# Why does the expanding universe redshift light?

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• tovisonnenberg
In summary, the expansion of space causes light to lose energy due to the cosmological redshift. This is because the wavelength of the light increases as the universe expands, resulting in a decrease in frequency. However, energy is not an inherent property of light and is relative to a chosen frame of reference. This can lead to different interpretations of cosmological redshift, including Doppler shifts and the scale factor in the Robertson-Walker metric. It is important to note that inflation, which occurred before the release of the Cosmic Microwave Background (CMB), has no effect on CMB wavelength.

#### tovisonnenberg

How does the expansion of space cause light to lose energy?

Wikipedia has a good article on redshift. Could you narrow the question down so that someone can recognize which part is confusing?

You can look at waves in a puddle, pond, or a large bucket. The frequency of the waves is the number of times per second that the wave peaks reach a point. Suppose your "point" is moving, maybe like a fly above a pond. When the fly flies toward the location where a pebble created the waves it will pass more peaks per second. If the fly is flying away from the splash it will pass fewer peaks per second. The frequency measured from the fly's perspective changes when the relative velocity of the source changes.

The light has not really changed energy. If someone throws a baseball from the back of moving pickup truck it will not be going very fast when you catch it. It would hit your glove hard if they threw it forwards and you caught it. The pitcher throws the ball with the same energy/momentum each time. It is only the measurement from your perspective that changes with each pitch.

stefan r said:
The light has not really changed energy.
That is not correct. In an expanding universe light emitted from a cosmologically remote point DOES lose energy as it travels and is red-shifted more and more, and loses energy more and more, as the point of reception is farther and farther away. There is no conservation of energy on cosmological scales.

PeroK
First of all, you should be aware of the fact that energy is not something inherent of the light itself. It only has an energy relative to some chosen frame of reference. Redshift is the shift in the observed frequency relative to that frequency that would be observed by the emitter. That being said, one usually looks at comoving observers in cosmology and there are several different, equivalent, interpretations of cosmological redshift. They may sound different, but it is all a question of what coordinates you use to describe things. To just name a couple:
• You can see nearby comoving observers as moving relative to each other locally on scales so small that everything looks like Minkowski space. In that sense, the cosmological redshift is an accumulation of Doppler shifts as the light passes from one comoving observer to the next.
• You can look at the scale factor ##a(t)## in the Robertson-Walker metric, which describes the overall scale of the homogenous and isotropic spatial slices of the universe. In this description, as ##a(t)## grows, the wavelength of the light relative to the comoving observers grows and therefore the frequency that they would observe would be decreasing.

phinds said:
That is not correct. In an expanding universe light emitted from a cosmologically remote point DOES lose energy as it travels and is red-shifted more and more, and loses energy more and more, as the point of reception is farther and farther away. There is no conservation of energy on cosmological scales.
Just to be clear, this refers specifically to the energy relative to comoving observers, an assumption that is not always stated explicitly. Energy is not an inherent property of a light signal by itself (the stress-energy tensor is). In that sense, the light has not changed energy, because energy is not a property inherently associated to it.

stefan r said:
If someone throws a baseball from the back of moving pickup truck it will not be going very fast when you catch it. It would hit your glove hard if they threw it forwards and you caught it. The pitcher throws the ball with the same energy/momentum each time. It is only the measurement from your perspective that changes with each pitch.
This is missing a qualifying statement. The baseball does not have an inherent energy and momentum either - it only has a particular energy and momentum given some fixed frame. As we all know, energy and momentum are not Galilei invariant. They will take different values in different inertial frames and no frame can be said to be preferred over another.

stefan r and PeroK
Orodruin said:
Just to be clear, this refers specifically to the energy relative to comoving observers, an assumption that is not always stated explicitly. Energy is not an inherent property of a light signal by itself (the stress-energy tensor is). In that sense, the light has not changed energy, because energy is not a property inherently associated to it.
Good point. Thank you for that clarification.

So, inflation itself has zero effect on (for example) CMB wavelength and it's shift to microwave can be explained only by evaluating frames of reference?

Ilythiiri said:
So, inflation itself has zero effect on (for example) CMB wavelength
Inflation has no effect on CMB wavelength because it happened before the CMB was released. Do not confuse inflation with expansion. Expansion is the scale of the universe increasing with time, inflation is a hypothetical period of rapid expansion in the very beginning of the universe, before CMB, before nucleosynthesis, intended to explain (among other things) why the universe is so homogeneous.

Also, do not misjudge the effect of expansion on the CMB redshift. What you have to realize is that in GR the "cause" of some effect may be described differently in different coordinates (this is true in SR too). I am not sure what you mean by "evaluating frames of reference". That is not something that one does. What I said was that you can split the redshift into several small step where every step can be described as a Doppler shift between comoving observers. What defines comoving observers is still something that depends on the overall geometry of the spacetime, which is preferentially given in Robertson-Walker coordinates and the coordinate independent statement is that a light signal from one comoving observer to the another will be redshifted if the scale factor at the receiving event is larger (and vice versa). The coordinate-independent maths behind it can be boiled down to comparing the emitter 4-velocity with the 4-frequency of the light to the receiver 4-velocity with the 4-frequency of the light under the knowledge that the 4-frequency is parallel transported along the light world-line. I described this in a technical PF Insight (at A-level) some time ago.

## 1. What is redshift in the context of the expanding universe?

In the context of the expanding universe, redshift refers to the phenomenon where light from distant galaxies appears to have longer wavelengths, shifting towards the red end of the visible light spectrum. This is due to the stretching of space caused by the expansion of the universe, causing the light to appear to have longer wavelengths.

## 2. Why does the expanding universe cause redshift?

The expanding universe causes redshift because as space expands, it stretches the wavelengths of light that travel through it. This stretching of wavelengths is known as cosmological redshift. The farther a galaxy is from us, the more space has expanded and the more redshifted its light will appear.

## 3. How is redshift used to measure the expansion of the universe?

Redshift is used to measure the expansion of the universe by observing the redshift of light from distant galaxies and using that information to calculate the distance of those galaxies. By measuring the redshift and distance of many galaxies, scientists can plot a graph of the relationship between redshift and distance, known as the Hubble diagram, which can be used to determine the rate of expansion of the universe.

## 4. Can redshift also be caused by other factors?

Yes, redshift can also be caused by other factors such as the relative motion of the light source and the observer. This is known as Doppler redshift and is caused by the motion of an object towards or away from us. However, for objects at very large distances, cosmological redshift is the dominant factor.

## 5. What implications does redshift have for the fate of the universe?

Redshift has significant implications for the fate of the universe. The observation of redshift in the light from distant galaxies led to the discovery of the expanding universe, which in turn led to the theory of the Big Bang. Redshift also provides evidence for the accelerating expansion of the universe, which suggests that the universe will continue to expand indefinitely and may result in a "Big Freeze" or "Heat Death" scenario.