INTRODUCTION

In my last big save, “W80 Nuclear Warhead", I chose a scale that would simply look nice and allow for lots of detail. However, I've started to wonder how realistic of a scale that is, and how particles behave in game compared to real life.

The scale I decided upon was 80 cm to 448 pixels, as that's the length of the W80 warhead, meaning the game screen would be about 110 cm across, and one pixel would be about 1.78 mm. We can use this scale to calculate the speed and energy of particles.

   CALCULATING LIGHT SPEED

All subatomic particles, both in TPT and especially in real life, move at significant fractions of the speed of light, also called “relativistic” speeds.. It is therefore extremely important to determine the speed of light, to have a scale of time along with our scale of distance.

The average speed of a photon in TPT is 3 pixels per frame, which equates to 5.34 scale mm. We can therefore derive that at this scale, one frame is roughly 17.8 picoseconds, and one second is just over one nanosecond, assuming 60 frames per second. Now that we have our frame of reference and speed limit, we can find out a lot more about other particles.

From my observations, protons, neutrons, and electrons, by default, all move at about 1 or 2 pixels per frame, or 1.78 to 3.56 mm per 17.8 nanoseconds, which is almost exactly 1/3 the speed of light. Assuming these particles have the same masses they do in real life, we can calculate their kinetic energies. Those calculations are as follows:

KE (at relativistic speeds) = m * c^2 (sqrt(1 - v^2 / c^2) -1)

Protons: 1.673 * 10^-27 kg * c^2 (sqrt(1 - 1 * 10^8 m/s / c^2) -1) = 57.01 to 321.3 MeV

Neutrons: 1.675 * 10^-27 kg * c^2 (sqrt(1 - 1 * 10^8 m/s / c^2) -1) =  = 57.08 to 321.7 MeV

Electrons: 9.109 * 10^-31 ^ c^2 (sqrt(1 - 1 * 10^8 m/s / c^2) -1) = 0.031 to 0.175 MeV

Note that throughout this essay I will be assuming the default velocities, that is, the velocity particles have when they are first spawned in, and not under the influence of any outside forces. If not for this assumption, particles could easily go many thousands of times faster than the speed of light, e.g. under the influence of GRVT, PGRV, NGRV, etc.

   REALISM

Firstly, as far as protons go, they have a kinetic energy roughly consistent with the beams used in proton therapy. This is a technology that uses carefully controlled proton beams to destroy cancerous cells. The beam energy can range from 70 MeV up to 250 MeV, which is within an order of magnitude of the 57 to 321 MeV of protons in TPT. The proton beams found in particle accelerators are very different; they can get up to an energy of 70 TeV, or 70,000,000 MeV, about 200,000 times more energy than even the fastest protons in TPT. To match that energy, though, you'd only have to accelerate the proton to 3x default speed. This is because, as the formula shows, energy is proportional to velocity squared, meaning that even the smallest increase in velocity would result in an exponentially larger increase in energy.

Next, on to neutrons. The fission of one atom of Plutonium-239 produces, on average, 5.9 MeV of prompt neutrons. In game, the fission of one pixel of PLUT produces roughly 114 - 228 MeV of prompt neutrons. At first glance, might seem like a total disconnect from reality, but it's actually very comparable. This is becausse in TPT, PLUT doesn't emit beta, gamma, or any other type of radiation besides neutrons. The neutrons make up the difference. Subtracting the energy of decay products, which TPT doesn't simulate, Pu-239 releases an average energy of 193.9 MeV, which fits perfectly within the range of the energy from the neutrons it emits in TPT.

Finally, we can discuss electrons. The cathode ray tube is a device that uses electromagnets to guide an electron beam to scan across a screen. The electrons hit phosphors and cause them to light up. Most electron guns used in CRTs operate in the range of 5 to 35 KeV, which is consistent with TPT slow electrons' 30 KeV. Some particle accelerators may also use electron beams, and as with the proton beams (and every other thing in the universe), energy is proportional to velocity squared, and goes to infinity as it approaches C, so accelerating electrons to near the speed of light would easily get them to the 70 TeV goal.

   CONCLUSION

I'd imagine that almost anybody who plays this game wouldn't expect the subatomic physics simulations to be realistic, however, I've found that when it comes to kinetic energy, given the correct scale, all of the subatomic particles in TPT operate surprisngly well within the laws of physics, and are not at all unrealistic representations of their real life counterparts. The interactions between particles with each other or with elements, and especially the processes of fission and fusion, are beyond the scope of this essay, and will require an investigation of their own.

   AFTERWORD

I am by no means a nuclear physicist, I'm just bored, and did a lot of reading, so if anybody that’s more knowledgeable than me would like to make a correction or suggest an edit, by all means, please do!