#Redshift #CosmicExpansion #HubbleLaw #Astronomy #Universe #photons #Astrophysics #SpaceTime #Cosmology #Galaxies

Today, we’re going to discuss how cosmic redshift happens. This involves understanding the relationship between a galaxy’s speed of recession and the redshift of the light from that galaxy. We’ll delve into the mathematics behind it and the measurement principles.

The Basics of Redshift and Vibrating Atoms:
Atoms and molecules vibrate, and when they do, they create electromagnetic waves—photons. Imagine a proton vibrating; although it’s typically electrons that create these waves, the concept remains. When this charge moves, it creates a propagation disturbance—a photon. A photon is essentially a wave packet in the electromagnetic field.

Photon Characteristics and Wave Packets:
A photon has a beginning, middle, and end, forming a wave packet. The wavelength of a photon is the distance between successive wave crests within this packet. As the universe expands, these wave crests stretch, which is a tiny but cumulative effect over long distances.

Measuring Distance in Cosmic Time:
To measure cosmic distances, we use a metric describing a uniformly expanding (or contracting) universe that is isotropic and homogeneous. The key here is to simplify this metric by focusing on photons traveling directly towards us and assuming a flat universe.

Deriving the Redshift Equation:
Starting with the metric, we simplify it to focus on the scale factor, a(T), which changes over time. We sum up all contributions of time and distance from emission to observation, leading us to the integral expression of the scale factor. By focusing on the differences between successive wave crests, we derive an equation showing that the observed wavelength over the emitted wavelength equals the inverse ratio of the scale factors at those two times.

Linking Redshift to Hubble’s Law:
The redshift we observe is directly linked to the Hubble expansion. The redshift, z, is related to velocity via the speed of light. With this relationship, we can measure distances and velocities, linking back to Hubble’s Law, which states the universe is expanding.

Understanding the Scale Factor:
The redshift provides information about the scale factor of the universe. By defining the scale factor today as one, we simplify our calculations. This method helps in understanding cosmic distances and times based on redshift observations.

We now have a concrete way to measure the redshift of a galaxy by knowing its emitted and observed wavelengths, which then give us distances and velocities via Hubble’s Law. This understanding of redshift naturally arises from the expanding universe described by the Friedman-Robertson-Walker metric. Next time, we’ll explore further implications and applications of this knowledge. See you then!


Redshift: https://en.wikipedia.org/wiki/Redshift
Hubble's Law: https://en.wikipedia.org/wiki/Hubble%...
Cosmic Scale Factor: https://en.wikipedia.org/wiki/Scale_f...)
FLRW Metric: https://en.wikipedia.org/wiki/Friedma...