The History of Non-Euclidean Geometry - The World We Know - Part 5 - Extra History

Summary

In 1887, the Michelson-Morley Experiment sought to detect the aether wind, a hypothesized medium for light waves. Despite the experiment's precision, no aether was found, challenging the scientific community. This led to Einstein's Special Relativity in 1905, which discarded the aether concept and proposed a constant speed of light, independent of the observer's motion. Special Relativity introduced a non-Euclidean universe, where space-time is curved by gravity, as further explained by Einstein's General Relativity in 1915. The script concludes by highlighting the evolving nature of knowledge and the excitement of exploring quantum mechanics and computing in a forthcoming series.

Takeaways

• 🕰️ The year is 1887, and physics is on the brink of understanding the universe's fundamental workings, with the aether wind being the last great question.
• 🔍 The Michelson-Morley Experiment was set up to detect the aether, the invisible fluid believed to be the medium through which light travels.
• 🌌 At the time, light was thought to be a wave that required a medium, but it was observed to travel through a vacuum, leading to the hypothesis of the aether.
• 🧩 The aether was theorized to be a fluid with paradoxical properties: rigid yet massless, incompressible yet transparent, and the medium for light waves.
• 🔬 Michelson and Morley's experiment aimed to measure the effect of Earth's motion on the speed of light, expecting to find variations due to the aether wind.
• 🚫 The experiment's results were null, showing no effect of the aether wind, which contradicted the prevailing theory and caused a crisis in physics.
• 💡 Einstein's special relativity, proposed in 1905, resolved this crisis by doing away with the concept of an absolute frame of reference, the aether.
• 🌀 Special relativity introduced the idea that the speed of light is constant and not affected by the observer's motion, unifying space and time into a single entity.
• 🌐 General relativity, introduced by Einstein in 1915, extended these concepts to include the effects of gravity, suggesting that space-time is curved and warped by massive objects.
• 📚 The acceptance of relativity meant acknowledging a non-Euclidean universe, where traditional Euclidean geometry is only an approximation on a large scale.
• 🔮 The script concludes by hinting at a future series on quantum mechanics and quantum computing, suggesting that there are even more profound mysteries to explore beyond relativity.

Q & A

What was the central mystery in physics at the end of the 19th century?

The central mystery was the question of the aether wind, which was about how light travels and the existence of an invisible fluid, the aether, through which light was believed to move.

Why was the aether theory essential for understanding light as a wave?

The aether theory was essential because, like sound and water waves, light was thought to be a wave that needed a medium to propagate. Since light could travel through a vacuum, the aether was theorized to be this medium.

What were the contradictory properties assigned to the aether as physics advanced?

As physics advanced, the aether was assigned properties that were contradictory, such as being both fluid and rigid, incompressible yet massless, and transparent while also serving as a medium for light.

Who were Michelson and Morley, and what were they trying to prove with their experiment?

Michelson and Morley were scientists who conducted the Michelson-Morley Experiment to detect the effect of the Earth's motion on the speed of light, seeking proof of the aether.

What was the significance of the Michelson-Morley experiment's results?

The experiment's results were significant because they showed no effect of the aether wind on the speed of light, suggesting that the aether did not exist and challenging the existing understanding of physics.

What was the year when Einstein proposed his theory of special relativity, and how did it relate to the Michelson-Morley experiment?

Einstein proposed his theory of special relativity in 1905, which was inspired by the Michelson-Morley experiment and did away with the concept of an absolute frame of reference, such as the aether.

What is the concept of special relativity, and how does it differ from the previous understanding of physics?

Special relativity is a theory that eliminates the concept of an absolute frame of reference and proposes that the speed of light in a vacuum is constant, unaffected by the observer's motion. It differs from previous understanding by unifying space and time into a single continuum.

What is the difference between special relativity and general relativity proposed by Einstein?

Special relativity deals with physics without gravitational distortion, while general relativity, proposed in 1915, is a more complex theory that includes the effects of gravity and describes how it warps space-time.

What does the acceptance of relativity imply about the nature of the universe?

Accepting relativity implies that we live in a non-Euclidean universe where space-time is curved and can be affected by gravity, challenging the traditional Euclidean geometry.

How did the Michelson-Morley experiment and the theory of relativity affect our understanding of geometry?

The Michelson-Morley experiment and the theory of relativity led to the realization that Euclidean geometry is an approximation and that non-Euclidean geometries, such as those developed by Bolyai, Lobachevsky, and Riemann, are more accurate representations of the universe.

What is the philosophical implication of the shift from Euclidean to non-Euclidean geometry in physics?

The shift implies that our knowledge is always evolving and that mathematics should be seen as well-reasoned rather than strictly true or false, allowing for the discovery of new truths and the reevaluation of old ones.

Outlines

00:00

🔬 The Michelson-Morley Experiment and the Demise of Aether Theory

In 1887, the scientific community believed that light traveled through an invisible medium called 'aether'. The Michelson-Morley experiment, conducted in a basement at Case Western, aimed to detect the 'aether wind' and prove the existence of aether. The experiment was designed to measure the speed of light and its interaction with the earth's movement through space. Despite its precision, the experiment found no evidence of aether, suggesting that light traveled at a constant speed regardless of the observer's motion. This null result was a significant blow to the aether theory and led to a reevaluation of the fundamental understanding of light and motion.

05:03

🌌 The Advent of Relativity and the Rejection of Euclidean Geometry

The failure of the Michelson-Morley experiment to detect aether led to a paradigm shift in physics. In 1905, Albert Einstein proposed the theory of special relativity, which discarded the concept of an absolute frame of reference, such as aether, and postulated that the speed of light in a vacuum is constant, unaffected by the observer's motion. This theory also implied a unified view of space and time. Einstein further developed general relativity in 1915, which accounted for gravitational effects on space-time, suggesting that gravity could curve space-time. The acceptance of relativity challenged the Euclidean geometry that had underpinned physics and mathematics, introducing non-Euclidean geometries as a more accurate description of the universe. The video concludes with a teaser for an upcoming series on quantum mechanics and quantum computing, promising further exploration of the strange and fascinating nature of our universe.

Keywords

💡Physics

Physics is the natural science that studies matter, its motion, and behavior through space and time, and the related entities of energy and force. In the video, it is the overarching field of study that the narrative is based on, especially as it pertains to the understanding of light and the universe's fundamental structure.

💡Aether

The concept of aether was a theoretical medium once believed to be the carrier of light waves in the 19th century. In the script, aether is presented as the invisible fluid that was thought to permeate all things and through which light was believed to travel, highlighting a central mystery in physics at the time.

💡Michelson-Morley Experiment

The Michelson-Morley Experiment was a crucial test for the existence of aether, aiming to detect the relative motion of matter through the aether by measuring the speed of light. The experiment's failure to find any effect of aether wind is a pivotal moment in the video, leading to the rejection of the aether theory.

💡Light

Light is electromagnetic radiation that is visible to the human eye and is central to the discussion in the video. It is presented as a wave that travels through a vacuum, which was a mystery since waves, as understood at the time, required a medium to propagate, challenging the concept of aether.

💡Waves

Waves in the video are used to describe the propagation of disturbances through a medium, such as water waves or sound waves. This concept is contrasted with light, which was thought to behave as a wave but was found to travel through a vacuum, leading to the problem of how light propagates without a medium.

💡Special Relativity

Special Relativity is a theory proposed by Albert Einstein, which the video mentions as a solution to the aether problem. It introduced the idea that the speed of light is constant in a vacuum, regardless of the observer's frame of reference, and it did away with the concept of absolute space and time.

💡General Relativity

General Relativity, also by Einstein, is a theory of gravitation that extends special relativity to include gravity. The video mentions it as the more complex theory that explains the curvature of space-time due to gravity, applicable even in the presence of massive objects like stars or black holes.

💡Space-Time

Space-Time is a concept in physics that combines space and time into a single continuum. The video discusses how Einstein's theories of relativity led to the understanding of space-time as a single entity, rather than separate concepts, which is crucial for understanding gravity and the universe's large-scale structure.

💡Non-Euclidean Geometry

Non-Euclidean Geometry refers to any geometric system that differs from Euclidean geometry, which traditionally assumes flat, two-dimensional space. The video discusses how accepting relativity means accepting a non-Euclidean universe, where the geometries of Bolyai, Lobachevsky, and Riemann are more accurate representations of the universe's structure.

💡Quantum Mechanics

Quantum Mechanics is a branch of physics that deals with phenomena on an atomic and subatomic level. The video script announces a follow-up series on quantum computing, which is based on the principles of quantum mechanics, hinting at the further exploration of the strange and non-intuitive nature of the universe.

💡Einstein

Albert Einstein is a renowned physicist who developed the theories of special and general relativity. In the video, his work is highlighted as a turning point in physics, providing explanations for the behavior of light and the structure of the universe that replaced the outdated aether theory.

Highlights

In 1887, the Michelson-Morley experiment was set to answer the central mystery of how light travels without a medium.

Light was thought to require an 'aether' medium to propagate like other waves, but it could travel through a vacuum.

The aether was theorized to be a fluid that filled the universe, allowing light to move.

As physics advanced, the aether was assigned paradoxical properties like being both rigid and massless.

The Michelson-Morley experiment aimed to detect the effect of Earth's motion on the speed of light.

The experiment's precision was designed to measure minute effects of the aether wind on light speed.

Despite meticulous setup, the Michelson-Morley experiment found no effect of the aether on light speed.

The null result of the experiment indicated that the aether might not exist, causing a crisis in physics.

Einstein's special relativity, proposed in 1905, explained the constancy of light speed without the need for an aether.

Special relativity introduced the concept that space and time are a single entity, not separate.

Einstein's theory suggested that space-time might be curved and affected by gravity.

General Relativity, introduced in 1915, described gravity as the curvature of space-time.

Accepting relativity meant acknowledging a non-Euclidean universe, contrary to traditional geometry.

Non-Euclidean geometries of Bolyai, Lobachevsky, and Riemann were more accurate for the universe's large scales.

Euclidean geometry was revealed to be a useful approximation rather than an absolute truth.

The evolution of knowledge in mathematics and physics shows that what is well-reasoned can evolve.

The history of non-Euclidean geometry teaches us that there is always more to learn and discover.

A surprise follow-up series on quantum mechanics and quantum computing is announced.

Transcripts

It's 1887

Physics is almost complete

We almost know enough to see the clockwork of the universe

Only one last great question remains

The question of the aether wind

The question of the way that light travels

*Intro Music*

Two men are setting up a series of mirrors deep in a stone basement of a dorm in Case Western

Their strange apparatus sits on a monumental block of sandstone resting on top of a pool of mercury

They are about to perform one of the most important experiments of all time

The Michelson-Morley Experiments

They are looking for proof of the great invisible fluid

through which light flows

See, this was the central mystery stuck in the craw of physics

By the end of the 19th century,

this problem of how light moves

was becoming impossible to ignore

Because at the time light was largely assumed to be a wave,

just like sound, or waves of water

But the thing about those types of waves is that they have to travel through stuff.

A wave is just a motion,

and to have motion you have to have something being moved

Waves of water are simply motion propagated through the molecules of water

Waves of sound work the same way,

travelling by rippling through the air

But light travels through a vacuum,

and that's a problem

Experiment after experiment had been done where a complete vacuum was created

Where the air and other matter was pumped out of a container

and then waves were pushed through

Sound died.

The wave couldn't travel through nothing

But light.

Light travelled across the void

How did it do that?

The theory at the time was that there was some giant, invisible,

incompressible fluid that permeated all things

They called it the aether

It filled the dark between the stars,

and subsumed the void between worlds

And it was through this fluid

that waves of light moved.

The only problem was that,

well as physics got more and more advanced

We started to have to assign wilder

and wilder properties to this aether

It had to be fluid, but

totally rigid also

And it had to be incompressible, but also totally massless

It had to be utterly transparent, and yet also be a medium for light

Still, there was no better explanation

So, even as serious questions were raised about it,

the idea of the aether served as the working theorem for most of the scientific world.

But as the 19th century began to draw to a close

People were finally starting to figure out ways to build a contraption sensitive enough to test for the aether

Those people were Michelson and Morley

They had created a device so precise

that it should be able to detect the effect of speed of the earth on the speed of light

What does this mean?

Well, imagine that you've got two sets of people playing catch

One set of people are on a moving train

One set of people are on the ground next to the train

They both throw the ball at the same speed

But, relative to the people on the ground the ball thrown on the train either moves much faster or much slower

Depending on whether it was thrown with or against the motion of the train

By this point in history,

we had already worked out a speed for light against the fixed reference of the aether

Which in our previous analogy is basically like the people on the ground throwing the ball

What Michelson and Morely set out to do was work out the case for the people on the train

How did being on the planet earth,

hurtling through space affect the speed of light?

Unfortunately, the earth doesn't move very fast compared to the speed of light

Which made this a pretty challenging thing to test

Instead of throwing a ball on top of a train

This was sort of like

trying to measure the effect of throwing a ball from on top of the worlds

biggest slowest sloth

Hence them burying the experiment underground

resting it on mercury,

and placing limestone on that mercury

They would need to measure something so small

they couldn't have any wayward tremors messing up their results

Even as they adjusted their experiment and spun it around

But, and this is one of the triumphs of experimental physics

They did it!

Their experiment was so exact,

that it was hard to dispute that it should be able to pick up the affects of the aether wind

Only....

It didn't

There was none.

They got no effect at all.

Light moved at the same speed, no matter how they turned their device,

no matter when they took their readings

It was astonishing.

Countless times, people would refine this experiment hoping for a different result

And countless times it would just confirm

There was no aether.

Aether was not a thing

This threw science into chaos.

What could the explanation possibly be?

How could we make sense of this?

Well, in 1905

a young man named Einstein would propose a solution

Inspired by the Michelson-Morley experiments,

he would offer us special relativity

Which is called relativity because it does away with the concept of an absolute

frame of reference in physics

By which I mean "the aether"

This lead to a number of other conclusions

Such as, proposing that the speed of light in a vacuum was constant

That it wasn't actually affected by frame of reference.

And that we would have to see space and time as one contiguous thing

Rather than two completely separate ideas

But it's called special relativity for a reason

This paper pointed to something else

Something even stranger than the idea that space and time were one

And that was the idea that space-time might be curved

And that the curvature of space-time

might be affected by gravity

The special version of relativity only dealt with physics where gravitational distortion wasn't really present

But in 1915 Einstein would give the world the far more complex theory

of General Relativity

One that was applicable even where stars or black holes bent and warped the fabric of space-time

And it's that curvature of space-time, and the way that those curves get warped and changed

that we are interested in here, in this series

Because one of the most frightening things about accepting this new way of thinking

Of accepting relativity

Is that it also means that we have to accept

that we live in a non-Euclidean universe

Postulate 5 really isn't true in any higher sense

It doesn't represent the world as it actually is

In fact the strange geometries of Bolyai, Lobachevsky, and Riemann

were much closer to the truth

They're a far more accurate representation of the universe as we now understand it

And it is those geometries that we now use for much of modern physics

So the geometry that we built

all of mathematics on

That we built all of our calculus and our Cartesian coordinate system out of

That gave us Newtonian physics,

in the end,

it wasn't in any way real

It was and is,

simply a useful tool created by humankind

It was a way of thinking and a way of reasoning that turned out to be profoundly valuable

But that only mimicked the real world on a very terrestrial scale

When we look at the vastly large, or the imperceptibly small,

we find that Euclidean geometry only offers us an approximation

A short hand for the world as it really is

Now, does this mean that Riemann was right and Euclid was wrong?

Well, no. It just means that our knowledge is always evolving

It means that it might be the wrong idea to think of mathematics as

true or not true

Rather, it might be more useful to simply ask:

Is it well reasoned?

This frees us from the trap of having to prove the unproveable

And allows us to find reason in the unreasonable

Because, if the history of non-Euclidean geometry teaches us one thing it's that:

There is always more out there to learn and discover.

So welcome to a world where straight lines might not exist

And where parallels may not function the way you thought they functioned

It's not a frightening place really

You've actually lived there all your life

And when you think about it, it's pretty exciting, because there are limitless mysteries for us to unravel

And it is at this point I would like to announce a surprise follow up to this series

Sponsored by one of you who wanted to see us go even further

And explore Quantum Mechanics and Quantum Computing

We're going to have a multi-part series on quantum computing coming to this channel soon

And if you thought this math was wild... just you wait!

We will see you then

*Outro Music*