A brief history of Lambda, or why Ethan instills

In the next opus of Ethan Siegel, the phrase

After observing remote supernovae and measuring how the universe expanded for billions of years, astronomers discovered something surprising, mysterious and unexpected .

And no, the translation is all right, the original is even more yellow:

By observing distant supernovae and astronomers , it had

wat?

What kind of surprises are we talking about? After all, there is a completely elegant story 80 years long with bright discoveries and closings. The story is about how real science is actually done. History is more about physicists than about physics.

What is all the fuss about?

The first version of the General Theory of Relativity (GTR) Albert Einstein presented to the public on November 25, 1915. In the original equation of Einstein’s GR, it looked like this:


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or, in a modern record, like this:



For a reader who does not know the tensors, the equation (1) in the original Einstein record is more understandable. It says that the energy-momentum of matter G is equal to the curvature of space R plus the Ricci tensor S. (This Ricci tensor is also curvature, only in a more different form).
Now, when solving the GRT equation, the energy-momentum is usually considered known, and just the curvature is sought. Therefore, in modern writing, the sides of the equation are reversed. At the same time, the _letters were changed: G → T, S → R _μν .

Where did lambda go

One of the first serious mathematicians who began checking Einstein’s calculations was Eli Joseph Cartan (not to be confused with his son Henri, also a famous mathematician).
Cartan-papa found in Einstein a number of technical errors, in particular, one that the current generation of the Unified State Examination is known under the code name "to lose the constant when integrated." Today this lost constant is designated by the capital Greek letter lambda, Λ.

But physics is not math. Here you can not take the formula and add additional components to it just like that. You need to have very good reasons, both theoretical and experimental.

Although below you will see how little Einstein knew about the Universe in those years, but then, in 1916, he had such grounds. Albert Germanovich knew for sure that the stars did not fall on each other and are absolutely not going to do this in the foreseeable future. However, in GTR-1915 there was only an attraction that needed something to balance.

The lambda introduced into the equations was exactly responsible for repulsion. Therefore, in 1917, Einstein published a “supplemented and improved” version of GR with the cosmological constant Λ. In modern writing, the equation looks like this:

The first physical interpretation of the meaning of lambda

Take the equation of the GTR-1917 and put out of brackets the metric tensor . Then inside the brackets we will have the expression (R / 2 - Λ). Here R without indices is the usual, “school” scalar curvature. If on the fingers it is the number opposite to the radius of the circle / sphere. Flat space corresponds to R = 0.

In this interpretation, a nonzero value of Λ means that our Universe is curved by itself, including in the absence of any gravity. Well, this is how we got the world. However, most physicists do not believe this, and believe that the observed curvature should have some kind of internal reason. Some hitherto unknown garbage that can be opened.

Friedman's Universe

Meanwhile in Russia, despite the wars and revolutions, Ensign (and part-time professor) Alexander Alexandrovich Fridman fought over the theory of GR. He reviewed all the lambda options and found out the following:

When Λ <0, only the forces of attraction, both gravitational and caused by the curvature of the convex concave space, take place. Sooner or later, the stars and galaxies in such a world do fall on each other. And the end will be unexpectedly fast and very hot.

When Λ> 0, geometry steers at large distances, and the stars and galaxies fly away “from the slide” (Einstein's 1917 version). With a sufficiently large lambda, not a single star can remain in the sky at all except the Sun, with a moderate value - only our galaxy will remain, merging with its nearest neighbors.

But the most interesting thing happens when Λ = 0. Everything here depends on the initial conditions - i.e. coordinates and speeds of specific galaxies. Three options are possible: large compression, large expansion and stationary option, when galaxies fly away, but with relatively low speeds and without acceleration.

Today, the situations described above are called Friedmann cosmological solutions.

The articles of Friedman of 1922 and 1924 abolished the need for a member of the lambda, which was why Einstein was at first hostile.

For his work, Friedman could easily claim the Nobel Prize.


From the decisions of Friedman it followed that the universe could have a beginning. This idea was picked up by many physicists, and headed by what was later called the “Big Bang Theory”, the Russian-American Georgy Gamow, who believed Λ = 0.

And yes, an article by Ethan about an approximate schedule (specifically, the data for 2010 is taken into account):


Here, horizontally, z is plotted - this is the redshift, vertically, the observed brightness of supernovae of a special type Ia, which always release the same amount of energy. In general, these are two ways to measure the same distance, but, so to speak, at different points in time.

Gray sticks are observed events with their measurement error. The blue dotted line is the prediction at Λ = 0, the red line is the approximation of the actually observed values. The deviation of the red line from the straight line means that the universe is expanding rapidly. But Einstein never found out about it.

Captain's Universe

Let us turn to the experimental part.

Dutch astronomer Jacobus Cornelius Kapteyn discovered Kapteyn's star in 1897, after which he began opus magnum his whole life. Combining a huge number of observations of different observatories, he tried to create the first map of the universe. According to his map, the universe has the form of a rotating (sic!) Disk of a roofing lid at that time of 40,000 light-years, and the Sun is not at the center, but quite in the outskirts. This work was completed and published only in 1922.

To understand the level of knowledge of the time: what Captain considered to be an incredibly huge universe, today is considered quite ordinary, unremarkable among billions of the same ... Milky Way galaxy. Nevertheless, Kapteyn's merit is that he opened its rotation and approximately calculated its center.

Observations of Hubble (astronomer, not telescope)

If we talk about astronomers, then most of all for the history of lambda did Edwin Hubble. He felt that something was wrong with the nebulae, and in 1922 he suggested that some of them were not clouds of gas, but very distant objects. Testing his theory, in 1924 he was the first in the world to see individual stars in the Andromeda nebula (yes, he had been lucky all his life on very good telescopes. And after death, he continued to carry). It was Hubble who proposed the term “galaxy” - in fact, this is the “milky way” in Greek.

An article with its discoveries, from which it followed that the Universe is much larger than our Milky Way, was presented to the American astronomical society on January 1, 1925. For which he was booed by his hangover colleagues, who had barely gotten together with Captain.

Hubble did not let up and screwed the spectrometer to the telescope. Analyzing the redshift of galaxies, he found that galaxies are scattering, and the Universe, respectively, is expanding. At the same time, he discovered the law of the name of himself with the constant name of himself (however, the law was predicted by Lemaitre), and described all this in articles by the end of the 20s. According to his observations, the Friedmann model was true for Λ = 0.

It knocked out from under the lambda now and experimental grounds for its existence.

Einstein, looking at this, promptly struck out the cosmological constant of the equations of general relativity, and at the end of his life considered the history with the lambda "his biggest mistake."

So, besides all his discoveries, Hubble also unwittingly “closed” the lambda. As much as 70 years.

Here it is also necessary to mention that the initial estimates of Hubble were very much inaccurate and showed the age of the Universe about 2 billion years. Later, this will conflict with the data of geophysicists, who, using radioisotope analysis, will estimate the earth’s age at several billion years, and will be the strongest headache for cosmologists in physics for decades.

Hoyle's Stationary Universe

Since the beginning of the 30s, the lambda issue has been considered resolved, and no one from the mainstream physicists has really dealt with it. One of the rare exceptions that risked poperet against Einstein himself, was the Briton Fred Hoyle.


Hoyle was quite an authoritative scientist in the field of cosmology, and, unlike many colleagues, so to say “applied”, i.e. relatively easy to verify, cosmology. It was he who explained how stars and galaxies are formed from homogeneous rarefied gas clouds by gravitational compression. Also, Hoyle came up with the name "Big Bang", and used this name in an abusive sense.

Hoyle and his co-authors, Bondi and Gold, didn’t like the “big clap” (a more correct translation of the phrase big bang), in which the Universe has a beginning. They believed that just as all points of space are equal, all points in time should be equal. Such a universe has no beginning, no end, and at the same time it is constantly, although expanding very slowly.

However, from quantum fluctuations a new substance is constantly being born, and so that the average density of matter remains the same. Calculations show that in one cubic kilometer of space only one proton should be born once in 300,000 years (as well as one electron or something like that in order to save electric charge). The perfect number to exclude any possibility of any experimental verification!

The theory of the stationary universe was seriously considered as an alternative to the big bang theory in the 50s and early 60s. But the experimental discovery in 1964 of the relict radiation predicted by the TBB put an end to it.

Hoyle, however, did not let up and improved his theory until his retirement. The latest edition, developed in conjunction with his friend Jeffrey Burbidge in 1993, the so-called "quasi-stationary Universe", involves local mini-explosions and explains almost all the observed facts, but does not enjoy any popularity. And yes, it is suspiciously similar to the generally accepted theory of inflation (but differs with plus or minus signs in some places).

For the article B²FH gave Nobel Prize. But only to Fowler, who ordered a ten-day experiment. Neither the Spouses Burbidzham, who conducted long-term astronomical observations and actually wrote the article, nor the author of the idea, Hoyle, was given the Nobel Prize for persisting in cosmological heresy.

The most interesting thing is that Hoyle survived until experimental confirmation of the accelerated scattering of galaxies in 1998. But even this did not cause the Nobel Committee to correct an obvious mistake.

Quantum lambda

Returning to the GR equation.

On the left (in the modern record) is the curvature of space, that is to say, gravity on GR. On the right is the energy-momentum tensor. Under this tensor there is a terribly complex matan, but the essence is as follows: there all the whole-all matter of the Universe in all types and states is taken into account. And ordinary matter, and all sorts of cunning particles, and all types of radiation (except for gravity, which is on the left).

Now mentally move the lambda to the right. In such a record, it will not be an extra curvature, but some unaccounted energy (I note, negative, since we consider lambda positive). And here are two possibilities.

The first hypothesis is that lambda is the energy of the vacuum itself. It sounds weird, but in fact is quite consistent with quantum mechanics. Take a piece of space and remove from it all that at least in principle can be removed. Remove all matter, all particles and all waves, regardless of their nature. Only the physical fields in the unperturbed state will remain. Complete calm

So, some fields (eg, Higgs) have a nonzero value in the void. And theoretically they have some energy. In addition, due to the principle of uncertainty, any fields have quantum fluctuations - and they also have some energy.

There is, however, a little technical problem. If everything is carefully calculated, the calculated result differs from the observed by 120 - no, not once, by 120 orders of magnitude. 100 billion billion google times! This is considered to be "the worst prediction in the history of theoretical physics."

The second possibility: the physicists still forgot to count something when they calculated the energy-momentum tensor. This “something” should be very strange (give negative pressure), we don’t know anything like it, so the situation “didn’t know - didn’t know, and forgot”. Now this “something” is called “dark energy”, and this energy should be approximately two times more than the energy of ordinary and dark matter combined. ← modern physics is here.

Instead of conclusion

Calls about the non-zero value of lambda began to appear at the turn of the 90s - from accurate measurements of the CMB, etc., and by 1997 had turned into a bell. It is not surprising that at once two groups of physicists armed themselves with modern tools and rushed to recheck Hubble’s grandfather. Therefore, when Ethan writes about “quite unexpectedly,” he, to put it mildly, instills.

And as long as we have nothing better than “dark energy” to explain the lambda, this story will continue.

Thanks for attention!