What is the relationship between momentum and mass in the context of light?

[SimonB]

Hi

This is probably very naive!

What is wrong with the following

The (momentum of light) = E/c so it is then possible to write this as
(mass of light x speed of light) = E/c

and thus ... E = mc^2

... this came up after I read the following with my students

http://www.davidbodanis.com/pages/promised_note_high school2.html

Which starts with Momentum = E/c but then takes a long route round to E = mc^2

Simon

 

[CompuChip]

What's wrong with it, is that "mass of light" is zero, so you are saying 0 = E / c.
For light, the momentum is related to the wavelength, not the mass. The correct formula is
E^2 = (pc)^2 + (mc^2)^2
which for a particle at rest reduces to E = mc^2 and for a photon with momentum p to E / c = p.

In fact, you may want to read https://www.physicsforums.com/showpost.php?p=1285138&postcount=6 ).

 

[HallsofIvy]

"momentum= mass times velocity" does not apply to light.

 

[jnorman]

"the momentum is related to the wavelength,"

and the wavelength is related to the energy. the total energy of any system is the critical element of consideration, and there is a reason why a system is treated mathematically via its total energy, rather than addressing mass and energy separately in a moving or accelerating system. it seems disingenuous to attempt to deal with mass and energy as f they were different entities - they are only different manifestations of the same thing.