I have asked this elsewhere years ago and combed the internet and never found an answer aside from how its derived mathematically. My question is, why would velocity be squared in E=mc^2? How can the energy be greater than mass x maximum possible velocity? Also, a photon is considered a massless particle (m=density*volume) so either it has no density or no volume? If it is massless E=0c^2, we know multiplying by zero equals zero so a massless photon should have zero energy. However, we know this cant be true because photons produce a force (see Crookes radiometer). Anyone have some insight?
Aside from linear velocity the only other velocity the mass is imparting is spin. If this is correct can we say particles spin at the speed of light?
Even in non-relativistic physics, certain forms of energy of a particle involves the square of its velocity For example, the kinetic energy of a particle is mv<sup>2 </sup>/ 2 . Radiation pressure in general isn't a relativistic mass-energy transformational effect. It occurs as the result of the magnetic component of the electromagnetic field of the photons interacting with the electrical charges that it is impinging upon - namely, the electrons in the atoms of the material the photon is interacting with. The direction of the Lorentz Force thus produced, being a cross product - q(v x B) - is in the direction of the propagation of the photon and thus produces a slight force (or change in momentum) in that direction.. Electron, above, in target atom is moving according to vector v. A photon with oscillating E and B fields moves from S in z direction, interacts with electron at the origin. The magnetic B-field portion of the interaction with the moving charge produces a Lorentz force, F, in the direction shown and according to F = q(v x B), where q id the charge of the electron, v is the electron's instantaneous velocity vector, and B is the photon's instantaneous magnetic field vector. You can read more about this force or pressure in Feynman Lectures, Vol 1: The momentum of light This is true radiation pressure as opposed to the effect displayed by Crooke's Radiometer, which is explained better by such thermodynamic considerations as "thermal transpiration". True electromagnetic radiation pressure isn't of sufficient strength to drive the vanes of the various radiometer devices such as Crooke's even though they are frequently used for that purpose.
Well parta of your equations show up as smiley faces with sunglasses lmao. Idk what to do about that since i use GC app. Anyway, unless in my ignorance i missed it, your response just touches on my photon mass question not the first question? Also that picture is a gif, so its supposed to move right? Cant see gifs either lol. So in regards to the radiometer you are saying indeed photons have no mass but the heat is the cause of its movement? Ty for the reply and i appreciate in advance for your patience.
Photons have mass. They don't have rest mass, but they have relativistic mass. Einsteins equation isn't just E=mc^2, that's the shortened popular version that isn't scientifically accurate for what you are asking. Its actually E=m[rel]c^2. So you see, you wouldn't be multiplying by 0 in that equation because everything has mass.
E=mc^2 means energy and mass are inter-convertible. So a photon with a certain energy can, in principle, be converted to mass, and vice versa (hence why nuclear fission/fusion give off so much energy). So instead of saying the photon has zero mass and solving for E, you should be plugging in the energy of the photon for E and solving for m to give you relativistic mass. Look up a derivation for E=mc^2 to see why the c is squared. It also ensure the units on both sides of the equation are equivalent.
Thanks guys. A photon has no rest mass because it is never at rest correct? As far as e=mc^2 i am not so much interested on how its derived (ive seen that plenty). I want to know why its c^2 and not c. What is that telling us? Am i wrong about it accounting for spins?
Sort of. Nothing is ever at rest because all motion is relative. That's why its called relativity. -yuri
When an object is at rest (relative to the observer), it has the usual (inertial = tendency to resist an applied force) mass that we are all familiar with. It's c^2 because of velocity. Check constant acceleration under Equation of motion. https://en.wikipedia.org/wiki/Velocity
But how could it be linear velocity alone when its constant velocity is just c? Spin would be calculated with angular momentum so it must play a part in its total energy. A top at rest cannot have the same energy as a top in motion, even if it isnt travelling in any x direction. Btw my analogies are to help me pull out the answer and understand it, not to be argumentative. As i said ive looked high and low for a satisfactory answer and havent found one thats why i brought the question here
Also Markus, that link mentioned velocity in a straight line, but straight lines are a concept not a reality (assuming space is curved). Even photons corkscrew as the propogate (or is that just a special case as with an optical vortex)?
c^2 in E=mc^2 represents the velocity limit, which is the velocity of the speed of light. Since it's a constant, the speed and velocity of light are exactly the same. Check out these two links (Specifically the second link): http://www.emc2-explained.info/Emc2/Derive.htm#.VVK5PxiYLAo http://www.emc2-explained.info/Emc2/Deriving.htm#.VVK6YBiYLAo
Again though, the derivation only shows how its obtained mathematically, it doesnt tell me what it relates to. How can c^2 be a velocity when its maximum velocity is the square root of c^2 (or just c)?
I'm not sure what kind of an answer you are looking for. I would imagine c^2 is squared for the same reason kinetic energy is proportional to velocity^2.
I'm pretty sure this is just not accurate Norse. As everyone has said there are plenty of instances in physics where the velocity squared is related to energy like kinetic energy. No one ever says that speed is the speed of light squared. What people are saying is that the energy is proportional to the product of mass and c^2, not that it actually is moving at a velocity of c^2, because I'm pretty sure that's physically impossible. I haven't taken too much advanced physics but I touched on this concept a little in chemistry. From my understanding the idea is basically just how matter is converted to energy and vice versa, but I'm sure that's a vast oversimplification. Have you ever heard of an idea called mass defect and binding energy. If not I would definitely check it out and it may help you answer some of your questions. Feel free to disagree with me, like I said physics isn't my area of expertise.
c squared is merely a constant of proportionality in relating total energy to mass. Don't think of it as a velocity. It has units of distance squared divided by time squared.(meters<sup>2 </sup>/ seconds<sup>2</sup> in the MKS system). That isn't a velocity and should never be thought of one. It's a number that relates two physical quantitities with appropriate units to relate the units of mass and energy. Also, photons are massless. They are quantized bundles of electromagnetic energy. They possess energy given by E = hf where h is Planck's Constant and f is the frequency of the oscillating E-B fields of the photon. The electric field and magnetic field co-produce each other as changes in the one produces the other and vice versa. Neither field possess mass alone, nor do they possess mass in combination. However, an E-B field can interact with massive electric charges (such as electrons and protons) and produce changes in their motion. That's what E and B fields do - affect the motion of electrical charges. Also, changes in one field affects the amplitude of the other. The fields affect the motion of massive charged particles even though the fields themselves are massless. The fact that they can produce changes in the motion of charged, massive bodies means they do can work on them and thus possess energy. But only the electric field components of the photon can do work since the magnetic field is ALWAYS perpendicular to the instantaneous velocity of the charge being influenced. A photon affects the motion of an atom in a Crooke's Radiometer when the photon's magnetic field shoves one of its electrons at right angles to the electron's velocity, which is also in the direction of the photon's trajectory. The magnetic field produces the radiation pressure on the atom but does zero work in its "efforts". The magnetic force produces motion of a charged particle at right angles to both the B-field magnetic force as well as the direction of motion of the charged particle and thus does no work. Strange deal, but true. When mass is converted to energy, for example in nuclear fission or fusion reactions, there is a little less mass afterwards than before. The difference ("mass defect") has been converted to electromagnetic energy - gamma radiation in this example - and the conversion is according to E=mc<sup>2</sup> where the c<sup>2 </sup>is the constant of proportionality that relates the quantities. The equation only has relevance when conversion between energy and mass or vice versa occurs. Matter-energy conversions only occur in certain subsets of physical interactions. For all of this we really need to ask what we even mean by the term "mass". For starters, think of it as a body's resistance to a change in motion when some force is applied. We apply a force to a body and get a resultant change in velocity. The mass is the ratio of these two In that regard it becomes another proportionality constant that relates a given quantity of applied force and a resultant change in motion (change in velocity). Maybe next post...