all right welcome back to physics and
human affairs oh my goodness well I
guess we're all trying not to make each
other sick that's a good thing
welcome to the new reality which is
hopefully temporary just some basic
things of course you've heard this a
thousand times but really take it to
heart
if you were young and blessed with a
good immune system please be conscious
of people who aren't you know like maybe
the elderly people in your family for
example more importantly don't get
information from me or anyone else who
speaks loud and speaks with authority
get information from the experts at the Centers
for Disease Control and Prevention the
CDC I've included a link here but me
being not very good with YouTube it you
probably won't be able to click on it I
don't frickin' know I'll learn YouTube
one of these days if you are scrolling
through the slides which I've also
posted then you'll be able to click the
link otherwise just google CDC don't
listen to the guy down the street he
doesn't know what he's talking about. The
class will continue and here's how: first
off everything I say here is subject to
revision everything I told you in the
previous email subject to revision
because you know we're all figuring out
what we're doing but as of now here's
what it looks like we're gonna do:
classes will be recorded. they will not
be given live.  I'm gonna upload
videos to YouTube and then upload post a
link to blackboard and here's why:
blackboard sucks. let's be real about
this. blackboard is shady on a good day
it throws up errors for no reason at all
it's not even compatible with Chrome
who's not compatible with Chrome? come on! blackboard is terrible, and now that the
whole world's gone online I don't trust the blackboard
servers will rise to the challenge so in
case they don't we're still having class.
we're going to YouTube because YouTube
understands volume. YouTube is not going
to crash just because
all the teachers in the world went
online or at least that's what I'm
betting on. so the videos will be
uploaded to YouTube. please right now if
you are watching this from the
blackboard link or even if you're
watching it on YouTube subscribe to my
youtube channel.  you can find it by
googling physics and astronomy with dr.
Douglas Shields. let's see if we can
figure this out here: alright there we go
I guess you probably should search
directly from YouTube not Google. there
we go put that in the search bar: boom
b-boom there it is
[incoherent rambling]
[more rambling]
so let's
go back to the class. a link to the video
will be posted here. syllabus lectures
and clicker class work on on blackboard.
feel free to ask questions in the comments in the YouTube.
[confused Gen-X'er talk]
and feel free to ask questions
in the comments on the YouTube file on
the YouTube page I will totally answer
them from the comments. since we're not
doing it live, we're not gonna be using
clickers anymore. however you will
continue to accumulate clicker classwork
points by taking a quiz over the day's
lecture and you have until the end of
the day any given class day to do that
and the lecture quizzes are down the
newest link on blackboard
right below Blackboard Collaborate.
Blackboard Collaborate is where I will
have office hours so if you have any
questions for me then hey go to office
hours I will figure out how
to do that alright let's talk about
physics welcome to the second half of
the book we've gotten through what I
consider the boring stuff
remember this class is a chronological
exploration of physics beginning with
the ancient Greeks on up to the present
day so in the first half of the semester
we learned about physics that was
discovered right up before the year 1900
roundabout really more like 1905 let's
recap everything that we've learned so
far the Greeks got it wrong
Aristotle brilliant as he was thought
that heavy things fall faster than light
things because he was he was baffled by
friction air resistance got him the
great intellect of Aristotle was broken
by air resistance and friction it was
not until scientists learned to build
laboratories where friction is minimized
like you do in lab class that Newton's
laws of motion were discovered and
really that began with Galileo so
Galileo discovered the law of falling if
you can neglect air resistance if air
resistance is very small then all
objects fall with the same acceleration
about 10 meters per second per second
that means every second something is
falling it is gaining 10 meters of
second per speed so it's accelerating at
10 meters per second per second  
or 10 meters per second squared it's
really more like 9.8 meters per second
squared
Galileo also discovered what Newton
would later co-opt as Newton's first law
of motion sometimes known as the law of
inertia which is that if not for
friction a moving object will keep
moving forever in a straight line with
constant speed in other words a moving
object will maintain its velocity
forever until it hits something or
interacts with something or feels a net
force acting on it speaking of forces
after Galileo there was Newton and
Newton really put it all together boy
when there's a plague outside and you
have a lot of money and you can go home
and do nothing but study for years which
is what Newton did good thing Newton
didn't have YouTube to distract him all
he did during his plague was study and
boy did he discover a lot of science we
did not even begin to cover all of the
science that Newton discovered what's
important for this class is his second
law which we in this class call Newton's
law of motion which is the more massive
you are the harder it is to accelerate
you for a given force (a given net force)
applied to an object the more massive
the object is the less it will
accelerate if I flick a marble [ping]
it'll go across the room if I give the
same flick (the same force) to a bowling
ball though it's barely going to
accelerate at all so we usually write
Newton's second law as a equation F = ma but in
this class were more concerned with the
concept: for
given force a less massive object will
accelerate more. then finally Newton's
third law which is sometimes known as
the law of force pairs: if I push
on you, you push on me back with equal
force. in other words forces always come
in equal but opposite pairs: equal
magnitude force in opposite directions
it's a little bit strange if you think
about it, right? if a Mack truck hits a
bicycle intuitively the naive student
might think the Mack truck puts more
force on the bicycle than the
the bicycle puts back on the Mack truck
but that's not true. the Mack truck and
the bicycle collide which means they put
forces on each other
equal in magnitude but opposite in
direction. well if the bicycle puts just
as strong a force on the Mack truck as
the Mack truck puts on the bicycle,
why then does the bicycle fly off and
the Mack truck barely slowed down at all?
well that is Newton's second law? the
bicycle does most of the accelerating
(most of the bouncing) because the truck
has most of the mass so Newton's third
law says objects always apply equal
forces in opposite directions when they
interact. their acceleration however is
governed by Newton's second law: the
more massive object will accelerate less
in response to the force that these two
objects put on each other. Newton also
discovered the law of gravity: every mass
in the universe attracts every other
mass. of course that doesn't mean he
discovered that things fall down (oh look
a thing fell I just discovered gravity)
no new what Newton discovered was the
force that causes this pencil to fall is
the same force that keeps the moon in
orbit around the earth and the earth in
orbit around the Sun. it is the universal
law of gravity and it says that every
mass in the universe attracts every
other mass. the more massive two objects
are the stronger their mutual attraction
is going to be; the more distant two
objects are the weaker their attraction
is going to be. now Newton's law of
gravity is really good under most
circumstances. it works really well in our
solar system for example. we use Newton's
law of gravity to put astronauts in
orbit around the earth and send probes
to, Pluto no
problem but it's not perfect.
technically speaking Newton's law of
gravity is wrong.
we now have an updated theory of gravity
a modern theory of gravity which we'll
learn about in the second half of this
course. we also learned about conservation laws some quantities are
conserved and what that means is
constant with time. they cannot be created
or destroyed. the most important
conserved quantity is energy, the
capacity to do work or
eat things up. energy cannot be created
out of nothing at least not since the
Big Bang and whether it was created out
of nothing at the Big Bang we just don't
know but since then the total
energy in the universe has remained
constant. you can transfer energy from
one object to another like when you kick
a ball you're spending your calories to
giving those calories to that ball and
you can transform energy from one type
to another so when you spend your
calories you're spending chemical energy
in your body and transforming it to
kinetic energy when you move your foot
and then transferring that kinetic
energy to the ball. energy is not created
at any point in this process nor is it
destroyed however it is siphoned off as
thermal energy. thermal energy is like
the government - it takes its cut from
most transactions. in fact your body
being a very inefficient machine spends
most of your calories heating up your
muscles only a small fraction of the
calories that you spend actually 
go to doing the things you do in
everyday life like picking up a pencil. a
very a small percentage of my calories
that I'm spending right now is going
toward moving this pencil. most of my
calories are going toward heating up my
muscles. another conserved quantity is
momentum, the tendency for an object to
keep moving. momentum cannot be created
or destroyed. if two objects are at rest
and they kick off of each other,
one object is going to have rightward momentum
and the other is going to have leftward
momentum. the rightward momentum will
be positive momentum the leftward
will be negative and they will add up
to zero because before they kicked off
each other they were zero. so momentum
was conserved through that interaction. another conserved quantity, which we didn't hit very
hard in this class is angular momentum or
the tendency for a spinning object to
keep spinning. so the earth is spinning
and unless something interferes
with it - unless something from the
outside puts a torque on the earth - it's
just going to keep spinning forever.
likewise the earth is orbiting that the
Sun. that
takes angular momentum, and again because
angular momentum is conserved it will
keep orbiting forever unless something
interferes with it.
another conserved quantity we've
discussed in this class is electric
charge (positive or negative) it turns out
that the universe as a whole (at least
according to the data we can see with
our telescopes) appears to be
electrically neutral. there are just as
many positive charges as there are
negative charges and in every reaction
that we know of, whether a chemical
reaction or nuclear reaction or any sort of
reaction or interaction
we've been able to observe in laboratory
or in telescopes or in nature, charge has been conserved if the
total charge was zero at the beginning
it will be zero in the end. now that
doesn't mean that a neutral particle
can't suddenly have charge - it can suddenly split into a positive
charge plus a negative charge so that
the net charge remains zero. the total
charge is conserved. we learned about
thermodynamics, light and atoms. the most
important law of thermodynamics is the
second one which has several ways that
you can state it: the technical
definition of the second law of
thermodynamics is quite
advanced mathematically so we're not
doing that. we're doing the concepts so
conceptually you can think of the second
law in several different ways. one way is
that atoms in the universe get more and
more disordered with time and there
there's a quantity for that, a
mathematical description called entropy.
the total entropy of the universe
increases with time. a way to think about
that is: it's easier to
heat things up than it is to make things
move. so if you spend energy to make
things move like when I push push a cart
down the street at least some of
the energy that I spend will go toward
heating up my body because thermal
energy - the energy of heat - means my atoms
and molecules are vibrating in random
motions. it means they are disordered. so
when you heat something up entropy goes
way up. the simplest way to dump entropy
into the environment is to heat
something up. light (radiation) will do
that as well. another consequence of the
second law of thermodynamics is that
heat engines like gasoline engines
cannot be a hundred percent efficient.
heat engines are engines that use
thermal energy to do work. so gasoline
combusts it pushes up a piston does work
on the piston the piston comes back down
and then it compresses gasoline vapor
and air and then that combusts. thermal
energy pushes the piston back up. it is a
cyclical process. so a heat engine by
definition is a cyclical process by
which work is done from thermal energy
and how the second law of thermodynamics
applies is that heat engines are
severely limited on their efficiency
because if you try to build a heat
engine without an exhaust to get rid of
your entropy that heat engine will very
quickly overheat and  your
engine will no longer be able to do any
work. you'll ruin your engine the second
law of thermodynamics means a gasoline
engine must have an exhaust pipe and
that exhaust pipe will be hot and that
that thermal energy is wasted energy. it's
energy you spent with your gasoline that
does not make your car go. gasoline
engines are incredibly inefficient. they
must be because of the way they're
designed, because of the second
law of thermo-dynamics. why we're still
using gasoline engines I don't know
maybe. we still live in the 19th century?
maybe we'll want to make the 19th
century great again? I don't know
electric motors are much much much much
much much more efficient because they
don't because they don't have to dump
their entropy into the environment
because they don't use thermal energy to
do work. we learned about like the
electromagnetic theory of light. light
is a ripple in the electric field and
the magnetic field and it travels at the
speed of light so if light is a ripple in the
electric field going this way
then it is a ripple in the magnetic
field going back and forth so the
displacement in the electric field and
the magnetic field are at 90-degree
angles from each other and then the
light is traveling at 90 degree angle
from both. we learned about the planetary
model of the atom which is what chemists
still use today even though it's
technically wrong. the planetary model
says the atom is a nucleus of positively
charged protons with sometimes some
neutrons in there - that much at least
is correct. according to the planetary
model electrons orbit the nucleus like
like planets orbit the Sun. we now
know that's not true.
electrons are clouds. they surround the
nucleus but the planetary model gives
good results for chemical reactions and
it's a hell of a lot easier than the
cloud model (the quantum model) so we use it when it works, just like we
used Newton's law of gravity for orbital
mechanics because it's good enough and
it's a hell of a lot simpler than the
modern theory of gravity (General Relativity) the
planetary model is much much much much
simpler than the quantum model. so we use
it when it works and discard it when it
doesn't.
all right well that was the first half
of the semester. now it gets weird. gosh
I'm gonna miss being in class with you
because we get to talk about some really
weird stuff but hey you know what it's
YouTube we can be weird here too. by 1900
scientists were a bit complacent some of
them thought you know what we've got
physics figured out and yet there were
clues there were clues that everyday
human experience might not give us the
whole story of how the universe works
and it's easy to look back and see what
they were missing or at least see what
they were missing that we now have. of
course we don't know what we're still
missing. one of the things they were
missing is light. If
you're blessed with vision you can see
all the colors of the rainbow: red orange
yellow green blue violet and
every combination thereof. awesome, but
you can't see infrared you can't see
radio waves you can't see microwaves you
can't see ultraviolet light you can't
see x-rays you can't see gamma rays
there's a lot more light in the universe
than what we can see with our eyes.
we're also limited in our everyday
experience by the size of things
we can't see things like germs & viruses
that are microscopic nor can we see very
large things like clusters of galaxies
they're just beyond the scope of our
eyes ability to see them. we need scientific
instruments to see both of those things.
another way that we're limited in
understanding the universe based only on
our experience is time. the human brain
can't perceive things that happen really
really really quickly turns out more
quickly than about a movie frame one
thirtieth of a second roundabout, nor can
we in our everyday experience
understand things that are beyond our
own lifespan now once you throw
technology in there then of course and
by technology I mean simple writing
that's a technology once writing was
invented suddenly we had history. even
language we could tell stories from our
past but again that's all we had was
stories, then writing, then once we started
recording things that helped. but really
what allows us to see farthest in the
past is two things: number one being
geology, being able to look at the oldest
rocks and the fossils embedded in those
rocks; and telescopes because light
travels at a finite speed (the speed of
light) so the farther away you look in
space the farther back in time you're
looking. so when we look at a galaxy that
is five billion light years away we are
seeing that galaxy five billion years in
the past.
so with technology we can see things in
the past. our everyday experience also
limits us with speed we only see
everyday objects, and everyday objects
are subject to friction and what does
friction do to the speed of things? it
slows things down so everyday objects
move slowly and if you push a chair
across a room there's a good chance it's
gonna come to a stop on the floor
because of friction. in fact most of the
objects that we see move much much much
much much much much much much more
slowly than the speed of light, and it
turns out objects moving near the speed
of light behave differently than objects
moving at everyday speeds. we're gonna
learn about that today. our everyday
experience does also not allow us to
understand gravity in its full
complexity.
Once Galileo was able to build a laboratory
and then once
Newton discovered calculus those two
things together allowed Newton
to formulate his law of gravity, but
 even Newton only could experience
gravity in very weak forms like the
gravity near Earth and gravity of the
planets orbiting the Sun. as far as the
universe goes, those are both very
weak gravitational fields. gravity it
turns out behaves much differently in
strong regions of gravity  (in strong
gravitational fields). It
turns out Newton's law of gravity does
not apply to regions of extremely strong
gravity. so now we begin the 20th century.
the 20th century began the technology
that allowed physicists to see things
that our everyday experience simply
can't,
so discoveries that would be made in the
20th century and continuing into the
21st would involve things that we simply
don't perceive in everyday life and that
makes them really hard really hard to
grasp.
Einstein's theory of special relativity
which we'll learn about today governs
the behavior of things moving near light
speed. now according to special
relativity you cannot move past light
speed. you can get closer and closer to
Lightspeed but you cannot exceed it.
special relativity is called special
relativity because it's a special case
of general relativity which is the
broader theory of relativity (the general
general means broad) general relativity is the
behavior of things not only near light
speed but also in regions of strong
gravity. another way that special
relativity is a special case is it only
applies
objects that are not accelerating,
objects that have constant velocity
whereas general relativity incorporates
acceleration so you can be accelerating
and general relativity will govern
your motion. about the time special
relativity and then general relativity
were formulated (special was 1905 general was
1915) through the 20s we get the really
weird stuff: quantum mechanics quantum
mechanics is the physics of extremely
small objects like electrons. in old
physics, 19th century classical
physics, we would have thought of
electrons say as a point particle, a
little-bitty point in space like a
little BB. Quantum mechanics says that's not
true.
particles are not bb's they are clouds
they're waves. once telescopes got better
and better we were able to have a better
a larger and larger understanding of
cosmology, which is the study of the
universe as a whole and even now we're
limited by the range of our telescopes.
 we'll talk about that later on as
well. radioactivity and nuclear energy,
these are things that were discovered in
the 20th century that led to some
amazing advances and very horrifying
advances in science including nuclear
weapons, so radioactivity involves how
the nucleus of an atom will change into
some other nucleus. it will decay and
we'll talk about that later on in the
semester as well and nuclear physics is
intimately tied with particle physics,
the physics of individual particles and
both of these are intimately tied to
quantum mechanics (quantum physics your
book calls it)  so
that's what we're going to talk about
for the
rest of the semester we're also going to
be moving more quickly. we're going to be
covering one whole chapter per lecture
now that means we're gonna move quickly
through the slide so please please
please read your book read your book now
you'll learn this material a lot better
if you engage it in multiple ways. yes
listen to the lecture take take the
lecture quizzes at the end and also read
the book. It'd be better if you read the book
before the lecture but however you want
to do it, reading and taking notes is a
great way to learn if you do that you'll
just ace the exam.
buckle up I'm not kidding it gets weird
from here. beginning with this guy: hi
Albert!
Albert Einstein look how old he is well
when he made his the discoveries that
made him famous special relativity and
general relativity he was a very young
man he was in his 20s. before we talk
about special relativity we've got to
define something: a frame of reference. a
frame of reference is a specific point
of view from which velocities are
measured. so far in this class we could
have glossed over this concept because
when we talk about velocities on earth
we generally assume a specific frame of
reference. we assume  the ground
frame of reference so for example if I
am running at 20 miles an hour (I cannot
run 20 miles an hour you know I walk
like a banana and run like a coconut)
but if I were a runner and I can
run at 20 miles an hour,
what we all understand it to mean is
that I am moving 20 miles an hour with
respect to the ground, not with respect
to another runner who's also running 20
miles an hour.  from his point of
view I'm standing still. from his frame
of reference I'm standing still but from
the frame of reference of the ground I
am running 20 miles an hour.
special relativity only applies to
inertial frames of reference, that is a
point of view which itself is not
accelerating. so in special relativity or
in even old 
Galileo's relativity for that matter two
runners both running at twenty miles an
hour would see one another standing
still and those are perfectly acceptable
frames of reference. they are also
inertial frames of reference so they're
perfectly valid. however if one runner
starts slowing down why that runners
velocity is changing therefore that
runner is  accelerating
(backwards) which means it is no longer an
inertial frame of reference so if you're
if the person doing the measuring - if the
person looking at everything else is
speeding up slowing down or changing
direction - special relativity cannot be
used so we're gonna use this
phrase
frame of reference a lot. we're also
going to use the term 'relative to' and
they mean the same thing. so when I say
an object's velocity in your frame of
reference, or an object's velocity
relative to you, those both mean the same
thing.  those both mean the velocity
that you measure an object moving or if
we say an object's velocity in the
ground's frame of reference that means
the velocity as measured by someone on
the ground
like a cop sitting on the side of the
road. and  earth we generally gloss
over the idea of frames of reference
because we all agree on what a preferred
frame of reference is - it's the frame of
reference of the ground. when the cop
when the cop gives you a ticket for
doing 90 and a 70 which I hope never
happens the cop is not
saying you were doing 90 in the frame of
reference of another car doing 90 - you
weren't - in that frame you were standing still. the cop gave you
a ticket because you were doing 90 miles
an hour in the frame of reference of the
ground - that is, if the cop
was sitting sitting still, the cops radar
gun would have bounced off your car and
measured 90 miles an hour.
okay the gun would not have bounced. the
radar signal would have bounced
otherwise the cop would be throwing his
radar gun at you and that means the cop
would have been able to throw at greater
than 90 miles an hour which means he
would have been a major league baseball
player who turned into a cop [sigh].
[rabble rabble rabble]
In space we talk about spaceships moving
back and forth with respect to each
other. there is no ground. there is no
common frame of reference from which to
to assume, so when we discuss velocities
in space we have to be really careful to
define our frame of reference. when someone says I am moving through
space at half the speed of light
questions would always be half the speed
of light compared to what? because you're
not moving half the speed of light
compared to yourself - you're standing
still compared to yourself - you're always
standing still in your own frame of
reference. when we say you have a
velocity that's not zero we are assuming
there is some other frame of reference
from which that would be measured, from which
it could be measured so before we get
into Einstein's theory of [special]
relativity let's talk about old
relativity from the 1600s: Galilean
relativity. Galileo discovered relativity
but of course Galileo's relativity only
applied to objects moving very slowly,
not near the speed of light. but in order
to understand Einstein's relativity it
really helps first to understand Galileo
relativity. Galileo's relativity says the
law of motion the laws of motion are the
same in all inertial frames of reference
so that means as long as the person
taking the measurement is not
accelerating then that person is going
to experience the laws of physics that
we have learned in class.
again this only
applies where Galilean relativity
applies which is for object moving
slowly, so again let's talk about frames
of reference. you have a frame of
reference - you are sitting still or maybe
you're moving - maybe you're
in a car or watching this video but you
have a frame of reference, a point of
view from which you can measure
velocities. in your frame of reference
you are standing still always. if I'm
moving in the same velocity as you that
is with the same speed in the same
direction that means I too
am standing still, now there's a weird
consequence to this: it means if you are
in a closed box and you're not accelerating
and you can't see the
outside world or feel any outside
vibrations - in other words if you have no
contact with the outside world at all -
then you have no way of knowing whether
or not you're moving. to understand this
let's consider two examples
well three really but one of these
examples will be an example that shows
the concept and another will be an
*apparent* contradiction - if
you've ever flown on a plane that plane
may be flying at few hundred miles an
hour and yet you can doze off. it feels
to you when you close your eyes like
you're standing still. it doesn't feel
completely that way because you do have
some interaction with the outside world
for example there might be some
turbulence that would be a clue that
you're moving, also in order to make you
move the engines have to whirl or the
engines have to do something whether
they're spinning or shooting some jet
fuel at the back whatever kind of plane
you're in, and so you can feel the engine
doing what it does. nonetheless that's
not the same as feeling your speed you
don't feel your speed even though you're
moving hundreds of miles an hour but you
do feel your acceleration. when that
plane slows down you get pulled forward.
you do feel your own acceleration. you
don't feel your speed you feel your
acceleration
likewise when that plane speeds up
you're pulling backward because you're
accelerating think of moving in a car
likewise you don't feel your speed. now
that might seem like a contradiction
right? you can go to sleep and you can
know if you're moving fast or not because you can feel the vibrations
but again that is a 
combination of the engine vibrating
which is not the same as your speed and
wheels going over the ground which is
caused by your speed but it's also
contact with the outside world it's the
outside world telling you that you're
moving fast. you don't feel your own
motion. you don't feel your own speed.
however when you accelerate you do. you
put on the gas pedal [sound effect] you get pulled
backward you feel your own acceleration
likewise when you hit on the brake
[sound effect] you move forward because
you're accelerating - you're accelerating
backwards - that flings you forward.
hopefully you're wearing a seat belt so
that if you get in a wreck you break
your collarbone instead of your skull.
that's what seat belts do. if a seat belt
has ever broken your collarbone it has
saved your life.
likewise remember there are three ways
to accelerate: speed up slow down or
change direction. if you turn your wheel
to the left then you're gonna be pulled
to the right because you're accelerating.
you feel your own acceleration.
so we haven't gotten to Einstein yet
this is just Galileo's relativity right
now. consider what's on the screen here:
two trains with the same velocity.
this is what got on Stein's brain moving.
this is what really inspired Einstein to
take Galileo's relativity further if
you're in a train and you're sitting in
a rail yard with a bunch of other trains
and you're moving really slowly so you
can't feel any vibrations then you have
no way of knowing if you're moving or
not and if you see another train moving
backward you don't know if you're moving
forward or if the train is moving
backward or both, or if you're both
moving forward but you're just moving
forward faster. all you know about that
train is its *relative* velocity - its
velocity relative to you. you don't know
its velocity relative to the ground. all
you know is its velocity in your frame
of reference. if you're moving forward
and you see it
moving backward then all you know is it's
is moving backward in your frame of
reference. whether it's moving backward
along the ground and you're you moving
forward you don't know.
you only know its relative
velocity, its velocity relative to you.
if you and the train are both moving
at the same speed then you share the
same frame of reference, so you see the
other train standing still, even if
you're both moving along the tracks, even
if you're both in motion in the ground's
frame of reference. so let's leave the
comfort of Earth. let's leave the comfort
of knowing our frame of the preferred
frame of reference that we all take for
granted. the ground. let's go into space
where there is no ground. there is no
preferred frame of reference. you're in a
spaceship. in your frame of reference
you're standing still you're floating in
your spaceship unless you're
accelerating let's assume we're
being inertial here there's no
acceleration that means you're floating.
(this is not science fiction so we don't
have like artificial gravity or anything)
if you are not accelerating in space
you're floating because you're in
freefall and so is a spaceship you're
floating with the spaceship all right
cool.
well then another spaceship is floating
to the right at 90 miles an hour from
your point of view, so from your frame of
reference you're standing still - floating
still - and Jackie over here is floating
to the right at 90 miles an hour all
right cool. well now pretend you're
Jackie. well in Jackie's 
spaceship from Jackie's point of view in
Jackie's frame of reference she's
standing still. in Jackie's frame of
reference you're the one who's moving
and if you see Jackie moving to the
right then Jackie sees you moving to the
left you see one another moving in
opposite directions. you measure one
another's velocities in the opposite
direction - same speed, opposite direction
so what this means is that if there is
some third frame of reference that we
consider sacred like the ground or the earth
if
there is some third frame of reference
or 3rd observer that's watching us both,
then what your velocity effects
then
Jackie's velocity depends on your frame
of reference. Jackie's velocity with
respect to you depends on your velocity.
your motion affects how you see others.
if you catch up to Jackie then suddenly
you and Jackie are the same frame of
reference now Jackie is standing still
in your frame of reference even if you
and Jackie are both moving with respect
to the earth.
and there's an equation for that let's
consider the Earth's frame the ground
frame to be the sacred one because it's
the one we're used to. so some objects
velocity and Earth's frame of reference
equals that object's velocity in my
frame of reference, plus my velocity in
Earth's frame, oh boy are you confused?
sorry about that.
let's try to clear it up. let's consider
a person walking on a moving train,
cool. the Train is moving two
miles an hour eastward along the tracks
two miles an hour in the
grounds frame of reference all
right cool. well you, a person, naturally
just walk at three miles an hour so you
were walking along the Train at three
miles an hour, so how fast are you moving
with respect to the earth? that is if I
were to shoot a radar but if I were
standing on the ground and were to
shoot a radar gun at you, how fast would
I clock you? well not only are you moving
with the three miles an hour that you're
propelling yourself, but the train is
also propelling you at two miles an hour,
so your total velocity is the sum of the
two: the trains velocity plus your
velocity along the Train. three miles an
hour plus two equals five miles an hour
would be your speed.
then remember velocity has a direction
would be five miles an hour
eastward. okay cool. well now supposing
the train moves west but you're still
moving east.
the trains like 'I'm gonna back up' and
you're like 'I'm gonna keep going forward'
so now the train is moving westward at
two miles an hour and you're moving
eastward at three miles an hour. how fast
will I see you walk? well now your
velocity is opposed to the trains
velocity you're moving in opposite
direction
so the answer is you would subtract the
two speeds 3 minus 2 is 1 mile an
hour. and which direction would that be
well the faster speed wins. you're moving
faster your your velocity is 3 eastward
and the Train is only 2 westward so you
get the excess. your total velocity in the
grounds frame of reference is going to
be eastward because you're moving faster
eastward on the ground then the train is
moving westward so if the person walking
on the train is moving in the same
direction as the Train velocities add if
they're moving in the opposite direction
they subtract. *** sounds like a good
quiz problem ***
we're still in the 1600s so far our
discussion of relativity is not Einstein.
its Galileo and it works it works for
most circumstances it certainly works
really well for objects here on earth
because objects here on earth for the
most part for the most part do not
travel near the speed of light but when
objects do travel near the speed of
light Galilean relativity does not work
velocities do not add the way we just
described for objects that are traveling
at nearly the speed of light. that's
weird it should be weird if you're not
blown away by that yet you will be, and
if you're not by the end of the lecture
watch the lecture again because this is
super weird. if you're walking on a train
and the train is moving then your
velocities add as long as you're not
moving near the speed of light. your
velocities do not add in the same way if
you are traveling near the speed of
light they add but the equation is more
complicated you can't just add one
number to another that
so that's where we come to Einstein. in 1905
Einstein modified Galileo's relativity
into what we now call special relativity
the special theory of relativity that is
relativity where we don't take into
account acceleration and we don't take
into account gravity at least not strong
gravity. special relativity then governs
the motion velocities and behavior of
objects moving near the speed of light
and also for light itself, so special
relativity combines two principles one
the principle of relativity which is
essentially a slightly modified
form of Galileo's principle of
relativity - every inertial reference
frame (that is reference frame that is
not accelerating) has the same laws of
motion, the same laws of physics. so as long
as you are in an inertial frame of
reference you're not going to get thrown
backward you're not going to get thrown
forward right you don't feel your own
motion. only when you accelerate do you
spontaneously get thrown forward or
backward or to the side.  when you
hit the gas on your car then you're
accelerating then you get thrown back
when you hit the brake now you're
accelerating you get thrown forward when
you turn the steering wheel then you're
accelerating so you get thrown to the
side. so Einstein modified the
principle of relativity that's not
anything new the new. thing that Einstein
added which is super weird and
completely changed all of physics: the
constancy of light speed. the speed of
light is the same for all inertial
reference frames. this violates Galilean
relativity. einstein's principle of relativity
is a slight modification of Galilean
relativity because it has to take into
account the constancy of light speed. no
matter how fast you're moving
you will always clock the speed of light
to be the same, no matter how fast the
source of light is moving toward you.
light and objects moving near the speed
of light do not obey Galilean
relativity. let's do this thought
experiment of the train again alright so
the train is moving to the east but
instead of you walking at three miles an
hour you shine a beam of light. shouldn't
those velocities add? suppose the Train
is moving at half light
speed. okay maybe it's a space train. and
then you're standing on the train in
your spacesuit with magnetic boots
however realistic we want to make this
and you shoot a beam of light eastward
ok well according to Galileo if the
Train is moving at half light speed and
the light leaves your flashlight at
light speed then who someone who is
standing still in the third frame of
reference from which we're stating the
train speed - they should see the light be
moving faster, right? just like if you're
sitting on the ground and I'm driving
down the road at 70 mile an hour and I
throw a rock at you it's gonna hurt real
bad because the rock speed is added to
the car speed when it hits you but light
does not do that! if the train is moving
in your frame of reference and half the
speed of light and then the the beam
of light leaves the flashlight at light
speed, according to Galileo the
light from that flashlight should hit
you at time and a half light speed, at
greater than light speed, but according to
Einstein it doesn't. that flashlight beam
hits you at precisely the speed of light
no matter how fast the train was moving
no matter how fast the flashlight was
moving no matter how fast you're moving
light speed is constant. that light will
always hit you at the speed of light. you
will always
measure the speed of light the same. that
is the fundamental principle of
Einstein's theory of special relativity
the speed of light is constant in all
inertial reference frames no matter how
fast you're moving no matter how fast
the source is moving a beam of light
will always hit you at the speed of
light, so if the beam of light is only
hitting you at light speed does that
mean that the light left the flashlight
moving more slowly?
no, all observers clock light moving
the same speed, so yes light leaves the
flashlight at light speed and it hits
you at light speed
despite the fact that the flashlight is
moving toward you at some significant
fraction of light speed. there are some
consequences to this. one consequence is
that massive objects cannot reach light
speed. Einstein had this epiphany when he
was doing a thought experiment he said
okay supposing this is true, that
the speed of light is the same for all
observers, okay now what would happen if
you try to catch up with a beam of light?
what would happen if you tried to outrun
a photon? well the answer is you can't do
it. you can never catch up to a photon
which means you, massive object, human,
cannot reach light speed and we have
over a hundred years of evidence to
support this
this lots and lots of evidence one piece
of evidence is particle accelerators.
these are laboratories where they
accelerate individual particles or
atomic nuclei to nearly light speed in
these giant circular tubes so close to
the speed of light
they put
so much energy into these particles that
if Newton's laws of motion were
correct these particles would travel at
much greater than the speed of light
many times over but they don't. they get
closer and closer to the speed of light
but never cross it when these objects
approach light speed they they can't
cross it when you give them more and
more energy when you accelerate them and
accelerate them accelerate them all you
do is get them closer and closer to the
speed of light it's kind of like if
you're a really bad football team *ahem*
that
is backed up to its own goal line and it
gets a penalty and that penalty would
normally take your across your own goal line
well it can't do that what does it do
instead it takes you half the distance
to the goal now you get another pimply
penalty, half the distance to the goal
again. another penalty half the distance
to the goal again. but penalties will
never get you back beyond the goal.
likewise if you have a particle
traveling at nearly the speed of light
and you try to accelerate it, it'll take
you half the distance to the goal. it'll
take you closer to the speed of light
but not over it. add some more energy
accelerate some more it'll take you
closer to the speed of light but not
beyond it, so this violates Newton's laws
of motion. Newton's laws of motion that
we learned in the first quarter of the
semester do not work at all
for objects moving near the speed of
light. another piece of evidence we have
for this are muons .these are particles
that  shower down on us from
the upper atmosphere from when radiation
from space hits the top of the
atmosphere it showers down particles
called muons and we can tell their
clocks
(what times they are experiencing) by how
quickly they decay, so that will bring us
to time dilation. if all objects measure
Lightspeed to be the same no matter how
fast they're moving that means if two
objects relative to one another are
moving near the speed of light each
objects sees the other objects clock
moving slowly. in other words if a
spaceship
moves away from Earth at near light
speed and tries to talk to us then we
are going to hear the voice that is
being broadcast by radio wave or
whatever moving slowly that person is
going to be talking slowly and from his
frame of reference you're moving near
light speed remember from his frame of
reference he's standing still if he's
moving away from Earth at near light
speed from his view you on earth are
moving backward at near light speed
which means
when you talk to him over radio he will
hear your voice going slow.  each object will see
the other objects clock runs slow and by
clock I mean anything that moves through
time. this is this is where we get
evidence from muons decaying in the
atmosphere because when with particles
that are not stable decay 
the rate at which they decay is a clock
and we see these muons showering down
through the atmosphere decaying more
slowly because they are moving at near
light speed than they do in laboratory
we can also
measure this directly by putting atomic
clocks in space which was
done in I think 1960 you put an atomic
clock in space and you compare how fast
it runs to a clock on the ground
and it will run through the clock on the
they will run at different speeds you
got to be careful here each clock will
see the other runs slowly that is the
clock on the ground will see the one in
space move slowly and the one in space
will see the one on the ground move
slowly because they are moving with
respect to each other the one on the
ground sees the the satellite move
where the satellite sees the ground
moving backward. there's another effect
though the that will deal with in
general relativity the clock in space
sees the one on the ground moving more
slowly because we on earth feel more
gravity but again that's a general
relativity thing we'll get to that later.
so when two objects are moving at some
fraction of the speed of light  with
respect to one another each object sees
the other's clock moving more slowly.
there's another weird
consequence of the constancy of light
speed: length contraction. if you leave
earth and you travel at near light speed
with respect to all the stars that are
moving pretty slowly with respect to
each other, you're gonna see the
distances between those stars contract.
in other words you're gonna see the
whole universe get smaller
each object will see the others
reference frame shrink. on the other hand
if you're on earth and a ship zooms by
at nearly the speed of light you're
gonna see that ship smushed. if it's if
that ship is normally 100 meters
long you might only see it 50 meters
long you. might measure it at 25 meters
long depending on how fast it's moving,
how close to the speed of light it's
moving. and again the evidence for that
is muons decaying in the atmosphere from
our point of view the muons are
traveling at nearly the speed of light
so their clock
is running slowly so they decay more
slowly than they do in a laboratory. from
the muons point of view earth is coming
upward at nearly the speed of light, the
whole atmosphere through which they're
moving is coming upward at nearly the
speed of light because from their point
of view they're standing still. so from
the muons point of view the distance
through which they travel has shrank
which means they move farther down - they
make it far closer to the ground than
they otherwise would. in fact some of
them make it all the way to the ground.
they wouldn't if they were moving more
slowly. because you cannot pass the speed
of light, when you approach the speed of
light it becomes more and more difficult
to accelerate you. well consider
Newton's second law: net force equals mass
times acceleration. what does that really
mean? it means that mass can be
thought of as a resistance to
acceleration. the more massive you are
the harder it is to accelerate you so
there's a concept in special relativity
called mass increase. when an
object approaches the speed of light its
inertial mass increases. that's not to
say that there's more stuff that
suddenly goes in it -  we
often think of mass as the amount of
stuff in an object, and just because an
object's moving near light speed doesn't
mean it suddenly has more stuff in it -
we're not talking about
that definition of mass. we're talking
about inertial mass. we're talking about
how difficult it is to accelerate an
object. so the closer to the speed of
light you get, the harder it is to
accelerate you so your inertial mass has effectively increased. and we know that from
particle accelerators.
Here is the very famous equation e equals mc-squared.
you may have heard it maybe you can
recite it off the top of your head but
what does it mean? it means that mass is
a form of energy and it can be converted
to other forms. now let's look at this
real close:  how
much energy does mass contain? well it's
the mass in kilograms times the speed of light squared.
all right now intuitively the
speed of light is pretty fast right
186,000 miles per second 300,000
kilometers per second pretty fast right
and if you want to make a large quantity
bigger square it so C squared is an
extremely large quantity. what does that
mean in terms of relativity? what it
means is that a very small amount of
mass contains a huge amount of energy.
and we know this from nuclear power
plants nuclear weapons and the Sun.
the Sun shines because 400 million tons
of mass is converted to light in the
core of the Sun every second. all right
now let's let's pontificate a little bit
here right I'm saying some weird stuff
I'm saying that if if I jump on a
spaceship and move out of here at near
light speed you're going to see my clock
run slow we call this time dilation so
if time is dilating what is time anyway
I mean philosophers will quibble over
what time is but physicists don't
physicists are biased by what can be
measured so for a physicist we don't
care about philosophers definition of
time to a physicist time is a very
simple concept it is what can be
measured by a clock
likewise distance when we say length is
contracted if a ship moves by at near
light speed you will see it's length
contracted you will see it smushed what
that means is that you will measure it
smooshed so when we say length or
distance all we mean is what can be
measured by a ruler which could be a
physical ruler but more likely the ruler
that we use is light itself. all right so
a clock then is anything that runs
through time which is really anything
with a frequency an atomic clock is the
is a very very very precise timekeeper
an old-school grandfather clock is just
a swinging pendulum that counts dude to
do decaying particles like muons coming
through the atmosphere that's a clock
because they have a set decay rate your
heartbeat has a has a frequency to it so
it's it would be considered a clock in
terms of things that dilate your
metabolism and your aging process your
thoughts are a clock because they are
neurons firing your voice this is both
the pitch of your voice and how fast you
talk so if you are moving at nearly the
speed of light and communicating by
radio to earth earth will hear your
voice slow and low so anything that
changes with time is a clock in term in
terms of relativity let's look at this a
little more detail jump in a spaceship
and fly away at near light speed you're
the one flying away now at near light
speed how you do that well that's
technology we don't have but let's
assume let's be sci-fi enough that you
figured out how to do it you would see
time moving slowly on earth you would
measure clocks on earth moving
slowly you would see your family members
aging slowly on earth talking slowly
aging slowly if you can measure their
thought patterns you would measure them
thinking slowly likewise this is
symmetric remember in your point of view
earth is going backward at near light
speed but from Earth's point of year
you're zooming off at near light speed
so earth and the rest of the universe
will see your clock slowing down they
will see you talking slowly breathing
slowly thinking slowly aging slowly why
is that in order to understand this
einstein said let's make the simplest
clock that we possibly can
let's imagine my sign was great about
thought experiments let's do a thought
experiment let's imagine the simplest
possible clock a light clock photons
bouncing up and down with a sink with a
simple frequency Oh awesome
so you're in a spaceship doesn't matter
how fast you are moving from your point
of view
you are standing still well you're not
accelerating now remember we're dealing
with inertial reference frames
you are not accelerating moving in a
straight line with constant speed which
means from your own reference frame from
your own point of view you're standing
still so this clock moves up and down
with a certain frequency
bum-bum-bum all right cool but the
people on earth who are also listening
to your clock who are also taking a
signal from your clock every time it
bounces listening to the bump bump they
from their point of view the photon has
a longer distance through which to
travel which means that clock is going
to have a lower frequency so instead of
in your point of view it's gonna go bump
bomb from Earth point of view it's gonna
go bomb it's gonna take longer for for
those to tip for the tick-tock
to tick for the tick to talking to talk
to tick tick tock tick tock we'll take
longer in fact everything that happens
on the ship will take longer from the
girl farting it doesn't matter
everything will take longer as viewed
from Earth as it does than it does as
viewed from inside the spaceship
so earth will see the spaceships clock
moving more slowly so let's watch a
youtube video and I want to be clear on
this we are watching a YouTube video
inside a YouTube video that's great if
you want the link to this video I'm
assuming that it won't just show up but
rather you can oh well put it the
description oh you can do that yeah I'm
learning I'm learning technology to
spaceships are traveling together
through the galaxy at close to the speed
of light mounted on one ship is a laser
that can fire pulses of light and on the
other a mirror the pilot of the first
ship fires a pulse at the mirror and
watches as it is reflected back a clock
on board measures how long the
round-trip takes but now suppose that he
does this as the ships are passing an
observer on a nearby asteroid according
to relativity theory this observer sees
the pulse moving through space at
exactly the same speed that the pilot
does namely the speed of light but he
also sees the pulse traveling a longer
distance because from his perspective he
must add the forward motion of the ships
to the motion of the pulse between them
so he measures a longer time interval
for this round-trip than the pilot does
because he's watching the pulse go
farther without going any faster this
effect is called time dilation if two
observers are moving with respect to one
another each perceives that the other's
time is flowing more slowly
all righty then let's continue alright
so there's time dilation now what about
length contraction so if one observer
sees another flying at nearly light
speed then they're seeing each other
moving at nearly light speed if I see
you moving forward at nearly light speed
you see moving the other direction each
one of us will see the others clock run
slow each one will see the others time
moving slowly so what about distances
well
distances have to give because each
observer sees the other moving at the
same speed right if you see me moving
this way at half light speed then I'm
gonna see you moving the other way at
half light speed same speed though but
we each see the other's time moving more
slowly and distance equals speed times
times so we each see the other's
reference frame shrink we see the
other's time moving slowly and we see
the other's reference frame shrinking in
other words if a ship moves flies by it
nearly the speed of light we see it
smushed we see it smaller than it was
that's smaller than it is in its rest
frame in the captains frame of reference
so if you leave earth and move at nearly
light speed with respect to earth and
practically everything else around you
then a couple of strange things will
happen time around you will move more
slowly and everyone on earth will see
your time moving more slowly but also
you will see the whole universe shrink
and the universe will see your ship
shrink alright well let's let's talk
about what might be a paradox here this
is called the twin paradox
all right supposing you and I are twins
cool I get on a spaceship and fly away
at nearly the speed of light almost the
speed of light we're talking point nine
nine nine nine nine nine nine nine nine
nine times the speed of light and I go
to the nearest star Proxima Centauri
get up get off look around hey that's
cool I'm gonna get back on my spaceship
and come back to earth at nearly the
speed of light point nein nein nein nein
nein nein nein nein nein nein nein nein
nein nein nein the speed of light cool
what will happen when I get there well I
see I mean according to you on earth my
I aged slowly but according to me you
aged slowly so who did it who's older
you were me which twin is older and the
answer is sorry wrong theory relativity
does not apply in this case special
relativity does not apply in this case
why is that remember special relativity
only works with inertial reference frame
that means there's no acceleration well
in the example I'm the one who
accelerated I'm the one who got in the
ship and jumped to nearly light speed
slowed down looked around sped back up
again and then slowed down and came back
to earth so while I was in flight yes
there was a cemetery there I saw you
moving slowly you saw me moving slowly
but while I was accelerating that
symmetry was broken and the real answer
is you the person who stayed on Earth
will be much much much much much much
older in fact you may be dead and gone
generations may be dead and gone it I
may come back to earth ten thousand
years later even though I was only in
transit for eight years oh well here's
here's the answer
so in order to take acceleration into
account we can't use special relativity
we must use general relativity remember
special relativity is a special case of
general relativity where nobody's
accelerating and there's not a lot of
gravity not not a strong gravitational
feel around Oh Earth's gravity doesn't
count even the Sun's gravity isn't much
really strong gravity would be like a
black hole an object in space with so
much gravity and cold space and time
with it as it spins and from its grasp
nothing can escape not even light
that's where general relativity really
shines so that's the spoiler alert when
the traveler returns to earth
the person who remained on earth will be
older and perhaps much older perhaps
dead and gone all right well I don't
know we can't really do we can't really
do call-and-response
like we do in class but hell let's do
it anyway when I say physics you say
rocks. physics! (did you do it?) (come on, dooo itttt) repeat after: me when you
approach the speed of light (dooo ittt) Newton's
laws are no longer right you see earth
time running slow an earth sees your
time running slow you see the universe
smushed and the universe sees you
smushed but all seems a bit crazy
you can blame Einstein's theory of
special relativity physics rocks all
right thank you so much for your
patience this is hard for us all I hope
this video helped you and please let me
know any questions you have in the
comments would probably be the best I
mean you can email me questions but if
they're questions that involve the
material please do it in a public way so
that everyone else
can have the benefit of here seeing the
answer if you have a question believe me
dozens of other people do - you're not
stupid
physics is hard
