Physics, Lecture 21, 22: The Hubble Law,

• - absorption / emission lines are the "thumbprints" of elements
• - we measure the wavelengths while at rest ( at a lab on earth)
• - identify them in a celestial object, measure their shift from the "rest wavelength", and then we can calculate how fast the star is moving away from / towards us
• - ∆λ / λ = v / c - where v = speed of source, and c is the speed of light
• - depends on how fast the object is moving relative to the speed of light (speed gives shift. wont see shift if moving parallel)
• - whole thing is a shift to the blue or red end.

• - then their gravities would have had enough time that their mutual gravities would all be pulling on eachother --> galaxies would be moving randomly. (Each would have a 50/50 chance of moving either toward us or away from us)
• - spectrum observed from Doppler Shift Measurements show us that they are all moving away from us
• - Vesto Slipher (1912)

- using a cepheid variable

• - first truly useful standard candle - very bright stars
• - Henrietta Leavitt (1886 - 1921) - discovered 2,400
• - vary periodically (2-60 days) inbetween peaks of luminosity - pulsating variable stars
• - higher flux (more luminous)--> longer periods. Thus period is a function of the stars luminosity.
• *allows us to determine luminosity by measureing period. Then use inverse square law to determine distance

• - first: measure the distance to a bunch of Cepheids, calibrate their period-luminosity relationship (easier if all at same distance)
• - then measure the period and flux of a cepheid at an unknown distance. Using previous observations, you can get the luminosity from the observed period. And with flux you can get distance

- used by Hubble to discover the expansion of the universe

• - 1920's: measured the distance vs velocity of galaxies
• - the father away from us a Galaxy is, the faster it is moving

• - expansion rate of the universe (how much speed you gain the farther out you go)
• - about 71 km /s
• - implies that all galaxies were at some finite time in the past, all in the same exact place --> leads to big bang theory

• - not all galaxies come from the milky way
• - think of galaxies as being placed on a grid, called "space-time"
• - each cube on the grid gets larger, and so every galaxy moves away from every other galaxy (galaxies stay at the same coordinate on the grid, but the grid itself gets larger!)
• - galaxies which are much more distant from each other have higher relative velocities

- for all galaxies, the more distant they are, the faster they are moving away

• - No.
• - It is true that galaxies which are very far apart do have velocities determined by the hubble law
• - but galaxies which are very near each other have significant gravitational attraction --> changes their velocities relative to background hubble flow

- Perviously thought the universe is static and unchanging, infinite in size

- Now: Universe had a beginning: everything formed at 1 place, sometime in past. And everything evolved (universe is aging and evolving itself)

No.

Gravity is stronger than the force of expansion (small scale)

only notice expansion over very large distances, where force of gravity is weak in comarison

• - expansion is not an explosion
• - expansion of space --> happening everywhere
• - if there is a center (may not be), it would be in a higher dimension that we cant perceive (like the center of a balloon being the center of expansion for its 2-dimensional surface
• - can think of every point in the universe as the "center" of expansion, bc every point in the universe is expanding away from every other point
• - so you are the center of the universe, but so is your neighbor

• - no edge
• - if it is expanding into something (might not be) it would be a higher dimension we cant perceive (like 2D balloon expanding into 3D space)

• - may think of redshift as due to Doppler effece (ie motion) for simplicity
• - redshift is actually due to the wavelength of photons being stretched along with the expansion of the universe

- wavelength of protons do too --> REDDER!

• - photons that travel for a longer time (and distance) experience more expansion
• (bigger distance = bigger redshift)
• - further = faster!

• - distant galaxy emits a short-wavelength photon towards our galaxy
• - the expansion of space-time stretches the photon to a longer wavelength as it travels
• - the farther the photon has to travel, the more it is stretched
• - when the photon arrives at our galaxy, we see it with a longer wavelength - a redshift that is proportional to distance

• - smaller yesterday
• - smaller still the day before that, ect.
• - at some point it was at an infinitely small point --> THE UNIVERSE HAD A BEGINNING

We know how far apart galaxies are today (D - from standard candle) and how fast they are moving apart (V - from redshift)

• V = H₀D
• H₀ = 71+/- 4 km/s/Mpc (best measured value)

• So Duration = D/V = 1/H₀ = about 14 billion yrs.
• *not the exact age, b/c the rate of expansion wasn't always the same, but pretty close

• - smaller, denser, hotter
• - matter is diluted as the universe expands(but not dark matter) (not enough now to draw universe back together) but matter won at first
• - all from measure how fast galaxies are moving away from us, and how far they each are.

- redshifts (already tells the age and scale of the universe). Hubble constant tells you the distance

- if we dont know the distance to an object, we can infer its distance from its redshift

• Example: z = (WLobs-WL)/ WL= v/c
• Therefore: v = cz, D=v/H0
• If a Galaxy is moving 4000km/s away from us, if it is caught up in the Hubble flow, then it is a distance D=(4000 km/s)/ (74 km/s/Mpc) = 54 Mpc
• • Does this mean we can get distances from velocity only? NO! But, we can use the velocity as a distance indicator.

• Planck Era (10^-43 sec old) - we dont know
• Gut Era (10^-38 sec) - elementary particles? - sudden huge expansion of universe (Inflationary Epoch)
• Electroweak Era (10^-10 sec)- weak electromagnetic forces
• Particle Era (end .001 sec) - elementary particles - protons and neutrons, antimatter common. At end, matter annhialates antimatter
• Era of Nucleosynthesis (.001 sec - 3 min) - protons, neutrons, electrons. End of fusion - 3:1 Hydrogen:Helium
• Era of Nuclei (end 380,000 yrs) - plasma of hydrogen and helium nuclei plus electrons: nuclei move independently of electrons. - atoms form photons - they bounce rapidly from one electron to the next. At the end (recombination) temperature cools enough that the nuclei can capture finally forming neutral atoms. The universe becomes transparent: photons that were formerly trapped among electrons stream freely across universe. These photons are Cosmic Microwave Background Radiation
• Era of Atoms (end 1 billion yrs): atmos and plasma (stars begin to form) - end first galaxies form
• Gera of Galaxies -( end in present) - stars galaxies and clusters of galaxies (made of atoms and plasma)

• - random kinetic energy of an ensemble of particles and photons
• - decreased linearly since beginning of universe
• - about 2.726 K (but hot temps are only .00001 K higher than the cool temps)

(hot stove - kinetic energy is large enough (particles moving fast enough) to transfer energy to your fingers

• - Temperature of universe dropped below 3000K
• - cool enough that individual protons can capture free electrons - form neutron Hydrogen!
• - The first time neutral atoms formed in the universe

• Penzias and Wilson - 2 engineers working for Bell Laboratories (AT&T)
• They won the Nobel Prize in 1978

- photons arriving at Earth directly from the end of the era of nuclei (380,000 yrs after big bang). Because neutral atoms finally could remain stable, they captured most of the electrons in the universe. With no more free electrons to block them, the photons have flown unobstructed through the universe ever since

- Thus, when we observe the CMBR, we essentially are seeing back to a time when the universe was only 380,000 yrs old. --> light from the most distant regions of the observable universe

- surface of last scatter - analogous to light coming through the clouds to our eye on a cloudy day. we can only see the surface of the could where light was last scattered

• - time of recombination: universe cooled to below 3000K - that was 300,000 yrs after the Big Bang
• - if we look in 2 opposite directions in the sky (see a surface of the universe at time of recombination), light from both directions took about 13.7 billion yrs to get to us - they are outside causal contact, but they are both at almost exactly the same temperature

• - a short period of the universe when it expanded faster than the speed of light
• - explains how all parts of the universe are at the same temperature
• - size of ripple before inflation = size of atomic nucleus, size after = size of nucleus.