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Space, Time, and the Fabric of Existence: 

Space, Time, and the Fabric of Existence Einstein’s Universe

A Deceptively Simple Question: 

A Deceptively Simple Question What is space? Not outer space, not the cosmos, just space Even harder, what is time?

A Not So Simple Answer: 

A Not So Simple Answer Space is a fundamental quantity idea in physics It can’t be reduced any further For lack of a better definition: Space is the extent that separates objects

A Not So Simple Answer: 

A Not So Simple Answer Time is also a fundamental quantity For lack of a better definition: Time is that which separates two events

The Nature of Space: 

The Nature of Space We are all used to thinking about space in three dimensions We can move up and down through space We can move side to side through space We can move front and back through space

The Nature of Time: 

The Nature of Time How many ways can we move through time? Why?

Space, Time, and Space-time: 

Space, Time, and Space-time If we can move forward through time, can we think of it is as another dimension? The answer is yes

Space, Time, and Space-time: 

Space, Time, and Space-time Einstein, in his special theory of relativity, found that things worked better if time was treated as a fourth dimension This was a huge breakthrough in thinking Why didn’t people think of it this way before?

Space, Time, and Space-time: 

Space, Time, and Space-time People always thought of time as being absolute There was no reason to treat it like a fourth dimension because it was the same for everyone

Space, Time, and Space-time: 

Space, Time, and Space-time Einstein did away with the notion of absolute time and in doing so put time on equal footing with space

Space, Time, and Space-time: 

Space, Time, and Space-time But the special theory of relativity only worked in special circumstances Namely, non-accelerating reference frames Einstein wanted something more general…

Space, Time, and Space-time: 

Space, Time, and Space-time The answer was the general theory of relativity It took Einstein 10 years from the publication of special relativity to the publication of GR It is commonly said that only a handful of people, even today, really understand the theory

Space, Time, and Space-time: 

Space, Time, and Space-time In GR, Einstein took the notion of space and time one step forward, and combined the two into an idea called space-time What is space-time?

Space, Time, and Space-time: 

Space, Time, and Space-time Space-time is like the stage upon which the events of the universe are played out Einstein also described gravity as the curvature of space-time

Curves and Gravity: 

Curves and Gravity We usually think of space-time as a sheet Massive objects are placed on the sheet, and bend it The more massive an object, the greater the curvature

Curves and Gravity: 

Curves and Gravity Einstein’s universe is beautiful and elegant Answer this question…why do planets go around the sun in (rough) circles? Because on a curved surface, a circle is the shortest route to go

Gravity and Curvature: 

Gravity and Curvature Why does gravity bend light (like in a gravitational lens)? The light just takes the shortest, easiest route

Curves and Gravity: 

Curves and Gravity Why does mass cause time to slow down? Because time and space are two sides of the same coin What is a black hole? A curvature so steep light cannot “climb out”

In Einstein’s treatment of gravity, why do planets travel on curved paths?: 

In Einstein’s treatment of gravity, why do planets travel on curved paths? The inner pull of gravity is balanced by the forward motion of the planet They are following the shortest distance in curved space They are spiraling in towards the Sun

The Mind’s Eye: 

The Mind’s Eye A savvy observer will notice something fishy with the way we have drawn space-time in these pictures… It is 2-D – a “sheet” But we live in a 3-D universe

The Mind’s Eye: 

The Mind’s Eye Representing space-time in 3-D is difficult, so for sanity’s sake we usually just take the easy route and switch to 2-D

Space-time and Mass: 

Space-time and Mass This view of gravity is a elegant, and often summed up in the statement: “Mass tells space-time how to curve, and space-time tells matter how to move”

Space-time and Energy: 

Space-time and Energy But remember that mass and energy are equivalent Energy also causes space-time to curve!

Space-time and Energy: 

Space-time and Energy More specifically, it is an energy density and mass density that determine the curvature of space-time High densities lead to greater curvature

Space-time and the Universe: 

Space-time and the Universe This means that everything in the Universe contributes to the curvature of space-time How does this affect our view of the universe itself?

Space-time and the Universe: 

Space-time and the Universe We usually think of space-time as localized The space-time around the sun, or a black hole But we can describe the entire universe in terms of space-time

Space-time and the Universe: 

Space-time and the Universe Wrap your brain around this statement We are going to be taking a look at the overall curvature of the entire universe

Space-time and the Universe: 

Space-time and the Universe What we will not be doing is looking at a small piece of the universe The curvature of space-time in this room, or in the solar system, or around the Milky Way is much different than the curvature of the Universe as a whole

Space-time and the Universe: 

Space-time and the Universe But these are like valleys on the surface of the Earth The overall curvature of the Earth is still the same

The curvature of space around the moon is indicative of the overall curvature of the universe.: 

The curvature of space around the moon is indicative of the overall curvature of the universe. True False

Three Worlds: 

Three Worlds We describe the curvature in one three ways Closed Flat Open

A Closed Universe: 

A Closed Universe A closed universe would have positive curvature Pictured in 2-D, the surface would be like that of a globe

A Closed Universe: 

A Closed Universe The curvature is described as “closed” because it curves back in on itself In a close universe, very big triangles would have angles that add up to more than 180°

A Closed Universe: 

A Closed Universe A word about that pesky third dimension The surface of our universe is represented as 2-D with the curvature in the third dimension The analogy with our true universe would be a 3-D space with curvature in a “4th spatial dimension” I will buy you lunch if you can draw that on the board…

A Flat Universe: 

A Flat Universe A flat universe is pretty simple The angles of triangles add up to exactly 180° The Universe does not curve back on itself But does it go on forever?

An Open Universe: 

An Open Universe Picturing an open universe is difficult The curvature is said to be negative There is no object that we can draw that has negative curvature everywhere But we can draw small pieces of space that have negative curvature

An Open Universe: 

An Open Universe In an open universe, the angles of triangles add up to less than 180° Draw this in 3-D, with the curvature in the 4th dimension, and you get a steak dinner…

Summary…: 

Summary…

Will an open universe ever curve back in on itself?: 

Will an open universe ever curve back in on itself? Yes No

Which Is It?: 

Which Is It? Which of these three universes do we live in? It all depends on the overall, average density of our universe This is a mass and energy density

Which Is It?: 

Which Is It? We can calculate the exact density we need to have a flat universe We call this the critical density In everyday units, this is about 9.7 × 10-27 kg / m3

Which Is It?: 

Which Is It? This is an exceedingly small density by our standards The density of air in this room is 1.3 kg / m3 The density of the best vacuums we can make on Earth are about 10-9 kg / m3

Which Is It?: 

Which Is It? To make things clearer, we usually talk about the density of the universe compared to the critical density We simply divide the actual density of the universe by the critical density, and call this W

Which Is It?: 

Which Is It? If W = 1, the Universe has the critical density and is flat If W > 1, the Universe is more dense than the critical density and is closed If W < 1, the universe is less dense than the critical and is open

So Which Is It Already?: 

So Which Is It Already? To find out, we have to have a way of measuring the average density of the whole universe Obviously, the region around the Earth is not a good place to go Neither is the solar system

Just Tell Us!: 

Just Tell Us! Galaxy clusters begin to give us a good estimate of the average density of the Universe

Finally!: 

Finally! As far as we can measure, the value of W is… 1.00 ± 0.02

Our Universe: 

Our Universe We live in a flat universe What does this mean for the fate of our universe…?

How will our flat universe end?: 

How will our flat universe end? It will end in a big crunch It will coast on forever, never quite stopping It will keep on expanding, never even getting close to stopping

Our Universe: 

Our Universe There was a time (15 years ago), when this would have meant that our universe would not end in big crunch We can no longer make that statement

Our Universe: 

Our Universe Understanding the ultimate fate of our Universe has gotten more complicated, but we do know it

Our Universe: 

Our Universe But to understand where we are going, we must first understand where we have been, and how we got to where we are today This will be the topic of the next lecture…

The Beginning of the Universe: 

The Beginning of the Universe The Big Bang

A Cosmic Perspective: 

A Cosmic Perspective People have been trying to answer the question “How did we get here?” since the invention of the question

A Cosmic Perspective: 

A Cosmic Perspective For millennia, this was the realm of religion in philosophy In many ways, it still is But as scientists learned more about their world, they began to tackle the question

A Cosmic Perspective: 

A Cosmic Perspective First they tried to answer the question “What is the Universe?” By 1920, there was still no consensus At issue was just how big the Universe is

The Distance Ladder: 

The Distance Ladder Measuring distances is much harder than it seems at first Nothing like this in space…

The Distance Ladder: 

The Distance Ladder The first step, and most reliable, is to measure the distance to the planets This defines the Earth-Sun distance, or the AU

The Distance Ladder: 

The Distance Ladder Next we use parallaxes This is based on the Earth-Sun distance It is also very reliable

The Distance Ladder: 

The Distance Ladder But parallax only works out to about 100 light-years But we can use this to make the H-R diagram After that, we use main sequence fitting

The Distance Ladder: 

The Distance Ladder We know how the main sequence should look, in terms of absolute magnitude If all the stars are at the same distance, we can also make an H-R diagram in terms of apparent magnitude Next, we just adjust it and use the distance modulus

The Distance Ladder: 

The Distance Ladder That gets us out to about 300,000 light-years This is about the distance of the nearest dwarf galaxies, the Magellanic Clouds Now what?

The Distance Ladder: 

The Distance Ladder There are certain stars, called Cepheid variables, that pulse Their brightness goes up and down in a regular manner

The Distance Ladder: 

The Distance Ladder These Cepheid variables have an amazing property The period of their pulsation is related to their intrinsic luminosity They are a type of standard candle

The Distance Ladder: 

The Distance Ladder Once we calibrate this using main sequence fitting, we can measure distance out to about 13 million light-years

The Distance Ladder: 

The Distance Ladder Past this point, Cepheids become too dim to be useful We need something really bright, but with a known luminosity… Type Ia supernovae

The Distance Ladder: 

The Distance Ladder This gets us out to about 1 billion light years After that, we are sort of stuck…

The Distance Ladder: 

The Distance Ladder Anything more than 1 billion light years away must have sent out its light at least 1 billion years ago! The universe was a different place, and we have trouble finding standard candles that we can calibrate

Enter Edwin Hubble: 

Enter Edwin Hubble To measure these even greater distances, we have to look at the work of Edwin Hubble When we last saw Hubble, he was classifying galaxies…

Receding Galaxies: 

Receding Galaxies It was known that galaxies (spiral nebulae) had large velocities relative to the Earth This could be measured using Doppler shifts But no one had tried yet gotten a good distance to the galaxies

Receding Galaxies: 

Receding Galaxies Then Cepheids were discovered Hubble used Cepheids to measure the distance to many galaxies He then compared this to their velocities What did he find?

Hubble’s Law: 

Hubble’s Law Astoundingly, the farther away a galaxy was, the faster it was receding This was an amazing result!

Hubble’s Law: 

Hubble’s Law Although Hubble’s initial numbers were way off, the trend was exactly right And notice that it is a linear relationship

The Hubble Parameter: 

The Hubble Parameter We can represent this with a beautiful equation

The Hubble Parameter: 

The Hubble Parameter The current best estimate for H0 is 72 5 km/s/Mpc Or, for every million parsecs, a galaxy moves away 72 km/s faster