Deeper Physics Discussions of “Antman and the Wasp”.
Even if I conclude that Antman and the Wasp’s shrinking and reexpanding are not physically possible, thinking about them allows one to present physics teaching in an interesting context.
First I will calculate the energy needed by E = m c^2 for Antman to reexpand with his full mass. Then I will explain that Baryon number and lepton number conservation would not allow this to happen.
We will use the MKS system or Meters-Kilogram-Second system, often called the metric system. The formulas we use are first Newton’s second law of motion: F = m a, or force = mass X acceleration. Then we use the equation for energy expended as a force times a distance. Then, we convert the energy to electrical energy as watt hours, and compare it to the US yearly electrical energy production. Finally, we convert the energy to megatons of TNT.
We start with the energy appearing after shrinking or disappearing the mass of a 70 kg man, or supplying the energy to recreate him. At 2.2 pounds per kilogram, this would be a fit and medium height 154 pound man.
Einsteins formula for the amount of energy stored in mass is the remarkable but easy E = m c^2. We now calculate this for Antman in the MKS system. The velocity of light c is 3 X 10^8 meters per second, or m/s. We will separate out the units of mass X acceleration to make the MKS unit of force, being a Newton, abbreviated as “n”.
E = m c^2 = 70 kg X (3 X 10^8 m/s)^2 = 630 X 10^16 (kg m/s^2) X m = 6300 X 10^15 n X m.
The Newton X meter is now the unit of a force times a distance, or energy, whose MKS unit is a joule. So:
E = 6300 X 10^15 joules.
We now convert that to TeraWatt hours (TWh), where Tera means 10^12 (mega is 10^6, and Giga is 10^9).
A joule is a Watt of power X 1 second. So a TeraWatt hour of energy is:
TWh = 10^12 Watt X 3600 sec = 3.6 X 10^ 15 joules.
This allows us to convert energy in joules to energy in TWh:
E = 6300 X 10^15 joule X 1 TWh / 3.6 X 10^15 joule = 6300/3.6 TWh = 1750 TWh.
The US electrical output in 2016 was 3762 TWh. So the Energy in Antman’s mass is about half of the US yearly electrical energy output. More precisely the fraction is
1750 / 3762 = 0.465 or 46.5%.
Since this much energy is given off in a small space, we also want to convert E in joules to megatons of TNT. 1 megaton of TNT =. 4.184 X 10^15 joules. The energy given off by Antman’s shrinking is then:
E = 6300 X 10^15 joule X 1 megaton / 4.184 X 10^15 joules = 1,506 megatons of TNT.
Since the START treaty limits the US and Russia to 1,500 readily usable nuclear weapons each, that would be the total output of each nuclear force if each warhead was as large as a megaton.
This illustrates how much m c^2 energy is stored merely in each of our bodies.
Fortunately, none of this is available, unless Antman met anti-Antman, or even any anti-matter object, which would be composed totally of antimatter.
We cannot annihilate any part of ourselves because of the stability of protons and neutrons. Since protons and neutrons are two kinds of heavy strongly interacting particles, they are also called Baryons. Baryon number is totally conserved by itself, as far as we know. Of course a free neutron decays into a lighter proton plus electron plus an anti-electron neutrino, but Baryon number is still conserved here, since both proton and neutron have the same baryon number.
Enormous tanks of clear water have been monitored for decades, in the experiment called Super-Kamiokande in Japan, and no proton decays to lighter particles have been seen. This experiment gives lower limits on the order of 10^52 years for the lifetime of the proton. Compare this to the actual existence of the universe of 13.7 billion (10^9) years.
There also is a conservation of electron number. This is not absolute, because of virtual neutrino oscillations, but the particles the electron could turn into are heavier, and would not occur spontaneously in a decay.