# Interference in time

1. Jun 29, 2004

### anuj

Is it possible to interfere two light waves in the time domain? Does anyone has come across an experiment like this?

1. Treat time as the fourth dimention of space.
2. Consider two slits of time duration T1 seperated by
time delay T2.
3. Make sure the wavefront emerging from the two time
slits do undergo diffraction (time domain).
4. The two emitted wavefronts will broaden in time
domain and hence interfere in the overlapped time
region.
5. What do we expect: A beat pattern of varying
intensity in the time domain if the slit widths and
gap are appropriate(?). The pattern may be simmilar to
the one we observe in double slit experiment in the
space domain.

2. Jun 30, 2004

### zefram_c

Such an effect cannot be observed. A photon wavefunction can interfere with itself as it passes through a spacelike double slit because the wavefront emerging from one slit can arrive at the same point in spacetime as the wavefront from the other slit; only with a different phase. But this sort of timelike interference cannot happen... one wavefront cannot "catch up" to the past light front, nor can it ever encounter other fronts that are behind it. (This is the concept of the light cone.)
More generally, while SR unites space and time in a single framework, the timelike dimension retains a special place as causality must be preserved. You can see this even in the Maxwell equation for the electric fields (the magnetic fields are similar)
$$\nabla^2 E - \frac{\partial^2 E}{\partial t^2} = 0$$
Note the timelike dimension gets a minus sign wrt the spacelike terms. In fact you can perform a 'rotation' $$\tau = i t$$, and you can use $$\tau$$ on equal footing with x, y, z.

3. Jun 30, 2004

### anuj

Normally, we think of a phase front propagating along the three spacial dimensions as a function of time. Can't we consider a phase front in the time domain that is propagating along the special dimensions.

I mean, try to observe the interference on the time axis at a fixed location in space.

4. Jun 30, 2004

### ram1024

i don't think you're allowed to say "fixed location in space" :D

5. Jun 30, 2004

### anuj

The interference on the time axis at a "fixed location in space" means Try to observe the interference pattern at "one point on a two dimensional screen" as a function of time. Treat time asis as the screen in this case.

6. Jun 30, 2004

### Alkatran

I'm having a hard time wrapping my mind around this concept. :uhh:

I get exactly what you mean, that's no trouble, but actually seeing it... I'll have to think some more...

7. Jun 30, 2004

### zefram_c

How exactly would you suggest to create slits in the time domain?

8. Jun 30, 2004

### anuj

Switch on the light source for a short duration, followed by off, on and again off. Or use a ultra short duration pulsed light source. It is the duration of pulse width that will decide the fate of diffraction (in time) pattern.

Last edited: Jun 30, 2004
9. Jul 1, 2004

### zefram_c

I still don't think it would work. Here's my view on it:

Interference happens when two wavefronts meet at a point in spacetime and add linearly, resulting in a net disturbance. Those wavefronts might be emitted from different sources (the typical two-point interference pattern), or one source but passing through a slit of some sort. In the latter case, it is really more appropiate to think of the source(s) as being the slit(s), so it's similar to the first case.

Now, let's say two slits/emitters are spatially separated. It is then certainly possible for light from those sources to meet at a point in spacetime. If the sources are originally off, then interference will first occur at those points equidistant from the sources. At other points, it occurs as soon as light from the farther source will reach it. Once that happens, the pattern remains so if both sources are on "since t = minus infinity" then the pattern will be fully visible throughout space. What I'm getting at is that for interference to occur, you need to send two different messages (ie light waves) that arrive at one place at the same time . (This simultaneity of arrival is Lorentz invariant)

But now, let's say that there is only one emitter that's being turned on and off. Again you'd want your two messages to reach the same point in spacetime. But now you have a huge problem: your only available messenger is light, and the speed of light is always constant. Once you send one message, another will never catch up with it; it's gone and out of contact (unless of course you slow down the first one or speed up the second by using various materials, but I don't think that's what you mean). Think about it: if you could do that with light waves, you can do that with electric fields. This would mean that you could see an electric charge AND its past self at the same time, or that you could see an interference pattern from the charge's own electric fields.

Perhaps if you could write down some simple equations for the wavefronts after they pass through the "time separated slits" it would be easier for us to see if such a thing is possible.

10. Jul 1, 2004

### anuj

I agree with the earlier views on this topic. But, I suppose, Its more important to know the physics behind this effect I am talking about.

Any interference observed in the time domain would also mean that there is diffraction in the time domain. That would mean the spread of the wave function in the time domain instead of space domain. We all know from the quantum mechanics that a wave function spreads from -infinity to +infinity in the space domain and this wavefunction propagates in space as a function of time. We never talk about the spread of the same wave function in time. Do we?

Just Imagine a small window (ultra short duration pulse) in time, that causes the diffraction of light in the time domain (i.e. -infinity to + infinity). The wavefunction will still travel with the velocity of light. And two such small windows will surely produce the interference effect. It is something that can be experimentally confirmed.

11. Jul 1, 2004

### gptejms

I like to believe that just as the
wavefunction in non-relativistic quantum mechanics
gives probability density in space,the wavefunction in
relativistic quantum mechanics should give the
probability density in space-time---because space and
time are at par in relativity.So what this really
means is that a particle has some probability of going
a tiny time,centred around the present,into the past
as well as the future.In such a scenario the
continuity equation will not be satisfied(as is the
case in Klein Gordon equation)----because there are
sources and sinks(particles are appearing and
disappearing).What is the wavefunction or field(which
is a function of time t,that we understand) that we
use in say the K.G. equation----it would be the
average over time t' of the real wavefunction(which is
a function of time t',centred around t,going a little
into the past and future).So the wavefunction or field
that we see is really the average over a bit of past &
future of the real wavefunction.If this is so,perhaps,
we could design an experiment to see some interference
in time kind of effects.

Jagmeet

12. Jul 2, 2004

### anuj

Here is one more explanation by Jagmeet. It sounds good.

13. Jul 2, 2004

### zefram_c

anuj,
Are you perhaps thinking of interference in momentum space? If so, then your suggestion is correct and is in fact quite well known.

14. Jul 3, 2004

### anuj

Zefram,
No, I am not talking about the interference in momentum space. I am talking about pure time dimension.

15. Jul 3, 2004

### zefram_c

Ah. Then consider the following. Instead of a double slit, we'll have only one slit. So the experiment will look like this: the source has always been off, then at some point we turn it on for limited time, then off again. If interference in the time domain were possible, then you'd expect to see a standard diffraction pattern, and that, as you know, would extend in the time domain to before you ever turned the source on! So what would happen, then, if after we see some of this light before we turn the source on, we decide to give up and we never turn the light on?

16. Jul 4, 2004

### gptejms

This would not only violate causality but also energy.Diffraction in time domain is possible in the following sense---you have a screen blocking a matter wave which is suddenly removed(constituting an edge in time).Then there is a finite probability of finding the particle at a point distance d away in a time different from d/v,where v is the speed of the particle.In fact such a calculation has been done(see Phys. Rev. A,? & Zeilinger,3804-3824,1997)--the basic reason is fast spreading of matter wave-packets due to the presence of high momentum (Fourier)components (constituting the (sharp) wavepacket)--so the probability density reaches out faster than the speed of the particle.Such an effect is absent in the case of classical wave-equation(light) as there is no dispersion in free space.

Jagmeet

17. Jul 4, 2004

### geistkiesel

Experimental results show the particles detected as a point source. being as rational as possible, the maniopulation of the particle is over by the time they leave their respective slits and are now permanently point like particles, hence they probably do not interfer with each other, certainly not as waves, probability or otherwise.

The final statement of yours is probably incorrect as a single particle is known to "interfere with itself" and is part of wave-particle duality (which I do not buy into), but in any event two particles are not required for the patterns seen in experiment. And further it would seem irrational to conclude that two particles interferring with each other is equivalemt, or even analogous, to one particle interferring with itself, if this is all you know about the phenomenon.

18. Jul 4, 2004

### anuj

This is all known. Please remember, In the double slit interference experiments as we all know, the light waves take two different paths (special dimensions), hence different flight times resulting in the phase difference and the interference effect.

What if, the two light waves take the same path but different flight times resulting in an interference effect along the time axis. Do not treat light as a quanta that is travelling with the velocity of light. Treat it as a wave having the spread in time.

As far as the presence of interference before we open the slit is concerned, that is not allowed by the initial boundary conditions. I have a question in this regard. In the double slit expt, do we ever observe the interference pattern on the screen placed on -z axis (+z axis direction of light flight). In the same way, if t=0 is the time of opening the slit then interference will be observed along the time axis t>0 only.

19. Jul 5, 2004

### zefram_c

You are right that we would not observe the interference pattern for z<0, only z>0. But you forgot the 'other' B.C. that we only observe the interference for t>0, i.e. once the light has already arrived there. It seems to me that you're trying to get the time axis to do double work, both for regular propagation forward in time(which cannot be ignored) and for interference.
While we can ignore the quantum aspect and treat light as a regular EM wave, it still travels at the velocity of light; we can't change that. It is one of the fundamental tenets of modern physics. However, in a non-vacuum, you can do a lot of nice tricks to it, and so it *may* be possible to realize your idea. It would require us to introduce some medium to slow down the leading wave while removing it for the passage of the second wave. Is this what you have in mind?

20. Jul 5, 2004

### gptejms

How can interference be observed even before the slit is opened?This violates causality.Similarly you can't have interference on a -z coordinate,because light is not going to reverse its path while in transit unless there is a reflector.