Athena

God of Science and Astronomy

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Exploring Dark Energy in a Multiverse
By Robert Buckalew                         April 18, 2011, May 27, 2011
The increased speculation that our universe is part of a multiverse system allows the inclusion of possible external forces and relative motions as contributors to the acceleration of the expansion of our universe. I will here consider that rotational motion within the reference space of a multiverse contributes to the energy accelerating the expansion of our universe.
Defining dark energy as undetectable seems uncomfortably reminiscent of the 19th century definition of luminiferous Ether as a ‘ubiquitous and undetectable medium through which electromagnetic waves propagate’. If our universe exists in a larger multiverse context, forces outside this universe may produce the acceleration on the mater accredited to dark energy. Einstein, after the experimental refutation of the existence of ether, noted that acceleration of a mass in space will produce a force indistinguishable from the force of gravity. In the same way rotation of the universe (in a larger reference space) would produce a force indistinguishable from dark energy, i.e. an undetectable force producing outward acceleration of mass in our universe. This outwardly accelerating inertial force would be as undetectable to us from inside our closed rotating universe as acceleration would be indistinguishable from gravity when inside a closed box. It would, however, necessitate locating the universe within a larger context to establish a reference frame for the rotational speed and allow the possibility of other multiverses existing in that larger reference frame. Current rotational velocities could be calculated by using the current rate of expansive acceleration and the current size of the universe. Once the current rotational velocity is determined the expansion could be run backward in time including increases in rotational value due to the conservation of angular momentum. In this way the rotational values could be calculated for various diameters. Here I will hypothesize the rotational value for the end of the inflationary period, 10-32s. At the end of this period the universe is the diameter of a grape fruit or soccer ball. If the surface velocity of this universe is near (or just below) the speed of light, then contracting the universe to the size of a proton would increase rotational velocities that would exceed the speed of light. Such velocities in the early mass-less universe would not be problematic. When mass is introduced into the universal mix (at 10-35s with introduction of the Higgs field and the formation gluons and gluinos) a contradiction in the newly created laws of physics would occur since the kinetic energy in mass traveling faster then the speed of light would be infinite. This contradiction might have triggered the rapid inflationary expansion and consequent slowing of rotation necessary to resolve the contradictory conditions.
Assuming the resulting soccer ball sized universe has a surface velocity at just below the speed of light is a beginning point for the following calculations. Learning this rotational value and then applying the law of conservation of angular momentum to the present sized universe would produce a present day rotational value. Using this value on the mass of a typical galaxy would give us the inertial force and acceleration that would result from this present day rotation.
Minimum rotational speed for a proton’s surface to reach the speed of light. Being mass-less it contains no inertial or kinetic energy:
proton radius = .8768 femtometres  1 femtometre = 10 –15 meters
proton circumference = .8768 x 2 x 3.1416 = 1.7536 x 3.1416 = 5.5 femtometres = 5.5 x 10 –15 m or
0.0000000000000055 m
speed of light 3 x 108 m/s
Minimum initial rotational velocity- 3 x 108  m/s / 5.5 x 10 –15 = 16.5 x 1023 rps (revolutions per second)
Final rotational velocity after hyper inflation bringing the mass in the universe into compliance with laws of physics:
Soccer ball circumference = .7m
Speed of light = 30×107 m/s
30 x 107 m/s/ .7 m = 42.8  x 107 = 4.28 x 108 rps
Maximum rotational velocity of soccer ball sized universe at the end of inflation: 4.28 x 108  revolutions/second
 
Angular momentum of soccer ball sized universe:
 
Angular momentum = L = mass * angular velocity * distance to center squared or  = m * w * r2
Mass of observable universe = 3.35 x 1054 kg (based on critical density)
Soccer ball diameter = 22 cm equals Soccer ball radius = .11 m
Angular velocity = 4.28 x 108  – from above calculation – the maximum rotational speed of universe after inflation
Mass of soccer ball universe (assumed unchanged since hyper inflation) = 3 x 1055
Angular Momentum: L = m*w*r2  = 3.35 x 1054 kg * 4.28 x 108 rps * .11m2= 14.34 x 1062 x .0121 = .1735 x 1062 = 1.74 x 1061
Angular momentum of universe: 1.74 x 1061 joule seconds
 
Rotational value of current universe, using current (visible universe) diameter and conservation of angular momentum (negating torque loss or frame dragging):
Diameter of visible universe = 8.8 x 1026 meters
Radius of visible universe = 4.4 x 1026 m
Soccer ball universe angular momentum = 1.74 x 1061 joule seconds
Angular momentum = m*w*r2 solving for w
Angular momentum = 1.74 x 1061  = 3.35 x 1054 * w * (4.4 x 1026) 2
 1.74 x 1061 =  3.35 x 1054 * 19.36 x 1052 * w = 64.86 x 10106 * w
w = 1.74 x 1061 / 64.86 x 10106 = .0268 x 10-45 = 2.68 x 10-47 revolutions/second
 
Proposed current rotational velocity of the universe   = 2.68 x 10-47 revolutions / second
Force on average galaxies due to rotational value:
Formula for centrifugal force (newtons):  F = mv2/r
mass of our galaxy = 6 x 1042 kg
v = velocity= meters/second
d = diameter of universe = 8.8 x 1026 meters
circumference = pi x d = 3.1416 x 8.8 x 1026 = 27.6 x 1026 meters
rotation = 2.68 x 10-47 revolutions/second
velocity = circumference x rps = 27.6 x 1026 meters x 2.68 x 10-47 revolutions/ sec = 73.97 x 10-21 meters/sec
v = 7.39 x 10-22
F = 6 x 1042 kg x (7.39 x 10-22)2 / 4.4 x 1026 = 6 x 1042 x 54.6 x 10-44/ 4.4 x 1026 = 327.6 x 10-2/ 4.4 x 1026 = 74.5 x 10-28 = 7.45 x 10-27
Outward inertial force on typical galaxy: F = 7.45 x 10-27 newtons
Acceleration on a galaxy due to rotation of our Universe:
F=ma or a=F/m
7.45 x 10-27 / 6 x 1042 = 44.7 x 10-69  = 4.47 x 10-68 m/s2
Conclusion:
The inertial acceleration on a galaxy from the proposed rotation of our universe would be insignificant and cannot be a factor in the observed accelerating expansion of the universe.

Arp 273

Relativism of a Straight Line

Consider a simple problem about centrifugal force. Imagine you stood at a pole of the earth, say the North Pole and constructed a wheel whose axis extended from the calculated axis of the earth. (This wheel would spin parallel to the plane of the equator.) Imagine that this wheel contained a precision force gauge whose output you could remotely read as the centrifugal force at the wheel’s rim.

You spin the wheel clockwise (from the top view) and recorded the force at the wheel’s rim. By spinning in the clockwise direction the wheel would be spinning opposite that of the earth’s rotation. Would the rotation of the earth, in effect, be subtracted from the spin of the wheel? Would the centrifugal force readout be higher if the earth did not rotate?

Now you stop the wheel and spin it in the opposite direction, i.e. counter clockwise at precisely the same speed (RPM) relative to you standing on the earth. Again you read the output of the force gauge and record it. In this direction would the earth’s rotation add to the wheel spin? Will the output of the second (counterclockwise) spin have an added centrifugal component that would show up on the force gauge? Or will the wheel produce the same centrifugal force? Does your effort, imparting a force in the wheel, somehow create it’s own frame of reference relative to you (the force) and the wheel? Or could the proximity of the wheel to the earth’s gravity somehow envelop and include the wheel in its rotational motion allowing the two opposite direction spins to produce an identical force output?

The speed of the wheel obviously depends on where you stand when you determine the wheel speed. If you float in space above the pole you will see the wheel spinning at different speeds. The counter clockwise wheel spin being 2 Revolutions per day (RPD) faster than the clockwise direction. And from that point of view you would expect the centrifugal force to be higher in the counterclockwise direction. If you took the remote readout of the force gauge in space above the pole, would the readout be different?

Centrifugal force is derived from the inertia of an object in motion (which prefers to travel in a straight line). Inertial resistance to that ever-changing circular motion produces the force. It is technically called angular momentum. Also, the velocity of that body in motion determines the amplitude of that force. So the question boils down to the immediate straight line moment of velocity of a point on the rim. However, this brings us back to the original problem. If you measured the moment of velocity at a point on the rim standing at the at the earth’s pole (or anywhere on the earth), it would again be the same in both directions. If you measured the moment of velocity from space, it would again be higher in the counter clockwise direction. It seems simple Newtonian motion is relative to the observer’s position and motion.

Our individual motion standing on the earth is far from simple. We are not only moving on a spinning earth but also orbit around the sun, which is moving through the galaxy. This galaxy is spinning around its center and moving relative to the local cluster. And this cluster is moving relative to the more distant background galaxies. So even the task of throwing a ball in space, which would appear to the thrower to go in a straight line, (producing no force of angular momentum) would not be moving in a Newtonian straight line if observed from, for instance, the moon.

So is the straight line motion of the ball solely determined by the force applied, from the point of applied force? If so the wheel would produce the same centrifugal force in both directions as the applied force is equal (though opposite). If the motion of a thrown ball is not a universal straight line but follows the curves and spins of an orbiting earth and moving sun, then the centrifugal force of the wheel will be different between a clockwise spin and a counter clockwise spin.

If the observer’s motion determines weather a line of motion is straight or curved, then consider an observer above the earth, watching a bullet fired from the equator to the north pole. It will naturally take the shortest path, (a straight line for us watching on earth). To eliminate any confusion about following the curvature of the earth I have will make the northern hemisphere a cone with the equator as the base and the north pole the apex and removed the attraction of gravity. From the firing position on the equator the bullet would describe a perfect straight line. From space above the rotating cone the path of the bullet would describe a tightening spiral. So the outside observer would see the bullet traveling a curved path and therefore assume that some outside force was causing the mass to travel a path other than a straight line. They would also assume that there was a side force on the projectile produced by the angular momentum. They would expect anyone traveling inside the bullet to experience this side force as one in a car when turning a corner.

So where lies this frame of reference for determining what is a straight line? The answer could come from the measurement of centrifugal force itself. It could be determined by performing our original experiment of spinning a wheel. If the centrifugal force is identical with both spins, the frame of reference is the wheel itself. If it is additive and subtractive by the earth’s rotation, the frame of reference then occurs in a larger context beyond the earth’s influence.

If the later was true, this experiment on a larger scale could determine the absolute frame of  reference for all motion. It would be possible that the reference frame could be the universe and with a large enough wheel we could determine if the universe itself is in relative motion. We could measure this by a series of wheel spins (or tethered weight spins) in space with a precise force sensor. By changing the orientation and speed we could find the condition of zero angular momentum, when the wheel is at rest relative to the universe.  The wheel speed and orientation would match the rotation and orientation of the universe. This would also mean that our universe not self contained but part of a larger framework possibly containing other multi-verses.

However, if the reference frame is that of the point of origin of the applied force, then every moving object in the universe determines its own straight line. And producing a universal straight line would be impossible. It would mean that straight line inertial motion is as relativistic as the speed of light. That any straight line motion is determined by the last applied motion changing force. Traveling in space (away from any influencing source of gravity) you would know that you were going in your own straight line but it would be impossible to prove it by observing outside motion.

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