I have a question regarding the energy-mass conversion. Well, when a particle starts moving with a speed comparable to that of light, its (relativistic) mass increases that means some matter is created and that too of the same particle...energy being converted to mass is ok but how does energy perceive what atoms it has to form? Say I take a stone to a high speed, then constituents of stone is formed. And if I perform same thing with another substance, its constituents are formed..How? Energy can be converted to mass but a mass of what? Does that mean we can create matter of any desirable substance?

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    $\begingroup$ There is no matter created. A single particle, say an electron, at high speed will remain a single electron. $\endgroup$ – MBN Dec 7 '13 at 12:32
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    $\begingroup$ The mass $m$ of a particle is constant. It does not depend on the speed of the particle. For massive particles, the energy and the momentum depend on the mass and the speed : $E = \dfrac{mc^2}{\sqrt{1- \dfrac{v^2}{c^2}}}, \vec p = \dfrac{m \vec v}{\sqrt{1- \dfrac{v^2}{c^2}}}$ $\endgroup$ – Trimok Dec 7 '13 at 12:49
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    $\begingroup$ This question (v2) seems spurred by a confusion between rest/invariant mass and relativistic mass. See e.g. this Phys.SE post, and a couple of paragraphs down on this Wikipedia page. $\endgroup$ – Qmechanic Dec 7 '13 at 15:14

The basic constituents of matter are the components of the Standard Model.


These elementary particles have a fixed mass, called rest mass always. It is given by the measure of the four momentum vector, in analogy to the length of a three vector

invmass , in units where c=1

No matter how much energy is given to them, their rest mass is an invariant of the Lorenz transformation.

The relativistic mass involved in the famous E=mc**2 is a concept that describes the inertial behavior of a fast moving relativistic particle, but is confusing when one does energy budgets, answering "how" new particles can form.

If you look at the table you will see that the basic elementary particles are accompanied by quantum numbers. In any interaction some of them have to be conserved. Particularly in the strong interaction all of them have to be conserved, and together with conservation of energy and momentum the allowed particle creation channels are opened.

To form a proton, the quarks in the primordial quark gluon plasma have to be of low enough momentum to fit in the solution that characterizes a proton. To form a hydrogen atom the electron has to have low enough energy so that it can bind with the proton. Sequentially up to higher atomic number nuclei.

Does that mean we can create matter of any desirable substance?

Let us ask a simpler question. In order to conserve all the quantum numbers not only energy has to be taken into account but also momentum conservation at the center of mass. Is it possible to create a hydrogen antihydrogen pair from gluon gluon scattering, for example? All quantum numbers are conserved together with momentum conservation. Theoretically it can happen, but the probability is very very low as the electromagnetic constant enters in powers , because the hydrogen and antihydrogen have an electron bound to the proton. So the electron and positron have to be created coherently with a proton antiproton at the exact energy levels for binding into a hydrogen and antihydrogen.

We create antihydrogen in the lab by cooling antiprotons and letting them capture positrons. Hard though it is, the probability of making it is finite and people have succeeded to do it.

In conclusion , converting energy to mass can only happen if all quantum numbers of elementary particles are conserved and this has a measurable probability to happen in simple two body interactions, and usually in particle antiparticle pairs.


"how does energy perceive what atoms it has to form"

May i correct you here energy will not create new matter(or new atoms as you mentioned) in the case you mentioned. It will just increase the mass of the existing matter. For if you accelerates an electron from rest to a speed comparable to speed of light what you will get is the same electron with an increased mass. Similarly if you accelerates a stone to a speed comparable to $c$ the number of atoms in the stone will remain the same but the mass of each atom will be increased.

If you are interested in creating matter you should consider something like pair production. It would be more precise to use the word relativistic mass if you consider mass as an amount of matter


If you accelerate a stone to relativistic speeds, no new atoms are created in the stone. There is constant amount of atoms. If new atoms were created, that would mean than these atoms have to disappear when you decelerate the stone. And now think about someone accelerating together with the stone. From the perspective of accelerating observer, the stone does not get heavier. So from their perspective no new atoms would be needed.

The quantity that is increasing during acceleration is the total energy. Relativistic mass (that's the "mass" which is increasing) is in fact nothing else but the kinetic energy. The amount of atoms is unchanged. The kinetic energy can be calculated into kilograms with the relation E=mc^2, but such result is not really useful. What matters is the energy. That's why the concept of relativistic mass (which increases with speed) is not used. Only the rest mass (whcih does not change with speed) is important.

The increase of energy manifests itself as higher resistance to further acceleration, which somehow vaguely relates that to mass (inertial mass namely), but using the concept of relativistic mass is not useful. The total energy is what matters.


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