Special and General Relativity Explained Simply
In 1894, a high school teacher suggested to one of his pupils, a 15 year old precocious teenager that he should leave school because he was unhappy. The teenager took that advice and did not come back. Later he tried to apply to a prestigious university in Switzerland, but failed the entrance exam. Later in his life, when he tried to get his dream job as a professor, no one would hire him. He had to settle for a lowly job as a clerk at a patent office.
History does not remember the name of that teacher or the names of the universities that rejected him for a job, but it will never forget that teenager, because he went on to not only revolutionize physics, but change the way we view reality itself. In 1999, Time Magazine named him “Man of the century.” Today his name is synonymous with “Genius.”
I am talking of course about Albert Einstein. Yet this entire revolution in physics started with a simple thought experiments, conjured up in his prolific imagination before he even graduated from high school.
What was this simple thought experiments, and how did it lead to probably the biggest revolution in physics since Isaac Newton? That’s coming up right now.
Einstein’s theory of special relativity is convention today. But to understand how revolutionary it was for its time, it is helpful to look at what the conventional understanding of physics was during the time of Einstein’s teenage years.
In 1801, Thomas Young had conducted a simple double slit experiment that showed that light behaved like a wave. So the predominant theory about light at the time was that it was a wave.
The problem is that a wave, it was thought, had to move through some sort of medium. Something has to be there to make the wave – similar to how a wave on an ocean needs water to create a wave.
But light was known to travel through outer space, obvious because you can see starlight. Yet, outer space was believed to be empty containing nothing. And it could be easily demonstrated that light can travel through a vacuum. So scientists thought that the only way light waves could travel through this vacuum was if there was some kind of medium that pervaded space and the entire cosmos.
They called this substance the luminiferous aether.
And this theory of the aether was the standard theory of physics for most of the 19th century.
Late in that same century, in 1887, two scientists by the name of Albert Michelson and Edward Morely came up with an idea to test the existence of the aether. The background ether was believed to be unmoving and static, but because the Earth was moving it was thought that it should affect the speed of particles or waves. If the wave was traveling in the same direction as the earth, the speed of the wave should be higher in the direction of the speed of the earth.
This would be similar to how a boat moves faster if it is moving with the flow of the current than if it is moving against the current.
To test this hypothesis, Michelson and Morley designed a device that split a beam of light and bounced it off mirrors so that it moved in different directions and finally hit the same target. The idea was that if two beams traveled the same distance along different paths through the ether, they should move at different speeds and therefore when they hit the final target screen those light beams would be slightly out of phase with each other, which would create an interference pattern.
But the results were astonishing. They showed that there was no difference in the speed of light of the two measurements. No matter which path the beam took, light seemed to be moving at precisely the same speed. This seriously jeopardized the aether theory.
No one could make sense of it or come up with an alternate theory to explain it.
It was labelled the “Greatest failed experiment of all time.”
This is where Albert Einstein comes in.
The term “Relativity” had been around before Albert Einstein, but it was thought of in a completely different way. Galileo Galilei and Isaac Newton had demonstrated that for example if you are walking in a moving train, and someone stationary on the ground is watching, your speed relative to the observer will be the sum of the speed of the train and your walking speed. You’re in one inertial frame of reference as the stationary observer, and the train and you walking on the train are in another. This makes logical sense.
But something seemed wrong with this classical interpretation of relativity as it applied to light.
Einstein knew this, so he came up with a thought experiment as a 16 year old. His thought was to imagine that he was chasing a beam of light while travelling at the speed of light himself. What would he see?
If young Albert could catch up to the beam, he writes in his notes, “”…I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however,…”
In other words, Einstein should see a stationary wave of light.
Yet that was impossible. Einstein knew such stationary fields would violate the equations of electromagnetism developed by James Clerk Maxwell 20 years earlier. The laws were quite strict: Any ripples in the electromagnetic fields have to move at the speed of light and cannot stand still—there are no exceptions.
In addition, Einstein reasoned that if someone was travelling on a non accelerating train at close to the speed of light, there would be no way for that person to know how fast he was going if there were no windows. This had been the classical view of relativity. Why should the laws of physics be different for a person traveling at some fixed velocity vs someone standing still? This seemed untenable to Einstein.
So he came up with two postulates, and tried to figure out what the physics would be like if the two postulates were true.
Postulate 1 was that the laws of physics are the same for all inertial reference frames. This was part of the classical view of relativity pioneered by Galileo.
Postulate 2 was that the speed of light in a vacuum is constant for all inertial reference frames.
The first postulate is pretty much common sense and had been assumed for hundreds of years. The second postulate, however, was the revolution.
It was a consequence of massless photons moving at the velocity c in a vacuum. You would always measure a light beam’s velocity to be 186,000 miles per second.
This meant that young Einstein would never see the stationary, oscillating fields, because he could never catch the light beam. This was the only way Einstein could see to reconcile Maxwell’s equations with the principle of relativity.
But this solution seemed to have fatal flaw. Einstein later explained the problem with another thought experiment:
(Show Einstein from above scene with a thought bubble, “Fatal flaw?”)
Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say, 2,000 miles a second. Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second.
If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railcar, Einstein concluded, and his first postulate, that the laws of physics must be the same for all frames of reference, would be violated.
This apparent contradiction left Einstein spinning his wheels for almost a year. But then, on a morning in May 1905, he was walking to work with his best friend Michele Besso, an engineer he had known since their student days.
The two men were talking with about this dilemma. And suddenly, Einstein saw the solution, and when they met the next morning, Einstein told Besso, “Thank you. I’ve completely solved the problem.” Einstein even gave partial credit to his friend for helping him solve this issue.
The solution to his thought experiment was that a person traveling on the train must experience time differently than the person on the embankment. Observers in relative motion experience time differently.
This was the moment of the revolution. It completely overturned hundreds of years of classical physics pioneered by Galileo and Newton in which time was fixed and absolute in the universe.
Einstein showed that time is relative, and varies in different frames of reference. There is no absolute frame of reference that the aether was theorized to provide. Thus the idea of the aether was no longer needed.
This one realization that reality is not the same for different frames of reference also led to other implications of special relativity:
That Fast moving object appear shorter
That Fast moving objects appears to have increased mass
And finally, the equivalence of mass and energy. This is the most famous equation in science E=MC2
That mass and energy are equivalent.
So, now the big question is how did Einstein come up with his most famous equation based on his original two postulates? The math is rather complicated, but let’s just look at this conceptually.
There was a time when mass was always conserved. In Special and General Relativity Explained Simply
In 1894, a high school teacher suggested to one of his pupils, a 15 year old precocious teenager that he should leave school because he was unhappy. The teenager took that advice and did not come back. Later he tried to apply to a prestigious university in Switzerland, but failed the entrance exam. Later in his life, when he tried to get his dream job as a professor, no one would hire him. He had to settle for a lowly job as a clerk at a patent office.
History does not remember the name of that teacher or the names of the universities that rejected him for a job, but it will never forget that teenager, because he went on to not only revolutionize physics, but change the way we view reality itself. In 1999, Time Magazine named him “Man of the century.” Today his name is synonymous with “Genius.”
I am talking of course about Albert Einstein. Yet this entire revolution in physics started with a simple thought experiments, conjured up in his prolific imagination before he even graduated from high school.
What was this simple thought experiments, and how did it lead to probably the biggest revolution in physics since Isaac Newton? That’s coming up right now.
Einstein’s theory of special relativity is convention today. But to understand how revolutionary it was for its time, it is helpful to look at what the conventional understanding of physics was during the time of Einstein’s teenage years.
In 1801, Thomas Young had conducted a simple double slit experiment that showed that light behaved like a wave. So the predominant theory about light at the time was that it was a wave.
The problem is that a wave, it was thought, had to move through some sort of medium. Something has to be there to make the wave – similar to how a wave on an ocean needs water to create a wave.
But light was known to travel through outer space, obvious because you can see starlight. Yet, outer space was believed to be empty containing nothing. And it could be easily demonstrated that light can travel through a vacuum. So scientists thought that the only way light waves could travel through this vacuum was if there was some kind of medium that pervaded space and the entire cosmos.
They called this substance the luminiferous aether.
And this theory of the aether was the standard theory of physics for most of the 19th century.
Late in that same century, in 1887, two scientists by the name of Albert Michelson and Edward Morely came up with an idea to test the existence of the aether. The background ether was believed to be unmoving and static, but because the Earth was moving it was thought that it should affect the speed of particles or waves. If the wave was travelling in the same direction as the earth, the speed of the wave should be higher in the direction of the speed of the earth.
This would be similar to how a boat moves faster if it is moving with the flow of the current than if it is moving against the current.
To test this hypothesis, Michelson and Morley designed a device that split a beam of light and bounced it off mirrors so that it moved in different directions and finally hit the same target. The idea was that if two beams traveled the same distance along different paths through the ether, they should move at different speeds and therefore when they hit the final target screen those light beams would be slightly out of phase with each other, which would create an interference pattern.
But the results were astonishing. They showed that there was no difference in the speed of light of the two measurements. No matter which path the beam took, light seemed to be moving at precisely the same speed. This seriously jeopardized the aether theory.
No one could make sense of it or come up with an alternate theory to explain it.
It was labelled the “Greatest failed experiment of all time.”
This is where Albert Einstein comes in.
The term “Relativity” had been around before Albert Einstein, but it was thought of in a completely different way. Galileo Galilei and Isaac Newton had demonstrated that for example if you are walking in a moving train, and someone stationary on the ground is watching, your speed relative to the observer will be the sum of the speed of the train and your walking speed. You’re in one inertial frame of reference as the stationary observer, and the train and you walking on the train are in another. This makes logical sense.
But something seemed wrong with this classical interpretation of relativity as it applied to light.
Einstein knew this, so he came up with a thought experiment as a 16 year old. His thought was to imagine that he was chasing a beam of light while travelling at the speed of light himself. What would he see?
If young Albert could catch up to the beam, he writes in his notes, “”…I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however,…”
In other words, Einstein should see a stationary wave of light. But nothing like this stationary wave of light had ever been observed. And all indications were that the speed of light is the same for every one. An aether scientist might argue that we don’t observe it because we are not moving at the speed of light, and if you could, then you would observe a stationary beam of light.
——- 1
But Einstein reasoned that if someone was travelling on a non accelerating train at close to the speed of light, there would be no way for that person to know how fast he was going if there were no windows. This had been the classical view of relativity. Why should the laws of physics be different for a person traveling at some velocity vs someone standing still? This seemed to be untenable.
So he came up with two postulates, and tried to figure out what the physics would be like if the two postulates were true.
Postulate 1 was that the laws of physics are the same for all inertial reference frames. This is what Galeleo and Newton had also postulated.
Postulate 2 was that the speed of light in a vacuum is constant for all inertial reference frames. This was unique.
Part 2
Yet that was impossible. Einstein knew such stationary fields would violate the equations of electromagnetism developed by James Clerk Maxwell 20 years earlier. The laws were quite strict: Any ripples in the electromagnetic fields have to move at the speed of light and cannot stand still—there are no exceptions.
In addition, Einstein reasoned that if someone was travelling on a non accelerating train at close to the speed of light, there would be no way for that person to know how fast he was going if there were no windows. This had been the classical view of relativity. Why should the laws of physics be different for a person traveling at some fixed velocity vs someone standing still? This seemed untenable to Einstein.
So he came up with two postulates, and tried to figure out what the physics would be like if the two postulates were true.
Postulate 1 was that the laws of physics are the same for all inertial reference frames. This was part of the classical view of relativity pioneered by Galileo.
Postulate 2 was that the speed of light in a vacuum is constant for all inertial reference frames.
The first postulate is pretty much common sense and had been assumed for hundreds of years. The second postulate, however, was the revolution.
It was a consequence of massless photons moving at the velocity c in a vacuum. You would always measure a light beam’s velocity to be 186,000 miles per second.
This meant that young Einstein would never see the stationary, oscillating fields, because he could never catch the light beam. This was the only way Einstein could see to reconcile Maxwell’s equations with the principle of relativity.
But this solution seemed to have fatal flaw. Einstein later explained the problem with another thought experiment:
(Show Einstein from above scene with a thought bubble, “Fatal flaw?”)
Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say, 2,000 miles a second. Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second.
If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railcar, Einstein concluded, and his first postulate, that the laws of physics must be the same for all frames of reference, would be violated.
This apparent contradiction left Einstein spinning his wheels for almost a year. But then, on a morning in May 1905, he was walking to work with his best friend Michele Besso, an engineer he had known since their student days.
The two men were talking with about this dilemma. And suddenly, Einstein saw the solution, and when they met the next morning, Einstein told Besso, “Thank you. I’ve completely solved the problem.” Einstein even gave partial credit to his friend for helping him solve this issue.
The solution to his thought experiment was that a person traveling on the train must experience time differently than the person on the embankment. Observers in relative motion experience time differently.
This was the moment of the revolution. It completely overturned hundreds of years of classical physics pioneered by Galileo and Newton in which time was fixed and absolute in the universe.
Einstein showed that time is relative, and varies in different frames of reference. There is no absolute frame of reference that the aether was theorized to provide. Thus the idea of the aether was no longer needed.
This one realization that reality is not the same for different frames of reference also led to other implications of special relativity:
That Fast moving object appear shorter
That Fast moving objects appears to have increased mass
And finally, the equivalence of mass and energy. This is the most famous equation in science E=MC2
That mass and energy are equivalent.
So, now the big question is how did Einstein come up with his most famous equation based on his original two postulates? The math is rather complicated, but let’s just look at this conceptually.
There was a time when mass was always conserved. In any reaction, whatever mass you put in must be the mass you got out. But if conservation of mass is interpreted as conservation of rest mass, this did not hold true in special relativity.
Since different observers would disagree about what the energy of a system was, the mass and energy taken together must be conserved, not just the mass on its own.
A train travelling close to the speed of light has a lot more energy than a train at rest.
But a person riding on the non-accelerating train may not know that the train is moving. The massive object is moving from the point of view of one observer, but at rest as seen by another observer. One observer would seem to measure zero energy of the object, while the other observer would measure a higher energy.
It turns out that for the laws of physics, namely conservation of energy and momentum, to be consistent in the two “reference frames” of two observers moving with respect to each other, there has to be an energy associated with a body at rest, not just a body in motion. And that is what E=MC2 implies – the M in the equation is the mass at rest. All masses even at rest must have energy.
Some people point out that much of the actual work for special relativity had already been done by the time Einstein presented it.
The concepts of time dilation and simultaneity for moving objects, for example, were already in place and the mathematics had already been developed by Lorentz & Poincare.
Some have even called Einstein a plagiarist. There is no doubt that the “revolution” of Einstein was built on the shoulders of other great scientists. And Einstein may have gotten a lot more credit than others who did prior work.
At the same time, Einstein still deserves the accolades because he took the bits and pieces of the puzzle found by others and put them all together into a whole new theoretical framework.
He rejected the idea of the ether all together which other scientists had not done, and boldly proclaimed a new fundamental understanding of time and reality. And the idea of mass and energy equivalence via E=MC2 is solely Einstein.
Scientists who had done prior work like Thomson, Larmor, Lorentz, or Poincare had never implied such a bold proposition. And just as in life, history tends to favor the bold.
————– (5000 characters)
Einstein’s Special Relativity Explained Simply – no math
This entire revolution in physics started with a simple thought experiments, in the prolific imagination before Einstein even graduated from high school. Einstein’s theory of special relativity is convention today. But to understand how revolutionary it was for its time, it is helpful to look at what the conventional understanding of physics was during the time of Einstein’s teenage years.
In 1801, Thomas Young had conducted a simple double slit experiment that showed that light behaved like a wave. So the theory about light at the time was that it was a wave. The problem is that a wave, it was thought, had to move through some sort of medium. They called this substance the luminiferous aether.
But in 1887, two scientists by the name of Albert Michelson and Edward Morely came up with an idea to test the existence of the aether. The background ether was believed to be unmoving and static, so if the wave was traveling in the same direction as the earth, the speed of the wave should be higher in the direction of the speed of the earth. Michelson and Morley showed that there was no difference in the speed of light of the two measurements. This seriously jeopardized the aether theory.
Einstein knew this, so he came up with a thought experiment as a 16 year old. His thought was to imagine that he was chasing a beam of light while traveling at the speed of light himself. What would he see? If young Albert could catch up to the beam, he should see a stationary wave.
Yet that was impossible. Einstein knew such stationary fields would violate the equations of electromagnetism developed by James Clerk Maxwell 20 years earlier.
So he came up with two postulates, and tried to figure out what the physics would be if the two postulates were true.
Postulate 1 was that the laws of physics are the same for all inertial reference frames.
Postulate 2 was that the speed of light in a vacuum is constant for all inertial reference frames.
The first postulate had been assumed for hundreds of years. The second postulate, however, was the revolution.
This meant that young Einstein would never see the stationary, oscillating fields, because he could never catch the light beam.
But this solution seemed to have fatal flaw. Einstein later explained the problem with another thought experiment:
Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say, 2,000 miles a second. Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second.
If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railcar, and the first postulate would be violated. The solution to his thought experiment was that observers in relative motion experience time differently. This completely overturned hundreds of years of classical physics in which time was absolute in the universe. Einstein showed that time is relative, and varies in different frames of reference. The idea of the aether was no longer needed.
This one realization that reality is not the same for different frames of reference also led to other implications of special relativity:
That Fast moving object appear shorter
That Fast moving objects appears to have increased mass
And finally, the most famous equation in science E=MC2
That mass and energy are equivalent.
So, how did Einstein come up with his most famous equation based on his original two postulates? Let’s look at this conceptually.
If conservation of mass is interpreted as conservation of rest mass, this did not hold true in special relativity. Since different observers would disagree about what the energy of a system was, the mass and energy taken together must be conserved, not just the mass on its own.
It turns out that for the laws of physics, namely conservation of energy and momentum, to be consistent in the two “reference frames” of two observers moving with respect to each other, there has to be an energy associated with a body at rest, not just a body in motion. And that is what E=MC2 implies – the M in the equation is the mass at rest.
Some people point out that much of the actual work for special relativity had already been done by the time Einstein presented it. The concepts of time dilation for moving objects, were already in place and the mathematics had already been developed by Lorentz & Poincare. Einstein still deserves the accolades because he rejected the idea of the ether all together which other scientists had not done, and the idea of mass and energy equivalence via E=MC2 is solely Einstein. Scientists who had done prior work like Thomson, Larmor, Lorentz, or Poincare had never implied such a bold proposition.
reaction, whatever mass you put in must be the mass you got out. But if conservation of mass is interpreted as conservation of rest mass, this did not hold true in special relativity.
Since different observers would disagree about what the energy of a system was, the mass and energy taken together must be conserved, not just the mass on its own.
A train travelling close to the speed of light has a lot more energy than a train at rest.
But a person riding on the non-accelerating train may not know that the train is moving. The massive object is moving from the point of view of one observer, but at rest as seen by another observer. One observer would seem to measure zero energy of the object, while the other observer would measure a higher energy.
It turns out that for the laws of physics, namely conservation of energy and momentum, to be consistent in the two “reference frames” of two observers moving with respect to each other, there has to be an energy associated with a body at rest, not just a body in motion. And that is what E=MC2 implies – the M in the equation is the mass at rest. All masses even at rest must have energy.
Some people point out that much of the actual work for special relativity had already been done by the time Einstein presented it.
The concepts of time dilation and simultaneity for moving objects, for example, were already in place and the mathematics had already been developed by Lorentz & Poincare.
Some have even called Einstein a plagiarist. There is no doubt that the “revolution” of Einstein was built on the shoulders of other great scientists. And Einstein may have gotten a lot more credit than others who did prior work.
At the same time, Einstein still deserves the accolades because he took the bits and pieces of the puzzle found by others and put them all together into a whole new theoretical framework.
He rejected the idea of the ether all together which other scientists had not done, and boldly proclaimed a new fundamental understanding of time and reality. And the idea of mass and energy equivalence via E=MC2 is solely Einstein.
Scientists who had done prior work like Thomson, Larmor, Lorentz, or Poincare had never implied such a bold proposition. And just as in life, history tends to favor the bold.
————– (5000 characters)
Einstein’s Special Relativity Explained Simply – no math
This entire revolution in physics started with a simple thought experiments, in the prolific imagination before Einstein even graduated from high school. Einstein’s theory of special relativity is convention today. But to understand how revolutionary it was for its time, it is helpful to look at what the conventional understanding of physics was during the time of Einstein’s teenage years.
In 1801, Thomas Young had conducted a simple double slit experiment that showed that light behaved like a wave. So the theory about light at the time was that it was a wave. The problem is that a wave, it was thought, had to move through some sort of medium. They called this substance the luminiferous aether.
But in 1887, two scientists by the name of Albert Michelson and Edward Morely came up with an idea to test the existence of the aether. The background ether was believed to be unmoving and static, so if the wave was traveling in the same direction as the earth, the speed of the wave should be higher in the direction of the speed of the earth. Michelson and Morley showed that there was no difference in the speed of light of the two measurements. This seriously jeopardized the aether theory.
Einstein knew this, so he came up with a thought experiment as a 16 year old. His thought was to imagine that he was chasing a beam of light while traveling at the speed of light himself. What would he see? If young Albert could catch up to the beam, he should see a stationary wave.
Yet that was impossible. Einstein knew such stationary fields would violate the equations of electromagnetism developed by James Clerk Maxwell 20 years earlier.
So he came up with two postulates, and tried to figure out what the physics would be if the two postulates were true.
Postulate 1 was that the laws of physics are the same for all inertial reference frames.
Postulate 2 was that the speed of light in a vacuum is constant for all inertial reference frames.
The first postulate had been assumed for hundreds of years. The second postulate, however, was the revolution.
This meant that young Einstein would never see the stationary, oscillating fields, because he could never catch the light beam.
But this solution seemed to have fatal flaw. Einstein later explained the problem with another thought experiment:
Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say, 2,000 miles a second. Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second.
If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railcar, and the first postulate would be violated. The solution to his thought experiment was that observers in relative motion experience time differently. This completely overturned hundreds of years of classical physics in which time was absolute in the universe. Einstein showed that time is relative, and varies in different frames of reference. The idea of the aether was no longer needed.
This one realization that reality is not the same for different frames of reference also led to other implications of special relativity:
That Fast moving object appear shorter
That Fast moving objects appears to have increased mass
And finally, the most famous equation in science E=MC2
That mass and energy are equivalent.
So, how did Einstein come up with his most famous equation based on his original two postulates? Let’s look at this conceptually.
If conservation of mass is interpreted as conservation of rest mass, this did not hold true in special relativity. Since different observers would disagree about what the energy of a system was, the mass and energy taken together must be conserved, not just the mass on its own.
It turns out that for the laws of physics, namely conservation of energy and momentum, to be consistent in the two “reference frames” of two observers moving with respect to each other, there has to be an energy associated with a body at rest, not just a body in motion. And that is what E=MC2 implies – the M in the equation is the mass at rest.
Some people point out that much of the actual work for special relativity had already been done by the time Einstein presented it. The concepts of time dilation for moving objects, were already in place and the mathematics had already been developed by Lorentz & Poincare. Einstein still deserves the accolades because he rejected the idea of the ether all together which other scientists had not done, and the idea of mass and energy equivalence via E=MC2 is solely Einstein. Scientists who had done prior work like Thomson, Larmor, Lorentz, or Poincare had never implied such a bold proposition.
