As is mentioned quite concisely in this page on waves, waves that meet each other undergo superposition and either constructive or destructive interference. This can be seen straight from Maxwell’s equations and so for a long time this was not questioned. It was eventually discovered that it is actually possible for photons to collide with each other in an effect called light by light scattering. According to particle physics such an interaction where two photons end up bouncing off each other is controlled by the W± bosons. Despite considerable effort being exerted from some very powerful lasers there has still not been direct observational evidence of elastic light by light scattering. Most of the information for its existence has come from parallel observations involving the anomalous values of the magnetic moment in electrons and muons.
The importance of the Sun in our solar system cannot be overstated. When considered, it is quickly realised that almost all sources of energy on this planet come from the Sun. For solar power it is obvious, but wind power is caused by the temperature gradient the Sun produces and fossil fuels originally started out as plants absorbing energy through photosynthesis. The two main exceptions are tidal power, which is a conversion of the Earth and Moon’s rotational kinetic energy and geothermal power, which is gained from nuclear decay in the Earth’s core.
Ultra high energy cosmic ray (UHECR) are cosmic rays which are measured to have over 1018 eV of kinetic energy. Many of these particles exist beyond the Greisen–Zatsepin–Kuzmin limit, a theoretical limit based on the interaction of the cosmic rays above a certain energy threshold and the photons of the cosmic microwave background radiation. In essence if the particles were of too high energy they would of interacted and slowed down, but this restriction only applies over a certain distance. UHECRs are believed to be produced locally and so are not restricted by the limit. There is also a possibility that heavier nuclei my circumvent the limit also but what particles make up UHECRs are still unknown. Despite this the mass compositions have been measured by the Pierre Auger Observatory in Argentina which is believed to show particles of higher mass than helium with an upper limit of about iron.
When a charge is placed in an alternating electric field it will oscillate according to the alternating force on it. If the time spent in each field direction is equal it should return to the same position after one cycle. This assumption is only true under the condition that the electric field is perfectly homogeneous and so there is no change of electric field strength as a function of distance. If the field is inhomogeneous, it will clearly have a gradient of field strength over the distance the charge oscillates. While the charge performs its half cycle within the stronger field it will experience greater returning force than the half of the cycle in the weaker section of field. This leads to, over one complete oscillation, an average force transporting the particle from strong to weak field. This is called the ponderomotive force and has the mathematical form:
Where e and m are the charge and mass of the particle, ω is the angular frequency of the fields oscillations and the final term is the gradient of the electric field strength, E, squared (if E is small enough the action of the magnetic field can be ignored).
The simplest of all antiatoms to fabricate is antihydrogen, composed of only a single positron and antiproton. This makes it the easiest complex system to study when it comes to symmetry between matter and antimatter. The Antiproton Decelerator at CERN is used to produce antiprotons and antiatoms. It works by firing high energy protons into a block of high density metal which then produces a range of secondary particles with high energy antiprotons among them. Strong electric fields are used to slow down these antiprotons (hence why its called a decelerator) so that they can be used in experiments. All aspects of antihydrogen are put under scrutiny such as band structure, band splitting, overall neutrality as well as the charge to mass ratio and magnetic moment of the antiproton. If even a small discrepancy could be found, despite how unlikely it seems at the moment, it would be the most revolutionary discovery in the last 50 years.
Back in 1855 a mathematical physicist turned doctor, called Adolf Eugen Fick, created what is now known as Fick’s laws of diffusion. The first is simply that the the diffusive flux is proportional to the concentration gradient and the second is that the rate of concentration change is proportional to the derivative of the concentration gradient. Later the same conclusion was reached when applying the method of random walks to particles in suspension and the final result was reached where the mean squared displacement of a particle is proportional to the time since it stared to move. This is considered the standard description of the diffusion process:
〈 χ2 〉 ∝ t
Resistance is actually quite a complicated thing to explain properly but the basic explanation that it is the effect of the material getting in the electrons way will suffice here. This theory describes electrons as having mean free paths through the metal, average distances they will travel before colliding with an an element of the lattice and being scattered forced to change momentum. Now ballistic electrons are those that exist in a material which have such low electrical resistivity that the mean free path of the electron is longer than the material that its travelling in. This means the electrons will only scatter and change direction when they meet the edge of the wire for instance, unable to escape due to the work function they ricochet back into the metal and continue on their elongated path until reaching another boundary.