PHYSICS

QUANTUM FIELD THEORY :PART 1

Make everything as simple as possible but not simpler(Albert Einstein)

Origin of particles from fields in spacetime

According to quantum field theory the universe has a large number of fields in a background of space time. Fields are numbers which represent the intensity of some property of a field. Temperature is a scalar field. Thus the distribution of temperature in atmosphere will give the indication of air agitation  at that point. Fields may have direction. Thus wind is a vector field. Thus it has a magnitude as well as direction at every point in atmosphere. Moreover the two fields may be causally related. Temperature differences in atmosphere can lead to wind.

Field strengths can undergo oscillations under certain circumstances. Particles in the universe are a result of these oscillations. However a single wave cannot represent a particle. If it was so the amplitude of the wave will be uniform all over the universe. In QFT amplitude or maximum height of a wave squared represents  the the maximum probability of finding a particle at that location. A single wave will not have any definite position .To obviate this particles are supposed to be comprised of a bunch of waves having different frequencies and amplitude. The location where their peaks coincide a particle exists.Now the location of a particle is independent of the amplitude of a specific wave .

Particle velocity and phase velocity

The individual waves comprising a particle have different velocities. The velocity of the particle is independent of the individual component waves. The point where the peaks of the waves coincide this is the position of the particle and its velocity is particle or group velocity. This velocity is less than the velocity of the individual waves.However over a period of time the different waves comprising the particle moving with different velocities separate out. The position peak thus gets broadened. But the wave now has a single momentum and its amplitude can be anywhere in the universe. The same does not occur with massless particles where all phase velocities coincide as they move at speed of light. 

   The particles are supposed to move in a background of spacetime. This is also called vacuum. The vacuum has an elasticity which allows waves to pass through it. However another field,the Higgs field also acts as a background.The Higgs field has a uniform value in space. Many particles can interact with the Higgs field and it acts similar to vacuum by providing elasticity to the particle waves.The particles which interact with Higgs field face more resistance than vacuum.

    The photon which is massless does  not interact with Higgs field and travels at the speed of light.Fermions and other Bosons with mass interact with Higgs field and face more resistance due to increased elasticity.The mass is actually the elasticity that Higgs field gives these particles during motion. As a result of this the relation between energy  and wavelength is very different at low and high velocities for massive particles.

Lenth contraction and time dilation with velocity

With all particles as velocity increases the energy is more . In a wave this leads to increased frequency. As frequency is related by velocity /wavelength there is an increase in wave velocity as well as a decrease in wavelength. As the velocity of a massive particle approaches the speed of light an increase in energy cannot lead to higher velocity . As per special relativity velocity cannot exceed speed of light which is given by the elasticity of vacuum.Now with increasing energy the frequency  tends to increase but  since velocity cannot increase the wavelength decreases more by an extra amount. This is length contraction. However now the frequency also cannot increase as much with energy. A extra decrease in frequency means larger time period of waves and time dilation.

Path integral and the origin of forces

The particle can travel from one point to another as a wave. But the wave does not travel in a straight line by itself. Here the concept of path integral comes.A particle wave travels by all possible routes between two points. Paths which are far from a straight line have waves which interfere destructively due to wide phase difference with nearby paths. As a result these paths are not the actual path travelled by the wave. Wave pathways which are in a straight line between two points have phases which do not interfere destructively with nearby pathways. These are the pathways which occur in nature

When two particles of same charge approach each other they repel.  This can be explained by path integrals. Both the particles while approaching slow down. Thus they loose momentum but gain potential.As a result their masses increase mass being equal to increased resistance in a medium..But it does not lead to a shorter wavelength because total energy for combined particles have to be constant. So the energy or frequency of the particle decreases and this leads to increase in wavelength of the particle.Now if we compare three waves of the particle while it approaches a second particle the path with largest wavelength will curve towards the second particle and then repel. The other curves with normal or decreased wavelength will remain faraway as their wavelengths are not affected by the interaction. The path with largest wavelength is also the shortest path. Thus the particle follows a bent path and gets a repulsion force.

Symmetry and gauge fields

Massive particles acquire their mass from oscillations of the Higgs field when they move through it. The coupling of a particle to Higgs depends on coupling constant of that field. This in turn gives a characteristic frequency with which the particle wave will oscillate and its resulting mass. Again when charged particles interact ,the medium of transmission of momentum is through particles called Bosons. The photon is a massless boson which transmits momentum and potential between fermions. Bosons belong to a class of fields called gauge fields. Since there are four different fundamental forces there should be different mechanism of their production and transmission by gauge fields.

Gauge fields are fields which have symmetry. The simplest symmetry belongs to the photon which has symmetry in a plane. The photon wave can be represented as a circle.  It is produced when phase of fermions change during electromagnetic interactions.Each photon has an angle in the circle which represents the phase of the wave. This can be represented in a positive or negative direction representing positive or negative charge of electromotive force.The magnitude or amplitude of photon is represented by the radius of the circle which is constant.This is called U1 symmetry. It can be thought as a wave travelling along the inside of a circular dimension. Such an idea of relating force to dimensions was first made by Kaluza and Klein.                          

                  In  SU 2 symmetry the circle in turn has an inclination. This incination angle represents  the amplitude of the wave.Thus the bosons of weak force can be changed in two variables including along a circle and then inclination of the circle. In weak force interactions both phase and amplitude of fermions can change though total wave size or probability has to be conserved. This is achieved by rotating the wave form in four dimensions. Rotations in four dimensions into two states can be done in four ways.: state 1to2 ,state2to1 and two self rotations :state1to1 andstate2to2. The latter two are redundant.There are three bosons which correspond to the three ways to change the states:these are the W+ ,W- and Z0 bosons.SU2 symmetry can also be imagined as a higher dimension rotation. In a two dimensional world a cylinder can be projected in two ways. One along the length and other the face. In three dimensions one can be rotated to another. Therefore they are two faces of the same object.

Rotations can take place if there are three states also. Now there are nine dimensions and  rotations have to preserve the size of the wave . Rotations can occur from state 1to 2,2to3and3to1. Then there are three reverse rotations and three self rotations out of which one is redundant. Rotation in three states occur in strong interactions. 

Virtual particles and entropy

There is another way to look at particle movement and interactions. This is through exchange of virtual particles. Each real particle ,electron or photon can undergo disturbances in its potential in time. The disturbances in potential are more ,shorter the time. Potentials can create a bunch of waves or a virtual particle. The potential of the virtual particle is not enough to exist independently as it is not a multiple of natural frequency of vacuum or Higgs field. However it can transmit momentum.

  Each electron is supposed to be surrounded by a cloud of virtual photons which is constantly forming and disappearing. Again a photon is surrounded by a cloud of virtual electron positron pairs. When a photon approaches an electron the virtual photons cloud interact with the virtual electron positron cloud and form real photons. The electron will absorb the real photon and gain energy.

    QFT interactions thus have a statistical mechanism and follows the second law of thermodynamics of increasing entropy.  The interaction and mixing of virtual photons is analogous to mixing of particles of two gases.The alternative explanation of virtual particles is by path integrals. Since disturbances cannot exist independantly they represent wave paths which cannot sustain themselves by constructive interference.

Entanglement and decoherence

  In the universe each electron or photon has nearby objects comprising billions of particles. When a photon approaches another object its virtual cloud interacts with the virtual cloud of all these particles of the object.So when it again goes far away the interaction memory is preserved. This is called entanglement. The detection of momentum of the particle even at the other end of the universe will be determined by its past entanglement.

Again when a photon interacts with an object the interaction of all the virtual clouds immediately entangles the object. The object now has existence  as a joint wave and this is called decoherence. The classical world objects are a result of decoherence

Ack:Particles,fields and forces