Q&A: E=mc^2 and the Mass of Light
E=mc^2 and the Mass of Light
Question
Hello Rabbi,
On the Sabbath I happened to read a bit in the book “Does the World Really Exist,” and it mentioned a thought experiment proposed by Einstein in which light is trapped in a box hanging on a spring, and the moment you open an opening in that box, light escapes from it, causing the box’s total energy to decrease and therefore its total mass to decrease. What I didn’t understand is that apparently this implies that light has mass, because the departure of a photon from the box causes it to become lighter. But from what I saw online, the equation E=mc^2 is true only for bodies with no momentum, and a photon has momentum. So it seemed a bit strange to me that Einstein thought the mass would decrease and not only the momentum. How do you think this can be explained?
Best regards,
Answer
What do you mean by bodies with no momentum? The equation is correct for every body. Besides, a photon has momentum (h/L), where L is the wavelength (lambda).
Discussion on Answer
I’m not well-versed in this topic, but in principle a photon has mass. It has no rest mass. When it hits the walls of the box it exchanges momentum with it, and that means that effectively it has mass.
By the way, if it is located inside a sealed box then it has a defined position (with an uncertainty on the scale of the size of the box), and therefore according to the uncertainty principle it does not have well-defined momentum, so this is not a pure photon but something built from a collection of waves with different wavelengths.
The full equation also includes the body’s momentum; this is the equation:
E^2=(Mc^2)^2+(PC)^2
In the case where the momentum equals zero, the equation goes back to being E=Mc^2
In any case, even without getting into the equation itself: how can it be that when a photon escapes from a box, the box becomes lighter? Does the photon that escaped have mass? The only explanation I can think of is that when the photon originally enters the box and goes from a “free” state to a “trapped” state, then its velocity and also its average momentum relative to the box go from C to zero, and in such a state its mass goes from zero to some finite mass. That is, the process of trapping the photon basically converts the photon’s energy into mass. In other words, this is the reverse of nuclear fission, which converts mass into energy. Does that sound right to you?