Light Sphere Paradox: A Conundrum with No Solution?

[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 independent 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 occurrence 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.