Quantum Mechanics and General Relativity Astronomy 315 Professor Lee Carkner Special Lecture

Exercise #20 AGN  Energy due to dropping Earth down black hole   m = 5.97X10 24 kg  E = (0.1)(5.97X10 24 )(3X10 8 ) 2 =  Quasar luminosity of W (J/s)  (10 40 J/s)(60 s/min) =  How many Earths per minute to power the quasar?  (6X10 41 )/(5.37X10 40 ) =

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 20 th 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