General Relativity Explained simply & visually

Summary

This video explores Einstein's groundbreaking theory of relativity, which revolutionized our understanding of gravity as a curvature of space-time. It discusses Einstein's thought experiments, the mathematical formulation with Grossman's help, and the theory's confirmation through Mercury's orbit and the 1919 solar eclipse. The video also touches on the implications of time dilation and the ongoing quest for a quantum gravity theory.

Takeaways

• 🌌 Einstein's Special Theory of Relativity was initially met with skepticism and ridicule when published in 1905.
• 🏛️ Critics dismissed Einstein's ideas, questioning his credentials as a patent clerk and even insulting his religious background.
• 🤔 Einstein himself was not fully satisfied with the Special Theory, as it did not account for gravity or acceleration.
• 🧐 His thought experiment involving a window washer falling led to a profound insight about the equivalence of gravity and acceleration.
• 🚀 Einstein imagined scenarios in a spaceship accelerating at 9.8 m/s², realizing that the effects of acceleration would mimic gravity.
• 🔦 He hypothesized that light would curve in a gravitational field, challenging the notion that light always travels in a straight line.
• 🌍 Einstein theorized that gravity might cause a curvature of space itself, leading to the concept of space-time.
• 📚 With the help of mathematician Marcel Grossman, Einstein developed the complex mathematics of curved space-time, forming the basis of General Relativity.
• 🪐 General Relativity revolutionized the understanding of gravity, suggesting it emerges from the interaction of space and mass, rather than being a mysterious force.
• 🌞 The theory's predictions, such as the precession of Mercury's orbit and the bending of light near the sun, were confirmed through observations, solidifying Einstein's fame.
• ⏳ General Relativity also implies that time is affected by gravity, running slower in stronger gravitational fields, which has practical implications for GPS technology.

Q & A

What was the initial reaction to Einstein's Special Theory of Relativity in 1905?

Einstein's Special Theory of Relativity was met with ridicule or indifference when it was first published. People found it too radical and considered Einstein, a patent clerk, as overstepping his bounds by challenging the established theories of Isaac Newton.

Why was Einstein not satisfied with his own Special Theory of Relativity?

Einstein was not satisfied because the Special Theory of Relativity only applied to observers moving in a straight line at a constant speed and did not account for the presence of gravity or acceleration.

What thought experiment led Einstein to develop his theory further?

Einstein's thought experiment involved imagining what a window washer would experience if falling from a ladder. He considered the sensation of weightlessness during free fall and how this related to the absence of any force pushing against the falling body.

How did Einstein conceptualize the equivalence of gravity and acceleration?

Einstein realized that in free fall, gravity is the only force acting, and the falling person would feel weightless, similar to being in space. This led him to the insight that gravity and acceleration are different ways to describe the same phenomenon.

What did Einstein hypothesize about the nature of space in the presence of gravity?

Einstein hypothesized that space itself might be curved due to the presence of mass and energy, causing the shortest path for light to be a curved one, rather than a straight line.

What mathematical theory did Einstein use to express his insights about gravity and space?

Einstein used the mathematical theory of Reimannian Geometry, with the help of his friend Marcel Grossman, to express his insights about the curvature of space-time.

How did Einstein's General Relativity differ from Newtonian concepts of space and time?

General Relativity proposed that gravity is not a force acting at a distance but emerges from the interaction of space and massive objects, contrasting with Newtonian concepts where space and time were fixed, and gravity acted within them.

What astronomical observation confirmed Einstein's General Relativity?

The observation of stars near the sun during a total solar eclipse by Arthur Eddington's team in 1919 confirmed that light was bent by the sun's gravity, as predicted by General Relativity.

How does the curvature of space affect the passage of time according to General Relativity?

In the presence of a gravitational field, time passes slower relative to time in empty space to maintain the constant speed of light, indicating that time is distorted by gravity along with space.

What unresolved questions about gravity remain despite the success of General Relativity?

General Relativity does not explain what gravity actually is or the nature of singularities within black holes, where the theory fails. It also does not integrate well with quantum mechanics, indicating the need for a new theory of quantum gravity.

How does the theory of General Relativity account for the orbit of Mercury?

General Relativity predicted the precession of Mercury's orbit, which was a mystery under Newtonian physics, by accounting for the curvature of space-time caused by the sun's mass.

Outlines

00:00

🔬 Einstein's Early Challenges

When Albert Einstein first published the Special Theory of Relativity in 1905, he faced ridicule and skepticism due to his non-scientist status as a patent clerk and the radical nature of his theory, which contradicted the established Newtonian physics. Some even attacked his heritage, calling it 'Jewish science.' However, Einstein himself was dissatisfied with his theory's limitations, as it only applied to non-accelerating frames and did not account for gravity.

05:02

🤔 Einstein's Thought Experiment

Einstein's imaginative thought experiment, inspired by watching a window washer, led him to a groundbreaking realization. By considering what the window washer would experience while falling, he understood that free fall equates to weightlessness, similar to being in space. This insight revealed the equivalence of gravity and acceleration, paving the way for connecting gravity with the theory of relativity.

10:07

🚀 The Equivalence Principle

Einstein's thought experiment extended to imagining a room accelerating in space. He realized that an accelerating room would mimic the effects of gravity, making it indistinguishable from being on Earth. This led him to hypothesize that gravity causes space to curve, affecting the path of light. Collaborating with mathematician Marcel Grossman, Einstein developed the complex mathematics of curved space-time, forming the basis of General Relativity.

🪐 General Relativity vs. Newtonian Gravity

Einstein's General Relativity revolutionized our understanding of gravity, describing it not as a force but as the curvature of space-time caused by mass. This new perspective explained the peculiar precession of Mercury's orbit, which Newton's laws couldn't. Einstein's theory predicted Mercury's orbit precisely, providing strong evidence for General Relativity.

🌌 Confirming General Relativity

Despite initial skepticism, General Relativity gained credibility with Arthur Eddington's 1919 solar eclipse observations, which confirmed the bending of light by gravity. This empirical validation marked Einstein's rise to fame and solidified his theory's acceptance in the scientific community.

⏳ Space-Time and Time Dilation

Einstein's Special Relativity introduced the concept that the speed of light is constant, leading to time dilation in gravitational fields. Time passes slower in strong gravitational fields to keep the speed of light constant. This phenomenon has been experimentally confirmed and is crucial for technologies like GPS, which require precise timekeeping.

🕳️ Unresolved Mysteries and Future Directions

While General Relativity is a monumental achievement, it doesn't explain why massive objects distort space-time or what gravity fundamentally is. It predicts phenomena like black holes but fails at singularities where quantum mechanics should apply. The quest to unify General Relativity with quantum mechanics continues, aiming to develop a theory of quantum gravity.

Keywords

💡Special Theory of Relativity

Einstein's theory published in 1905 that revolutionized the understanding of space and time, stating that the laws of physics are the same for all non-accelerating observers, and that the speed of light in a vacuum is constant regardless of the motion of the light source. This theory is foundational to the video's theme of how Einstein's ideas challenged and ultimately reshaped scientific views on space, time, and gravity.

💡Gravity

A fundamental force that attracts two bodies towards each other, typically experienced as the force that gives weight to objects with mass and causes them to fall to the ground when dropped. The video discusses Einstein's dissatisfaction with how his initial theory didn't account for gravity and explores his insights into how gravity and acceleration are related.

💡Thought Experiment

A hypothetical scenario used to understand and explore complex ideas and theories. Einstein's thought experiment of a window washer falling led him to realize that gravity and acceleration could be equivalent, a pivotal insight in developing the General Theory of Relativity.

💡General Theory of Relativity

Einstein's theory that extends the Special Theory of Relativity to include gravity, proposing that gravity is not a force between masses but a curvature of space-time caused by mass and energy. This theory is central to the video's explanation of how Einstein connected gravity with the curvature of space-time.

💡Space-time

The four-dimensional continuum that blends the three dimensions of space and the one dimension of time into a single construct. The video describes how Einstein's theories showed that mass and energy can curve space-time, affecting the motion of objects and the passage of time.

💡Equivalence Principle

The principle stating that the effects of gravity are indistinguishable from the effects of acceleration. Einstein used this principle to develop his theory of General Relativity, as discussed in the video through his thought experiment involving an accelerating room and a beam of light.

💡Curved Space

A concept in General Relativity where space is not flat but curved by the presence of mass and energy. The video explains how Einstein theorized that light bends in a gravitational field because space itself is curved, which was confirmed by the observation of starlight bending near the Sun.

💡Mercury's Precession

The phenomenon where Mercury's elliptical orbit around the Sun shifts over time, which could not be explained by Newtonian mechanics. The video highlights how Einstein's General Relativity successfully predicted this precession, providing strong evidence for his theory.

💡Black Hole

A region of space where the gravitational pull is so strong that nothing, not even light, can escape. The video mentions that General Relativity predicts the existence of black holes and discusses the challenges and questions that arise when trying to understand their singularities.

💡Singularity

A point in space where the density of matter and the curvature of space-time become infinite. The video touches on the concept of singularities within black holes and the limitations of General Relativity in describing these extreme conditions, highlighting the need for a theory of quantum gravity.

💡Quantum Gravity

A theoretical framework that seeks to describe gravity according to the principles of quantum mechanics. The video concludes by addressing the unresolved questions in Einstein's theories, emphasizing the ongoing quest to unify General Relativity with quantum mechanics to fully understand gravity.

💡Arthur Eddington

An English astronomer who led an expedition in 1919 to photograph stars near the Sun during a solar eclipse, providing empirical evidence for General Relativity by showing that starlight bends around the Sun. The video credits Eddington's observations with solidifying Einstein's fame and the acceptance of his theories.

💡Riemannian Geometry

A branch of mathematics dealing with curved surfaces, which was crucial for Einstein in formulating General Relativity. The video notes how mathematician Marcel Grossman assisted Einstein with the complex mathematics required to describe curved space-time.

Highlights

Albert Einstein's Special Theory of Relativity was initially met with ridicule and skepticism due to its radical nature.

Einstein, a patent clerk at the time, challenged the long-standing theories of Isaac Newton, which were considered unassailable.

Einstein's theory faced political and religious criticism, being derogatorily labeled as 'Jewish science'.

Einstein was not satisfied with the limitations of his Special Theory, which did not account for gravity or acceleration.

A thought experiment involving a falling window washer led to a pivotal insight in the development of the General Theory of Relativity.

Einstein's realization that gravity and acceleration are equivalent concepts was a key step towards understanding gravity in the context of relativity.

The equivalence principle suggests that the effects of gravity and acceleration are indistinguishable in a closed system.

Einstein hypothesized that light bends in a gravitational field, challenging the notion that light always travels in a straight line.

The concept of space-time curvature was a revolutionary idea that gravity causes a distortion in the fabric of space-time itself.

Einstein collaborated with mathematician Marcel Grossman to develop the complex mathematical framework of General Relativity using Reimannian Geometry.

General Relativity redefined gravity not as a force but as a curvature of space-time caused by mass and energy.

The precession of Mercury's orbit provided empirical evidence supporting General Relativity and its explanation of gravitational effects.

The 1919 solar eclipse experiment led by Arthur Eddington provided direct observational confirmation of General Relativity's predictions.

Time dilation is a consequence of General Relativity, where time passes slower in a gravitational field compared to empty space.

General Relativity has practical implications, such as the necessity to adjust GPS satellite clocks to account for time dilation effects.

The theory of General Relativity, while groundbreaking, does not answer all questions about gravity and raises the need for a quantum gravity theory.

Transcripts

When Albert Einstein first published the Special Theory of relativity in 1905, he was either

vehemently ridiculed or ignored.

People thought it was just too weird and radical to be real. This guy is not even a working

scientist, he’s just a patent clerk, some said. How dare he challenge the greatest scientist

that ever lived – Isaac Newton, whose theories have been proven to be correct for hundreds

of years.

Some politicians even insulted his religious heritage and called it "Jewish science" – a

way to subvert traditional culture and thinking.

How did Einstein feel about this? Well, he wasn’t satisfied with his theory either.

He was unhappy because the theory only applied to observers moving in a straight line at

a constant speed. The theory did not apply if Gravity was present or if the observer

was accelerating.

Einstein was known, however, to have a very vivid imagination. And one day, as legend has it,

while observing a window washer on a ladder near his patent office, he had one of his

famous thought experiments that would go on to change the course of scientific history.

He imagined what would happen if the worker were to fall. But he didn’t think of it

the way you and I would think of it. What was his thought experiment? And how did it

lead to perhaps the greatest single scientific theory of the past 100 years…that’s coming

up right now!

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While watching the window washer on a ladder, Einstein thought about what would happen if

the window washer fell. For most people, imagining this would just conjure up disturbing images

of the poor guy landing on the ground below, and the story would not have a happy ending.

Einstein thought about it differently. He put himself in the window washer’s perspective,

and imagined not what would happen when he met the ground, but what he would experience as

he was falling.

What he realized was that if he was falling, gravity would be the only force acting on

him. He would be accelerating towards the ground, but since the ground would not be

pushing up on his body, he would feel no weight. With no wind resistance, he would be in free

fall. And this would be no different than being weightless in space.

In a way, gravity and acceleration were different ways to describe the same thing. This is where

Einstein had a huge insight. The way to connect gravity with the theory of relativity was through

the idea of acceleration, since the two are equivalent.

Einstein imagined being in a room with no windows. And if the room had a bathroom scale

handy, what would happen if you stepped on the scale. Well if anywhere stationary on

earth, you would weigh 80 Kgs, or whatever your weight is.

Now he imagined being in the same room in space. Now, what if the room was on a space

on a space ship that accelerating in an upward direction at 9.8 meters/second/second, which

happens to be exactly the same as gravitational acceleration on earth. What would happen

if he stepped on the scale then?

Well, the scale would read 80 kgs, just like it did on earth. The acceleration on a spaceship

would appear to him, inside the room as being indistinguishable from being stationary on

earth. If he didn’t know he was on a space ship, he could just as well presume he was

on earth.

There would be no way to tell the difference. Or would there?

Einstein thought about this, and asked himself if there was a way to tell the difference.

He imagined what would happen if he took a flashlight or a laser beam and pointed it

from one side of the room to the other, as the space ship was accelerating upwards.

If he had a sensitive measuring device, he could measure the height of the light on the

other side of the room. He realized that the height he would find on the other side would

be slight lower than the source of the light.

Why? Because the floor of the room would be rushing upwards at ever faster speeds, as the

light was propagating across the room. since the room was accelerating upwards at 9.8 meters/second/second.

The light beam would appear to curve downward.

However, If you were on earth, and you measured the two heights, you may think that there

should be no difference. That light should go straight to the other side of the room.

Although this appears to be common sense.

Einstein thought it can’t be because it violate the principle of equivalence. Acceleration

of the room on a space should be no different than the room under the influence of gravity

on earth.

He realized that this meant light must bend in the presence of a gravitational field.

But how could this be, because light always takes the shortest path between two points?

It should be going straight.

Then he realized, wait a minute, maybe the light IS taking the shortest path between

two points. Maybe the shortest path is not a straight line.

He imagined the curved surface of the earth. The shortest path between any two distant points on earth,

if you're restricted to the surface of the earth, is never a straight line, because you have to traverse

the curvature of earth. So the shortest path is always curved.

So maybe gravity somehow causes a curvature of space itself. He hypothesized that in space,

perhaps a straight line is NOT the shortest path between two points, and that perhaps

in the presence of mass and energy, space somehow becomes curved, so that the shortest

path that light can take is a curved path.

This was the key insight that Einstein had about gravity.

But in order to express this mathematically, it required very complicated mathematics that

even a genius like Einstein could not easily figure out.

He contacted an old buddy of his from college days, mathematician Marcel Grossman.

Grossman had just finished his PhD dissertation on the topic of, wouldn’t you know it, the geometry

of curved spaces, called Reimannian Geometry. With his help, Einstein figured out the mathematics

of curved space time. And this curved geometry is really the basis of General relativity.

Now, you have to realize how different this was than the status quo of the time which was

Newtonian space and time, which presumed that time was fixed, space was fixed, and gravity

was a mysterious force that could act at a distance from one massive object to another

without touching it. In this model, Gravity did not affect the underlying space and time,

but acted within it.

Einstein’s theory was now that gravity was not a force between massive objects, but something

that emerges from the interaction of space and massive objects. John Wheeler would later

summarize this theory in 12 short words: “Space-time tells matter how to move; matter tells space-time

how to curve.” That’s it. That’s General relativity in a nutshell.

And orbits of planets could now be explained not by some mysterious force that acts at

a distance, but rather an interaction that takes place locally with mass or energy, and

the space around it. And this can be visually represented by the kind of graphic you see

here to show how massive objects like planets form orbits around other massive objects.

It’s important to note that the trampoline analogy you normally see on TV shows and youtube

videos like this is a 2D plane used for visualization purposes only. The interaction occurs obviously

in three dimension, not just two. It looks more like this graphic. This is much more difficult

to visualize and animate, so it is typically not used. But it is more accurate.

However, in order for this theory to really be taken seriously, it had to make a prediction

that could be tested. And that prediction could not be explained in any other way.

This test came in the form of Mercury. Mercury’s orbit had been a mystery for decades because

it was unusual. All planets orbited the sun in an ellipse. The planet closest to the sun,

Mercury, also orbited in an ellipse. But it did something weird. It had something called

a precession.

What this means is that its elipse never closes. The point of the orbit that was farthest from

the sun advances a little bit every time Mercury goes around the Sun. It’s as if the ellipse

itself is orbiting the sun.

No one could ever figure this out using Newton’s equations.

When Einstein applied his new curved space theory to this orbit, the new theory predicted

exactly the precession that Mercury actually has. Finally, a theory perfectly matched the

observation which had been a mystery for decades.

You can only imagine how Einstein felt when he figured this out. There was a time when

Einstein was the only person in the world who realized that the universe actually works

this way.

But many skeptics still remained. Many scientists still had doubts about Einstein’s theory.

But the most fool-proof confirmation of his theory came 4 years after he published it.

That’s when a team led English Astronomer, Arthur Eddington. in 1919, photographed stars

near the sun during a total solar eclipse.

If Einstein was right, then the position of the stars near the sun would appear different

than predicted location based on where they should be as seen at night. This would happen

because as light passed near the sun, it should be bent by the curvature of space due to

gravity. And that’s exactly what he found, confirming that the theory was correct. This

is the moment Einstein became a celebrity.

You might ask, ok I get it. I get space curvature. But it’s called space-time. How does time

enter into the picture? Why is this not just a distortion of space but also of time?

This is where Einstein’s first theory, special relativity comes in. The essential presumption

in special relativity is that light always moves at the same speed regardless of perspective

or reference frame. This means that light will have the same speed in an accelerating

reference frame as it will in a resting reference frame.

If this is the case then it means that the speed of light in the presence of gravity

will be the same as its speed in empty space.

Speed equals distance over time. S = D/T

But since the distance traveled by the beam of light in a gravitational field is longer

due the curving of space, in order for the speed of light to remain constant, time itself

must pass slower in the gravitational field relative to time in empty space.

In other words, time increases proportionately with the curvature of space near a gravitational

field, compared to empty space, to keep the speed of light constant in both reference

frames. This is why time is considered distorted by gravity along with space. It is really

just part of the same fabric called space-time. This has some massive implications. It implies

that the observer experiencing no gravity at all, sees the clock in a gravitational field running

slower. This means that the clocks on earth run slightly slower than clocks on the international

space station. This effect has been confirmed by many experiments, and is taken into account

in order keep the clocks of GPS satellites in sync with the clocks on earth. Otherwise

your GPS apps like google maps would give you inaccurate locations.

You should know that although General relativity is an astounding achievement by one the greatest

scientists of all time, it does not answer everything. Questions remain. Although it

tells us how gravity works, it doesn’t tell us what exactly it is. Why do massive

objects distort space time? What is the underlying connection between mass and space-time?

It also predicts regions of space where space time can get so distorted that nothing escapes

including light. This is called a black hole. But it shows that within these black holes

lies something that seems impossible, and that is a mass concentrated to an infinitely

small point with infinite density. This is called the singularity and is theorized to

exist within the black hole. General relativity fails to work at this singularity.

But infinities like this in science usually indicate some sort of incompleteness of theories rather

than things that actually exist.

To figure this out what happens at these really small scales, we need our old friend Quantum

mechanics. But alas, the equations of quantum mechanics make no sense in terms of singularities,

or in terms of general relativity.

So for now the two theories remain incompatible. If we can bring these two theories together, and

truly understand how gravity behaves at the tiniest scales, we may answer the question of what

gravity actually is. We will need a new theory to figure this one out – and that theory

is called quantum gravity.

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