Redshift and Hubble's Law Show an Expanding Universe
Nova floats at the center of a holographic sphere of galaxies, each pair connected by bidirectional arrows showing mutual recession in every direction at once; a glowing balloon-surface inset in the corner shows evenly spaced dots drifting apart uniformly with no central dot, while spectral strips of stretched red starlight scroll across Nova's data visor.
- Explain how the redshift of a galaxy's light spectrum indicates that space expanded while the photon traveled toward Earth.
- Identify the relationship between a galaxy's distance and its recessional velocity as described by Hubble's Law.
- Compare the spectra of nearby and distant galaxies to infer how the degree of redshift changes with distance.
- Calculate recessional velocity using Hubble's Law given a galaxy's distance and the Hubble constant.
- Argue from spectroscopic evidence why uniform, centerless expansion of space best explains the observed pattern of redshifts.
Key terms
- Cosmological redshift
- The lengthening of a photon's wavelength caused by space expanding during its journey, not by motion through static space.
- Hubble's Law
- The relation v = H₀d, in which a galaxy's recessional velocity is proportional to its distance from the observer.
- Hubble constant
- The present-day expansion rate H₀, approximately 70 km/s per megaparsec, relating recession speed to distance.
- Hubble time
- The reciprocal of the Hubble constant, 1/H₀ ≈ 14 billion years, a characteristic timescale distinct from the universe's true age.
Stretching Space, Not Motion Through It
Cosmological redshift superficially resembles the Doppler effect, but its mechanism differs fundamentally. The galaxy is not racing through space like a siren; rather, the space between us and the galaxy expands while the photon is in flight, so the photon's wavelength stretches along with that space. By the time it reaches the telescope, its wavelength is longer and redder. This distinction matters because it explains why even galaxies with no peculiar motion still show redshift proportional to distance: greater distance means more expanding space crossed and thus more stretching.
A Centerless Expansion
Hubble's clean v = H₀d relation might suggest we sit at a special center, but the balloon analogy dispels that. On the surface of an inflating balloon, every dot recedes from every other dot, and more distant dots separate faster, yet no dot is the center of expansion. Likewise, an observer in any galaxy would measure the same Hubble relationship in every direction. The expansion has no privileged location; it is a uniform property of space itself, which is precisely why the same law holds for all observers.
Worked examples
Find the recessional velocity of a galaxy 600 Mpc away using H₀ = 70 km/s/Mpc.
- Write Hubble's Law: v = H₀ × d.
- Substitute the values: v = 70 km/s/Mpc × 600 Mpc.
- Multiply, canceling Mpc: v = 42,000 km/s.
Answer: 42,000 km/s — a galaxy at 200 Mpc would recede at only 14,000 km/s, confirming velocity is proportional to distance.
Activity
Match each galaxy's spectral strip to its correct distance category by dragging the spectra onto the distance scale, then rank them from slowest to fastest recessional velocity.
Practice
A galaxy lies 350 Mpc away. Calculate its recessional velocity with H₀ = 70 km/s/Mpc and state how it would change if the distance doubled.
Refute the claim that observed redshifts prove Earth sits at the center of the universe, using the property of uniform centerless expansion.
Common mistakes to avoid
- Cosmological redshift is galaxies moving through space.It is space itself expanding and stretching the photon's wavelength in transit, not the galaxy traveling through static space.
- Redshift proves Earth is the center of expansion.Every observer in any galaxy sees the same Hubble relationship in all directions, so no location is special or central.
Check your understanding
A galaxy's spectrum shows its calcium absorption lines shifted from their lab wavelength of 393 nm to 432 nm. What does this observation most directly indicate?
Galaxy X is 200 Mpc away; Galaxy Y is 600 Mpc away. Using H₀ = 70 km/s/Mpc, what is the recessional velocity of Galaxy Y?
A student argues that the observed redshifts prove Earth is at the center of the universe because all galaxies appear to move away from us. Which response best refutes this claim?
Cosmological redshift differs from the classical Doppler effect in an important way. Which statement correctly describes this difference?
Recap
Redshift in galaxy spectra reveals that space expanded while light traveled to us, and Hubble's Law v = H₀d shows recession velocity rising with distance; the expansion is uniform and centerless, making the Hubble time a rough but distinct cousin of the universe's true age.
Reflect
Why is it so counterintuitive yet important that the universe can expand uniformly without having any center at all?