Relativistic Mass And Trigonometry*

This posting has been added to section 5) of "The Theory Of Stationary Space".

Just have a look at this. Here is something that I cannot see has ever been pointed out about Relativity. There is a simple connection between Relativity and ordinary trigonometry that again verifies everything that my theory, "The Theory Of Stationary Space" in the posting on this blog by that name, has claimed.

Einstein's Special Theory of Relativity stipulates that the mass of an object increases as it approaches the speed of light. This increase is known as "relativistic mass". When the object reaches the speed of light, it's mass would be infinite. To accelerate the object to a higher speed would require an infinite amount of energy which is, of course, impossible. That is why the speed of light is the highest possible speed that anything can travel.

The increase in relativistic mass with velocity proceeds slowly. At half the speed of light the relativistic mass would still be only 1.155 of the mass at rest, an increase of only fifteen and a half percent.

According to my cosmology theory, detailed in the compound posting on this blog, "The Theory Of Stationary Space", we actually inhabit four-dimensional space. Particles of matter, such as electrons, are really one-dimensional strings in this four-dimensional space. We perceive them as particles, rather than strings, because the direction in which the strings are primarily aligned is what we perceive as time. We can move at will in only the other three spatial dimensions.

Our consciousnesses are moving along the bundles of strings that comprise our bodies and brains at what we perceive as the speed of light, which is why we see that as the maximum possible speed. What we perceive as speed or velocity is actually the angle between the alignment of different bundles of strings, which we perceive as objects. If another bundle of strings is perfectly parallel to the bundle that comprises our bodies and brains, we will perceive it as an object at rest.

The reason for relativistic mass increase is that, when a line which is the bundle of strings of an object is at an angle to us, there is more of it interfacing our bundle of strings along the dimension in which our strings are aligned. This is simply because the diagonal (or hypotenuse) of a right triangle has to be longer than the X-axis or line of it's base. When a bundle of strings is bent at a right angle to our bundle, we pass all of it's remaining length in a moment so we perceive it as moving at the speed of light and having infinite mass.

The strings and bundles of strings comprising the universe are actually at rest, hence the name of the theory "The Theory Of Stationary Space". Electromagnetic radiation is really stationary ripples in the space that is composed of alternating negative and positive electric charges. The only "new" motion is that produced by us and other living things.

What we always have to remember, that is the essence of my theory, is that we see the universe as we do not only because of what it is but also because of what we are.

Everything is ultimately composed of infinitesimal electric charges. Space is composed of a perfectly alternating checkerboard pattern of negative and positive electric charges. Waves are perceived as electromagnetic because they disturb this perfect balance of underlying electric charges. Matter is defined as any concentration of like charges and, since like charges repel, matter must be held together against like-charge electric repulsion by energy. This is why any mass is equivalent to a given amount of energy, which we refer to as the well-known Mass-Energy Equivalence.

Apparently, the only way to release the energy in mass is to react equal amounts of matter and antimatter together. Antimatter is simply matter with the electric charges reversed so that negatively-charged electrons in orbitals are replaced with positively-charged positrons. Upon being brought into contact, the energy in the Mass-Energy Equivalence that was holding like charges together in both the matter and the antimatter is released, as a fantastic burst of energy, and the electric charges in both rearrange back into the alternating negative and positive charges of empty space.

But yet we experience the universe as having only three spatial dimensions, as well as one-dimensional time. I am trying to convince everyone that we are really in four-dimensional space, time is a dimension of space because the strings comprising our bodies and brains are aligned in it, and that is why see matter as composed of particles rather than strings. In no way does this mean that there are only four dimensions of space, there could well be an infinite number, but the matter from the Big Bang of which we and our familiar universe are composed was scattered over only our four dimensions.

All right now here is what is so interesting that I cannot see has ever been noticed.

The relativistic mass at half the speed of light is 1.155. The reciprocal of this is .866. If you have studied mathematics, does this number sound familiar? If it does, it is because it is the trigonometric cosine of a 30 degree angle, or the sine of a 60 degree angle because the sine and cosine are inverse functions. A 30 degree angle is an important angle because it is 1 / 3 of a right angle, a 90 degree angle, and .866 is it's cosine. In trigonometry, the reciprocal of the cosine is called the secant so that 1.155 is the secant of a 30 degree angle.

Just a quick review of trigonometry. The functions are simply ratios of the sides of a right triangle, which is a triangle with one right angle which is 90 degrees. The other two angles have to add up to 90 degrees, because the three angles of a triangle always add up to 180 degrees.

https://en.wikipedia.org/wiki/Trigonometric_functions#/media/File:Trigonometry_triangle.svg

Sometimes the horizontal side is referred to as the X-axis and the vertical side as the Y-axis, with the hypotenuse as the diagonal side. The trigonometric functions refer to the lengths of sides in the triangle with various angles. The hypotenuse, or diagonal, always has to be longer than either the X or Y axis. The diagonal is sometimes referred to as R, for radius. The three primary trigonometric functions are as follows:

Sine (sin) = Y / R
Cosine (cos) = X / R
Tangent (tan) = Y / X

Since the diagonal, R, must always be longer than either the X or Y axis, the values of the sine and cosine must always be less than 1. Since the two angles other than the right angle in the right triangle must always add to 90 degrees, that means that the sine of one angle must be equal to the cosine of the other.

There are three other, lesser-used, trigonometric functions that we get simply by taking the reciprocals of the above functions. Three of the six total functions have the prefix co-. This means that the value gets smaller as the angle gets larger. Unlike the sine and cosine, the values of the cosecant and secant must always be greater than 1.

Cosecant (csc) reciprocal of sine = R / Y
Secant (sec) reciprocal of cosine = R / X
Cotangent (cot) reciprocal of tangent = X / Y

In my cosmology theory, the X-axis (horizontal) can represent the dimension in which our strings are primarily aligned. We perceive this dimension as time, and the other three as space, because our consciousnesses are moving along the strings of the time dimension, at what we perceive as the speed of light, and we cannot move at will in this direction.

Velocity is actually an angle relative to the alignment of our bundle of strings. The greater the angle, the greater the apparent velocity. 90 degrees represents the speed of light because that is the greatest possible angle and the speed of light is the greatest possible speed that an object can move at. This means that what we perceive as an object moving at the speed of light would actually be a bundle of strings bent at a 90 degree angle.

So the fact that the relativistic mass increase at half the speed of light is exactly equal to the trigonometric functions for a 30 degree angle, 1 / 3 of a right angle, shows a definite link between Relativity and ordinary trigonometry.

But then a question arises. In my cosmology theory, an object at rest is represented by a zero angle and an object moving at the speed of light is represented by a 90 degree angle. This means that an object moving at half the speed of light is actually a 45 degree angle, which is half of 90 degrees. So then why is the relativistic mass of an object moving at half the speed of light equal to the secant or cosine of a 30 degree angle, rather than a 45 degree angle?

The answer actually confirms what we saw in section 5) of "The Theory Of Stationary Space". When I wrote all of that, I had not noticed this simple trigonometric connection that verifies it.

We saw in section 5) that, if an amount of energy equivalent to the energy of the mass-energy equivalence in an object were applied to accelerate the object, it would accelerate it to 2 / 3 the speed of light. There is a reason that it would only accelerate to 2 / 3 the speed of light, and not all the way to the speed of light. The reason involves the electric charges of which everything is composed.

I won't go into detail here because it is explained in section 5) of "The Theory Of Stationary Space" but we saw how space is composed of a perfectly alternating checkerboard of negative and positive electric charges but matter is a concentration of like charges, held together by energy, and this energy is what we refer to as the Mass-Energy Equivalence.

The explanation that my theory has for gravity is that if the two electric charges, negative and positive, are equal then the two basic rules of electric charges, that opposite charges attract and like charges repel, must also be equal. The energy of the Mass-Energy Equivalence enables matter to form by overcoming the repulsion between like charges so that matter is defined as a concentration of like charges. But that means that there must be a net attractive force associated with matter, and that is what we refer to as gravity.

An interface between two like electric charges has three times as much energy as an interface between two opposite charges. But only 2 / 5 of all the interfaces between electric charges in matter are between like charges, either negative to negative or positive to positive. The other 3 / 5 are between opposite, positive to negative, charges. There is energy between opposite charges but obviously it requires more energy to hold like charges together because they mutually repel, according to the basic electrical rules that opposite charges attract while like charges repel.

But this still means that there is exactly twice as much energy within matter in interfaces between like charges as there is in interfaces between opposite charges. This then means that 2 / 3 of all the energy within matter is in the interfaces between like charges, holding them together against electrical repulsion. In a matter-antimatter reaction, this energy would be released.

Notice that number, 2 / 3.

In the cosmology theory, since a 90 degree angle represents velocity at the speed of light a 45 degree angle would be half the speed of light. But yet the relativistic mass increase of an object moving at half the speed of light is identical to the trigonometric secant-cosine of a 30 degree angle.

But 30 degrees is 2 / 3 of 45 degrees.

What happens, and the reason for this difference, is simple. The relativistic mass increase, of an object made of matter, applies only to the mass-energy of the interfaces between like electric charges, and not to those between opposite electric charges. My cosmology theory defines matter as a concentration of like charges, held together by energy, so that the interfaces between opposite charges, even though within the matter, do not count.

The reason that the interfaces between opposite charges within the matter do not count is that space is defined as a perfect checkerboard pattern of opposite charges in multiple dimensions. If the object made of matter was not there then it would just be empty space, and so the interfaces between opposite charges which are the same as those in empty space do not factor in to relativistic mass.

The increase in relativistic mass from 0 degrees, at rest, to 90 degrees, the speed of light, is not linear. It starts slowly and then increases rapidly as the velocity gets near the speed of light. So it is as half the speed of light where this 2 / 3 relationship between the energy in like-charge interfaces compared to those in opposite-charge interfaces shows up.

Half the speed of light is really a bundle of strings bent at a 45 degree angle but the relativistic mass increase, which is actually the increase in the length of the diagonal, R, relative to the X-axis, is actually equal to the trigonometric functions, secant-cosine, of a 30 degree angle, which is 2 / 3 of the 45 degree angle.

Why else would the numbers for relativistic mass increase and trigonometric functions of a primary angle match perfectly? The relativistic mass of an object moving at one-half the speed of light, which in my theory is really one-half of a right angle, is identical to the trigonometric functions (secant and cosine) of a 30 degree angle, which is one-third of a right angle.

The workings of the 30 degree angle being one-third of a right angle and two-thirds of the 45 degree angle which is half the speed of light can be seen as reflected in the operation of quarks, which combine to form protons and neutrons. An up quark has a charge of +2 / 3 and a down quark of -1 / 3. Two up quarks and one down quark give a net charge of +1 to form a proton. Two down quarks and one up quark give a net charge of zero to form a neutron.

At this most basic level of physical reality we are dealing with things defined by low integral numbers. The length of a line at a 45 degree angle, the hypotenuse or diagonal in a right triangle, is the square root of 2, which is 1.414, times the horizontal line or X-axis. The length of a line at 30 degrees is 2 / the square root of 3. And this 45 and 30 degrees is where the relativistic mass and the trigonometric functions intersect. Just the fact that the square root is so involved shows that velocity must really involve another dimension, and that is the fourth spatial dimension of my cosmology theory that we perceive as time.

It has baffled the world for over a hundred years how these bizarre effects of Relativity can occur which are impossible to explain by the rules of ordinary physics. The way my "Theory Of Stationary Space" explains it is that relativistic effects, such as the mass increase that we have dealt with here, require a fourth dimension of space and matter to be seen as strings aligned primarily in that dimension. Ordinary physics is "three-dimensional physics" that work fine for most things but cannot explain realms such as Relativity and Quantum Physics.