The Uniformity of the CMB

23 June 2013

The CMB is seen as uniform because it was emitted from the radiant expanding shell of the Cosmos at different times and the radiation of all the expanding shells reach us at the same time. See the geometry of the ellipse below.


The ellipse is the path of point that moves, so that the sum of its distance from the two foci is constant. A whisper at one focus of an elliptical room, is heard at the other focus in the room, because the distance and travel time from focus to focus, is the same for any path of sound reflecting off the walls.

Light acts the same, with the same geometry, with ellipsoidal mirrors. The two foci can be called the origin and the destination. Light leaves the origin as an expanding sphere and reflects at the ellipsoidal surface as a ring. It is a ring because it is the intersection of a sphere and ellipsoid. This reflection focuses the light on to the destination. The overall travel time from the origin to reflection, to destination, is always the same for all angles of light departing from the origin.

If we retain the origin and destination and change to a luminous expanding sphere we can eliminate the mirror and reflection while keeping the geometry of the intersection of an expanding sphere and ellipsoid. The luminous sphere is the shell of cosmos which emits the CMB. Now the ellipsoid is an abstraction that exists in concept but not in reality. The ellipsoid defines the path of things that are perceptible at our location at a certain time.

Click to enlarge! Ellipsoids and equations

r = c*age/2*(1-fr2)/(1+cos(angle)*fr).

This is the ellipse drawn from the center focus, which is the origin, o on the figure. The eccentricity of the ellipse is fr. The radius of the expanding sphere, which intersects the ellipse is r in the equation. As the angle is varied, the points form an ellipse stretched in the radial direction with fr*c*age as the distance between the foci, od on Figure 3. The sum of the distances from the two foci, to a point, is always equal to c*age. The angle and radius when rotated around the centerline trace a ring that is the intersection of the sphere and the ellipsoid, aa or bb or cc on Figure 3. This nested series of rings may partially polarize the CMB, along the axis of the origin. Other polarizations seem likely. There is evidence that light traveling through space is polarized in a non-random direction. There is also evidence from the WMAP satellite that space could be rotating. We are located at someplace like d, at an unknown fr, on Figure 3, on a concentric radius = fr*c*age and are moving radially and tangentially with a velocity = fr*c.

Uniformity of the CMB:
The question of the uniformity of the CMB, is usually answered; that we appear to be at the center of the Big Bang, because the Big Bang explosion happened everywhere. A more quantitative, and less miraculous solution, looks again at Figure 3.

A ray of CMB reaches us, after two distinct intervals. The first interval starts at the center focus, at the origin, at point o, on Figure 3. It is with the expanding and cooling spherical shell, before the ray of CMB, which we will be observing, is emitted. Examples on Figure 3; are the lines oa, ob and oc. The temperature and watts/meter2, of the expanding sphere, is proportional to the inverse square of the radius.

The second interval, is the travel of the ray of CMB through space, after it leaves the expanding spherical shell. Examples on Figure 3; are the lines ad, bd and cd. It ends with the reception of the CMB, at the observer at point d. The temperature and watts/meters2, of the CMB during the second interval, is also proportional to the inverse square of the radius.

The two intervals always add up to c*age meters in age seconds in any direction the observer looks. For CMB emitted early in the cosmos, there is a shorter interval with the expanding sphere, and a much longer path through space interval to reach the observer. For CMB emitted later, there is a longer spherical expansion interval, before the CMB is emitted, but a shorter path through space interval to the observer. The expanding spherical shell, the CMB which it emits, and the CMB during its travel through space, all have a temperature proportional to, the inverse square of the distance traveled from the origin, o.

When the radius of the cosmos was oa, it emitted CMB from the entire spherical surface. Only that from the ring, on the sphere at aa will reach d at the same time as the other rings on the same ellipsoid. A similar argument can be seen in the rings bb and cc. All the CMB from the various rings which intersect the ellipse arrive at point d at the same time and temperature. oa + ad = ob + bd = oc + cd = or = c*age.

The formulas in the next section, show the relationship between radius and temperature. The CMB had a temperature at point a of 5.4_K when the Cosmos was one forth its age and size. It arrived at point d at 2.7_K after expanding for three fourths the age of the Cosmos. The temperature at point b was 3.8_K when the Cosmos was one half its age and size. It arrived at point d at 2.7_K after expanding for half the age of the Cosmos.The temperature at point c was 3.2_K when the Cosmos was three forths its age and size. It arrived at point d at 2.7_K after expanding for one forth the age of the Cosmos.

Blackbody watts from the CMB radiation

A flux of radiation has a Kelvin temperature. We see the temperature of the CMB as 2.735 Kelvin. We can convert this to watts/meter2 for blackbody radiation with the Stephan and Boltzmann law.

K4*5.5698E-8_W/(m2*K4) = W/m2
2.735 Kelvin = 3.11E-6_W/m2
When one sees something, it is in terms of W/m2 and the inverse square law.
The W/m2 times the area of the cosmos = wattage of the CMB, because as we saw in Figure 3, the temperature at point d, where the observer is located, is the same as a point r, the radius of the cosmos.
(2.735_K)4*5.5698E-8_W/(m2*K4)*4*pi*ru2 = 7.9E47_W = watts = power = energy /second
The CMB has the luminosity of a 7.9E47 watt light bulb seen from a distance of 15 billion light years. This is the same as 7.9E47 watts stretched over the area of a sphere with a radius of 15 billion light years.

The CMB is emitted from the expanding radiant shell which is where light orbits at the perimeter of the Cosmos. The impact of photons on this spherical shell is the source of the CMB. The light was accumulated as the Cosmos gained mass and light through the merging of Black holes. The energy emitted in 15 billion years by the CMB, if the energy output is constant, is 7.9E47_Watts*age = 3.7E65_J. For comparison, the energy of the Cosmos, Mc*c2=1.7E70_J is 46,000 times bigger. If the CMB is the remnant energy from the Big Bang, why is it so feeble? However, if the CMB is emitted instead throught the impact of photons at the perimeter of the Cosmos then this small value of energy makes sense.

The gravitational and centrifugal accelerations on the photon in orbit are c/age. As the Cosmos expands the photons orbit at a larger radius and the orbital accelerations decrease. The rate of change of the acceleration is 1/age2. The W/m2 of the CMB is 7.9E47_W/(4*pi*ru2) = 7.9E47_W/(4*pi*c2*age2). The rate of change of the orbital acceleration is proportional to the W/m2 of the CMB. This has the character of a Compton scattering or non-doppler redshift like process. How does this work?

We can map the power of the CMB onto the smaller spheres and higher temperature when the cosmos was younger, as long as we keep well clear of infinities.
(7.9E47/(5.5698E-8*4*pi))1/2 /(temperature_K2) = radius in meters
1.0615E27_m/(temperature_K2) = radius in meters

The radius, of the expanding sphere of the shell, is proportional to the inverse square of the temperature.
The following examples map temperature and radius.
1.0615E27_m /(2.735_K)2 = 1.42E26_m = ru = the radius of the cosmos currently.
1.0615E27_m /(273.5_K)2 = 1.42E22_m = ru/10000 = 1.5 million light years, at an age of 1.5 million years, at the freezing point of water of 273_K
At a temperature of 3000_K plasma becomes transparent to light. The radius becomes 1.18E20_m = 12466 light years at an age of 12466 years.

What is reasonable?
This last examples would fit in the core of a galaxy. This is only the CMB, but this much power would require an absurdly large star. An inside out or hollow star since its radiation comes to us from every direction. We have allowed the ease of doing calculations to project something absurd. We can see that these formulas and others like them might be used to trace back to a creation event at a point of infinite temperature and density. This has become dogma, trussed up with patches, which helps obscure the absurdity of physical infinities. Another way of looking at it is; at its present mass, our cosmos could never have been that small or young.

Since little ones make big ones, the cosmos came about by the merging of black holes. Low density black holes are big, old and expanding fast so they incorporate a lot of space over time. Big ones present a bigger target for merging. Old ones present a target for merging that has been around for a long time. Space seems well populated with black holes. It is a small step, for our dynamic unit, our cosmos, to be just another ordinary low density black hole in a universe full of the same.

A ledger might have beliefs on the left side, and evidence for those beliefs on right side. The dynamics described here are mathematically consistent beliefs, which don’t require physical infinities. The evidence is the values presented by the mass, radius and density of the cosmos, uniformity of the CMB, the flat rotation curves of galaxies and prevalence of dark matter. All the parts slip together seamlessly, and the dynamics locks all the parts together. There are no free parameters which might be adjusted to reflect a point of view.

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