Fourth Axis World

2012-10-08T03:21:00.000-07:00

In 1915, Albert Einstein first proposed his theory of special relativity. Essentially, this theory proposes the universe we live in includes 4 dimensions, the first three being what we know as space, and the fourth being space time, which is a dimension where time and space are inextricably linked. According to Einstein, two people observing the same event in the same way could perceive the singular event occurring at two different times, depending upon their distance from the event in question. These types of differences arise from the time it takes for light to travel through space. Since light does travel at a finite and ever-constant speed, an observer from a more distant point will perceive an event as occurring later in time; however, the event is "actually" occurring at the same instant in time. Thus, "time" is dependent on space.

Gravitational Time Dilation

An important aspect of Einstein's theory of relativity to note is that he proposed matter causes space to curve. If we pretend that "space" is a two-dimensional sheet, a planet place on this "sheet" would cause it to curve (see diagram below). This curvature of space results in what we perceive as gravity. Smaller objects are attracted to larger ones because they "roll" through the curved space towards the most massive objects, which cause the greatest degree of curvature. In relation to time, this curvature causes the gravitational time dilation effect. Under normal circumstances, this effect is impossible to observe. However, in the presence of the extremes of our universe (such as black holes, where a huge amount of matter is compressed into an extremely small volume), this effect becomes much more obvious. To a distant observer, an object falling into a black hole would appear to never reach it, due to time dilation causing time to "progress" extremely slower, at least relative to the distant observer (the object in question, however, would very rapidly be destroyed by the black hole).

A second aspect to the gravitational time dilation postulate is that the faster an object is moving, the slower time progresses for that object in relation to a stationary observer. While in everyday circumstances, this effect goes entirely unnoticed, it has proven to be true. An atomic clock placed on a jet airplane was shown to "tick" more slowly than an atomic clock at rest. However, even with the speeds achieved by a jet aircraft, the time dilation effect was minimal. A more solid example can be seen through an experiment performed on the International Space Station (ISS). After the first 6 months in space, the crew of the ISS aged .007 seconds less than the rest of us on earth (the relatively stationary observers). The station moves at approximately 18,000 miles per hour (see applet below to track the location and speed of the ISS), much faster than the range of normal human speeds. Even with such speeds, however, time dilation is minimal unless you approach speeds close to the speed of light (300,000 km/sec.).

Time as a Fourth Dimension

To understand time as a fourth dimension, it is necessary to recognize that any human attempt to "draw" or "represent" time beyond out immediate perception of it (baisc, linear progression), is inherently flawed, because out mental capacity is limited to three dimensions. However, time, like space, is a dimension in itself, and objects can transverse it in a similar way as they do through the third dimension. A popular way of viewing time is using a coordinate set of axes, except instead of using a plane with simple x and y axes, a z axes can be added. The graphic to the left represents a possible way of viewing time. As a person walks forward, he is traveling though the three dimensions of space, and a fourth as he progresses forward through time. Thus, for humans, time travel (or traveling through the fourth dimension) is entirely possible, however, only in one direction. Relativity has shown us that it is possible to change our perception of time based on distance, gravitational dilation, or speed, but the direction of time has remained constant and singular.

Consequences of Einstein's Scientific Revolution
The changes Einstein ushered in with his radical theories of relativity resulted in the now ubiquitous E = mc² equation, which essentially states that matter and energy are interchangeable (this discovery eventually led to the creation of the first nuclear fission bomb). However, Einstein's equations also predicted the presence of black holes and gravitational waves, and were initially excused as inconsequential aberrations, however there is now substantial evidence to support the existence of black holes. Just as importantly, Einstein ushered in an entirely new age of theoretical physics, helping to tremendously advance our perception of the universe and directly contributing to today's modern string theory, an attempt to unify the theories of relativity and since-discovered quantum mechanics into a unified explanation of the universe.

he fourth dimension is generally understood to refer to a hypothetical fourth spatial dimension, added on to our normal three dimensions. It should not be confused with the view of space-time, which adds a fourth dimension of time to the universe. The space in which a fourth dimension exists is referred to as 4-dimensional Euclidean space.Beginning in the early part of the 19th century, people began to consider the possibilities of a fourth dimension of space. Mobius, for example, understood that in a fourth dimension, a three dimension object could be taken and rotated on to its mirror image. The most common form of this, the four dimensional cube or tesseract, is generally used as a visual representation of a fourth dimension. Later in the century, Riemann set out the foundations for true four-dimensional geometry, which later mathematicians would build on. In our three dimensional world, we can look at all space as existing on three dimensions. All things can move along three different axes: altitude, latitude, and longitude. Altitude would cover the up and down movements, latitude the north and south or forward and backward movements, and longitude the east and west or left and right movements. Each pair of directions is at a right angle to each other, and therefore is referred to as mutually orthogonal.
In the fourth dimension, these same three axes continue to exist. Added to them, however, is another axis entirely. While the three common axes are generally referred to as the x, y, and z axes, the fourth dimension falls on the w axis. The directions that objects move along in the fourth dimension are generally called ana and kata. These terms were coined by Charles Hinton, a British mathematician and sci-fi author, who was particularly interested in the fourth dimension. He also coined the term tesseract to describe the four dimensional cube. Understanding the fourth dimension in practical terms can be rather difficult. After all, if someone is told to move five steps forward, six steps to the left, and two steps up, she would know how to move, and where she would end up in relation to where she began. If, on the other hand, a person was told to also move nine steps ana, or five steps kata, she would have no concrete way to understand that, or to visualize where it would place her. There is a good tool to understand how to visualize the fourth dimension, however, and that is by first looking at how the third dimension is drawn. After all, a piece of paper is a two-dimension object, roughly, and so cannot truly convey a three dimensional object, like a cube. Nonetheless, drawing a cube, and representing three-dimensional space in two dimensions, turns out to be surprisingly easy. What one does is to simply draw two sets of two-dimensional cubes, or squares, and then connect them with diagonal lines that link the vertices. To draw a tesseract, or hypercube, one can follow a similar procedure, drawing multiple cubes and connecting their vertices as well. What is Gravity? All of us know the effects of the mysterious force called gravity. However, the question 'what is gravity' is not easy to answer at all. The reason is that we don't really understand what this force actually is (if it is a force at all). The 'Giants' It would have been nice if we could have popped the question 'what is gravity' to the 'gravity-giants' like Kepler, Newton and Einstein. Maybe they could explain the characteristics and effects of this phenomenon properly and we could then (perhaps) answer the question. Kepler could not explain gravity, but amazingly, he worked out the details of how the orbits of the moon and planets can be described mathematically. This is known as the Kepler laws of planetary motion, as described later, but it does not answer the question 'what is gravity'. Newton, reportedly while observing an apple falling from a tree, got an inspiration that allowed him to work out how the force of gravity can be described mathematically. It later became apparent that there are some scenarios where Newton's mathematical description does not quite hold, but it still the simplest way of describing gravity. It does however also not answer the 'what is' question. Einstein later worked out how the force of gravity is not quite a force, but rather an artifact of the natural movement of objects through curved four-dimensional spacetime. Einstein reportedly got the inspiration for this imaginative leap in understanding of gravity by contemplating a man falling off a building. Such a falling man would not experience any force while he is falling, at least not before hitting the ground and suffering severe forces. Kepler's Gravity (1605) Johannes Kepler's noted his three laws of planetary motion in 1605, by studying the precise measurement of the orbits of the planets by Tycho Brahe. He found that these observations followed three relatively simple mathematical laws, i.e. 1. The orbit of every planet is an ellipse with the Sun at one of the two focus points. 2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The squares of the orbital periods of planets are directly proportional to the cubes of the major axis (the "length" of the ellipse) of the orbits. However, the physical explanation of this behaviour of the planets came almost a century later when Sir Isaac Newton was able to deduce Kepler's laws from his laws of motion and his law of universal gravity, using his prior invention of calculus. Newton's Gravity (1687) In his 'Principia' of 1687, Isaac Newton included his famous three laws of motion and the law of 'universal gravitation', which can be briefly stated as: 1. An object in motion will remain in motion unless acted upon by a net force. 2. Force equals mass multiplied by acceleration. 3. To every action there is an equal and opposite reaction. 4. The force of gravity is proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses. Double one of the two masses and the force of gravity will also double. Double the distance between the masses and the force of gravity will be four times weaker. Newton was uncomfortable with his own theory of gravity and in his words, never "assigned the cause of this power. He was unable to experimentally identify what produces the force of gravity and he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was not sound science. It is now known that Newton's universal gravitation does not fully describe the effects of gravity when the gravitational field is very strong, or when objects move at very high speed in the field. This is where Einstein's general theory of relativity rules. Einstein's Gravity (1916) In his monumental 1916 work 'The Foundation of the General Theory of Relativity', Albert Einstein unified his own Special relativity, Newton's law of universal gravitation, and the crucial insight that the effects of gravity can be described by the curvature of space and time, usually just called 'space-time' curvature. It is reasonably easy to accept that space can be curved � after all, we all know that a disk has a curved edge, but how can time be 'curved'? The secret lurks in the way that space and time is combined into space-time. Normally, a space-time diagram is drawn with a straight horizontal spatial axis and a straight vertical time axis. Just bend the two straight axes a little and we have curved space-time. The horizontal axis of the diagram represents space and the vertical axis time (actually time multiplied by the speed of light) - hence it is a spacetime diagram. The mass M disturbs the spacetime in such a way that it causes the spacetime path of a particle P to be curved towards the mass. At a particular radial distance r from the mass, the particle P follows a curved path that has a center at a distance R from the particle, defining a point called the center of spacetime curvature. Although it may look like it, this diagram does not represent a particle in orbit around the mass, or around the center of curvature. Because it is a spacetime diagram, it represents the flow of time PLUS the movement of particle P towards the mass M - i.e., the particle is starting to fall directly towards the mass. The radius of spacetime curvature is indicated on the diagram as R. As you will spot, the radius of curvature has something to do with the acceleration that the particle will suffer - the centripetal acceleration towards the center of curvature. If we plug in real values, like Earth's mass as M, the gravitational constant G and the radius of Earth as r (with c the speed of light, what else?), we find that the centripetal acceleration is just about the acceleration of 1g that keeps us firmly on the surface of Earth. The tiny difference is due to Earth's rotation, Earth's uneven density and the fact that Earth's is not a perfect sphere. The above holds well for weak gravity fields and low speed movement, i.e., the Newtonian limit of general relativity. In strong gravity fields, the curvature of spacetime and the effect of velocity must be catered for. They both have the effect of lengthening the radius of curvature of the path of the particle. The diagram below illustrates this shift in the position of the center of curvature in an exaggerated fashion. Essentially, the center of curvature drops below the x-axis, firstly due to curved space-time and then also due to velocity. The resultant radius of curvature is hence modified by a relativistic factor, which is rather difficult to express in simple terms. In essence, the original (quasi-Newtonian gravity) radius of curvature is shortened - first by a gravitational time dilation term end then by a velocity time dilation term. This causes the acceleration of a radially falling object, as experienced by the free falling object to be larger than what Newton predicted. Einstein came the closest of the three 'giants' in answering the question 'what is gravity?' Summary So, what is gravity? The truth is that at the most fundamental level, no one really knows. This page covered the basics of Newton's and Einstein's gravity in terms of the gravitational acceleration that is caused by curved spacetime and velocity. We may have to wait for 'quantum gravity' to be completed before we will know a better answer to the topical question: 'what is gravity?'.

Fourth Axis World

Fourth Axis World

What is Gravity?