Light Sphere Paradox: A Conundrum with No Solution?

[Austin0]

Regarding the lightning strike hitting the rear of the train and tracks;

The source would be the lightning strike. The origens would be the rear of the train and the colocated point on the tracks at the event.

((1)) SO tell me what is the velocity of the source or the origen as measured or assumed in either frame?

Self evidently both frames would measure the origen [coordinate point ] in the other frame as having a velocity relative to their frame but that is not what I was talking about.

((2))Would you argue that the source and origen were not considered at rest within both frames?

(1)The velocity of the source of any light is zero in whichever frame observes identical frequencies in each direction. And very much like The Highlander, "there can be only one".

(2)Absolutely. Both frames logically cannot detect identical frequencies in each direction. Again, "there can be only one".

(In this example, there may actually be multiple sources of light, since light may be emitted from parts of the train and parts of the track. But the above is still true for each light ray.)

Light always has a source, and the velocity of the source is frame dependent. Therefore the frequency of light from any source is frame dependent. That's why the motion of a source of light can be determined from measuring the frequency of the light.

Hi Al68

I want to thank you for your clear and specific responce to my points above.

It was very helpful in attaining the realization that I was wrong.

In the confusion of source vs origen and the midstream change from my original concept of spontaneous cosmic occurance to a specific attached source I failed to give the new parameters enough thought.

Having done so I see that I missed the most obvious. Thinking of the source as instantaneous and so without motion in x I completely forgot that from the perspective of the frames it didnt just appear there but the orthogonal frame itself was moving prior to the emission. So in fact both frames would assume an anisotropic wave form.

SO the event [observation] was at rest in both frames but the source within the context of physical source was not.

You were perfectly correct in your conclusion in this case although regarding the two frames in question it was.."There can be only none"

But your logic, which is the logic of the real world ,where conclusions can drawn based on empirical measurements is not always applicable.

------------------Consider the original spheres "paradox" scenario.

All frames must measure a constant c

All frames must calculate that they remain in the center of the sphere.

---------------Wouldn't the field have to be measured as either isotropic in all frames or anisotropic in all frames??

Otherwise it would not be consistent with their evaluation of being at the center.

If you apply the same real world logic to this case regarding the geometric center of an expanding sphere

It would be incontrovertably true that ;..."There can be only one"

Which I would agree with, but it is not consistent with the view within the frames . Or the assumptions we make looking at all frames from the outside perspective of Minkowski diagrams etc. etc.

In this case if we did assume a cosmic source: from the perspective of any given frame wouldn't they assume they were at rest and therefore the source which just appeared from nowhere would be considered at rest with the expectation of isotropic wave form in all frames??


This thread has undergone a lot of unneccessary argument because of a problem with my original condition of an unattached cosmic light source. With objections based on the real world logic that there can be no such thing.

Yet in Einstein's 1918 gravity based resolution of the twins paradox as reported in your link, there is massive use of dissappearing gravitational fields and magical undefined external forces negating these fields when required .
...But you have no problem accepting these conditions but reject my light source which is actually much more conceivable as a real world possibility.
It appears to me , to paraphrase an old arabic saying:

"You swallowed a camel whole but choked on a gnat"

In any case I have renovated my original conditions:

I now realize that orthogonal motion doesn't change anything and makes computation more complex so I am assuming a frame moving along x such that both frames have a relative velocity of.5c wrt the source frame and .8c wrt each other.

I am in the process of including both Doppler and aberration on top of irradiance falloff.
Is there anything else you can think of?

I can see now that I should do not only the numerical calculations but also Minkowski diagrams for those who don't like verbal descriptions and logic.

SO thanks again for your help and input, But I will make a prediction; If you reach a point of understanding the actual problem I am presenting you will then realize that all this extra complexity is irrelevant as it is all reciprocal and relative. ...IMHO

 

[Dale]

I am in the process of including both Doppler and aberration on top of irradiance falloff.
Is there anything else you can think of?

I would transform the fields also, since that should be a good way to double-check and give you better confidence in your results.

But I will make a prediction; If you reach a point of understanding the actual problem I am presenting you will then realize that all this extra complexity is irrelevant as it is all reciprocal and relative. ...IMHO

I am looking forward to it.

 

[Al68]

If you apply the same real world logic to this case regarding the geometric center of an expanding sphere

It would be incontrovertably true that ;..."There can be only one"

"There can be only one" is true for the source being at rest, ie no doppler shift. It's not true for spherical propagation, ie constant speed of light. Light from a source still propagates at c in every direction in every inertial frame, regardless of the motion of the source.

...But you have no problem accepting these conditions but reject my light source which is actually much more conceivable as a real world possibility.

I only rejected the idea that a single source could have the same velocity (0) in two different frames in motion wrt each other, which is the equivalent of a single source having two different velocities in the same reference frame.

A source of light must be adequately defined in a scenario, including its motion, especially in the context of detected frequency.

 

[Austin0]

Hi Al68




If you apply the same real world logic to this case regarding the geometric center of an expanding sphere

It would be incontrovertably true that ;..."There can be only one"
Which I would agree with, but it is not consistent with the view within the frames . Or the assumptions we make looking at all frames from the outside perspective of Minkowski diagrams etc. etc.

ADDITION TO ORIGINALIn this case if we did assume a cosmic source: from the perspective of any given frame wouldn't they assume they were at rest and therefore the source which just appeared from nowhere would be considered at rest with the expectation of isotropic wave form in that frame??

Specifically: Given the perspective of a frame being at rest and without an identifiable mechanism for a source with a specific velocity , the assumption would be that the wave form would be symmetric in that frame and asymmetric in the other "moving" frame.
This would apply to both frames.
Of course in reality I.e. two actual frames; empirical tests would show that either one or none of the frames would measure an isotropic wave.

Yet in Einstein's 1918 gravity based resolution of the twins paradox as reported in your link, there is massive use of dissappearing gravitational fields and magical undefined external forces negating these fields when required .
...But you have no problem accepting these conditions but reject my light source which is actually much more conceivable as a real world possibility.

"There can be only one" is true for the source being at rest, ie no doppler shift. ((1)))It's not true for spherical propagation, ie constant speed of light. Light from a source still propagates at c in every direction in every inertial frame, regardless of the motion of the source.I only rejected the idea that (((2)))a single source could have the same velocity (0) in two different frames in motion wrt each other, which is the equivalent of a single source having two different velocities in the same reference frame.

A source of light must be adequately defined in a scenario, including its motion, especially in the context of detected frequency.

(((1))) You didn't answer or respond to my actual point which was regarding the geometric center of the sphere not about light speed.
ABout real world logic applied to that center.(((2))) Here you responded with real world logic to the proposition that a single source could "have" the same velocity in two frames.[Answer NO ... No argument].

The actual proposition was could two frames "consider" the source to have 0 velocity [unchanging location] in their frames. See above.

 

[atyy]

(1)The velocity of the source of any light is zero in whichever frame observes identical frequencies in each direction. And very much like The Highlander, "there can be only one".

In the end, there can be only one. So before the end ...

 

[DrGreg]

The expanding light sphere is an idealised mathematical model, as it works on the assumption that, at any location, the light is a "flash" of zero time duration. This is OK as a mathematical model, but in the real world this is impossible: all light must persist over a non-zero period of time, and if you want to measure its frequency, you have to measure something over a period of time.

So, in the light-sphere model there is just a single source event, but in the real world there would need to be a collection of source events (forming a worldline in spacetime). You could think of the real-world scenario as a collection of expanding light spheres, each sphere centred on the static location of each source-event (relative to any single frame). There will be only one frame in which all the source-locations coincide and therefore in which all the spheres share the same centre.

Think of the spheres being wavefronts (peaks in the wave amplitude, using a classical coherent wave model). In one frame, all the wavefronts share the same static centre. In other frames, each wavefront has a static centre but they are all different centres, so adjacent wavefronts will be closer to each other in some directions than others (doppler shift).

 

[Austin0]

Of course in reality I.e. two actual frames; empirical tests would show that either one or none of the frames would measure an isotropic wave.



(((1))) You didn't answer or respond to my actual point which was regarding the geometric center of the sphere not about light speed.
ABout real world logic applied to that center.

(((2))) Here you responded with real world logic to the proposition that a single source could "have" the same velocity in two frames.[Answer NO ... No argument].The actual proposition was could two frames "consider" the source to have 0 velocity [unchanging location] in their frames. See above.

(1)The velocity of the source of any light is zero in whichever frame observes identical frequencies in each direction. And very much like The Highlander, "there can be only one".

In the end, there can be only one. So before the end ...

Thanks atyy I think maybe?
Your responce suggests some slight strawman possibility. As if I am arguing against the Al68 comment above , when in fact I have clearly stated that I have no argument with it its context.
If I am misreading you forgive me.

In any case it seems that we are talking about different things and it is not worth pursuing.
I am surely foolish in that regard as it is not germaine to the actual thread.

Thanks for sure.

 

[Al68]

(((1))) You didn't answer or respond to my actual point which was regarding the geometric center of the sphere not about light speed.
ABout real world logic applied to that center.

They're the same point, if we're talking about the center of a "light sphere". The "sphere" geometry is a consequence of the speed of light being constant.

(((2))) Here you responded with real world logic to the proposition that a single source could "have" the same velocity in two frames.[Answer NO ... No argument].

The actual proposition was could two frames "consider" the source to have 0 velocity [unchanging location] in their frames. See above.

Sure they could, but at least one of them would be wrong.

 

[Austin0]

The expanding light sphere is an idealised mathematical model, as it works on the assumption that, at any location, the light is a "flash" of zero time duration. This is OK as a mathematical model, but in the real world this is impossible: all light must persist over a non-zero period of time, and if you want to measure its frequency, you have to measure something over a period of time.

Hi...DrGreg ...All of the above has been my assumption from the beginning with the exception that I assumed the emission itself to be without duration. But not receptionto be instantaneous.
I understood that this was not founded on realworld light where both emission and reception must have duration due to the spatial extent of the photon wave packet, but was a conveniece for the conditions of the problem.

The other conception of the light sphere I employed was not a mathematical one but was based on the assumption that the invariance of light was not only a relative invariance as measured per 2nd P but was also an absolute invariance based on our physical model where c is a real constant wrt to the limit of motion or propagation and all photons are assumed to be actually moving at the same speed through any given locale of vacuus flat spacetime.

A)...From this I infered that the geometric shape itself was a singular , perfect sphere with an absolute center independant of any frame's measurement or calculation.

Was this a valid assumption??

((1))..So, in the light-sphere model there is just a single source event, but in the real world there would need to be a collection of source events (forming a worldline in spacetime).

((2))..You could think of the real-world scenario as a collection of expanding light spheres, each sphere centred on the static location of each source-event (relative to any single frame). There will be only one frame in which all the source-locations coincide and therefore in which all the spheres share the same centre.

((1)) ...Agreed. ,,,,,,,,,,earlier in this thread I described this exact point. That there would actually be a collection of world lines and suggested for convenience that this collection could be referred to as a single worldline (as you seem to be doing here).
Only to meet with complete negation of the idea.

((2))...I think the term real world is ambiguous and the source of a lot of confusion:

a) There is the real world as per A) above. This is purely a conception without possibility of assigning coordinates.

b) There is the real world as seen from our objective perspective , outside the frames under consideration.Seeing them all at once and applying the appropriate math relevant to each.

c)..There is the real world as perceived , measured and calculated from inside each frame.

d) There is the real world we occupy in this semi inertial frame where we can make some actual measurments and a sphere always only has one center.


So I understand what you mean in ((2))when you say a collection of spheres etc.

This is a conception derived from perspective b) where we can see that their notion of a static center is fallacious and the calculated spheres from those centers is unique to each frame and only one frame can actually be centered over time.

This also is consistent with perspectives a) and d) but not consistent with c)

I was hoping to avoid the confusion of a multiplicity of spheres by adopting the b) perspective of a single sphere (at any point in time) that different frames observe simultaneously but assign different time and space coordinates to.

Or alternately; a single light cone (or sphere) that is intersected by different worldlines
at different points.

Fundamental to my problem is the assumption that colocated observations must occur at the same point in the actual evolution of the sphere.

DO you see any problem with any of these assumptions?

Think of the spheres being wavefronts (peaks in the wave amplitude, using a classical coherent wave model). In one frame, all the wavefronts share the same static centre. In other frames, each wavefront has a static centre but they are all different centres, so adjacent wavefronts will be closer to each other in some directions than others (doppler shift).

Understood and there has never been any question about this. This is a b) perspective.

I would suggest that in actuallity from a ...b),,perspective analysis or from the
c)...internal perspective of any arbitrary rest frame that it would not be spheres but ellipsoids in all other frames.

WOuld you agree?

In any case I am glad to receive your responce.
Thanks

 

[Austin0]

(((1))) You didn't answer or respond to my actual point which was regarding the geometric center of the sphere not about light speed.
ABout real world logic applied to that center.(((2))) Here you responded with real world logic to the proposition that a single source could "have" the same velocity in two frames.[Answer NO ... No argument]..

They're the same point, if we're talking about the center of a "light sphere". The "sphere" geometry is a consequence of the speed of light being constant..

No they are not the same points;

In the sphere scenario there are any number of frames (all) that calculate the center is statically located in their frame.

1) If you apply your real world logic where a sphere can only have one center.
Therefore; "there can be only one" that is right.

2) If you apply the logic that applies within the frames , then there can be any number of centers and none of them are wrong.

Which do you choose?

The actual proposition was could two frames "consider" the source to have 0 velocity [unchanging location] in their frames. See above.

Sure they could, but at least one of them would be wrong.

OK Agreement. I never suggested otherwise. This a large part of my scenario. The difference between what is easily seen and logically derived from outside, in contrast with what is considered to be happening within frames.

Thanks for responding

 

[Al68]

No they are not the same points;

In the sphere scenario there are any number of frames (all) that calculate the center is statically located in their frame.

The center of a light sphere is the point in a frame that is equidistant between simultaneous detections. That point will not be static in both frames.

The reason I called "geometric center of the sphere" and "light speed" the same point in this context is because spherical propagation from the source (center) is a direct consequence of a constant speed of light in each frame.

1) If you apply your real world logic where a sphere can only have one center.
Therefore; "there can be only one" that is right.

2) If you apply the logic that applies within the frames , then there can be any number of centers and none of them are wrong.

Which do you choose?

1. The center of the sphere represents the location of the (single) light source.

 

[Austin0]

No they are not the same points;

In the sphere scenario there are any number of frames (all) that calculate the center is statically located in their frame.

The center of a light sphere is the point in a frame that is equidistant between simultaneous detections. That point will not be static in both frames.

The first part is of course true. The second part I think is false within the context of SR
where every frame has to calculate a static center. IMHO

1) If you apply your real world logic where a sphere can only have one center.
Therefore; "there can be only one" that is right.

2) If you apply the logic that applies within the frames , then there can be any number of centers and none of them are wrong.

Choose one

.1. The center of the sphere represents the location of the (single) light source.

I totally agree with this as applied to my abstract absolute light sphere. But in that case it is impossible to assign a coordinate location to that center.

In the real world and in the world of SR we work with (via math and diagrams) it is not only false but is in complete opposition to the fundamental principle of SR ...IMHO

In this world, the "real" singular center is indeterminant, unknowable, so all static assignments in every frame must be equally valid . "There can be only many"

In a real way this is all relevant to the actual basis of the problem

Thanks for responding ;-)

 

[matheinste]

I posted this some time ago in another thread entitled the light sphere problem and so some of the wording may seem odd in the present context and may not be directly relevant as an answer to any questiond here. But it may help.

---What you are considering is a two or three spatial dimensional representation of the scenario. What you are seeing is the projection of four dimensional spacetime onto two or three spatial dimensions. In four dimensional spacetime, which we cannot visualize, the origins remain coincident. The coincidence of the emission and the origins is a spacetime event and cannot move in space or time as it has no spatial or temporal extension.

The apparent movement in these projections is because the moving observer assigns to the event chageing coordinate values. Same event, differing assigned coordinates. This reprentation makes no claims about the centrality of the moving observer with respect to the light circle (sphere), in fact in this representation the moving observer does not remain central to the expanding CIRCLE of light represented in the same diagram. It is not expected to. However, interchange the observers and the situation is reversed. The other one now is represented as central. Each observer remains central from his own viewpoint. There is nothing to resolve, this representation is exactly as expected for the given scenario.

The best representation, though not perfect, is the projection of the cross sections of the light cone onto the x/y plane. In this representation the event is represented as the origin of a light cone, the same light cone for both observers and emitter, it does not matter if one of the observers is the emittrer or whether the emitter is considered to be moving or not. But although they all share the same light cone, the cross sections of the expanding light cone, which represent the planes of simultaneity for the two observers, are not the same shape when projected on to the x/y axes. One of cross sections is circular and one is not, as it is tilted at an angle in the cone representation. The tilted one represents the plane of simultaneity of the moving observer. The tilted one shows, in the three dimensional light cone representation, one extreme of the cross section as being lower down the time axis of the stationary observer than the other extreme. This means that the times at which the light front reaches points on the perimeter of the projection of that cross section are not simultaneous in the stationary observer's frame and so the moving observer is not considered to be central according to the stationary observer. But for the circular cross section they are simultaneous and so the stationary observer considers himself central. The difference reflects the relative motion of the observers. We are at liberty to take either as being at rest and changeing the drawing to suit. The effects are reciprocal.

Matheinste

 

[Dale]

Hi Austin0, perhaps it would help if you thought about the light cone rather than the light sphere. There is one light cone, which is a single 4D geometric object that all reference frames agree on. There are, however, an infinite number of light spheres, which are each 3D sections of the 4D light cone. The section that one frame calls a sphere another frame will call an ellipsoid (and it will be non-simultaneous). All frames agree on the apex of the light cone, but since they don't agree on which events comprise any of the infinite number of light spheres it shouldn't be surprising that they may assign different centers to different sets of events.

 

[Al68]

The first part is of course true. The second part I think is false within the context of SR
where every frame has to calculate a static center. IMHO

SR has no such requirement. The light source is in motion in one of the frames.

I totally agree with this as applied to my abstract absolute light sphere. But in that case it is impossible to assign a coordinate location to that center.

In the real world and in the world of SR we work with (via math and diagrams) it is not only false but is in complete opposition to the fundamental principle of SR ...IMHO

In this world, the "real" singular center is indeterminant, unknowable, so all static assignments in every frame must be equally valid . "There can be only many"

The center is the point equidistant between simultaneous detections in each frame. It's easy to determine and know.

 

[Austin0]

Hi...DrGreg ... .

From this I infered that the geometric shape itself was a singular , perfect sphere with an absolute center independant of any frame's measurement or calculation.I was hoping to avoid the confusion of a multiplicity of spheres by adopting the b) perspective of a single sphere (at any point in time) that different frames observe simultaneously but assign different time and space coordinates to.
Or alternately; a single light cone (or sphere) that is intersected by different worldlines
at different points.

I would suggest that in actuallity from a ...b),,perspective analysis or from the
c)...internal perspective of any arbitrary rest frame that it would not be spheres but ellipsoids in all other frames.
WOuld you agree?

AUG 24/09 to DrGreg...I myself stumbled on the ellipsoid long ago, simply through contemplation of the simultaneity train. Picturing the track observer central to a sphere of brief fireworks , a quick flash of small points which he would perceive as a single event. Then imagining ,from the track point of view, the same occurance happening on the train. Where the points would start at the rear and proceed forward to the front while the observer was moving.
It seemed sure that the geometry was ellipsoid ,so I concluded that a sphere in one frame was extended through time to become an ellipsoid in another frame.
..

Hi Austin0, perhaps it would help if you thought about the light cone rather than the light sphere. There is one light cone, which is a single 4D geometric object that all reference frames agree on. There are, however, an infinite number of light spheres, which are each 3D sections of the 4D light cone. The section that one frame calls a sphere another frame will call an ellipsoid (and it will be non-simultaneous). All frames agree on the apex of the light cone, but since they don't agree on which events comprise any of the infinite number of light spheres it shouldn't be surprising that they may assign different centers to different sets of events.

Hi DaleSpam. If you could please look at the above first.

Tick...Tick...Tick...Tick.........

I have great appreciation both of your knowledge and the opportunity I have to communicate with you. More than you can know. But there is a monumental communication gap going on. Things are frequently taken out of context and replied to with the assumption and implication that I am lacking in understanding of fundamental principals.

Everything you have said here or Matheiniste just said, I not only understand but have explicitly stated the same things in the course of this thread .

Al68 made a bare logical assertion earlier in this thread.
I said that it was not neccessarily valid generally and pointed to the light sphere center question of the original.

He denied this and my last post to him was a demonstration of my point.

It had nothing to do with what I think,,, it was about what he thought or at least had explicitly said.

The conditions I have used as a basis of my statement of the problem of this thread has all been based on exactly the understanding and principles that you have stated here.

Now if somewhere in this thread I have said something that is not consistent with those principles I would be glad to here it. If you see some logical problem with my answer to Als68's assertions and responces I would be glad to hear it and learn.
I really have no problem with being shown I am wrong.I may not enjoy it anymore that anyone else but I would much rather see it, learn, admit it and move on, than carry on with false info or assumptions.
I am sure that many think I am simply argumentative,stubborn or looking for flaws in SR etc etc.
I assure you that is not the case.

Or that I am willfully eccentric in my expression and visualizations.

Most of my basic knowledge of physics and SR came from a 4 year period many years ago , of obsessive self study through my local library. The material was limited to the fundamentals, the basic math and principles .Because there was no one around with the interest or knowledge for me to question or test ideas with I had no motivation or source to learn the formalism. I proceeded with the logic and conceptualization I had learned from A Einstein.
The same simplistic conceptualizations that everyone here seems to think needs to be discouraged and indicates lack of understanding. WHich led me to a recognition of the importance of the ellipse long before I was exposed to lightcone sections which came after this forum.
After that time I went on to other things , largely because of the lack of communication. Until I chanced on this forum; which literally changed my life, re kindling the intense study and thought and providing an opportunity for communication. But it also made me aware of my lack and need of the terminology and accepted forms of expression to really take advantage of that opportunity. SO I have been making a concerted effort during the sporadic time I have been able to participate to learn those forms. I understand it creates a certain strain for you to deal with and i appreciate your patience.

SO I do greatly appreciate your help and feedback and hope it will continue and improve.
I also hope this little explanation isn't too inappropriate for this forum.

Thanks

 

[Dale]

Hi Austin0, I do appreciate the effort that you are making, but I think that the current confusion is an inevitable result of too much English and not enough math. There is simply too much ambiguity and you are trying to say one thing and each person reading is understanding something different. Perhaps we can try the following:

Why don't we use F for some arbitrary Minkowski reference frame, F'(v) for a reference frame boosted by v, (t,x,y,z) for the coordinates in F, (t',x',y',z') for the coordinates in F'(v), L for the light-cone and S(t0',v) for the light sphere formed by the intersection of t'=t0' and L.

Perhaps you and Al68 can use this notation to quickly resolve any misunderstanding.

As for my part in the conversation, I am not really interested in discussing the geometry of the light cone since I think you are clear on that and understand it correctly despite the miscommunications.

What I am interested in discussing is the irradiance, which is where I believe that you have a misunderstanding that goes beyond any miscommunication. I think the root of your misunderstanding there is that you think that the invariance in the geometry of the light cone implies an invariance in the isotropy of the irradiance. I hope that you are working on the math as you mentioned a few posts ago, and I am still quite interested in the results.