Shulou(Shulou.com)11/24 Report--

When it comes to the measurement of length, we are no stranger. Everything from rulers to lasers can be a tool for us to measure distance. American Apollo astronauts placed reflectors on the moon when they landed on the moon, and ground workers obtained the distance between the earth and the moon through the time of laser return. However, humans have not yet landed on other planets, and no matter how far away they are, they will not be able to measure distance through lasers. However, the use of light for ranging is still the main method of measuring the universe.

Figure 1 | the scale of the laser reflector on the moon is too large in the universe. Because of the limitation of the speed of light, the measurement of distance in the universe is different from that measured by a ruler on Earth. Before we understand the method of measuring the size of the universe, we need to discuss the basic principles of measuring distance in the universe.

In a relatively small range of space, such as the earth-moon system, we can get the distance by using a simple formula of time and velocity, but space is not the same as a small space.

1. Isn't distance / speed of light equal to time? First, we assume that there is a newly born galaxy in space, located at position B, about 1 billion light-years away from Earth; the first light emitted at the birth of the galaxy flies to Earth at point B. Assuming that both the earth and the galaxy are at rest, it is obvious that the flight time of this beam of light is: time of flight = distance / speed of light. As a result, it takes 1 billion years for this light to fly from point B of the galaxy to Earth.

But the space in the universe is not static, but expanding. According to the discovery of Hubble's law, we know that the receding speed of galaxies far away from Earth is proportional to their distance from Earth. In other words, the farther away the galaxy is, the faster it seems to us to be away from us.

Figure 2 | the universe that has been expanding since the Big Bang because the expansion of the universe has led to the expansion of space, making galaxies far away from us moving faster relative to Earth. In this process, the spread of light from distant galaxies to Earth will also be affected by the expansion of the universe. Therefore, we must consider the influence of cosmic expansion on the time of light propagation.

If we want to calculate the time it takes for light to reach Earth from a galaxy 100 million light-years away, we need to consider the impact of cosmic expansion on light propagation. In this case, we need to use more complex cosmological models to calculate the exact time.

Therefore, even if the Earth and the galaxy remain stationary, the distance between them will gradually increase as space expands. This means that after 1 billion years, light has actually reached only where the earth was originally located. In the meantime, however, the earth has moved to position C. Light continues to chase the earth until D catches up with it at some point. At the same time, the galaxy reached point E due to the expansion and regression of space.

2. light travel distance at this time we found a problem, and there are two distances in this model:

(1) the distance of light flight D1

(2) the actual distance D2 between the two

Assuming that the retrogressive distance of the galaxy during this period is D, then there are:

Actual distance D2 = distance of light flight D1 + retrogression distance D

Taking into account the expansion of the universe, the distance D1 will actually be smaller than the linear distance between galaxy B and Earth D. BD. We can express this missing distance as Δ d. In addition, we can mark the distance from galaxy B to Earth's original position An as d0. , there are:

The distance of light travel can directly express the time experienced by light propagation. The value of the distance of light is equal to the time elapsed between the emission of light and the present. For example, if the distance of light is 1.5 billion light-years (1.5 billion light-years), then the beam of light was emitted 1.5 billion years ago.

In general, the distance mentioned in the news report, if not specified, usually refers to the distance of light travel. Therefore, light distance is also one of the most common concepts of distance in our daily life.

By using the distance of light, we can more easily understand and compare the temporal and spatial relationships between different celestial bodies, galaxies and cosmic events. This method of measurement is widely used in astronomy and cosmology to help us understand the evolution of the universe and measure the distance between distant celestial bodies.

Then there is the actual distance between the two, that is, the DE distance, which we call the inherent distance (dP). The inherent distance is changing all the time, and its physical meaning is the real distance between the two.

Therefore, the inherent distance is a dependent variable related to time; for example, the distance between AB is the inherent distance between the two at the time when light is emitted, and the distance between DE is the inherent distance when the earth receives light, and the inherent distance generally increases with time (remember the expansion of the universe? ).

A constantly changing inherent distance obviously brings a lot of trouble to astronomical research. for the convenience of research, astronomers have defined the concept of "common motion distance" (dC:comoving distance) and established a "co-motion coordinate system". The so-called co-motion distance is to take the inherent distance between galaxies at the current moment as the standard, and then how the universe expands and how the inherent distance changes, and the co-motion distance remains unchanged, which eliminates the distance result that does not expand with space.

The definition of common motion distance is as follows:

Taking the above example as an assumption, if we measure the inherent distance DE=1.5bly between the earth and the galaxy at this time, the common distance between the two is 1.5bly; no matter how long it takes and how the inherent distance changes, the common distance between the two is defined as 1.5bly.

Thus it can be seen that the common motion distance is a defined distance; for a particular celestial body, its value is determined, only the coordinate system changes, and the coordinate system is lengthened with the expansion of the universe, so the measured distance remains the same.

Figure 3 | the relationship between redshift and common distance: the vertical axis is the distance value (which can also represent time), in units of one billion light-years; the horizontal axis is the redshift value. 3. Measuring the size of the universe after introducing the definition of various distances in the universe, we can begin to talk about the measurement of the size of the observable universe.

Going back to the original model, galaxies emit light to Earth, and there is a receding speed between the two, so there are three situations:

(1) if the retrogression speed of the earth is less than the speed of light, the light will catch up with the earth at point D.

(2) if the receding speed of the earth is equal to the speed of light, the light will always keep a certain distance from the earth for a limited time.

(3) if the receding speed of the earth is greater than the speed of light, the distance between them will be farther and farther apart and they will never catch up.

From Hubble's law, we know that the relative velocity between the earth and galaxies is related to the inherent distance between the two. When the inherent distance reaches a certain size, the relative velocity will be equal to the speed of light, which is the radius of the observable universe.

Therefore, we can assume that the radius of the observable universe is R, and the retrogression velocity between the earth and the galaxy is Vf, and the speed of light is c, then we can make the retrogression velocity Vf = c; this equation means that when the inherent distance reaches the radius of the observable universe, the relative velocity between the earth and the galaxy is equal to the speed of light. This means that these galaxies are moving away from us at the same speed as the speed of light, and galaxies beyond that distance will move away from us at a faster speed.

Because Vf = c; and the receding velocity Vf is related to the radius of the observable universe R, we can get the following relationship

Among them, H0 represents the Hubble constant, which describes the rate of expansion of the universe, that is, the farther away the object in the universe is from us, the faster it recedes. When H0 = 67.8km/s/Mpc, R = 14.4bly, that is, 14.4 billion light-years.

But no, didn't scientists say that the radius of the observable universe is not 46.5 billion light-years? Why is it 14.4 billion light-years?

Looking closely at the formula of Hubble's law, we find that the calculated R is actually the inherent distance when light is emitted, not the inherent distance when we receive light. Or is it because the expansion of the universe has caused the inherent distance to change, and by the time the light from 14.4 billion light-years away reaches our position, the universe will have expanded a lot; so how to calculate this number?

Suppose r is the radius of the observable universe, there are:

Where z is the redshift, which is calculated as follows:

Suppose the inherent distance dP = 13.7bly (which is related to the age of our universe), and substitute the above formula to calculate r = 46.5bly, which is the current radius of the observable universe: 46.5 billion light-years.

Today's universe is only 13.7 billion years old, so in the inherent distance of 14.4 billion light-years, light from 13.7 billion light-years away has not yet reached the earth, so let dP = 13.7bly. With the increase of time, the remaining light slowly reaches the earth, and the dP will gradually tend to 14.4bly. When dP = 14.4bly, r = 63.0bly.

As a result, the radius of the observable universe will continue to increase and approach 63 billion light-years, which is the maximum radius of the observable universe.

This article is from the official account of Wechat: stone popular Science Studio (ID:Dr__Stone), author: Tianyin

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