Interference Pattern versus SR

[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.

 

[Adel Makram]

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.

your calculation and mine is right and shows that the time difference depends on s

 

[Adel Makram]

The matter will be much easier if there is no relativity, as from the diagram, the light sphere reaches A and B at the same time both for the ground and the slit observer,,, The phase will be equal too

thttps://www.physicsforums.com/attachment.php?attachmentid=43214&stc=1&d=1327756868oo

 

[Dale]

your calculation and mine is right and shows that the time difference depends on s

That isn't a contradiction, unless you have some other calculation which shows that it does not. Show your math, how you determined that there is a contradiction.

 

[Adel Makram]

OK,,,
consider the last diagram post in 88, and the attached diagram ( the left hand diagram is for slit A and the right hand is for B)

The source is also moving relative to the slit-FOR with -vt`

(cta`)^2 = s^2 + (ab`/2 - vt`)^2
(ctb`)^2 = s^2 + (ab`/2 + vt`)^2

where ta`and tb` are the time received by A and B relative to slit observer

after some transformation the quadratic equation yields the value of ta` and tb` as follow:
ta`= -ab` v +/- √[(ab`v )^2 + 4 (c^2-v^2)( s^2 + (ab`/2)^2] / 2(c^2-v^2)
tb`= +ab` v +/- √[(ab`v )^2 + 4 (c^2-v^2)( s^2 + (ab`/2)^2] / 2(c^2-v^2)

So clearly the s will disappear from the difference as you said,,,

But still the time difference Δt` = ab`v/(c^2-v^2) = ab`v/c^2 / 1-v^2/c^2

But for LT , Δt`= abv/c^2 / √(1 - v^2/c^2)

sorry for the bad shape,,, again you are right that s will disappear but still there is a difference

https://www.physicsforums.com/attachment.php?attachmentid=43216&stc=1&d=1327760313

 

[Adel Makram]

I got it :

Still ab` should be transformed also according to LT and the final time difference will be the same Δt`= abv/c^2 / √(1 - v^2/c^2)

Final i suppose :)

 

[Adel Makram]

in conclusion:

1) The time difference between 2 slits is the same as measured by LT where no s appears
2) The phase is the same at A & B

Oh at last it becomes clear,,, thanks DaleSpam for inspiration

But Still I believe QM has a different opinion

I appreciate your comment please on my calculation ( although on bad shape)

 

[Adel Makram]

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.

:) But SR is still not plausible for me. It used a circular logistic to yield the same result. Like the quadratic equation where u solve the equation and then substitute the root in the former equation to yield zero :)

It is a trick in math rather than a true physics

 

[PAllen]

But Still I believe QM has a different opinion
...

What do you mean by this? Quantum theory today is QFT, which include SR and the LT. So all analysis of slit timing, phase, etc. would carry over. Only the interaction theory would change (QED versus Maxwell), but the results and interpretation here would be essentially identical.

 

[Adel Makram]

What do you mean by this? Quantum theory today is QFT, which include SR and the LT. So all analysis of slit timing, phase, etc. would carry over. Only the interaction theory would change (QED versus Maxwell), but the results and interpretation here would be essentially identical.

I mean Quantum information eraser effect where the information of state of an entangled photon at 2 slits will change the appearance of the pattern as long as the time is different

It is just a broad map idea but I think it works

 

[Adel Makram]

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.

So shall we congratulate OPERA team?

 

[PAllen]

So shall we congratulate OPERA team?

If the OPERA result holds up, there will be Nobels for sure. That's the question, though.

 

[Adel Makram]

If the OPERA result holds up, there will be Nobels for sure. That's the question, though.

I wish so, I got tired from that circular logistic that called Special Relativity

 

[zonde]

:) But SR is still not plausible for me. It used a circular logistic to yield the same result. Like the quadratic equation where u solve the equation and then substitute the root in the former equation to yield zero :)

It is a trick in math rather than a true physics

It's a good idea to sort out what is physical in SR and what is just "a trick of math".
Lorentz transformation is just changing coordinate system - it's just relabeling of points in space and time. So you can call it just "a trick of math".

But there is physical part as well. It's when you say that two identical objects look and behave the same way in their respective rest frames and that these reference frames (coordinate systems) are related to each other by LT.

 

[JDoolin]

I've been discussing this with Mentz114

The Number of Wavelengths is NOT an Invariant.

This is loosely based on Mentz114's proof, but with corrections and clarifications in the definitions of β, β_obs, and β_Away.

 

[Dale]

Oh at last it becomes clear,,, thanks DaleSpam for inspiration

I appreciate your comment please on my calculation ( although on bad shape)

You are welcome! The set up equations look good, but the follow up calculations got too messy to follow on my mobile device. But the conclusion is reasonable, so I have no reason to doubt the intermediate steps.

But Still I believe QM has a different opinion

Modern QM (QED and QFT) is fully relativistic, so I would doubt it. Again, this is something you need to work through the math on.

 

[Dale]

:) But SR is still not plausible for me. It used a circular logistic to yield the same result. Like the quadratic equation where u solve the equation and then substitute the root in the former equation to yield zero :)

It is a trick in math rather than a true physics

No circular logic is involved. Start with the two postulates, derive the Lorentz transform, make experimental predictions. Where is the circle?

As far as a math trick vs true physics, the difference between math and physics is experiment. The experimental evidence supporting SR is overwhelming. To protest about SR being math tricks rather than true physics is somewhat like a five year old closing their eyes and sticking their fingers in their ears so as not to hear something they don't want to hear.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[Mentz114]

I've been discussing this with Mentz114

The Number of Wavelengths is NOT an Invariant.

This is loosely based on Mentz114's proof, but with corrections and clarifications in the definitions of β, β_obs, and β_Away.

I have to say that JD's article is incomprehensible to me. In my little work I just transform 2 points and recalculate L, the coordinate distance between them, which turns out to transform like wavelength. So the ratio L/λ is the same in both frames. Only one β appears in the transformation of L and λ.

In JD's article there are two velocities (?) which baffles me.

This quote from JDs article

In short, the number of wavelengths that FIT between two EVENTS varies with Lorentz Transformation. However, the number of waves that actually EXIST between two WORLDLINES does not vary with Lorentz Transformation.

seems to disagree with the title of the article.

If anyone can point out an error in my calculation I'd be grateful.

http://www.blatword.co.uk/space-time/srphase.pdf

 

[zonde]

If anyone can point out an error in my calculation I'd be grateful.

http://www.blatword.co.uk/space-time/srphase.pdf

Haven't you changed signature of spacetime from (-,+,+,+) to (+,+,+,+) in your transformation?

 

[JDoolin]

Haven't you changed signature of spacetime from (-,+,+,+) to (+,+,+,+) in your transformation?

The problem is that if you use the (-,+,+,+) spacetime signature to determine the distance of a null interval, you get zero.

There is a bit more discussion in Mentz114's earlier copy of the proof, in Post #52 of this thread.

You will see somewhere in the first couple of paragraphs a mention of a constant of proportionality k, relating Δx and ΔL and \sqrt{\Delta x^2 + \Delta t ^2}.

If you use the (+,+,+,+) spacetime signature to determine the distance of a null interval you get an observer dependent quantity which is proportional to the spatial distance, Δx, between the two events.

So he has defined ΔL to be a quantity which is proportional to the spatial distance, rather than exactly the spatial distance.

Since in the end, we are simply looking for whether or not ΔL/λ is an invariant, the extra constant factor does not make a difference, so long as that factor is also invariant. Since that factor is only a function of c, which is invariant, it does indeed work.

Now referring back to Mentz114's earlier proof, you will see he mentions a parameter k. Feel free to check my math, but I believe it can be calculated as follows. (And if something doesn't make sense, ask for more explicit definitions of the variables!)

\begin{align*}<br /> \Delta x &amp;= \Delta L \\ <br /> \Delta t &amp;= \frac{\Delta L}{ c}\\ <br /> \Delta x^2+\Delta t^2 &amp;=\left ( 1+\frac{1}{c^2} \right )\Delta L^2\\<br /> k \left ( \Delta x^2+\Delta t^2 \right )&amp;=\Delta L^2\\<br /> \therefore k&amp;=\frac{c^2}{c^2+1}<br /> \end{align*}

In Mentz114's later proof, he changes the definition of ΔL, so it is no longer equal to Δx, but just proportional to it, although I'm not sure he makes this entirely clear.

 

[JDoolin]

Only one β appears in the transformation of L and λ.

Here is your error, sir. There are two β's.

They are different equations, different contexts, different definitions, and most importantly, different sign conventions.

In the Lorentz Transformation equation, (the usual form with negative signs) β is the speed of the observer in the source's reference frame.

In the Doppler shift equation, β is the speed of the emitter AWAY from the observer.

Is this still baffling you?

 

[Mentz114]

I've just remembered that radar distance transforms exactly like wavelength between inertial frames, so obviously (radar distance)/wavelength is the same invariant as the one I showed earlier.

It is more intuitive because if the radar is moving towards the sender/receiver then the wavelength looks smaller, as does the distance, by the same factor. And both look longer if the radar is moving away.

[Edit] JDoolin, your post above is wrong, as demonstrated by the above.

Anyhow, I think this is hijacking the thread so we should keep this to PMs.

 

[Adel Makram]

Here is my calculation of Δt` in PDF

https://www.physicsforums.com/attachment.php?attachmentid=43252&stc=1&d=1327862756

 

[zonde]

I've just remembered that radar distance transforms exactly like wavelength between inertial frames, so obviously (radar distance)/wavelength is the same invariant as the one I showed earlier.

This seems very clear argument why number of wavelength between two events remains the same after LT.

 

[JDoolin]

I've just remembered that radar distance transforms exactly like wavelength between inertial frames

Who are you quoting here?

If you go back to your source for this, I'm sure you'll either find that they mean something different than you by radar distance, or wavelength, or inertial frames, or, they've made the exact same error you did.

Since "radar distance" and "wavelength" and "inertial frames" seem like pretty unambiguous terms to me, I suspect the most likely explanation is that they've made exactly the same error you did, which is using β in the LT and β in the Doppler shift equation without paying attention to the sign convention.

Specifically, they miscalculated the radar distance, not recognizing that it must go up as the observer accelerates toward the source.

This is VERY counterintuitive. This is such a common mistake among General Relativity Experts, I can't really blame you for it.

But please see

http://www.spoonfedrelativity.com/pages/Galilean-Transformation.php

and

http://www.spoonfedrelativity.com/pages/SR-Starter-Questions.php

and

http://www.spoonfedrelativity.com/pages/coordinate_concept_quiz.php

And TRY to understand!

 

[Mentz114]

I've just remembered that radar distance transforms exactly like wavelength between inertial frames

Who are you quoting here?

For example
http://www.phil-inst.hu/~szekely/PIRT_BP_2/papers/pierseaux_09_ft.pdf
Page 9 equation (26) and following. Especially,

... the transformation of length and wavelength are the same

This is such a common mistake among General Relativity Experts, I can't really blame you for it.

I'm not so you can. Here's me making some more mistakes,

http://www.blatword.co.uk/space-time/radarlc.pdf

 

[Mentz114]

This seems very clear argument why number of wavelength between two events remains the same after LT.

Yes, it is. It isn't intuitive that the spatial coordinate difference should transform the same way, but I can't see an error in the (trivial) calculation I did.

[Edit]In flat spacetime, radar distance is coordinate distance, so that solves that one. Dear me, is that the kind of mistake general relatvists typically make

 

[JDoolin]

For example
http://www.phil-inst.hu/~szekely/PIRT_BP_2/papers/pierseaux_09_ft.pdf
Page 9 equation (26) and following. Especially,

\sqrt{\frac{1+\beta}{1-\beta}}+\sqrt{\frac{1-\beta }{1+\beta}}=2 \gamma

assuming β is a real number between -1 and 1,

and assuming

\gamma = \frac{1}{\sqrt{1-\beta^2}}

Is that equation

(a) Always true?
(b) Sometimes true?
(c) never true


Let's make a small modification to that equation:

\sqrt{\frac{1+\beta}{1-\beta}}+\sqrt{\frac{1-\beta }{1+\beta}}=\pm 2 \gamma

Is that equation

(a) Always true?
(b) Sometimes true?
(c) never true

Now I don't mind looking stupid so long as I can learn something, so I'm going to ask the stupid questions. Where does radar time appear in the equation? Where does wavelength appear in the equation? What relevance does this equation have to our conversation up to this point?

 

[Mentz114]

\sqrt{\frac{1+\beta}{1-\beta}}+\sqrt{\frac{1-\beta }{1+\beta}}= 2 \gamma

The left hand side is symmetric in β. Changing its sign will not change the rhs which is always 2γ.

The sign convention for the LT - if two observers are separating then the relative velocity is +beta. If they are approaching the relative velocity is -beta.

This is true in both frames. Doing an LT can't make converging obervers begin to separate. My calculation is for positive beta ( separating) and gets the right result.

 

[JDoolin]

Yes, it is. It isn't intuitive that the spatial coordinate difference should transform the same way, but I can't see an error in the (trivial) calculation I did.

[Edit]In flat spacetime, radar distance is coordinate distance, so that solves that one. Dear me, is that the kind of mistake general relatvists typically make

Yeah, that's pretty close! "the kind of mistake general relatvists typically make" is to first say "the meaning of distance is arbitrary" and then not to acknowledge the different definitions of distance.

So, obviously my list of "definitions of distance and length" is not complete since I have not included this "radar distance" in the list.

You have defined what you mean by radar distance here:

http://www.blatword.co.uk/space-time/radarlc.pdf

This looks pretty good to me. I haven't worked through it in close detail, but the way you've defined radar distance, L, here, you will be correct in saying the quantity

\frac{L}{\lambda }

is invariant IF you say L is the radar distance and λ is the wavelength of the reflected signal.However, in my understanding, the problem we've been working on is what happens to

\frac{L}{\lambda }

if L is the spatial distance to an event currently being observed, and λ is the wavelength of a NON-reflected signal.

This is an entirely different problem-set-up.

To clarify:

Spatial distance (to an event)
I look at my dresser, 10 feet away, and see an event that happened to it 10 nanoseconds ago, and say, "That event looks about 10 feet away."

More mathematically, if we have two events (x0,t0) and (x1,t1) then the spatial distance between those two events is |x1-x0|.

Radar distance (to an object)
I flash a light at an object, and see the return flash about 20 nanoseconds later, divide 20 nanoseconds by the speed of light and say, "I calculate it to be about 10 feet away."

So at least I understand now that we are definitely talking about two different situations; different contexts; different problems; different definitions of the same variables. With one definition of the variables, it is true to say L/λ is invariant. With another definition of variables, it is true to say L*λ is invariant.

 

[zonde]

I've been discussing this with Mentz114

The Number of Wavelengths is NOT an Invariant.

This is loosely based on Mentz114's proof, but with corrections and clarifications in the definitions of β, β_obs, and β_Away.

Say sender is sending short pulses of light toward receiver. Number of pulses in transit between two spacetime events (one on wordline of sender other on receiver's wordline) does not change with LT. I think this works as a model for number of wavelength as well.

And if we take your picture from post #50 and imagine performing LT with it I would say that number of light wordlines crossing horizontal line will change with LT. So that number of wavelength between wordlines of sender and receiver should change with LT.