Quantum Mechanics and General Relativity

Astronomy 315Professor Lee

CarknerSpecial 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 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

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