Light has inertia

1.4 Mass and momentum of the photons

For a correct description of photons, some aids from the special theory of relativity (SRT) are necessary. For a particle of rest mass m0 applies with the gamma factor :

From this it can be read:

Squaring the relationships for W. and p and forms the difference , it results:

so:





1.
According to the SRT, mass and energy are equivalent. Photons have energy - do they also have mass and momentum?

An electromagnetic wave has the energy density

.

If the above equation (3) is applied to electromagnetic waves that deal with v = c spread out, so follows

It is W. the energy in a certain volume, which results from the integral of the energy density:

The impulse pthe wave after the relationship p = W./c is correspondingly as the integral over a spatial momentum density to understand:

Comparing the relationship for an electromagnetic wave

with the general energy-momentum relation (4)

then there is only agreement for :

The rest mass of photons is zero.

This is also to be expected: Photons always move at the speed of light. Particles with rest mass different from zero cannot do this because of For their indolence tends towards infinity.



2.
Mass can be proven by its inertia and its gravity. Since mass and energy are equivalent, one can ask: Are photons also inert and heavy?

To investigate the behavior of photons in the gravitational field, the following process is considered:

A photon at A with becomes a particle with rest mass m0 transformed. His energy is then .

The particle overcomes height D in the gravitational fieldH, with its energy decreasing

.

At B the particle turns into a photon with transformed.

Because of energy conservation applies

Difference:

Elimination of m0:

This results in

So the frequency of the light decreases and it becomes longer-wave:

This is a shift towards the red end of the spectrum. Hence this effect is called Gravitational redshift designated. This shift in spectral lines can be demonstrated in light emanating from the sun. The first evidence on earth was carried out in 1962/65 by Pound, Rebka and Snider. With a height difference of DH = 22.6 m, the theoretical value for the relative frequency change resulted:





3.
The momentum of a photon results in

Particles hit by light experience an impact. This can be clearly seen from the comet's tails made up of dust particles: these always point away from the sun. Further, atoms that emit a photon experience a recoil according to the law of momentum.



4.
If one observes the momentum of the photon, the knowledge about the photoelectric effect is deepened.

Light of wavelength falls on a Cs photocell (W.A. = 1.94 eV). The energy of the fastest photoelectrons is then

The momentum of the electrons results from

The photons have a momentum of

So is . The photon cannot push the electron out of the atom as a particle in the Newtonian sense would. The photon does not behave like a "little billiard ball". In the photo effect, the photon only serves as an "energy supplier". The atom must act as a "supplier of impulses".



Note on the mass

In older representations of the special theory of relativity, the one in energy W. and the impulse p occurring term referred to as "dynamic mass":

This is where the relationship comes from

The application of this relation to photons then leads to the fact that one speaks of a "mass of the photon":

This must not be taken literally, since photons are the rest mass m0 = 0 and the speed v = c exhibit. The above term for the "dynamic mass" is therefore not defined for photons.

A meaningful interpretation of the term is to understand this as the mass that a particle would have to have as rest mass so that its rest energy is equal to the photon energy.



Exercises

Do some research on the keywords:

  • positron

  • Positronium

  • Pair creation

  • Annihilation

Try to answer the following questions:

  • Why does a photon have a minimum frequency fmin so that it can create an electron-positron pair? What is this minimum frequency?

  • Why can pair creation only take place with the assistance of an atomic nucleus?

  • Why does the annihilation have to produce 2 photons?