Do Photons have Mass?

Do photons have mass?
The quick answer: NO

However, this is where it gets a bit confusing for most people. This is because, in physics, there are several ways to define and measure a quantity that we call “mass”. Now, it doesn’t create any confusion among physicists because we tend to know in what context such a quantity is defined. However, for the general public trying to decipher scientific papers and presentations, this is a trap that many fall into and can be the source of much confusion.

In physics, the most important definition of a bare mass (we are not going to deal with effective mass that is a part of solid state/condensed matter physics) is what is known as the invariant mass. Invariant mass ([itex]m_0[/itex]) (aka rest mass, proper mass, or intrinsic mass) is independent of the reference frame. In other words, an object’s invariant mass has the same value no matter who is observing the object and no matter what its velocity is relative to the object. The invariant mass of a particle is defined as the total energy of the particle measured in the particle’s rest frame divided by the speed of light squared. More generally, the invariant mass is defined via the general relationship
[tex]E^2 = (m_0 c^2)^2 + (pc)^2[/tex]
which leads to
[tex]m_0 = \sqrt{\frac{E^2}{c^4} – \frac{p^2}{c^2}}[/tex]
Now for a photon, this is zero since [itex]E = pc[/itex]. In many aspects, this is all that we need to know. In physics, something that is invariant after some operation is very desirable.

But photons have energy. By [itex]E = mc^2[/itex], doesn’t this mean that they have A mass?

A photon can still have zero invariant mass ([itex]m_0[/itex]), and can still have energy. There’s nothing inconsistent here. All of the photon’s energy is in the term [itex]pc[/itex]. Some people would say that this is the photon’s “inertial mass” since it is similar to the inertia that one feels when trying to stop a moving mass. This may or may not be useful to consider. However, it certainly should not be confused with the concept of the ordinary mass that most people are familiar with.

There are, of course, other definitions of mass. The most commonly used terminology is something called “relativistic mass”. This mass is defined as
[tex]m = \gamma m_0[/tex]
where
[tex]\gamma = \frac{1}{\sqrt{1-\beta^2}}\\
\beta = \frac{v}{c}[/tex]
This “relativistic mass” is what most people attribute to the “gain in mass” of a particle moving at relativistic speeds. However, one needs to be aware that in professional circles, such a concept is very seldom used. One very seldom hears this when one attends a high-energy physics seminar, for example, or reads a particle collider experiment paper. This is because in citing a relativistic mass, one must also cite the speed of the particle concerning what reference frame. This is cumbersome and unnecessary especially when the invariant mass would have been clearer (that’s why we love invariant anything).

You can read more about this at the Usenet FAQ.

Photons and Mass: FAQs

Do photons have mass?

No, photons do not have mass. More specifically, they lack invariant mass (also known as rest mass). Invariant mass is a fundamental property of a particle that remains constant regardless of its motion or reference frame.

But photons have energy, and E=mc², so doesn’t that mean they have mass?

While it’s true that photons have energy and E=mc², this equation doesn’t imply that photons have invariant mass. The energy of a photon is related to its momentum (p) by the equation E=pc. This means a photon can possess energy without having mass.

What is “relativistic mass,” and do photons have it?

Relativistic mass is a concept that attempts to describe the increase in a particle’s energy as its velocity approaches the speed of light. However, this concept is outdated and rarely used in modern physics because it depends on the particle’s velocity relative to a specific reference frame. Since photons always travel at the speed of light, their relativistic mass would be infinite, which is not a physically meaningful quantity.

What is the significance of invariant mass in physics?

Invariant mass is a crucial concept in physics because it provides a fundamental and unchanging property of particles, irrespective of their motion or the observer’s frame of reference. It is a key parameter in understanding particle interactions and fundamental forces.

If photons don’t have mass, how can they exert pressure, like in solar sails?

Although photons lack mass, they carry momentum. When photons collide with a surface, they transfer this momentum, creating a force that can be used to propel objects, such as solar sails.

How do we know that photons don’t have mass?

Numerous experiments and observations support the conclusion that photons are massless. For instance, if photons had mass, light from distant stars would be bent by the Sun’s gravity differently than what we observe. The precise agreement between the observed and predicted bending of starlight confirms the massless nature of photons.

What’s the difference between “inertial mass” and “invariant mass”?

Inertial mass is a measure of an object’s resistance to acceleration when a force is applied. While some argue that photons have “inertial mass” because they carry momentum and can exert pressure, this concept is not equivalent to invariant mass and can be misleading.

Does the concept of a photon’s mass have any practical implications?

While the debate about photon mass might seem theoretical, it has profound implications for our understanding of the universe. For example, if photons had even a tiny mass, it would affect the range of the electromagnetic force and have consequences for the evolution of the universe and the formation of galaxies.

The following forum members have contributed to this FAQ:
Hootenanny
jtbell
ZapperZ