Physics
The Science Of Repulsors: Photon Momentum in Special Relativity
If you're familiar with Iron Man, you’ll probably remember the scenes synonymous with the character.
Repulsors
Rays of light, blasting from the various outlets of the suit, with immense concussive power.
Throughout the entire cinematic depiction of Iron Man, they’ve ranged from being able to knock a fully grown human clean off his feet, to being able to practically incinerate an alien spaceship.
And in this case, a rocket booster that enables spaceflight at orbital velocity.
Our understanding of momentum
Most of us are familiar with notion of momentum in newtonian physics.
We recall those dreary days we spent calculating the velocity and angles of balls on pool tables.
And indeed this notion of momentum has served us well for a very long time.
We use it to calculate momentum in almost 100% of daily scientific and engineering applications.
But light has no mass?
However, once we start to discuss light, this definition breaks down.
How can a ray of light has momentum, if it has zero mass?
Isn’t zero multiplied by the velocity of light, 3x10⁸ m/s still zero?
p = 0 x (3x10⁸) = 0
How can light have momentum????
Understanding Special Relativity
The answer to this apparent paradox lies in reframing our definition of momentum within the lense of Special Relativity (SR).
In SR, light is quantized into finite, discrete and massless bits called photons.
The basic unit of light.
And in SR, the relation of momentum of an object with its velocity is governed by the following relation.
And since we have established that the photon is massless, the second term vanishes. The equation reduces to:
Or, square rooted:
Reconciling this definition with the expression of the energy of the photon:
And we arrive at:
Let’s try to calculate the power of a possible repulsor through some estimates.
So we see a scene where a person is thrown backward with enough force to break concrete. Let’s throw in some ballpark figures to calculate the energy of a repulsor blast.
(I know its the person that hits the concrete, not the concrete that is hit directly.)
According to this article an approximate force to break concrete is about 3000 Newtons.
And in this article, an average impact time of a piano falling of a crane and hitting a roof is approximately 0.1 seconds.
So the impulse of the blast is approximately 300 kg m/s.
And the energy of the blast upon contact is recovered by multiplying the momentum by the speed of light, c = 3x10⁸ m/s.
As per the formula.
E = 300 * 3x10⁸ = 9 x 10¹⁰ J
According these estimates, a rocket propelled grenade has an explosive yield of about 4.2x10⁹ J.
So our repulsor blast is about an order of magnitude higher, not bad at all!
=================================
References:
https://nuclearweaponsedproj.mit.edu/orders-of-magnitude
https://gizmodo.com/how-karate-chops-break-concrete-blocks-5591320
https://www.wired.com/2014/07/how-do-you-estimate-impact-force/
