The Cosmological Principle

The latter part of the 19th century and especially the early part of the 20th century is known as the Golden Age of Physics. Progress in lots of different branches of physics was occurring at break-neck speeds and there was a growing recognition that physics had to be universal. The embodiment of this recognition is known as The Cosmological Principle which asserts that the Universe must be homogeneous and isotropic. Put another way, the Cosmological Principle holds that the Universe is not arbitrary and, hence, any local physics that is observed must also exist on larger scales. Thus, Newton's formulation of gravity should be universal in its application. Gravity should not behave differently on the Earth or in the Solar System as it would at any other location in the Universe.

This idea of universality, however, is often challenged by students who wonder how is it we can know that the laws of physics are the same elsewhere as on the Earth. In asking that question, most students don't realize they are asking the same question as "How do we know the laws of physics in Philadelphia are the same as in Vladivostok?". That is, since nothing is special about Earth, there is no reason to think the Earth is anymore as unique, in terms of physics, as Philly. Initial verification of the universality of physics was provided by William Herschel. In addition to cataloging stellar positions, Herschel also made accurate measurements of the positions of "double stars". Analysis of these observations showed that the position changes represented a mutual orbit of the two stars and that these orbits could be fully explained by Newtonian gravity. Thus, the same force that keeps the moon in orbit about the Earth, holds for distances many millions of kilometers from the Earth. Hence, it would seem that Gravity really is a universal force which must be of primary importance in shaping the nature of the observable Universe. But, as we will shortly see, Newton's formulation of gravity is not completely correct and requires a further modification. This modification was provided by Einstein in the form of general relativity.

Curved Spacetime

The early 20th century brought many new and profound developments to our cosmology and for the first time showed that Newtonian theory was not a complete specification of gravity. In the late 19th century, precision observations of the position of Mercury showed that it did not agree with the predictions from Newtonian theory. This is similar to the case of Mars, where Kepler used positional discrepancies to show that planetary orbits had to be elliptical in shape. The resolution for Mercury isn't quite so simple. It turns out that Newton never explicitly considered the "shape" of spacetime but implicitly assumed that space is completely flat. The resolution of the positional discrepancy of Mercury requires that space be "curved" in the vicinity of Mercury so that Mercury orbits inside this curvature. Such an orbit will differ slightly from an orbit in purely flat space. This is Shown in Figure 2.1.


Figure 2.1 Visualization of the orbital precession of Mercury as it is orbiting in curved space near the Sun. The curved space causes the orbit to precess over time thus tracing out a different orbital path.


But, why would space be curved in the vicinity of Mercury? The answer lies in Mercury's proximity to the Sun. Einstein postulated that gravity is really the manifestation of curved space and that very massive objects cause a greater degree of curvature and hence have a greater gravitational influence. Mercury is sufficiently close to the Sun that it orbits in curved space. The rest of the planets are far enough away from the Sun that the degree of curvature caused by the mass of the Sun is negligible. While a full description of the General Theory of Relativity is well beyond our scope, we can summarize it qualitatively as follows:

Space communicates with matter and instructs it how to move and, in turn, matter communicates with space and instructs it how to curve.

In this way, the distribution of mass determines the overall curvature of the Universe as well as the particular pathways that objects, including light, must follow. These concepts will be further elucidated below.



The Equivalence Principle: E = mc2

In addition to General Relativity, Einstein also developed the case of Special Relativity which asserts that the laws of physics are identical in all inertial frames. In fact, this is a requirement for the Cosmological Principle to be true and provides another answer to a frequent student question: how come the speed of light isn't infinite? For the laws of physics to be the same in different inertial frames, the speed of light must also be the same in different inertial frames, even if those frames are in relative motion. This condition requires that the speed of light be a universal constant and independent of the motion of the source. Thus, for an object that is one million light years, the time it takes for light emitted by that object to reach us is one million years away, regardless if the object is stationary or moving. If this were not the case one could do the following though experiment.

Another example from your every day experience may also help you to believe the counter-intuitive concept that the speed of light is independent of the motion of the source. That is, the speed of the light in an automobile headlight doesn't depend on whether the automobile is going 20 or 200 mph. If you wish, you can think about the difficulty of nighttime driving if, in fact, the speed of the light was different for cars of different velocity!

If the speed of light is a constant, then there is finite communication time between events. This leads to the important concept of causality in which events that occur in the Universe can be traced back sequentially in time. In Newtonian Cosmology, there is no finite communication time which means, in principle, every event that occurs in the Universe reaches the same point (i.e. your eyes) at the same time and there would be no causality, only confusion!

Special relativity allows a number of important effects to be derived. For instance, for objects moving near the speed of light, time runs slower, lengths become shorter and masses increase. These effects are all very real in particle accelerators and need to be taken into account. The effect of mass increasing with velocity can be understood through relativity as a relation between the increase of kinetic energy in one frame and a mass increase in another. This leads to the important principle of equivalence, E= mc2 where c is the speed of light.

This principle established that energy and mass are equivalent and therefore subject to the same physical laws. Any object which has energy also has mass and is therefore affected by gravity. Therefore, light can "bend" in a strong gravitational field (this effect has been directly observed). In addition, mass can be converted into energy and energy into mass. This explains the energy source available to stars. Prior to establishing the mass-energy relation, the only credible source to explain the huge energy outputs of stars was developed by Lord Kelvin who suggested that stars are radiating energy as a result of gravitational collapse. The problem with Kelvin's models, is that our Sun could only last for a few hundred million years and evidence was mounting that the Earth was, in fact, a few billion years old. Thus, there must be another energy source for the Sun and that source is thermonuclear fusion which converts mass into energy according to E= mc2 . Because c is a very large number already, c2 is enormous and it is this enormity that allows the stars to radiate the energy that is observed. This equivalence principle also has other important applications. We will see later that the physics of the very early Universe is dominated by mass-energy exchange.