Robert DiSalle: Gravity, Geometry, Philosophy: 100 Years in Einstein's Universe
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
- ๐ 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.
- ๐ 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.
- ๐ 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.
- ๐ 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.
- ๐ต๏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.
- ๐ 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.
- ๐ 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.
- ๐ฐ๏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.
- ๐ 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.
- ๐ฎ 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.
- ๐ 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
๐ 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.
๐ 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.
๐ญ 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.
๐ 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.
๐งฒ 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.
๐ 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.
๐ 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.
๐ 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
Keywords
๐กGeneral Theory of Relativity
๐กEinstein
๐กSpace-Time
๐กPhilosophy of Science
๐กGeometry
๐กInertial Frame
๐กGravitational Lensing
๐กBlack Hole
๐กGPS
๐กCosmology
๐กMach's Principle
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
good evening everybody
um thanks for coming out on a cold
evening to
uh to learn some philosophy and physics
um
i think we're gonna have a lot of fun um
my name is carl heifer and i'm a member
of the rotman institute of philosophy at
western university and this is our first
event
in a series of events that we're holding
this year in 2015
to mark the 100th anniversary of the
discovery of einstein's general theory
of relativity
um so this is our inaugural event
and we're very pleased to have professor
robert desal
uh here he's also a professor of
philosophy at western
an expert on our understanding of time
and space
and physical theories in general and
we're going to hear about the work
and the discoveries of about our
universe
achieved by albert einstein who is the
most uh
influential and famous philosopher
scientist in history
now for many of you it will be
surprising to hear einstein described as
a philosopher scientist
but einstein himself would have happily
embraced that label
uh reading philosophers and thinking
about nature in a philosophical way was
absolutely central to what einstein
achieved as professor desal will uh will
be
explaining to you tonight and so since
the roman institute of philosophy is all
about
promoting the engagement of philosophers
today with working scientists
we find it very appropriate to to
celebrate the most
striking historical example of the
successful engagement of philosophy with
science
uh which happened in the life and work
of albert einstein
professor desal has been a distinguished
professor of philosophy
at western ontario for a number of years
and he's
the author of a book called
understanding space time
which takes you on a journey from
newton and newton's predecessors all the
way through einstein's theories of
relativity
explaining how our notions of space and
time
evolved inevitably to the the form which
we have today
so without further ado let me hand
things over to professor robert desal
thanks for that introduction carl thank
you all for coming
i'd like to offer um i'd like to just
say my
say my belated appreciation to joe
rotman whose enthusiasm for
doing this project helped to get it
going and unfortunately he isn't here
to see the results but his efforts are
really
deeply appreciated i'd like to talk to
you about einstein
the philosopher and einstein the
scientists and about how these two
aspects of einstein
were really inseparable
i'd like to start by considering a
couple of questions
that are kind of governing the structure
of this talk
first of all what does it mean to say we
live in einstein's universe
uh what characterizes the universe we
live in as particularly einstein in
i think this is particularly interesting
question in light of the fact that most
physicists today would say the correct
theory of gravitation is not einsteins
but some quantum theory of gravity of
one or another sort
that you know perhaps down this down the
road in waterloo someone's going to come
up with
or is working on right now as we speak
and so what does it mean to say we live
in an einsteinian universe if it turns
out this isn't really the final theory
which is usually how theories turn out
the second thing is what's the
connection between gravity and geometry
so one of the things i hope that you'll
get out of the next
little while is some appreciation of of
how einstein made this connection
in the first place between geometry
which had
up to that time been understood as a
kind of formal abstract theory
uh how did he associate that with
something dynamical like a physical
field
and finally what's the connection
between gravity and geometry on the one
hand
and philosophy on the other i hope that
will become clear
in other words how did einstein's
insights into the physics of gravitation
and the physical nature of geometry
arise from his pursuit of
philosophical problems
well one thing i'd like to point out
that's really interesting about the
einsteinian revolution that i think
isn't sufficiently appreciated is
that we have a lot of questions that we
ask about the universe today that really
wouldn't have made any sense in a
pre-einstein context
for example how did the universe begin
there really wasn't a theory of that in
the newtonian theory of course
there are previous theories of creation
but newtonian physics didn't supply
even a way of asking that question how
did the universe come to be
that's a peculiarly einsteinian question
the curvature of space-time this is
another thing that
people really didn't have any way to
think about before einstein
how does the structure of space-time
vary throughout the universe these are
things that we think of as basic
questions to ask in cosmology again
wouldn't have made any sense at all what
is inside of a black hole these are all
concepts that we consider basic to the
science of the large scale structure of
the universe
all of them have to do with concepts
that really
came to be well defined by einstein this
is the sense in which what einstein did
was not merely
a physical theory but a conceptual
revolution
so how did all this come to be well
first of all it became necessary to
think about geometry in a different way
this is what i'm contending is the
primary philosophical problem that
einstein had to solve
how to think about geometry as a
dynamical aspect of the physical world
if you look back through history there
are lots of
conceptions of geometry none of them
quite like einstein's
there's a very long tradition among
rationalist philosophers whom
whose names you may know kant plato
in descartes leibniz people who in one
way or another thought
that geometry was a science that was
absolutely necessary truth that had
nothing to do with experience at all
then there was another notion that goes
all the way back to the ancient
egyptians and babylonians
and had champions in the 19th century
like the philosopher john stuart mill
that geometry the principles of geometry
are basically codifications of
empirical recipes for actually solving
particular problems
and our confidence in them comes from
the number of times we've repeated
these basic geometrical operations from
building the pyramids to building houses
and railroads
but then there was another conception
that was really quite revolutionary
which could be said to have begun with
newton but really came into its own in
the 19th century
with scientists like uh hermann von
helmholtz and henry poincare
culprit regauss bernard riemann
the notion that geometrical principles
considered by themselves are just a kind
of formal abstract structure
and that if you want to talk about
geometry as the geometry of space that
is to say is characterizing the world in
some way as describing the world we live
in
you have to somehow connect the abstract
mathematical principles of geometry with
something
physical so there's some connection that
has to be made between the laws of
physics
and the mathematics of space and that
was a revolutionary development that
in a way paved the way for einstein and
made his whole way of thinking possible
but what einstein did was something
quite do quite new
even compared to that that is to think
of
to find a way to think of geometry not
as a kind of fixed
background within which the physical
laws are articulated
within which we move and measure
but to think of it as itself a kind of
dynamical field
like the electromagnetic field or the
gravitational field
that interacts with other fields in
nature this dynamical conception of
geometry
is the basis for the general theory of
relativity
but it's again it's something that
without a kind of conceptual
investigation that einstein did
it's a concept that no one could even
have understood in the 19th century
with a few possible exceptions
this is a question that einstein asked
reflecting on
the philosophical background to his way
of thinking about geometry he asked the
question how can it be that mathematics
being after all a product of human
thought which is independent of
experience
is so admirably appropriate to the
objects of reality
is human reason then without experience
merely by taking
thought able to fathom the properties of
real things
in my opinion the answer to this
question is briefly this
as far as the laws of mathematics refer
to reality
they are not certain as far as they are
certain they do not refer to reality
yet on the other hand it is certain that
mathematics generally and particularly
geometry owes its existence to the need
to learn something about the relations
of real things to one another
the very word geometry which means earth
measuring proves this
for earth measuring has to do with the
possibilities of the disposition of
certain natural objects with respect to
one another
it's clear that the system of concepts
of axiomatic geometry alone
cannot make any assertions as to the
relations of real objects
of this kind which we will call
practically rigid bodies
in order to make such assertions
geometry must be stripped of its
merely logical formal character by the
coordination of real objects of
experience with the empty
conceptual framework of axiomatic
geometry
to accomplish this we need only add the
proposition solid bodies are related
with respect to their possible
dispositions
as our bodies in euclidean geometry this
is really the key point he was trying to
make then the propositions of euclid
contain affirmations as to the relations
of practically rigid bodies
geometry thus completed is
evidently a natural science we may in
fact regard it as the most
ancient branch of physics its
affirmations rest
essentially on inductions from
experience but not on logical inferences
only
i attach special importance to the this
view of geometry
because without it i should have been
unable to formulate the theory of
relativity
that was as clear as statement as you
could get from einstein that he really
thought that
this new philosophical conception of the
relationship between geometry and
physics
that had developed in the 19th century
was fundamental to who's creating the
theories that he created
although as we'll see he carried them to
a different direction altogether
some of his philosophical forebears you
can see in this picture
maybe i'll give you a quiz at the end
see if you can recognize who they are
if you're a philosophy professor no
telling
i'd like to begin by uh
considering two ways of thinking about
in what way is einstein's theory part of
our world
well you can think of a scientific
theory
as an instrument because after all if
you're worried about the fact that
tomorrow we might not believe this
theory
what is its value if we don't think it's
really true well you can
you can think of it as simply a
practical tool for prediction
and for the control of nature now some
of you probably have heard this story
there really is one technological
application of general relativity that's
extremely
important and it's gps navigation when i
was in graduate school
relativity students used to say we
should try to convince the government
that we're working on a relativity bomb
because maybe then we'll get more
funding
because they were trying they didn't
come up with one needless to say
but eventually the gps was developed
which is a very important application of
special and general relativity
but in a way more general relativity
because you have satellites
orbiting the earth at 20 000 kilometers
and at 14 000 kilometers per hour
and you have to make timing corrections
for the high velocity
because of special relativity and
because of general relativity because of
the difference in clock timing in
stronger and weaker
places of space-time curvature you have
to correct
for the time speeding up
so if you subtract the time slowing down
from the time speeding up you get a
delay of 38 microseconds per day which
doesn't sound like much
but if you didn't correct for this you
would have errors accumulating at a rate
of
kilometers per day and your gps
navigation system would
would be completely off so this is a
practical application of einstein's
theory
but i'd like to think about
einstein's theory as an instrument of a
different kind for a moment that is to
say is an instrument of understanding
and of exploring
now this is a remark that was made uh
by pierre simon de la platz
200 years ago about newton's theory of
universal gravitation
and i think it was an interesting remark
that illustrates the sense in which
a physical theory which we now regard as
not true
nonetheless is an instrument for the
exploration of nature like
a telescope as laplace put it
he says the theory of gravity having
become by so many applications a means
of discovery
as certain as by observation itself
has made known several new inequalities
it's enabled the mathematician to
predict the return of the comet of
1759. he's been able enabled by this
means to deduce some observation as from
a rich mind a great number of important
and delicate elements which without the
aid of analysis would have been forever
hidden from view
the masses of the sun the planets their
satellites the velocity of light
the ellipticity of jupiter the shape of
the earth
now this is that's a really important
point that i think laplace was making a
theory that we don't actually believe
anymore has nonetheless
taught us something about the universe
that
was otherwise hidden from observation we
know more about
empirical things like the masses of the
planets and their orbits
from newton's theory then we were able
to tell by staring at them through
telescopes
now if you ask well what has einstein's
theory done of a similar nature
well for one thing one of the most
familiar ideas of einstein's theory is
the theory of the black hole
the black hole as we understand it is a
concept
that really didn't quite make sense
according to newtonian theory
there was a newtonian notion of a black
hole what the
what laplace and british astronomer john
mitchell in the 18th century
called a dark star because they imagined
that if light was made of tiny particles
that must have some mass then presumably
they must be subject to the
gravitational field and there could be a
gravitational field so strong
that the escape velocity would be faster
than the velocity of light and they
would trap
the light but it's a long time since
physicists stopped believing that light
was made of little massive particles
anyway
in einstein's theory the notion that
light as a massless particle can somehow
be trapped
around a star or in other words around a
collapsed star or a black hole
that's an aspect of his theory that you
can only understand through the notion
of space-time geometry
which we'll come back to but this is an
aspect of our universe that einstein's
theory
is the only theory that that allows us
to explore
so it's being used as a tool for the
exploration of these distant objects and
there's no substitute for it
just as just as securely as newton's
theory was used as
a tool for exploring aspects of the
universe and this is something that
this is something that bears out what it
means in my opinion to say we live in an
einsteinian universe
even if the theory isn't quite the right
one
another aspect is gravitational lensing
the fact that we can
see we can see for example stars that
ought to be occulted by other stars
because of the bending of light as they
go around more massive objects
the simplest example of this was
einstein's prediction
of the bending of starlight by the sun
in 1919
but more complicated examples are things
that that we
sometimes see in deep space photographs
like this one from the hubble telescope
of the lensing of light from
from a distant galaxy passing around an
intervening object
this is another way in which einstein's
theory is not merely
a way of making useful predictions like
making a tool like the gps it's a way of
understanding
how the universe is structured
and finally one of the most the most
dramatic example of
an einsteinian picture of the universe
that was not possible before is just the
very idea we have
of the history of the universe of the
universe having a beginning
an expansion and various scenarios for a
possible end
which uh isn't coming anytime soon i
think
but these are notions that didn't really
make sense in a newtonian context
but when we say this is in our
einsteinian universe it's a universe in
which we can think of it as having a
kind of structure like this on a large
scale
so for example we we can ask a question
which wasn't really meaningful before
what is the shape of space on a large
scale if you consider a slice of space
time and
right a large slice of the universe what
is its spatial structure
is it curved like a sphere is it curved
like a saddle
or is it flat well these these weren't
even interesting
they weren't even possible questions to
ask before einstein
made the philosophical effort to figure
out how such questions could make sense
now how did einstein get started on this
path with the
with he started with a simple question
that he got
from reading works by ann smock a 19th
century physicist whose name you might
know from the speed of sound
how do we really know that the earth is
rotating instead of having the stars
revolve around it well newton
found a way to settle this question in
1687.
we know the earth is rotating because it
bulges out at the equator and in various
other
ways displays centrifugal effects by the
19th century
the end of the 19th century when mach
wrote this
book on mechanics there were further
proofs like the coriolis effect
the foucault pendulum demonstrating the
rotation of the earth
but mark asked the question
do we really know from these effects
that it's the earth rotating relative to
the stars
or the stars rotating relative to the
earth
and there's a lot of philosophical
mystification about this idea but part
of
i won't read the entire quote to you
part of
what mach had in mind was a simple
application of the experimental method
if you'd like to be sure that it's the
earth's rotation and not the stars
rotation that's creating the centrifugal
effects on the earth
you ought to be able to vary as a matter
of experimental method you ought to be
able to vary the two things separately
do we know what would happen if this saw
if the star is rotated around the earth
of course we don't know that because as
mark said the world is only given to us
once
the ptolemaic or copernican system is
our interpretation
but both are equally real
so the earth is not given to us twice
once with an earth at rest
and once with an earth in motion but
only once with its relative motions
which are alone determinable
therefore we cannot say how it would be
if the earth did not rotate
we can interpret the one case that is
given to us in different ways
if however we interpret it in such a way
that we come into conflict with
experience our interpretation is wrong
now when i wanted to read the original
edition of this book
the only place i could find it was in
the bertrand russell archive at mcmaster
so it was bertrand russell's copy the
great
one of the great philosophers of the
20th the early 20th century
so i i read this remark uh the universe
is not given to us twice
and you know we cannot say how it would
be if the earth did not rotate and
russell had written in the margin
rubbish and
because what he meant by that was of
course you can say what
what would happen if the earth didn't
rotate but the stars did because you
have newtonian physics it tells you
what would happen in every conceivable
situation
any kind of you you just tell newtonian
physics
what the matter distribution is and what
the forces are and it will tell you what
will happen
but mock's point was we don't really
know if these are the laws of physics at
least this is the philosophical notion
that einstein got we could be skeptical
since we don't know what would happen in
these other situations we don't know if
if we have the right physical laws now
so when einstein looked at this
situation and said suppose you have two
spheres rotating relative to one another
and one is bulging out at the equator
and one isn't
how do you explain the difference
between these two between the two
spheres
and his answer was well
the only epistemologically satisfactory
answer has to be something that points
to facts of experience
newtonian mechanics does not give a
satisfactory answer
because it says the laws of mechanics
apply to the space
r1 in which the body s1 the spherical
one is rotating
is at rest sorry but not to the space r2
in which the body s2 is at rest but the
privilege space r1 is a merely
factitious cause
he's applying a philosophical principle
here to say
the newtonian laws of physics probably
aren't the right laws because
they have this philosophical difficulty
that they're appealing to something
unobservable
instead of explaining the effects of
rotation by by
visible causes by observable causes of
some kind
the only satisfactory answer according
to einstein is that the physical system
reveals within itself no imaginable
cause
to which the differing behavior of s1
and s2 can be referred
the cause must lie outside the system
in the distant masses which we haven't
been considering
excuse me
these distant masses must be regarded as
the seat of the causes
which must be susceptible to observation
of the different behavior
of s1 and s2 they take over the role of
the fictitious cause
r1 in other words the space
of all the imaginable spaces in any kind
of motion there is none which we may
look upon as privileged a priori without
reviving
the above mentioned epistemological
objection
the laws of physics must be of such a
nature that they apply to systems
of reference in any kind of motion along
this way we
we arrive at an extension of the
postulate of relativity
in other words einstein knew that in
newtonian mechanics and in
special relativity there was a
relativity principle
you that whether a system is moving
uniformly or at rest
is a completely relative matter but what
about systems that aren't moving
uniformly
systems that are rotating or
accelerating
why are they supposed to be different
it was a purely philosophical problem
and there's a
great deal more to it than i can go into
this evening
but the important thing is that einstein
thought it was
odd for the theory to single out certain
kinds of
coordinate systems or reference frames
because he asked the question why should
nature care about our coordinate systems
why should there be infinitely many
inertial systems moving uniformly
are distinguished from all other rigid
systems now people had been asking this
question
for hundreds of years in various ways
the real interesting thing is why in
einstein's case
was this philosophical problem
made into a real line of physical
inquiry
that actually led to a new theory
i'll skip to that one let me start by
considering the idea of an inertial
frame if you haven't heard the term
before you
it won't be very hard to figure out
if you were sort of enclosed in a box in
an empty space
and no forces were acting on you in any
way
you would be in what newtonian physics
or special relativity would call an
inertial state
so imagine you're in a box there are no
forces that you're somewhere
far from as far as you like from all
possible matter
you're just floating around in a way
that might look familiar to you from say
space capsules or orbiting
space stations it would be as if no
forces are acting on you
at all
now einstein was einstein considered
this other possibility however what if
that same box were falling in a
gravitational field
well because of a peculiar fact about
gravitation
you wouldn't be able to tell the
difference between being
in this box falling in the gravitational
field and being all alone in empty space
with no
forces acting of any kind some of you
may have heard this before
einstein's elevator argument
he was the first person to really
consider the implications of this
problem that
an inertial frame of reference is
impossible to distinguish from a frame
of reference that's falling now why is
that the case
because of something that was discovered
by galileo that gravity has the same
effect on all bodies near the earth
so if i'm falling out of a if i'm
falling in a gravitational field
and i pull a couple of bowling pins out
of my pocket or a ruler
or a grapefruit or whatever i've got in
my pockets
they're not going to fall any slower and
faster than i am so i won't notice that
i'm in a gravitational field
i won't feel the top of my body weighing
down on the bottom of my body it will
all be the same
it will be as if no forces are acting on
me at all
this is why astronauts in orbit feel
weightless
because the same force is acting on them
and all the parts of their body and
everything else in their
shuttle now if you imagine
a similar example where you have the
same box but now it's sitting on the
earth
now of course the man in the box feels
his weight on the floor
he lets go an object it just falls to
the ground
9.8 meters per second
and he has to make some effort to hold
that bowling pin up
right now that seems pretty obvious
but now imagine einstein's evil twin
is his brother frankie the one nobody
talks about
now the evil twin is in a very similar
box
but the box starts being pulled upwards
oh that's sorry that no
that's totally wrong
well it's einstein's evil twin at work
the point is if the box
if the box were accelerating upwards
you would feel the exact same effect
because you your inertia would be
holding you back while the bottom of the
box is pushing you upwards
if if you were accelerating at exactly
the opposite of the earth's
gravitational field at 9.8 meters per
second in the opposite direction
then you would feel exactly the same
thing you'd feel from your weight on the
floor
so in other words the inertial effect of
having the
frame of reference or the box that
you're going to accelerate upwards is
the same as the gravitational effect
of having your weight pull you down just
as
the effect of being an inertial frame
with no forces acting on you is the same
as the effect
of falling in a gravitational field
freely
now what does all this mean well
it doesn't necessarily mean anything new
right einstein said well it's clear that
you can't distinguish gravity from
inertia
because to the observer in the box if
the box is at rest in a gravitational
field it's not clear whether the
whether you're sitting in a
gravitational field
or the box is being pulled up and it's
not clear
there's no way to tell from an
experiment whether the box is falling in
a gravitational field or being acted on
by no forces at all
but this isn't by itself a really
strange idea this is an idea that newton
had
there's the relativity theory of
newton's principia
as stated in these corollaries that he
derived from the laws of motion
first he proved that
the bodies contained in a given space
will have the same motions among
themselves if the space is at rest
or moving uniformly this is the
newtonian principle of relativity
derived from galileo and huygens but
expressed in this form by newton but
newton pointed out
this more radical step that if bodies
are moving in any way whatsoever among
themselves
and are urged by equal accelerative
forces along parallel lines
they will all continue to move with
respect to one another in the same way
as they would if they were not acted on
by those forces
so newton already understood that if you
have
a system of bodies that's falling in a
gravitational field
it will behave exactly the same as if it
were at rest
you might wonder why was newton worried
about something like that
and the answer is he was concerned about
understanding things like
the system of jupiter and its moons can
i analyze the system of jupiter and its
moons
when the whole system is being
accelerated toward the sun
and the answer is yes i can because
the actions of the sun on the on jupiter
and its moons
because they're so far away from the sun
they're almost equal
and almost parallel and you can treat
that system as if it were at rest
now what about the whole solar system
newton has a very detailed argument for
universal gravitation
would that argument be undermined
if you found out that the whole solar
system
is falling in a larger gravitational
field
and the answer is because of corollary
six no
it would behave exactly the way it does
now as long as the accelerations
caused by that distant mass
the the whole solar system is falling
towards as long as those accelerations
are nearly equal and nearly parallel
we're not going to notice them
so the basic idea of gravitational free
fall producing this kind of relativity
of acceleration
is something that goes back to newton
and it doesn't have to have the kind of
far-reaching implications
it doesn't obviously have to have the
kind of far-reaching implications that
einstein saw there is again
but why does it have these applications
now if you consider
why does it have these implications
excuse me consider einstein again and
his evil twin and they're both
thrown off of the chrysler building in
their little frames of reference
um what happens
well as far as einstein is concerned
he can consider himself as being in an
inertial frame and he can consider
the path of his
little box as nothing but an inertial
trajectory of a body not being acted
upon by force he can consider himself as
an
unaccelerated body but what about
his brother
he will feel the same way because he'll
have the same effect of being freely
falling into gravitational field and not
experiencing any acceleration but when
they observe
each other each one will look at the
other and say that they're
accelerating that the other is
accelerating
because relative to einstein
relative to albert einstein frankie is
accelerating and vice versa
so if you consider in special relativity
locally you could always feel like
you're in an inertial frame but if you
look at another
if you look at another trajectory if
it's falling in a gravitational field it
might look like it's accelerating
now how does that lead to
how does that lead to a new kind of
physics well einstein first had to make
this conjecture
that absolutely nothing in physics would
ever make a distinction between
freely falling and being in an inertial
state
if there's anything you could do
any material for example that didn't
respond in the same way as everything
else to gravity
right then this whole theory wouldn't
work
see newton's theory newton didn't really
know what the nature of light was he
didn't know how light would be affected
by gravity
so he didn't know how far this principle
might extend
so for example if you tried to trick
somebody into thinking there was gravity
with a magnetic field
right well the person could always you
know use pieces of wood that
aren't falling in the magnetic field
right something that's not magnetic to
prove that
you know it's not really gravity right
so this is why einstein said
um if there were just to exist one
single thing that falls in the
gravitational field differently from all
the others
then with its help the observer could
recognize that he is in a gravitational
field and is falling in it if such a
thing does not exist however as
experience is shown with great precision
then the observer lacks any objective
ground on which to consider himself as
falling
in a gravitational field he has the
right to consider his state as one of
rest
and his surroundings is field free
but this is where this physical fact
about gravity connects with the
philosophical argument that he made
before
because he says the experimental fact of
the acceleration of fall is independent
of the material
is a powerful argument that the
relativity postulate has to be extended
to coordinate systems which relative to
each other
are in non-uniform motion i'll skip that
one
but you can you can make a comparison to
the curvature of the earth
you could imagine a small piece of the
earth where you're standing and thinking
this is a flat plain if i could just
extend my this plane forever
i would see that the earth is flat if i
raise a flagpole here it's perpendicular
to the surface of the earth
but of course somebody somewhere else
can say if i raise the flagpole here
it's perpendicular to the earth
how is it possible to fit these two
non-parallel flagpoles
into a system in which they're both
perpendicular to the surface of the
earth
we'll come back to that
einstein's answer the answer to this is
something that he called the geodesic
principle that we now call the geodesic
principle
if the path of a falling body cannot be
distinguished by any evidence from the
path of a body that's subject to no
forces
at all then the path of a falling body
is physically equivalent
to something moving into the path of a
body that's moving inertially
this means that just as we can interpret
straightest lines on the earth
as geodesics or lines of longitude
we can associate the straightest lines
that you can fall on in space time
with the paths of falling bodies i'll
try to make this a little bit more
pictorial
right the newtonian view was well the
body is in orbit because
there's a force preventing it from going
off on the tangent
so if you ask you know what's holding a
body in orbit well
if it were moving inertially it would
move on this geodesic track g
but in fact there's a force binding it
in orbit and that's why it goes around
the sun
if you imagine this as going forward in
time
right with space horizontally and time
moving upwards
right as time goes on uh the revolution
of a planet around the earth
is this kind of helical path
now if you imagine two separate
particles falling in the earth's
gravitational field right falling toward
the center of the earth
how should you interpret that fall well
newton would say if they're falling
if they're following the straight lines
of space-time the
the inertial trajectories g
uh the force will make them withdraw
from those inertial trajectories and
fall toward the planet
now einstein says well there's no way to
distinguish the actual path of the
falling body
from an inertial path so these straight
lines are purely imaginary we don't have
a physical way to distinguish those
so we have every right to say that the
paths of these particles that are
accelerating toward the earth
really are the inertial trajectories of
space-time
so you could look at this in in terms of
coordinates you could say well in my
coordinate system
you're accelerating right
you should be moving on this straight
line g but in fact some force is causing
you to move in a curve
my equation of motion is well the
acceleration is zero because i'm
an inertial observer and i think your
equation of motion is well your actual
you have this acceleration that's
proportional to the gravitational
potential
but of course if you think back to the
the example of einstein and his brother
well einstein's brother has the same
right to say no i'm
in an inertial trajectory my
acceleration is zero
you are accelerating
i'll skip that one now what kind
of a world is it where
two observers are moving inertially no
forces are acting on them
and yet they accelerate toward one
another what kind of a world would that
be
well it's just the kind of
four-dimensional analog of the surface
that we
live on if two observers start from the
equator moving
in lines that are perpendicular to the
equator and they move in straight lines
as straight as they can using
for maybe a compass or an inertial
guidance system even
well if they follow the straight lines
of the earth the lines of longitude
they're going to find
that they accelerate toward one another
they converge on one another uniformly
at the north pole
if they happen to be going north
and that's exactly what's happening in
this example
right in this case we say well this is a
bizarre thing
that wouldn't have happened if the earth
weren't a curved surface
and einstein's point was this is a
bizarre thing that wouldn't have
happened
if space-time weren't curved the
trajectories
of inertial observers in space-time
have the same non-euclidean behavior
indicating curvature
that these straight lines of
longitude on the earth have that
indicates the
spherical shape of the earth
and this is the sense this is that
connection finally we've gone from a
philosophical idea
to a physical idea about gravity to a
radical new idea about geometry
but the thing about geometry is this is
what's radical about this idea is
geometry is related to gravity but
gravity isn't something that's fixed
as geometry was supposed to be gravity
is something that varies through
space-time
according to the distribution of mass
it's very powerful
near a very massive object it's weaker
near a weaker object
now if gravity is the same as space-time
curvature then
that means we've taken a dramatic step
we found that
the actual geometry of space-time
varies according to the distribution of
mass
that makes geometry as i suggested at
the beginning it makes geometry
something that it never was before a
kind of dynamical physical field
whose changes depend on the distribution
of mass
newton would have told you well the
gravitational field that forces bodies
not to travel in straight lines
is determined by the distribution of
mass
einstein says well that's the space-time
curvature the way in which straight
lines accelerate toward one another
that's an indication of the distribution
of mass so of course mass energy in the
relativistic context
there's a common empirical basis what
what are we observing we're observing
how inertial trajectories accelerate
toward one another how the paths of
falling bodies accelerate toward one
another
we're just interpreting it in two ways
newton interpreted as a field that's
causing bodies to deviate from their
straight-line motion
einstein interprets it as the geometry
itself being affected by the presence of
mass
now some people call that geometrizing
physics but that isn't how einstein
thought of it einstein thought of it as
physicalizing geometry making it into
something dynamical like a physical
field
now this takes you back to einstein's
remarks about coordinates
right the method hitherto employed for
laying down coordinates in the
space-time continuum thus
breaks down i won't read all of this
there's no way but what he means is i'll
just
if you think about classical space-time
right or a flat coordinate system if i
thought the universe was flat i could
imagine that my coordinate system as on
the far left of your screen
was simply a flat coordinate system that
could be extended infinitely in every
direction
but einstein introduces this idea
instead of a reference frame
that's rigid like a cartesian coordinate
system or a plane
something that's kind of wiggly and
squishy like a mollusk
and so when you have two observers who
locally
feel like they're on a flat plane
but if you try to come you can't fit
them both into
a larger frame in which they both fit
into the same flat plane
this is the situation you have with
inertial observers falling in general
relativity
that you have einstein and his brother
locally
it's as if they're in flat cartesian
coordinates
but if they compare each coordinate
system to the other one you find well
the simple idea of coordinates
doesn't work anymore the idea of
extending a coordinate system to the
entire universe or even to a very large
area of the universe just breaks down
so this is how all of einstein's ideas
come together in this the phyllis
starting with the philosophical idea
well there's something wrong with the
idea
of a rigid rest frame
a flat coordinate system that sort of
characterizes the entire universe
is privileged is separate from all
physical interactions
there's something wrong with the idea of
an inertial reference frame being
distinguished from all others
those were initially just philosophical
ideas but it was this peculiar feature
of gravity
that it enables you to treat a system
that's
falling in a gravitational field as if
it were moving uniformly in a straight
line
because locally you can't tell the
difference
so that was a physical reason to take
this old philosophical idea and say that
it actually has physical content that
has to do with gravity
but this physical content is the key to
uniting gravity with geometry
and showing that if you want a coherent
picture of the reference frame of
one inertial observer and the reference
frame of another observer
who's equally inertial but relative to
the first one accelerating
then there simply isn't a flat
coordinate system into which you can fit
them both the only
the only system in which you can fit
them both is a curved geometry
so that's a rough sketch
that i hope conveyed something of the
philosophical
path that einstein took from
a combination of philosophical
problems that he found in the existing
physics
facts about gravitation that he thought
were never really
quite understood properly in the
newtonian theory and a new conception of
how
the relation between physics and
geometry
can be explored and developed
and in a sense that's general relativity
in a nutshell that's where all of our
that's why the
the talk of curved space-time is
meaningful
it's meaningful in the same way that
talking about the earth being curved is
meaningful
because we can follow straight lines on
the earth and we know that their
convergence indicates the curvature of
the earth
we can follow inertial trajectories in
space-time and say
their funny converging and diverging
behavior indicates the curvature of
space-time
now that's a remarkable philosophical
achievement and
you might think it would be a terrible
thing to throw this away
uh just because we need to have a
quantum theory of gravity and maybe the
quantum theory of gravity won't
incorporate
these great ideas of einsteins
now you could just adopt a definition
and say well if the next theory doesn't
include these great ideas then that
means they weren't so great
you don't have to think about it that
way
there are there are probably more than
three ways but you
you could consider these three ways in
which a theory can survive
after physicists have decided that some
other theory is more correct
now the obvious one is of course a
useful theory of
uh a useful tool for making predictions
and for
practical applications i mean lots of
old theories are still good in this way
especially newtonian gravity
another way that's a little bit
more serious for a theory to be to
survive in a future theory is with to be
a limiting case of the theory
so we say of special relativity well
it's that's actually what the world
looks like in very small regions even if
general relativity is true
it's a limiting case in which you
consider
very relatively small masses
and therefore nearly zero curvature
or newton's theory related to special
relativity it's a theory you have when
you consider
very slow velocities and uh
relative to which the velocity of light
appears infinite infinite
but another way you can think of it of a
theory surviving is when
the theory can still be regarded as a
source of insight into the way that
parts of the physical world are
connected with one another
and that i think is certainly it's
certainly true of newton's theory
of gravitation but it's even more true
in a sense of einstein's because of the
remarkable connections that
his theory has revealed
some of the things that i mentioned at
the beginning of my talk we understand
things about
large-scale structure
this is a famous remark by by henry
plancary about this very
question he says of course it seems to
us that theories only last a day
and that ruins upon ruins accumulate
today
theories are born tomorrow they're the
fashion the day after tomorrow they're
classic
the fourth day they're superannuated and
the fifth they are forgotten
but if we look more closely we see that
what thus succumb
are the theories properly so-called
those which pretend to teach us what
things
are but there is in them something which
usually survives
if one of them taught us a true relation
this relation is definitively acquired
it will be found again under a new
disguise in the other theories which
successively come to reign in the place
of the old
now let's think about general relativity
well of course it's the most empirically
successful theory of gravity
its predictions will probably continue
to be useful
at least as long as people continue to
use gps's
it'll be an easier way of doing that
probably than any quantum theory of
gravity which is likely to be
highly complex and it's likely to be a
limiting case for
a future quantum theory of gravity
but i think at a deeper level it's a
unique and indispensable
window into physical connections even on
the very largest cosmic scales which no
previous theory gave us any inkling of
large-scale cosmic structures in space
that is to say considering just the
spatial part of the universe and its
curvature or flatness
in time just considering the evolution
of the universe from
what seems like a beginning to what
might be an end
and space-time the combination of the
two
and one more thing that has to be said i
think and i hope i've convinced you of
is that the general theory of relativity
is not only those three things but it's
also
clearly a product of einstein's critical
philosophical analysis of established
conceptions of gravity and geometry
and that's why we celebrate him as a
philosopher science
scientist and that's why we'll continue
celebrating that all this year
thank you very much for listening
you
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