RE: Visualizing magnetic field in real time - question for lemouth
Edit photons have no mass but they have energy which can act as mass. Been a while since I took the class
So in reference to your question of bending something without mass like a photon, easy, a photon has mass just not rest mess.
What I mean is that a photon has inertial mass and gravitational mass (i.e. using einsteins mass-energy equivalence we can find that there is mass present, it is just very very very very small)
Remember the equation is E2=(mc2)2+(pc)2
and since a photon has no rest mass we can remove that term and make it:
E = |pc|
and since the energy of a photon can also be calculated as
E = hc/λ you have
hc/λ = |pc|
p = |hc/λ|/c
mc = |h/λ|
m = |h/λc|
Or roughly 2.2*10-41 kg.for a photon of wavelength 100cm (microwaves/radiowaves)
Basically, photons have no rest mass but since they have inertial mass (and Einstein postulated in his theory of general relativity that passive gravitational mass will be equal to the inertial mass) gravity still effects them
I am afraid to say that this is wrong. A photon has no mass, all experimental test trying to falsify this didn't work. The mass is an intrinsic properties of any particle or system and is fixed and constant.
In fact, what is sometimes called the relativistic mass is not the mass of the particle, but its energy up to some constant. In particle physics, we by the way simply call this energy.
In your reasoning, I don't understand this:
This implies that p = mc. I don't understand where this comes from.
My apologies it may have been a couple of years since I took a class involving relativity (little fuzzy) but doesn't the energy-mass relationship give a photon something like virtual mass, as in if there is a given amount of energy within a location then it can act as if it had mass? I mean thats how it was explained to me is that a photon has no rest mass but its energy can act as if it has mass which is why it is affected by the curvature of spacetime since the curvature is more of a resistance that affects the motion of mass itself.
I can be completely wrong and spewing crap here but it was explained to me that the energy produces a sort of virtual mass (might have the word wrong). As for the equations, they were pulled from my notes (from the class) on how to calculate the "virtual mass" or relativistic mass at which would be acted upon.
I think it is just a wording issue about what a mass is... Don't worry. I will try to clarify.
The mass is a real and well measured quantity for any particle. It is thus constant. Period. This is what is called the rest mass in your comment.
Now, one can do the following exercise. First, we start from the energy of the particle (which contains the mass, the kinetic energy and the potential energy) and by having the E = mc2 relation in mind, we can calculate a 'mass' that is given by the energy over the speed of flight squared. This has nothing to do with the (rest) mass of the particle, but it often called the relativistic mass. This wording is very misleading (I even would say obsolete) as this is roughly speaking the energy of the particle.
And now you have a third kind of mass that is called the inertial mass. It can be derived by applying a force on the particle and measuring the acceleration, having in mind Newton's law (F = ma). However, it has to be equal to the gravitational mass, or just the mass of the object. This stems from the equivalence principle. Up to now, physicists are trying to find deviations here. So far, data shown the the gravitational mass and the inertial mass are equal at the 10-13 level (we expect an improvement to 10-15 by the end of this year thanks to the Microscope experiment).
I hope that this clarifies :)
I have to say I was not familiar with inertial mass and gravitational mass of a photon. Or I have forgotten about it? They always leave (pc)2 part out of the famous equation.
E=mc2 is only valid for objects at rest :)