Special Relativity: An Origins Story

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Albert Einstein’s paper (screenshot shown here) introduced Special Relativity, a theory that changed the way we see space and time.

Albert Einstein introduced Special Relativity (SR) in his paper in 1905 (in the Resources section, below this article, you can read the paper in its entirety). SR changed the way we see space and time, from a stationary stage where physics was taking place to an object that itself abides by the laws of physics.

Here, we are not going to explore Special Relativity in much detail – instead, we are going to explore why such a bizarre theory was needed in the first place.

Galileo’s Ship

The concept of relativity was not a new idea in physics when Einstein came along. Galileo Galilei designed a thought experiment.

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Fish in a tank in the bottom of a ship will swim the same, no matter what the ship’s velocity is. Image by Danny DeBruyne

Imagine being in a basement of a ship with some friends. There are also some butterflies and some fish in a fish tank. You can perform any series of experiments in that basement while the ship is at rest. Jump up and down, play catch with friends or observe the animals and the direction in which they are flying/swimming.

Then you can repeat those experiments while the ship is in motion. As long as it is moving at a constant velocity you won’t get different results(ref2). The point being that there is no experiment that you can do on the ship that can tell you how fast the ship is moving. Inside the basement all of the objects had the same velocities relative to each other, no matter the ships velocity as that velocity was added to all of them equally.

In other words “The laws of physics are the same in all inertial frames of reference.” That wording would later become the principle of relativity and the first postulate of Special Relativity.

Sir Isaac Newton is the father of classical physics, but he stood on the shoulders of the intellectual giants before him. Image courtesy of the University of Cambridge

Newton, Father of Physics

Sir Isaac Newton once famously said:

If I have seen further, it is by standing on the shoulders of giants.”

Galileo was probably one of those giants, if not the giant upon whose shoulders Newton stood. Newton studied the works of great thinkers that came before him, from Aristotle to Galileo and Kepler. He created classical physics and, by the way, the mathematics needed to understand it.

Newton’s three laws of motion and the law of gravitation could explain most of the world. Scholars could now use mathematics to accurately predict the motions of objects, from the collision of two rocks to the orbit of the moon using a few simple equations!

Classical physics theory was consistent and there was not much reason to believe Newton’s laws would need modifications. Perhaps more precise measurements were to be taken in the future, but classical mechanics looked like it was here to stay.

Maxwell’s Weird Speed

The first challenge to classical physics came from an unlikely source. James Clerk Maxwell studied the phenomena of electricity and magnetism. He explained that both electricity and magnetism were different manifestations of the same fundamental force.

Maxwell summed up the knowledge of this new force (electromagnetic) in four elegant equations, known as Maxwell’s equations.

Electromagnetism is propagated by electromagnetic waves of various frequencies. The waves we can see, we call the visible light. Maxwell’s equations predicted the speed of these waves – the speed of light. But there was a big problem; the speed of light was a constant. It was not relative to anything, it did not care how fast its stage was moving. If there was a light source in the basement of a ship, it did not carry the ship’s velocity with it, therefore light was in contradiction to classical physics!

Either Maxwell or Newton were wrong – not a good fight for Maxwell to take on, and there was a need for another giant to settle this conflict.

Relative but Special

The laws of physics are the same in all inertial frames of reference” and “The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.” Two seemingly contradictory statements; these are the two principles of Special Relativity.

To understand why it seems impossible for the two statements to be both true we will visit Alice and Bob (‘A’ and ‘B,’ two frequently used characters in thought experiments, who often live in a vacuum).

Alice is standing still holding a torch, while Bob is moving to the right, away from Alice, with a constant velocity that is equal to half of the speed of light, also carrying a torch.

The light from Alice’s torch travels at the speed of light, ‘c’, relative to Alice.

The same can be said about the light coming from Bob’s torch with relation to Bob.

As Alice is standing still and Bob is moving with a constant velocity, they are both in an inertial frame of reference.

It all makes sense until we try to compare the speed of the two light beams. Classical physics would tell us that Bob’s light is one and a half times the speed of Alice’s light relative to Alice. This is in clear conflict with Maxwell’s prediction or the second principle of Special Relativity.

The two beams should travel at the same speed, but how? How does the universe resolve this experiment?

Einstein pondered about similar problems, chasing a light beam and being in a train that moves at speeds close to the speed of light. In the year 1905 he published a paper titled “On the Electrodynamics of Moving Bodies” that resolves this problem. He redefined time and space not as absolute, the same everywhere to all, but as different to different observers. So as an observer moves faster and faster, he experiences time dilation and length contraction!

More precisely, two observers with a large relative speed to each other, observe time and length differently.

The passage of time is relative. Image by edward w.

From Alice’s perspective, Bob’s watch moves slower than hers! And it just so happens that the difference in time experienced allows for both of them to measure the same speed for the light beam.

Bob is perfectly valid to claim that he is standing still and that it is Alice that is moving to the left, and the same rules apply.

The passage of time is relative! This theory contradicts common sense. But not only does it resolve the Maxwell-Newton conflict, it has also stood the test of time – so far over one hundred years.

For example, muons are elementary particles that have a very short life-span. Yet when they move at high velocities their life-span is extended considerably due to them experiencing the passage of time very slowly, as seen from our frame of reference. There have been numerous other experimental confirmations of Special Relativity.

The Beginning of the End for Common Sense

The human mind has an inherent understanding of the universe on a scale familiar to us. Masses of grams and kilograms moving at speeds of a few meters per second. When we consider the extreme cases (great velocities or very small dimensions) the data show that our common sense is of no use. It took intellectual giants stacked on top of other intellectual giants to grant us an understanding beyond our usual limitations.

Special Relativity was just one of the great breakthroughs in twentieth century physics. Its generalisation, General Relativity, and Quantum Mechanics have produced even more bizarre predictions. But these two theories also appear to be in conflict, similar to how Maxwell and Newton once were. It’s a question that remains unanswered – what theory will reconcile the two? And what bizarre predictions will it have?

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