I. Math Means Something: The Lorentz-Fitzgerald Contraction Equation If we wanted to figure out the difference in area between two squares, we follow a logical thought process in order to arrive at the conclusion. With the measurement of one side of each square, and we know that we are dealing with a two dimensional object, so when we square each measurement we know the area of each square, we have a description of the square with that equation. Because we are trying to find the difference between the two areas we know the subtract. While an easy example, it addresses an issue that seems to have been forgotten; math means something. Each part, every function, of the equations means and represents something. We can use words to describe equations and we can use equations to describe words. We use the equations in geometry to describe shapes. Two dimensional objects have squares to describe their area, three dimensional objects have cubes to describe their volume. In Relativity Simply Explained by Martin Gardner, I learned the Lorentz-Fitzgerald equation is used to describe the relative changes observed between two objects in uniform relative motion. This equation is: t = sqrt ( 1 - v ^ 2 / c ^ 2 ) Nowhere have I found a good narrative for this equation, everyone seems to be focused on telling you what the results are, Time Dilation, Length Decrease, Mass Increase. The results, however interesting, are not a NARRATIVE of the equation! We will deconstruct this equation and give it meaning! v is the relative velocity of an object, c the speed of light - the maximum amount of spacetime an object can occupy. The squares represent the addition of a dimension, just as in Geometry. The objects we are measuring are only traveling in one dimension of space, the other dimension they are traveling in is time. What we are calculating with the division is a measure of how much spacetime the object is occupying (with movement only). 1 is meant as 1.0 or 100%. The information we are calculating is changing from the percentage of spacetime it is occupying, to the percentage left unoccupied. The square root REMOVES the Time dimension, but not without leaving that dimension dilated. This narrative holds out no matter how you solve the equation; for 1, c, v or t. We can only further our knowledge by solving for these variables to see how our universe handles their calculation. The results of the equation tell a tale of their own, especially when combined with the above knowledge. Time dilation, Length contraction, and increased mass, they are one and all the same. To imagine the structure of spacetime we must imagine a wire-frame structure in empty space, each cube of the wireframe measures one cubic meter. In one of the cubes, place a grain of sand so that it floats in the center of the cube. Now, imagine that grain of sand becoming more and more massive but only occupying the Time dimension, never growing in size in space. As you approach the limit of density, the rate of time around the sand would begin to slow. This slowing of time would cause the wire-frame around the grain of sand to begin to shrink in size, more at the center and less around the edges, this shrinking is a result of the time inside the box slowing, a meter stick would still measure a meter inside the box, four dimensionally, the box is still one cubic meter. Length contraction is a result of nothing more than the dilation of time. Length, space itself is the result of the 4th dimension, time, having a value greater than zero. If time is not passing, there is no relative length. Length is a result of time. In fact, the three dimensions of space cannot exist without the time dimension. This is why objects moving the speed of light are regarded as having zero length and why black holes are regarded as a point. While each of objects would themselves still be able to measure a certain length. The speed of light acts as a universal yard stick - a way of giving our units of measurement meaning. Otherwise, how else does the universe know what ridiculous form of measurement we use (like the distance between some mans out stretched thumb and nose). II. Time Time is a rate. Time is not a list of time-stamped numbers going backwards. Time is not a slider bar on a youtube video or a rewind button on a VCR. The idea that all time is connected going forwards and back is solely of human creation. The only time it ever is, is now, and there is only the rate at which now is passing by. When we measure time, we are measuring how many instants of now have passed. Everything; mass, length, gravity, inertia, energy, and matter are all TIME or the result of TIME. The interactions that occur between all of these things require no other mechanisms or mode of propagation other than the existence of the system of four dimensional spacetime itself. E=mc^2 is evidence of this. III. Equivalence Expanded The squares that add the time dimension in the Lorentz-Fitzgerald equation tell us that as an object occupies space, it also occupies and equal amount of the time dimension. Velocity occupies space per unit of time, thus we should logically conclude there must be an equivalent opposite - density, which occupies time per unit of space. Mass and distance, it can be concluded, are related - an object traveling the speed of light can travel whatever amount of distance it wants, a body of matter (will eventually collapse into a black hole, but nonetheless) can increase to be whatever amount of mass. Density and velocity are the measurements which are restricted to the definite, finite, limitations of spacetime. Gravity and Inertia are the same in that the rate of time differs and acceleration occurs. Meaning that, in measuring velocity there is an associated amount of time dilation corresponding to every velocity, no matter what the rate of acceleration. In gravity and inertia, the cause of the acceleration is the equal opposite. In inertia, there is an outside force causing acceleration that causes the object that is accelerating to have time dilation. Inertia has time dilation due to acceleration. In gravity, the curvature of spacetime, the dilation of time over a distance is the cause of the acceleration. Gravity has acceleration due to time dilation. Gravity and Inertia both have inner and outer effects, that is, there is one effect that changes the rate of time inside the body and there is another that affects the rate of time around it; the former we call mass, the latter we call gravity. This is why, when an object increases in velocity it also increases mass which causes it to increase gravity. As the Lorentz-Fitzgerald equation is to inertia, there should be an equivalent for gravity described t = sqrt ( 1 - d ^ 2 / D ^ 2) where d is density and D is the maximum density. To my knowledge Einstein never made such implications, an error I relate to continue using Newton who could have never possibly predicted the 4 dimensional structure of spacetime put forth by Minkowski. IV. Rotating Disks In finding the acceleration of an object on a rotating disk, we find the velocity of the outer edge (its rate of time), and divide by the radius of the circle. This tells us the rate of change in time dilation for that distance. Whether this is gravitational or inertial is completely irrelevant, they are one and the same. The rate of time dilation is always linked to the rate of acceleration, the overall time dilation is always linked to the velocity. V. The Very, Very Small We have discussed what happens when spacetime is heavily occupied what, then, happens when a single unit of space is occupied with only a miniscule amount of matter (time)? If we think of the duration of the instant that is now and imagine only a small portion of that is occupied, then what happens during the time which it does not occupy? Why would observation change the results of an experiment? By equating the occupation of time and the occupation of space we can come to the conclusion that observation causes the objects location to be calculated by its occupation of space, when unobserved it causes its location to be calculated using its location in time. Thus, the smaller the mass the less the certainty of its location. VI. Einsteins Relativity Special Relativity remains untouched by the ideas above, it remains accurate and relevant in the physics today. When Einstein gave the example of the man in a chest accelerating upwards, Einstein claimed that the man could not tell if he was in a gravitational or inertial field, this is not true. If the manhad to extremely accurate clocks, such as atomic clocks, he could measure the rate of time at both his head and feet. in a gravitational field the time at his feet would pass more slowly then the time at his head. The force of acceleration is applied to the chest, as well as the man inside as if it is all one rigid body. this is not the case in a gravitational field, where the force is applied unequally across the entire body. Even if we are to accept all of Einsteins premises, the issue of units of measurement comes into play. Our units of mass hold no meaning to the universe. F=ma gives arbitrary results. The link between distance and mass pointed out above restricts us from using Newtons equation because we have not expressed equivalence, or any kind of limitation on spacetime in regards to density. -Bradley Oliver Boesel
Posted on: Wed, 08 Oct 2014 04:48:07 +0000
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