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.

Edited June 18, 2013 by LaurieAG

[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 Centre of Mass and not rotating around it.

[CraigD]

I found you diagrams very pretty, Laurie, but your labeling points with pairs of integers confusing, because I at first took them to be 2-dimensional coordinates.

 

I could make no sense of many of your statements. For example, you wrote

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.

But the distance between the point’s you appear to have labeled “1,4” and called “the observer”, and the one you have labeled “C.O.M” doesn’t depend on the circumference of the circle centered at point “C.O,M” and passing through point “1,0”, which is what you appear to be saying. It’s just an arbitrary, constant distance, which I don’t find you giving.

 

Eventually, you appear to arrive at this conclusion:

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 Centre of Mass and not rotating around it.

I don't believe this is at all true.

 

Comparing the observed frequencies of photons where their frequencies when emitted is known by some means, such as knowing the material that emitted it and its temperature, and where the effect of gravity is either negligible effect or known, and the distance between source and observer sufficiently small (ie: within the same or nearby galaxies, so not significantly affected by cosmic expansion), is a reliable way to determine the recessional speed of source and observer relative to one another, and is know as using red/blueshift. They work regardless of the distance of the electrons of the atom emitting the photons (typical starlight photons are emitted this way, and for the sake of discussion, other ways can be ignored) from the center of mass of their star or other bodies. This is useful, because in addition to being used to determine the speed with which stars are moving toward or away from us, red/blueshift is an important way that the rotation of stars is determined, light from the part of the star moving toward us due to its rotation showing blueshift, from the part moving away showing redshift.

 

For sufficiently small speeds, distances, and masses, classical Newtonian physics give an adequate approximation of red/blueshift. It’s not necessary to understand Relativity or quantum mechanics to understand typical redblueshift, though QM is helpful in avoiding the conundrum of the requirement of a medium for light, which must have wave properties for red/blueshift to occur.

 

Red/blueshift is not used only to measure the velocities of stars. For example, it’s used in radar devices that measure the speed of things such as rain, planes, cars, and baseballs. This technology is very well understood and proven.

[LaurieAG]

Hi CraigD,

 

But the distance between the point’s you appear to have labeled “1,4” and called “the observer”, and the one you have labeled “C.O.M” doesn’t depend on the circumference of the circle centered at point “C.O,M” and passing through point “1,0”, which is what you appear to be saying.

 

Consider the C.O.M. as the galactic C.O.M. of all the emitting sources in the galaxy.

 

The point 1,4 is where the light emitted from the source at point 1,0 is after 4 quarters of rotation. Similarly 2,3 is where the light emitted from point 2,0 is after 3 quarters of rotation etc. The distance is how far light will travel during one complete rotation i.e. 2*Pi*r around the Center of Mass of the galaxy.

 

If we were viewing a pair of sources that rotated once around the Milky Ways (i.e. our own) C.O.M. then the distance between the observer and C.O.M. would be our own radius of rotation and the 2 sources radius of rotation would be (our radius of rotation)/(2*Pi).

 

Red/blueshift is not used only to measure the velocities of stars. For example, it’s used in radar devices that measure the speed of things such as rain, planes, cars, and baseballs. This technology is very well understood and proven.

 

For discrete non rotating sources. I don't have any problem with Red/Blue Shift of discrete non rotating sources. The main problem is that light cannot escape from the galactic C.O.M.'s in the universe and everything else that we can observe is the light that is emitted from a source that rotates around these galactic C.O.M.'s.

[CraigD]

Hi Laurie!

 

The point 1,4 is where the light emitted from the source at point 1,0 is after 4 quarters of rotation. Similarly 2,3 is where the light emitted from point 2,0 is after 3 quarters of rotation etc. The distance is how far light will travel during one complete rotation i.e. 2*Pi*r around the Center of Mass of the galaxy.

The distance light will travel in vacuum for any interval of time [imath]t[/imath] is [imath]ct[/imath], where [imath]c[/imath] is the speed of light. Your conclusion (at least I think that’s what you’ve concluded) that it travels different distances depending on the place from which its emitted isn’t supported by physics.

 

If we were viewing a pair of sources that rotated once around the Milky Ways (i.e. our own) C.O.M. then the distance between the observer and C.O.M. would be our own radius of rotation and the 2 sources radius of rotation would be (our radius of rotation)/(2*Pi).

No, the distance between us and our center of rotation (conventionally, the word for this is “revolution” rather than “rotation” – rotation is conventionally used for solid bodies, revolution for separate ones: “the Earth rotates on its axis as it revolves around the Sun”) is, assuming a circular orbit, just our “radius of revolution”. There’s no factor of [imath]\pi[/imath] or some other bodies’ distance (radius) from point “C.O.M” in this distance. Likewise, there’s no factor of [imath]\pi[/imath] in the distance between us and some other body.

 

There’s a factor of [imath]\pi[/imath] in distances only when they are parts of the circumference of a circle, ellipse, or similar curve. Ignoring the usually slight bending effect of gravity, light travels in straight lines, not in some curve depending on the orbiting motion of its source or receiver.

 

For discrete non rotating sources. I don't have any problem with Red/Blue Shift of discrete non rotating sources.

To get over your problem with the usefulness of measuring red/blueshift of all sources, consider that what is actually emitting light doesn’t “know” it’s part of a larger collection of particles. Light from the atoms of a star doesn’t know those atoms are swirling around the surface of the star, nor that the star is orbiting the center of a galaxy, and so on.

 

As I previously mentioned, circular motion isn’t a problem for red/blueshift, rather red/blueshift is useful for measuring circular motion.

 

The main problem is that light cannot escape from the galactic C.O.M.'s in the universe and everything else that we can observe is the light that is emitted from a source that rotates around these galactic C.O.M.'s.

It’s true that light can’t escape from a black hole, and that every galaxy appears to have a supermassive one in its center. However, light from stars outside of the event horizon of that central black hole can escape. If this were not the case, we wouldn’t be able to see other galaxies at all.

 

In your first post, you said

In this model there are no (1) small sizes, (2) great speeds or (3) huge masses involved ...

so I’m puzzled that you’re now adding galactic black holes.

 

However, the effect of gravity only introduces a new kind of red/blueshift, gravitational. Gravitational redshift is mostly useful as evidence supporting the theory of General Relativity, not astronomy, because its effect for most visible astronomical bodies – stars – is much smaller than red/blueshift due to motion (Doppler effect).

[LaurieAG]

Hi CraigD,

 

Maybe this walk through will help you understand. 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.

[CraigD]

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).

The distance the light sources travel in one complete revolution is [imath]2 \pi r[/imath], but the distance light from them travels to a distant observer is not. It’s not difficult to calculate, given the necessary data, but there’s not factor of [imath]\pi[/imath] in it. As we’d usually assume the distance to the observer d is much greater than r, we can safely ignore r, and consider the distance to be just d.

 

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.

This just isn’t a correct approach to calculating Doppler red/blueshift. You can tell without considering its details, because it doesn’t have a speed (distance/time) term. Red/blueshift can’t be calculated from distance (“change in physical location”) alone.

 

To calculate the red/blueshift of the system you describe – 2 light sources opposite one another in circular orbits of the same radius, the plane of their orbits inclined 45% relative to a line from their center to a distant observer – we need to define some additional values. Let’s pick somewhat realistic ones: the light sources are stars identical to the Sun, separated by exactly 2 astronomical units (299195741400 m), giving them a period of exactly 2 years, and an orbital speed of about v = 14892.35 m/s.

 

The component of their velocity toward the observer at its greatest, then, is [imath]v_r = \frac{v}{\sqrt2} \,\dot=\, 10530.47 \,\mbox{m/s}[/imath]. So the red/blueshift is about [imath]z = \pm \frac{v_r}{c} \,\dot=\, 3.5125897 \times 10^{-5}[/imath].

 

:confused: I’m don’t understand what you’re trying to say in this thread, Laurie, or more, your underlying motives. Do you believe there is something wrong with the usual ways red/blueshift is calculated?

[LaurieAG]

Hi CraigD,

 

Your references below refer to the center of mass with respect to a solar system comprised of 2 stars rotating around each other as opposed to a galactic system, such as the Milky Way where all star systems rotate around a higher level galactic center of mass.

 

The distance the light sources travel in one complete revolution is [imath]2 \pi r[/imath], but the distance light from them travels to a distant observer is not. It’s not difficult to calculate, given the necessary data, but there’s not factor of [imath]\pi[/imath] in it. As we’d usually assume the distance to the observer d is much greater than r, we can safely ignore r, and consider the distance to be just d.

 

All measurements in the diagrams are light years and are based on time. If a source travels [imath]2 \pi r[/imath] in one complete rotation the light emitted also travels the same distance in the same time. The example I gave with regards to sources rotating around the Milky Ways centre of mass and being observed by us shows that the radius of rotation of those sources would not be negligible and should not be ignored. The use of a simple balanced 2 source system is just to break the problem down to its lowest level. These 2 sources could be regarded simply as two galaxies that emit the same amount of light in consolidation and rotate around a higher level center of mass.

 

To calculate the red/blueshift of the system you describe – 2 light sources opposite one another in circular orbits of the same radius, the plane of their orbits inclined 45% relative to a line from their center to a distant observer – we need to define some additional values. Let’s pick somewhat realistic ones: the light sources are stars identical to the Sun, separated by exactly 2 astronomical units (299195741400 m), giving them a period of exactly 2 years, and an orbital speed of about v = 14892.35 m/s.

 

Consider the example I gave within the Milky Way. It takes our solar system approximately one quarter of a billion years to rotate around the Milky Ways galactic center. Our own radius of rotation in light years approximately equals 0.04 billion years. In this example the two light sources will make one complete rotation around the Milky Ways during this time so the 2 sources radius of rotation approximately equals 0.006 of a billion light years. In your example the period of rotation is 0.000000002 of a billion light years so the difference between the two periods is approximately 19 million times. If we were observing the same sources as the two you describe and they were in a balanced galaxy (i.e. their rotation was balanced by a similar pair of sources on the opposite side of the galactic center) such as our Milky Way your calculations fail to take this higher level rotation and its incumbent shift into consideration.

 

Do you believe there is something wrong with the usual ways red/blueshift is calculated?

 

You appear to be using velocities with respect to the sources local center of mass and not their galactic center of mass. If it takes approximately 0.04 billion light years for the sources to rotate around their galactic center in the example given you cannot use the component of their velocity toward the observer at its greatest with respect to their local center of mass.

 

At point 3,0 the component of their velocity towards the observer is at its greatest and at point 1,0 the component of their velocity away from the observer is greatest.

[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 anomally 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 centre.

 

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 appears to be our present location turns out with no shift. i.e. at the overlap they cancel out.