Those of us who are new to the universe are likely to wonder why two basic truisms seem to contradict each other: the universe is 13.8 billion years old, but the diameter of the universe is 93 billion light-years, and isn't it true that no object travels faster than the speed of light?

 

According to the understanding of this understanding, from the Big Bang all the way up to the present 13.8 billion years, astronomers must have found evidence, such as photons of light produced by the Big Bang, that have finally been captured by us after a long flight of 13.8 billion years. (It would be like archaeologists finding fossils of Tyrannosaurus Rex and thus determining that they had lived 60 million years ago.)

 

But this is actually caused by the expansion of the universe, for example: you walk on an escalator in a shopping mall, your speed is 1m/s, but to an observer who is stationary relative to the ground, your speed is greater than 1m/s, because you are moving and so is the escalator. By the same token, a photon representing the age of the universe is able to span 46.5 billion light years, despite a flight time of 13.8 billion years.

 

But then the question arises, isn't this considerably faster than the speed of light? And how is the expansion of the universe measured?

 

Let's start with the size of the universe, usually referred to as 93 billion light years, the diameter of the observable universe.

 

What is the observable universe again? Simply put, it is the extent of the universe that can be observed with the observer at the center. By implication, the observable universe is only a part of the larger universe. On the large scale of the universe, the scope of the observable universe varies from observer to observer. Taking us as an example, the current observable universe of human beings is actually a sphere: a super, super, super, super sphere with a radius of 46.5 billion light-years. What's outside the sphere? It's actually still part of the larger universe, but we just don't have the ability to observe it yet.

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And where does this currently known radius come from?

Actually, it's not that we've observed a star 46.5 billion light-years away from Earth. The farthest star currently observed by humans is GN-z11, which is 13.4 billion years old and 32 billion light-years away.

 

Measuring the radius of the observable universe is actually done by determining the redshift of the CMBR (Cosmic Microwave Background Radiation) particles and getting the co-moving distance, which is about 46.5 billion light years.

 

Wait, what about redshift and co-movement distance?

 

There are three types of distances often used in cosmology: the light travel distance, the intrinsic distance, and the co-moving distance.

 

Light travel distance is best understood by the general public as a measure of distance in terms of the time it takes light to travel. A prerequisite for light travel distance is that it does not take into account the expansion of the universe. For ease of use, light travel distance derives from light travel time: the time it takes for light to travel this distance, sometimes called back time. Indeed, the age of the universe, 13.8 billion years, can also be said to be light travel time, or back time is 13.8 billion years.

 

As another example, when we say that the stars of Altair are 16 light years apart, we mean that the distance between them requires 16 years of light flight, 16 light years of light travel distance, and 16 years of light travel time/return time.

But if we consider the expansion of the universe, the previously mentioned observation of the farthest galaxy - 32 billion light-years away from us - is in fact not so simple. This is because the entire universe is constantly expanding during this time of 32 billion years of light travel. So, to determine the true distance of stars, you also need to consider how much has the universe actually expanded over such a long period of time?

 

The expansion of the universe is like blowing up a balloon. Point two dots on a deflated balloon and blow on it, and you'll find the dots getting farther and farther apart.

 

A co-moving distance is one that co-moves with the expansion of the universe, and the distance measured by this imaginary measuring tape is the co-moving distance. This means that what is measured is still the pre-inflation value, so the co-moving distance is a fixed value. The radius of the observable universe is 46.5 billion light years, which would be the co-moving distance.

 

Although the intrinsic distance is practically impossible to measure directly, it is a concept that comes closest to the real distance in the eyes of astronomers. So, scientists found an alternative, which is the amount of redshift. The so-called redshift is the phenomenon that the wavelength of photon radiation, which is stretched out with the expansion of the universe, moves from the short waves of the blue color of the spectrum to the long waves of the red color, thus creating the phenomenon of redshift. Redshift = (observed wavelength - true wavelength) / true wavelength.

 

Keep in mind that redshift is the only measurement that we can specify when we talk about cosmic scales and stellar distances, while other things such as light travel distance, co-moving distance, and retracement time are all derived quantities. As for how these quantities are converted to each other, there are a bunch of mathematical formulas to be involved, so it's better to skim over that. The simplest and most useful thing for us is a comparison table.