Is this mass-energy conversion explanation accurate?

I know that forums like Reddit or Quora can often include all manner of quacky answers and exchanges that are often not at all reliable. But the following one intrigued me, and I’d like confirmation from any physisicts about whether this is a good explanation or not. I’ll paste this Quora response below. It was in response to the question:

“Is it possible to convert energy back to its mass?”

Viktor T. Toth

IT pro, part-time physicistUpvoted by

Radhika Prasad

, MSc Physics, Indian Institute of Technology, Kanpur (2020)Author has 9.4K answers and 148.5M answer viewsFeb 20

Sure. But first, let’s clarify what energy and mass really are.

Energy comes in two forms. Kinetic energy (the energy of motion), and potential energy (the ability to do work, i.e., create motion, due to some interaction).

As to mass, let us remember the actual meaning of the one famous physics expression everyone remembers, E=mc^2. It means that the inertia (inertial mass) of an object is determined by its internal energy-content.

So then, allow me to offer a thought experiment that shows how we can convert inertia into kinetic energy. This experiment would be hard to realize in practice (there are no perfect ping-pong balls!) but hopefully, easy to imagine.

That is, imagine a box, a very large box, full of perfect ping-pong balls. These ping-pong balls are bouncing back-and-forth between the walls of the box. Both the ping-pong balls and the box are lightweight and “perfect”, which is to say, the collision between a ball and the inside wall of the box is perfectly elastic, with no loss of energy.

Now try to push that box in order to accelerate it. You will notice that there will be resistance. The wall you push will be pushing against incoming ping-pong balls, accelerating them a little bit in the opposite direction. This requires a force. Meanwhile, ping-pong balls on the opposite wall of the box will impinge with a little less power as that wall would be “running away” from them. All this means that it will be a bit harder to push the box compared to a similar box in which the ping-pong balls are at rest. In fact, the faster the ping-pong balls bounce around, the harder it will be to push the box that contains them.

Now the interesting thing is, if you were to calculate the total kinetic energy of the ping-pong balls inside that box in the reference frame of the box’s own center-of-mass, you will find that it will be proportional to the extra inertia you feel when you try to push that box.

But now let us do something else! Open a hole in one side of the box. Out stream a bunch of ping-pong balls. The box, in turn, accelerates away in the opposite direction. Now try to push that box. It will have fewer ping-pong balls in it, so their contribution to the box’s inertia will be less. The box of ping-pong balls lost some inertial mass! Where did it go? Why, it is now the combined kinetic energy of the box and the ejected ping-pong balls. There, we converted inertial mass into kinetic energy!

And yes, sure, it can be done in reverse. Just make the box capture some fast ping-pong balls, letting them bounce around inside.

I hope this thought experiment, however bizarre, helps demystify a bit the meaning of “energy” and the meaning of Einstein’s famous formula.

In the “real world”, we of course do not have perfect ping-pong balls and perfect elastic collisions inside perfect boxes. But we do have particle accelerators, with particles serving as ping-pong balls. These accelerators are used routinely to create particles that do not normally occur in Nature under ordinary circumstances. How? By using the combined kinetic energy of colliding particles, which is then converted into the mass-energy of the heavy particle that the accelerator creates. So yes, that’s a direct example of converting kinetic energy into mass. This is how particles, such as the Higgs boson, get created in accelerator experiments: it is quite literally a conversion of kinetic energy into the rest mass of the particles that are being produced and studied.

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And just to give my own initial reaction to the above - it seems like an over-simplification to me.

My own “counter-thought-experiment” would be: Wouldn’t this simply be like having a box with a mounted ball on a spring inside it. So that now if I accelerate that box (against the spring), the ball on that spring simply shifts (compressing the spring) making the box harder for me to accelerate (but it’s also shifting the center-of-mass of the box because the ball inside it moved backward in the box as a result of the box’s forward acceleration. In the end - my continued steady acceleration of that box (after the spring-ball inside has shifted into its new, compressed equilibrium position) would simply be the same as if the whole contraption inside the box was all rigid with the box. As it must be, because in a Newtonian sense, the overall mass of the box and its contents is constant (whether the spring is compressed or not) right? The initial higher force required for acceleration (to get the spring compressed) would be countered on the far side in a corresponding deceleration where now the spring stretches and makes the box less hard to stop too (but only while the spring is stretching and allowing the c.o.m. of the box to shift the other way).

It all seems pretty ordinarily Newtonian to me in all these regards. And the gas (or ping pong balls) themselves act as a sort of spring in the same way as my spring ball system right? Sort of akin to the enclosed truck load of parakeets all flying in their cages at the moment - and yet the truck is still the same weight on its wheels as if the parakeets were all perched. Am I missing something?

Mass is created from kinetic energy in particle accelerators. You get out more mass than you put into the collision.

Of course, this is more of a description of the effect than the cause. I think the example you are citing is trying to explain the theory behind the observation.


Yeah - I think they’re trying to bring it out of the less-intuitive, relativistic domain of Einstein by a simple, Newtonian way of viewing the same problem. So, for those of you who fully grasp Einsteinian, relativistic properties of matter/energy - did this example totally violate or depart from actual and accurate relativistic understanding in the pursuit of increased intuitive accessibility?

Viktor is pretty good at reducing complex things for readers who aren’t familiar with various fields. Assuming that inside the box is a vacuum so the “perfect” ping-pong balls move freely, I think his explanation is correct.

I agree. Even if the ping-pong balls are moving at significant fractions of the speed of light, the result is still Newtonian.

On the other hand a group at Stanford University noted that it will make a difference if the birds were all very large and few rather than small and numerous, since a bird exerts downward force with a downstroke of its wings but nearly none on the upstroke, so that the mass averaged over time will be constant but will vary over time in very small amounts depending on which directions the wings are moving, and how many birds are flapping their wings in unison at a given moment.

BTW, if you know of the metronome synchronization phenomenon, it applies here: any flock of birds flying together will over time come to have synchronized wing motion; if the Stanford team is correct then the weight of the truck will eventually rise on the birds’ downstroke and fall on the upstroke.


I got a B in the relativity section of university physics but only because I knew what equations to apply when; I don’t claim to understand it.

That said, if the ping-pong balls are moving at ordinary speeds, relativistic effects are negligible – after all, NASA doesn’t bother with relativity in plotting spacecraft courses around the solar system, and those are moving a lot faster than any ping-pong balls (or parakeets).

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What about the conversion of some of the energy into heat after the “ping pong balls” impact each other?

Friction due to air isnt the only problem. There is friction from impacts as well and this illustrates the second form of energy.

However, that would suggest to me that with each impact, energy transfer to heat occurs and as such momentum is negatively affected even in a vacume?

That too is a fascinating concept. And the quick (and I believe entirely accurate) answer for it is that no energy is lost in these impacts! Because at the atomic level, those collisions are 100% elastic - meaning that no kinetic energy is lost whatsoever. (Where would it go?)

Otherwise, you would have a situation where a gas just spontaneously cools, without its heat actually being transferred anywhere (to its suroundings), and the 1st law of thermodynamics would be shown to be inaccurate.

So the friction that happens in impacts is only in the “macro” objects made up of many particles, whose bonds with each other can be affected or broken by said impacts - and that is the friction that makes an impact less than perfectly elastic. But at the atomic level, unless the nature of a particle itself gets altered somehow, there is nothing that can be changed by the impact - so the rebound (due to electron repulsion between one atom and another) is 100% elastic. (Or … if an electron is jarred to a more excited state, then the energy is only absorbed until it returns to its ground state - and the emitted photon transfers that now-radiated energy elsewhere, satisfying the 1st law.)

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I think that is included in “perfect ping-pong balls”, just as loss of energy due to impacts with the walls was for the sake of the illustration, which is a simplification of a sort that physicists utilize regularly in order to address some point. Depending on the matter at hand, they may or may not factor back in items that were excluded. So ping-pong balls impacting others would transfer momentum but not heat.

Hmmm, nah i am certain that whilst there is an equal and opposite reaction, not all of that reaction is momentum in the opposite direction…some of the reaction enegy is transfered to other forms…such as heat and that heat is not contained within the atoms of the object, it is radiated out of the object…even in space. This says to me that even in space, an impact changes the reactions momentum to an amount that is less than the original. I think we have generally been deluded into thinking friction only occurs in an environment where there is, for example, air.

Conservation of energy and matter is not defied by transfer into other forms such as heat or even light. This transfer means momentum cannot be maintained after an impact…some of it must be lost to another energy form, otherwise, “we” (our interpretations/beliefs) are creating.

“No energy is lost” only because the ping-pong balls were specified as being “perfect”. In reality when two ping-pong balls collide a small amount of the energy is turned to heat, making the balls warmer. The amount of heat will depend on the energy of the impact.

This doesn’t happen if instead of ping-pong balls you use atoms because the motion of atoms is what heat is. But the moment you have molecules instead of atoms the collisions are not 100% elastic because atoms within the molecule can vibrate – impart enough energy and the temperature will reach a point where it breaks the bonds and the molecule comes apart.


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Newton’s “equal and opposite reaction” assumes the same sort of “perfect” interactions as the illustration in the OP. IIRC Galileo was the one who first utilized this exclusion of negligible factors in order to get equations that describe “ideal” situations, and that in order to have equations that can apply across the broad range of a given phenomenon.

This is why, for example, in rocket propulsion the “equal and opposite” reaction that is given in Δv is actually a maximum. But in practice the difference is negligible, so NASA can ignore the fact that a tiny amount of the heat of propulsion is transferred to the spacecraft and that tiny amount of thrust is lost.

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That latter part is true. But in an isolated system (where not even radiated energy escapes - imagine a totally insulatory, reflective thermal barrier) there can be no escape of heat. What you are claiming - if I understand you correctly, makes it sound like even this isolated system would slowly lose its kinetic (thermal) energy just due to some sort of “internal frictions” among the particles themselves. And that implies a loss of energy to … nothing (contra the 1st law). Friction, like temperature and heat is an emergent property of lots of bonded or interacting (or not! - as in an ideal gas) particles, but not individual particles. And even if that weren’t true (and somehow bounces between atoms weren’t 100% elastic), even then system momentum is always conserved. So your latter conclusion (about momentum loss) is wrong at both levels I think. But if I’m wrong in any of this, I still hope anybody with more physics knowledge can still weigh in to confirm or correct.

Thanks, @St.Roymond for already sharing your additional insights.

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It would go into emitting photons, otherwise known as blackbody radiation. Those photons could be absorbed by other “ping pong balls”, or they could escape the system and be absorbed by matter outside of the box. In the case of the classical view of “heat”, these would be photons in the infrared.


Yeah - that was the only caveat I could think of for how an individual atom might absorb and then dissipate energy (as radiation). I just posted a new response above as you did this reply simultaneously - so I think I’m going along the same lines as what you propose. But any additional reaction you have to what I just posted above would also be welcome.

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Interestingly, I found an explanation of mass-energy conversion based on the conservation of momentum.

In this example, there has to be an increase in mass for objects moving at relativistic speeds in order for momentum to be conserved.


My counter thought experiment is to take the same kind of idealized box, make it long, and have all of the balls bouncing back and forth at the far end and perpendicularly to the force you’re applying to the box. The kinetic energy in the box/ball system is the same as before, but the balls now have no effect on the movement of the box (until you push it far enough that the start hitting the near end). So I’m skeptical.


Let’s consider the electron and its anti-particle, the positron. Both have electric charge so that their masses can be accurately measured. Their masses are well known and equal. When they collide, the mass disappears and two electromagnetic photons appear…whose energies can be measured. The energy released is, indeed, equal to the mass times the square of the speed of light. The above process is called positron annihilation. The process can be reversed in a process called pair-production. A single photon with energy higher than the masses of the position and electron can interact with the charge on a heavy nucleus and produce a position and an electron. The excess energy of the single photon above that needed to produce the masses of the position and electron adds into the kinetic energy of the new electron and position. All of these processes can be measured. Pair production can be viewed in photographic plates, bubble chambers and spark chambers.


This is the basis for PET (Positron Emission Tomography) scans. They use unstable isotopes that produce positrons as part of their decay, and then measure the gamma rays emitted by the collision of positrons and electrons.

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