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
Postulate
1:
Observers can never detect their uniform motion
except relative to other objects. There is no fundamental or preferred
frame of reference in the universe. Or, in other words:
The Laws of Physics look the same to all observers as long as they are
not accelerating.
Postulate
2:
The speed of light is the same for all observers
regardless of their relative motions.
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 10^{11}J of
energy. So, from a 10 g sugar how much energy can I get? Use E = mc^{2}. I would get: E = (0.010 kg)(3x10^{8}m/s)^{2} =
9 x 10^{14}J
of energy! Since I use 3.6 x 10^{11}J of energy per year I discover
that I can power my house for:
T = 9 x 10^{14}J/ 3.6 x 10^{11}J/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:
Observers cannot distinguish locally
between forces due to acceleration and forces due to gravitation.
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:
Matter tells spacetime how
to curve; Spacetime tells matter how to move.
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
9 x 10^{-26} kg/m^{3} = critical density
then the universe will be "flat".
If the density is greater than the critical density then space will be positively
curved and less than the critical density would imply negative curvature. What does this mean? The following section and table summarizes
the different aspects of the possible geometries of space.
Space - In 3
Flavours!
One of the strangest ideas in modern astrophysics is that spacetime can be curved! Around the a black hole the curvature is extreme but the universe itself may (or may not) have curvature. The complex mathematics of curved spaces was worked in the mid-19th century by the German mathematician Riemann.
There are 3 basic ways in which space may curve:
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/m^{3} 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.
To understand some of the contributions made by Einstein and how they changed astronomy
click on calculator icon to launch a relativistic effects calculator