Difference between revisions of "General and Special Relativity"
Latest revision as of 04:11, 9 July 2008
General and Special Relativity
General Relativity was created by Einstein. This deals with the cosmos at large, and explains how matter and energy are equivalent, and how that everything that matters, is contained within space and time. It suggests that matter and energy are fluctuations of the spacetime fabric: Quite literally nothing but ‘’creased’’ spacetime. These creases cause spacetime warps, found around all matter and all energy, and causes the spacetime to become stretched. The affects of such curvature, can be found stronger nearer quark stars, or even black holes. It also predicts singularities. Matter tends to curl into itself, causing an inward state of mass. This is the strong force at work. If we didn’t have the strong force, all matter would act as though it was a single ripe particle with its energy dissipating over a period of time.
Special Relativity was also created by Einstein, but this work didn’t take as long as the general theory. It explains two observers moving relative to each other. It shows that there is no absolute clock in the sky, so nothing could be fixed. This was the law of time dilation. Two observers could experience distortions in the imaginary time dimension, in this case, two twins. One observer could travel away off into space, at near lightspeed, and return, to find that his twin has aged tens of years, whilst he has hardly aged at all.
Quantum Mechanics is a troublesome theory. Albert Einstein expressed his feelings quite clearly about Quantum Physics. At least the theory of relativity is consistent, with its predictions of matter, space and time. In Einstien’s general and special theories of Relativity, there is an unbounded relationship between space and time and matter. It is out of here, a special relationship between mind and matter arises also. We conclude that space is time. They are two sides of the same thing. You cannot move through space without moving through time, unless you exist as a zero-time particle, which is just another weird situation in relativity.
This description of matter, makes way for the world of consciousness. The function of all awareness, those boxed neural networks interpret time and space, including matter in its own enclosed dimensions of perception. In fact, if all that we deal with in the external world are all connected to each other like the chain of 'space-matter-time-energy' must also be the same in the internal world of feelings and of self-being, meaning that mind is apart of that great unbounded chain. What we visualize is some type of imaginary reality... Imaginary in the sense that what exists as matter, with shape, color or even texture, it is all retinal pictures cast into the three-dimensional phenomenon of mental imaging.
Let us have a little look at the mind and its conceptual relationship with time. The time i feel is 'real time' - no other time can exist but present time. Using this description, we can say that everything of the outside world is not real reality, since the perception of time (and that must mean space and matter) are all nothing but a product of my consciousness - a product of my deranged imagination. If we throw the mind out of the picture here, time in the outside world all happens in one fraction - without consciousness, time happens in one swift go, and exists as a single frame. When consciousness exists, time is cut down to simple frames, running in its forward directionality with two boundaries of past and future. This time i feel and sense is real when it comes to my personal description of it. In other words, its very real to me... but it is completely false, if i try and think that the space-time-matter that i observe and sense is the real world - again, it is a retinal image, cast into three-dimensions, powered by the neural networks of the brain... it is completely false... but here comes another point of view. One can say it is the only one and true reality that exists. After all, it is the only reality we come to know - using this idea, if no life existed in the universe, the universe would not exist, because there would be no one there to say it did.
Einstein (March 14th 1879 - April 18th 1955) born in Germany, published his theories in 1905, and published his general papers in 1915 - they revolutionized our ways of thinking about the universe. He received his Nobel Prize in 1921 for his work on the 'Annus Mirabilis,' which describes 'photoelectric effects' including his contributions to theoretical physics - in fact, some scientists believe he should have received more Nobel prizes for his work on 'the Brownian Movement' and special relativity - since the Brownian Movement itself showed the existences of atoms - something that was not widely excepted before Einstein.
Relativity is a complex theory in certain area's... and according to a recent survey, it is universally misunderstood. However, to help us understand what Einstein was going on about, we can use his relativistic puzzles to help us build a clearer picture. We will have a look at a few of them soon - but first, let's see why Einstien's mind was on curves... Einstein was concerned about a flat spacetime. Gravity was difficult to explain in a flat Euclidean universe. This was why he decided to bring a new vision into our universe. He figured that if you are in an elevator that is accelerating upwards, you can imagine that the elevator would push up against you. This is a product of the force of the mass moving upward, against the gravitational force of earth pulling you back down. Using this description, Einstein made a new notion of gravity. When the elevator moved upward, whilst the platform would be pushing up against you, turned out to be like the force pulling you back down to planet earth called gravity.
He figured that an object accelerating was the same as a curvature. In fact, he found that gravity was also the product of acceleration, so a little thought indicates that gravity, that weakest force is directly equivalent to curvature. Thus a universe full of curvature was a universe full of gravity. The curvature of spacetime was proven in 1919, when rays of light where seen to be bending around the sun during an eclipse. This did indeed confirm a universe where light was even bent in the curves of space and time, and the final verification was reported in 'the Times' - with the headline, 'Revolution in Science - New Theory of the Universe - Newtonian idea's overthrown'. This was the secret of Einstien’s curvy universe.
From relativity we learn many secrets, including the 'Twin Paradox.' In this theory, a twin that travels away from earth a fraction shy of c (lightspeed), time becomes highly stretched. Let's say he travels a distance of 1,500 lightyears at a speed of 185,888 mps, and when he finally returns, he will find his twin brother on earth has aged remarkably... in fact, his twin brother will probably be six foot under, while he himself might have only aged a couple of years! This is the paradox of space and time when you move through it at a very fast speed. The twin who traveled the 1,500 lightyears moved so fast that his time slowed down. Let us look at some particles here, to describe some velocities, and how the speed of something marks a territory between real time (imaginary space), zero-time and real space (imaginary time). A Bradyon, also known as a tardyon, (v<c) moves always with a velocity under c. The speed of light, it turns out, is a kind of border - this barrier is able to limit all Bradyons with a speed always under 186,000 miles per second. For a mass to exceed the velocity of c, means that it needs to increase in mass (we are Bradyons, thus we cannot travel faster-than-light). Thus if a particle exceeded the speed of light, it would need to double in mass - it would also require an infinite amount of energy! This is what relativity explains. A particle that moves like a Bradyon moves in 'real time' - which is the same as 'imaginary space.' We move so fast through time, and we hardly ever move through space. Time moves through us at the speed of light. We move through time at 186,000 miles per second - this means you are 186,000 miles away from where you where just sitting or standing in each passing second. The root word Brady literally means 'slow' - hence the fictional family, 'the [Brady] bunch', hinting at a family with slow-working intelligence. A particle with a velocity equaling c is a bit of a surprise. This particle is ageless. This is, what is called a zero-time particle. A zero-time particle also means zero-space, as it neither moves in 'real space' (which is imaginary time) or 'real time' (which is imaginary space). A photon is a zero-time particle, and ever since it left its source, it existed as if no time was ever spent. In this sense, a photon is never really born, and never really dies! There is a hypothetical substance called, tachyonic matter. This matter travels in imaginary time. It spends no time in real time, as it will oscillate back and forth throughout the time dimension. This tachyonic matter moves faster than the speed of light. Such a substance is permitted by relativity because it started with a velocity over c. It is also made of a strange substance called 'imaginary matter'. The word 'tachy' comes from 'tachycardia,' which is fast heart rate. To make your way through all these imaginary concepts, just remember this following rule; A Bradyon, like most matter in the universe moves below the speed of light, which means it will travel in real time, which is the same as imaginary space. A particle that moves at the speed of light means it experiences no time at all, nor any space. And a particle that moves with a velocity over the speed of light moves in real space, which is in relativity, imaginary time.
Einstein also shows examples of one observer in respect of another. In this next example, that you may know, is that suppose a train was moving 5 miles per hour, and aboard the train where Jack and James, and they wanted to play a game of catch with a ball. Imagine Jack stood at one end of the cart and James stood at the other end. Now, Jack throws the ball to James at six miles per hour, and James throws it back, at the same speed. Aboard the train nothing looks wrong. The ball is thrown back and forth at the same speed. For those stationed on the platform watching the game, it is a little different. When Jack throws the ball to James, the ball is observed to move faster with a speed of eleven miles per hour. When James throws the ball it moves considerably slower, only one mile per hour. Why does the ball move at different speeds? - Well, one needs to take into consideration the velocity of the train, including the direction the ball is thrown. If Jack throws the ball, the speed of the ball works with the train, so the speed of the train must be added with the speed of the ball. If James throws it, the speed of the train must be deducted from the speed of the ball, because the throw is going against the momentum of the train. If the ball was a photon (fastest particle of light), things change. The photon will be seen to be traveling at the same speed according to the observers on the platform and the observers aboard the train, no matter how fast it was moving!
Yes... Einstein has shown us a lot. He has brought back the importance of the role of an observer. If he where alive today, he might even be amazed with the progression of science and the observer - or he might be deeply disappointed. What gave Einstein his intelligent insight into reality? Einstein was arguably the best mind that ever lived - next to Stephen Hawkings; he had an amazing insight into reality... though, saying all this, he was not impervious to mistake. Einstien’s mother, when he was born, developed an unusually large head. This condition is named 'macrocephaly', in which individuals are born with unusually large heads, which isn't a disease, but rather the modern interpretation says that it is an evolutionary mistake... In fact, careful recent studies predict that brain size, or cranial size actually might have something to do with be intelligence development. This development can be traced to an 'intelligence gene.' Those who do not have the normal gene, including the second evolutionary gene step (the advanced gene), are born with extremely small heads called 'microcephilacs'; that is equivalent to the chimp family, and is considered as a throwback in evolution, a disease as sorts. Photographs today prove that Einstien’s head was in fact disproportionate to his body!
Coincidental or not, was the problem that Einstein had a delay in his language [which is related to ADHD]. I have always wondered if this might have been a case of his overlarge brain capacity - perhaps his brain, as large as it was for his age might have had certain functions slowed down by his 'mental production', with the minimal amount of brain power needed; but as time progressed, he worked his way out of this arena and he began to excel in his intelligence. Now, i have no medical interests - but you can imagine i was delightfully surprised to hear from a Dr. Neuroscientist Stephen Pinker who believes that his speech delay was caused by a rapid prenatal development in his brain that might have 'robbed' other functions and capabilities of the brain, such as speech development.
He began to talk at the age of nine; despite this, he was the top pupil at his high school. In later years, his success to say the least made some professors envious - some extremely repulsed by his intelligence even right into the1920's and 30's! The recurring talk that Einstein actually failed mathematics in untrue.
His first job was working at a Swiss Patent Office in 1902; he was to evaluate the Patent Applications regarding the electromagnetic devices. Einstein married Mileva Maric on January the 6th (one of a dozen women he would come to love in his lifetime), and she [is thought] to have assisted him in a lot of his calculations. She even checked his E=Mc^2 equation, just before publishing it. It is now understood, that their relationship was unbounded, but spatially separated. He would say that a respectful distance would be made, just enough room for his intellectual isolation. His job at the patent office became permanent as he was passed over to promotion until he 'mastered machine technology'. The size of his cranium is a bit more than just a coincidence when compared to his intelligence. It undoubtedly had something to do with his mathematical and imaginary insights. His intelligence and contributions will, and have left the world in awe, maybe even leaving us slightly worried and annoyed about Einstien’s universe - and something about this world is simultaneously comforting and mystical.
Einstein’s abrupt death was by internal bleeding caused by a rupture of an aortic aneurism; the autopsy was performed by Dr. Thomas Stoltz Harvey, who decided to remove and even preserve his brain, even though at first glance, the brain looked perfectly normal - then not long ago the pickled brain of Albert Einstein was finally taken out of its container. After 52 years, dissecting the brain, we could see that Einstein had an unusual amount of extra white matter. Further investigation in 1999 at McMaster’s University showed that the parietal operculum region was missing... and to compensate this missing matter his 'inferior parietal lobe' was 15% times wider. The inferior parietal region is in fact responsible for mathematical reasoning, visuospatial cognition and imagery of movement - all pivotal traits in quantum physics. His brain also contained a whopping 73% more 'glial cells' than the average brain.
Was this what gave Einstein his superintelligence? Some have even postulated he might have had autism, perhaps dyslexia or another form of ADHD (Attention Deficit Hyperactivity Disorder), or even an extremely rare disorder called 'synesthesia.' This is a neural disorder, and can create ghostly three-dimensional images at will for the observer. Some peoples brain associate ghostly colors to particular letters on a newspaper, for instance, or associates colors with musical notes. Others can taste words, and a case was reported that a man, born blind could see color! Whatever gave Einstein his insight let us be glad he left earth leaving behind his relativity theories. We have taken a juicy chunk out of the apple of physics and optics from the tree of relativity - and just like Eve in the Garden of Eden, our eyes have been opened - but the problem is, we still do not know what to do with it all! No better way could end this part, than to recite something Einstein once said in regards to having an imaginative idea and conclusion of what could possibly come out of any speculation about a theory, before any measurement is made and thus deducting and rationalizing by means of simple observation.
Einstein worked (from) Newton’s equations describing matter and gravity: And he also changed a lot of it too, describing gravity in whole new terms to physicists. Newton’s law of gravitation is given as:
F = G M1M2/d2
Where G is the gravitational constant, m1 is mass one, and m2 is the second body with mass, and F was the force distributed between them. Also, Einstein worked with the already existing equation describing the laws between two masses m1 and m2, finding a square force that weakened over greater factors: Charles Augustine de Coulomb in 1785 showed that the force of attraction and the force of repulsion between two electrically charged bodies and also between magnetic poles also obey an inverse square law. The force for two magnetic bodies are given as: Fm = (1/µ)(p1p2/r2) With what Einstein had in mind for this universe, which was pure curvature, he was able to use these concepts to create a geometrical vision of our cosmos. It described that matter was actually an energy:
E=Mc2 Which converts to the negative of E=Mc2
E=-Mc2+(E=Mc2) = 1022KeV of gamma energy
Which is the reverse of E=Mc2 and was first developed by Poncair. This scientist was also known for his remarkable work on relativity, and is often forgotten. In fact, General Relativity unifies the work of Poncair and Einstein in their theories describing Special Relativity with Newtons law of Gravitation.
Matter warped space, and time told matter how to move. And it can be said that time warped matter, and that matter told space how to act. This is because of Einstein’s equivalence principle, which covers a massive scope in his mathematically-genius work.
This next equation is Einstein’s field tensor, and you will most certainly learn it in a standard course of physics at college or university:
This equation is very important, where is the Gab Einstein Tensor Factor, and the Stress Energy Tensor is given as and Tab and k is a constant. This equation relates to the curvature of space and time, saying that stress energy is what causes the disturbance of spacetime. As we have seen, Einstein used Newton’s law of Gravity in his Field Equations, then we find the constant of k to have a value of:
Where π is pi, and G is the gravitational constant.
General Relativity was by far the more difficult to create, as it took Einstein so many more years to finish it. Special Relativity was also mathematically beautiful, and so very straight forward when one began to appreciate it.
Special Relativity Time Dilation and Length Contraction
In these relativistic principles, we need to know some concepts.
Minkowski’s flat vector spacetime is best used in physics today. It is given as (-, -, -, +) or (+,+,+,-) and with a matrix of, and in special conditions, can be written as (0,0,0,0) in zero-dimensions:
The following equations are called ‘’Cartesian’’ coordinated systems, and they describe the distance between two points:
s2 = (∆x) 2 + (∆y) 2
In a rotated system, we twist coordinates around in space, and we find them as a geometry of distance. The new coordinates are given as:
s2 = (∆x′)2 + (∆y′)2
Being almost identical math, they are easy to remember. In this case, we say that distance is an invariant of these equations. More interesting is that we learn that time is also an invariant of space.
Because of this, we can therefore find the following equation describing a spacetime interval:
s2 = −(c∆t) 2 + (∆x) 2 + (∆y) 2 + (∆z) 2
Where (t, x, y and z) are the coordinates of spacetime, because we can rotate space, and find a corresponding value with time, and this is why we say that space and time are one thing.
Before relativity, we never considered time as a vector of space. Now we cannot remove either, as it has been shown that time is a distance as well in space. To move through space, is to take a massive journey in time for us. In fact, time moves at the speed of light, and because we live in such a slow part of the universe, we cannot help but flow along with it.
Relativity was also developed to answer for optical phenomenon. One of these the Length Contraction of a physical body accelerating through spacetime.
The Length Contraction formula is given as:
L=L0 (1-v2/c2) 1/2
Here, L0 is the proper length, and v is for velocity and c is for the speed of light. This equation shows that an object moving through spacetime is found to contract in length to the observer. Such paradoxes like, the pole and barn paradox are prime examples of this optical phenomenon.
So in short notation, we say that space contracts and time dilates by a factor of:
As I explained, one example of Length Contraction is given by the pole-barn paradox. This is where a pole is traveling through space, and is physically contracted. If the pole is larger than the barn to begin with, and now it is shorter because of length contraction it can fit in the barn. Paradox is, how can a pole larger than the barn be length contracted so that it fits as it passes by? In this next set of equations, we work with a pole traveling through space which has a proper length of 20 meters. An observer moving at a speed v = 0.98 c will experience a contraction as shown:
L0 = 20 m L = L0 (1 - v2/c2)1/2 = 20 [ 1 - (0.98)2 ]1/2 = 3.98 m
If an object is accelerating through spacetime, it will experience a time warp. This is also been known to be called time dilation. If we experience time warps, then according to relativity this must also mean space warps.
We don’t experience space warps so much because we move so fast through time. In fact, we spend more time in the time dimension than we do in space. The time dilation formula is given as:
In relativity, we learn that E=Mc2, and that energy can be transferred through angular momentum of a system, and the conservation of physics states that the loss of energy is equal to the gain of energy given as:
Where mass gained is a loss in energy. And we also find that energy gained or lost, is equivalent to a gain in mass:
Where L is the angular momentum, r is the position of the particle, x is the cross product and p is the linear momentum:
This shows, as it does in any text book, that momentum p is related to mass multiplied by the velocity v. The importance of this equation is that energy can only ever be transferred through angular momentum. So the particle is said to be given as:
L=r x p
And between two objects, one finds that one gains momentum and the other looses momentum, given as:
Because everything is conserved, the state of momenta found prior to the transfer is equal to the momenta afterwards:
These equations are beautiful. I have also equated that if an end is desired by time and the cosmos, then somehow mass and energy is an illusion:
And if ‘’c’’ is not equal to zero, which we know it isn’t, then we find through algebra that:
This can be found to be true about this universe. All matter comes to zero when added with the energy in the vacuum:
(E=Mc2)+(E=-Mc2) = 0
So the converse can be accumulated:
Then all energy comes to zero as well:
The reason why this happens, is because we are adding all the matter and energy, about 1080 particles ‘’pop’’ into existence, and when added to the negative energy of the vacuum produces a zero-total. The negative reservoir is called The Dirac Sea, and it is filled with negative spinning particles. In fact, Dirac postulated this sea using relativity. Virtual particles, like the kind found in this sea, don’t share the same properties as real energy:
E2 = m2c4
And is found to reduce to this instead of the normal energy and momentum formula:
E2 = p2c2 + m2c4
… for when a particle is at rest p=0. Where p is momentum and c is the speed of light. This new relativistic outlook on the electron allowed Dirac to formulate his famous equations describing antimatter.
Which shows the negative solution to:
These relativistic formulae show that every time an electron ‘’pops’’ into existence, it leaves behind a hole. This hole is found to be its antipartner, the positron.
To measure the Kinetic energy of something, you must calculate it with the formula:
And the total energy is found as:
E=Mc2 (1-v2/c2) 1/2
And the rest energy is given in relativity as:
Pure simplicity at its best. These equations have been the most influential in the world. These equations can describe the motions of little particles as well.
The complications of this are amazingly dull. Time dilation in relativity means that a twin traveling off into the far reaches of spacetime a fraction short of c would return to earth hardly aged a year, whilst his twin is an old man. Einstein has shown the world of physics that time is not a fixed clock in the sky, and two events that are relative to each other will experience different times traveling at different speeds.