M20 Hubble's Law and the Big Bang

Scale of the Universe

In the 1920s, astronomers debated whether the Milky Way constituted the entire universe

Hubble and Scale of the Universe

Hubble resolved this by measuring Cepheid variable stars in the Andromeda Galaxy

• Proved they were external to the Milky Way

• Made the universe feel “uncomfortably large”

Tunhuang Manuscript

Ancient sky maps (e.g. Tunhuang Manuscript) show basically the same stars in the same positions we see today

• Seemed as though the cosmos didn’t change much from a human perspective

gives rise to the Steady State Model

Steady State Model

A model of the universe where there is no change or boundaries/change

• There was no beginning or end to the current universe

• The universe has always existed in its current form

Olber’s Problem

The Steady State Model proposes the universe is infinite in size and age

• Therefore, every line of sight should end at a star’s surface

• The night sky would be as bright as the Sun’s surface in every direction

but this is not the case

Olber’s Problem Analogy

The universe is a forest and the trees are individual stars

• If the forest is infinite, going in one direction will eventually come to a point where you hit a tree

• There are no empty gaps (i.e. dark space)

Hubble Observation

In the 1920s, Edwin Hubble observed that:

• The further away a distant galaxy is, the more its spectral lines are shifted to longer wavelengths (i.e. redshifted)

Nearby Individual Galaxies

This ‘redshifting phenomenon’ doesn’t apply to nearby galaxies which can be redshifted or blueshifted according to their individual motions toward or away from us

Hubble’s Law

A galaxy’s redshift (z) is directly proportional to its distance (d)

• on a Redshift vs Distance graph, this is a linear relationship

Hubble’s Law Equation

z = H_od

z = redshift of a galaxy

H_o = Hubble Constant

d = distance from Milky Way to the galaxy

Hubble’s Law Original Interpretation

Hubble and other astronomers initially interpreted redshifts as Doppler shifts

• Converted redshifts to recessional speeds (v) — or speed at which the galaxy is moving away from the Milky Way

Doppler Effect

Source moving away (e.g. ambulance flying past): Wavelengths are lengthened (redshifted)

Source coming towards you (e.g. ambulance coming towards you): Wavelengths are shortened (blueshifted)

Recessional Speed vs Distance

The original (incorrect) interpretation that redshifts are a result of galaxies moving away from us

• Plots Recessional Speed (v) as being directly proportional to Redshift (z)

Hubble’s Law Incorrect Equation

z = H_od = v/c

z = redshift of a galaxy

H_o = Hubble Constant

d = distance from Milky Way to the galaxy

v = recessional speed of galaxy

c = speed of light

Incorrect Equation Explanation

But why is the equation wrong?

• One clue is that we routinely measure objects with redshifts larger than 1

• If that were true, imagine an object with a redshift of 5

z = v/c

5 = v/c

5c = v

We now get a galaxy moving away at 5x the speed of light

• Violates special relativity for objects moving through space

however, we do find that much of the universe actually is moving away from us at more than the speed of light

Spacetime Expansion

In reality, galaxies are essentially at rest but the spacetime between them is expanding

• Special relativity is not violated: objects are not moving faster than c through space—rather, space itself is expanding faster than c

Bread Analogy

You can think of widely-separated galaxies as raisins in a loaf of raisin bread that rises and expands while it bakes.

• Each individual raisin is staying still relative to the dough around it, but as the dough expands, the raisins move apart.

Bread Analogy and Galaxy Speeds

In this model, more distant galaxies move faster away from us than closer ones (cause there’s more space expanding between them and us)

• The difference lies in how we interpret “motion”

Local vs Cosmic Motion

In the bread analogy, no raisin in the loaf is at the center of expansion

• Every raisin is being pushed away from every other raisin. In other words, there’s no common center

there is of course a center to the loaf, but the loaf is not expanding from that point specifically. it’s expanding because the yeast in the dough makes it expand from every point

No Center to the Expansion

Every observer in every galaxy measures the same Hubble’s Law

• In other words, everyone sees all other distant galaxies moving away from them

  • Everyone can consider themselves to be the center of the expansion OR say that there is no center

Expanding Earth Analogy

Think of the Earth’s surface being inflated like a balloon

• Every part expands equally. No singular city is the center of the expansion; each of them get farther apart from every other city

Hubble’s Law and Universe Expansion

Hubble’s Law tells us that the universe is expanding (i.e. getting bigger with time)

• If you “rewind” Hubble’s Law, you can come to the conclusion that the universe potentially had a beginning