Journey Through Time

by Ivica Hausmeister

  Picture 6.18

  GENERAL RELATIVITY

  I have made an effort to explain the special theory of relativity focusing on particular points which were confusing to me initially. These points prevented me having a better understanding of this concept when I read about it for the first time. I hope that I have managed to explain this in a way that makes sense. In doing this, I did not go into a very detailed explanation regarding the Lorentz transformation, for example. Nevertheless, I believe I have provided a decent amount of material there.

  As far as the general theory of relativity is concerned, I will not really go into so much detail, not only because it is not necessary for the purpose of my book but because it is a very complicated topic which requires a high level of mathematical skill and knowledge that are well beyond my capability.

  The essence of the general theory of relativity is that gravity is understood as the result of space-time geometry or precisely it is caused by acceleration due to the fact that space-time is curved.

  Einstein finished his general theory of relativity in 1916. It is based on two postulates:

  1.Relativity principle

  Local physics is governed by the theory of special relativity

  2.Equivalence principle

  There is no way to make a difference locally between gravity and acceleration

  Einstein’s approach initially to solving a gravity problem was to apply a famous thought experiment. He thought about a man standing in a lift where the lift suddenly gets detached from its main cable. It is the situation where the man and lift suddenly start to accelerate equally towards the Earth. As both accelerate or speed up at the same rate, then both the lift and the man fall towards the bottom of the building at the same rate of speed, which is experienced as weightlessness. If the man had a ball in his hand and he decided to let go of the ball from his hand then the ball would remain in the air next to his hand after he let it go from his hand. The reason is that all of them – the man, the ball and the lift – are speeding up at the same rate towards Earth. It is the same principle which is used to experience weightlessness in an airplane used for this purpose. The airplane flies high in the atmosphere and then lets gravity take the plane down for a while. It is a free fall due to acceleration caused by gravity where all the objects in the plane fall at the same rate involving people. That is how weightlessness is experienced.

  Einstein has imagined also the situation where a man is in a lift in the space accelerating at the same rate. With no window in this lift, the man will not be able to know whether he is in space or he is falling to Earth due to acceleration.

  The next experiment demonstrated that light beams bend due to acceleration.

  To make it easier to understand, let’s try to imagine a lift which moves upwards with a constant velocity. There is no acceleration, but constant velocity or an inertial reference frame. If we shine a light at one moment from the left-hand side of this lift, then light will travel towards the other side of the lift and will reach the other side of the lift after a short time. Let’s say the lift was travelling at a constant speed of 20km/hr. At the moment that light enters the space from the lift it was travelling upwards at 20 km/hr. The light will remain at this speed upwards. As both the light and the lift continue at the same speed upwards then light will reach the other side of the lift at the same height from where it left the left-hand side of the lift. In other words, the light beam will be parallel with the floor or ceiling of the lift. The man in the lift will see that light beam as straight light. I did not draw the man in the lift again in order to give a clear illustration, but you can just imagine the man standing in the lift.

  Picture 6.19

  Let’s now imagine that this lift moves upwards but is accelerating or its speed is changing.

  We now have acceleration with changing velocity or a non-inertial reference frame. We now shine light again from the left-hand side of the lift when the lift was at the speed of 20 km/hr. The light will continue to move upwards at the speed of 20 km/hr, while it is moving horizontally towards the right-hand side of the lift. However, during the time the light or beam of this light is travelling through the space from the left at the constant speed of 20 km/hr upwards, the lift is already moving upwards at the speed of 60km/hr as it is constantly accelerating upwards. So by the time the light beam passes half of the space on its way to the other side of the lift, the lift has moved significantly upwards. It will have moved even more by the time the beam of light reaches the other side of the lift. So although the light travels in a straight line from the left-hand side to the right-hand side side of the lift, it enters the lift on the left-hand side at the top of this side and reaches the other side of the lift close to the point where the right-hand side meets the floor of the lift. For the man standing in the lift, the beam of this light has bent due to acceleration, which is the result of gravity. I again tried to demonstrate it with an illustration with no man inside the lift for the sake of clarity of the illustration. Here, however, I did not show all the light beam but just one of the photons which goes one after another making a straight line of a light beam: similarly to drops of water that go so close to each other at such a speed that altogether they give the impression of a water jet. In the following illustration it can be seen how the photon of that light (all of these photons make this particular light beam) leaves the lift on the left-hand side at the top of the wall and hits the other side of the lift wall at the bottom. This happens because now the lift does not go up at a constant speed but accelerates.

  Picture 6.20

  According to Newton’s law of gravitation, the force of gravitation is equal to the product of G gravitational constant, M mass of one object and m mass of another object divided by r2 radius on squared:

  This equation cannot be applied to light, as light is massless. Einstein therefore rejected mass as the reason for gravitational attraction or force. Instead, he believed that space-time is curved which makes light bend. Light continues to go in a straight line but as it comes across curved space-time it takes the shortest part or geodesic.

  If we look again at the space-time diagram which shows movement with constant velocity of the object moving in an inertial reference frame then we can see that every world line is straight due to constant velocity (left-hand diagram on illustration below). If, however, we have acceleration then the world line becomes curved (right-hand diagram in the illustration). The space is curved due to the massive object, which is manifested with acceleration. The movement which is non inertial (acceleration or changing velocity) is a real movement in relation to movement with constant velocity. It causes dilatation of the time and contraction of the space as manifestation of curved space.

  Picture 6.21

  Einstein worked for around ten years to finalise his general theory of relativity. In this process he had the support of many great minds in physics and mathematics at that time. Handrik Lorentz, Dutch physicist, was one of them. He calculated the famous transformation inspired by Albert Michelson and Edward W. Morley’s discovery that the speed of light is constant and that there is no ether. It was, however, Albert Einstein who put things together and created the general theory of relativity, which has been tested and proved over and over.

  As we all know, the satellite navigation system that we all use in our cars, is controlled by satellites located in orbit around Earth. As they are at a distance from the Earth, their acceleration is slightly weaker than on Earth. So objects on Earth are moving slightly faster, which means that their clocks are slightly slower than the ones in satellites. This needs to be taken into account and calculations need to be made for clocks in satellites. If this is not done, then very quickly their guide will become out of precision and will not be useful. The difference in time is incredibly small but would quickly become significant for devices not to be able to function properly.

  Einstein became the most celebrated
scientist in the twentieth century. He was seen on many occasions and in the company of many celebrities at that time. On one such occasion he was invited to the premiere of the Chaplin film City Lights where he appeared together with Charlie Chaplin. When they were mobbed by thousands, Chaplin remarked, “The people applaud me because everybody understands me, and they applaud you because no one understands you.” Einstein asked Chaplin, “What does it all mean?” Chaplin replied, “Nothing.”

  SUMMARY

  The universe is composed of everything that exists. It was created around 13.7 billion years ago in the Big Bang explosion, details of which I will focus on in the next part of the book.

  The main components of the universe such as time, space, matter, dark matter, fundamental forces, energy and dark energy were all created in the Big Bang explosion. Before that, nothing existed.

  Scientists have calculated that matter occupies only 4% of the universe while dark matter makes up 23% and the remaining 73% is made of dark energy.

  Ordinary matter is composed of elementary particles. There are altogether only twelve elementary particles from which all matter of the universe is made up. There are six quarks and six leptons with the difference between them being such that quarks are affected by strong nuclear forces while leptons are not.

  The elementary particles have one important property referring to their spin of rotation around their own axes. According to this property, all particles are divided into those which have ½ of a spin called fermions, and those with a whole spin called bosons. Fermions are subject to the Pauli principle of exclusion. That roughly means that two fermions cannot be in the same place at the same time. The fermion’s job is to create all matter while the boson’s job is to establish communications between particles in each of four fundamental interactions. Bosons are not subject to the Pauli principle of exclusion, which means that an unlimited amount of bosons can be in the same place at the same time.

  With the creation of matter, all four fundamental interactions between particles came to light and were responsible for the arrangement of matter at microscopic and macroscopic levels.

  At a microscopic level, strong nuclear interactions created strong, tight connections between three quarks forming protons and neutrons. Weak nuclear interactions enable the transformation of one proton to one neutron, which sets part for the formation of a helium atom, for example. The next electromagnetic fundamental interaction helps the creation of stable atoms consisting of protons and neutrons in an atomic nucleus and electrons orbiting around the nucleus at a distance. An atom with a different number of protons inside had a particular specific property of so-called elements of which this atom was the smallest part. These atoms belonging to different elements were able to combine among them, creating compounds with a different property. This was possible thanks to electromagnetic fundamental interactions. We can say that strong and weak nuclear interactions together with electromagnetic fundamental interactions help the arrangement of matter at a microscopic level.

  The arrangement of matter at macroscopic level or at the level of the universe in the form of stars, planets and galaxies was possible thanks to the fourth fundamental interaction – gravitation.

  Sir Isaac Newton formulated gravitation as a force, which depends on the product of gravitational constant, and two masses, which attract each other, divided by radius of their separation squared. It was during the time when it was believed that time and space had absolute value and as such had invariant property. With the discovery of invariant property of the speed of light being at a constant speed of around 300 000 km/second, regardless of the reference frame from where it is observed, Einstein developed his special and general theory of relativity. The last one, on which he had been working for almost 10 years following the special theory of relativity, explained gravitational force from a completely different angle. It basically states that gravitational force is the result of curved space-time fabric where the quantity of the mass dictates how much space- time will be curved and the curvature of space-time will determine the movement of another mass that approaches this curved space-time fabric. Time and space are not invariant but are flexible and changeable which is experienced as time dilatation and space contraction when those two properties are observed in a non-inertial reference frame (which is acceleration or gravitational force) in relation to an inertial reference frame (which is state at rest or movement at constant velocity).

  Therefore, it could be said that three fundamental interactions shape or arrange matter at a microscopic level while a fourth fundamental interaction – gravitation – shapes matter at a macroscopic level as well as time-space fabric itself.

  Interactions among particles and the movement of matter within time-space are possible thanks to energy, which can be defined as the capacity to do work from the aspect of classic physics. Matter itself has energy, which is locked inside matter and is expressed by Einstein’s famous equation E= mc2. The equation represents formula, which helps to calculate the amount of energy, which mass contains when it is at rest; in other words, when there is no movement of the mass or added kinetic energy. It is also an expression of mass-energy equivalence where one can be transformed into another and vice versa. The previous knowledge of conservation of matter and energy as separate entities has to be defined more precisely as conservation of mass- energy within the closed system. It means that the amount of energy-mass created at the beginning of the universe has remained constant throughout time and space of the created universe although it is possible that one transfers to another to some extent and vice versa, but the total amount remains the same. These conservation laws are examples of invariance in modern physics. There are plenty of invariances such as the constant speed of light and the Planck constant, for example. There is also one of many philosophical approaches which tries to explain why the universe has developed the way it has. It is called the anthropic principle, which goes from the presumption that the universe has developed in this way with such particular forms of invariances or constants to allow life form to develop within such a universe.

  Alongside energy, which can be described and formulated from the aspect of classical physics and the aspect of Einstein’s special theory of relativity which referred to ordinary energy within the universe, there is also energy, which is the opposite of gravity and tends to expand the universe. It is named dark energy.

  Before this energy was discovered, we discovered another form of matter. This matter cannot be seen but was detected with the help of gravitational lensing and orbital velocity. With the help of gravitational lensing, it was discovered that dark matter is arranged like a spider’s web throughout the universe and serves as scaffolding or support for building galaxies and clusters of galaxies of which ordinary matter is made.

  As far as dark energy is concerned, it has been discovered that the universe has accelerated in its expansion over the last 5 billion years. This was detected thanks to distances between galaxies which were measured with the help of light emitted from type 1a supernovas which come from different galaxies (standard candles) and with the help of baryon acoustic oscillations (standard rulers).

  From this recent discovery it can be argued that the future of our universe faces the so-called big reap where the universe will finally disappear, expending infinitely. Also, entropy where useful energy is transferred into less useful energy, all the time, will bring the universe to the point where the whole existing energy will be in a form of useless energy, bringing the universe to an end. In any case, the future looks quite bleak.

  I myself now feel depressed as I am coming to the end of the first part of the book, but I am happy that I will start from the beginning of everything in the next part of the book.

  Bibliography

  Books

  Foundations of modern cosmology, Hawley, John Frederic Holcomb, Katherine A.

  The rough guide to the universe, John Scalzi

>   Chemistry essentials for dummies Moore, John T.Atkins’ physical chemistry, Atkins, P. W. (Peter William)

  Higgs the invention and discovery of the ‘God Particle’, Baggott, J. E.

  The bigger bang, Lidsey James E.

  Higgs DiscoveryThe Power of Empty Space, Randall, Lisa

  Antimatter the ultimate mirror, Fraser Gordon

  Physics II for dummies, Holzner Steven

  The discovery of subatomic particles, Weinberg, Steven

  Magnetism a very short introduction, Blundell, Stephen

  On space and time, Connes, Alain Majid, Shahn

  North Pole, South Pole, Turner Gillian

  The Space Book, Jim Bell

  Dark Matter, Dark Energy, Dark Gravity, Stephen Perrenod

  Way does E=mc2?, Brian Cox, Jeff Forshaw

  The First Three Minutes, Weinberg, Steven

  Big Bang, Simon Singh

  Astronomy A beginner’s guide to the sky at night, Paul Sutherland

  History of the Universe, Wyken Seagrave

  Binding Energy, Fission and the Strong, Nuclear Force

  Online Materials

  http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html

  http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html#torq

  http://www.youtube.com/watch?v=s_R8d3isJDA

  http://www.britannica.com/EBchecked/topic/181349/Albert-Einstein/256585/World-renown-and-Nobel-Prize

  http://abyss.uoregon.edu/~jscosmo/lectures/lec05.html

  http://www.youtube.comwatch?v=UkLkiXiOCWU

  http://www.bing.com/search?q=proton+size&FORM=MSNSHL