September 17, 2011
Is a photon always moving at the speed of light?
Photons are said to be the quantum (प्र-भागी) that carries the energy of unified electromagnetic fields. A unified field is an advance treatment of electric and magnetic fields that are treated “same” because of a great idea of Einstein’s special theory of relativity. Like the equivalence of space-distance and time-intervals, electric field and magnetic fields are the manifestation of the same “gauge” fields which is necessary if one observes the electric and magnetic phenomena from a space-point (or frame of reference) which is moving so fast with respect to the highest speeds attainable in our Universe that if something moves even at 1/20th the speed of light differences start to show up in our calculation from so called classical understanding.
A classical understanding is something that you readily see in a day to day world, eg rotating a magnet piece very fast, say; like a manual-pedal bicycle wheel, so that electric current is produced from it. A “gauge” is the idea that the mathematical functions that describe the electric currents, the space around electric currents and charges, the space around magnets, when they are still or moving are not unique. Rather one can add constants and specially chosen functions and we still describe the original behavior of electric and magnetic phenomena. These are specially chosen so that we do not violate the already observed behavior.
In other words if we experimentally observe certain behaviors no matter what “gauge” function we chose to describe our phenomena we must see the same effect under the same circumstances. This is called a “symmetry under transformation” of physical laws. Symmetry refers to conservation of the same form of phenomena or same behavior while transformation refers to the ability to see the phenomena from a different perspective, a different frame of reference or a different situation.
The gauge functions are basically not in terms of a electric field (E), space around a electric matter or energy) or a magnetic field (B), space around a magnetic matter or energy; these latter functions are still vector or scalar quantites like the E, B field. Theory of Relatvity, the special kind as opposed to the general kind called Theory of Relativity: General is formulated in terms of these gauge functions as a fundamental field, more fundamental than teh E, B field. The gauge scalar function is denoted as Greek letter PHI and gauge vector function is denoted as Roman letter A. In this formulation E (as well as B) are functions of PHI and A. Specially Theory of Relativity says there are sets of laws that treats these gauge functions, PHI and A with equal importance; that is these two functions can be dealt in the same frame of reference so that the “set of laws” are valid without inconsistency. These laws in terms of B, E are not self-consistent. In other words B, E are not the fundamental fields but are special cases of PHI and A when the speed of various constituents that describe the phenomena is quite quite large to what we see on a day to day affair. B, E are valid only when the speed is quite less compared to the speed of light.
A photon is a particle that constitutes of functions of these PHI (scalar) and A (vector) functions. A photon is a function or more correctly a wave-function so that it satisfies the Schrodinger’s equation. It has both vector and scalar properties therefore, eg it’s spin 1 which says it’s a vector particle, but the fact that you can talk about number of photons means it’s a scalar properties of the particle. The catch is if you want to add photon numbers you can not directly do so without violating fundamental laws of nature; namely quantum mechanics or Schrodinger’s equation. SO more correctly a photon is a vector which is added like a scalar only when the number of photon is so large that the essential error you make in adding the photons is not practically a problem.
A photon for the same reason must not be connected to the E and B field directly unless the E and B field are perhaps so large that the number of photons is proportionately collosal. When the field are small we better be careful, it’s the amplitudes we are adding and not the number of photons. If you remember this from basic physics (Quantum field theory) a “photon” is an energy value of creation/anihilation operators, more appropriately the difference between the n’th and it’s penultimate state.
Now that we are careful how to deal with the photon, we can safely say when we rotate the magnets or electrically charged conductors we produce the photons. The larger the field value of electric and magnetic fileds the larger the number of photons we produce. It is only in that situation that a photon has enough energy to be produced and move at it’s will which is c=3×10^8 meters/sec. When the magnets and currents are small, as small as we observe in our day to day affairs it is difficult to say how many photons were produced without first calculting the entire complex configuration.
What happens is the electrons are the only freely available electric charge hence they carry away the energy available to them from the fields. A photon will carry the energy only if it is produced. It’s a misunderstanding that photons are necessarily produced when we rotate a magnet.
(I am not saying it’s not, but no one has calculated the exact laws)
The photons once produced all it’s energy is kinetic energy and it moves at the speed of light.
(a photon is by definition one that moves at speed of light to make the associated laws Lorentz invariant)
If it’s not produced there are other free charges such as electrons that carry away this energy. Electrons having “large” masses (not compared to the other particles but compared to how it will eat up the available energy) they can not move at a fast pace, as fast as photons. The lightening is an example that involves production of photons in some cases and no production in some cases, but there are plenty of other charges not just the electrons that carry away the PHI and A fields.