One hundred
years ago in November 1915, Albert Einstein presented to the Prussian Academy
of Sciences his new theory of general relativity. It is fair to say the theory
turned out to be a great success.

General
relativity was built on Einstein’s special relativity, which provided solutions
to some of the greatest puzzles of the 19th century theoretical physics.

So in order
to grasp the meaning and significance of general relativity, it is worth
reflecting on the state of physics in the 19th century to see how Einstein came
to realize that space, time and geometry are not absolute but depend on the
physical environment.

**The beauty of invariance**

In the 17th
century, Isaac Newton developed a set of equations that described the physical
properties of the world around us. These equations were very successful, from a
description of the flight of a cannonball, to the motion of the planets.

They also
had a very appealing property: all observers, regardless of whether they are
moving or not – i.e. regardless of which “inertial frame” they are in – are
equivalent when it comes to their description of the world around them. So two
individuals moving in different directions would see events unfold in the same
way.

Even though
formally these individuals would see things in a different way – one might say
that things move from left to right, whereas the other might say they move from
right to left – still the fundamental description of the unfolding events would
remain the same, and the laws of physics derived by these individuals would
have literally the same form.

But in the
19th century, people started noticing that not everything plays accordingly to
this rule.

**Problems with electromagnetism**

The 19th
century was a time of extensive study of the phenomena of electricity,
magnetism and light. In 1865 James Clerk Maxwell published a set of equations
that combined all these phenomena into a single phenomenon of
“electromagnetism”.

Soon after
Maxwell’s discovery, people realised that there is something strange when it
comes to his equations. Their form changes when we move from one inertial frame
to another. So an individual who is not moving can observe distinctively
different physical phenomena than a person who is moving.

All the
beauty of invariance and irrelevance of observers that we had got used to in
Newtonian physics was gone. It now looked like some frames were preferable to
others when it came to describing events in nature.

Then, at the
turn of the 20th century, a new mathematical transformation was discovered that
could preserve the structure of Maxwell’s equations when moving from one frame
to another. Although many people contributed to this discovery, we now refer to
it as the “Lorentz transformation”.

The Lorentz
transformation was different from the standard transformation of inertial
frames that had been used in the Newtonian physics. In Newtonian physics,
length and time are absolute, so the length of an object in one frame is the
same as the length of that object in another frame. Also, time passes in the
same way in one frame as in the other frame.

However, if
taken literally, the Lorentz transformation implies that time and length do
actually change, depending on which frame of reference you are in.

**Principle of relativity**

This got
Einstein wondering whether the transformation that preserved the structure of
Maxwell’s equations was merely a mathematical trick or whether there was
something fundamental about it. He wondered whether time and space were
absolute, or whether the principle of invariance of the laws of physics should
be paramount.

In 1905,
Einstein decided that it is the in-variance of the laws of physics that should
have the highest status, and postulated the principle of relativity: that all
inertial frames are equivalent, the observer’s motion (with constant velocity)
is irrelevant, and that all laws of physics should have the same form in all
inertial frames.

When
combined with electromagnetism, this principle would require that the
transformation from one inertial frame to another must have a structure of the
Lorentz transformation, meaning that time and space are no longer absolute and
change their properties when changing from one inertial frame to another.

**What about gravity?**

In 1907
Einstein realised that his theory was not complete. The principle of relativity
was only applicable to observers moving with a constant velocity. It also did
not fit with the Newtonian description of gravity.

Einstein,
being a patent officer, did not have access to laboratory equipment. To
compensate, he had to engage himself in thought experiments. He considered
various scenarios in his head and worked through them step by step.

These
thought experiments showed to him that gravity is not different from
acceleration. So standing stationary on the Earth feels just the same as
standing in a rocket ship accelerating at a constant 1G.

It also
showed that the accelerated observer would observe that fundamental geometrical
properties change. For example, that the number π (a mathematical constant)
could no longer be defined as a ratio of a circle’s circumference to its
diameter.

So it was
not just time and space that lost their absolute meaning, but Einstein realised
that also geometry itself was not absolute and could be susceptible to physical
conditions.

**The road to general relativity**

All this
reasoning convinced Einstein that the geometry of the spacetime and the
physical processes that take place in the spacetime are related to each other
and that one can affect the other.

It also led
to a striking conclusion: what we perceive as gravity is just a consequence of
the motion through the spacetime. The larger the curvature of the spacetime the
stronger gravity is.

It took
Einstein eight years to find the relation between the geometry of spacetime and
physics.

The
equations that he presented in 1915 not only led to a completely different
interpretation of events around us but also provided an explanation for some
baffling or yet to be discovered phenomena: from the anomalous orbit of the
planet Mercury, through the bending of light by the Sun’s gravity, to
predicting the existence of black holes and expanding universe.

It was a
bumpy road from Newtownian physics to special and then general relativity. But
each step, driven by Einstein’s insight, drove inexorably towards a picture of
the universe that persists to this day.

Krzysztof Bolejko, Cosmologist, University of Sydney.

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