Einstein and Relativity

Albert Einstein is considered to be one of the greatest physicists of all time - on par perhaps with Newton. His radical views on space and time profoundly changed the landscape of both physics and astronomy. In this section you will be introduced to some of his radical thinking!
	Figure 4.37 Image of Einstein from 1921 when he was at the height of his fame. (Image is in the public domain)

A brief survey of the life of Albert Einstein

• 1700 - 1880: The Newtonian worldview successful and dominant. Maxwell had explained light, electricity and magnetism and together with Newton everything physical seemed knowable.
• 1879: Einstein born Ulm, Germany.
• 1885 - 1925: Michelson and Morley began a series of puzzling experiments
• 1900: Max Planck shocked the physics community with the concept of quantization
• 1905: The miracle year in physics: Einstein published papers on Brownian motion as well as the seminal papers on his theory of relativity
• 1915: Einstein extended his discussion of relativity to include gravity and thereby explained the problem of Mercury.
• 1919: Eddington confirms Einstein's prediction concerning deflection of starlight.
• 1915 - 1925: Einstein was a co-leader in the birth and development of quantum mechanics
• 1925 - 1935: Einstein and Bohr engaged in a fascinating series of "debates" over the interpretations of physics especially the notion of determinism (God does not play dice)
• 1930 - 1955: Einstein searches for a unified theory of the universe
• 1933 - Hubble and Humanson discover the recessional nature of galaxies - Einstein's theories of the universe take shape.
• 1955: Einstein dies, Princeton, N.J.

The Greatest Experiment that Never Worked! - The Micheslon-Morley Experiment

The Earth is moving at about 30 km/s through space as it orbits the sun. Does this motion affect the speed of light. Most physicists in 1880 would have said YES and this formed the basis of a conceptually simple experiment by the young American physicist Albert Michelson and (eventually) his colleague at the Case Western University in Washington - Edward Morley.

Figure 4.38 Michelson-Morley applet simulates the famous experiment that "never worked".

Figure 4.38 provides you with an applet to assist you in visualizing the Michelson-Morley experiment. Although the Michelson-Morley experiment did not directly influence Einstein in the development of his theory it is one of the earliest demonstration of the ideas of relativity and is easily understood in the light of The Special Theory of Relativity.

The Special Theory Of Relativity

Some Features of Special Relativity

 

Speed of light (c) is the speed limit for matter. No material thing can travel faster than light.

Mass appears to increases with increasing velocity. In fact, it is the momentum that changes faster than Newtonian physics predicts and this gives the appearance of increased mass. This is shown in Figure 4.39

Figure 4.39 Apparent mass increases with velocity and becomes infinite at the speed of light

Time slows down with increasing velocity. The applet shown in Figure 4.40 illustrates this. This gives rise to the famous "twin paradox".

Figure 4.40 Time dilation applet

Lengths "contract" (rotate) as objects move (click here to see an MPEG illustrating how shapes would change as you zoomed past Saturn at 0.99c )

Figure 4.41 Video of a relativistic fly-by of Saturn

Mass and energy are interchangeable- in a fundamental way equivalent. This is one of the most famous of Einstein's discoveries

Example 4.10 Suppose you traveled at an average speed of 0.99C to the new Oort Cloud Resort situated 0.2 ly away from Earth but sadly couldn't stay and returned as soon as you got there. You had a library book along with you which was due 3 weeks from the day you left. Is your library book overdue when you get back?

Solution: Let's first consider the librarian's point of view. You traveled a total distance of 0.4 light years at an average speed of 0.99C. Seems simple enough, your
trip took

:

Since 0,404 years is about 21 weeks you are WAY overdue!!!
BUT WAIT A MINUTE!!!! you protest...From your frame of reference the trip was much shorter. Use the relativistic effects calculator or the time dilation formula:

which is 2.96 weeks - the books are still OK (barely)!

Example 4.11 How long could you power your house on the energy "locked inside" a single sugar cube?

Solution: My gas and electrical bills indicate that I use about 30 GJ of energy each month. So, in one year I use about 360 GJ or 3.6 x 10¹¹J of energy. So, from a 10 g sugar how much energy can I get? Use E = mc². I would get: E = (0.010 kg)(3x10⁸m/s)² = 9 x 10¹⁴J of energy! Since I use 3.6 x 10¹¹J of energy per year I discover that I can power my house for:

T = 9 x 10¹⁴J/ 3.6 x 10¹¹J/year = 2.5 thousand years!

The General Theory of Relativity

Einstein finished his special theory in 1905. Then he was a completely unknown physicist. By 1915 he was the most famous (or soon to be) physicist in the world and was about to publish his general theory which is his theory of gravity and curved space.

Principle of Equivalence:

Einstein's Theory of Gravity, Curved Space and Model Universes

On the largest scale of the universe gravity (we think) is the dominant shaping force. In order to erect a mathematics of cosmology we need as complete a theory of gravity as possible. Einstein extended Newton's theory of gravitation during the first part of the 20th century. In simplest terms Einstein's theory can be summarized as:

So What's "spacetime"?

Perhaps the most profound implication of Einstein's Theory of Relativity is the union of the ideas of space and time. If you move a clock through space, for example, you alter its rate of measuring time. Since we can no longer treat these as independent ideas physicists now use the term spacetime to discuss both space and time.

Einstein's equations governing the structure of space are very complex. In 1917 Einstein was vexed by a problem that these equations implied. Left on its own the universe would expand! This is particularly puzzling since, if anything you might suspect that it would contract. To "fix" this problem Einstein introduced into his equations the now famous cosmological constant. By the 1920's a number of mathematicians had published solutions of Einstein's equations that made universal expansion a key feature of the universe and in 1929 Hubble provided the empirical evidence that our universe is expanding. Einstein rued that introducing the cosmological constant was "the greatest blunder" of his career.

The Critical Density and The Curvature of Space

One of the key questions of cosmology concerns the "shape" or geometry of space. According to Einstein's theory matter distorts space. The amount of distortion or curvature will depend on the amount of matter - more accurately the density of matter - in the universe. It is fairly easy to relate the shape of space to the density of matter in the universe. If the density of the universe is

Space - In 3 Flavours!

	Positive Curvature: This is sometimes called the closed universe and is analogous to a spherical shape. Imagine that you are an ant living on a spherical surface. Your space is closed, finite and without bound. Some consequences of positive space would be density > critical density If the universe has a positive curvature it will expand but the rate of expansion will slow to zero and then begin to contract back to a point.
Figure4.42a 2-dimensional analog of positively curved space
	Zero Curvature: This is the "normal" space that we experience in every day life. All the laws of geometry are Euclidean. density = critical density space would expand forever but the expansion rate would slow to zero (in the limit)
Figure 4.42b 2-dimensional analog of flat space
	Negative Curvature: This is sometimes called the open universe and is analogous to a saddle shape. Negative space is open,infinite and without bound. Some consequences of negative space would be density< critical density the universe would expand forever in this case.
Figure 4.42c 2-dimensional analog of negatively curved space
Table 4.3 The 3 possible geometries of space

So where are we right now? Our best estimate of the universal density - based on what we see - is about 5 x 10^-27 kg/m³ or about 10% of the critical density. This implies that the universe is either flat or open. In the next section we will consider the reasons why current evidence favours a flat universe.

We will return to this in greater depth in Chapter 15.

Some Features of General Relativity

Spacetime is curved in the vicinity of matter. Figure 4.43 shows this graphically in an image in which the background images of distant galaxies are stretched into arcs by the "bending of space" created by the mass of a foreground cluster of galaxies.

Figure 4.43 Space curved by the mass of the distant cluster of galaxies Abell 2218

Here is a link to a recent JWST image showing how gravitational lensing can be used to turn a galaxy cluster into an enormous telescope!   A more playful way to see how mass curves space is provide in the video clip shown in Figure 4.44

Figure 4.44 Bending of space by the presence of matter

Time slows down in the presence of gravitational fields and light is deflected in gravitational fields. This is shown in Figure 4.45 and was the first critical test of Einstein's theory.

Figure 4.45 Deflection of the position of a star as seen during a solar eclipse.

Historic Images from 1919 Solar Eclipse

Figure 4.46a Stasr as seen near the solar limb during the 1919 solar eclipse.	Figure 4.46b Deflection of the position of a star as seen during the solar eclipse.