Interference of Light Waves in Time Domain

[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 separated 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.

 

[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.

 

[anuj]

Normally, we think of a phase front propagating along the three spatial 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.

 

[ram1024]

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

 

[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.

 

[Alkatran]

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

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

 

[zefram_c]

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

 

[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.

 

[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.

 

[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.

 

[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

 

[anuj]

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

 

[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.

 

[anuj]

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

 

[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?

 

[gptejms]

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?

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

 

[geistkiesel]

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 separated 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.

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.

 

[anuj]

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 .

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 traveling 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.

 

[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.

Do not treat light as a quanta that is traveling with the velocity of light. Treat it as a wave having the spread in time.

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?

 

[gptejms]

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.

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.

 

[anuj]

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,

Thats correct, Here too, the interference will be observed for t>0 and z>0 (direction of propagation) but instead of fringes on a plane, we will need to perform the measurements at a point on the plane.

I do not think we need dispersion to explain this effect. If the interference pattern from a double slit expt requires the presence of a dispersive medium to be explained then of course we need a dispersive medium to explain the INTERFERENCE IN TIME. I don't think the physics works in this way.

 

[gptejms]

I do not think we need dispersion to explain this effect. If the interference pattern from a double slit expt requires the presence of a dispersive medium to be explained then of course we need a dispersive medium to explain the INTERFERENCE IN TIME. I don't think the physics works in this way.

You require a dispersive medium if you want to see diffraction in time kind of effects with light waves---this case is then similar to diffraction in time of matter waves(see Phys Rev paper I mentioned).If you can propose or prove a newer mode of diffraction/interference in time(e.g. probability density in spacetime) then you may have effects not foreseen by the paper.

 

[geistkiesel]

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 traveling 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.

I do not disagree with what you say. Thee is aniother parallel explanation that does not contradict you story. JS Bell tells us that all quantum effects involve nonlocal forces. Si kight, one photon is probably includes the Horizontal and Vertical polarization vectors that oscillate through time like ...HVHVHVHVHVHV... and so on. Or more generally y= Y(10f) whee it is understood that a '1' means the charactristic is observed, 0 measn the charteristic is nonlocal, or unobserved. Therofre we can shw he ime hiosotry as Y(10f) Y(01f) Y(10f) Y(01f) and so on. wher the 1 and zero are altrnating as drawn at a frequency f.

If there are two slits, the photon can transit through one of the holes and the Y(10f) through the other (or the Y(01f), or a '1' can go with the photon and the '0' through the other hole. With two holes open we see the pattern we are familiar with. With one hole it is different, which would mean that instead of going through the other hole the '1' or the '0' is now following the photon through one hole. This story tells us the interaction of the nonlocal forces is crucial to pattern development wrt to the parallel or single file transition of the nonlocal force centers of the photon.

Whatever your conclusion however, you must use nonlocal force centers in your model for a minimum satisfaction of "model completeness", or so proved JS Bell.

If the z axis is the direction of flight you are suggesting that the pattern extend back into the space in front of the pattern?

It would necessarily have to extend in front of the screen, for one simple reason: There are no zero thickness photons, so at least for some t > zero there is a three dimensional pattern before the photon collpases, like an accordion, into the screen. This might be technically difficult to observe, but there are a lot of good engineers out there. Just remember the photons will only be detected as point particles when actually scintillating on the screen, or at least that is what the liddle birdy that is sitting on my shoulder is telling me at the moment.

Well it is an opinion.

 

[geistkiesel]

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

make an exception ram1024. You can afford it. Remember that a light beam is is not dependent on the velocty of the source for anything. If you have two parallel mirrors and a photon is emitted between the mirriors the beam is fixed in space as if planted there in concrete, or stainless steel, or the best "supoer glue". The beam, once emitted is a well defined coordinate axis as the beam cannot be manipulated by frames whizzing by or even when SR theorists start considering how they are going to consider what they are going to do the this pesky absolute coordinate axis in absolute space. The axis is a good refeence frame for all inertial and noniertial frames. The invariant beam is pure like communism was beofore the bolshevicks and republicans got ahold of it, remember?

If the two parallel mirrors start to move parallel to the mirror surfaces th ebeam is not dragged along and neither can observers use off angle radiation form the beam as a substitute for the fixed axis. Eventuall the apparatus will move into the fixed beam but thsi can be compensated for. I have a post around somewhere that I describe a modified ram1024 buo

Six sided, sources at the center of facing sides. If the buouy moves in the x direction say, the minus x face will strike the oncoming photon first, As the plus face is moving away the photon will arrive there later, eventually the photons will arrive simulatneously to t where the new midpoint of the two faces of the cube is located. To zero the velocity, just determine any xyz motion direction the cube is mioving, apply brakes and one has an absolute modified zero velocity ram1024 space buoy. You can get a lot of money for just one of those. Get to the patent office Monday as soon as they open.

 

[anuj]

This thread was started in July 04 with the view to understand if interference in time is possible. I am surprised to see that a group of scientists have recently observed this effect. One can see the site

http://physicsweb.org/articles/news/9/3/1/1?rss=2.0