Interference Pattern versus SR

[MikeLizzi]

Oh, your statement on that diagram is wrong. Your diagram shows the sequence of events if the slit is moving with respect to the observer. A does not open before B relative to the slit observer. A opens before B relative to the light source observer.

Disregard above. I misunderstood your diagram. Something is wrong with it. I'll get back to you.

Update to my previous comment about your recent diagram. You have a “v” with an arrow that seems to indicate that the Double Slit is moving. So the two diagrams appear to me to be a sequence showing a single light wave at different times from the FOR of the light source. And yes, the single light wave will intersect the two slits at two different times in the FOR of the light source. I don’t have to know physics to recognize that.

But, as DaleSpam said, the differences in times are not frame invariant. You are not entitled to declare that the intersections take place at two different times in the FOR of the Double Slit. You have to calculate that. And what if it turns out that they do? Again, as DaleSpam said, “so what”? You conclude that this fact contradicts an equation. I don’t know what equation that is, but I doubt it was derived for the condition where the light source was moving perpendicular to the orientation of the double slit.

 

[Adel Makram]

Are you sure about your wording? If I want to transform a scene having many spheres moving at different velocities to an observer traveling at .9c with respect to the current observer, I transform all the spheres using the Lorentz Transformation. The position, proper time and geometry (contraction) of all the spheres change. But, if there is a light sphere in the scene, I don't bother transforming it because it's stays a sphere. No? Or am I cheating?

For the moving and the ground observers, the light sphere remains a complete sphere, but the ground observer watches the moving one sees the sphere in his FOR contracted in the direction of motion

 

[Dale]

for sake of simplicity, consider the attached diagram
the time to A = 1/c (sA)
the time to B = 1/c (√(sA^2 + (AB – vt)^2))

where AB is the distance between the 2 slits

In LT, Δt= AB * v/c^2 (√(1-v^2/c^2))

That would be correct if slit A were at rest and slit B were moving, but I thought that you intended for the slits to be moving in the same direction at the same speed. If the location of the source is the origin, and the location of slit A is (vt, s) and the location of slit B is (ab + vt, s) then the flash from the source at t=0 reaches A at
0=c^2 t_A^2 - (vt_A)^2-s^2
and it reaches B at
0=c^2 t_B^2 - (ab+vt_B)^2-s^2

 

[Adel Makram]

Update to my previous comment about your recent diagram. You have a “v” with an arrow that seems to indicate that the Double Slit is moving. So the two diagrams appear to me to be a sequence showing a single light wave at different times from the FOR of the light source. And yes, the single light wave will intersect the two slits at two different times in the FOR of the light source. I don’t have to know physics to recognize that.

But, as DaleSpam said, the differences in times are not frame invariant. You are not entitled to declare that the intersections take place at two different times in the FOR of the Double Slit. You have to calculate that. And what if it turns out that they do? Again, as DaleSpam said, “so what”? You conclude that this fact contradicts an equation. I don’t know what equation that is, but I doubt it was derived for the condition where the light source was moving perpendicular to the orientation of the double slit.

the derivation of the difference between the time when the light front hits the 2 slits depends on the geometry of the setup shown. But as the ground observer watches the slits open simultaneously, the LT tells that there should be difference in the time of slits opening relative to the moving one by an amount related only to the distance between the 2 slits and the velocity of the slit not the geometry of the setup.

 

[Adel Makram]

That would be correct if slit A were at rest and slit B were moving, but I thought that you intended for the slits to be moving in the same direction at the same speed.

no, both of them moving,,, actually you should imagine the diagram as a projection of 2 diagrams in 2 different time where the source is fixed in location

 

[Dale]

no, both of them moving,,, actually you should imagine the diagram as a projection of 2 diagrams in 2 different time where the source is fixed in location

Understood, so your math is incorrect. See the corrected math I just posted above in post 93.

 

[Adel Makram]

Understood, so your math is incorrect. See the corrected math I just posted above in post 93.

it is the same like mine but with different orientations,,, any way (s) appears in your equation as well while it should be s-free by LT

 

[Dale]

it is the same like mine but with different orientations,,, any way (s) appears in your equation as well while it should be s-free by LT

Why? The LT certainly does not imply that light travels instantaneously in the y direction.

 

[Adel Makram]

of course no, but LT does not consider (s) when calculating the time difference between 2 slits. It considers only ab and v

 

[Dale]

Agreed. So what?

 

[Adel Makram]

so the time difference is different in the 2 calculation

 

[PAllen]

Are you sure about your wording? If I want to transform a scene having many spheres moving at different velocities to an observer traveling at .9c with respect to the current observer, I transform all the spheres using the Lorentz Transformation. The position, proper time and geometry (contraction) of all the spheres change. But, if there is a light sphere in the scene, I don't bother transforming it because it's stays a sphere. No? Or am I cheating?

It depends. If the only thing you are interested in is a complete spherical wave front, you can just LT its emission event, and then track the sphere expanding at c from the emission event. However, if you ask about a section of spherical wave front, the size of solid angle as well as the orientation change. Applying LT to the light front itself is the most direct way to account for this.

 

[Dale]

so the time difference is different in the 2 calculation

What 2 calculations? So far there is only one.

 

[Adel Makram]

What 2 calculations? So far there is only one.

,,, ok let's see it from side of the ground observer this time,,, he watches 2 slits open simultaneously, but the slit-rider records 2 different times,,, this is the first calculation

From the source side now: when the light front reaches the 2 slits in different time ( given the same phase),,, the slit calculate that difference considering (s),,, this is the second calculation

 

[Dale]

Show your math, please. Just because the Lorentz transform doesn't involve s doesn't mean that it doesn't show up in the equations. That is why it is important to actually work things out and not simply make assumptions.

 

[Adel Makram]

either, my assumption is right which implies that; there is an inherited antagonism about the calculation of the time of opening of 2 slits,,, or the phase of light is different when reaching and leaving the slits which also carries inherited antagonism

But I am making up my mind to correct that too

 

[Adel Makram]

the conflict arises from the different way of calculation times,,, for SR, always a mid-train observer used to calculate when he receives the signal from both slits, I think because no remark to the meaning of simultaneity at both slits without involving the mid-train observer. While in the pattern experiment, the phase invariance can do the job at both ends without involving any mid-train observer

 

[MikeLizzi]

It depends. If the only thing you are interested in is a complete spherical wave front, you can just LT its emission event, and then track the sphere expanding at c from the emission event. However, if you ask about a section of spherical wave front, the size of solid angle as well as the orientation change. Applying LT to the light front itself is the most direct way to account for this.

Is that a polite way of agreeing with me? You can't use the LT to transform the shape if the light sphere, can you?

Maybe you have a simpler way, but this is how I do it.
1. Determine the time of the emission of the light in the current observer reference frame based on the radius of the light sphere.
2. Transform that time/position to the target reference frame.
3. Transform the specific event time/position to the target reference frame.
4. Scale the sphere according to the time obtained in 3, but center it using the position obtained in 2.

That's what I was trying to point.

 

[PAllen]

Is that a polite way of agreeing with me? You can't use the LT to transform the shape if the light sphere, can you?

Maybe you have a simpler way, but this is how I do it.
1. Determine the time of the emission of the light in the current observer reference frame based on the radius of the light sphere.
2. Transform that time/position to the target reference frame.
3. Transform the specific event time/position to the target reference frame.
4. Scale the sphere according to the time obtained in 3, but center it using the position obtained in 2.

That's what I was trying to point.

No, it's a polite way of disagreeing, noting that your claim is true for only the case I mentioned - that you are only interested in a complete spherical wave front.

You can, and in many cases, should apply the LT to the wavefront itself. There is no reason to treat it differently than anything else. That a complete sphere transforms to a complete sphere is derivable from the LT (though also expected via axioms of SR).

Your procedure above ignores what you do if you have only section of the spherical wave front. It is hard to generalize to that case. Meanwhile, applying LT to the equation of a wave front (section or complete sphere, or plane wave, or whatever) covers all cases correctly.

[Edit: Direct application of LT to wave front can show, for example, how a 30 degree section of a wave front in one frame can become arbitrarily close to a complete sphere in another frame. Yes, the surface is still sphere, but one would hardly call these the same shape.]

 

[ghwellsjr]

I posted this thought experiment in a previous thread before 4 months or so, but I would like to reiterate it now:
A frame of reference (FOR) has double slits moves relative to a ground FOR. Let`s make an arrangement so that when the 2 ends of FORs coincide, 2 small slits of moving FOR are opened at the same time relative to the ground observer for a brief moment to allow just 2 photons to enter from an electromagnetic source put on the opposite side of him. Let `s make the distance between the 2 slit small enough comparable to the wave-length of the photons to cause an interference pattern.
For the ground observer, he sees 2 slits open at the same time and therefore the 2 photons entering the 2 slits and create an interference pattern on a screen on his frame.
But according to SR interpretation, the moving FOR`s observer sees the front slit opens for a brief moment and then shuts before the rear one opens,,, so at one time, only one slit opens and therefore no interference pattern could ever occur. But when he looks at the screen from his window, he will see an interference pattern on the ground screen.
Can the train observer now explain why this interference pattern occurs when just the slits open one at a time?

The source emits 2 beams of light at the same time. For the ground observer, her sees the slit A and B open simultaneously, so the pattern will form on his screen at the defined point to the left side.

Adel, as near as I can tell, your scenario could be described like this:

We start by thinking of a conventional two-slit experiment at rest in a ground frame in which photons are emitted from a source, travel through two slits, and impinge on a screen forming an interference pattern. We then make a slight modification by putting shutters on the two slits so that only a pair of photons can get through at the same time but they still form an interference pattern (assuming that we repeat the experiment many times). Then we make one more modification so that just the apparatus containing the two slits and the shutters are moving at a high speed relative to the photon source and the screen but the slits are opened at the same time in the ground frame so that the interference pattern will form as before. It's this final configuration that you are describing, correct?

 

[Dale]

the conflict arises from the different way of calculation times,,,

What conflict? What different calculation? Please show. You made a mistake in your previous calculation, so I suspect that you are making a mistake in this calculation also, but until you post it we cannot tell.

 

[Dale]

Ooops. So what is the formal way of saying "you can't transform the position or shape of a light sphere" using the Lorentz transformation because it is traveling at the speed of light and gamma is undefined".

You can transform the position and shape of a light sphere. It will be a light sphere in any other frame. What you cannot do is transform to the rest frame of light.

 

[Dale]

no, both of them moving,, source is fixed in location

Is the source fixed in location relative to the slits or the frame? I.e. Are the source and the slits moving relative to each other?

 

[Adel Makram]

Adel, as near as I can tell, your scenario could be described like this:

We start by thinking of a conventional two-slit experiment at rest in a ground frame in which photons are emitted from a source, travel through two slits, and impinge on a screen forming an interference pattern. We then make a slight modification by putting shutters on the two slits so that only a pair of photons can get through at the same time but they still form an interference pattern (assuming that we repeat the experiment many times). Then we make one more modification so that just the apparatus containing the two slits and the shutters are moving at a high speed relative to the photon source and the screen but the slits are opened at the same time in the ground frame so that the interference pattern will form as before. It's this final configuration that you are describing, correct?

exactly so!

 

[Adel Makram]

Is the source fixed in location relative to the slits or the frame? I.e. Are the source and the slits moving relative to each other?

The source and the screen are fixed relative to the moving frame of reference of the 2 slits

The FOR of the 2 slits is moving and the 2 slits appears opening at the same time relative to the ground observer

 

[Adel Makram]

Again my question; if the pattern is the same, so does the phase of the 2 photons hitting the 2 slits relative to both ground and the slit observer. Then the time difference of the opening of 2 slits will depends on the geometry of the setup including the source, the distance between the 2 slits and the velocity of the slit on one hand and on the distance between the 2 slits and the velocity on the other hand according to LT. SO how that could be swallowed?

And if the time difference is the same in the 2 calculation, there must be a difference in the phase of 2 photons received when slits open, which will be in a disagreement with the ground observer who sees a same phase ?

 

[Dale]

The source and the screen are fixed relative to the moving frame of reference of the 2 slits

OK, then the above equation, both yours and my correction, is wrong since it had the source moving relative to the slits.

And if the time difference is the same in the 2 calculation, there must be a difference in the phase of 2 photons received when slits open, which will be in a disagreement with the ground observer who sees a same phase ?

What two calculations? Now we have 0 calculations.

 

[Adel Makram]

OK, then the above equation, both yours and my correction, is wrong since it had the source moving relative to the slits.

What two calculations? Now we have 0 calculations.[/QUOT]

The slit observer has to calculate the time difference between the 2 slits any way :)

 

[Adel Makram]

OK, then the above equation, both yours and my correction, is wrong since it had the source moving relative to the slits.

What two calculations? Now we have 0 calculations.

He has to calculate the difference considering the geometry and then compare it with the actual measurement based on LT

 

[Dale]

And you are claiming that there is some inconsistency in the calculations. So show it.

Have you actually performed the calculations? If so, then why are you unwilling to post the details? If not, then you don't know that they contradict each other.

For you to claim to have found some inconsistency in SR is a HUGE claim, on the Nobel prize level. You better have some math to back it up, and the math had better be correct.