Robert DiSalle: Gravity, Geometry, Philosophy: 100 Years in Einstein's Universe

Rotman Institute of Philosophy
5 Mar 201553:43
EducationalLearning
32 Likes 10 Comments

TLDRIn this lecture, Carl Heifer introduces Professor Robert Desal, who discusses Einstein's profound impact on our understanding of the universe through his general theory of relativity. Desal explores Einstein's philosophical approach to physics, particularly his revolutionary concept of space-time curvature and its dynamic nature influenced by mass distribution. He also touches on how Einstein's theories have shaped our current questions about the universe's structure, such as the origins, expansion, and potential end of the cosmos.

Takeaways
  • ๐Ÿ“š Carl Heifer introduces the event celebrating Einstein's General Theory of Relativity, highlighting its 100th anniversary and the intersection of philosophy and physics in Einstein's work.
  • ๐ŸŒŒ Professor Robert Desal discusses Einstein as a philosopher-scientist, emphasizing the importance of philosophical thought in the development of Einstein's theories of time, space, and gravitation.
  • ๐Ÿ”— Desal explores the concept of living in an 'Einsteinian universe,' pondering how our understanding of the universe is shaped by Einstein's theories, even as we anticipate a quantum theory of gravity.
  • ๐Ÿ“ The connection between gravity and geometry is a central theme, with Desal explaining how Einstein revolutionized our understanding of space-time as a dynamic entity influenced by mass and energy.
  • ๐Ÿ•ต๏ธ Einstein's philosophical inquiries led him to challenge traditional views of geometry as a static backdrop, proposing instead a geometry that is shaped by and responds to the physical world.
  • ๐ŸŒŸ Desal illustrates Einstein's thought process, showing how he questioned the necessity of a fixed, absolute reference frame and the implications of a universe where inertial and gravitational effects are indistinguishable.
  • ๐ŸŒ€ The geodesic principle, central to general relativity, is presented as a way to understand how the paths of objects in free fall are not forced deviations from straight lines but are the straightest possible paths in a curved space-time.
  • ๐Ÿ›ฐ๏ธ Practical applications of Einstein's theories are mentioned, such as GPS navigation, which relies on corrections derived from both special and general relativity to account for time dilation and gravitational effects.
  • ๐ŸŒ The philosophical underpinnings of Einstein's work are underscored, with the speaker highlighting how Einstein's critical analysis of existing concepts of gravity and geometry led to his groundbreaking theory.
  • ๐Ÿ”ฎ Desal suggests that even if a quantum theory of gravity supersedes general relativity, the latter will remain a valuable tool for understanding the universe, a limiting case, and a source of enduring insights.
  • ๐ŸŽ‰ The event concludes with a recognition of Einstein's legacy as not just a scientific one but also a philosophical one, with his theories continuing to inspire and inform both scientific and philosophical discourse.
Q & A
  • What is the main theme of the event that Carl Heifer introduced?

    -The main theme of the event is the exploration of Einstein's General Theory of Relativity, marking its 100th anniversary and discussing the philosophical and scientific aspects of Einstein's work.

  • Who is Professor Robert Desal, and what is his expertise?

    -Professor Robert Desal is a professor of philosophy at Western University, specializing in our understanding of time, space, and physical theories. He is also the author of a book called 'Understanding Space Time'.

  • Why is Einstein considered a philosopher-scientist?

    -Einstein is considered a philosopher-scientist because he embraced the label and integrated philosophical thinking with his scientific work, which was central to his achievements in developing the theories of relativity.

  • What is the significance of the GPS system in relation to Einstein's theory?

    -The GPS system is a significant technological application of Einstein's theory, specifically general relativity, as it requires corrections for time dilation effects caused by both special and general relativity to maintain accurate positioning.

  • What is the philosophical problem that Einstein had to address regarding geometry?

    -Einstein had to address the philosophical problem of how to think about geometry as a dynamical aspect of the physical world, rather than a fixed background, which was a departure from traditional conceptions of geometry.

  • What is the connection between gravity and geometry that Einstein explored?

    -Einstein explored the connection between gravity and geometry by proposing that gravity is not a force but a curvature of space-time, making geometry a dynamical field influenced by the distribution of mass.

  • What is the 'geodesic principle' Einstein referred to in his theory?

    -The geodesic principle states that the path of a falling body is physically equivalent to the path of a body moving inertially, suggesting that the trajectories of inertial observers in space-time indicate the curvature of space-time.

  • How did Einstein's theory change the way we think about the universe's structure and history?

    -Einstein's theory introduced the concepts of space-time curvature, black holes, and the large-scale structure of the universe, allowing us to consider the universe's history, including its beginning, expansion, and possible end.

  • What is the role of philosophy in the development of Einstein's theories?

    -Philosophy played a crucial role in the development of Einstein's theories by providing a critical analysis of established conceptions of gravity and geometry, leading to a new understanding of the relationship between physics and geometry.

  • How might future theories of gravity relate to Einstein's General Theory of Relativity?

    -Future theories of gravity might incorporate Einstein's General Theory of Relativity as a limiting case for small masses and low velocities, or as a source of insight into the large-scale cosmic structures and the evolution of the universe.

Outlines
00:00
๐Ÿ“š Introduction to the Einstein Anniversary Event

The speaker, Carl Heifer, opens the event commemorating the 100th anniversary of Einstein's general theory of relativity. He introduces the Rotman Institute of Philosophy's series of events for 2015 and welcomes Professor Robert Desal, an expert in philosophy and physical theories. Desal is expected to discuss Einstein's work and its philosophical underpinnings, emphasizing Einstein's role as a philosopher-scientist. The introduction also highlights the importance of philosophy in the development of scientific theories, particularly in Einstein's case.

05:00
๐ŸŒŒ The Einsteinian Universe and Its Philosophical Foundations

Professor Desal delves into the questions that define our understanding of the universe as Einsteinian, despite the potential for future theories to supersede Einstein's. He discusses the conceptual revolution brought about by Einstein, which includes questions about the universe's origin, the curvature of space-time, and the nature of black holes. Desal also explores various historical conceptions of geometry and how Einstein's theory of relativity dynamically connects geometry with the physical world, marking a significant departure from traditional views.

10:01
๐Ÿ”ญ Practical and Conceptual Impacts of Einstein's Theories

Desal highlights the practical applications of Einstein's theories, such as GPS navigation, which relies on corrections for time dilation due to both special and general relativity. He then transitions to the conceptual impact of Einstein's work, like the prediction of black holes and gravitational lensing, which have expanded our understanding of the universe's large-scale structure. Desal emphasizes that even if Einstein's theory is not the final word on gravitation, it has provided invaluable insights into the cosmos.

15:03
๐ŸŒ The Philosophical Journey to General Relativity

The speaker outlines Einstein's philosophical journey that led to the general theory of relativity. Starting with a simple question about the Earth's rotation, Einstein explored the philosophical implications of Newtonian mechanics and the nature of physical laws. He questioned the privileged status of certain reference frames and the unobservable causes in Newtonian physics, advocating for a theory based on observable facts. This philosophical inquiry laid the groundwork for a new understanding of gravity and its relation to the fabric of space-time.

20:04
๐Ÿงฒ The Principle of Equivalence and Its Implications

Einstein's principle of equivalence, which states that there is no experiment that can distinguish between gravity and acceleration, is discussed in detail. The speaker explains how this principle led to a deeper understanding of inertial frames and the equivalence of gravitational and inertial effects. This concept is central to the development of general relativity and challenges the traditional Newtonian view of gravity.

25:05
๐ŸŒŒ The Geodesic Principle and Curvature of Space-Time

Desal introduces the geodesic principle, which posits that the path of a falling body is physically equivalent to an inertial path in the absence of forces. This concept is key to understanding how Einstein reinterpreted the motion of bodies in a gravitational field as the natural motion in curved space-time. The speaker illustrates this with the analogy of the Earth's surface and how straight lines of longitude indicate its curvature, drawing a parallel to the behavior of inertial trajectories in space-time indicating space-time curvature.

30:07
๐Ÿ“‰ The Dynamical Nature of Geometry in General Relativity

The speaker discusses the radical idea that geometry, as understood in general relativity, is not static but dynamic, varying with the distribution of mass-energy in the universe. This dynamical geometry is a fundamental aspect of Einstein's theory, where the curvature of space-time is directly related to the presence of mass, thus geometrizing the concept of gravity and making geometry a physical field influenced by mass-energy distribution.

35:08
๐ŸŒŸ The Legacy and Future of Einstein's General Relativity

Desal reflects on the enduring legacy of Einstein's general theory of relativity, considering its potential survival beyond the development of a quantum theory of gravity. He suggests that while the theory may not be the final word on gravity, it could continue to be useful for predictions and practical applications, serve as a limiting case for future theories, and provide unique insights into the large-scale structure of the universe. The speaker concludes by celebrating Einstein's work as a product of critical philosophical analysis and a testament to his identity as a philosopher-scientist.

Mindmap
Survival of Theories
Quantum Theory of Gravity
Conceptual Insights
Empirical Success
Geodesic Principle
Thought Experiments
Gravitational Lensing
GPS Technology
Cosmological Implications
Concept of Space-Time
Dynamical Geometry
Philosophical Foundations
Einstein's Queries
Newtonian Theory
Conceptual Revolution
Philosophical Influence
Robert Desal's Expertise
Carl Heifer's Introduction
Future of Theoretical Physics
The Legacy of Einstein's Theory
Einstein's Methodology
Practical and Theoretical Applications
Einstein's Universe
Philosophy and Physics
Theoretical Context
Einstein as a Philosopher-Scientist
Introduction to Einstein
Einstein's General Theory of Relativity
Alert
Keywords
๐Ÿ’กGeneral Theory of Relativity
The General Theory of Relativity is a fundamental theory in physics that describes the gravitational force as the curvature of space-time caused by mass and energy. It is central to the video's theme as it celebrates the 100th anniversary of its discovery by Albert Einstein. The script discusses how this theory revolutionized our understanding of the universe, introducing concepts like space-time curvature and gravitational waves.
๐Ÿ’กEinstein
Albert Einstein is a pivotal figure in the script, renowned for his work in theoretical physics, particularly the theory of relativity. The video explores his dual identity as a philosopher-scientist, emphasizing how his philosophical inquiries into the nature of space, time, and gravitation led to the formulation of the General Theory of Relativity.
๐Ÿ’กSpace-Time
Space-Time is a concept in physics that combines the three dimensions of space with the one dimension of time into a single four-dimensional continuum. In the script, space-time is crucial as it is the fabric of the universe that is warped by mass and energy, leading to the phenomenon of gravity as described by Einstein's General Theory of Relativity.
๐Ÿ’กPhilosophy of Science
The philosophy of science is the study of assumptions, foundations, and implications of science. The script highlights Einstein's deep engagement with philosophical questions, such as the nature of geometry and its relation to physical reality, which significantly influenced his scientific work and the development of the General Theory of Relativity.
๐Ÿ’กGeometry
Geometry is a branch of mathematics concerned with the properties and relations of points, lines, surfaces, and higher-dimensional spaces. In the context of the video, geometry is discussed as a dynamical aspect of the physical world, with Einstein's theory suggesting that the geometry of space-time is affected by the presence of mass, a departure from the traditional view of geometry as static and abstract.
๐Ÿ’กInertial Frame
An inertial frame is a frame of reference in which an object moves in a straight line at a constant speed unless acted upon by an external force. The script discusses the concept of inertial frames in relation to Einstein's theory, explaining how they cannot be distinguished locally from a frame in free fall in a gravitational field, which is a key insight in the development of General Relativity.
๐Ÿ’กGravitational Lensing
Gravitational lensing is a phenomenon where light from a distant source is bent due to the gravitational field of a massive object between the source and the observer. The script mentions this as an application of Einstein's theory, demonstrating how it has expanded our understanding of the universe by allowing us to observe objects that would otherwise be obscured.
๐Ÿ’กBlack Hole
A black hole is a region of space-time with a gravitational pull so strong that nothing, not even light, can escape from it. The concept of black holes is discussed in the script as a direct consequence of Einstein's theory of General Relativity, which describes how mass can curve space-time to such an extent that it forms a black hole.
๐Ÿ’กGPS
GPS, or Global Positioning System, is a satellite-based navigation system that provides location and time information. The script uses GPS as an example of a practical application of Einstein's theories, particularly General Relativity, which accounts for time dilation effects caused by the relative motion and gravity of the GPS satellites.
๐Ÿ’กCosmology
Cosmology is the scientific study of the universe's origin, evolution, and eventual fate. The script touches on cosmology by discussing how Einstein's theory has shaped our understanding of the universe's large-scale structure and history, including questions about its beginning, expansion, and possible end.
๐Ÿ’กMach's Principle
Mach's Principle is a concept in physics that suggests that the inertia of an object depends on the distribution of all other masses in the universe. While not directly mentioned by name in the script, the idea is alluded to when discussing Einstein's philosophical considerations about the nature of inertia and gravitation, and how they relate to the motion of bodies in the universe.
Highlights

Carl Heifer introduces the event celebrating the 100th anniversary of Einstein's general theory of relativity.

Professor Robert Desal discusses Einstein's dual role as a philosopher and scientist, emphasizing the inseparable nature of these aspects in his work.

Desal explains the conceptual revolution brought by Einstein, particularly how his theories redefined our understanding of space-time and gravity.

The importance of geometry in Einstein's theory is highlighted, showing how it became a dynamical field rather than a static background.

Einstein's philosophical approach to geometry is underscored as essential to the development of the general theory of relativity.

Desal explores the question of how we can live in an 'Einsteinian universe' even when the final theory of gravitation might be a quantum one.

The connection between gravity and geometry is discussed, illustrating how Einstein associated abstract geometric principles with physical fields.

Desal highlights Einstein's philosophical inquiries into the nature of physical laws and their relation to observable reality.

The practical application of general relativity in GPS navigation systems is explained, showing the theory's real-world impact.

Einstein's theory is considered as an instrument for understanding and exploring the universe, not just for making predictions.

Desal delves into the historical development of geometrical principles and how they paved the way for Einstein's revolutionary ideas.

Einstein's philosophical background and its influence on his approach to the physics of gravitation and the nature of geometry are examined.

The concept of inertial frames and the equivalence principle are discussed in the context of Einstein's thought process.

Desal explains how Einstein's theory allows us to explore cosmic phenomena like black holes and gravitational lensing.

The philosophical significance of Einstein's general theory of relativity as a conceptual revolution is emphasized.

Einstein's ideas on the geodesic principle and how they relate to the curvature of space-time are presented.

Desal concludes by reflecting on the enduring legacy of Einstein's work, its philosophical underpinnings, and its impact on our understanding of the universe.

Transcripts
00:18

good evening everybody

00:19

um thanks for coming out on a cold

00:22

evening to

00:23

uh to learn some philosophy and physics

00:26

um

00:26

i think we're gonna have a lot of fun um

00:28

my name is carl heifer and i'm a member

00:30

of the rotman institute of philosophy at

00:32

western university and this is our first

00:36

event

00:37

in a series of events that we're holding

00:38

this year in 2015

00:41

to mark the 100th anniversary of the

00:43

discovery of einstein's general theory

00:45

of relativity

00:47

um so this is our inaugural event

00:50

and we're very pleased to have professor

00:53

robert desal

00:54

uh here he's also a professor of

00:56

philosophy at western

00:58

an expert on our understanding of time

01:01

and space

01:02

and physical theories in general and

01:05

we're going to hear about the work

01:08

and the discoveries of about our

01:10

universe

01:11

achieved by albert einstein who is the

01:13

most uh

01:15

influential and famous philosopher

01:16

scientist in history

01:18

now for many of you it will be

01:20

surprising to hear einstein described as

01:22

a philosopher scientist

01:24

but einstein himself would have happily

01:26

embraced that label

01:28

uh reading philosophers and thinking

01:31

about nature in a philosophical way was

01:33

absolutely central to what einstein

01:35

achieved as professor desal will uh will

01:38

be

01:39

explaining to you tonight and so since

01:41

the roman institute of philosophy is all

01:43

about

01:43

promoting the engagement of philosophers

01:47

today with working scientists

01:49

we find it very appropriate to to

01:51

celebrate the most

01:52

striking historical example of the

01:55

successful engagement of philosophy with

01:57

science

01:57

uh which happened in the life and work

01:59

of albert einstein

02:01

professor desal has been a distinguished

02:03

professor of philosophy

02:05

at western ontario for a number of years

02:07

and he's

02:08

the author of a book called

02:10

understanding space time

02:12

which takes you on a journey from

02:15

newton and newton's predecessors all the

02:17

way through einstein's theories of

02:19

relativity

02:20

explaining how our notions of space and

02:22

time

02:23

evolved inevitably to the the form which

02:26

we have today

02:28

so without further ado let me hand

02:30

things over to professor robert desal

02:38

thanks for that introduction carl thank

02:39

you all for coming

02:41

i'd like to offer um i'd like to just

02:43

say my

02:44

say my belated appreciation to joe

02:47

rotman whose enthusiasm for

02:49

doing this project helped to get it

02:52

going and unfortunately he isn't here

02:54

to see the results but his efforts are

02:58

really

02:58

deeply appreciated i'd like to talk to

03:01

you about einstein

03:03

the philosopher and einstein the

03:05

scientists and about how these two

03:07

aspects of einstein

03:08

were really inseparable

03:12

i'd like to start by considering a

03:14

couple of questions

03:15

that are kind of governing the structure

03:18

of this talk

03:19

first of all what does it mean to say we

03:20

live in einstein's universe

03:23

uh what characterizes the universe we

03:25

live in as particularly einstein in

03:27

i think this is particularly interesting

03:29

question in light of the fact that most

03:32

physicists today would say the correct

03:33

theory of gravitation is not einsteins

03:36

but some quantum theory of gravity of

03:39

one or another sort

03:41

that you know perhaps down this down the

03:43

road in waterloo someone's going to come

03:45

up with

03:46

or is working on right now as we speak

03:50

and so what does it mean to say we live

03:53

in an einsteinian universe if it turns

03:54

out this isn't really the final theory

03:57

which is usually how theories turn out

04:01

the second thing is what's the

04:02

connection between gravity and geometry

04:05

so one of the things i hope that you'll

04:07

get out of the next

04:09

little while is some appreciation of of

04:12

how einstein made this connection

04:14

in the first place between geometry

04:17

which had

04:17

up to that time been understood as a

04:19

kind of formal abstract theory

04:23

uh how did he associate that with

04:25

something dynamical like a physical

04:27

field

04:29

and finally what's the connection

04:31

between gravity and geometry on the one

04:33

hand

04:34

and philosophy on the other i hope that

04:37

will become clear

04:38

in other words how did einstein's

04:39

insights into the physics of gravitation

04:42

and the physical nature of geometry

04:45

arise from his pursuit of

04:47

philosophical problems

04:53

well one thing i'd like to point out

04:55

that's really interesting about the

04:56

einsteinian revolution that i think

04:58

isn't sufficiently appreciated is

05:00

that we have a lot of questions that we

05:01

ask about the universe today that really

05:03

wouldn't have made any sense in a

05:05

pre-einstein context

05:07

for example how did the universe begin

05:10

there really wasn't a theory of that in

05:12

the newtonian theory of course

05:14

there are previous theories of creation

05:16

but newtonian physics didn't supply

05:18

even a way of asking that question how

05:20

did the universe come to be

05:22

that's a peculiarly einsteinian question

05:26

the curvature of space-time this is

05:28

another thing that

05:29

people really didn't have any way to

05:31

think about before einstein

05:36

how does the structure of space-time

05:38

vary throughout the universe these are

05:39

things that we think of as basic

05:41

questions to ask in cosmology again

05:45

wouldn't have made any sense at all what

05:48

is inside of a black hole these are all

05:51

concepts that we consider basic to the

05:53

science of the large scale structure of

05:55

the universe

05:57

all of them have to do with concepts

05:59

that really

06:00

came to be well defined by einstein this

06:02

is the sense in which what einstein did

06:04

was not merely

06:05

a physical theory but a conceptual

06:08

revolution

06:12

so how did all this come to be well

06:16

first of all it became necessary to

06:18

think about geometry in a different way

06:20

this is what i'm contending is the

06:22

primary philosophical problem that

06:24

einstein had to solve

06:25

how to think about geometry as a

06:28

dynamical aspect of the physical world

06:30

if you look back through history there

06:32

are lots of

06:34

conceptions of geometry none of them

06:35

quite like einstein's

06:37

there's a very long tradition among

06:39

rationalist philosophers whom

06:41

whose names you may know kant plato

06:45

in descartes leibniz people who in one

06:48

way or another thought

06:49

that geometry was a science that was

06:53

absolutely necessary truth that had

06:55

nothing to do with experience at all

06:59

then there was another notion that goes

07:02

all the way back to the ancient

07:03

egyptians and babylonians

07:05

and had champions in the 19th century

07:07

like the philosopher john stuart mill

07:09

that geometry the principles of geometry

07:12

are basically codifications of

07:14

empirical recipes for actually solving

07:16

particular problems

07:18

and our confidence in them comes from

07:19

the number of times we've repeated

07:21

these basic geometrical operations from

07:24

building the pyramids to building houses

07:26

and railroads

07:28

but then there was another conception

07:30

that was really quite revolutionary

07:32

which could be said to have begun with

07:33

newton but really came into its own in

07:35

the 19th century

07:36

with scientists like uh hermann von

07:39

helmholtz and henry poincare

07:41

culprit regauss bernard riemann

07:46

the notion that geometrical principles

07:48

considered by themselves are just a kind

07:50

of formal abstract structure

07:53

and that if you want to talk about

07:54

geometry as the geometry of space that

07:58

is to say is characterizing the world in

08:00

some way as describing the world we live

08:02

in

08:02

you have to somehow connect the abstract

08:04

mathematical principles of geometry with

08:06

something

08:07

physical so there's some connection that

08:09

has to be made between the laws of

08:11

physics

08:12

and the mathematics of space and that

08:15

was a revolutionary development that

08:16

in a way paved the way for einstein and

08:19

made his whole way of thinking possible

08:22

but what einstein did was something

08:24

quite do quite new

08:25

even compared to that that is to think

08:28

of

08:28

to find a way to think of geometry not

08:30

as a kind of fixed

08:32

background within which the physical

08:33

laws are articulated

08:35

within which we move and measure

08:39

but to think of it as itself a kind of

08:41

dynamical field

08:43

like the electromagnetic field or the

08:45

gravitational field

08:47

that interacts with other fields in

08:49

nature this dynamical conception of

08:51

geometry

08:52

is the basis for the general theory of

08:55

relativity

08:56

but it's again it's something that

08:58

without a kind of conceptual

08:59

investigation that einstein did

09:02

it's a concept that no one could even

09:03

have understood in the 19th century

09:07

with a few possible exceptions

09:10

this is a question that einstein asked

09:13

reflecting on

09:14

the philosophical background to his way

09:17

of thinking about geometry he asked the

09:18

question how can it be that mathematics

09:21

being after all a product of human

09:22

thought which is independent of

09:24

experience

09:25

is so admirably appropriate to the

09:27

objects of reality

09:29

is human reason then without experience

09:32

merely by taking

09:33

thought able to fathom the properties of

09:35

real things

09:37

in my opinion the answer to this

09:38

question is briefly this

09:40

as far as the laws of mathematics refer

09:42

to reality

09:43

they are not certain as far as they are

09:46

certain they do not refer to reality

09:50

yet on the other hand it is certain that

09:52

mathematics generally and particularly

09:53

geometry owes its existence to the need

09:55

to learn something about the relations

09:57

of real things to one another

09:59

the very word geometry which means earth

10:01

measuring proves this

10:03

for earth measuring has to do with the

10:04

possibilities of the disposition of

10:06

certain natural objects with respect to

10:08

one another

10:09

it's clear that the system of concepts

10:11

of axiomatic geometry alone

10:13

cannot make any assertions as to the

10:15

relations of real objects

10:17

of this kind which we will call

10:19

practically rigid bodies

10:22

in order to make such assertions

10:24

geometry must be stripped of its

10:26

merely logical formal character by the

10:29

coordination of real objects of

10:30

experience with the empty

10:32

conceptual framework of axiomatic

10:33

geometry

10:35

to accomplish this we need only add the

10:37

proposition solid bodies are related

10:40

with respect to their possible

10:41

dispositions

10:42

as our bodies in euclidean geometry this

10:45

is really the key point he was trying to

10:47

make then the propositions of euclid

10:49

contain affirmations as to the relations

10:51

of practically rigid bodies

10:53

geometry thus completed is

10:57

evidently a natural science we may in

11:00

fact regard it as the most

11:01

ancient branch of physics its

11:04

affirmations rest

11:05

essentially on inductions from

11:07

experience but not on logical inferences

11:09

only

11:11

i attach special importance to the this

11:13

view of geometry

11:15

because without it i should have been

11:16

unable to formulate the theory of

11:18

relativity

11:19

that was as clear as statement as you

11:20

could get from einstein that he really

11:22

thought that

11:23

this new philosophical conception of the

11:26

relationship between geometry and

11:27

physics

11:28

that had developed in the 19th century

11:31

was fundamental to who's creating the

11:33

theories that he created

11:35

although as we'll see he carried them to

11:36

a different direction altogether

11:39

some of his philosophical forebears you

11:41

can see in this picture

11:42

maybe i'll give you a quiz at the end

11:44

see if you can recognize who they are

11:49

if you're a philosophy professor no

11:51

telling

11:54

i'd like to begin by uh

11:57

considering two ways of thinking about

11:59

in what way is einstein's theory part of

12:02

our world

12:03

well you can think of a scientific

12:05

theory

12:06

as an instrument because after all if

12:08

you're worried about the fact that

12:09

tomorrow we might not believe this

12:11

theory

12:12

what is its value if we don't think it's

12:15

really true well you can

12:17

you can think of it as simply a

12:18

practical tool for prediction

12:20

and for the control of nature now some

12:23

of you probably have heard this story

12:25

there really is one technological

12:28

application of general relativity that's

12:30

extremely

12:30

important and it's gps navigation when i

12:34

was in graduate school

12:35

relativity students used to say we

12:37

should try to convince the government

12:38

that we're working on a relativity bomb

12:41

because maybe then we'll get more

12:43

funding

12:45

because they were trying they didn't

12:47

come up with one needless to say

12:50

but eventually the gps was developed

12:54

which is a very important application of

12:56

special and general relativity

12:58

but in a way more general relativity

13:01

because you have satellites

13:02

orbiting the earth at 20 000 kilometers

13:05

and at 14 000 kilometers per hour

13:08

and you have to make timing corrections

13:10

for the high velocity

13:12

because of special relativity and

13:14

because of general relativity because of

13:15

the difference in clock timing in

13:17

stronger and weaker

13:19

places of space-time curvature you have

13:21

to correct

13:22

for the time speeding up

13:26

so if you subtract the time slowing down

13:29

from the time speeding up you get a

13:31

delay of 38 microseconds per day which

13:33

doesn't sound like much

13:35

but if you didn't correct for this you

13:37

would have errors accumulating at a rate

13:39

of

13:40

kilometers per day and your gps

13:42

navigation system would

13:43

would be completely off so this is a

13:46

practical application of einstein's

13:48

theory

13:52

but i'd like to think about

13:55

einstein's theory as an instrument of a

13:57

different kind for a moment that is to

13:59

say is an instrument of understanding

14:00

and of exploring

14:03

now this is a remark that was made uh

14:06

by pierre simon de la platz

14:09

200 years ago about newton's theory of

14:11

universal gravitation

14:13

and i think it was an interesting remark

14:16

that illustrates the sense in which

14:17

a physical theory which we now regard as

14:19

not true

14:21

nonetheless is an instrument for the

14:23

exploration of nature like

14:25

a telescope as laplace put it

14:29

he says the theory of gravity having

14:31

become by so many applications a means

14:34

of discovery

14:35

as certain as by observation itself

14:39

has made known several new inequalities

14:41

it's enabled the mathematician to

14:43

predict the return of the comet of

14:44

1759. he's been able enabled by this

14:48

means to deduce some observation as from

14:50

a rich mind a great number of important

14:52

and delicate elements which without the

14:55

aid of analysis would have been forever

14:56

hidden from view

14:58

the masses of the sun the planets their

15:00

satellites the velocity of light

15:02

the ellipticity of jupiter the shape of

15:05

the earth

15:09

now this is that's a really important

15:12

point that i think laplace was making a

15:14

theory that we don't actually believe

15:15

anymore has nonetheless

15:17

taught us something about the universe

15:19

that

15:21

was otherwise hidden from observation we

15:23

know more about

15:25

empirical things like the masses of the

15:27

planets and their orbits

15:28

from newton's theory then we were able

15:30

to tell by staring at them through

15:32

telescopes

15:34

now if you ask well what has einstein's

15:35

theory done of a similar nature

15:38

well for one thing one of the most

15:40

familiar ideas of einstein's theory is

15:42

the theory of the black hole

15:45

the black hole as we understand it is a

15:47

concept

15:48

that really didn't quite make sense

15:50

according to newtonian theory

15:53

there was a newtonian notion of a black

15:55

hole what the

15:57

what laplace and british astronomer john

16:00

mitchell in the 18th century

16:02

called a dark star because they imagined

16:06

that if light was made of tiny particles

16:11

that must have some mass then presumably

16:14

they must be subject to the

16:16

gravitational field and there could be a

16:17

gravitational field so strong

16:20

that the escape velocity would be faster

16:22

than the velocity of light and they

16:23

would trap

16:24

the light but it's a long time since

16:28

physicists stopped believing that light

16:30

was made of little massive particles

16:32

anyway

16:33

in einstein's theory the notion that

16:35

light as a massless particle can somehow

16:37

be trapped

16:39

around a star or in other words around a

16:42

collapsed star or a black hole

16:44

that's an aspect of his theory that you

16:46

can only understand through the notion

16:47

of space-time geometry

16:50

which we'll come back to but this is an

16:53

aspect of our universe that einstein's

16:56

theory

16:56

is the only theory that that allows us

16:59

to explore

17:00

so it's being used as a tool for the

17:02

exploration of these distant objects and

17:04

there's no substitute for it

17:07

just as just as securely as newton's

17:10

theory was used as

17:11

a tool for exploring aspects of the

17:13

universe and this is something that

17:16

this is something that bears out what it

17:18

means in my opinion to say we live in an

17:20

einsteinian universe

17:21

even if the theory isn't quite the right

17:23

one

17:25

another aspect is gravitational lensing

17:28

the fact that we can

17:29

see we can see for example stars that

17:31

ought to be occulted by other stars

17:34

because of the bending of light as they

17:35

go around more massive objects

17:38

the simplest example of this was

17:40

einstein's prediction

17:41

of the bending of starlight by the sun

17:43

in 1919

17:47

but more complicated examples are things

17:49

that that we

17:50

sometimes see in deep space photographs

17:53

like this one from the hubble telescope

17:55

of the lensing of light from

17:59

from a distant galaxy passing around an

18:02

intervening object

18:04

this is another way in which einstein's

18:06

theory is not merely

18:08

a way of making useful predictions like

18:10

making a tool like the gps it's a way of

18:12

understanding

18:13

how the universe is structured

18:17

and finally one of the most the most

18:20

dramatic example of

18:21

an einsteinian picture of the universe

18:23

that was not possible before is just the

18:25

very idea we have

18:27

of the history of the universe of the

18:29

universe having a beginning

18:30

an expansion and various scenarios for a

18:34

possible end

18:35

which uh isn't coming anytime soon i

18:40

think

18:42

but these are notions that didn't really

18:43

make sense in a newtonian context

18:47

but when we say this is in our

18:48

einsteinian universe it's a universe in

18:50

which we can think of it as having a

18:52

kind of structure like this on a large

18:54

scale

18:59

so for example we we can ask a question

19:02

which wasn't really meaningful before

19:05

what is the shape of space on a large

19:07

scale if you consider a slice of space

19:09

time and

19:10

right a large slice of the universe what

19:12

is its spatial structure

19:14

is it curved like a sphere is it curved

19:17

like a saddle

19:18

or is it flat well these these weren't

19:20

even interesting

19:21

they weren't even possible questions to

19:23

ask before einstein

19:25

made the philosophical effort to figure

19:27

out how such questions could make sense

19:34

now how did einstein get started on this

19:38

path with the

19:39

with he started with a simple question

19:40

that he got

19:42

from reading works by ann smock a 19th

19:44

century physicist whose name you might

19:45

know from the speed of sound

19:48

how do we really know that the earth is

19:51

rotating instead of having the stars

19:53

revolve around it well newton

19:57

found a way to settle this question in

20:00

1687.

20:02

we know the earth is rotating because it

20:03

bulges out at the equator and in various

20:05

other

20:06

ways displays centrifugal effects by the

20:09

19th century

20:10

the end of the 19th century when mach

20:13

wrote this

20:14

book on mechanics there were further

20:16

proofs like the coriolis effect

20:18

the foucault pendulum demonstrating the

20:20

rotation of the earth

20:23

but mark asked the question

20:26

do we really know from these effects

20:28

that it's the earth rotating relative to

20:29

the stars

20:31

or the stars rotating relative to the

20:33

earth

20:35

and there's a lot of philosophical

20:37

mystification about this idea but part

20:39

of

20:40

i won't read the entire quote to you

20:42

part of

20:44

what mach had in mind was a simple

20:45

application of the experimental method

20:49

if you'd like to be sure that it's the

20:51

earth's rotation and not the stars

20:53

rotation that's creating the centrifugal

20:55

effects on the earth

20:57

you ought to be able to vary as a matter

20:59

of experimental method you ought to be

21:01

able to vary the two things separately

21:03

do we know what would happen if this saw

21:05

if the star is rotated around the earth

21:10

of course we don't know that because as

21:12

mark said the world is only given to us

21:14

once

21:15

the ptolemaic or copernican system is

21:17

our interpretation

21:20

but both are equally real

21:26

so the earth is not given to us twice

21:28

once with an earth at rest

21:30

and once with an earth in motion but

21:31

only once with its relative motions

21:33

which are alone determinable

21:35

therefore we cannot say how it would be

21:38

if the earth did not rotate

21:41

we can interpret the one case that is

21:42

given to us in different ways

21:46

if however we interpret it in such a way

21:48

that we come into conflict with

21:49

experience our interpretation is wrong

21:53

now when i wanted to read the original

21:55

edition of this book

21:57

the only place i could find it was in

21:58

the bertrand russell archive at mcmaster

22:01

so it was bertrand russell's copy the

22:04

great

22:05

one of the great philosophers of the

22:06

20th the early 20th century

22:10

so i i read this remark uh the universe

22:13

is not given to us twice

22:15

and you know we cannot say how it would

22:17

be if the earth did not rotate and

22:18

russell had written in the margin

22:20

rubbish and

22:24

because what he meant by that was of

22:26

course you can say what

22:28

what would happen if the earth didn't

22:30

rotate but the stars did because you

22:32

have newtonian physics it tells you

22:34

what would happen in every conceivable

22:36

situation

22:37

any kind of you you just tell newtonian

22:40

physics

22:41

what the matter distribution is and what

22:42

the forces are and it will tell you what

22:44

will happen

22:46

but mock's point was we don't really

22:48

know if these are the laws of physics at

22:50

least this is the philosophical notion

22:52

that einstein got we could be skeptical

22:54

since we don't know what would happen in

22:56

these other situations we don't know if

22:58

if we have the right physical laws now

23:02

so when einstein looked at this

23:04

situation and said suppose you have two

23:06

spheres rotating relative to one another

23:11

and one is bulging out at the equator

23:13

and one isn't

23:14

how do you explain the difference

23:16

between these two between the two

23:18

spheres

23:19

and his answer was well

23:22

the only epistemologically satisfactory

23:25

answer has to be something that points

23:26

to facts of experience

23:28

newtonian mechanics does not give a

23:31

satisfactory answer

23:32

because it says the laws of mechanics

23:34

apply to the space

23:36

r1 in which the body s1 the spherical

23:39

one is rotating

23:41

is at rest sorry but not to the space r2

23:44

in which the body s2 is at rest but the

23:47

privilege space r1 is a merely

23:49

factitious cause

23:51

he's applying a philosophical principle

23:53

here to say

23:55

the newtonian laws of physics probably

23:57

aren't the right laws because

23:59

they have this philosophical difficulty

24:01

that they're appealing to something

24:02

unobservable

24:03

instead of explaining the effects of

24:05

rotation by by

24:07

visible causes by observable causes of

24:09

some kind

24:13

the only satisfactory answer according

24:15

to einstein is that the physical system

24:17

reveals within itself no imaginable

24:19

cause

24:20

to which the differing behavior of s1

24:22

and s2 can be referred

24:24

the cause must lie outside the system

24:30

in the distant masses which we haven't

24:32

been considering

24:33

excuse me

24:38

these distant masses must be regarded as

24:40

the seat of the causes

24:42

which must be susceptible to observation

24:44

of the different behavior

24:46

of s1 and s2 they take over the role of

24:48

the fictitious cause

24:50

r1 in other words the space

24:55

of all the imaginable spaces in any kind

24:58

of motion there is none which we may

25:00

look upon as privileged a priori without

25:02

reviving

25:03

the above mentioned epistemological

25:05

objection

25:06

the laws of physics must be of such a

25:08

nature that they apply to systems

25:10

of reference in any kind of motion along

25:13

this way we

25:14

we arrive at an extension of the

25:15

postulate of relativity

25:17

in other words einstein knew that in

25:19

newtonian mechanics and in

25:21

special relativity there was a

25:23

relativity principle

25:24

you that whether a system is moving

25:27

uniformly or at rest

25:29

is a completely relative matter but what

25:31

about systems that aren't moving

25:33

uniformly

25:34

systems that are rotating or

25:35

accelerating

25:37

why are they supposed to be different

25:41

it was a purely philosophical problem

25:44

and there's a

25:45

great deal more to it than i can go into

25:47

this evening

25:49

but the important thing is that einstein

25:51

thought it was

25:52

odd for the theory to single out certain

25:55

kinds of

25:56

coordinate systems or reference frames

25:59

because he asked the question why should

26:00

nature care about our coordinate systems

26:04

why should there be infinitely many

26:06

inertial systems moving uniformly

26:10

are distinguished from all other rigid

26:11

systems now people had been asking this

26:14

question

26:14

for hundreds of years in various ways

26:17

the real interesting thing is why in

26:20

einstein's case

26:21

was this philosophical problem

26:24

made into a real line of physical

26:28

inquiry

26:29

that actually led to a new theory

26:32

i'll skip to that one let me start by

26:35

considering the idea of an inertial

26:36

frame if you haven't heard the term

26:37

before you

26:38

it won't be very hard to figure out

26:42

if you were sort of enclosed in a box in

26:44

an empty space

26:45

and no forces were acting on you in any

26:47

way

26:49

you would be in what newtonian physics

26:50

or special relativity would call an

26:52

inertial state

26:56

so imagine you're in a box there are no

26:58

forces that you're somewhere

27:00

far from as far as you like from all

27:02

possible matter

27:04

you're just floating around in a way

27:06

that might look familiar to you from say

27:08

space capsules or orbiting

27:11

space stations it would be as if no

27:14

forces are acting on you

27:15

at all

27:19

now einstein was einstein considered

27:22

this other possibility however what if

27:23

that same box were falling in a

27:27

gravitational field

27:29

well because of a peculiar fact about

27:32

gravitation

27:34

you wouldn't be able to tell the

27:35

difference between being

27:38

in this box falling in the gravitational

27:40

field and being all alone in empty space

27:42

with no

27:42

forces acting of any kind some of you

27:46

may have heard this before

27:47

einstein's elevator argument

27:50

he was the first person to really

27:52

consider the implications of this

27:53

problem that

27:55

an inertial frame of reference is

27:57

impossible to distinguish from a frame

27:59

of reference that's falling now why is

28:01

that the case

28:02

because of something that was discovered

28:04

by galileo that gravity has the same

28:06

effect on all bodies near the earth

28:08

so if i'm falling out of a if i'm

28:11

falling in a gravitational field

28:13

and i pull a couple of bowling pins out

28:15

of my pocket or a ruler

28:17

or a grapefruit or whatever i've got in

28:21

my pockets

28:22

they're not going to fall any slower and

28:24

faster than i am so i won't notice that

28:26

i'm in a gravitational field

28:28

i won't feel the top of my body weighing

28:30

down on the bottom of my body it will

28:32

all be the same

28:33

it will be as if no forces are acting on

28:35

me at all

28:37

this is why astronauts in orbit feel

28:40

weightless

28:41

because the same force is acting on them

28:43

and all the parts of their body and

28:45

everything else in their

28:47

shuttle now if you imagine

28:50

a similar example where you have the

28:52

same box but now it's sitting on the

28:54

earth

28:56

now of course the man in the box feels

28:59

his weight on the floor

29:02

he lets go an object it just falls to

29:04

the ground

29:05

9.8 meters per second

29:09

and he has to make some effort to hold

29:11

that bowling pin up

29:13

right now that seems pretty obvious

29:17

but now imagine einstein's evil twin

29:22

is his brother frankie the one nobody

29:24

talks about

29:28

now the evil twin is in a very similar

29:31

box

29:32

but the box starts being pulled upwards

29:37

oh that's sorry that no

29:42

that's totally wrong

29:50

well it's einstein's evil twin at work

29:52

the point is if the box

29:54

if the box were accelerating upwards

29:57

you would feel the exact same effect

29:59

because you your inertia would be

30:01

holding you back while the bottom of the

30:04

box is pushing you upwards

30:06

if if you were accelerating at exactly

30:08

the opposite of the earth's

30:10

gravitational field at 9.8 meters per

30:12

second in the opposite direction

30:14

then you would feel exactly the same

30:15

thing you'd feel from your weight on the

30:16

floor

30:20

so in other words the inertial effect of

30:23

having the

30:24

frame of reference or the box that

30:26

you're going to accelerate upwards is

30:27

the same as the gravitational effect

30:29

of having your weight pull you down just

30:32

as

30:33

the effect of being an inertial frame

30:34

with no forces acting on you is the same

30:37

as the effect

30:38

of falling in a gravitational field

30:40

freely

30:42

now what does all this mean well

30:46

it doesn't necessarily mean anything new

30:51

right einstein said well it's clear that

30:54

you can't distinguish gravity from

30:56

inertia

30:57

because to the observer in the box if

30:59

the box is at rest in a gravitational

31:01

field it's not clear whether the

31:03

whether you're sitting in a

31:04

gravitational field

31:06

or the box is being pulled up and it's

31:08

not clear

31:09

there's no way to tell from an

31:11

experiment whether the box is falling in

31:13

a gravitational field or being acted on

31:15

by no forces at all

31:19

but this isn't by itself a really

31:20

strange idea this is an idea that newton

31:22

had

31:24

there's the relativity theory of

31:26

newton's principia

31:28

as stated in these corollaries that he

31:30

derived from the laws of motion

31:32

first he proved that

31:35

the bodies contained in a given space

31:37

will have the same motions among

31:38

themselves if the space is at rest

31:40

or moving uniformly this is the

31:42

newtonian principle of relativity

31:45

derived from galileo and huygens but

31:48

expressed in this form by newton but

31:50

newton pointed out

31:51

this more radical step that if bodies

31:54

are moving in any way whatsoever among

31:56

themselves

31:57

and are urged by equal accelerative

31:59

forces along parallel lines

32:01

they will all continue to move with

32:03

respect to one another in the same way

32:05

as they would if they were not acted on

32:06

by those forces

32:08

so newton already understood that if you

32:11

have

32:11

a system of bodies that's falling in a

32:13

gravitational field

32:14

it will behave exactly the same as if it

32:16

were at rest

32:18

you might wonder why was newton worried

32:20

about something like that

32:21

and the answer is he was concerned about

32:24

understanding things like

32:26

the system of jupiter and its moons can

32:28

i analyze the system of jupiter and its

32:30

moons

32:31

when the whole system is being

32:33

accelerated toward the sun

32:36

and the answer is yes i can because

32:39

the actions of the sun on the on jupiter

32:41

and its moons

32:43

because they're so far away from the sun

32:45

they're almost equal

32:46

and almost parallel and you can treat

32:48

that system as if it were at rest

32:52

now what about the whole solar system

32:56

newton has a very detailed argument for

32:58

universal gravitation

33:00

would that argument be undermined

33:04

if you found out that the whole solar

33:06

system

33:07

is falling in a larger gravitational

33:09

field

33:10

and the answer is because of corollary

33:12

six no

33:15

it would behave exactly the way it does

33:17

now as long as the accelerations

33:19

caused by that distant mass

33:23

the the whole solar system is falling

33:25

towards as long as those accelerations

33:27

are nearly equal and nearly parallel

33:29

we're not going to notice them

33:32

so the basic idea of gravitational free

33:35

fall producing this kind of relativity

33:37

of acceleration

33:39

is something that goes back to newton

33:40

and it doesn't have to have the kind of

33:42

far-reaching implications

33:44

it doesn't obviously have to have the

33:46

kind of far-reaching implications that

33:48

einstein saw there is again

33:53

but why does it have these applications

33:55

now if you consider

33:57

why does it have these implications

33:58

excuse me consider einstein again and

34:00

his evil twin and they're both

34:02

thrown off of the chrysler building in

34:05

their little frames of reference

34:09

um what happens

34:12

well as far as einstein is concerned

34:18

he can consider himself as being in an

34:20

inertial frame and he can consider

34:22

the path of his

34:26

little box as nothing but an inertial

34:29

trajectory of a body not being acted

34:31

upon by force he can consider himself as

34:33

an

34:33

unaccelerated body but what about

34:36

his brother

34:40

he will feel the same way because he'll

34:42

have the same effect of being freely

34:44

falling into gravitational field and not

34:46

experiencing any acceleration but when

34:49

they observe

34:50

each other each one will look at the

34:52

other and say that they're

34:53

accelerating that the other is

34:55

accelerating

34:57

because relative to einstein

35:00

relative to albert einstein frankie is

35:03

accelerating and vice versa

35:07

so if you consider in special relativity

35:13

locally you could always feel like

35:14

you're in an inertial frame but if you

35:16

look at another

35:17

if you look at another trajectory if

35:19

it's falling in a gravitational field it

35:21

might look like it's accelerating

35:24

now how does that lead to

35:27

how does that lead to a new kind of

35:30

physics well einstein first had to make

35:32

this conjecture

35:33

that absolutely nothing in physics would

35:36

ever make a distinction between

35:38

freely falling and being in an inertial

35:41

state

35:42

if there's anything you could do

35:46

any material for example that didn't

35:47

respond in the same way as everything

35:49

else to gravity

35:51

right then this whole theory wouldn't

35:54

work

35:54

see newton's theory newton didn't really

35:56

know what the nature of light was he

35:58

didn't know how light would be affected

35:59

by gravity

36:00

so he didn't know how far this principle

36:03

might extend

36:04

so for example if you tried to trick

36:06

somebody into thinking there was gravity

36:08

with a magnetic field

36:10

right well the person could always you

36:12

know use pieces of wood that

36:13

aren't falling in the magnetic field

36:15

right something that's not magnetic to

36:17

prove that

36:18

you know it's not really gravity right

36:21

so this is why einstein said

36:23

um if there were just to exist one

36:26

single thing that falls in the

36:27

gravitational field differently from all

36:29

the others

36:30

then with its help the observer could

36:32

recognize that he is in a gravitational

36:34

field and is falling in it if such a

36:40

thing does not exist however as

36:41

experience is shown with great precision

36:44

then the observer lacks any objective

36:46

ground on which to consider himself as

36:47

falling

36:48

in a gravitational field he has the

36:50

right to consider his state as one of

36:52

rest

36:52

and his surroundings is field free

36:58

but this is where this physical fact

37:00

about gravity connects with the

37:02

philosophical argument that he made

37:03

before

37:04

because he says the experimental fact of

37:06

the acceleration of fall is independent

37:08

of the material

37:09

is a powerful argument that the

37:11

relativity postulate has to be extended

37:13

to coordinate systems which relative to

37:15

each other

37:15

are in non-uniform motion i'll skip that

37:19

one

37:21

but you can you can make a comparison to

37:23

the curvature of the earth

37:24

you could imagine a small piece of the

37:28

earth where you're standing and thinking

37:29

this is a flat plain if i could just

37:31

extend my this plane forever

37:33

i would see that the earth is flat if i

37:36

raise a flagpole here it's perpendicular

37:38

to the surface of the earth

37:40

but of course somebody somewhere else

37:41

can say if i raise the flagpole here

37:43

it's perpendicular to the earth

37:45

how is it possible to fit these two

37:49

non-parallel flagpoles

37:54

into a system in which they're both

37:55

perpendicular to the surface of the

37:57

earth

37:58

we'll come back to that

38:01

einstein's answer the answer to this is

38:05

something that he called the geodesic

38:06

principle that we now call the geodesic

38:08

principle

38:11

if the path of a falling body cannot be

38:13

distinguished by any evidence from the

38:15

path of a body that's subject to no

38:17

forces

38:18

at all then the path of a falling body

38:21

is physically equivalent

38:23

to something moving into the path of a

38:25

body that's moving inertially

38:29

this means that just as we can interpret

38:32

straightest lines on the earth

38:36

as geodesics or lines of longitude

38:39

we can associate the straightest lines

38:41

that you can fall on in space time

38:43

with the paths of falling bodies i'll

38:46

try to make this a little bit more

38:48

pictorial

38:49

right the newtonian view was well the

38:50

body is in orbit because

38:52

there's a force preventing it from going

38:54

off on the tangent

38:58

so if you ask you know what's holding a

38:59

body in orbit well

39:01

if it were moving inertially it would

39:03

move on this geodesic track g

39:05

but in fact there's a force binding it

39:07

in orbit and that's why it goes around

39:08

the sun

39:09

if you imagine this as going forward in

39:12

time

39:14

right with space horizontally and time

39:18

moving upwards

39:19

right as time goes on uh the revolution

39:22

of a planet around the earth

39:24

is this kind of helical path

39:29

now if you imagine two separate

39:31

particles falling in the earth's

39:32

gravitational field right falling toward

39:34

the center of the earth

39:35

how should you interpret that fall well

39:39

newton would say if they're falling

39:42

if they're following the straight lines

39:43

of space-time the

39:45

the inertial trajectories g

39:48

uh the force will make them withdraw

39:50

from those inertial trajectories and

39:52

fall toward the planet

39:56

now einstein says well there's no way to

40:00

distinguish the actual path of the

40:02

falling body

40:03

from an inertial path so these straight

40:06

lines are purely imaginary we don't have

40:07

a physical way to distinguish those

40:10

so we have every right to say that the

40:13

paths of these particles that are

40:14

accelerating toward the earth

40:16

really are the inertial trajectories of

40:18

space-time

40:23

so you could look at this in in terms of

40:25

coordinates you could say well in my

40:26

coordinate system

40:29

you're accelerating right

40:33

you should be moving on this straight

40:34

line g but in fact some force is causing

40:37

you to move in a curve

40:39

my equation of motion is well the

40:41

acceleration is zero because i'm

40:43

an inertial observer and i think your

40:46

equation of motion is well your actual

40:48

you have this acceleration that's

40:49

proportional to the gravitational

40:51

potential

40:52

but of course if you think back to the

40:53

the example of einstein and his brother

40:56

well einstein's brother has the same

40:58

right to say no i'm

41:01

in an inertial trajectory my

41:02

acceleration is zero

41:04

you are accelerating

41:10

i'll skip that one now what kind

41:13

of a world is it where

41:16

two observers are moving inertially no

41:19

forces are acting on them

41:21

and yet they accelerate toward one

41:22

another what kind of a world would that

41:24

be

41:29

well it's just the kind of

41:31

four-dimensional analog of the surface

41:33

that we

41:34

live on if two observers start from the

41:37

equator moving

41:38

in lines that are perpendicular to the

41:41

equator and they move in straight lines

41:42

as straight as they can using

41:44

for maybe a compass or an inertial

41:46

guidance system even

41:49

well if they follow the straight lines

41:51

of the earth the lines of longitude

41:52

they're going to find

41:54

that they accelerate toward one another

41:56

they converge on one another uniformly

41:58

at the north pole

42:00

if they happen to be going north

42:04

and that's exactly what's happening in

42:06

this example

42:07

right in this case we say well this is a

42:11

bizarre thing

42:12

that wouldn't have happened if the earth

42:14

weren't a curved surface

42:17

and einstein's point was this is a

42:18

bizarre thing that wouldn't have

42:20

happened

42:21

if space-time weren't curved the

42:23

trajectories

42:25

of inertial observers in space-time

42:28

have the same non-euclidean behavior

42:32

indicating curvature

42:35

that these straight lines of

42:39

longitude on the earth have that

42:41

indicates the

42:42

spherical shape of the earth

42:45

and this is the sense this is that

42:47

connection finally we've gone from a

42:49

philosophical idea

42:52

to a physical idea about gravity to a

42:55

radical new idea about geometry

42:58

but the thing about geometry is this is

43:00

what's radical about this idea is

43:02

geometry is related to gravity but

43:05

gravity isn't something that's fixed

43:07

as geometry was supposed to be gravity

43:10

is something that varies through

43:12

space-time

43:13

according to the distribution of mass

43:15

it's very powerful

43:17

near a very massive object it's weaker

43:19

near a weaker object

43:21

now if gravity is the same as space-time

43:25

curvature then

43:26

that means we've taken a dramatic step

43:28

we found that

43:30

the actual geometry of space-time

43:33

varies according to the distribution of

43:35

mass

43:36

that makes geometry as i suggested at

43:39

the beginning it makes geometry

43:40

something that it never was before a

43:42

kind of dynamical physical field

43:44

whose changes depend on the distribution

43:48

of mass

43:49

newton would have told you well the

43:50

gravitational field that forces bodies

43:53

not to travel in straight lines

43:55

is determined by the distribution of

43:57

mass

43:58

einstein says well that's the space-time

44:00

curvature the way in which straight

44:02

lines accelerate toward one another

44:06

that's an indication of the distribution

44:07

of mass so of course mass energy in the

44:09

relativistic context

44:11

there's a common empirical basis what

44:14

what are we observing we're observing

44:16

how inertial trajectories accelerate

44:18

toward one another how the paths of

44:20

falling bodies accelerate toward one

44:22

another

44:23

we're just interpreting it in two ways

44:26

newton interpreted as a field that's

44:29

causing bodies to deviate from their

44:31

straight-line motion

44:33

einstein interprets it as the geometry

44:36

itself being affected by the presence of

44:38

mass

44:41

now some people call that geometrizing

44:44

physics but that isn't how einstein

44:45

thought of it einstein thought of it as

44:48

physicalizing geometry making it into

44:50

something dynamical like a physical

44:52

field

44:56

now this takes you back to einstein's

44:58

remarks about coordinates

45:00

right the method hitherto employed for

45:02

laying down coordinates in the

45:03

space-time continuum thus

45:05

breaks down i won't read all of this

45:10

there's no way but what he means is i'll

45:12

just

45:13

if you think about classical space-time

45:16

right or a flat coordinate system if i

45:19

thought the universe was flat i could

45:21

imagine that my coordinate system as on

45:23

the far left of your screen

45:26

was simply a flat coordinate system that

45:29

could be extended infinitely in every

45:31

direction

45:33

but einstein introduces this idea

45:35

instead of a reference frame

45:37

that's rigid like a cartesian coordinate

45:39

system or a plane

45:41

something that's kind of wiggly and

45:43

squishy like a mollusk

45:47

and so when you have two observers who

45:49

locally

45:50

feel like they're on a flat plane

45:53

but if you try to come you can't fit

45:55

them both into

45:57

a larger frame in which they both fit

45:59

into the same flat plane

46:02

this is the situation you have with

46:04

inertial observers falling in general

46:05

relativity

46:07

that you have einstein and his brother

46:09

locally

46:10

it's as if they're in flat cartesian

46:13

coordinates

46:14

but if they compare each coordinate

46:17

system to the other one you find well

46:18

the simple idea of coordinates

46:21

doesn't work anymore the idea of

46:23

extending a coordinate system to the

46:24

entire universe or even to a very large

46:26

area of the universe just breaks down

46:31

so this is how all of einstein's ideas

46:36

come together in this the phyllis

46:37

starting with the philosophical idea

46:39

well there's something wrong with the

46:40

idea

46:42

of a rigid rest frame

46:45

a flat coordinate system that sort of

46:47

characterizes the entire universe

46:49

is privileged is separate from all

46:52

physical interactions

46:55

there's something wrong with the idea of

46:58

an inertial reference frame being

46:59

distinguished from all others

47:02

those were initially just philosophical

47:04

ideas but it was this peculiar feature

47:06

of gravity

47:08

that it enables you to treat a system

47:10

that's

47:11

falling in a gravitational field as if

47:13

it were moving uniformly in a straight

47:14

line

47:15

because locally you can't tell the

47:16

difference

47:19

so that was a physical reason to take

47:21

this old philosophical idea and say that

47:23

it actually has physical content that

47:25

has to do with gravity

47:28

but this physical content is the key to

47:30

uniting gravity with geometry

47:33

and showing that if you want a coherent

47:35

picture of the reference frame of

47:38

one inertial observer and the reference

47:40

frame of another observer

47:42

who's equally inertial but relative to

47:44

the first one accelerating

47:46

then there simply isn't a flat

47:49

coordinate system into which you can fit

47:50

them both the only

47:52

the only system in which you can fit

47:54

them both is a curved geometry

47:59

so that's a rough sketch

48:02

that i hope conveyed something of the

48:05

philosophical

48:06

path that einstein took from

48:09

a combination of philosophical

48:13

problems that he found in the existing

48:15

physics

48:16

facts about gravitation that he thought

48:18

were never really

48:20

quite understood properly in the

48:22

newtonian theory and a new conception of

48:24

how

48:25

the relation between physics and

48:26

geometry

48:28

can be explored and developed

48:32

and in a sense that's general relativity

48:35

in a nutshell that's where all of our

48:36

that's why the

48:37

the talk of curved space-time is

48:39

meaningful

48:40

it's meaningful in the same way that

48:42

talking about the earth being curved is

48:43

meaningful

48:44

because we can follow straight lines on

48:47

the earth and we know that their

48:48

convergence indicates the curvature of

48:50

the earth

48:51

we can follow inertial trajectories in

48:52

space-time and say

48:54

their funny converging and diverging

48:57

behavior indicates the curvature of

48:58

space-time

49:00

now that's a remarkable philosophical

49:02

achievement and

49:06

you might think it would be a terrible

49:07

thing to throw this away

49:10

uh just because we need to have a

49:12

quantum theory of gravity and maybe the

49:14

quantum theory of gravity won't

49:15

incorporate

49:17

these great ideas of einsteins

49:21

now you could just adopt a definition

49:22

and say well if the next theory doesn't

49:24

include these great ideas then that

49:26

means they weren't so great

49:30

you don't have to think about it that

49:31

way

49:34

there are there are probably more than

49:36

three ways but you

49:37

you could consider these three ways in

49:38

which a theory can survive

49:42

after physicists have decided that some

49:44

other theory is more correct

49:46

now the obvious one is of course a

49:48

useful theory of

49:50

uh a useful tool for making predictions

49:52

and for

49:53

practical applications i mean lots of

49:56

old theories are still good in this way

49:57

especially newtonian gravity

50:02

another way that's a little bit

50:05

more serious for a theory to be to

50:08

survive in a future theory is with to be

50:10

a limiting case of the theory

50:12

so we say of special relativity well

50:14

it's that's actually what the world

50:16

looks like in very small regions even if

50:18

general relativity is true

50:20

it's a limiting case in which you

50:22

consider

50:23

very relatively small masses

50:26

and therefore nearly zero curvature

50:30

or newton's theory related to special

50:32

relativity it's a theory you have when

50:33

you consider

50:34

very slow velocities and uh

50:37

relative to which the velocity of light

50:39

appears infinite infinite

50:42

but another way you can think of it of a

50:44

theory surviving is when

50:46

the theory can still be regarded as a

50:48

source of insight into the way that

50:50

parts of the physical world are

50:51

connected with one another

50:54

and that i think is certainly it's

50:57

certainly true of newton's theory

50:59

of gravitation but it's even more true

51:02

in a sense of einstein's because of the

51:04

remarkable connections that

51:05

his theory has revealed

51:09

some of the things that i mentioned at

51:10

the beginning of my talk we understand

51:12

things about

51:13

large-scale structure

51:18

this is a famous remark by by henry

51:20

plancary about this very

51:22

question he says of course it seems to

51:24

us that theories only last a day

51:26

and that ruins upon ruins accumulate

51:29

today

51:29

theories are born tomorrow they're the

51:31

fashion the day after tomorrow they're

51:32

classic

51:33

the fourth day they're superannuated and

51:35

the fifth they are forgotten

51:38

but if we look more closely we see that

51:40

what thus succumb

51:41

are the theories properly so-called

51:43

those which pretend to teach us what

51:45

things

51:45

are but there is in them something which

51:48

usually survives

51:50

if one of them taught us a true relation

51:52

this relation is definitively acquired

51:55

it will be found again under a new

51:56

disguise in the other theories which

51:58

successively come to reign in the place

52:00

of the old

52:02

now let's think about general relativity

52:04

well of course it's the most empirically

52:06

successful theory of gravity

52:09

its predictions will probably continue

52:10

to be useful

52:12

at least as long as people continue to

52:14

use gps's

52:16

it'll be an easier way of doing that

52:17

probably than any quantum theory of

52:19

gravity which is likely to be

52:20

highly complex and it's likely to be a

52:23

limiting case for

52:26

a future quantum theory of gravity

52:30

but i think at a deeper level it's a

52:32

unique and indispensable

52:33

window into physical connections even on

52:36

the very largest cosmic scales which no

52:39

previous theory gave us any inkling of

52:43

large-scale cosmic structures in space

52:46

that is to say considering just the

52:48

spatial part of the universe and its

52:49

curvature or flatness

52:51

in time just considering the evolution

52:54

of the universe from

52:55

what seems like a beginning to what

52:58

might be an end

53:00

and space-time the combination of the

53:02

two

53:04

and one more thing that has to be said i

53:06

think and i hope i've convinced you of

53:09

is that the general theory of relativity

53:11

is not only those three things but it's

53:13

also

53:14

clearly a product of einstein's critical

53:16

philosophical analysis of established

53:18

conceptions of gravity and geometry

53:20

and that's why we celebrate him as a

53:23

philosopher science

53:24

scientist and that's why we'll continue

53:27

celebrating that all this year

53:28

thank you very much for listening

53:42

you

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