The application of trigonometry to the relativity equations led the page author to some startling
conclusions:
While reviewing the equations on the Relativity effects on length, mass, time, and motion, the page author noticed that they
have trigonometric equivalents. Those then revealed more information, plus a visual model that doesn't use speeding trains.
EVERYTHING MOVES AT
THE SPEED OF LIGHT
In the equations for length, mass, time, and motion at relativistic speeds, there are equal signs, not less-or-equal
signs. When all of these equations are applied simultaneously, they show that everything moves at the speed of light in one
way or another.
So how do we see objects moving at speeds slower than light? They are moving relative to each other at speeds slower than
light. Their lightspeed motion vectors produce a resultant relative speed slower than the speed of light.
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TIME IS THE MOTION
AT THE SPEED OF LIGHT
We do not notice the motion at the speed of light as a motion through space. We notice this motion as the flow of time
instead. The direction of the lightspeed motion (called the lightspeed motion vector) becomes the time dimension for the
observer within that frame of reference.
Motion though the dimension the observer is moving through at lightspeed is normally measured in intervals of time, rather
than in distances through space. But this distance can be calculated for the case of the motion of empty space through time.
Multiply the speed of light by the elapsed time to get the distance though the time dimension that this space traveled.
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THE TIME DIMENSION IS
LORENTZ-CONTRACTED TO 0
Because the space the observer is in is moving at the speed of light in the direction of the time dimension, the time
dimension is Lorentz-contracted to zero length, as seen by the observer. Thus, we do not see it as a physical dimension.
But note that the time dimension is in a different direction for observers moving in different directions through
spacetime. We see part of the other observer's time dimension, and the other observer sees part of our time dimension. The
various Relativity effects are caused by the different lightspeed vector angles of the observers, and the correspondingly
different directions of each observer's time dimension.
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INTERNAL MOTIONS
SLOW MATTER DOWN
Because matter has rotating and vibrating components that are part of the characteristics of matter, nothing made of
matter can achieve the speed of light in the linear direction of the motion through time. The lightspeed vectors are
curved into helixes and sinewaves by the rotations and vibrations fo the particle components of the matter.
This means that matter slows down a little in the linear direction of the lightspeed vector of the space around it. It
moves slower than empty space would otherwise move along its time axis. Although the individual infinitesimal parts of a
particle are all moving at exactly the speed of light through spacetime, the collective object made of this moving matter
is moving slower in a linear direction. The rest of the motion at the speed of light is used up in the rotation and
vibration of the parts that make up the object.
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SLOWER MOVING MATTER
BENDS SPACE BACKWARD
Because the collective matter in a real object is moving forward in the time dimension time at a slower speed than
lightspeed, the matter bends space backward in the time dimension. Space then acts like a giant rubber sheet, stretching
to pull the slower matter along behind it. This curves the space around the matter, slowing down and bending the light
passing through that space.
The limit on the speeds of all of the parts of matter could also explain quantum mechanics, as well as radioactivity and
particle decay probabilities. Something might be forced to choose between moving at a speed other than lightspeed, and
falling apart while maintaining lightspeed for all of the resulting parts. Lightspeed always wins.
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THE BACKWARD BENDING OF
SPACE CAUSES GRAVITY
The rubber sheet theory of gravity is real! As the space bends backward in time around a massive object, the space is
sloped on each side of that object. The presence of other objects also pulling backward on the motion of space through
time causes the space around one object to be sloped toward the other object. Thus, the tow object will tend to move
toward each other. This bending of space causes gravity.
The bending of space to cause gravity also shows why antigravity is impossible. To bend counteract the bending of
space backward in the time dimension, an object would either have to have its individual particle components traveling
faster than light, or it would have to stop all of the rotating and vibrating motions of its particle components. In
either case, it would stop being matter.
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THE UNIVERSE IS AN
EXPANDING 4-D SPHERE
The Big Bang should really be referred to as the Big Flash, because it should be totally energy in the beginning. At
the time of the Big Flash, the universe was very small. Space became the expanding surface of a 4-dimensional sphere
surrounding the original point of the Big Flash.
All points in today's space are nearly equidistant from the original point of the Big Flash. They surround it within
the surface of the 4-D sphere. Space directions are directions around the surface of the 4-D sphere, while the
lightspeed motion through time is usually oriented in a direction away from the center of expansion, moving along a
radius going back to the center of this 4-D sphere. Light follows an equiangular spiral from its source to the point of
observation, following the curve of expanding space.
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THE UNIVERSE EXPANDS
AT THE SPEED OF LIGHT
The space in the universe is moving outward along any radius at the speed of light. Thus, the circumference is
expanding along any great circle at 2 times pi times the speed of light. This means that we can't see any part of the
universe that is moving away from us relatively at a speed greater than lightspeed.
Note that the relative speed of two objects can be any speed. But the relative speeds of objects in the same part
of space cannot exceed lightspeed. Only the expansion of space itself can make objects move away from each other at
speeds greater than lightspeed. Those objects must be farther apart than the radius of the 4_D sphere.
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THERE IS NO
INFLATIONARY PERIOD
This model of the universe needs no inflationary period to make the area of the emission of the 3-kelvin
background radiation be large. As the universe expanded, the light followed the curvature of the expanding 4-D
sphere of space. As the curvature changed the angle of the light, it also redshifted it.
Thus, the part of the universe that emitted this background radiation was very small when the radiation was
originally emitted. The radiation followed the curvature of space as the space expanded.
This also explains the extreme uniformity of the background radiation as it is seen in all directions. The
radiating area WAS very small at the time the radiation was released. So there is no mystery about why the
background radiation is so uniform.
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THE INCREASING EXPANSION
IS A RELATIVITY EFFECT
Because the universe is an expanding 4-D sphere, the various observed expansion speeds are actually cosine
observation effects. The speeds of distant objects are being observed at angles, because they are partway around the
curvature of space on the 4-D sphere.
The objects are actually moving close to the speed of light, but we see a speed resulting from the angle between
the object's lightspeed velocity vector and the observer's lightspeed velocity vector. The farther away the object
is, the larger the angle between the vectors. The distance to the object seems greater too, because the light
followed the curve of the shell of space to get here.
Thus, space is not really expanding at an increasing rate. Instead, the observation that it expanded slower
at an earlier time is another effect of relativity.
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THE 4-D SPHERE EXPLAINS
DARK MATTER AND ENERGY
The universe has more matter in it than we can see. The dark matter is in the portion of the universe that is
moving away faster than lightspeed. It is on the other side fo the 4-D sphere. But since most of that matter is also
located in a direct line that is in a direction backward in time, through the center of expansion and out the other
side, it might have detectable effects.
Dark energy is likewise found in the invisible parts of the universe on the other side of the 4-D sphere. But it
is not needed to explain the speed of the expansion of the universe. There is no need of another explanation for the
expansion of the universe if everything moves at lightspeed. On the contrary, an explanation would be needed if the
universe were not expanding.
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GRAVITY CAN'T SLOW
THE UNIVERSE EXPANSION
Because the expansion of the universe causes gravity, gravity will never brake the expansion. But the expansion
of the universe does not expand the space inside matter. We will always be able to see the same objects in space,
because space is always expanding at the same speed. They will just appear to be farther apart.
The speed of the expansion of the universe depends on only the speed of light. Nothing else, including the
amount of matter in the universe has anything to do with the speed of expansion. The speed of light forces the
speed of expansion to be a specific value.
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ACCELERATION CHANGES THE VECTOR
ANGLE, NOT THE SPEED
As power is applied to an object to change its velocity, its actual speed does not change. This speed, in the
direction of the lightspeed motion vector for the object (the direction of the flow of time), is fixed by the mass
effects of that object. What does change is the direction of the object's direction of motion through
spacetime.
As a car speeds up on the freeway, it changes its lightspeed motion vector angle, so it is at a slight angle to
the lightspeed motion vector angle of the road. Thus, the car appears to be moving at a speed less than the speed
of light, relative to the road. That's why you can be arrested for exceeding 65 mph, even though the road, the car,
and the police car are all moving at speeds near lightspeed.
In the book notes below, I call the lightspeed motion vector of an object the object's
c-vector. This is explained early in the book, and makes the diagrams much easier to create.
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A ROCKET AND A BULLET HAVE
DIFFERENT RELATIVITY EFFECTS
Because the power source is in a different frame of reference, a bullet will take more energy than a rocket will
to reach the same speed. All of the energy needed to accelerate a bullet to a very high velocity must come from the
power source in the other frame of reference. This is the effect where an atom smasher has to exert more and more
force to make the particle move faster as the speed increases. The particle sees a weaker and weaker force being
applied to it as it speeds up, because the force is exerted at an angle to the velocity vector.
The rocket should not have this trouble, because its frame of reference is changing as it applies the force to
speed up. The rocket is carrying its power source. The person on board the rocket will also not see it taking more
power to go faster. But the person in the frame of reference the rocket left behind will see an increase in power
and mass, and a decrease in acceleration, due to the relativity effects.
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A WORMHOLE IS NOT
MUCH OF A SHORTCUT
Some physicists have postulated that a wormhole could be used to travel quickly from one part of the universe
to another. But with the speed of expansion and the size of the universe shown by this theory, it would take
longer to get there through the wormhole than it would take following normal space.
Black holes use up their entire lightspeed motion vectors rotating the matter components inside them, so they do not
move forward in normal time.
Possibilities of time travel do appear in this model, but enormous amounts of energy would be needed to
accomplish it. We know forward travel is possible. But we do not know what would happen if someone somehow aimed
a lightspeed motion vector in the opposite direction to the normal flow of time.
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