How does light not have mass?

Question

How is it possible for light to have zero mass because it was my understanding that in order for "stuff" to exist it has to have some form of mass? And if it does not have mass then can it be affected by gravity.

Answer 1

Generally, most natural scientists recognize that there are two kinds of "stuff" in the universe. Matter and also, energy. Although modern physics asserts that matter and energy are equivalent in the sense that they are interchangeable, i.e. $E=mc^2$, energy is not required to posses mass. Energy can stem purely from field momentum. In fact the famous mass-energy relation alluded to earlier is but a special case of the full relativistic energy-momentum-mass relationship given by:$$E^2=p^2c^2+m^2c^4.$$ The relation $E=mc^2$ comes from the extreme case when energy is totally comprised of the massive type, where $p=0$, similarly, light represents an extreme when the energy is present without any massive contribution, i.e. $m=0$ gives the result that: $E^2=p^2c^2$. This is the kind of energy that light has; and is the source of energy that powers the photoelectric effect employed in many modern technologies.
As for light's interaction with gravity, despite its lack of mass, one must account for a fuller understanding of gravitation that goes beyond Newton's concept of universal gravity. Particularly, gravity is now identified with the intrinsic geometry of the space-time continuum, rather than a long range action at a distance type of force like the electromagnetic field. Light is bent by gravity because it is travelling, unaccelerated, through a curved space-time along a path of minimal distance known as a "geodesic". All of the above phenomena are the result of improved knowledge of physics that has come about as a 20th century revolution in physics largely initiated by Albert Einstein. You may well enjoy adding some introductory reading on Einstein's special and general theory of relativity to fill the gaps in your traditional understanding of matter and energy and space-time.

Answer 2

At its core, things fall because of time dilation. Nobel Laureate Kip Thorne referred to what he calls “Einstein’s Law of Time Warps”. He said, “Things like to live where they age the most slowly. Gravity pulls them there. And so as an application, the Earth's mass warps time according to Einstein. It slows time near the surface of the Earth. And this time warp is what produces gravity.”

This dilation of time near a planet, star or galaxy is also responsible for the bending of light, but for a slightly different reason. And this shows you why light does not need mass in order to be affected by gravity. You have seen the refraction of light when it enters a prism at an angle. The explanation given was always because the glass prism is a denser material. But what this really means is that light travels at a slower speed inside the glass then it does in the air. So when light hits the glass at an angle, it bends towards the slower speed. The same thing happens when light approaches a planet at an angle. It hits the dilated time near the planet and bends towards the planet. It's just refraction.

This does not in any way disagree with the other answers given to your question, it just provides a concrete, non-mathy explanation for how relativity explains the bending of light.

Answer 3

Two questions come to mind:

1. What is mass?
2. What is energy?

The second question is difficult, but let us lose all of generality and speak of energy Conservation instead. In classical physics (Analytical is always better), it is a scalar quantity conserved with respect to the passage of Time. Hamiltonian formulation of mechanics, where the Hamiltonian function is the Hero, is a sophisticated way to formulate total energy of a system, where total mean Kinetic (Energy of motion, which is $0$ in a physically static system) and Potential (Literally potentially kinetic, but is not kinetic) Energies, added together.

The mother of all four-vectors (Meaning the principle of Special Relativity (SR) has a chance to realize itself as a mathematical procedure, and its output is not affected by applying transformations called Lorentz Transformations) is infinitesimal space-time displacement. It has two realizations, like any four vector. In SR it is most favorable to start with a covariant vector, which has the index not in the top, but at the bottom. It does not carry the signature of the metric tensor. Applying the Minkowski metric tensor (It is its own inverse as a matrix) negates the time component and raises the index, and outputs a contravariant vector:

$$X^\mu := \eta^{\mu\nu } X_\nu=\eta^{\mu 0 } cdt + \eta^{\mu 1 } dx + \eta^{\mu 2 } dy + \eta^{\mu 3 } dz=-\delta^{\mu 0} cdt + \delta^{\mu 1} dx + \delta^{\mu 2} dy + \delta^{\mu 3} dz$$

$$d \tau ^2= X_\mu X^\mu=-c^2dt^2+dx^2+dy^2+dz^2$$

$$P_\mu := mV_\mu := m\frac {dX_{\mu }}{d\tau}$$

The last is the Four-Momentum. The $0$ component is Relativistic Energy, No longer conserved in different speed of motion, but Squaring it and subtracting the square of magnitude of spatial momentum is indeed conserved. We might as well then remain seated in our Rest Frame and calculate this invariant with ease. No motion means no spatial momentum, and the Relativistic Energy is as such, but we multiply by $c^2$ to have dimensions of energy:

$$E_0^2:= -c^2 \eta_{\mu\nu } P^\nu P^\mu =-c^2 P_0 P^0 = m^2 c^4 \frac{dt^2}{d\tau^2}=m^2 c^4$$

$$E_0=mc^2$$

A static frame, meaning this is no other than potential energy, for the sake of existence, a mass exists.

Promoting the procedure to a relativistic picture of non relativistic motion we get:

$$E=mc^2 \sqrt{1+ \frac{P^2}{m^2 c^2}}=mc^2+\frac{P^2}{2m}$$

The quadratic term in the Quadratic McLaurin expansion is Newton's kinetic energy. This is a double whammy, because we already knew $mc^2$ is supposed to be potential energy.

This brings us to question $1$, which we had now answered somehow by asking about the nature of energy.!

About your train of though:

I believe it is appropriate to replace "Stuff" with Causality.

Light is the upper bound, and turn out to be the maximal (Also an upper bound but is included rather than left with a chance to be excluded from the set of speeds) speed that allows two events to be in cause-effect relation with each other.

The bizzare fact is that a massive mediator ($m>0$) cannot reach this maximum, and light, being massless, can never leave this maximum.

In General Relativity, photons do have a VIP seat:

In terms of being Electro Magnetic field, then in case of a central charge the empty space time around it obeys the field equation: "Ricci Tensor = Constant * Stress-Energy Tensor". The scalar vanishes because the field strength tensor is anti symmetric.

$$R_{\mu\nu}=CT_{\mu\nu}$$

It means that photons pave the curvature and also portray it. They curve by twice the amount of massive objects.