Modelling the locations of in transit photons emitted from rotating sources

[LaurieAG]

Part 1

Abstract

I maintain that light always travels in a straight line from its emission point to its observation point at c (in a vacuum) and the details contained within this thread comply at all times with this basic rule of SR.

There are some misconceptions about with regards to the discrete paths that in transit photons take, after they are emitted from a rotating/orbiting source, until they are captured by an observer. I will initially describe a solution to the relativistic rolling wheel/ring "optical appearance" problem outlined in Øyvind Grøn's PHD paper "Space geometry in rotating reference frames: A historical appraisal" to show how SR has been used to construct a plane of "retarded points in time" to solve the problem. I will then outline how this method/plane can be extended to plot the paths of in transit photons and verify that the method/plane presented is just a direct extension of mainstream SR though. Please also note that there is no mention whatsoever of the word 'orbit' in Øyvind Grøn's paper and SR is not GR.

Modeling relativistic rolling/orbiting wheels/rings in SR

Unfortunately copies of Øyvind Grøn's paper are no longer available without payment (it is a very interesting read). Not only does it provide a compendium of all the various approaches through history, he puts forward a solution (albeit without any methodology/math) to a intriguing problem, Figure 9 part C below. The images below are from the following post on another forum that produced the same solution. http://www.thephysicsforum.com/speci...html#post12704



From Grøn's paper

The positions of points on a rolling ring at retarded points of time were calculated with reference to 0 K by Ø. Grøn [111]. The result is shown in Fig. 9. Part C of the figure shows the “optical appearance” of a rolling ring, i.e. the positions of emission events where the emitted light from all the points arrives at a fixed point of time at the point of contact of the ring with the ground. In other words it is the position of the points when they emitted light that arrives at a camera on the ground just as the ring passes the camera.

One thing the paper did not mention is that the length of straight lines drawn from each of the emission points to the camera in the image are equal to the actual distances and path traveled by the photon due to the construction of the plane of retarded points of time. This is because all of the units of the models x and y dimensions (z=0 to remove issues of Born rigidity) can be regarded as time.



Adapting this plane/model to other rotation/orbit applications is made easier when you realise that the observer/camera is stationary and in the same plane as the rotating/orbiting wheel/ring. I contributed to the solution shown by suggesting that the results should be in emission order to determine if the axle velocity between emission events is consistent.

Part 1 of 3

[LaurieAG]

Part 2

https://www.google.com/search?q=sparkler+circles

Many people can remember taking photo's of themselves or others waving sparklers in the air, capturing figure eights or circles and having great fun while they were at it. It's trivial to take a picture approximately 6 feet away from someone waving a sparkler in a circle of 1 foot radius. If the pictures exposure time matches the time it takes to make one complete rotation/orbit of the sparkler then the photo will show a complete circle. If this exposure time is halved the image will show half a circle and if the exposure time is doubled the image will capture 2 circles (sparkler speed constant). I don't doubt that many of the photons, emitted from the tip of the sparkler, travelled in a straight line at near c directly to the camera/observer, at all times during the exposure period. There are some obvious problems with doing the above experiment on a local galactic scale so some caveats are necessary. There is no mass as this optical appearance model only contains emission points on the circumference of a rotating/orbiting ring, in transit photons (at retarded points of time) and an observer.

Basic galactic scale model

Consider 2 equal light sources that continue to emit a consistent stream of photons as they rotate/orbit around a stationary Centre Of Mass (C.O.M.) in a plane inclined at 45 degrees to the observer who is stationary wrt the sources C.O.M. These streams, of in transit photons, travel at the speed of light, in a straight line without deviation or obstruction, from their point of emission to the Observer.

The important thing to note is that while each photon travels from its rotating/orbiting emission point to a stationary observer the emission points change over one complete rotation/orbit of the source around its C.O.M.. While the emitting source has returned to its original starting point after one complete rotation/orbit the stationary observer would have to wait for another complete rotation/orbit before it would capture another photon emitted from that source at that discrete location.

The following image shows the Top view of the model/plane and the following text describes how the image is formed over 4 quarters of rotation/orbit of the source.



Quarters image generation method

In the first quarter of rotation/orbit the light emitted from the source(s) at point 1,0 has traveled to point 1,1 in a straight line at c and the source has traveled to point 4,0. The light from the source emitted at point 3.0 has traveled to point 3,1 in a straight line at c and the source has traveled to point 2,0.

In the second quarter of rotation/orbit the light emitted from the source at point 4,0 has traveled to point 4,1 in a straight line at c and the source has traveled to point 3,0. The light from the source at point 2.0 has traveled to point 2,1 in a straight line at c and the source has traveled to point 1,0. The light emitted during the first quarter continues to travel in a straight line from its point of emission towards the observer at c.

In the third quarter of rotation/orbit the light emitted from the source at point 3,0 has traveled to point 3,1 in a straight line at c and the source has traveled to point 2,0. The light from the source at point 1.0 has traveled to point 1,1 in a straight line at c and the source has traveled to point 4,0. The light emitted during the first two quarters continues to travel in a straight line from their point of emission towards the observer at c.

In the last quarter of rotation/orbit the light emitted from the source at point 2,0 has traveled to point 2,1 in a straight line at c and the source has returned to its start point 1,0. The light from the source at point 4,0 has traveled to point 4,1 in a straight line at c and the source has returned to its start point 3,0. The light emitted during the first three quarters continues to travel in a straight line from their point of emission towards the observer at c.

This simple geometric model complies with the basic SR rule that all photons travel in a straight line at c (in a vacuum).

Part 2 of 3

[LaurieAG]

Part 3

Why 45 degrees to the observer?

Grøn's Fig. 9. Part C shows the stationary observer/camera being in the same plane as the wheel i.e. the observer and the entire wheel occupy the same plane so the Observer is stationary and at 0 degrees to the plane of rotation of the wheel. If anybody can show why the distance traveled by a photon emitted from point 1,0, that travels in a straight line directly to the observer at c, can be any different if the source travels at the same velocity and it and the observer are at the same physical locations but the plane of rotation of the source is 90 degrees to the observer, then please enlighten me. As far as I am aware shift doesn't change the velocity of light, only its frequency.

Extending the model to all angles of rotation/orbit.

Basic calculations (non relative)

On non relativistic scales the distance between the observer and the models stationary C.O.M, = 2 * Pi * r c/v where r is the radius of rotation/orbit of the 2 sources and v is the angular velocity of the source(s). The time taken for the source to rotate/orbit through one quarter = (2 * Pi * r)/4. This mapping only shows emitted photons that are still in transit at the time the observation is made and, during a period of one complete rotation/orbit, all these currently in transit photons would eventually be observed at the observation point, that stayed stationary relative to the C.O.M.

Basic calculations (relative)

At relativistic scales, and where the observer is at 0 degrees to the plane of rotation of the sources (per Grøn's Fig. 9. Part C solution), there would be maximum length contraction of the 'spoke', that is the point on the wheel's circumference where the source rested on, while it emitted photons. This 'spoke' length contraction would be consistent for wheels/rings rotating/orbiting at the same relativistic velocity when the observer is at different angles to the plane of rotation. The distance doesn't change between the observer and the C.O.M. at the same start point, only the shift changes. The images below show the observer at different angles to the plane of rotation/orbit for sources with the same angular velocity.





Note: the colors of the in transit photon lines are Red, Blue and Black. Red denotes when the source was moving away from the observer at the point of emission, Blue designates that the source was moving towards the observer at the time of emission and black designates that the plane of rotation of the source was at 90 degrees to the observer at the point of emission. As per the 4 quarters image from part 2, these colors move towards the observer along with their in transit photons.

If anybody has difficulty obtaining a copy of Øyvind Grøn's paper please pm me.

Part 3 of 3

[Reality Check]

I maintain that light always travels in a straight line from its emission point to its observation point at c (in a vacuum) and the details contained within this thread comply at all times with this basic rule of SR.

A very minor point: This "basic rule of SR" existed before SR, LaurieAG. Newton's first law is In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

An accessible source for Space Geometry in Rotating Reference Frames: A Historical Appraisal

Abstract
The problem of giving a relativistic description of the geometry of a rotating disk has a history nearly as old as that of the theory of relativity itself. Already in 1909 Ehrenfest formulated his famous paradox in the context of the special theory of relativity. A few years later Einstein made heuristic use of this problem in order to motivate the introduction of non-Euclidean geometry in a relativistic theory of gravity. We shall here follow the conceptual evolution of this topic from Ehrenfest and Einstein to the present time. In particular we emphasise the importance of taking the relativity of simultaneity properly into account in order to obtain a full understanding of the issues connected with Ehrenfest’s paradox.

This is a thesis on the history of the relativistic description of the geometry of a rotating disk such as the disk in Ehrenfest’s paradox. That is not a rotating source of photons.
ETA: Page 39 describes light emitted from the rim of a rolling disk as the rim contacts the ground.

Page 39 is about the "positions of points on a rolling ring at retarded points of time" (not a rotating source of photons) with "Fig. 9. Points on a rolling ring. A: Observed by simultaneity in its rotating rest frame K ; B: observed by simultaneity in the frame 0 K : C: observed in 0 K at retarded points of time."

Part C of the figure shows the “optical appearance” of a rolling ring, i.e. the positions of emission events where the emitted light from all the points arrives at a fixed point of time at the point of contact of the ring with the ground.

The full math behind the figure should be in his reference: [111] Ø. Grøn, “Optical Appearance” of a Rolling Ring, Int. J. Th. Phys. 22, 821 (1983).

You seem to be making the points on a rotating ring sources of photons and using mainstream physics from the thesis as in the description of Fig 9. That might not be ATM.

[Hornblower]

Please highlight what statements in your presentation so far are ATM in your opinion, and give the mainstream opinion for comparison.

[Reality Check]

Basic galactic scale model...

This and the next post look like mainstream physics - light traveling in straight lines from 2 sources to a central observer. As you seem to know and state in the first paragraph of this post, irrelevant to the first post about light from the rim of a rolling disk to an external observer. But then we have "per Grøn's Fig. 9. Part C solution" in the next post.

[LaurieAG]

You seem to be making the points on a rotating ring sources of photons and using mainstream physics from the thesis as in the description of Fig 9. That might not be ATM.

Reality Check, I was not the one who insisted on posting in this area of the forum.

When you've already been infracted once for ATM in a Q&A thread, and a second moderator says to knock off the ATM discussion, continuing the discussion on the topic and the moderation will result in another infraction. This will also result in your suspension.

[Strange]

Part 1

Abstract

I maintain that light always travels in a straight line from its emission point to its observation point at c (in a vacuum) and the details contained within this thread comply at all times with this basic rule of SR.

Does anyone disagree with that? (Apart from the generalisation to null geodesics instead of straight lines in GR.)

It appears to be contradicted by your diagrams, but I assume that is because they are not actually showing the paths of photons (as labelled).

So, as you claim there is nothing ATM here, what is the point of this thread what exactly do you want to discuss? (Edit: realised that wording could be misinterpreted.)

[Hornblower]

I agree with Strange. Those boldly colored spiral patterns could be misconstrued by a novice as paths of individual photons, when I think they are simply the locus of successive photons from emitters that are going around in circular paths. Is the latter correct? If so it would be analogous to the curved jets of water we see coming out of a rotary sprinkler.

[Reality Check]

Reality Check, I was not the one who insisted on posting in this area of the forum.

That is an explanation of the forum rules. I cannot see an explicitly stated ATM idea in this thread. I read a citation of mainstream physics that you are not arguing against. The rest seems textbook physics, e.g. the straight paths of light in 1 frame will appear curved in a rotating frame. From that and your citation you have made some images.

[LaurieAG]

That is an explanation of the forum rules. I cannot see an explicitly stated ATM idea in this thread. I read a citation of mainstream physics that you are not arguing against. The rest seems textbook physics, e.g. the straight paths of light in 1 frame will appear curved in a rotating frame. From that and your citation you have made some images.

https://forum.cosmoquest.org/showthr...-through-space

[Strange]

https://forum.cosmoquest.org/showthr...-through-space

That doesn't answer the question: what is it (ATM or otherwise) that you wish to discuss in this thread?

[LaurieAG]

That doesn't answer the question: what is it (ATM or otherwise) that you wish to discuss in this thread?

As long as there are no ATM issues with the images this thread may as well be closed.

[Strange]

As long as there are no ATM issues with the images this thread may as well be closed.

They would need a very careful explanation (and perhaps some more diagrams of each step) with clearer terminology (not "photon paths" for example) for them to make any sense. But apart from that, it doesn't seem to contain anything new.

[LaurieAG]

They would need a very careful explanation (and perhaps some more diagrams of each step) with clearer terminology (not "photon paths" for example) for them to make any sense. But apart from that, it doesn't seem to contain anything new.

I have looked for words to describe photons that have been emitted but have not been absorbed/received/observed and the most appropriate one is light beam or beam of light defined as a directional projection of light energy radiating from a light source.

Do you have any preference or should I just use the above or in transit photons or in transit light?

[Strange]

I have looked for words to describe photons that have been emitted but have not been absorbed/received/observed and the most appropriate one is light beam or beam of light defined as a directional projection of light energy radiating from a light source.

Do you have any preference or should I just use the above or in transit photons or in transit light?

None of those seem appropriate because your curved lines are not beams of light or the paths of photons. Maybe "positions of previously emitted photons" (if I haven't misunderstood what they represent).

I wonder if it would be less confusing to represent this as the wavefront of the light (at an instant in time) rather than lines.

[Hornblower]

With more head scratching after sleeping on it I would say those colored spiral paths are indeed beams of light from emitters revolving near the speed of light. We would see them from the side if there was some smoke in the intervening space. The red and blue represent alternating redshift and blueshift as each emitter goes around in a circle that is inclined to the observer's point of view. Each black line is the path of one photon out of many in the respective beam. LaurieAG, am I correct here? Please say yes or no. If no, please tell me what you think I am missing.

Dr. Gron's presentation looks like mainstream Einstein. You appear not to be asserting that the light is propagating in anything other than straight lines in the observer's inertial frame of reference. Once again, please tell us what if anything in this presentation is ATM.

[grant hutchison]

You've certainly got to be careful about reference frames. If we're sitting in a rotating reference frame then light beams will curve as they propagate, all photons will follow the curving path, and we could in theory visualize this curved path, unmoving in our coordinates, by introducing some sort of scatterer like smoke into its path. That would correspond to the common understanding of a "beam of light", I think.
But if we're sitting in an inertial frame, observing photons emitted from a rotating source, then the curved "path" that shows up in the smoke will not be fixed in our coordinates, photons will not follow the curved path, and will actually by propagating in straight lines. That one doesn't seem like a "beam of light" to me.

In the first case the spiral we're seeing is what a fluid dynamicist would call a pathline (the path followed by an individual particle); in the second the spiral is a timeline (a line plotting the position of neighbouring particles at a given time).

Grant Hutchison

[LaurieAG]

None of those seem appropriate because your curved lines are not beams of light or the paths of photons. Maybe "positions of previously emitted photons" (if I haven't misunderstood what they represent).

Maybe "positions of previously emitted photons still in transit to the observer" would be a rather long but correct description. The point being that only these photons will arrive at the stationary observer during 1 complete rotation after the observation has been made.

I wonder if it would be less confusing to represent this as the wavefront of the light (at an instant in time) rather than lines.

Good point, further the lines could actually be described as a continuum of wavefronts between the source and the observer.

Philosophically, any observation made at any discrete location and time can only capture photons that were going to transit that exact same location at that discrete observation time regardless of whether the observer was actually present at that location or not.

[LaurieAG]

With more head scratching after sleeping on it I would say those colored spiral paths are indeed beams of light from emitters revolving near the speed of light. We would see them from the side if there was some smoke in the intervening space. The red and blue represent alternating redshift and blueshift as each emitter goes around in a circle that is inclined to the observer's point of view. Each black line is the path of one photon out of many in the respective beam. LaurieAG, am I correct here? Please say yes or no. If no, please tell me what you think I am missing.

Yes Hornblower, although the blue color indicates that the source was moving away from the observer at the time of emission, the red color indicates that the source was moving towards the observer at the time of emission and the black lines indicate that the observer was at 90 degrees to the plane of rotation of the source(s) at the time of emission. The thick dotted red, blue and black lines represent photons emitted from the second source.

On galactic scales the 'smoke' would typically be clouds of gas that could become ionised.

[LaurieAG]

You've certainly got to be careful about reference frames. If we're sitting in a rotating reference frame then light beams will curve as they propagate, all photons will follow the curving path, and we could in theory visualize this curved path, unmoving in our coordinates, by introducing some sort of scatterer like smoke into its path. That would correspond to the common understanding of a "beam of light", I think.
But if we're sitting in an inertial frame, observing photons emitted from a rotating source, then the curved "path" that shows up in the smoke will not be fixed in our coordinates, photons will not follow the curved path, and will actually by propagating in straight lines. That one doesn't seem like a "beam of light" to me.

In the first case the spiral we're seeing is what a fluid dynamicist would call a pathline (the path followed by an individual particle); in the second the spiral is a timeline (a line plotting the position of neighbouring particles at a given time).

Grant Hutchison

I agree, you have to be even more careful when you are modeling 'optical appearances' at 'retarded points in time'.

The observer is stationary relative to the center of rotation of the sources so it is not an inertial frame. Pathline, photon path or photon stream may be more applicable.

I called these lines Photon Paths in the images.

[Hornblower]

Yes Hornblower, although the blue color indicates that the source was moving away from the observer at the time of emission, the red color indicates that the source was moving towards the observer at the time of emission

No, blue should indicate the source moving toward the observer and the red moving away. That's what I learned in physics and that is what I see correctly indicated in the second illustration in post 3, with the plane of rotation inclined 45 degrees to the observer.

and the black lines indicate that the observer was at 90 degrees to the plane of rotation of the source(s) at the time of emission. The thick dotted red, blue and black lines represent photons emitted from the second source.

I was referring to the thin black lines on the top view in the second illustration in post 3. Those appear to be indicating the cone swept out by the lines of sight from the observer to the emitters on the circle. At the intersections 1,2 and 3,2 there should be photons from the respective emitters propagating along those black lines to the observer.

On galactic scales the 'smoke' would typically be clouds of gas that could become ionised.

To repeat my unanswered questions in posts 5 and 17, what item or items in your presentation do you consider to be ATM?

[Hornblower]

To repeat my unanswered questions in posts 5 and 17, what item or items in your presentation do you consider to be ATM?

Sorry, I missed post 13. My bad.

[PetersCreek]

As long as there are no ATM issues with the images this thread may as well be closed.

Given this and subsequent posts indicating that no ATM claim is being advocated, this thread is closed. If I am mistaken or if there is some other reason to reopen this thread, please report this post.

LaurieAG, the report button is also the preferred way to ask that a thread be closed.