# Conservation of energy in interference of light

In interference of light, I know that energy is conserved globally but how the energy disappeared at minima appears at maxima? Is there any path by which energy flowed or is it just energy couldn't reach at minima and all energy is at maxima. Is it right to say that energy can be destroyed if same amount of energy is created at same time in anywhere in the globe? What I am looking for is the relation between maxima and minima, I know they only appears simultaneously but what's the connection between them? If someone can explain in terms of wave theory it would be better.

• Energy is conserved locally in electrodynamics by Poynting's theorem. So no, energy cannot disappear/reappear in other places. Instead, the energy density has only moved into the maxima in the first place!
– user12029
Jun 21, 2016 at 19:09
• This is a good question! Of course we know energy is conserved, the real question is what the Poynting vector looks like in the double slit experiment. (Note that it's a purely classical question, you don't need QM for this.) Jun 21, 2016 at 21:12

The classical interference pattern is explained by the equations governing the behavior of light, and energy there is treated as a collective phenomenon, using the Pointing vector

Energy transfer in a light beam can be best understood as an emergent phenomenon from the underlying quantum mechanical level. Innumerable photons create the visible interference pattern where energy has been changing direction from uniform to bright and dark.

At the level of photons, each photon caries an energy equal to h*nu, where nu is the frequency of the light. This energy carried by the photon just changes direction when passing through slits etc, so that the confluence of photons creates the interference patterns.

Edit to describe a bit the mathematics of photons creating interference patterns:

The photon is a quantum mechanical entity, not a classical particle or wave. As such it obeys a quantum mechanical equation which when solved gives a wavefunction, psi, that describes its behavior. This is a form of the Maxwell equation where the differentials have become operators on the psi for the photon. The wavefunction is complex. The measurements of the photon position, as in an interference pattern even built up by single photons, are real numbers. The probability density of the photon being found at an (x,y,z) is the square of the wavefunction, according to the postulates of quantum mechanics. .

The indeterminacy of the Heisenberg uncertainty principle inherent in the micro framework of quantum mechanics is described mathematically in the wave function, which has a sinusoidal distribution in space and time. This explains interference patterns in scattering experiments as of two slits etc.

Photon photon interactions are very much suppressed, due to the small value of the electromagnetic coupling constant. A beam of photons can cross another beam and there is no measurable interaction. What are then the interference patterns? The wavefunctions of more than one photon are superimposed at a specific (x,y,z) , creating the classical electric and magnetic fields of the beams. As the wavefunction of each photon is sinusoidal, this is what can create interference patterns in the observed probability patterns ( sum of squares of wave functions with sinusoidal dependence).

• In second paragraph, what is the meaning of energy is changing direction from uniform to bright and dark.Is it that photons are changing their direction and if yes then why are they changing directions. Answer got bit complicated for me but basically is it that energy has just reached to bright fringes. Jun 23, 2016 at 7:22
• The simplest to think quantum mechanically is the Heisenberg uncertainty principle. The momentum of the photon has uncertainty in space, which includes direction. This is within the wavefunction of the photon, a complex function, which squared with its complex conjugate gives the probabilities. The light we see is a superposition of these wavefunctions of the photons. Where photons have high probability to materialize, it is bright. Where low, it is dark. Jun 23, 2016 at 8:28