Implications of E = mc2

The energy-related mass of photons has two important implications. Remember our exercise about rolling ball bearings in and out of the potential wells (curved space) in our rubber sheet - well we can apply that analogy to photons moving in and out of potential wells. Since photons are affected by gravity, then a photon has to expend some energy to escape from any gravitational field. This loss of energy to a gravitational field is known as a gravitational redshift. In the early Universe there are fluctuations of matter in the spacetime surface and thus there is a network of gravitational potential wells that the photons must navigate. Photons in the early Universe will therefore alternatively gain and lose energy as they move inside and out of these potential wells. As the Universe is expanding, the distribution and depth of these potential wells is changing. To first order, the distribution of photon energies is governed only by the temperature of the Universe. However, the interaction between the photons and gravity wells causes small fluctuations in the energy spectrum. The amplitude of these fluctuations is directly proportional to the overall amplitude of the potential wells.

Figure 2.8 Statistical temperature fluctuations in the CMB as measured by COBE. The blue and red areas represent slightly temperature differences. These temperature differences trace the density fluctuations out of which large scale structure eventually arises.


In probably the most important cosmological experiment yet done, the COBE satellite was able to measure this fluctuation signal as a small dispersion in the temperature distribution of the CMB. The COBE temperature fluctuation map is shown in Figure 2.8. This is a very fundamental observation because these temperature fluctuations are an imprint of the density fluctuations that existed in the early Universe and were later amplified to produce the structure (e.g. galaxies, clusters of galaxies) that we observe today. The COBE fluctuation map is then a glimpse into the very beginnings of galaxy formation in the Universe.

The relation between energy and mass also has another fortunate consequence as it allows the Universe to be observable. Recall that the distribution of mass determines both the large and small scale geometry of the surface of the Universe.

Figure 2.9 Ants in curved space time can only communicate with one another via the blue path. The red path does not follow the surface of the curved Universe.

Since this surface is shaped by gravity and since photons are effected by gravity, then light rays are constrained to follow the same pathways on this surface as any piece of matter follows. Thus, photons emitted from any source must follow the overall curvature of the Universe; they are not allowed to leave this surface. This means that if you place detectors on the surface, they will eventually be struck by photons thus allowing the Universe to be observed. This is conceptually shown in Figure 2.9 for the ant Universe. The ant with the flashlight wishes to communicate with another ant but curved spacetime separates them. The red pathway is not allowed as that would represent a geodesic which is no longer attached to the surface of the Universe. Only the blue pathway is allowed, indicating that no matter how severe the curvature is, the photons must still traverse that region.