supposed to mean that a photon comes to existance out of probability only when measured. thus a photon doesnt exist until u want it to do?

12. Aug 2, 2005

Staff Emeritus
Well, that's what happens if you push the formalism to be "a description of reality"; "The only photons that exist are the ones we see." But if you interpret the formalism to define what we can know about reality, then it becomes "The only photons we are concerned with are the ones we can see."

13. Aug 2, 2005

### Antiphon

I think mathematical object is closer to the truth.

Something exists objectively that will manifest various aspects of photonic
behavior when you interact with it.

As a mere Human Being, you cannot not "create" things merely by willing them to exist.

14. Aug 2, 2005

### LeonhardEuler

If light is a wave in the probability of its own position, then by what mechanism does it interact with charges? Is there also some electromagnetic characteristic to it?

15. Aug 2, 2005

### LeonhardEuler

You could take the gradient of a potential, but what would it mean? For example, if you took the gradient of the electric potential due to the nucleus of an atom and got a vector field, what would this vector field mean for an electron around the nucleus? Since the electron does not have a position, none of those vectors is really any more meaningful to the electron than another. You can't say the force on the electron is such and such, because the force varies over space. You could define force as the gradient of the potential, but would it mean anything?

16. Aug 7, 2005

### CarlB

First, I hope I never said that one could so define "the force on the electron", but instead simply said that by using the gradient this is how one can define the gradient. Second, I can't understand your logic here. It seems like you're saying that since electrons don't have specific positions, they cannot understand forces. It seems to me that the same argument would also apply to potentials, which also depend on position.

Third, classical mechanics already faced the problem of dealing with extended objects. It's called "continuum mechanics" and it includes the concept of forces being applied to objects that are not defined as having a single specific position. Naturally, we assume that what is really going on is a collection of atoms, but that was not what was assumed in the original classical work on the subject.

A good example of a classical object with an extended position and a force field or potential is the thermodynamics of a gas in the presence of a gravitational potential. This was worked out in the mid 19th century without recourse to atoms. As late as the 1890s, Mach, who was so influential on relativity and QM, was still saying "I do not believe in atoms". He felt that atoms should be disregarded since they were not (at that time) observable.

I recall a conversation I had with a professor of physics many years ago, when I was in my 3rd year of graduate school. I told him that I didn't understand what a force really was. He (jokingly) suggested that perhaps I shouldn't be studying physics. My guess is that you feel much the same way.

For a long time it has been the attitude of most physicists to, as Feynman said, "shut up and calculate". I believe that there are better ways of explaining the nature of forces, but here is not the place to discuss them. When discussing physics with people who don't understand the standard manner of looking at it, we should stick to the standard interpretations. Anything else is like giving condoms to kindergartners.

Carl

17. Aug 7, 2005

### LeonhardEuler

What I'm saying is that the force has no meaning. Shrodinger's equation gives meaning to potential because it describes its effect on the wave function. A particle with no definite position and one that is spread out in space are two different things. It is easy to define what a force is on an object that is spread out in space. For example, if you have an electric force that is acting over a body spread over a volume V, with charge density $\rho$ then the force on the whole body will be
$$\iiint \vec{E}(x,y,z)\rho (x,y,z)dxdydz$$
But if you have an object with no definite position this doesn't work. I understand that you can compute the gradient of the potential, but does it have any physical significance?

18. Aug 7, 2005

### Crosson

Photons are the carriers of the electromagnetic force. Light doesn't interact with charges, it is more correct to say that charges interact through light.

19. Aug 7, 2005

### CarlB

The Schroedinger's equation is of the form:

$$\frac{d}{dt} \psi(x,t) = \grad \psi + V \psi$$

where I hope you will forgive me for typing from memory and not including $$\hbar, m, i$$. This is the form that enters into the Copenhagen interpretation and sure enough, it uses a potential, not a force.

In the Bohmian interpretation of QM (which is the subject of a group at the University of Munich:
http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/bmstartE.htm )
one reinterprets the wave function as a "guiding" wave for the particle, and gives the particle a particular position. In order to do this, one has to add a "quantum potential", which accounts for the nonlocal effects. In other words, in Bohmian mechanics, which has exactly the same results as standard quantum mechanics (but which has not yet been made to reproduce QFT, to the best of my knowledge), the electron does possess a particular position. Thus in Bohmian mechanics, the force on the electron does make sense according to your requirements, and naturally enough, the calculated force on the electron works out to be exactly the gradient of the potential.

I should note that the above link, which gives the modern version of Bohmian mechanics for multiple particles, does not explicitly show that the force is given by the gradient of the potential. To see that it is, you can look in the first few pages of chapter 3 of Hiley and Bohm's book on the subject:
http://www.amazon.com/exec/obidos/tg/detail/-/041512185X

The above book uses a substitution (also found in Chapter I of Messiah in the discussion of the BKW approximation if I recall) for the complex valued wave function in terms of its magnitude and phase. I can't recall if I'm using Hiley's or Messiah's terms, but the substitution is something like this (ignoring h-bar):

$$\psi(x,t) = R(x,t) e^{iS(x,t)}$$

where psi is the usual complex valued wave function, R squared gives the probability density and S gives something that looks like a potential for a velocity field. In other words, $$\grad S(x,t)$$ is a velocity field. The electron paths used in Bohmian mechanics take their velocities from this field. In the mathematical sense they are orbits in this field.

Another interesting ontological reinterpretation of quantum mechanics is a statistical one. It's called the "stochastic interpretation" and it is orginally due to Nelson and was extended by Fenyes. In it, one substitutes:

$$\psi(x,t) = e^{U(x,t)} e^{iS(x,t)}$$

I believe that the stochastic interpretation has a smaller following than Bohmian mechanics, but I don't know why this would be the case; I prefer the stochastic mechanical interpretation. For examples of stochastic interpretation papers see:
http://www.iop.org/EJ/abstract/0305-4470/17/1/015
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0112063
http://arxiv.org/PS_cache/quant-ph/pdf/0112/0112063.pdf

This substitution has the advantage of giving a natural statistical mechanics interpretation of QM. That is, instead of the probability density being the ontological object, one instead has a field of energies, with h-bar corresponding to a sort of temperature.

By the way, I managed to survive many years of grad school without any of these alternative interpetations even coming up in conversation, so they really are not standard theories. But what I'm getting at with these alternative interpretations of quantum mechanics is that it is not all that obvious which of the things are fundamental and which are just the results of mathematical manipulation. I believe that finding fundamental (or ontological) variables in quantum mechanics is like trying to perform celestial navigation in a house of mirrors. Uh, that doesn't stop me from trying.

I've been interested in the details of these alternative interpretations, and the difference between potential energies and velocities for some time. For the appearance of the force in the Bohmian mechanics, if you can't get Bohm and Hiley's book, then see equation (20) from my obsolete write-up:
http://brannenworks.com/MsrEther.html

I'm now working on a paper that allows one to calculate the masses of the leptons based on principles that are essentially identical to those used in stochastic mechanics, but which are based on Clifford algebraic numbers instead of the usual complex numbers. It turns out that this makes the whole concept of exponentials more mathematically entertaining. Of course the standard model puts the masses of the leptons in as adjustable constants. The derivation is a thing of great beauty in that it really makes a good case for considering statistical mechanics as the underlying theory for quantum mechanics, at least in my opinion. For the arithmetic involved in the formula (but not the rather difficult derivation) see page 8 of:
http://arxiv.org/abs/hep-ph/0505220

Carl

Last edited: Aug 7, 2005
20. Aug 7, 2005

### Eppur si muove

A force in itself has no particular meaning but is rather defined by its effects. Thus what is usually meant by the magnitude of a force is really a rate, a change of momentum with time (or a derivative of momentum with respect to time). Hence, it is irrelevant whether particle-wave's position is fixed or not - as long as it undergoes a change in momentum, there is a force acting on the particle-wave.