question: How can a photon move an electron if it has no mass?
comment: Photons are little packets of energy that electrons absorb. It doesn't *move* the electron so much as energizes it into a higher energy state. There really isn't a good analogy, it's just how photons work. When electrons absorb a photon, they move up in their energy levels - essentially, a higher "orbit" around their atomic nuclei. Solar panels work by putting together materials so that there's a sandwich of three things: a side with slightly too many electrons, a side with slightly too few electrons, and a material in the middle that doesn't conduct electrons very well but *can* under certain circumstances. Photons hit the side with slightly too many electrons, which energizes them into a higher "orbit" which is a bit farther away from the nucleus. That means the nucleus can't hold onto the electron quite as well - the electron is normally attracted to the positive protons in the nucleus, but the farther away the electron is, the less force there is pulling it towards the protons. So the electron is already kind of precariously whizzing around the nucleus, not held down super well. When it absorbs a photon and moves even farther away from the nucleus, it's really not being held by that nucleus much at all. That won't automatically make an electron leave, though, because the electron doesn't have anywhere to go. That's what the other side with slightly too few electrons is for. That energized electron now has somewhere to go, that has a slightly positive pull (because there are protons without matching electrons). So, poof, it zips across that semi-conducting barrier and *flows* to the other side. That creates a new hole where the electron used to be, so a new electron jumps into that hole. *That* electron leaves a hole, so an electron behind it jumps into *that* hole, and so and so forth so that when you connect the two sides of the solar panel material sandwich, you get get a circle of electrons getting bumped across the barrier and pushing each other into the empty spots left by those electrons.
passages: where "r" is the orbit radius, "m" is the mass of an electron, formula_2is the component of the electron velocity perpendicular to the field, "e" is the electron charge and "B" is the magnitude of the applied magnetic field. Electrons that have a velocity component parallel to the magnetic field will proceed along helical trajectories.
  
  Section::::Geometric electron optics.:Electric fields.
   Section::::Contributions to the mass of a system.
   Hence each of two electrons (A and C) in a head-on collision at 45 GeV in the lab frame (B) would see the other coming toward them at "v" ~ "c" and "w" = 88,000(1 + 1) ~ 1.55×10 lightseconds per traveler second. Thus from the target's point of view, colliders can explore collisions with much higher projectile energy and momentum per unit mass.
  
  Section::::Applications.:Proper velocity-based dispersion relations.
   Henri Poincaré in 1906 argued that when mass is in fact the product of the electromagnetic field in the aether – implying that no "real" mass exists – and because matter is inseparably connected with mass, then also matter doesn't exist at all and electrons are only concavities in the aether.
  
  Section::::Charged particles.:Mass and speed.
  
  Section::::Charged particles.:Mass and speed.:Thomson and Searle.
  
  Thomson (1893) noticed that electromagnetic momentum and energy of charged bodies, and therefore their masses, depend on the speed of the bodies as well. He wrote:
   Photon
  
  The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force (even when static via virtual particles). The invariant mass of the photon is zero; it always moves at the speed of light within a vacuum.
   where, "h" is Planck's constant, "m" is the rest mass of an electron and "E" is the energy of the accelerated electron. Electrons are usually generated in an electron microscope by a process known as thermionic emission from a filament, usually tungsten, in the same manner as a light bulb, or alternatively by field electron emission. The electrons are then accelerated by an electric potential (measured in volts) and focused by electrostatic and electromagnetic lenses onto the sample. The transmitted beam contains information about electron density, phase and periodicity; this beam is used to form an image.
  
  Section::::Background.:Electron Source.
   So, eventually Lorentz arrived at the same conclusion as Thomson in 1893: no body can reach the speed of light because the mass becomes infinitely large at this velocity.
  
  Additionally, a third electron model was developed by Alfred Bucherer and Paul Langevin, in which the electron contracts in the line of motion, and expands perpendicular to it, so that the volume remains constant. This gives:
  
  Section::::Charged particles.:Mass and speed.:Kaufmann's experiments.
   In empty space, the photon moves at "c" (the speed of light) and its energy and momentum are related by , where "p" is the magnitude of the momentum vector p. This derives from the following relativistic relation, with :
  
  The energy and momentum of a photon depend only on its frequency ("ν") or inversely, its wavelength ("λ"):
  
  where k is the wave vector (where the wave number ), is the angular frequency, and is the reduced Planck constant.
  
  Since p points in the direction of the photon's propagation, the magnitude of the momentum is
   A photon's momentum is a function of its energy, but it is not proportional to the velocity, which is always c.
  
  For an object at rest, the momentum p is zero, therefore
  
  The rest mass is only proportional to the total energy in the rest frame of the object.
  
  When the object is moving, the total energy is given by
   According to Einstein's theory of special relativity, as an electron's speed approaches the speed of light, from an observer's point of view its relativistic mass increases, thereby making it more and more difficult to accelerate it from within the observer's frame of reference. The speed of an electron can approach, but never reach, the speed of light in a vacuum, "c". However, when relativistic electrons—that is, electrons moving at a speed close to "c"—are injected into a dielectric medium such as water, where the local speed of light is significantly less than "c", the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light called Cherenkov radiation.
   Imaging methods in TEM use the information contained in the electron waves exiting from the sample to form an image. The projector lenses allow for the correct positioning of this electron wave distribution onto the viewing system. The observed intensity, "I", of the image, assuming sufficiently high quality of imaging device, can be approximated as proportional to the time-averaged amplitude of the electron wavefunctions, where the wave that forms the exit beam is denoted by Ψ.
   BULLET::::2. Electrons jump between orbitals like particles. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon.
  
  BULLET::::3. The electrons retain particle-like properties such as: each wave state has the same electrical charge as its electron particle. Each wave state has a single discrete spin (spin up or spin down) depending on its superposition.
   Ballistic transport is observed when the mean free path of the electron is (much) longer than the dimension of the medium through which the electron travels. The electron alters its motion only upon collision with the "walls". In the case of a wire suspended in air/vacuum the surface of the wire plays the role of the "box" reflecting the electrons and preventing them from exiting toward the empty space/open air. This is because there is an energy to be paid to extract the electron from the medium (work function).
   A particle whose rest mass is zero is called "massless". Photons and gravitons are thought to be massless; and neutrinos are nearly so.
  
  Section::::Relativistic dynamics.:Mass–energy equivalence.
  
  The relativistic energy–momentum equation holds for all particles, even for massless particles for which "m" = 0. In this case:
  
  When substituted into "Ev" = "c""p", this gives "v" = "c": massless particles (such as photons) always travel at the speed of light.
   The concept of messenger particles dates back to the 18th century when the French physicist Charles Coulomb showed that the electrostatic force between electrically charged objects follows a law similar to Newton's Law of Gravitation. In time, this relationship became known as Coulomb's law. By 1862, Hermann von Helmholtz had described a ray of light as the "quickest of all the messengers". In 1905, Albert Einstein proposed the existence of a light-particle in answer to the question: "what are light quanta?" 
   One important thing to know about force carriers is that a particular force carrier particle can only be absorbed or produced by a matter particle which is affected by that particular force. For instance, electrons and protons have electric charge, so they can produce and absorb the electromagnetic force carrier, the photon. Neutrinos, on the other hand, have no electric charge, so they cannot absorb or produce photons.
  
  Section::::Exchange of force carriers in particle physics.:History.
   Electrons are charged particles (point charges with rest mass) with spin 1/2 (hence they are fermions). Electrons can be accelerated by suitable electric (or magnetic) fields, thereby acquiring kinetic energy. Given sufficient voltage, the electron can be accelerated sufficiently fast to exhibit measurable relativistic effects. According to wave particle duality, electrons can also be considered as matter waves with properties such as wavelength, phase and amplitude.
  
  Section::::Geometric electron optics.
  
  Section::::Geometric electron optics.:Magnetic fields.
   where the Lorentz factor is formula_3. In this expression "m" is the "rest mass", or more simply just the "mass" of the electron. This quantity "m" is frame invariant and velocity independent. However, some texts group the Lorentz factor with the mass factor to define a new quantity called the "relativistic mass", . This quantity is evidently velocity dependent, and from it arises the notion that "mass increases with speed". This construction is optional, however, and adds little insight into the dynamics of special relativity.
  
  Section::::Determination.
   Electron mobility
  
  In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor, when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility.
  
  Electron and hole mobility are special cases of electrical mobility of charged particles in a fluid under an applied electric field.
   In 1934, Tolman argued that the relativistic mass formula formula_38 holds for all particles, including those moving at the speed of light, while the formula formula_39 only applies to a slower-than-light particle (a particle with a nonzero rest mass). Tolman remarked on this relation that "We have, moreover, of course the experimental verification of the expression in the case of moving electrons ... We shall hence have no hesitation in accepting the expression as correct in general for the mass of a moving particle."
   According to quantum theory, light may be considered not only to be as an electro-magnetic wave but also as a "stream" of particles called photons which travel with "c", the vacuum speed of light. These particles should not be considered to be classical billiard balls, but as quantum mechanical particles described by a wavefunction spread over a finite region.
   However, when an electric field is applied, each electron or hole is accelerated by the electric field. If the electron were in a vacuum, it would be accelerated to ever-increasing velocity (called ballistic transport). However, in a solid, the electron repeatedly scatters off crystal defects, phonons, impurities, etc., so that it loses some energy and changes direction. The final result is that the electron moves with a finite average velocity, called the drift velocity. This net electron motion is usually much slower than the normally occurring random motion.
   If an observer runs away from a photon in the direction the photon travels from a source, and it catches up with the observer—when the photon catches up, the observer sees it as having less energy than it had at the source. The faster the observer is traveling with regard to the source when the photon catches up, the less energy the photon has. As an observer approaches the speed of light with regard to the source, the photon looks redder and redder, by relativistic Doppler effect (the Doppler shift is the relativistic formula), and the energy of a very long-wavelength photon approaches zero. This is because the photon is "massless"—the rest mass of a photon is zero.
   Section::::Meanings of the strict formula.:Massless particles.
  
  Massless particles have zero rest mass. Their relativistic mass is simply their relativistic energy, divided by , or . The energy for photons is , where is Planck's constant and is the photon frequency. This frequency and thus the relativistic energy are frame-dependent.
   Section::::The photon as a gauge boson.
  
  The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime. For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of complex numbers of absolute value 1, which reflects the ability to vary the phase of a complex field without affecting observables or real valued functions made from it, such as the energy or the Lagrangian.
  
presuppositions: photons move electrons Photons move electrons.
corrections: It doesn't move the electron, it energizes the electron. Photons energize electrons to a higher energy state.
raw_presuppositions: photons move electrons Photons move electrons.
raw_corrections: It doesn't move the electron, it energizes the electron. Photons energize electrons to a higher energy state.