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Old May 18, 2010, 07:21 PM
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General Relativity

Speed of light

NB: Ambitious theory

Video summary http://www.youtube.com/watch?v=06NRxaRi1pw

(Muslims) believe that angels are creatures without conventional mass, and that God created them originally from light. They move at any speed from zero up to the speed of light. It is the angels who carry out God's orders. Those angels take their orders from a Preserved Tablet somewhere in outer space, and not from God's Throne. They commute to and from this Preserved Tablet to get their orders from God. In the following verse, the Quran describes how angels travel when they commute to and from this Tablet. And the speed at which they commute to and from this Tablet turned out to be the known speed of light:

Quote:
[Quran 32.5] (Allah) Rules the cosmic affair from the heavens to the Earth. Then this affair travels to Him a distance in one day, at a measure of one thousand years of what you count.
It is the angels who carry out these orders. People in this society in this era didn’t measure the distances in kilometers nor in miles but rather by how much time they needed to walk. For example, a village two days away meant a distance equivalent to walking for two days; ten days away meant a distance equivalent to walking for ten days... However in this verse the Quran specifies 1000 years of what they counted (not what they walked). Those people back then followed the lunar calendar and counted 12 lunar months each year. These months are related to the moon and not related to the sun. Hence in 1 day the angels will travel a distance of 1000 years of what they counted (the moon). Since this verse is referring to distance, then God is saying that angels travel in one day the same distance that the moon travels in 12000 lunar orbits. Outside the gravitational field of the sun this speed turned out to be the known speed of light.

Since we are considering 12000 Lunar Orbits/Earth Day in free space (outside the gravitational field of the sun) then we have to remove the effects of the sun's gravity on the Earth-moon system:

If you spin on a chair, your legs tends to flay outwards. And that when your spin slows down your legs settle back inwards. This is the nature of centripetal forces. This is what also happens when the Earth-moon system gains or loses rotational kinetic energy, the distance to the moon changes (hence the length of the lunar orbit changes).

Do you know why the same half of the moon always faces Earth? The moon has been facing Earth like this for more than 4 billion years. Just like Earth rotates on its axis once every day with respect to stars, the moon also rotates on its axis with respect to stars. Since the moon keeps facing Earth this means that the moon needs to travel 360 degrees around Earth with respect to stars in order to rotate 360 degrees on its axis with respect to stars. When the moon first formed it was very close to Earth and it orbited Earth once every few hours, today this period is 27 days, and as the moon continues to recede this period will continue to increase; the greater the distance from Earth the greater this period becomes. When this period becomes 50 days, for example, this also means that it will take the moon 50 days to rotate 360 degrees on its axis with respect to stars. So as the moon recedes from Earth its spin with respect to stars slows down, that is, it loses rotational kinetic energy (this is different from moon's kinetic energy due to moon's motion around Earth). If the distance to Earth increases to infinity, the moon would stop spinning with respect to stars and hence its rotational kinetic energy decreases to zero. This proves that the moon's rotational kinetic energy is a function of the distance from Earth. Similarly, the total energy of the Earth-moon system is a function of the distance from the sun. Since the distance to the sun is not a constant then a definition using Lunar Orbits/Earth Day inside the gravitational field of the sun is impossible. However when the Earth-moon system exits the solar system (becomes isolated) 12000 Lunar Orbits/Earth Day becomes equal to the speed of light.

Every point in this orbit has a certain magnitude and a certain direction. As the moon heads to the sun it speeds up, and as it heads away from the sun it slows down. This creates a sector of the orbit where the moon is speeding up:



But as Earth goes around the sun, the position of the sun relative to Earth with respect to stars is changing. This makes the sector where the moon is speeding up move forward inside the orbit such that it points to the sun again; similarly the sector where the moon is slowing down moves forward inside the orbit such that it points away from the sun again. Hence the entire orbit changes direction with respect to stars by the same angle it orbits the sun (twist). This means that the orbit is influenced by a net rotational force (like torque around Earth). As the distance to the sun increases to infinity, ø decreases to zero and lunar orbit loses this twist. When we vectorially remove the energy gained from this twist we can calculate the total energy and hence the length of the lunar orbit outside gravitational fields
Distances:

Distance traveled by angels in one day = 12000 x Length of lunar orbit.
C t' = 12000 L'
Where:

C Is the speed of angels, which we intend to calculate and then compare to the known speed of light (no external forces, no acceleration, no deceleration).
t' Is Earth Day outside gravitational fields i.e. time for one rotation of Earth about its axis with respect to the stars.
L' Is the length of the lunar orbit outside gravitational fields (no external forces, no acceleration, no deceleration).

Time: This table below shows the lunar month and Earth day in both sidereal system (with respect to stars) and synodic (with respect to sun):

Period Synodic (sun) Sidereal (stars)
Earth day t 24 hours = 86400 sec 23 h 56 min 4.0906 sec = 86164.0906 sec
Lunar Month T 29.53059 synodic days 27.321661 synodic days = 655.71986 hours


But no matter what system you use when the Earth-moon system exits the solar system the synodic periods become equal to the sidereal periods. Why you may ask, because the sun becomes just another star.

When the Earth-moon system is still inside the solar system the position of the sun relative to Earth with respect to stars changes; this means that the moon has to make more than 360 degrees with respect to stars in order to point to the sun again. However when the Earth-moon system exits the solar system the position of the sun relative to Earth with respect to stars remains the same, that is, the moon now only has to make 360 degrees with respect to stars in order to point to the sun again (the synodic periods become equal to the sidereal periods). This means that the lunar month with respect to the sun becomes equal to lunar month with respect to stars and Earth day with respect to the sun becomes equal to Earth day with respect to stars. So the 1000 lunar years with respect to sun become equal to 12000 lunar months with respect to stars.

Every new moon (29.5 days) the moon will not return to the same point in the orbit (it will be at a different point). The moon returns to the same point in the orbit after only 27.3 days. When astronomers study the energy of orbits they use the sidereal system, that is, the moon has to return to the same position with respect to stars and not return to the same position with respect to the sun. When the moon returns to the same point with respect to stars the Earth-moon system would have moved 26.9 degrees around the sun (not 29.1 degrees).

In general relativity, the local inertial frames (where the measured speed of light is 299792.458 km/sec) are actually frames non-rotating with respect to stars (not non-rotating with respect to sun). If these frames are rotating with respect to stars then the measured speed of light would not be 299792.458 km/sec. Hence inside the gravitational field of the sun 12000 Lunar Orbits/Earth Day make 11% difference with 299792.458 km/sec when compared in a local frame non-rotating with respect to stars (sidereal system). A local frame non-rotating with respect to sun (synodic system) would be rotating with respect to stars and hence in this frame the measured speed of light is not 299792.458 km/sec in the first place. Some skeptics use the synodic system (rotating frame with respect to stars) and then compare it to the speed of light in a local inertial frame (non-rotating with respect to stars) however this comparison is invalid. Why? Because this is the same location but two different frames.

See the problem with the synodic system at footnote [2]

Length of Lunar Orbit:
Length of lunar orbit = Velocity x Time (L = V T)

The velocity of the moon is not a constant. NASA measured the instantaneous velocity of the moon at various points throughout its orbit. These measurements show that the velocity of the moon varies considerably (from 3470 km/hr up to 3873 km/hr); which means that the moon accelerates and decelerates continuously. The average lunar velocity is Vavg = 3682.8 km/hr (1.023 km/sec).

The lunar orbit relative to Earth is a low eccentricity ellipse. Most astronomers calculate the length of the lunar orbit manually by the following equivalent circle method:
L = V T = 2 π R
V = 2 π R / T

However this velocity is under the influence of the gravitational pull of the sun. We can vectorially calculate the velocity of the moon relative to Earth without the gravitational pull of the sun and hence the isolated length of the lunar orbit: Displacement is a vector (has magnitude and direction) and from this vector we get the velocity vector (magnitude and direction); from this velocity vector we get the kinetic energy. If external work is done we end up with a resultant displacement vector, resultant velocity vector and resultant kinetic energy. In our case we have to backtrack.

The work done by the gravitational field of the sun by creating a net rotational force on the lunar orbit (twist) is:



Without the sun (isolated Earth-moon system) the moon's isolated vector remains in the original direction with respect to stars (no twist); but with the sun (compounded system), the moon's compounded vector changes direction by angle ø with respect to stars each cycle around Earth (twist). This means that the moon's orbital energy is the sum of the energy acquired from this twist plus the intrinsic energy of Earth-moon system (kinetic energy of Earth's spin transferred to the lunar orbit by ocean friction).

Ocean Friction:

The oceanic high tides and low tides; they are caused by lunar gravity. This figure teaches you how ocean friction transfers the kinetic energy of Earth's spin to the lunar orbit:



As the moon acquires more energy from Earth's spin it does not actually speed up, instead it slows down because it orbits at a higher altitude (R' increases). (If Earth were spinning in the opposite direction the reverse process would have happened; the moon would have lost altitude and eventually crashed into Earth.)

Today's lunar orbit is a very low eccentricity ellipse (very close to a perfect circle) but when the moon first formed it was a very high eccentricity ellipse. The eccentric ellipse back then had a point very close to Earth and another point very far out. When the moon was nearest to Earth inside the ellipse the gravitational forces were stronger and hence more energy was transferred to the moon when it was closer to Earth than when the moon was farther out inside the ellipse. This made the moon recede more when it was closer to Earth than when it was farther out inside the ellipse. This difference in recession rates smoothed out the differences between the closest and the farthest points in the orbit (this is why today's lunar orbit is very close to a perfect circle). So for each direction the recession has different magnitude. Since this recession has magnitude and direction then it is a displacement vector. However in every direction this displacement vector is normal to the rotational force around Earth (always at right angles with the rotational force around Earth, 90 degrees). Thus the sum of these two vectors is determined by the Pythagorean Theorem:

Hence cosø is the only solution to this three-body problem.
Isolated Earth-Moon System:

The lunar orbital radius (R) is a function of total energy, however the total orbital energy comes form two sources: ocean friction and gravitational twist (two sources, not one). Since the distance to the sun is not a constant then as the distance to the sun increases to infinity the lunar orbit loses this twist; but without the energy gained from this twist the orbital radius decreases to R' = Rcosø (see proof at footnote [3]). Hence the moon's isolated orbital length becomes L' = 2πR' = 2πRcosø = Lcosø (i.e. 12000 L' / t' = 12000 Lcosø / t').

Today when the moon makes 360 degrees around Earth with respect to stars the Earth-moon system moves 26.92952225 degrees around the sun. Hence the lunar orbit's twist angle ø = 26.92952225 degrees. We can calculate ø from the period of one heliocentric revolution of the Earth-moon system (365.2421987 days):
ø = (360 degrees / 365.2421987 synodic days) x 27.32166088 synodic days = 26.92952225 degrees

Similarly, Earth's spin slows down by 6 seconds i.e. the isolated Earth day t' becomes 86170.43114 sec (see proof at footnote [4]).
Compare:

So finally we can check the accuracy of this equation in the Quran:
C t' 12000 L'
The distance traveled by light in one Earth Day = C t' = 299792.458 km/sec x 86170.43114 sec = 25833245358 km
The distance traveled by angels = 12000 L' = 12000 x 3682.8 km/hr x 655.71986 hr x cos(26.92952225) = 25836303825 km
By dividing the two distances we get the ratio of 1.00011839267.
Difference = 0.01%


Constant:

Since the distance to the sun is not a constant [5] then if it is defined inside the gravitational field of the sun then this definition will be wrong with time; however since it is defined in free space (outside the gravitational field of the sun) then this definition will be true forever:

Ocean friction is causing the rotation of Earth to slow down, that is, for the days to get longer (t' increases). And as Earth's rotation slows down the moon recedes (R' increases):

c = 12000 L' / t' = 12000 2 π R' / t'

Both R' and t' are increasing but due to a fundamental law in astrophysics the ratio R' / t' remains the same: The tidal force decelerating Earth is the same force pushing the moon. Since the force pushing the moon is gravitational, then it is inversely proportional to the square of the distance to the moon. Similarly, this same force decelerating Earth is proportional to the change in kinetic energy in Earth's spin, that is, it is inversely proportional to the square of Earth day. This makes the square of the distance to the moon to be directly proportional to the square of Earth day. This implies that the distance to the moon remains proportional to Earth day. Hence R' / t' is a constant equal to 3.976120966 (R' / t' = R cosø / t'). This makes the equation in the Quran c = 12000 L' / t' to be composed only of constants, with no variables. Hence, 12000 Lunar Orbits/Earth Day is a constant forever.

4.52 billion years ago the moon formed when a planet the size of Mars collided with Earth. On impact, Earth gained angular momentum (rotational speed). This angular momentum has been slowly transferring to the lunar orbit. On impact of that planet with Earth, the molten debris flung with a certain escape velocity and sucked vaporized water and some gases from Earth's atmosphere. This debris clustered to form the moon. But the moon couldn't maintain those gases because its gravity was extremely weak and it didn't have a strong magnetic shield; so it lost those gases and settled in orbit without this mass. The equation in the Quran c = 12000 Lunar Orbits/Earth Day has been true in the isolated system ever since the moon first lost this mass, that is, since the early creation of the Earth-moon; is true today and as the moon continues to recede this equation in the Quran will always be true.
To learn why there are two tidal bulges, one facing the moon and another one opposite to it, see footnote [6].

Lunar Orbits/Earth Day is common to all observers; Km/sec is not.
12000 Lunar Orbits/Earth Day = 299,792.458 km/s is the speed of light for observers standing outside gravitational fields and looking at light also traveling outside gravitational fields. But an observer near a black hole for example sees the speed of light outside gravitational fields a zillion km/s. This is because the velocity of light appears to vary with the intensity of the gravitational field (See proof at footnote [7]).
From General Relativity we know that an observer standing outside gravitational fields looks at events inside gravitational fields and sees them in slow motion. When he steps inside those gravitational fields he sees them in normal speeds. But now he looks back at where he was outside gravitational fields and sees the events there in fast motion. In our case the event is the moon orbiting Earth. When an observer in stronger gravitational fields, near a black hole for example, looks at the Earth-moon system he does not see the moon orbiting Earth once every month; instead he sees the moon orbiting Earth once every few seconds; he also sees the length of the lunar orbit to be much longer than we see it. This is because the gravitational field that he is in causes his clock to run slower and his ruler to shrink.

Not only will observers in different gravitational fields not agree on the time period for the lunar orbit but also they will not agree on the length of the lunar orbit either. By using classical orbital mechanics we discovered that all observers will see the speed of light outside gravitational fields equal to 12000 Lunar Orbits/Earth Day; but from General Relativity we know that they will never agree on a value in km/sec. An observer near a black hole for example sees the speed of light outside gravitational fields a zillion km/s, but still equal to 12000 Lunar Orbits/Earth Day! This means that if the speed of angels outside gravitational fields were defined in km/sec then it would have appeared to vary for observers in different gravitational fields; however since this speed was defined in Lunar Orbits/Earth Day then it will never appear to vary to anyone because 12000 Lunar Orbits/Earth Day is common to all observers. Hence the Quran gave us a better definition for time and distance: A definition common to all observers, forever.

Quote:
[Quran 10.5] It is He (Allah) who made the sun to shine and the moon to light, and destined it in stages; that you may learn to count the years and the mathematics. Allah only created this in truth. He details His Signs for those who are knowledgeable (scientists)
Relativistic Time Dilation

For an object to move it needs to accelerate; but acceleration causes clocks to run slower, the stronger the acceleration the slower the clock.

The Quran states another verse in which angels traveling at a certain velocity, appear to experience slower time than humans. But this agrees with Einstein’s theory of special relativity, which says that a faster moving object appears to experience slower time. Muslims use Einstein’s theory of special relativity with the following verse in the Quran to assert that angels indeed accelerate up to the speed of light:
Quote:
[Quran 70.4] The angels and the Spirit ascend to Him in a day, the measure of which is fifty thousand years.
Here angels will experience 1 day while humans will measure it as 50,000 years (time vs. time and not time vs. distance as the previous lunar verse). However, according to the theory of special relativity, given this time difference (time dilation), we can calculate the speed at which that object travelled. We can verify if those angels really accelerate up to the speed of light, as claimed by Muslims, or not. Outside gravitational fields it is:



(Where ∆to is the time measured for a mover by a mover; ∆t is the time measured for a mover by a stationary frame; v is the velocity of the mover relative to the stationary observer):

∆to is the time experienced by angels (1 day).
∆t is the time as measured by humans (50,000 lunar years x12 lunar months/lunar year x 27.321661 days/lunar month).
v is the velocity of angels in this case (which we intend to calculate and then compare to the known speed of light).
c is the nominal speed of light, 299792.458 km/s.
From the above equation we can solve for the unknown velocity



This time dilation (time difference) shows that angels indeed accelerate to relativistic speeds; outside gravitational fields this is the same speed calculated from the previous lunar verse also outside gravitational fields.

We cannot calculate our local speed of light from this time dilation however we can calculate at what percentage of the speed of light those angels are traveling relative to an observer on Earth. By this we can compare a time dilation (50,000 years vs. one day) with a speed (12000 Lunar Orbits/Earth Day). We can do this by translating both of them to a common speed in km/sec. Outside gravitational fields 50,000 years vs. one day shows angels traveling at 12000 Lunar Orbits/Earth Day; it is the same speed in km/sec. However inside gravitational fields 50,000 years vs. one day shows angels crossing a wormhole at a few meters/sec. This is a picture of a wormhole. The Quran says that angels use these wormholes to reach any place in the universe. An observer outside gravitational fields sees those angels passing by him at 99.99999...% of the speed of light (relativistic speeds, very close to the local speed of light), that is at 299792.457999...km/s. But when those angels enter the gravitational field of a wormhole this observer still sees those angels entering the wormhole at 99.99999...% of the speed of light however that would no longer be at 299792.457999...km/s. This is because the speed of light is a variable depending upon the reference frame of the observer. If he sees the speed of light in a wormhole at 10 meters/sec, for example, then he would see those angels traveling at only 9.999999...meters/sec, flapping their wings in slow motion, reddish in color and very dim (and in turn they would see him in fast motion, bluish in color and very bright).

A smaller time dilation (say 100 or 1000 years vs. one day) can also occur if we stand on Earth and angels stand on a pulsar or a neutron star (or resist their fall into a pulsar, see Gravitational Time Dilation below). This makes their velocity relative to us to be zero (and not 299792.457999... km/s). Naturally occurring wormholes connect distant black holes; however at a lower time dilation (100 or 1000 years vs. one day) the two entrances of the wormhole cannot connect; hence a wormhole cannot form. So with the time dilation stated in the Quran (50,000 years vs. 1 day) and the fact that angels are moving then those angels have to be crossing a wormhole. The pulsar scenario or any other combination cannot do.
Gravitational Time Dilation
Clocks run slower in stronger gravitational fields (near bigger mass).

Muslims believe that Paradise and Hell are both much bigger and much more massive than Earth (but still much smaller than God's Throne). The theory of general relativity says that time should pass slower near an object more massive than Earth (clocks run slower in stronger gravitational fields). So according to general relativity, time should pass in Paradise/Hell much slower than on Earth. Muslims say that this is what Allah says. It is stated in the Quran that 1 day in Paradise/Hell measures a 1000 years on Earth:

Quote:
[Quran 22.47] They challenge you to bring forth that torture [in Hell] and Allah will not break His promise; a day of your Lord [Paradise/Hell promise] is like a thousand years of what you count.
Here God promises those who do not believe in Hell and punishment that each day of their torture in Hell will measure a thousand years on Earth. So according to the Quran, time passes faster on Earth than in Paradise/Hell. But this agrees with the theory of general relativity which says that time passes slower near bigger mass. Paradise and Hell are much more massive than Earth and time should pass there much slower than on Earth.

Christians believe that God created the universe in 6 earthly days and rested on the 7th. Moslems believe that 6 days passed at God's Throne but we experienced 13.7 billion years on Earth:

Moslems believe that God is not bound to His Throne; rather He created it and set it as a reference. The Quran says that God's Throne is even wider than the whole universe; so how about the mass of God's Throne? God's Throne is much more massive than Earth. Time should pass there much slower than on Earth:

Our solar system is 4.5672 ± 0.0006 billion years old. Earth started accreting concurrently with the sun and our neighbouring planets 4.5672 billion years ago. However the universe is 13.7 ± 0.2 bln years old. This places the age of Earth at one third the age of the universe (4.5672 bln/13.7 bln = 1/3). Moslems say that this is what Allah says. The Quran says that in God's Throne time Earth is 2 days old while the Heavens, Earth and everything in between are 6 days old (2/6 = 1/3):

Quote:
[Quran 50.38]We [Allah] created the heavens and the Earth and all what's between them in six days, and We were not touched by fatigue.

[Quran 41.9]Say: "Is it that you deny Him [Allah] who created the Earth in two days? And you claim others to be equal to Him? He is the Lord of (all) the Worlds."
When God says that He created the Heavens, Earth and EVERYTHING IN BETWEEN in six days this means that He is referring to the period of existence. Earth has been in existence for 2 days (out of 6).

In God's Throne time, Earth is 2 days old while the Heavens, Earth and everything in between are 6 days old. This makes the age of Earth to be one third the age of the universe (2/6 = 1/3). Similarly in Earth time, the age of Earth is 4.5672 billion years while the age of the universe is 13.7 billion years; this is also one third (4.5672 bln/13.7 bln = 1/3). So it is the same ratio in Earth time or in God's Throne time [8]. The theory of general relativity explains why time at God's Throne passes slower than on Earth. General relativity explains why 6 days passed at God's Throne but we measured it as 13.7 billion years (that is each day at God's Throne measures around 2.28 billion years on Earth).

So according to the Quran: (The Christian Bible puts the creation of Earth on day one; making the age of Earth equal to the age of the universe)

God's Throne > Paradise/Hell > Earth
The smaller the mass, the faster the time
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Last edited by Nafi; May 19, 2010 at 05:17 AM..
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