Light Sphere Paradox: A Conundrum with No Solution?

In summary, the setup for this conundrum is like the light sphere illustration. Two frames, F and F' are used. F' is moving and at v=.8c, a light burst is emitted. Looking at two points at opposite sides of the expanding sphere, P+ and P-, P+ at x=10 and P- at x=-10, t=10, x'=3.334, t'=3
  • #1
Austin0
1,160
1
Hi
The setup for this conundrum is like the light sphere illustration.

Two frames F and F' ------- F' moving ---->+x at v=.8c

At the point of colocation of the origens: x=0 and x'=0 t=0,, t'=0 a light burst is emitted .

Looking at two points at opposite sides of the expanding sphere

P+ and P-

P+ at x=10. t=10 , x'=3.334, t'=3.334

P- at x=-10,t=10, x'=-30,t'=30

As these locations in both frames are large photosentive panels. Lensless photodiode
arrays directed at the origens and orthogonal to the motion so it can be assumed they are the same actual sizes. These measure the number of photons intersecting them over the whole area and output a luminosity value ( L)
The question is: What would the respective relative values be?

Assumptions :

Any photon in the sphere at a point in its worldline is actually simultaneous with all other photons at that time and all are absolutely equidistant from the origen.

Because of this the sphere can be viewed for convenience as having a single worldline.

The spheres luminosity will diminish along the worldline. Any local segment will have an absolute luminosity at any given point.

A point on the worldline may intersect relative frames at different points on their worldlines but it would be assumed that colocated observers at those points would be measuring the same point of the sphere.

1) Based on this,, it would seem that at any colocated point, the measurements would have to be equal.

Both frames at P+ would measure equal values:
P+ L+=L'+
P- L-=L'-

2) Based on the 1st Postulate and the fact that luminosity must diminish as a function of distance D ,,,dec reasing exponentially with increasing distance

it would mean that L+ with D=10 must equal L- with D=10

L'+ [D=3.334] must be greater than L'- [ D=30]
________________________________________________________________________

A) If we assume ----#1)

that the measurments must agree between both frames colocated at a point then the L values cannot be a function of distance in both frames because the distances are equal in one frame [F] but greatly unequal in the other [F']


B) If we assume -----# 2)

that the values must be a function of D then the frames cannot agree on colocated measurements.
The measurements must be equal in F but cannot be equal in F'


If A) then there is a violation of the 1st Postulate.

If B) then it has to be explained how two colocated measurements of the same point on the light cone could possibly be different?

Or alternately how two observers measuring two different points on the cone [with different luminosities ] could possibly be colocated ?.

As far as I can see:

---------- [Both A and B must be true]---- AND[---- Both A and B cannot be true.]------------

So any solutions or insights would be great.
Thanks
 
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  • #2
Did you account for the Doppler shift?
 
  • #3
DaleSpam said:
Did you account for the Doppler shift?

I thought about it but concluded it was not relevant because

1) it would be reciprocal in F'
the decrease in energy (L+) at x'=3.334
equal to the increase (L-) at x'=-30

Whereas the difference in magnitude of L due to distance would be exponential I would imagine by a factor of 4 pi(r2) ?

2) There are only two events. So just on principle whichever frame you choose to analyse it from the other frame will be the one dopplered. So that is reciprocal and self cancelling in this case as far as resolving the question.

I* also played with other ideas like a photon not being localized but existing from the point of emission through the whole path until absorbtion but this didn't seem to lead anywhere.
Thanks
 
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  • #4
Any photon in the sphere at a point in its worldline is actually simultaneous with all other photons at that time and all are absolutely equidistant from the origen.

Because of this the sphere can be viewed for convenience as having a single worldline.
No. If it's extended, it can not be viewed as having a single worldline. Never.
Based on this,, it would seem that at any colocated point, the measurements would have to be equal.
Acoordingly: no.
 
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  • #5
Austin0 said:
I thought about it but concluded it was not relevant
Then luminosity must be frame variant, not absolute. This really should not be too surprising since energy is frame variant and luminosity is related to energy.
 
  • #6
DaleSpam said:
Then luminosity must be frame variant, not absolute. This really should not be too surprising since energy is frame variant and luminosity is related to energy.

Energy is relevant within the context of the doppler effect. But unless you disagree with me about it not being enough to explain the difference in luminosity
then it is purely a question of how many photons reach a given area.

SO are you are saying that the number of photons in a given section of an expanding spherical surface at a single point must be frame variant?

or do you mean the electrical energy generated by the photons being frame variant?

Wouldn'y that be inconsistent with 1st Postulate??
 
  • #7
Ich said:
No. If it's extended, it can not be viewed as having a single worldline. Never.

I did say for convenience. But you are right . Spatially it is a collection of worldlines but temporally at a given moment, all parts share a common time and distance as measured simply as distance from origen.
You do understand I am not talking about it in coordinates of an inertial frame but viewing it as an absolute entity in reference to its point of origen.
 
  • #8
Sorry, I had a longer post but lost it. Here's the relevant thing:
2) Based on the 1st Postulate and the fact that luminosity must diminish as a function of distance D ,,,dec reasing exponentially with increasing distance

it would mean that L+ with D=10 must equal L- with D=10

L'+ [D=3.334] must be greater than L'- [ D=30]
Exactly. Concerning angular size and total photon number per area, a moving source looks like a stationary source in the distance it had at the time of emission in the observer's frame. This effect is called aberration.
Doppler shift additionally increases/decreases photon rate and energy per photon.
 
  • #9
Austin0 said:
Energy is relevant within the context of the doppler effect. But unless you disagree with me about it not being enough to explain the difference in luminosity
then it is purely a question of how many photons reach a given area.
I neither agree nor disagree. I would have to see the math, but I am certainly not convinced either way at this point and an argument that ignores something as ubiquitous as the Doppler effect seems pretty weak to me.

Austin0 said:
SO are you are saying that the number of photons in a given section of an expanding spherical surface at a single point must be frame variant?
The number of photons is often indeterminant even in a single frame, and it is also frame variant. See the Unruh effect for one example, I don't know if it is a more general principle.

Austin0 said:
Wouldn'y that be inconsistent with 1st Postulate??
Why would any of this be inconsistent with the 1st postulate?
 
  • #10
Austin0 said:
Hi
The setup for this conundrum is like the light sphere illustration.

Two frames F and F' ------- F' moving ---->+x at v=.8c

At the point of colocation of the origens: x=0 and x'=0 t=0,, t'=0 a light burst is emitted .

Looking at two points at opposite sides of the expanding sphere

P+ and P-

P+ at x=10. t=10 , x'=3.334, t'=3.334

P- at x=-10,t=10, x'=-30,t'=30

As these locations in both frames are large photosentive panels.

Ostensibly, the panels have a non-zero area. In order to solve your "paradox" (I don't think that there is any), you will need to calculate the flux falling on each panel.

Lensless photodiode
arrays directed at the origens and orthogonal to the motion so it can be assumed they are the same actual sizes. These measure the number of photons intersecting them over the whole area and output a luminosity value ( L)
The question is: What would the respective relative values be?

This question has been answered long ago by Einstein in his 1905 paper.

The ratio of amplitudes as viewed from frame F and F' is:

[tex]\frac{A'^2}{A^2}=\frac{1-v/c}{1+v/c}[/tex] (end of paragraph 7)

The ratio of energies is:[tex]\frac{E'}{E}=\sqrt{\frac{1-v/c}{1+v/c}}[/tex] (paragraph 8)

The above formulas look a lot like the relativistic Doppler effect because they are derived based on the Doppler effect:

[tex]\frac{\nu'}{\nu}=\sqrt{\frac{1-v/c}{1+v/c}}[/tex]

So, DaleSpam was right all along. Now, I did not read your post to the end , what is the paradox you are trying to figure out?
 
  • #11
Ich said:
Exactly. Concerning angular size and total photon number per area, a moving source looks like a stationary source in the distance it had at the time of emission in the observer's frame. This effect is called aberration.
Doppler shift additionally increases/decreases photon rate and energy per photon.

Hi Actually it was through studying aberration and pinhole cameras that I got onto this in the first place.
An emission event such as a large flat light panel emitting a single flash and subsequently observed in two frames should have different angular sizes depending on their motion relative to the flash. The flash of course occurs at a specific location in each frame and is stationary in both.

Because of this they must both agree on the angular size of the panel,, yet both see the other in motion relative to the image as it propagates to their receptors.
A pinhole camera explains why this this is possible.

From the frame where the other is perceived as moving toward the source it appears as if the received image must appear larger [greater subtended angle]
But in the moving camera the focal plane is moved closer to the aperture through length contraction and the motion of plane between entering the camera and hitting the plane.

This causes the size of the image on the focal plane to shrink and appear farther away.
Like wise if the camera is moving away from the source.

Doppler

Agreed ----D shift causes a decrease in photon rate and energy.

But in the current scenario photon rate is irrelevant. It is a singular, very short interval reception and it is just the total number of photons that arrive that is important not how many per unit time

On the energy increase/decrease through Doppler;
1) Remember the source is stationary in both frames.
It should be considered a spontaneous emmission from the quantum field,,, of unknown frequency.
I used one frame as a rest frame but the two events I derived must occur in both frames.. So Doppler can be applied from either frame in which case it will reciprocal and purely relative unlike the two events in my problem where boith frames agree.

SOrry you lost the rest. Thanks
 
  • #12
Remember the source is stationary in both frames
That's impossible.
 
  • #13
=DaleSpam;2788228]I neither agree nor disagree. I would have to see the math, but I am certainly not convinced either way at this point and an argument that ignores something as ubiquitous as the Doppler effect seems pretty weak to me.
Fair enough. Your riight , simply because I convinced myself it was not relevant is not sufficient. So I am in the process.

Assuming we apply the Doppler from the perspective of F' .
At P2 (x'=-30 t'=30 ), (x=-10.,t=10)
F' would calculate that the measurement (L) in F would be decreased.

At P1 (x'=3.334 ,t'=3.334) , (x=10 ,t=10)
F' would calculate that the measurement (L) in F would be increased.

If you assume that has any meaning then[/I:
]P1 (x=10) L cannot equal P2(x=-10) L

Different measurements at the same distance in a frame would seem to be inconsistent with the 1st Postulate.


The number of photons is often indeterminant even in a single frame, and it is also frame variant. See the Unruh effect for one example, I don't know if it is a more general principle.

Maybe you could explain a little about the indeterminancy?
Do you mean on a quantum level? Or just as a statistical margin of error?
I am thinking that you could make receptor array as large as you like.
I just read about people using the Canon latest CMOC cameras to determine photon counts , weighted values for frequency [which the receptors also determine], with claimed reasonable margins of error.
SO a (100 sq. m) matrix should make it fairly workable.

I checked out Unruh not applicable , black body radiation through acceleration.

Thanks
 
  • #14
austin0-----Remember the source is stationary in both frames

Ich said:
That's impossible.

Only if you think source means a mechanism. I was referring to the source of the sphere.

Unattached to any frame. The location of the initial observation of the phenomenon.


I purposely didn't locate a mechanism in the description ;the beginning of the light burst was simply a colocated event with the coincidence of the origens.

Would it make any real difference if it was the result of a mechanism located on a different frame passing orthogonally ??
 
  • #15
Would it make any real difference if it was the result of a mechanism located on a different frame passing orthogonally ??
Yes.
I'm not sure exactly how your setup is supposed to look like. I took it to be a "homogeneous" light sphere, and a light sphere looks homogeneous only in the source frame.
 
  • #16
starthaus said:
Ostensibly, the panels have a non-zero area. In order to solve your "paradox" (I don't think that there is any), you will need to calculate the flux falling on each panel.



This question has been answered long ago by Einstein in his 1905 paper.

The ratio of amplitudes as viewed from frame F and F' is:

[tex]\frac{A'^2}{A^2}=\frac{1-v/c}{1+v/c}[/tex] (end of paragraph 7)

The ratio of energies is:


[tex]\frac{E'}{E}=\sqrt{\frac{1-v/c}{1+v/c}}[/tex] (paragraph 8)

The above formulas look a lot like the relativistic Doppler effect because they are derived based on the Doppler effect:

[tex]\frac{\nu'}{\nu}=\sqrt{\frac{1-v/c}{1+v/c}}[/tex]

So, DaleSpam was right all along. Now, I did not read your post to the end , what is the paradox you are trying to figure out?


Thanks for the relevant math. YOu gentlemen have convinced me I am going to have to
work it in.

Just a first take;
at v=.8c it appears to be a reciprocal factor of 3 and .33

the luminance flux falloff at the distances in my setup [ x'=-30 and x' = 3.334]

are: 302 =900 ---------- 3.3342 = [tex]\approx[/tex]10

Hugely different ratios. In my problem its the ratios that are important as there is no quantitative comparison merely greater ,equal or lesser.
But I will keep working with it.
Also there is the CMOS info I posted above , which seems like it might remove the doppler factor because it makes possible weighted photon counts Devidng the enrgy by wavelength and deriving photon counts. It is purely phonton count that is the basis of apparent paradox.
I am sorry I can't think of a few words to explain it maybe some will come to me. But if you haven't read it , it may be a little early to conclude DaleSpam was right?
Thanks
 
  • #17
Austin0 said:
Maybe you could explain a little about the indeterminancy?
Do you mean on a quantum level? Or just as a statistical margin of error?
Yes, I mean on the quantum level. The best example I know of is a coherent state:
http://en.wikipedia.org/wiki/Coherent_state

In a coherent state the number of photons has an uncertainty relationship with the phase of the state. And detecting a photon leaves the state unchanged. Essentially, any state which is not an eigenstate of the Hamiltonian will not have a definite number of photons.

Austin0 said:
I checked out Unruh not applicable , black body radiation through acceleration.
Yes, I agree that the Unruh effect is not applicable, it was just intended as an example of the fact that the number of photons is frame variant. I don't know if there is a similar effect which is applicable for a pair of inertial frames.

Austin0 said:
it may be a little early to conclude DaleSpam was right?
:biggrin: It is never too early to conclude that DaleSpam was right!
 
  • #18
Austin0 said:
output a luminosity value ( L)
Austin0 said:
the luminance flux
Could you clarify. Are you interested in how the luminance or luminosity transforms? They are different quantities.
 
  • #19
DaleSpam said:
Yes, I mean on the quantum level. The best example I know of is a coherent state:
http://en.wikipedia.org/wiki/Coherent_state

In a coherent state the number of photons has an uncertainty relationship with the phase of the state. And detecting a photon leaves the state unchanged. Essentially, any state which is not an eigenstate of the Hamiltonian will not have a definite number of photons.

Yes, I agree that the Unruh effect is not applicable, it was just intended as an example of the fact that the number of photons is frame variant. I don't know if there is a similar effect which is applicable for a pair of inertial frames.

:biggrin: It is never too early to conclude that DaleSpam was right!

Once again you came up with a very interestin refernce. Thanks.
It appears to me to be more related to coherence in an emitting source as resonant phase buidups or reinforcements. I don't quite see how it would apply to a singular ideally short interval burst ? Or measuring the same through complex detectors and filters. Once again it doesn't seem to apply??
The initial conditions could be changed to install such detectors instead of CMOS but I also don't really see how that would significantly alter the picture.
Also it seemed to indicate that the higher the emitting energy the less statistical deviation was expected but I could have read that wrong.
Do you think that this level of quantum flux would really be significant given large detectors , the problem does not call for any kind of quantitative accuracy but rather large disproportionate ratios??

Its never too early to conclude DaleSpan has some sense of humor!
 
  • #20
Austin0 said:
Once again you came up with a very interestin refernce. Thanks.
It appears to me to be more related to coherence in an emitting source as resonant phase buidups or reinforcements. I don't quite see how it would apply to a singular ideally short interval burst ? Or measuring the same through complex detectors and filters. Once again it doesn't seem to apply??
Well, if you are really interested in number of photons then you will need to write out the wavefunction for your ideally short interval burst. Then you will need to find the eigenstates of the Hamiltonian. If your wavefunction is not an eigenstate (which I suspect it will not be) then the number of photons is not definite even in a single frame.

My thought is that this would be some serious overkill for what you really want to know which is how the luminance (or luminosity, please clarify) transforms. I would take a more starthaus-like approach and look at continuous fields rather than discrete photons. The transformation laws for the fields are well known.
 
  • #21
Austin0 said:
e

On the energy increase/decrease through Doppler;
1) Remember the source is stationary in both frames.

This can't be since the two frames are moving wrt each other.


I used one frame as a rest frame but the two events I derived must occur in both frames.. So Doppler can be applied from either frame in which case it will reciprocal and purely relative unlike the two events in my problem where boith frames agree.

What is this supposed to mean? What do you mean by "both frames agree"? Agree on what?
 
  • #22
DaleSpam said:
Could you clarify. Are you interested in how the luminance or luminosity transforms? They are different quantities.

In actuality I misused the term luminosity. I think luiminance or luminance flux is more correct.
In any case I believe it falls off as a function D2 or with a sphere -(r2).
AM I wrong in this?? In any case the whole subject of light measurement as normally applied is both complex and somewhat ambiguous about terms from what I have read.
But really; is it relevant?
In this case there is no need to relate it to any factor of the source intensity or normalize it in any was. WE know we are concerned simply with photon count relative to receptor area. Purely based on spherical surface area and expansion it would seem to follow the above function. No?

As far as transforms; are you talking about the energy function of relative velocity that espen posted?

Once again you can apply that but it must be applied reciprocally to both frames and:
a) It would have no real meaning because it is just another relative perspective
whereas the events are frame frame independant [between these two frames only, obviously]
b) If it was possible to resolve the problem with unilateral application this would in effect mean an actually preferrred frame. Which is really the basis of the paradox.

In all respect I suspect that you all ; read the post, assumed it was another twins or barn and ladder with a simple resolution and haven't really thought to much about understanding the basis of it.

I will tell you this. Last year I posted a version with the pinhole scenario. JesseM replied , mentioning having noticed the same enigma in the light spheres but didn't elaborate or propose any details, explanation or resolution.
That wasn't necessary as I immediately not only saw how it would apply but that the sphere was a much better context. Less directly obvious and more complex but offering a more complete exposition.
SO it may in the end ,turn out to be explainable but I really don't think it is going to be simple or obvious. But then I can vaguely remember being wrong once before.
 
  • #23
DaleSpam said:
Well, if you are really interested in number of photons then you will need to write out the wavefunction for your ideally short interval burst. Then you will need to find the eigenstates of the Hamiltonian. If your wavefunction is not an eigenstate (which I suspect it will not be) then the number of photons is not definite even in a single frame.

My thought is that this would be some serious overkill for what you really want to know which is how the luminance (or luminosity, please clarify) transforms. I would take a more starthaus-like approach and look at continuous fields rather than discrete photons. The transformation laws for the fields are well known.

The wave function is unknown because the wave frequency is unknown, you can't start with the source information. This is a onetime emission out of the cosmos.

The transformation laws by default simply return relative information. This problem is not based on determining actual values for the colocated measurements. This would be equivalent to calculating clock desynchronization.

This is a logical proposition. You assume agreement ,or difference , greater or lesser and look at the outcome of these possibilities.
There aren't that many.

But you seem to be suggesting that the photon detection, photometric measurement that takes place in labs all over the world is flawed because they didnt calculate the wave function of the source.
Of course there is going to be a degree of quantum uncertainty,
A small statistical error in instrument imperfection. But that doesn't negate there validity for their purpose. And much of it is directly based on measureing number of photons.

In this situation we can assume the light from the source will be equivalent in both frames and equal uncertainty and instrument error.
 
  • #24
=starthaus;2789355]This can't be since the two frames are moving wrt each other.

Only if you think source means a mechanism. I was referring to the source of the sphere.

Unattached to any frame. The location of the initial observation of the phenomenon.

COnsidered by both frames to be a staionary location in their frame [the origen]


I purposely didn't locate a mechanism in the description ;the beginning of the light burst was simply a colocated event with the coincidence of the origens.

Would it make any real difference if it was the result of a mechanism located on a different frame passing orthogonally ??


What is this supposed to mean? What do you mean by "both frames agree"? Agree on what ?

Agree on the colocation and simutaneous measurement at those coordinates.
At both P1 and P2 .
 
  • #25
Austin0 said:
Only if you think source means a mechanism. I was referring to the source of the sphere.

Unattached to any frame. The location of the initial observation of the phenomenon.

COnsidered by both frames to be a staionary location in their frame [the origen]
If you're referring to the center of the sphere as defined as the point equidistant between simultaneous detections of light in either direction, then yes, the center of the sphere is stationary in each frame. But notice that the origin of F' is not equidistant between the sensors you specified in your post 1, so they don't represent the simultaneous "edges" of a light sphere centered on the origin of F'. Those sensors will detect either edge of an expanding light sphere (centered at origin of F') at different times and distances from its center.

The center of a light sphere that is detected simultaneously by those sensors in F' (x'=3.334 and x'=-30) would be located at x'=-13.334 in F'.
 
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  • #26
Here is a quick visualization of what is happening. Let's say we have a metal sphere with a light source at the center. In the frame of the metal sphere, the photons will spread out equally in all directions as seen in the first part of the diagram. An observer in another frame that watches the metal sphere travel away at some speed will see the metal sphere contracted in the line of motion, so sort of oval shaped. According to the observer also, the light will originate from the center of the metal sphere at the place the metal sphere happened to be when the light was emitted.

However, if the light spreads out equally in all directions according to the frame of the metal sphere, it cannot do so according to the frame of the observer. This is because all observers must agree that all of the photons begin in the same place at the center of the metal sphere and also that they coincide with the same places upon striking the outer shell of the metal sphere. The observer, then, will see the paths of the photons angled differently. The green lines in the bottom part of the diagram, for instance, represent the photons that travel from the center of the sphere at the place the metal sphere was when it emitted them (blue) and strike the top and bottom and both sides of the metal sphere after it has moved some distance (red) because all observers must agree that the photons strike in the same places on the surface of the metal sphere. Since the metal sphere is moving according to the observer, the top and bottom of the sphere will have moved some distance during the time the photons take to get to those places, so the paths of those photons are angled slightly forward according to the observer. In fact, all of the paths end up angled slightly forward due to the motion of the sphere.

The bottom diagram is not drawn exact, however, so don't take it too literally. In reality it would take a lesser time for a photon to travel across the horizontal set of green lines to the back of the metal sphere while the back of the metal sphere travels toward that photon than it would for a photon to travel forward to the front of the metal sphere while the front of the metal sphere travels away, so the metal sphere will be in different places when each of those photons strike, as well as for each of the rest of the photons, depending upon each particular path the photons must take between their endpoints from the center of the metal sphere to same places that they coincide with the surface and the time it takes to do so, but the diagram is close enough for visualization with just the single representation of the metal sphere. Because all of the paths are angled more to the front according to the observer, the intensity will be observed as brighter when the metal sphere is traveling toward the observer than away, as can be seen from the extended lines at the bottom of the diagram.
 

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  • #27
Originally Posted by Austin0
Only if you think source means a mechanism. I was referring to the source of the sphere.

Unattached to any frame. The location of the initial observation of the phenomenon.

COnsidered by both frames to be a staionary location in their frame [the origen]

Al68 said:
If you're referring to the center of the sphere as defined as the point equidistant between simultaneous detections of light in either direction, then yes, the center of the sphere is stationary in each frame. But notice that the origin of F' is not equidistant between the sensors you specified in your post 1, so they don't represent the simultaneous "edges" of a light sphere centered on the origin of F'. Those sensors will detect either edge of an expanding light sphere (centered at origin of F') at different times and distances from its center.

The center of a light sphere that is detected simultaneously by those sensors in F' (x'=3.334 and x'=-30) would be located at x'=-13.334 in F'.

I was referring to the the point of initial observation which both frames regard as stationary in their own frame. SO it follows that this would be the same point occurring between simultaneous observations in any frame so your interpretation is also correct.

As is everything you said after that.

I never suggested that the observations at points P1 and P2 represented simultaneous edges of the light sphere. In fact it is obvious that they could not be because; if that were the case then frame F with equidistant measurements would be a preferred frame.
But that is not at all germaine to the issue.

The point was; that the sensors at F' (x'=3.334 and x'=-30) would measure their distance from F'( x'=0) and base the light falloff function on that distance. They would base their calculation of where the center of the sphere was from a comparison of measuremnts at (x'=-30) and (x'=30)
In both cases they would consider x'=0 as the center.

This problem has nothing to do with where the center "is" beyond that.

I am sorry if I may have confused the issue by describing the sphere itself in absolute terms. It was simply an attempt to make it clear that there is only one sphere and all colocated observations occur at a single point on that sphere [light cone]
To avoid the misconception, which I seen by many, that different frames are in effect, seeing different spheres [ where they are in the center] .

This problem simply starts with the light-sphere setup with exactly the normal outcome and understanding.
It isolates two points [events] and applies ordinary physics (light falloff) in both frames which we can do without recourse to transformation (1st Postulate )

ANd then from there logically looking at the possible measurements resulting from that physics. Since its inception there has now been added the relative factor of Doppler effects so there is an additional physics to be considered. In this case I believe the Doppler factor is 3 and .33 a ration of 9 /1 The falloff factor is 1/900 at (x'=-30) compared to 1/10 at (x'=3.334 ) --- 90/1

at (x'=-30) 3 /90 = .03343
at (x'=3.334 ) .334/1 =.334

If I am mistaken in this I would appreciate learning.

That no one has yet seemed to see the problem I am talking about, I attribute to my [admittedly] limited powers of description and communication.
I would be very surprised if it was because of any disagreement on basic SR.

Thanks for your input
 
  • #28
Austin0 said:
In actuality I misused the term luminosity. I think luiminance or luminance flux is more correct.
In any case I believe it falls off as a function D2 or with a sphere -(r2).
AM I wrong in this??
There is no such thing as "luminance flux" so I assume you mean "luminous flux". Luminance does fall off as D², but luminous flux does not. However, it seems like you are unsure of the terminology, so may I suggest that you may actually be interested in irradiance. Luminance and luminous flux are both perceptual measures, i.e. a 100 MW x-ray has 0 luminance and luminous flux because the x-ray wavelength is outside of the visible range. This could easily lead to the case where a blueshift actually reduces the luminance even though the energy has increased, and it will make the results of your inquiry depend strongly on the color of the light source. On the other hand, irradiance is a physical measure of electromagnetic power received per unit area (and it drops off as D² also) irrespective of wavelength.

Austin0 said:
WE know we are concerned simply with photon count relative to receptor area. Purely based on spherical surface area and expansion it would seem to follow the above function. No?
I disagree with this still. Suppose in one frame the radiation is spherically symmetric in power. Then in that frame the conservation of energy and spherical symmetry requires that the irradiance fall off as D² with no angular dependence. If we then boost that radiation into another reference frame then we will introduce an angular dependence with the polar angle from the direction of the boost (Doppler and abberation). By symmetry there will be no azimuthal angle dependence. In the boosted frame the irradiance will fall off as D², and will still have the polar angle dependence.

Austin0 said:
b) If it was possible to resolve the problem with unilateral application this would in effect mean an actually preferrred frame. Which is really the basis of the paradox.
There is at most one frame in which the irradiance is spherically symmetric. That doesn't mean that it is a preferred frame in the usual sense.

Austin0 said:
But you seem to be suggesting that the photon detection, photometric measurement that takes place in labs all over the world is flawed because they didnt calculate the wave function of the source.
No. What I am suggesting is that if you want to predict photon detection then you need to calculate the wave function. If you just want to measure it then you simply do so, but here we are talking about predicting what we would expect to measure. However, again, I do not think that the photon count is particularly useful to this scenario. I would stick with a purely classical treatment rather than a quantum treatment.
 
  • #29
=DaleSpam;2790885]There is no such thing as "luminance flux" so I assume you mean "luminous flux". Luminance does fall off as D², but luminous flux does not. However, it seems like you are unsure of the terminology, so may I suggest that you may actually be interested in irradiance. Luminance and luminous flux are both perceptual measures, i.e. a 100 MW x-ray has 0 luminance and luminous flux because the x-ray wavelength is outside of the visible range. This could easily lead to the case where a blueshift actually reduces the luminance even though the energy has increased, and it will make the results of your inquiry depend strongly on the color of the light source. On the other hand, irradiance is a physical measure of electromagnetic power received per unit area (and it drops off as D² also) irrespective of wavelength.

No question about my uncertainty. I did not think exact terminology was crucial.
I will check out irradiance . I wonder do CMOS receptors react to the invisible spectrum.

DO you see any reason why I couldn't just specify the boundary condition of visible light?

___________________________________________________________________________

Originally Posted by Austin0
WE know we are concerned simply with photon count relative to receptor area. Purely based on spherical surface area and expansion it would seem to follow the above function. No?

I disagree with this still. Suppose in one frame the radiation is spherically symmetric in power. Then in that frame the conservation of energy and spherical symmetry requires that the irradiance fall off as D² with no angular dependence. If we then boost that radiation into another reference frame then we will introduce an angular dependence with the polar angle from the direction of the boost (Doppler and abberation). By symmetry there will be no azimuthal angle dependence. In the boosted frame the irradiance will fall off as D², and will still have the polar angle dependence.

I agree that Doppler could be relevant and deserves consideration and inclusion.

Regarding abberation I have to disagree. That is why I tried to establish the absolute nature of the sphere and the fact that colocated simultaneous measurements are actually occurring at the same point of the light cone, the spheres evolution through time.

SO the coordinate distances from the coordinate locations of the "source" may be different in the frames [with a difference in resulting angles] but the distance and angle from the actual source cannot be different. SO the actual irradiance [number of photons] cannot be different.

Even with this condition, the Doppler effect would be expected to actually be different but not the angle or actual photon count.
_______________________________________________________________________

Originally Posted by Austin0
b) If it was possible to resolve the problem with unilateral application this would in effect mean an actually preferrred frame. Which is really the basis of the paradox.

There is at most one frame in which the irradiance is spherically symmetric. That doesn't mean that it is a preferred frame in the usual sense.

I am not sure what you mean here.

DO you mean that if out of a large number of different frames only one measured symmetric irradiance it wouldn't be evidence of a preffered frame??

DO you mean that in relation to the absolute sphere there is only one possible frame where the irradiance could be actually symmetric?? [ In which case I agree]

DO you mean that between the two frames under consideration only one could measure symmetric irradiance ? [ in this case I would have to disagree. That is the basis of this problem. By the 1st P both frames have to measure symmetric irradiance, don't they?.]

____________________________________________________________________

Originally Posted by Austin0
But you seem to be suggesting that the photon detection, photometric measurement that takes place in labs all over the world is flawed because they didnt calculate ...

No. What I am suggesting is that if you want to predict photon detection then you need to calculate the wave function. If you just want to measure it then you simply do so, but here we are talking about predicting what we would expect to measure. However, again, I do not think that the photon count is particularly useful to this scenario. I would stick with a purely classical treatment rather than a quantum treatment

I completely agree. I had no intention of considering QM
That the idea of photon count was simply conceptually useful,, but with no need to try and calculate quantitative counts.
I was operating under the assumption that the physics in the 1st P refers to all physics.
That the scenario, in principle ,could assume cheap light meters.

DO you reject the idea of assuming CMOS screens with frequency weighting to derive photon counts, WIth the assumption of equal statistical deviation at all sites?

Thanks for your feedback
 
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  • #30
Austin0 said:
No question about my uncertainty. I did not think exact terminology was crucial.
Well, we have gone through about 30 posts now and I am still unsure about what you think is paradoxical. Exact terminology always helps in communicating.


Austin0 said:
DO you see any reason why I couldn't just specify the boundary condition of visible light?
You could certainly specify it in one frame, but not both.


Austin0 said:
Regarding abberation I have to disagree. That is why I tried to establish the absolute nature of the sphere and the fact that colocated simultaneous measurements are actually occurring at the same point of the light cone, the spheres evolution through time.

SO the coordinate distances from the coordinate locations of the "source" may be different in the frames [with a difference in resulting angles] but the distance and angle from the actual source cannot be different. SO the actual irradiance [number of photons] cannot be different.
I don't follow what you are saying. Could you express it mathematically?

Abberation and Doppler are both well-known relativistic effects, so I would be surprised that either is not applicable. Although it is certainly possible that one or the other cancels out with some other effect in the end. That is why a mathematical analysis is important.


Austin0 said:
I am not sure what you mean here.

DO you mean that if out of a large number of different frames only one measured symmetric irradiance it wouldn't be evidence of a preffered frame??
Correct. This would not be evidence of a preferred frame any more than if you measure a space ship's velocity in a large number of frames and find only one where it is 0.


Austin0 said:
DO you mean that in relation to the absolute sphere there is only one possible frame where the irradiance could be actually symmetric?? [ In which case I agree]
I don't know what you mean by "absolute sphere" and "actually symmetric".


Austin0 said:
DO you mean that between the two frames under consideration only one could measure symmetric irradiance ?
Yes.


Austin0 said:
[ in this case I would have to disagree. That is the basis of this problem. By the 1st P both frames have to measure symmetric irradiance, don't they?.]
Why would the 1st postulate imply that? Symmetric irradiance is not a law of nature.

Austin0 said:
I had no intention of considering QM
Then let's not discuss photons and photon count. It is just confusing. If you want to "discretize" the problem then you can speak of classical pulses of light which would have a well-defined position and momentum and energy and doesn't carry all of the QM baggage of uncertainty, probability, wavefunctions etc.
 
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  • #31
This may be of some relevance. In Greiner W. Classical Mechanics. Point Particles and Relativity starting at Page 404 under the heading :-Light intensity distribution of a moving isotropic emitter.

Earlier pages also deal with the Terrell Penrose effect in some detail and refer to an Austrian physicist called Anton Lampa who published a paper on the effect in 1924 which was apparently largely ignored.

Matheinste
 
  • #32
matheinste said:
This may be of some relevance. In Greiner W. Classical Mechanics. Point Particles and Relativity starting at Page 404 under the heading :-Light intensity distribution of a moving isotropic emitter.

Earlier pages also deal with the Terrell Penrose effect in some detail and refer to an Austrian physicist called Anton Lampa who published a paper on the effect in 1924 which was apparently largely ignored.

Matheinste

Hi Matheinste Thanks for the reference as I am interested in both subjects. Unfortunately I am in Thailand so unless I can find access (free) on the net I am out of luck.

Maybe you could answer a couple of quick questions if you have read it.

1) Does the derived result deviate significantly from a combination of Doppler and the expected falloff factor??

2) When you say moving emitter does this mean a device located in a moving frame with known intrinsic emmission frequencies and magnitudes?

3) As my question is dealing with an ideally short burst [to the limit instantaneous]
and assumed to be a spontaneous cosmic occurence, unassociated with any mechanism or location.
Can this really be considered a moving source ??

I.e. Is there reason to assume any anisotropy at the source??

Thanks
 
  • #33
Austin0 said:
Hi Matheinste Thanks for the reference as I am interested in both subjects. Unfortunately I am in Thailand so unless I can find access (free) on the net I am out of luck.

Maybe you could answer a couple of quick questions if you have read it.

1) Does the derived result deviate significantly from a combination of Doppler and the expected falloff factor??

2) When you say moving emitter does this mean a device located in a moving frame with known intrinsic emmission frequencies and magnitudes?

3) As my question is dealing with an ideally short burst [to the limit instantaneous]
and assumed to be a spontaneous cosmic occurence, unassociated with any mechanism or location.
Can this really be considered a moving source ??

I.e. Is there reason to assume any anisotropy at the source??

Thanks

I am a little busy at the moment and as I am not familiar with the subject I will take a little time to read and hopefully understand the source to which I referred. I will learn from it and maybe I can be of some help.

Matheinste.
 
  • #34
Austin0 said:
3) As my question is dealing with an ideally short burst [to the limit instantaneous]
and assumed to be a spontaneous cosmic occurence, unassociated with any mechanism or location.
Can this really be considered a moving source ??
If it's not associated with a specific source, the speed of light wasn't measured at all, since the speed of light is based on the distance between detector and a physical source. In that case, it wouldn't make sense to speak of a "light sphere".

But in your scenario, the location and motion of the physical source of the light could be established from the locations and times of detection in each frame, if it's known that each detected pulse had a common source.
 
  • #35
Austin0 said:
3) As my question is dealing with an ideally short burst [to the limit instantaneous]
and assumed to be a spontaneous cosmic occurence, unassociated with any mechanism or location.
Can this really be considered a moving source ??

I.e. Is there reason to assume any anisotropy at the source??
Even for a field without a source you still have to follow the transformation rules for the fields themselves. The anisotropy is guaranteed by those transforms. If the field is isotropic in one frame it must be anisotropic in all other frames, regardless of any mechanism or source.

This is what starthaus was trying to explain back in post 10.
 
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