Apparent Red shift in a discrete Newtonian frame

[LaurieAG]

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

Newtonian Domain

In this model there are no (1) small sizes, (2) great speeds or (3) huge masses involved to allow the projections to be scaled proportionally in a 3D Euclidean space that represents the paths of current and already emitted photons at a discrete instance in time. The only divergence from a true Euclidean representation is made by measuring the distances traveled off the line directly from the C.O.M. to the Observer, to allow for comparison with relativistic constructs based on a C.O.M frame. While time is used for all x, y and z axis measurements the actual time of the discrete instance being represented in this frame is t=0.

Methodology

The distance between the observer and the stationary C.O.M, = 2 * Pi * r where r is the radius of rotation of the 2 sources. The time taken for the source to rotate through one quarter = (2 * Pi * r)/4. This mapping only shows emitted photons that are still active at the time the observation is made and, during a period of one complete rotation, all these currently active photons will eventually be observed at a stationary observation point.

If a photon was emitted from a rotating source at point 1,0 and the source completed one complete rotation in the time the photon took to travel to the observer at 1,4 the source will be back at point 1,0 and a line of photons will lead from the point 1,0 to the observer at point 1,4 at t=0. When the initial source rotated through one quarter it came to point 4,0 and emitted a photon that would travel from 4,0 to point 4,3 in the remaining 3 quarters before the source arrived back at 1,0 at t=0. After another quarter the source would be at point 3,0 and a photon travelling straight to the observer would have traveled another 2 quarters and be located at position 3,2 at the time the original photon sent from point 1,0 arrived at the observer at t=0. After a third quarter the source would be location at 2,0 and the photon emitted would travel to point 2,1 at the time the observation was made at t=0.

Consequently a stream of photons emitted continually from a rotating source at point 3,0 after one rotation will have a path at t=0 that arrives at the observation point at 3,4 and leads back through points 2,3, 1,2 and 4,1 to the current location of the source at point 3,0 all at the same instance in time.

SHIFT Determination method

The wavelength shift is determined by comparing the discrete length of each light path for each quarter shown in the Top or Side Elevation with the length of a straight quarter and determined that quarters with paths longer than this should be drawn in red to indicate that the source was moving away during that quarter and subsequently any quarters shorter than this are drawn in blue to indicate that the source was moving closer during that quarter.

SHIFT Consolidation methods

(1) Quarterly via Top and Side Elevations (x & y or x & z axis). The length of discrete red and blue lines are added up for each quarter and the percentages of red vs blue lengths are plotted for each quarter and displayed in a percent area chart. The percentage of blue lines goes up from 20 to 30 during the 4 quarters and the average percentages were 25% for blue and 75% for red over the Complete Rotation path. 2 groups of 3 consecutive eights (6/8) appear in the 4 quarters that give ratios of red to blue at 100% red with the remaining quarter (2 eights) comprising 2 dominantly blue but never 100% blue areas and the first 1/3 of the first quarter where the ratio was close to 50%. The sum of x, y or x, z shift lengths does not reflect two equal sources rotating around a stationary C.O.M.

(2) Complete Rotation via the End Elevation (x & y & z axis). The length of the discrete red and blue lines are added up and the average percentage of the sum of both blue and red lines is 50 percent.

Edited June 5, 2013 by LaurieAG

[LaurieAG]

I also plotted the apparent redshift if the C.O.M. is moving away or moving towards the observer.

As the clockwise rotating sources have an apparent redshift sum between 70-75% and anti clockwise rotating sources have an apparent blueshift sum between 70-75% this sum only tells us the direction of rotation. The x y z sum stays much the same at 50:50 and only indicates that the rotating sources are balanced.

Rotating sources are different to stationary sources, apparently.

[LaurieAG]

If you look at the light paths from non rotating point sources in the same frame you will also see apparent shift.

The apparent path is what appears (what we see/measure) so using shift to determine if sources are expanding or contracting or stationary is only meaningful if those sources are at a Center of Mass and not rotating around it.

[LaurieAG]

Basically all of these diagrams are to scale relative to the speed of light, the light travels in a straight line from source to observer and the distance travelled by the light from both rotating sources during one complete rotation equals 2 * Pi * the radius of rotation of the sources (i.e. the circumference of rotation in light years).

In the first quarter of rotation the light emitted from the source at point 1,0 has travelled to point 1,1 in a straight line at the speed of light and the source has travelled to point 4,0. The light from the source at point 3.0 has travelled to point 3,1 in a straight line at the speed of light and the source has travelled to point 2,0.

In the second quarter of rotation the light emitted from the source at point 4,0 has travelled to point 4,1 in a straight line at the speed of light and the source has travelled to point 3,0. The light from the source at point 2.0 has travelled to point 2,1 in a straight line at the speed of light and the source has travelled 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 the speed of light.

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

In the last quarter of rotation the light emitted from the source at point 2,0 has travelled to point 2,1 in a straight line at the speed of light and the source has returned to its start point 1,0. The light from the source at point 4,0 has travelled to point 4,1 in a straight line at the speed of light 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 its point of emission towards the observer at the speed of light.

The light emitted from both rotating sources is equal for each quarter of rotation but the apparent shift as shown in the diagrams is a result of the change of physical location of the source from the beginning of each quarter to the physical location of the source at the end of each quarter.

[LaurieAG]

This last diagram shows the photon paths from two sets of rotating sources (quasar or basic galaxy) that rotate around their own Local C.O.M. which also rotates around a higher level C.O.M. (H.L.C.O.M.) such as the galaxies and quasars that comprise the Milky Way. To keep things consistent for comparison purposes the photon paths from first diagram are shown and the pairs of sources take the same time to rotate once around their Local C.O.M. (L.C.O.M.) as their L.C.O.M. takes to rotate once around the H.L.C.O.M. (i.e. the pairs are in sync in their Local and Higher Level quarters).

It probably makes it easier to understand if you don't think of this Discrete Newtonian Reference Frame as a representation of 3D spacetime but more as a representation of a 3D timespace at a discrete moment (t0) with all the units of the x, y and z axis being measured by time and being consistent with each other. The apparent time dilation can also be measured as the times plotted are measured off the line between the H.L.C.O.M. and the observer and not the sources apparent position.

The Apparent Shift of the photon paths arriving at the observer at any discrete instance:-

(1) (a) Depends primarily on the shift produced by the largest moment of rotation of the sources L.C.O.M. (around a H.L.C.O.M) and secondarily by the shift produced by the sources rotating around their L.C.O.M. and (b) The secondary shift component produced by the L.C.O.M. rotation reduces in proportion to the ratio of the sources Local and Higher Level radii of rotation.

(2) Depends primarily on the start position of the source with respect to the H.L.C.O.M. and the number of rotations the sources L.C.O.M. has completed around the H.L.C.O.M.

I read a thread about someone who wanted to know how the integral and the area under the curve were related in calculus and was surprised that no one posted a simple diagram of a plot with the area under the curve shaded. Derivations from first principles can be a relatively useful tool for getting your head around apparently complex things.

[LaurieAG]

It's very interesting where you can go from first principles.

As the previous diagrams could be seen as the light paths produced from sources rotating around the Milky Way and being viewed by us I had a look at the Milky Way wiki ( http://en.wikipedia.org/wiki/Milky_Way ) and noticed a diagram of the various Milky Way arms.

I immediately thought that this image looked very similar to the light paths obtained from 4 rotating sources so I added another two sources to my original diagram. I then counted the arms, noted their respective positions and end points and realised that this mapping was more than one complete rotation. I added extra paths outside the existing first cycle paths until I came up with an extended end elevation as shown on the diagram below. The source at point 4, 0 had gone through an entire extra rotation (4 quarters).

Now while this extended end elevation was similar to the Milky Way arms diagram I had to do 2 transformations (reverse and skew) to this end elevation to get the closest match to the arms as shown. After the Transformations I changed the colors and compared my projection with the image as shown. The central bar was easy to determine and it had actually appeared to mask some of the earlier photon paths.

The only thing that didn't quite match up was the start location of the second arm from the right so I reversed the 2 simple transformations back to have a closer look at the start locations on the original model.

One thing the Milky Way arms image had was the start location of each of the 4 rotating sources (the arm start points) so, as the longest arm had gone through very close to 8 quarters of rotation (2 complete cycles), I decided to plot the sequence over 8 quarters from when each source started to emit. This longest arm/path (source rotating at point 4) did not actually reach the observation point after 8 quarters as shown in both the Milky Way arms diagram and in my own plot.

This start sequence was a bit strange as the object that started emitting at point 2 in the 7th (second) quarter of rotation was the source shown at point 3 on my plot. In the Milky Way arms diagram and my own plot the original start point should be, once transformed, on the opposite side of the projection. That doesn't make sense as if it did start at the opposite point it must have either 2 quarters less or 2 quarters to start emitting in sequence. This anomaly appears to be directly related to the gap in the outer and longest arm and the stub where our own galaxy is situated and the extra.

Emission Start Sequence Order (after each complete Quarter Rotation)

Start A Source starts emitting at point 4. This Source returns to the same position 4 after each complete cycle.

Quarter 1 A Source starts emitting at point 2. This Source returns to position 3 after each complete cycle.

Quarter 2 A Source starts emitting at point 3. This Source returns to position 1 after each complete cycle.

Quarter 3 A Source starts emitting at point 3. This Source returns to position 3 after each complete cycle.

Quarter 4 All sources 1, 4. 3, 2 are at positions 1, 4, 3, 2 respectively and rotate in this order for the last complete rotation (4 quarters).

It is apparent that what we see as observed Milky Way galaxy arms could easily be the photon paths from 4 emitting sources (galaxies) rotating around a common galactic center.

The scientific community needs to look seriously at all of the relevant facts and determine exactly what we are seeing in our cosmological observation datasets.

Maybe then it will be time for a paradigm shift on our current perceptions of dark matter, shift and an expanding universe.

Edited July 30, 2013 by LaurieAG

[LaurieAG]

The following diagram shows an alternate emission start point for source 3 that more closely resembles a sequence that would result in the Milky Way arm diagram. This variation has source 3 starting at position 4 and then traveling to position 1 in the opposite direction to all the other sources i.e. blue shifted not red. This explains how the area that we seem to think is our present location turns out with no shift. i.e. at the overlap they cancel out.

[LaurieAG]

While the above images represent what the paths would look like if the sources were rotating at c the distance traveled to the observer equals c/v * 2 * Pi * r where v is the angular velocity of the source. i.e. If the source had an angular velocity of 0.5 c the distance traveled would be c/0.5c = 2 times longer than at c.