Why is not the state m=0 of a photon concerned in the discussion of EMW?
465906
The state m=0 is only true of a photon, of which Electromagnetic Waves are made, if it is at rest and unmoving. While photons are considered to have no inherent mass, mass is imparted by the velocity of the wave. Why isn't it taken into consideration? The "relativistic mass" of an object is really just the same as its energy, and there isn't any reason to have another word for energy: "energy" is a perfectly good word. For those who would insist that photons have no mass, I can only quote Einstein's  E=mc2. Since photons are energy carriers, and mass is one of the integral components of the equation, then the velocity at which the photons are moving (c) must impart mass to the photons or there would be no energy (E).
255127
Quantum theory suggest that no, it doesn't-- the observer affects the Universe.\n\nBut in a Newtonian, objective Universe, all the laws of physics should apply regardless of if there is an observer or not.\n\nI propose the falling tree is in an eigenstate like Shroedinger's cat: it is both making a sound and NOT making a sound.\n\nIf you aren't familiar with Shroedinger's cat, look it up and prepare to have your mind blown!
32300
sure.  the thing about entangled states is that while the state may collapse "instantaneously", that doesn't mean that information is necessarily transmitted.\n\nconsider 2 atoms in an entangled state.  alice takes one, and bob takes the other and gets on a rocket ship and flies to pluto.  when he gets there, he radios back to earth "ok, alice, i'm here!" and waits the 7 hours or whatever it takes for a response to come back at the speed of light.\n\nso once alice and bob get all settled, alice performs a measurement on her part of the entangled pair.  she gets |0> (in qubit notation) or whatever the state is, with a certain probability - say, 50%.  since alice and bob have agreed on a pre-determined time to do this, 10 minutes later bob measures his state.  \n\nnow, because the quantum system collapsed from a mixed state to an eigenstate when alice did the measurement, that means bob's state instantly collapsed too.  but bob has no *a priori* knowledge of what alice measured!  alice's measurement came with some certain statistical probability, and when bob does his measurement, he will get a result with the same probability, since his mixed state collapsed too.  so bob measures a |1> because alice already measured a zero, but he has no way of knowing what outcome to expect before the measurement.  so to bob, the result is a random outcome as well.\n\nthe point is that alice cannot *control* the outcome of her experiment - all she can do is measure it because of the random nature of quantum mechanical systems.  \n\nif alice were to perform her measurement, and then radio ahead to bob and say "hey bob, i got |0>" then bob could be certain that when he measures his state, he gets |1>.  but now information has not traveled any faster than the speed of light, for this is "classical" information traveling by radio.\n\nso, anyway, there you go.  this is a rather simplified and not very clear explanation.  this seeming paradox is called the "EPR paradox" after einstein, podolsky and rosen who considered its ramifications.  you can read more about it here:\nhttp://www.physlink.com/Education/AskExperts/ae634.cfm\nhttp://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html\nhttp://en.wikipedia.org/wiki/EPR_paradox
100061
Notwithstanding quantum mechanical effects from quantum field theory involved in photons escaping confined regions that I'm not qualified to answer in regards to, and supposing that you had *ideal* mirrors that reflected all of the incident energy of the photon and if you could seal the box (or probably a better aparatus would be a sphere) before your incident light beam escaped, then I believe the answer is yes.\n\nI'm fairly sure that this is not quite as theoretical as I've made it sound by invoking ideal mirrors and actually is practical.  I'm fairly sure that there is a research group here at my University working on storing information encoded in photons by basically trapping it between two mirrors to bounce back and forth until released for further processing.  I haven't been able to find a link to any research publications on that, but I'll update you if I locate one.\n\nI hope that helps.
820557
It's only a paradox if you think of particles and waves as distinct entities, which in quantum terms they aren't - they're waveparticles. This is somewhat unintuitive, but the UC Berkeley lecture video in the source below contains the clearest explanation I've seen yet.
388909
Photons are EM waves. They have the same speed.
361537
the entanglement can only exist if the wave function is undisturbed, so yes. if particle a is observed as having spin +1/2, particle b will be observed as having spin -1/2.
648100
CIH is spot on, but you should also realise from what he said that electromagnetic waves or particles are ways of describing and calculating what a photon will do, they are not the actual photon itself (whatever that is). \n\nSometimes it easy to think that the description of an object IS the object, especially if it fits it well. If it was possible to write an equation or model which fully described a motor vehicle, you still wouldn't be able to drive it to the shops, but you would be able to accurately descibe how it drove there.\n\nIsn't physics wonderful! Philosopy and science all neatly wrapped up in one unifying theory of lots of theories!
267019
Given:\nh = Planck's constant = 6.626*10^-34\nf = frequency = 7.5*10^14\n\nBinding Energy = h*f = 6.626*10^-34*7.5*10^14 = 4.9695*10^-19 Joules\n\n============================================================\nGiven:\nh = Planck's constant = 6.626*10^-34\nf = frequency = 7.5*10^14\nc = speed of photon = 3*10^-8 m/s\nWavelength of photon = 366 nm = 3.66*10^-7 m\n\nFrequency of photon = c/wavelength of photon = 3.3*10^-8/3.66*10^-7 = 0.090163934 /s\nEnergy of photon = h*f = 6.626*10^-34*0.090163934 = 5.97426*10^-35 Joules\n\n============================================================\nSorry, I'm actually at work. Not being able to concentrate too much on it.\n\nEnergy of photon should have been bigger than the B.E. of electrons. Try to figure out, why its not.\n\nDifference of the two energies would be the energy of the realsed electrons from the surface.\n\nWhen I'm done with work I'll check back and try to finish it up.\n\nHope you understand.
6613
Quantum physics predicts the existence of an underlying sea of zero-point energy at every point in the universe. This is different from the cosmic microwave background and is also referred to as the electromagnetic quantum vacuum since it is the lowest state of otherwise empty space. This energy is so enormous that most physicists believe that even though zero-point energy seems to be an inescapable consequence of elementary quantum theory, it cannot be physically real, and so is subtracted away in calculations. \n\nA minority of physicists accept it as real energy which we cannot directly sense since it is the same everywhere, even inside our bodies and measuring devices. From this perspective, the ordinary world of matter and energy is like a foam atop the quantum vacuum sea. It does not matter to a ship how deep the ocean is below it. If the zero-point energy is real, there is the possibility that it can be tapped as a source of power or be harnassed to generate a propulsive force for space travel. \n\nThe propellor or the jet engine of an aircraft push air backwards to propel the aircraft forward. A ship or boat propellor does the same thing with water. On Earth there is always air or water available to push against. But a rocket in space has nothing to push against, and so it needs to carry propellant to eject in place of air or water. The fundamental problem is that a deep space rocket would have to start out with all the propellant it will ever need. This quickly results in the need to carry more and more propellant just to propel the propellant. The breakthrough one wishes for deep space travel is to overcome the need to carry propellant at all. How can one generate a propulsive force without carrying and ejecting propellant? \n\nThere is a force associated with the electromagnetic quantum vacuum: the Casimir force. This force is an attraction between parallel metallic plates that has now been well measured and can be attributed to a minutely tiny imbalance in the zero-point energy in the cavity between versus the region outside the plates. This is not useful for propulsion since it symmetrically pulls on the plates. However if some asymmetric variation of the Casimir force could be identified one could in effect sail through space as if propelled by a kind of quantum fluctuation wind. This is pure speculation. \n\nThe other requirement for space travel is energy. A thought experiment published by physicist Robert Forward in 1984 demonstrated how the Casimir force could in principle be used to extract energy from the quantum vacuum (Phys. Rev. B, 30, 1700, 1984). Theoretical studies in the early 1990s (Phys. Rev. E, 48, 1562, 1993) verified that this was not contradictory to the laws of thermodynamics (since the zero-point energy is different from a thermal reservoir of heat). Unfortunately the Forward process cannot be cycled to yield a continuous extraction of energy. A Casimir engine would be one whose cylinders could only fire once, after which the engine become useless. \n\nORIGIN OF ZERO-POINT ENERGY \n\nThe basis of zero-point energy is the Heisenberg uncertainty principle, one of the fundamental laws of quantum physics. According to this principle, the more precisely one measures the position of a moving particle, such as an electron, the less exact the best possible measurement of momentum (mass times velocity) will be, and vice versa. The least possible uncertainty of position times momentum is specified by Planck's constant, h. A parallel uncertainty exists between measurements involving time and energy. This minimum uncertainty is not due to any correctable flaws in measurement, but rather reflects an intrinsic quantum fuzziness in the very nature of energy and matter. \n\nA useful calculational tool in physics is the ideal harmonic oscillator: a hypothetical mass on a perfect spring moving back and forth. The Heisenberg uncertainty principle dictates that such an ideal harmonic oscillator -- one small
614021
zero-point energy \nIn a quantum mechanical system such as the particle in a box or the quantum harmonic oscillator, the lowest possible energy is called the zero-point energy. According to classical physics, the kinetic energy of a particle in a box or the kinetic energy of the harmonic oscillator may be zero if the velocity is zero. Quantum mechanics with its uncertainty principle implies that if the velocity is measured with certainty to be exactly zero, the uncertainty of the position must be infinite. This either violates the condition that the particle remain in the box, or it brings a new potential energy in the case of the harmonic oscillator. To avoid this paradox, quantum mechanics dictates that the minimal velocity is never equal to zero, and hence the minimal energy is never equal to zero.\n\n\nA few formulae\nA particle in a box is defined by the potential energy\n\nV(x) = 0 for  \nwhich is defined to be infinite for . The wave function with the minimal energy eigenvalue is then\n\nψ(x) = Csin(πx / l) \nwhere C is an important normalization constant. The (zero-point) energy of this wave function is pure kinetic and equal to\n\n \nwhich is non-zero. Similarly, the zero-point energy of the quantum harmonic oscillator with the frequency ω is equal to\n\n \nBoth of these simplest cases have a useful generalization to the case of quantum field theory. Quantum field theory - such as Quantum Electrodynamics - may be regarded as a collection of infinitely many harmonic oscillators, and quantum mechanics therefore predicts a nonzero vacuum energy. Although the absolute value of the vacuum energy is partly a matter of convention, the difference between the vacuum energy of various configurations has a physical meaning.\n\n\nExistence\nDoes electromagnetic zero-point energy exist, and if so, are there any practical applications and does it have any connection with dark energy? The theoretical basis for electromagnetic zero-point energy is clear. According to Sciama (1991):\n\n"Even in its ground state, a quantum system possesses fluctuations and an associated zero-point energy, since otherwise the uncertainty principle would be violated. In particular the vacuum state of a quantum field has these properties. For example, the electric and magnetic fields in the electromagnetic vacuum are fluctuating quantities." \nThe Casimir effect is an example of a one-loop effect in quantum electrodynamics that can be simply explained by the zero-point energy.\n\n\nHistory\nThe concept of zero-point energy originated with Max Planck in 1911. The average energy of a harmonic oscillator in this hypothesis is (where h is Planck's constant and ν is frequency):\n\n \nAt the same time Einstein and Hopf (1910) and Einstein and Stern (1913) were also studying the properties of zero-point energy. Shortly thereafter Nernst (1916) proposed that empty space was filled with zero-point electromagnetic radiation. Then in 1925 the existence of zero-point energy was shown to be “required by quantum mechanics, as a direct consequence of Heisenberg's uncertainty principle” (Sciama 1991). As any textbook on quantum optics will show (e.g. Loudon 1983), the way to quantize the electromagnetic field is to associate each mode of the field with a harmonic oscillator with the result that the minimum energy per mode of the electromagnetic quantum vacuum is hν / 2 .\n\n\nProblems and answers\nZero-point energy shares a problem with the Dirac sea: both are potentially infinite. In the case of zero-point energy, there are reasons for believing that a cutoff does exist in the zero-point spectrum corresponding to the Planck scale. Even this results in an enormous amount of zero-point energy whose existence is assumed to be negated (in spite of the unmistakable mandate of the Heisenberg uncertainty principle) by the claim that the mass equivalent of the energy should gravitate, resulting in an absurdly large cosmological constant, contrary to o
827091
Hi. I think it deals more with the interaction of radiation with particles (or a particle) than with speed. At any non-relativistic speed (less than .1 'c' say) the wavelength would not be infinite or unbounded. Just my opinion.
85622
His system is a total hoax. But one hoax does not rule out ZPE all together. \n\nIn a quantum mechanical system such as the particle in a box or the quantum harmonic oscillator, the lowest possible energy is called the zero-point energy. According to classical physics, the kinetic energy of a particle in a box or the kinetic energy of the harmonic oscillator may be zero if the velocity is zero. Quantum mechanics with its uncertainty principle implies that if the velocity is measured with certainty to be exactly zero, the uncertainty of the position must be infinite. This either violates the condition that the particle remains in the box, or it brings a new potential energy in the case of the harmonic oscillator. To avoid this paradox, quantum mechanics dictates that the minimal velocity is never equal to zero, and hence the minimal energy is never equal to zero.\n\nBut if Zero-point energy refers to quantum fluctuations of the electromagnetic force fields that are present everywhere in a vacuum. That's energy in a Vacuum? Free Energy! Whoo Hoo! Right? Well obviously this hasn't happened. When I originally put together a Zero Point Energy page for this site, ZPE's promise to be a viable source of power was unclear at best. More recent knowledge in the area makes it clear that although ZPE does exist (maybe) it's probably not the kind of thing your going to power a car with let alone a StarGate. Current research points to the total amount of ZPE that is harnesable being very low, perhaps being zero. The rest of ZPE in the universe is by it's very definition not something you can tap into. If you are looking for more detail, there is a fairly readable page on the subject over at the Scientific American web site.  This is not to say that very very small amounts of power aren't just the thing in certain applications. Quantum Fields LLC is doing research toward using ZPE to power microscopic electro mechanical systems. So the field isn't dead yet, just don't expect to replace you car engine with a magic ZPE engine. So here a thing they are working on over at Quantum Fields, they call it a MEMS oscillator. No clue what it is or even if they have built a real one or not, but there you go...
1171479
To add to debraj's answer, it may help to realise that light has the property of a particle when we force it to stop moving but the property of a wave when it is moving.\n\nIt isn't entirely accurate, but one way to visualise that is to imagine light as wave moving across a still pond. The wave itself has no mass, it is simply a disturbance in the medium (water). But when a wave strikes a massive object it can impart its momentum to that object and thus effectively increase the object’s mass.\n\nLight is also basically a disturbance in a medium, in this case the medium is space-time. While it is moving a photon has no mass of its own (since it only exists as a disturbance). Its existence and movement can only be known by reference to the base energy state of that particular point in space and the change that the passing photon produces. We know the photon exists because it disturbs the base state of a point in space as it passes through that point.\n\nBut when the disturbance strikes a massive object it disturbs that object. That disturbance changes the energy state of the massive object, and since any increase in energy also causes an increase ein mass the struck object becomes more massive. \n\nSo light behaves as though it has mass when we force it to interact with massive objects because mass and energy are interrelated. A photon has virtual mass under those circumstances because it has energy. But the photon itself never truly had mass, it only gained massive properties at the point that it ceased to exist as photon, ie after it collided with a massive object.\n\n(Caveat: that explanation is almost entirely untrue. But all verbal descriptions of quantum and relativistic effects are almost entirely untrue. However it is a very good lie and for the point you are at. Once you understand that lie you can then move onto the next stage, which really does demand mathematical descriptions.)
497395
1.\nBecause e to the power minus infinity is 0.
258518
Your analogy doesn't represent the problem at all.  \n\nWhen we say a particle is treated as a wave it refers to the particle actually not existing at any particular point.  It actually exists at all of points in some region with a certain probability (it is everywhere at once).
690504
in its present form, it can't describe the state of the universe at time=0.  Thus, it doesn't answer the question of where did all the mass and energy come from