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Quantum Mechanics and General
Relativity
Astronomy 315
Professor Lee Carkner
Special Lecture
Exercise #20 AGN
Energy due to dropping Earth down
black hole

m = 5.97X1024 kg
E = (0.1)(5.97X1024)(3X108)2 =
Quasar luminosity of 1040 W (J/s)
(1040 J/s)(60 s/min) =
How many Earths per minute to power
the quasar?
(6X1041)/(5.37X1040) =
Big and Small

Quantum mechanics

Atoms, electrons, photons, etc.
General relativity

Stars, galaxies, clusters, the universe, etc.
Problems
Each theory works well in its own realm

Like with a black hole

If you try to combine both theories, it doesn’t
work

Need a new “grand unified” theory that
reconciles them

Let us look at quantum mechanics and
general relativity to see where we are right
now
Quantum Hypothesis

 The only way he could do it is if he thought of the
emitted energy as being discrete instead of
continuous

 Like rain instead of a river
 In 1905 Einstein (and others) realized that this is a
fundamental rule

What does “Quantum” Mean?
Cannot have any value of the energy, only
multiples of the smallest quantum
Examples:

You can play any note on a guitar, but only
certain notes on a piano

For example, electrons can only be in certain
energy levels
Photons
The quantum of energy is called a photon

Each photon has as energy = hf

f is the frequency (in Hertz or 1/s)

We can think of light as stream of particles,
each with its own tiny amount of energy
Wave-Particle Duality

For example in diffraction experiments light
passing through a narrow slit makes patterns like
water waves passing through a narrow opening

It just does!

Light (and other sub-atomic particles) are their
own thing
de Broglie Wave

What about electron (and other) particles?

Every particle has a de Broglie wavelength that
depends on its mass and speed

but tiny particles (like electrons) have large
enough de Broglie wavelengths to act wavelike
Sub-atomic particles are not really particles (or waves)
they just sometimes act like it
The Jelly Bean Fallacy


“When the revolutionary ideas of quantum
physics were first coming out, people still
tried to understand them in terms of oldfashioned ideas … But at a certain point the
old-fashioned ideas would begin to fail, so a
warning was developed that said, in effect,
‘Your old-fashioned ideas are no damn good
…’ ”
-- Richard Feynman
The Bohr Model
 In the early 20th century atoms were understood by
the planetary model

 The electrons should have been able to have any orbit
and thus any energy, but in experiments it was found
they had specific energies

 Electrons can only have specific states defined by a quantum
number

 Explains line emission
Interaction

For example:

but light is photons, which have energy, which
will push on the particle

Also, the precision of our seeing is based on
the wavelength of light we use
but shorter wavelengths of light have more
energy and thus disturb the particle more
Uncertainty

We cannot know both the position of the
particle and the momentum of the particle
with the same accuracy

Called the Heisenburg Uncertainty Principle
We cannot have perfect information about the
universe!
Probability
In the 19th century the universe was thought
to be deterministic

We now know that the universe is
probabilistic

For example, we can’t tell where exactly an
electron is
but we know the probability it might be in one
place or another
The Stochastic Man

It doesn’t seem that way on our scale

Einstein famously said, “God does not
play dice with the universe.”
but he was wrong!
Quantum Tunneling
We can’t say exactly where an electron is

If we put the electron in a box, there is a high
probability it is in the box and a very (very) low
probability it is somewhere else

The electron could, in effect, tunnel through solid
material
This has been observed experimentally
The Quantum Universe

Not as macroscopic objects

For large particles and large numbers of
particles the statistics are so good that
everything seems deterministic
Similar to how a casino can make money
The Standard Model
Quantum mechanics only is important for very
small particles

Quarks
Six different types

best known hadrons are the proton and neutron
Leptons
Six different types

Gauge bosons
Carry the forces

Forces
There are 4 fundamental forces in the
universe
From strongest to weakest:
Strong nuclear force -Weak nuclear force --
Electromagnetism -Gravity --
Gravity
Gravity is by far the weakest of the four
forces

Most important force over large distances

However, our classical ideas about gravity
need to be replaced with Einstein’s general
relativity
Newtonian Gravity
We normally think of Newtonian
gravity
Put two masses together and they will
feel a force that will make them move
closer together

Einsteinian Gravity
Einstein proposed that mass causes spacetime
to curve

Like putting a bowling ball on a taut rubber sheet

The Sun’s mass makes a “bowl” in the center of
the solar system
The Earth has tangential velocity and so rolls
around and around in the “bowl”
Light and Gravity

Light is also affected by curved spacetime

This implies that spacetime is a real thing

Empty space is not really empty
QM and GR
General relativity is based on a smoothly
curving spacetime continuum

According to GR if we zoom in on a piece of
space it should be smooth unless a mass
distorts it

We need a new theory to reconcile these two
ideas
Next Time
Brian Greene talk tonight 7pm Olin
Auditorium
Also tomorrow at 10:30am in Sc 102
Sign in for extra credit
Hand in list 3 Friday
Quiz #3 Monday