Download Gravity in Einstein`s Universe

Einstein’s
Universe
Dr Martin Hendry
Dept of Physics and Astronomy,
University of Glasgow
Isaac Newton
Albert Einstein
Isaac Newton
Albert Einstein
Isaac Newton
Galileo Galilei
How do things move?….
Aristotle’s Theory:
1. Objects move only as
long as we apply a
force to them
2. Falling bodies fall at
a constant rate
3. Heavy bodies fall
faster than light ones
How do things move?….
v
Aristotle’s Theory:
Galileo’s Experiment:
1. Objects move only as
long as we apply a
force to them
2. Falling bodies fall at
a constant rate
3. Heavy bodies fall
faster than light ones
1. Objects keep moving
after we stop applying a
force (if no friction)
2. Falling bodies
accelerate as they fall
3. Heavy bodies fall at the
same rate as light ones
How do things move?….
Aristotle’s Theory:
Galileo’s Experiment:
1. Objects move only as
long as we apply a
force to them
2. Falling bodies fall at
a constant rate
3. Heavy bodies fall
faster than light ones
1. Objects keep moving
after we stop applying a
force (if no friction)
2. Falling bodies
accelerate as they fall
3. Heavy bodies fall at the
same rate as light ones
How do things move?….
v
Aristotle’s Theory:
Galileo’s Experiment:
1. Objects move only as
long as we apply a
force to them
2. Falling bodies fall at
a constant rate
3. Heavy bodies fall
faster than light ones
1. Objects keep moving
after we stop applying a
force (if no friction)
2. Falling bodies
accelerate as they fall
3. Heavy bodies fall at the
same rate as light ones
Apollo 15 astronaut David Scott
How do things move?….
Newton built on Galileo’s work
and proposed 3 laws of motion:
1. A body moves in a straight line
unless acted on by some force
How do things move?….
Newton built on Galileo’s work
and proposed 3 laws of motion:
1. A body moves in a straight line
unless acted on by some force
2. The acceleration of a body is
proportional to the force on it
F = ma
How do things move?….
Newton built on Galileo’s work
and proposed 3 laws of motion:
1. A body moves in a straight line
unless acted on by some force
2. The acceleration of a body is
proportional to the force on it
F = ma
3. To every action there is an equal
and opposite reaction
Isaac Newton:
1642 – 1727 AD
The Principia: 1684 - 1686
Moon’s orbit
Newton worked out
that the Moon feels a
‘circular’ force which
balances gravity
Earth
Classical Physics:
“All the World’s A Stage”
Newton’s physics assumes absolute
space and time.
Working out how things look to
different observers follows simple
rules, in different reference frames
Classical Physics:
“All the World’s A Stage”
Newton’s physics assumes absolute
space and time.
Working out how things look to
different observers follows simple
rules, in different reference frames
Classical Physics:
“All the World’s A Stage”
Newton’s physics assumes absolute
space and time.
Working out how things look to
different observers follows simple
rules, in different reference frames
Classical Physics:
“All the World’s A Stage”
Newton’s physics assumes absolute
space and time.
Working out how things look to
different observers follows simple
rules, in different reference frames
The laws of physics are the same
for everyone, everywhere!
Classical Physics:
Maxwell’s theory of light
Light is a wave – electromagnetic radiation
Classical Physics:
Maxwell’s theory of light
Light is a wave – electromagnetic radiation
Maxwell’s Equations imply
Speed of light = 300,000 km/s
Classical Physics:
Maxwell’s theory of light
Light is a wave – electromagnetic radiation
Maxwell’s Equations imply
Speed of light = 300,000 km/s
But how did light propagate?……
Through the Ether?…
Earth in January
Light from a
distant star
Sun
Earth in July
50mph
In Newton’s picture, the
relative speed of the two
trains is 50 + 50 = 100mph
50mph
50mph
50mph
Speed of light relative to the
ground faster than speed of
light relative to the train
Through the Ether?…
Light from
distant stars
Ether
drift
Michelson and Morley devised
an experiment to measure the
speed of light coming from
different directions
The Michelson and Morley
Experiment would try to
measure the “Ether Drift”
by timing different light
beams – like swimmers on
a fast-flowing river
River flow
The Michelson and Morley
Experiment would try to
measure the “Ether Drift”
by timing different light
beams – like swimmers on
a fast-flowing river
C
.
River flow
.
A
.
B
The Michelson and Morley
Experiment would try to
measure the “Ether Drift”
by timing different light
beams – like swimmers on
a fast-flowing river
C
.
River flow
They detected absolutely no Ether
Drift. Something weird was going on.
Light was not following Newton’s rules
.
A
.
B
Special Relativity: 1905
“Maxwell’s Equations of
Electromagnetism are the
same for all observers,
regardless of their
relative motion”
Special Relativity: 1905
Implies the speed of light
must be constant, measured
to be the same by any two
observers, regardless of
their relative motion”
There must be no ether,
and so no ether drift
Special Relativity: 1905
Implies the speed of light
must be constant, measured
to be the same by any two
observers, regardless of
their relative motion”
This abolished completely
Newton’s idea that space
and time were absolute
h
Train carriage
Let’s try to see why!
Torch beam
reflected off
roof of carriage
Train carriage
Let’s try to see why!
h
Distance = speed x time
Torch beam
reflected off
roof of carriage
Train carriage
h
Distance = speed x time
Torch beam
reflected off
roof of carriage
Train carriage
2h = c x tc
h
Now viewed from the platform…
Now viewed from the platform…
v
Now viewed from the platform…
v
Now viewed from the platform…
Now viewed from the platform…
Now viewed from the platform…
Now viewed from the platform…
Now viewed from the platform…
Now viewed from the platform…
Let’s call the time measured
on the platform tP
Now viewed from the platform…
Let’s call the time measured
on the platform tP
Now viewed from the platform…
Let’s call the time measured
on the platform tP
Now viewed from the platform…
v tP
The base of this triangle is v tP
Now viewed from the platform…
v tP
This is an isosceles triangle, so it’s made
up of two equal right angled triangles
Now viewed from the platform…
This is an isosceles triangle, so it’s made
up of two equal right angled triangles
Now viewed from the platform…
This is an isosceles triangle, so it’s made
up of two equal right angled triangles
Let’s look at this triangle.
What’s the length of its base?
1
2 v tP
Let’s look at this triangle.
What’s the length of its base?
1
2 v tP
What about its height?
h
Train carriage
h
1
2 v tP
What about its height?
h
1
Remember:
2 v tP
2h = c x tc
Distance = speed x time
Torch beam
reflected off
roof of carriage
Train carriage
2h = c x tc
h
1
2
c tc
1
Remember:
2 v tP
2h = c x tc
1
2
c tc
1
2 v tP
If both observers measure
the same speed of light, c…
Total distance
= c x tP
1
2
ctS
1
2
vtm
If both observers measure
the same speed of light, c…
1
1
c tc
2
1
c
t
P
2
2 v tP
If both observers measure
the same speed of light, c…
1
1
c tc
2
1
c
t
P
2
2 v tP
Using Pythagoras’ theorem,
(ctP)2
=
(vtP)2
+
(ctc)2
1
1
c tc
2
1
c
t
P
2
2 v tP
tc = tP ( 1
2
v
2
c)
It appears that time
is running more slowly
on the moving train!!
We need to think about
a unified spacetime
tc = tP ( 1
2
v
2
c)
Cosmic Ray
Muons
60km
Evidence for Time Dilation
Slow moving muons, would
never reach sea level…
but v = 0.999c, so muon
lifetime appears to us to
be greatly extended
Sea level
Einstein’s Relativity
300,000
1
kms
The speed of light is the
ultimate speed limit in
the Universe
Just as special relativity shows that space
and time are inextricably connected, so
too are energy and momentum
Just as special relativity shows that space
and time are inextricably connected, so
too are energy and momentum
Particles have a particular rest
mass, which is the mass you would
measure if the particle is at rest
Just as special relativity shows that space
and time are inextricably connected, so
too are energy and momentum
Particles have a particular rest
mass, which is the mass you would
measure if the particle is at rest
Mass and energy
are equivalent
E=
2
mc
Hydrogen fusion – fuelling a star’s nuclear furnace
H = Hydrogen
He = Helium
2
E = mc
Einstein’s Relativity
What about
accelerated
observers?
How does gravity
fit into this?
General Relativity: 1916
Isaac Newton:
1642 – 1727 AD
The Principia: 1684 - 1686
Moon’s orbit
But how does the
Moon know to
orbit the Earth?
How does gravity
act at a distance
across space?
Earth
Gravity in Einstein’s Universe
Gravity and
acceleration
are equivalent
Gravity is not a
force acting
through space and
time, but the result
of mass (and
energy) warping
spacetime itself
Einstein’s Relativity
Gravity in Einstein’s Universe
Matter causes
space
“Spacetime
tells matter
how
move,
to to
curve
orand
warp
matter tells spacetime
how to curve”
Gravity in Einstein’s Universe
v
Differences between Newton’s and
Einstein’s gravity predictions are tiny,
but can be detected in the Solar System
– and Einstein always wins!
Gravity in Einstein’s Universe
v
1. Precession of orbits –
observed for Mercury,
matching GR prediction
Gravity in Einstein’s
Matter causes space
to curve or warp
Universe
v
1. Precession of orbits –
observed for Mercury,
matching GR prediction
2. Bending of light close
to the Sun – visible
during total eclipse,
measured in 1919
Gravity in Einstein’s Universe
v
1. Precession of orbits –
observed for Mercury,
matching GR prediction
2. Bending of light close
to the Sun – visible
during total eclipse,
measured in 1919
Gravity in Einstein’s Universe
v
1. Precession of orbits –
observed for Mercury,
matching GR prediction
2. Bending of light close
to the Sun – visible
during total eclipse,
measured in 1919
Gravity in Einstein’s Universe
A ‘Black Hole’ warps spacetime so
much that even light can’t escape
Gravity in Einstein’s Universe
Close to a rotating black hole,
spacetime does very strange things:
Closed timelike loops are possible
Inside a black hole there may be a
wormhole which could allow Faster than
Light travel and communication
(but how do we open a wormhole?…)
Gravity in Einstein’s Universe
What is driving the cosmic acceleration?…
Einstein’s Greatest
Blunder?…
Could we use
To hold open wormholes?…
Well, it works in Star Trek DS9!!
Grand Unification Theories
“The generalisation
of the theory of
gravitation has
occupied me
unceasingly since
1916”
Einstein, 1952