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So mass can be created from energy when small protons speed up, 430 times bigger to be exact. I don't know if this is a stupid question, but I'm in middle school so cut me some slack. Where does all that mass go? Is it converted to thermal energy? Say we covered the earth with solar panels, that would produce a lot of energy, also producing a lot of mass. I don't know if that's the right wording, I don't want to sound like I don't know energy can't be created or destroyed but if anyone could answer these questions for me that'd be great.

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  • $\begingroup$ No slack required. Your question is much more complicated than it first appears. Firstly, SR does not talk at all about energy-mass conversion, its is not part of the framework at all. For that to occur we need to talk about Quantum Mechanics, which just arm waves it away (mass is just an unimportant number). $\endgroup$ – Aron Jun 19 '17 at 14:15
  • $\begingroup$ Mass and energy are the same thing, just measured differently. $\endgroup$ – Hot Licks Jun 19 '17 at 16:51
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The notion of "mass" is probably less deeply meaningful as you might think. Science has come a long way since the days when mass was thought to have such deep significance. Nowadays, energy is the primary concept, because there is a law of conservation of energy, and energy is linearly additive: that means that the sum of energies for two separate systems equals the total energy for the system as a whole. These two properties - conservation and linear additivity make energy a useful notion in physics.

Mass has neither of these properties. It is not conserved, and it is not additive. The rest mass of a system two photons moving in opposite directions is nonzero, whereas the rest mass of each is nought.

In particular, since mass is not conserved, it doesn't have to "go anywhere", unlike energy. It can simply disappear or appear, as in the photon example. So nowadays mass is less useful as a concept in physics.

Modern physics simply thinks of the notion of rest mass of a system, and this is a shorthand for the total energy of a system as measured from a reference frame at rest relative to the system (in SI units, we multiply by $c^2$ in the rest frame to get from mass to energy). But the notion is still all about energy. The rest mass $m_0$ can be used in the relativistic version $\mathbf{F}=\frac{\mathrm{d}}{\mathrm{d}\tau}(m_0\,\mathbf{u})$ of Newton's second law, where $\mathbf{F}$ is the Four Force and $\mathbf{u}$ the four velocity. As such, rest mass can also be thought of as measuring a system's inertia. Rest masses are important identifying data for fundamental particles, because the total energy of these particles is always the same when measured from a frame at rest relative to them. This last statement holds for massive particles: massless particles like the photon have no rest frame.

Incidentally, though, if you want to express the solar energy incident on Earth as a mass, then it works out to be roughly a kilogram each second. Of course, long term, all of that is radiated back into space. Human energy usage is about five tonnes per year, or about 0.2 grams per second.

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    $\begingroup$ Another interesting thing to note. Under GR the term for curvature of spacetime (or as Newtonian Physicists would call it Gravity) is actually the Energy Density part of the Energy/momentum four vector. Mass is simply the term we give for that four vector when we Lorentz boost it to the rest frame. $\endgroup$ – Aron Jun 19 '17 at 14:01
  • $\begingroup$ @Aron indeed - although the "source" in GR isn't the momentum four vector but rather the stress energy tensor. Energy density is the $0 0$ component of this tensor. $T^{i j}$ is the flux of the $i^{th}$ component of the momentum 4-vector across the surface of constant $j^{th}$ co-ordinate. You may be thinking of Gravitoelectromagnetism, an approximation to GR where the source is the momentum four vector. $\endgroup$ – WetSavannaAnimal Jun 19 '17 at 14:22
  • $\begingroup$ >_< Ah crap...THATS why I failed GR.... $\endgroup$ – Aron Jun 19 '17 at 14:24
  • $\begingroup$ @Aron :) You seem to have the general gist of it, though. $\endgroup$ – WetSavannaAnimal Jun 19 '17 at 14:28
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    $\begingroup$ @SGR Energy is always conserved (at least outside General Relativity). What I meant by that comment is along these lines: a photon has zero rest mass. But if it is captured in a resonator, or a black hole, the capturer's rest mass increases by the energy of the photon. Likewise, photons can be converted to things with nonzero rest mass, and back again. $\endgroup$ – WetSavannaAnimal Jun 19 '17 at 14:49
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Mass, as discovered by Albert Einstein in his Special Theory of Relativity, is no more than another form of energy. When a proton (or any other object) speeds up, it gains kinetic energy which in turn, according to special relativity, contributes to its mass. This mass of a moving object is called relativistic mass and it increases with the velocity of the object as opposed to its rest mass which is invariant. The relativistic mass of an object is actually defined as its total energy divided by the speed of light in vacuum squared: ${E\over c^2}$ and can also be found for objects with nonzero rest mass using the formula $m_{relative}=\gamma m_{rest}$ where $\gamma$ is the Lorentz factor which is equal to: $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$ where $v$ is the relative velocity between your reference frame and the object's and $c$ is the speed of light in vacuum. And of course, the change in energy that is expressed in change of the object's mass isn't created from nothing since it takes energy to accelerate an object and thus change its speed.

Now if what you meant is literally an object with nonzero rest mass being created out of energy as in "something created from nothing" so well, it can happen and it does happen but some conditions must be met due to the conservation laws such as the conservation of momentum, energy and charge. The most common example of this is when a pair of massive particles (particles with nonzero rest mass e.g. electrons, protons) is created by a pair of two massless particles (particles with zero rest mass e.g. photons) in a process known as pair production. The heavier the pair of massive particles, more energy is required to create it.

Additionally, there is the process in which massive particles are created from other massive particles. That is, some of the energy of the massive particles is converted into other massive particles. This happens in particle accelerators for example in which two particles are accelerated to extreme speeds (close to the speed of light) and upon collision lose some of their energy (and therefore, their mass) thus forming other massive particles which can be detected by detectors placed in those accelerators.

However, the reverse process, in which energy (massless particles) is created out of mass (massive particles) is much more common and happens constantly in the sun as well as in nuclear bombs where two isotopes of hydrogen form an isotope of helium while releasing a neutron, which are together less massive than the two hydrogens. The leftover mass is hence converted into energy which is in fact the energy that the sun produces (by fusing 620 million tons of hydrogen each second). This process is called nuclear fusion.

The only process which is more efficient in terms of converting mass into energy is called annihilation. It is the process that occurs when a subatomic particle collides with its antiparticle to produce other particles (e.g. an electron colliding with a positron to produce two photons). As with pair production, all the conservation laws must be preserved in the process.

P.S. If you are in middle school then I'm not much older than you (just finished high school) and if you find this stuff interesting then I sincerely encourage you to dive deeper into it and to start learning it when you're a bit older and after you've learned some fundamental physics such as Newtonian mechanics and some electromagnetism (electrostatics should be enough). The subject of Special Relativity really makes you think out of the box and grants you a unique view about some amazing phenomena which exist in our Universe in which the most nontrivial and unintuitive things can happen, without being too complicated (although it may seem intimidating at first).

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Please read the article Mass In Special Relativity which explains what happens with the energy as a particle is accelerated. It acquires additional "relativisitic mass". To quote:

https://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass

Relativistic mass

In special relativity, an object that has nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object's energy and momentum increase without bound.

In the first years after 1905, following Lorentz and Einstein, the terms longitudinal and transverse mass were still in use. However, those expressions were replaced by the concept of relativistic mass, an expression which was first defined by Gilbert N. Lewis and Richard C. Tolman in 1909.[16] They defined the total energy and mass of a body as

$$ m _{r e l} = \frac{E}{c^2}\!,$$

and of a body at rest

$$ m_ {0} = \frac{E_0}{c^2}$$

with the ratio

$$ \frac {m _ {r e l} }{ m _ 0} = \gamma\! . $$

Tolman in 1912 further elaborated on this concept, and stated: “the expression $m_0(1 - v^2/c^2)^{-\frac{1}{2}}$ is best suited for THE mass of a moving body.”[17][18][19]

In 1934, Tolman argued that the relativistic mass formula $m_{r e l} = E / c^ 2 $ holds for all particles, including those moving at the speed of light, while the formula $m_{ r e l} = γ m_ 0$ only applies to a slower than light particle (a particle with a nonzero rest mass). Tolman remarked on this relation that "We have, moreover, of course the experimental verification of the expression in the case of moving electrons to which we shall call attention in §29. We shall hence have no hesitation in accepting the expression as correct in general for the mass of a moving particle."[20]

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    $\begingroup$ Please do not use salutations or sign-offs, in particular do not post your email address in every answer you post - if you want people to be able to contact you, leave your email address in your user profile, as per this meta post. $\endgroup$ – ACuriousMind Jun 19 '17 at 11:16

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