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# e=m(c^2 +1/c)

New theory that proves Einstein was only approximating
 (-3) [vote for, against]

When using the exact numbers without any approximations, it turns out that the amount of energy in any mass is equal to the square of a tiny bit more than the speed of light, multiplied by the amount of mass.

This new theory can be checked and finally proven by allowing the Iranian scientists to finish their research, for the benefit of all humanity.

The immediate result will be the removal of all the mfd and "bad science" remarks from many HB entries, and an automatic Nobel prize to all fringe scientists.

 — pashute, Jul 21 2013

Energy–momentum relation http://en.wikipedia...y–momentum_relation
[xaviergisz, Jul 21 2013]

Actually:
E=((mc²)² + (pc)²)^œ
 — xaviergisz, Jul 21 2013

Given that energy equals mass times the speed of light squared, if I weigh a piece of coal, then burn it; work out how much hotter my living room gets, and take the square root of the heat divided by the weight, do I get the speed of light as the answer?
 — xenzag, Jul 21 2013

Let c=1
 — pocmloc, Jul 21 2013

 //do I get the speed of light as the answer?//

Assuming you can recover and weigh every bit of material lost into the air in the process of combustion (gas, ash, soot, and whatnot), you will find that the post-burning weight is ever so slightly smaller than the pre-burning weight (by a very, very tiny amount), and this lost mass would correspond to the amount of heat and light produced in the combustion according to e=mc^2.
 — ytk, Jul 21 2013

//The immediate result will be the removal of all the mfd and "bad science" remarks from many HB entries// You severely overestimate the causal power of reality over the HB.
 — lurch, Jul 21 2013

 xavier thanks for the interesting read. I saw that one way to calculate it was by using norm. Do you suppose it has anything to do with our HB user norm?

btw, in Amharic Xavier means God, as in: "Good morning" = Indiette Derrick? (literally: how is your way? or how's it going) and the answer: Xavier Mezgiv (God is great). - Actually I'm never sure. Sometimes it sounds like Xiever.
 — pashute, Jul 21 2013

 The E=mc2 describes the energy stored in the mass of atoms (or better defined as groups of protons), and released during the breakup of the atom in an "atomic reaction". That's what happens on the sun, and it seems that at the center of our planet earth as well.

 During combustion, you are only exposing the very small amount of molecular energy. Combustion is the breaking up of molecular bonds between atoms, not between protons within the atom. The protons stay intact during combustion, or usually do, as ytk pointed out correctly.

 During combustion the atoms find and connect to other atoms with tighter bonds, usually in smaller groups, while releasing energy as chaotic movement of these molecules - called "heat", and usually also emitting small particles such as light, infra red radiation, and electromagnetic radiation.

 Whereas in an atomic reaction, the atom itself disintegrates, most of the protons, usually the all the protons of the atom, are turned directly into radiation and heat, losing their mass.

 The amount of energy "released" (actually: exposed) is extremely high. So much, that one gram of disintegrating material will give off energy that could move 900 billion tons, or send a gram of some nearby material into orbit (if not for drag) at the speed of 270,000 km/h.

 I think I got the idea correctly. Please tell me if I'm wrong.

 Its good that people only think of good things to do with this power, if anybody would ever dare to use it in war, it could be mighty lethal. Not to speak of the lasting radioactivity in the ground, and its vast effects on large areas through atmospheric radioactive pollution.

So there we are back at my idea.
 — pashute, Jul 21 2013

 There's two things wrong with your understanding.

 The first is fundamental: In an atomic reaction, the atomic nucleus is not completely broken, usually only a single particle splits off (alpha, beta) or is added, and no particles are generally destroyed. The energy released (or absorbed) is simply the change in bonding energy between the nuclear particles. It happens that iron has the tightest nuclear binding, so if the atom is less massive then iron, fusion gives off energy, if it is more massive than iron, fission gives off energy. If the particle in question is a beta particle, then a neutron may convert to a proton or vice-versa, but again, no particle is destroyed, merely combined or split.

 The second, how mass comes into play is something I didn't understand for a long time. Einstein isn't saying that mass and energy are convertible, he's saying that they are the same thing. Any time energy is released, the materials involved become less massive. Any time energy is added, they become more massive. For most cases (as in the chemical bonds [xen] and [ytk] were discussing) this change in mass is so vanishingly small as to be immeasurable (or nearly so) with available instruments. It's only once we get into the nuclear range that it becomes readily measurable.

Anyway, [Marked-for-deletion] theory, and, unless you can provide some documentation for said theory, bad science.
 — MechE, Jul 22 2013

If you actually want to destroy a particle, then you are dealing with a particle/anti-particle pair, at which point the full mass of the particles is released as energy.
 — MechE, Jul 22 2013

 //Whereas in an atomic reaction, the atom itself disintegrates, most of the protons, usually the all the protons of the atom, are turned directly into radiation and heat, losing their mass.//

 When you make absurd, blatantly wrong statements, you're not helping to dismiss those tags of...

 In a fission or fusion reaction, the nucleon count is unchanged. No protons nor any neutrons are converted to radiation and heat. The energy emitted is from the change in the nuclear binding energy, and can be quantified by the change in the "mass defect" from the reacting elements to their daughter elements.

 The direct conversion of entire nucleons into energy has been observed in nature, but only accomplished by human artifice in particle colliders - crashing protons into anti-protons. If we could do such a thing in bulk, it would probably be a fair bit cleaner in terms of radioactive pollution than the bombs we've built in the past.

<edit>[MechE] beat me to the comment, so I'll just add: "what [MechE] said"</edit>
 — lurch, Jul 22 2013

 The idea was supposed to be TIC.

 The annotation in answer to xenzag, was serious. and as I now know - wrong. I stand corrected.

 Meche and lurch both pointed out something which I now realize, and as far as I can see in my old 5th grade science books especially on chemistry is a common mistake. My year at university in physics didn't cover this, and neither did my courses in organic chem or biochemistry. I recently re-read Lehninger, nothing about e=mc2 or atomic power. I can only suppose its because of the military taboo.

 We are taught about Lavoisier's discovery of conservation of mass, that atoms and elements react in whole numbers, the (disputed) discovery of the element table, and the explanation, that the number of protons basically determines the "weight" and hence mass of an atom. Protons were defined to have an atomic weight of 1, and Prout's hypothesis is still studied in highschool textbooks.

 Wikipedia - which is quite edited on these subjects and well sourced states about Prout's hypothesis: "which was disproved when more accurate values were measured." (WP:Proton) Let alone awareness to the fact that there "is no more" an atomic weight, and that that number is now correctly called: Relative Atomic Mass.

 So I'm sure many people like myself, figured that its just some inaccuracy, not a basic flaw - that mass is not due to the protons, but to the packing of the protons and their binds.

 I'm writing my answer again as a summary. Hope I got it right this time (according to your answers and Wikipedia: Mass-energy equivalence), here goes:

 xenzag asked: Given that energy equals mass times the speed of light squared, if I weigh a piece of coal, then burn it; work out how much hotter my living room gets, and take the square root of the heat divided by the weight, do I get the speed of light as the answer?

 The simple answer - is YES. but you must find the difference in weight (mass) of the original coal, and the current material left from the burning coal - including all the particles that left it as smoke. Also you must be able to know the exact quantity of energy released.

 For combustion, E=mc2 can be read E/c2=m, meaning any energy emitted or gained in a system, means that the system loses or gains an extremely small amount of mass.

 On the other hand, in a nuclear reaction, an extremely large amount of energy is released, and a perceivable loss (in fission, or gain in fusion) of mass is felt.

 In a typical fission reaction the bonds between protons in an atom are changed, leading to closer ties between the protons, in separate 'smaller' "bundles" (atoms). These have less mass than the original atom. That mass was released as energy , a 'massive' amount of energy, so to speak.

 In 1938 this was shown to occur, when uranium broke up (after being bombarded with nucleons), and barium was found. The final process of the Uranium breakup, after the barium atoms were created has the two main parts of the uranium breakup, one of them barium, moving away from each other at high speed. It was found that the resulting parts are lighter than the original at the weight of a fifth of a proton, per uranium atom participating.

 This lead scientists to realize the "explosive" potential of the process.

 for example in nuclear fission of Uranium, when the (236 neutron) Uranium protons can settle into a closer bind in (141 neutron) Barrium and (92 neutron) Kryptonite, also releasing three neutrons (at high speed) and a nice bit of radiation.

 This release of neutrons can lead to a chain reaction, breaking up a large amount of Uranium at once, or continuing the process over time.

 In fusion, two atoms collide creating a single atom, that have "closer" bonds, and less mass. That mass was released as energy.

Something similar is happening on the sun, and it seems that at the center of our planet earth as well.
 — pashute, Jul 22 2013

 // Barrium //

Sp. "Bohrium"
 — 8th of 7, Jul 22 2013

 Barrium schmarrium - what about //Kryptonite//?

Also, I hate to ask this without having gone through the whole post in detail, but isn't this just a re- statement of the bleedin' obvious? Or did I miss something?
 — MaxwellBuchanan, Jul 22 2013

 woops: Barium (Ba) Krypton (Kr)

 This entry was meant as a joke. If most of the writers agree I should delete it, I will.

 The idea did have an interesting turn: First xavier pointed out that in fact E is not equal to M*c squared, and that their is a small extra amount of mass involved.

 Then xenzag asked a question, the answer to which I thought was obvious, but I was wrong.

 My mistaken understanding was that there is a fundamental difference between chemical reactions and nuclear reactions.

I think the correction of that notion is NOT obvious at all.
 — pashute, Jul 26 2013

 There is a fundamental difference between nuclear and chemical reactions. One involves intra-atomic bonding energies, and one involves inter-atomic bonding energies.

 Other than that, no, no real difference.

And I believe, although I won't swear to it, that [xavier]'s equation goes away if you're using the apparent rather than rest mass of the object in question. That is, it is simply a way of relating the increase in energy due to velocity to the rest mass, which the relativistic mass already does.
 — MechE, Jul 26 2013

 //Einstein isn't saying that mass and energy are convertible, he's saying that they are the same thing.// This explains why it takes longer to eat a very hot meat pie than it does a cool one

//one gram of disintegrating material will give off energy that could move 900 billion tons// That makes no sense. Burning one gram of petrol will also give off energy that could move 900 billion tons.
 — MaxwellBuchanan, Nov 16 2019

 //Burning one gram of petrol will also give off energy that could move 900 billion tons.//

I dispute that: the movement would be impossible to prove even in hard vacuum, as natural atomic decay and interaction with the occasional Hydrogen atom would make more than enough noise to cancel it out unless said mass were packed in as sufficiently small area, in which case the noise from the explosion would do the same. Or if it were packed into an even smaller area there would be absolutely no provable effect from the petrol, the hydrogen, or atomic decay.
 — Voice, Nov 16 2019

 Nope. Put the 1 gram of petrol, plus air, in a sealed cylinder with a tight-fitting piston. Keep the cylinder fixed, the piston attached to the mass. Ignite the petrol. You will create a large and sustained pressure in the cylinder. If the mass is floating in microgravity, it will slowly start to move. If the piston pops out of the cylinder at full travel, your mass will continue moving slowly until forever.

 Or, if you don't like that, use your 1 gram of petrol to run a model aircraft engine for a minute. Engine drives a series of reducing gears. Last gear moves the mass; use a micrometer to measure the movement.

My point was - it is silly to talk about energy in terms of the mass it can move, unless that movement is for a known distance against a known force. I can say "this is enough energy to lift a billion tons 1 metre against 1 gravity" - fine. Or I can say "this energy is enough to accelerate a billion tons to a speed of 0.01m/s - also fine.
 — MaxwellBuchanan, Nov 16 2019

 //in Amharic Xavier means God,//

My 1946 edition of the Alone-Stokes Short Manual of the Amharic Language disagrees, [pashute]; could you quote your source?
 — pertinax, Nov 17 2019

 [annotate]

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