strategicman
061703, 05:42 PM
Hey, I'm just wondering why in E=mc^2, the speed of light is squared. Could somebody just try to explain it all? Thanks.

View Full Version : In E=mc^2, why is the speed of light squared? strategicman 061703, 05:42 PM Hey, I'm just wondering why in E=mc^2, the speed of light is squared. Could somebody just try to explain it all? Thanks. Mystech 061703, 06:33 PM It's squared because you're supposed to multiply it by itself in the equation ^.^ *Capitan obvious zooms off into the clouds* That is a good question, though why are you supposed to multiply the speed of light by itself? And why represent the speed of light with a variable, when it is a constant? Guess that's just so you can decide what units you want to work in *shrug* strategicman 061703, 06:45 PM lol, thanks captian obvious! But how could Einstein have thought of something like that? how would he have just thought "hey, it's not working when I use E=mc so I should square "c"". I just don't see how. ::shrugs:: Nasor 061703, 06:47 PM Originally posted by Mystech And why represent the speed of light with a variable, when it is a constant? Guess that's just so you can decide what units you want to work in *shrug* Usually in mathematics letters at the beginning of the alphabet (like C) are used to denote constants, while letters at the end of the alphabet (X,Y,Z) are used for variables. tempusme 061703, 08:08 PM Energy = Mass * Speed of light ^ 2 J = kg * m^2/s^2 J = (kg * m/s^2)*m J = N * m J = J But this might not be what you're looking for... James R 061703, 08:46 PM tempusme is right. If you're going to relate energy to speed and mass, the only way to do it is to have and equation of the form E=kmc<sup>2</sup>, where k is a dimensionless constant. That's necessary for the units (dimensions) on both sides of the equation to match. If we choose consistent units to define E, m and c, then k turns out to be equal to 1. one_raven 061703, 09:02 PM I think it has to do with the inverse square law. I am not a mathematician (if you want an answer from a mathematician, you should post this in the Physics and Math forum), however... When light propagates, it does so in much the same way that sound does. It does not go in a straight line, it does so omnidirectionally. It spreads out in all directions at once, and at a constant speed. Therefore, at any given time, if you follow light propagating from a single point, the light would spread evenly in all diorections, so the "front" of the light wave will be in the shape of a sphere. (see attachment. NOTE: Not my image, I stole it from somewhere, but I don't want to steal credit) All energy (includiong light) travels via electromagnetic waves and the Inverse Square Law applies to all energy propagation. Since the formula for the surface of a sphere is 4(pi)r^2, and light propagates in the shape of the face of a sphere I think that is where the ^2 comes from. I don't yet have the ability to break it down for you matematically (still learning the math behind it), but I think this is where the connection lies. Wish I could be of more help than that, but I am still trying to figure it all out myself. As I said, you would likely have a much better response from the Physics and Math forum. Good luck. (Q) 061703, 09:43 PM I'm just wondering why in E=mc^2, the speed of light is squared. Because at that speed (c^2) mass and energy are indistinguishable from one another. James R 061703, 11:49 PM Actually, the c<sup>2</sup> has nothing to do with the inverse square law. In the equation E=mc<sup>2</sup> it also has nothing to do with the speed of anything. It is merely a numerical conversion factor. rapid transit 061803, 12:07 AM http://www.tardyon.de/luxon.htm This guy presents an interesting theory. In his view it works out to e = pc where p = mv (momentum). It's hard to explain. Just read the site. :) Myq 061803, 05:06 AM Due to momentum conservation arguments in special relativity theory, you can get a formula for how the mass increases with velocity of an object. If you assume that the Rest Energy of mass can only vary with the first power of M (makes sense, double the mass double the massenergy), you can then use a low velocity limit to show that the constant in front of mass should be C^2 and only C^2. It works out in units, it works out in relativity, and in the low velocity limit, you get what you should expect: E=1/2mV^2 + mC^2 tempusme 061803, 07:04 AM Originally posted by rapid transit http://www.tardyon.de/luxon.htm This guy presents an interesting theory. In his view it works out to e = pc where p = mv (momentum). It's hard to explain. Just read the site. :) Also, E=hf. E=pc would be the same thing as e=mc^2, if v=c. (Q) 061903, 11:09 PM James In the equation E=mc2 it also has nothing to do with the speed of anything. I was watching an interview with Einstein (black and white) some time ago when someone in the crowd posed this question. That was the reply he gave. It caught me completely off gaurd. If I find the interview, I'll post a reference. Gifted 062403, 11:14 AM And why represent the speed of light with a variable, when it is a constant? Becuase it's easier to write/say C (one digit) rather than 186,000 mi/sec (thirteen digits). Mystech 062403, 03:48 PM Originally posted by Nasor Usually in mathematics letters at the beginning of the alphabet (like C) are used to denote constants, while letters at the end of the alphabet (X,Y,Z) are used for variables. Ahh, thanks for that. I myself am something of a mathematical moron, so I appreciate that. Every little bit helps, seeing how as I am required to take more math credits than I can handle to get the degree I'm going for, heh. errandir 070203, 02:54 PM The paradigm for a contravariant tensor is the differential displacement 4vector. The first term is the time term. The speed of light is the relationship between time and space. The energystrees tensor is a symetric second rank tensor. Since the paradigm contains a c in the first term, and since the stress tensor is symetric, then it follows that there should be a c^2 in this term in the stress tensor, which is basically the E = mc^2. To be more specific, the stress tensor is the product of the current density 4vector with the proper velocity 4vector. The 0th component of the current density is pho*c. The 0th component of the velocity is just c. Therefore, in the product, the 00 component is just rho*c*c = rho*c^2. This is just the mc^2 per unit mass. I don't remember the exact consequence of the top of my head, but I know that, if you just use mass instead of density, you will wind up with something that has ugly transformation properties. myhr 070703, 02:24 PM Einstein's theory of relativity isn't the formula E = m*c^2 , though it is the most known consequence of it. He actually set out to think about how would different observers (with different velocities) observe (or measure) the same mechanical and electromagnetical phenomena. From this he discovered formulas for addition of velocities, time dilation, length contraction, etc. In the end he also noted that in the limit of zero velocity the inertia (that is: mass) of a body is E/c^2. If I remember correctly the formula is never stated in the form E = m*c^2 in the original paper (which can by the way be found at http://fourmilab.to/etexts/einstein/E_mc2/www/) apolo 071203, 12:35 AM STRATIGIGMAN is posing a good question a real good question Why is energy equal to the mas multiplied by the speed of light multiplyed by itself ?? I have always asumed this formula to be corect,the bedrock of relativity theory. It basically says, that if you convert mas into pure energy, you get a hell of a lot of enenergy. (as in the atomic bomb) or in the fueson reaction in the sunH to He. As far as I know Einstein did not arive at this formula by experimentation or observation. It was a postulate ! My question is; Has anybody ever coroborated this by actual experiments PS. I'll read your answer JAMES R and I wont argue.(At least not on this subject) James R 071203, 02:56 AM <i>Has anybody ever coroborated this by actual experiments</i> Yep. It is verified in nuclear reactions and in accelerator experiments. Janus58 071203, 01:59 PM Originally posted by apolo STRATIGIGMAN is posing a good question a real good question Why is energy equal to the mas multiplied by the speed of light multiplyed by itself ?? I have always asumed this formula to be corect,the bedrock of relativity theory. It basically says, that if you convert mas into pure energy, you get a hell of a lot of enenergy. (as in the atomic bomb) or in the fueson reaction in the sunH to He. As far as I know Einstein did not arive at this formula by experimentation or observation. It was a postulate ! No, it is not a postulate in itself, but a natural conculsion of the postulates of Relativity, That the physical laws in all frames are the same, and that the speed of light in a vacuum is a constant. These two postulates lead naturally to the Lorentz contractions, t = t'/sqrt(1v²/c²) x = x sqrt(1v²/c²) If you reevalulate the classical formula E= mv²/2 taking these transformations into effect you get: E= mc²/sqrt(1v²/c²) Expanding this equation gives: E = mc² + mv²/2 + 3mv^4/8c² + .... Note that if v=0, we are left with the famous E=mc² Which is the potenetial energy content of the mass at rest. Also, if 0 < v <<c, everything from the third term on becomes insignificant and can be ignored, leaving E= mc²+ mv²/2 In normal circumstances, we are only interested in that part of the energy which is due to motion, so we get: E= mv²/2 Which is why we can still use the classical formula for kinetic energy in most common situations where v<<c. Gifted 071203, 04:22 PM Which is why we can still use the classical formula for kinetic energy in most common situations where v< Where V is less than what? Janus58 071203, 04:43 PM Originally posted by Gifted Where V is less than what? There should be another "less than" symbol and a 'c' following the "0 'less than' v 'less than' " and "v 'less than' " in my posts to represent "much less than c" The board must assume that the second 'less than' symbol is the start of a HTML tag, and thus fails to show it and the following text. sir Mojo Loren 072003, 02:25 PM [this proof is found in Max Born, “Einstein's Theory of Relativity,” pp 218222, 1962] "Einstein’s equation e=mc2, which states the proportionality of energy and inertial mass, is perhaps the most important result of the theory of relativity. We shall give another simple proof of it, due to Einstein himself, a proof which does not make use of the mathematical formalism of the theory of relativity. ( ) It is based on the fact that radiation exerts a pressure. From Maxwell’s field equations, supplemented by a theorem first deduced by Poynting (1884), it follows that a light wave which falls on an absorbing body exerts a pressure on it. It is found that the momentum transferred to an absorbing surface by a short flash of light is equal to e/c, where e is the energy of the light flash. This fact, which we will prove in the following section, was confirmed experimentally by Lebedew (1890) and again later with greater accuracy by Nichols and Hull (1901) and others. Exactly the same pressure is experienced by a body which first emits light, just as a gun experiences a recoil when a shot is fired." [ .... followed by the mathematical formalisms and diagrams and then...] Suitable calculations should now show that E = MC^2 [...] The vagueness of “proofs” based on unwarranted “assumptions”, using as experimental tools items such as light and heat and mass and energy whose ultimate nature was a total mystery, could have led only to the type of flagrant errors that now exist in the world of the theoretical mathematical physicists who constantly and uncritically permit and use such tactics. Though entropy and the second law of thermodynamics make it hard to accept this “proof” as valid, we are glad to discover that even this last stronghold of the Theory of Relativity, i.e., e = mc2, is independent of that fourdimensional Moebusinversion of logic and could have been assumed from classical physics." from The Orb by du Gabriel  www.anpheon.org John Connellan 073003, 12:20 PM Also, c is not actually constant! Changes in different mediums Janus58 073003, 01:43 PM Originally posted by John Connellan Also, c is not actually constant! Changes in different mediums Yes, c is always constant. c refers to the speed of light in a vacuum alone, and is not used to denote the speed of light in other mediums. John Connellan 073103, 04:17 AM So true, sorry bout that  a bit too hasty! Dalo 112604, 03:21 PM Hi, I'd like to clear up a few issues regarding Einstein's famous equation, E = mc². Section 1: Where did E = mc² come from? Let's see... Energy is some silly abstract idea which helps physicists keep a tally to help them solve their problems. You may recall that they have defined energy to by the product of force and distance: E = ∫F(x) · dx Ok, we all know that force (another abstract idea) is given by the product of the mass of an object and the acceleration its experiencing. Since the acceleration is given by the derivative of the velocity (with respect to time), we can write F = ma = m(dv/dt). We can plug in the second equation into the first (by substitution), and rearrange a little, to arrive at a third equation: E = ∫m(dv/dt)·dx = ∫m(dx/dt)·dv = ∫mv·dv Now, if we were to integrate right here, we would arrive at the classical mechanical formula for kinetic energy, E = ½mv². However, this would not take relativity into account. We must use another relationship of special relativity m = m0/√(1v²/c²). Ok, where the heck did this come from, and what does it mean. Ok, we all know that, according to speical relativity, as you travel faster and faster, time slows down. However, two other things occur at the same time (the reason why this is not well known is a mystery). The travelling vehicle shinks lengthwise (the length contraction effect), and the travelling vehicle gets more massive (not bigger, it just starts to weigh more)! Its the later effect that's being described by the equation above. In words the equation says, "the new mass of the object is equal to the rest mass of the object divided by the sqaure root of stuff." Ok, enough of that, we simply plug this ugly equation into our equation that we have been working on, and arrive at E = ∫m0v/√(1v²/c²)·dv. Ok, to finish things up, we integrate the right side of the equation (with the limits being 0 ―>v) Integration by trigonometric substitution will work best here (or a TI89, or Mathematica will do nicely). E = c²m√(1v²/c²) Since m√(1v²/c²) = m0, we arrive at Einstein's famous equation, E=mc². (Note, the 0 on m has been dropped for aesthetic purposes) geodesic 112704, 12:22 PM Is there any link here with E=mc^2 and c^2 = mu 0*epsilon 0? (Permeability and permitivity of vacuum) Dalo 112904, 08:21 AM Listen Einstein considered that the speen of light in vaccum is constant but i don't think so i'm doing some researches adn experiments in college about it and when i get to anything new i'll inform u about it Starman 112904, 06:43 PM Hey, I'm just wondering why in E=mc^2, the speed of light is squared. Could somebody just try to explain it all? Thanks. Einstein wanted to express his theorys so that the layman could understand. E=mc^2 is the relation of energy, Mass, and Light. All mass is energy in it's stored state. Mass must be multiplyed by the speed of light squared to quantify the amount of energy the mass contains. Ophiolite 113004, 02:19 PM Listen Einstein considered that the speen of light in vaccum is constant but i don't think so i'm doing some researches adn experiments in college about it and when i get to anything new i'll inform u about it Why don't you think so? FatalError 021906, 11:04 PM haha well u can put E=MC^2 as E=PC where P = momentum n c is speed of light as usual Then P can also = MV there4 E=MVC whereas V is the velocity of a photon which travels at the speed of light coz its light energy so there 4 u can subsitute V as C and making E=MCC then E=MC^2 Hurricane Angel 022006, 03:08 AM It is squared because that's how much potential energy there is within matter. You know... like an anhilliation between particles and antiparticles? Essentially you can turn energy into matter but that's quite impossible. CANGAS 022306, 12:10 AM Maxwell defined c as the mathematical result of a specific relationship between the permeability and the permittivity of whatever medium electromagnetic waves are travelling through. He did this about a half century before Einstein felt like it would be neat to postulate c to be constant. Does anybody know what an index of refraction is? Hurricane Angel 022606, 11:19 PM An index of refraction is the speed of electromagnetic radiation travelling through a given object w/ respect to a vacuum. This is unrelated to the constant c because of what happens at the microstate as the radiation travels through the object. As the radiation passes through the object theres a slight disturbance that occurs within the object's electrons, and then this oscillation gives off a radiation of the same frequency as the original source, but this radiation has been delayed. So essentially its a stopgostopgo situation, and c remains the same. Nasor 022706, 08:44 PM Essentially you can turn energy into matter but that's quite impossible. No it's not. You can expend energy to make elementary particles. Hurricane Angel 022706, 11:30 PM How can this be accomplished? CANGAS 022806, 12:16 AM "Essentially you can turn energy into matter but that's quite impossible." Somebody's participle is dangling out in the open, or, something like that. ..."but THAT'S quit impossible.".... To what is "THAT'S" referring? Pair annihilation and pair production are symmetrical reactions which are very well proven in both theory and practice and which perfectly illustrate conversation of mass into energy and energy into mass. Which THAT is posted as claimed to be impossible? Singularity 022806, 12:19 AM Doesnt that show theres something wrong with the whole theory ? CANGAS 022806, 12:51 AM Huricane Angel is obviously perplexed by the problem analgous to deciding which came first, the chicken or the egg? First, Maxwell rigorously devised a wave equation that explained the velocity of his newly theorized electromagnetic waves as being exactly related to the permeability and permittivity IN WHICH THE WAVES ARE TRAVELLING. His work was exactly mathematically and logically consistent with all experimental observations performed up to that time in the fields of electricity and magnetism. Second, or, next, or something like that, Einstein invented out of thin air the POSTULATE that all observers may observe the identical speed for c. Does anyone here know the difference between a rigorously derived mathetmatical equation and a POSTULATE? The meaning of the word POSTULATE might be found in some dictionaries. Hurricane Angel 022806, 12:54 AM So why did you bring up index of refraction? Did you hope someone wouldn't know that the electromagnetic radiation doesn't actually slow down, and that it proves that c isn't a constant? CANGAS 030106, 01:57 AM Are you not aware that there are many circumstances in which the electromagnetic radiation does actually slow down? I never hope that someone DOES NOT know something. I always hope that everyone knows everything that is true. I really believe that the truth WILL SET YOU FREE. Whether or not the velocity of light in vacuum is a constant has definitely not been conclusively proven pro or con. It is a definite historical fact that the only conclusive basis at present for calling it a constant is that it has been called a constant. Muslim 030106, 05:05 AM This is all bs. Weak Greek Stuff. Maths is b.s is all abstract shit, it was invented by the Greeks so they could talk shit all day. Hurricane Angel 030106, 03:13 PM Are you not aware that there are many circumstances in which the electromagnetic radiation does actually slow down? I never hope that someone DOES NOT know something. I always hope that everyone knows everything that is true. I really believe that the truth WILL SET YOU FREE. Whether or not the velocity of light in vacuum is a constant has definitely not been conclusively proven pro or con. It is a definite historical fact that the only conclusive basis at present for calling it a constant is that it has been called a constant. But this still doesn't explain to me how electromagnetism can slow down at any point. My explanation was of that "phase delay", but you're talking philosophy. If you want to get right down to the quantum mechanics of it, well; string theory states that light is a vibration from the 6th dimension. Meaning it's not possible to be slowed down by anything within our four dimensions. I'm open to be rebutted, and change my mind. CANGAS 030206, 02:10 AM If you really are open to be rebutted then you should have already done your own homework. Take a deep breath and hold it until I do your homework for you. There is a 150 year history of theory and experiment showing EM slowing down. String theory is taking its last gasp of breath. Just how much of an expert are you on ST? Hurricane Angel 030206, 02:15 PM No I was open to be rebutted, not open to go study on my own, because I have already done that and what I've learned contradicts you. So the ball is in your court. And I've read two books on superstrings, not supertechnical, but up to date. CANGAS 030306, 01:09 AM Any information about string theory that is REALLY up to date tells all of us that it it is in a coma and is not expected to recover. Hurricane Angel 030306, 01:13 AM So you're a fan of which model of the universe? CANGAS 030306, 01:20 AM I am presently exploring absolute space. When you have more statements than questions it might be possible to resume dialogue. Until then, CANGAS has left the building. Hurricane Angel 030306, 01:30 AM Your arrogance is misdirected, I can't give you good questions unless I know where you stand on related topics. Nasor 030306, 04:09 PM How can this be accomplished? A bit late in my answer, but: If you collide particles together that are traveling at very high velocities, some of the energy dissipated in the collision will go toward creating new particles. That's how antimatter is usually produced. There might be other schemes for converting energy to matter, but that's the only one I know of off the top of my head. crazeeeeeem 030306, 10:01 PM Thought it was something like kinetik energy = 1/2mv^2. Since max velocity is c than this is equal to 1/2mc^2. Loose the 1/2 because this is a measure of the average speed (not relevant here) and u get mc^2 CANGAS 030306, 10:20 PM The standard formula as quoted for kinetic energy is not based on AVERAGE speed. It is based on the instantaneous velocity at the moment of measurement. crazeeeeeem 030306, 11:32 PM The standard formula as quoted for kinetic energy is not based on AVERAGE speed. It is based on the instantaneous velocity at the moment of measurement. Wasnt that how it was derived originally. Have a faint memory of learning something like that a school. Anyway, heres a good URL http://hypertextbook.com/physics/mechanics/energykinetic/ CANGAS 030306, 11:44 PM I claim that the v in the standard equation of kinetic ( or is your spelling "kinetiK" actually correct ) energy refers to instantaneous velocity. You blatantly claim otherwise. 1. Show proof. 2. Prepare for laughter. LeeDa 030706, 09:38 AM Does anyone know how stupid people like me with no education can be valuable? LeeDa 030706, 09:39 AM *Grunt* LeeDa 030706, 09:40 AM Filler up? comisaru 030706, 09:54 AM This is all bs. Weak Greek Stuff. Maths is b.s is all abstract shit, it was invented by the Greeks so they could talk shit all day. Dear Muslim, the arabs produced more then the Kuran. For instance, only in mathematics, one of the most outstanding Arabic writers was alKhwarizmi (c. 780  c. 850). The title of his book, Ilm aljabr wa’d muqabalah, is the source of the English word “algebra”. AlKhwarizmi’s name has also become an English word, “algorism”, the old word for arithmetic. AlKhwarizmi drew from both Greek and Hindu sources, and through his writings the decimal system and the use of zero were transmitted to the west. James R 030806, 10:54 AM As something speeds up, both E and M in that formula increase (taking M as relativistic mass and E as total energy). sqrt(E/M) is always c. Anomalous 030806, 11:27 AM The mass is converted into energy used to propel, so ones bound to end up with less mass at later parts of journey and more speed. TheVisitor 030806, 05:50 PM Hey, I'm just wondering why in E=mc^2, the speed of light is squared. Could somebody just try to explain it all? Thanks. Matter is actually light that has been turned in on itself by some force powerfull enough to do so, creating a circular pattern traping the energy. Tesla called it the "small forces", when he refered to the force that holds all of creation in place. Molecular attraction, gravity...ect..on a micro or macro scale is the same force. It is what is released when matter turns back to energy, it's the original force used by God to hold it in place to begin with. The "force" is God. Hurricane Angel 030806, 05:58 PM Okay, why did you feel it was necessary to introduce a religious aspect to the speed of light and its relation to matter? TheVisitor 030806, 06:28 PM I said that force was of God, not religion....religion is a fairy tale/lie created by men. God is real. Science is just begining to unravel what God did. Einstein, and Tesla discovered the connection at the end of their lives. (Q) 030806, 08:27 PM Visitor I can see how easy it is for you to make up stuff as you go along, based on what you've already told us and the fact you live in a fastasy world. But, why do have to bring that crap into the science forums? Some people are here to learn things, not listen to someone elses fantasies. If you have something to offer from a scientific perspective, please feel free to do so, but don't flood these forums with god fantasies. There is a fantasy forum already set up for just such nonsense. TheVisitor 030906, 04:49 AM Matter is actually light that has been turned in on itself by some force powerfull enough to do so, creating a circular pattern traping the energy. Tesla called it the "small forces", when he refered to the force that holds all of creation in place. Molecular attraction, gravity...ect..on a micro or macro scale is the same force. It is what is released when matter turns back to energy, it's the original force used by God to hold it in place to begin with. Also, what scientist's have observed as "light years" judging distances with telescopes, spectroscopically, and "redshift" estimates are also flawed. They will find out someday their not seeing "millions" of light years in distance, but they are seeing light as it also being pulled into a circle by these same forces. Their are other worlds or dimensions right here close, where time as we perceive it is not constant to our world or dimension. Notice the word dimension is also used to measure a distance, or boundry of something. The "worlds" are seperated by dimensions of space and dimensions of time. You have to be "quickened" to see the kingdom of God. There are worlds overlaping this one right here, just exsisting or vibrating at a different speed so fast it's not visible. Science is observation of what already exsists.....it is limited by limited senses and only plays "catch up" in a way to the true. James R 030906, 05:23 PM TheVisitor: Matter is actually light that has been turned in on itself by some force powerfull enough to do so, creating a circular pattern traping the energy. How do you know that such a force exists? It is what is released when matter turns back to energy, it's the original force used by God to hold it in place to begin with. Energy and force are different physical concepts. It makes no sense to say that energy becomes force, or vice versa. You have to be "quickened" to see the kingdom of God. This the "General Science" forum, not the "Religion" forum. There are worlds overlaping this one right here, just exsisting or vibrating at a different speed so fast it's not visible. What's the scientific evidence for that? Science is observation of what already exsists... As opposed to what? Observation of what does not exist? Anomalous 031006, 10:32 AM Let's ROLL ! E = MC^2 C^2 = E/M C= Squareroot(E/M) As we speedup M always decreases and E always increases, So is C impossible ? Or should M still be Zero for that, but x/0 = ??? So much from a Medical Student.  BTW in which part of the atom does Mass increases ? Poincare's Stepchild 031006, 10:59 AM First, M increases as V increases. Secondly, to evaluate E/M as both E and M approach 0, you have to use limits. Recall your calculus? In this case the limit is c. An object with mass > 0 can not reach the speed of light, only approach it asymptotically. A massless particle, such as a photon, since it has energy can only travel at the speed of light. Interestingly, this last bit is how they first proved that neutrinos have mass. They detected that neutrinos change state. which implies... Neutrinos experience time. which implies... Neutrinos are not traveling at the speed of light. which implies... Neutrinos have mass. :D 