Why do photons have momentum

My students had read that light has momentum and they were right, light really does have momentum. But then I come to class and I'm all like, hey, guess what, light has no mass. Now my students are thinking to themselves, dude, but P equals MV. In other words, if momentum equals mass times velocity, how could light, which has no mass, ever have momentum? Well, I had to break it to my students that P equals MV isn't really accurate for things that travel close to the speed of light.

For things going that fast, you have to use special relativity. I don't wanna waste a lot of time talking about special relativity in this video so you're just gonna have to take my word for it that the rules of special relativity allow for a loophole.

This loophole provides a way for massless objects to have momentum. Alright, so the bad news is that we cannot use P equals MV to find the momentum of a photon.

The good news is that the formula for the momentum of a photon is simple, the momentum of a photon equals H over lambda. H is Planck's constant, 6. The idea of four-velocity is not really anything difficult. It is simply a velocity with four spacetime components t,x,y,z as opposed to the normal three space components x,y,z. The normal three velocity is defined as the derivative of the spacial components with respect to time.

Similarly, four-velocity is defined as the derivative of the spacetime components with respect to proper time. So, four-velocity is simply the relativistic analogue of the regular velocity. These are, in fact, nothing but the squares of the four-velocities! So, we can insert all of the things we derived so far like this:. Now, we just need to do one thing and that is to consider the relativistic total energy not including potential energy , which is defined as follows see in my article here :.

From the above formula we can indeed see what happens in the case of a photon, when the mass goes to zero forgetting about the i-index :. This tells us that the momentum of a photon is proportional to its energy, which is exactly what we would expect based on experimental results.

Well, that requires taking a look at the quantum mechanical model of a photon. If we really wish to consider the energies and momenta of particles, such as photons, we do have to take into account quantum mechanics as well. A photon is, after all, an elementary particle. At the turn of the 20th century, Max Planck deduced, partly by accident that the energy of electromagnetic radiation light was actually not continuous such as it is typically thought of, but rather comes in discrete energy packets that have energy proportional to the frequency of the electromagnetic radiation.

It was later Einstein who won the Nobel prize through his work on the photoelectric effect for showing that these energy packets are, in fact, massless elementary particles, which became known as photons. This is the same "m" that you multiply velocity by to find momentum p , and thus is sometimes called the inertial mass.

It's also the mass that provides the source of gravitational effects. Light has this "m" because it has energy. So it is indeed affected by gravity- not just in black holes but in all sorts of less extreme situations too.

In fact, the first important confirmation of General Relativity came in , when it was found that light from stars bends as it goes by the Sun. This is invariant because it doesn't change when you describe an object at rest or from the point of view of someone who says it's moving. Obviously that's a good type of "mass" to give when you want to make a list of masses of particles. There is no point of view from which the light is standing still! However, once you consider light traveling in a variety of directions, the E's from the different parts just add up to give the total E but the vector p 's don't.

In fact the total p can be zero if there are beams traveling opposite ways. So for many purposes the older definition of m the inertial mass is more convenient than the invariant particle mass, since it's the inertial mass that's just the sum of the inertial masses of the parts. Mike W. Do you think this is absolutely true or is not certainty?

It's not just true in quantum physics. Even classical electromagnetism, as in Maxwell's equations, required that light have momentum. It's been measured in countless experiments. It's just plain true. I think it was Einstine who proved that no mass can travel at the speed of light.

As any object of any arbitrary mass when approximates the speed of light increases in mass. When it reaches the vecinity of speed of light its mass is so enormous that it requires infinite amount of energy to propel it. Am I correct? Since photons have zero rest mass they can move with the speed of light.

Light has mass. Generally,Mass is defined as the amount of substance or matter contained in the body. Also , according to the Newton's gravitational law mass can be defined as a quantity which has gravitational property that is it can apply gravitational force to other body and also it can be influenced.

But you can say that the photon has relativistic mass if you really want to. In modern terminology the mass of an object is its invariant mass, which is zero for a photon. If we now return to the question "Does light have mass? By this definition a beam of light is massless like the photons it is composed of. However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in both directions symmetrically in the box, then the total momentum is zero in the box's frame of reference but the energy is not.

Therefore the light adds a small contribution to the mass of the box. This could be measured--in principle at least--either by the greater force required to accelerate the box, or by an increase in its gravitational pull. You might say that the light in the box has mass, but it would be more correct to say that the light contributes to the total mass of the box of light. You should not use this to justify the statement that light has mass in general. Part of this discussion is only concerned with semantics.

It might be thought that it would be better to regard the mass of the photons to be their nonzero relativistic mass, as opposed to their zero invariant mass. We could then consistently talk about the light having mass independently of whether or not it is contained.