quantum mechanics and general relativity astronomy 315 professor lee carkner special lecture
Post on 22-Dec-2015
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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 old-fashioned 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