PHYSICS:THEORY OF RELATIVITY

Space time tells matter how to move;matter tells space time how to curve-John Archibald wheeler

Time is an illusion ,albeit a very persistent one- Albert Einstein

Special theory of relativity

This was the first theory given by Albert Einstein about relativity. It can be understood clearly if we consider the universe to consist of fields in a background of space time. The fields undergo wave motion and create particles according to the rules of quantum field theory. According to the theory the velocity of light waves is the maximum velocity allowed in space time. All matter waves have velocity less than light waves which is massless. A consequence of this is that as matter waves gain velocity

and energy and approach speed of light the velocity cannot increase further. Now extra energy given to the waves decreases the momentum and wavelength. This leads to length contraction. Again frequency of the wave decreases leading to slowing of time.

     If we consider the universe as a whole special relativity gives a concept of unidirectional flow of time in a three dimensional universe. Time or frequency of waves is unidirectional because frequency is associated with positive energy. The light or matter waves cannot go back in time as it requires negative frequency or energy. The time axis is surrounded by a cone of velocity denoting speed of light. Since velocity of light is maximum possible all past and future waves lie within the light cone.By its nature waves move forward and time also goes from past to future. However the light cone as it progresses to future along the time axis can receive waves from the entire universe. 

General theory of relativity

Einstein gave his general theory of relativity subsequent to the special theory. Here he considered the three dimensions of space and time as being capable of curvature. When waves constituting a massive body travel in space they contract space dimensions in the radial direction and also decrease frequency in time dimension. This phenomena is completely different from the situation in special relativity where the waves themselves undergo contraction and their frequency slows down. A consequence of space time contraction within a matter wave is that outside the wave the space gets stretched in the radial direction. However the circular dimension of space becomes curved to compensate for the radial contraction. As a result of stretched  length in radial direction any object travelling in this space appears contracted as the space has expanded in radial direction. Moreover there is a curvature space in circular direction to compensate for radial stretching.Since time dimension is also affected in space near the mass time or frequency slows down. Thus while waves have to travel more in curved space they have more time to do so and there is exact compensation

   When a matter wave travels in a curved space it bends. .In QFT  when two charged protons approach each other their velocity reduces due to virtual cloud particles repelling each other . However they gain potential energy. But since total energy of both particles is constant mass energy increases and frequency decreases.The wavelength of the particles increase. This has an effect on the path the particles will take. According to path integral approach waves with longest wavelength are selected as they have less interfering nearby waves. The longest wavelengths waves travel in a curved path while shorter ones are cancelled.                                                                                                                                                             In curved space a proton with a higher velocity has more momentum and a shorter wavelength. When the initial wavelength is shorter the path that differs by half a wavelength is much closer to the original path. The proton thus deflects less at higher velocity. Thus inertia is the charge for curved space. The curved space deflects waves as per their momentum.When a wave travels in curved space it has to travel a longer distance due to stretching . The stretching changes and increases near  the mass and decreases far away from the mass. outside. Thus the wave travelling has more wavelengths near the mass, than further away. This causes more cancelling near the mass due to interference of nearby waves. Very far away though number of waves are less due to less stretching of space but total distance and number of waves is more. In between is a path with least number of waves and less distance to travel. This is the curved path a wave takes and is called shortest path or geodesic. The force of gravitation thus is a consequence of curved space.

Black holes and event horizon

When a massive star spends all it’s hydrogen in nuclear fusion and comes to the end of it’s life the heat from fuel burning is absent and unable to balance the gravitational attraction of it’s constituent mass. In this situation the star collapses and attains a size which is minuscule compared to its original size. As a result of the massive gravity of the collapsed star even light cannot escape its surface and the object becomes invisible,Black hole in space.

Due to effect of mass of its constituent waves the black hole contracts space and slows time within it. Just outside the black hole however a region of space expands in a curved manner as a compensation. Time also gradually becomes faster. There is a distance called Scwartzfield radius from centre of black hole. Here a transition occurs from the curved space around the black hole to the normal flat interstellar space. At this radius even light cannot escape once it has crossed it and it is called the event horizon

   When an object falls in a black hole it approaches the Schwartz field radius and crosses it. Once it crosses the SR it cannot turn back as gravity is so strong that even light cannot cross SR and escape. Apart from this the object does not mark any abnormalities as it crosses SR. However it now moves straight to the centre of the blach hole  and increasingly cannot even move sideways. The light cone of the object which was getting curved and parallel to the SR undergoes a vertical direction towards centre of the hole.An observer from faraway watching the object however sees it differently. As the object approaches SR light from it takes more time and ultimately stops comming.So the external observer sees the object slow down and ultimately stop at SR. Any subsequent object falling gets loaded on top of the first object.

   The light cone undergoes an exchange of coordinates at SR. The space axis gets changed by the time axis.The space axis outside SR stretches more and the time axis shortens more as an object nears SR. At SR speed of change in space axis equals speed of light. Inside the black hole and SR the space stretch is more than speed of light. Moreover time axis becomes negative after slowing to zero. A negative time axis points towards centre of black hole and gets exchanged with the space axis along which the object was falling till now.

The Swartz field radius is different for ordinary objects where it lies within it. Thus the SR of earth is only 9mm from centre. This means the earth cannot have a event horizon at SR and behaves gravitationally totally unlike a black hole

Emergent gravity and the 3dimensional universe

There are many theories which combine general relativity and quantum field theory and these are called quantum gravity theories. Some of them are quantum foam,string theory ,but all are incomplete and not tested experimentally. One of the theories is emergent gravity.

According to emergent gravity space time emerges from an entanglement of quantum waves. Entanglement of two quantum particles reduces the number of states held in superposition. Thus if particle one has two states and particle two has two states after entanglement the total states reduces to two. Since entanglement reduces the information required to be stored the same can be done on a surface rather than a volume. The event horizon of the black hole is a surface and all information of objects falling within is capable of being stored here rather than inside the volume.

     The entangled surface or space is capable of transmitting quantum waves . Waves have more information such as momentum,energy,frequency and this increases the information storage requirement of the surface. Moreover when waves decohere objects are formed whose Schwartz field radius is within them. Three dimensional space time results to store the extra information after decoherence. Gravitational force emerges as matter waves reduce entropy of a volume thus curving it. 

Rindler radius and time

In emergent gravity the space time is continuously stretched . This occurs as matter  waves are constantly reducing entropy around them and shrinking space. The remaining space gets stretched to compensate it. The universe thus appears to be expanding. At the cosmic horizon the stretching of space is faster than the speed of light. 

  At the event horizon of a black hole space stretches faster than the speed of light. Any object in this region of space undergoes acceleration due to stretching of space faster than light. For a non accelerated observer any event in the past will eventually enter his past light cone and he will be able to see it. However when space stretches the observer is accelerated and some events from past cannot reach him. This creates a horizon called Rindler horizon.When space stretches more than the speed of light as in our universe  past events cannot reach the light cone. The past is thus cutoff permanently

A fish swimming in a still pond will eventually receives all waves generated anywhere in the pond. In a stream  the fish will not receive some waves originating downstream. When velocity of stream is greater than speed of fish no waves from downstream will reach it

Ack:Understanding relativity: A conceptual journey into spacetime,Blackholes and gravitational waves