Physicists from Aarhus and Copenhagen Universities (Denmark) have proved that the center of the Earth is much younger than its crust, thus slightly correcting the Nobel laureate Richard Feynman. The study is published in the European Journal of Physics and is available at arXiv.org.
According to general relativity, the gravitational potential affects time: the smaller it is, the slower time goes. This means that a hypothetical measurement of the age of a massive body, such as the Earth or the Sun, on its surface and near its center will lead to different results.
The history of the formation of the Earth from a protoplanetary disk is not directly related to the determination of its age - in contrast to the aging of radioactive elements. In particular, there are more decay products of radioactive isotopes on the Earth's surface than in its center, which is associated with different conditions in which aging of isotopes occurs.
This was probably what Feynman had in mind when, in his lectures on gravity, delivered in 1962-1963 at the California Institute of Technology (USA), he said that “one should be much more careful in the future when talking about the age of objects such as the Earth, because the center of the earth should be a day or two younger than its surface."
This thought experiment is one of many observations made by Feynman about the physical world. The difference in the age of the center and the surface of the Earth indicated by him was cited in several works. However, research by Danish physicists gives a completely different result. It is not clear who was wrong - stenographer or Feynman, but instead of days there must be years.
The Danes tried to reproduce Feynman's reasoning for a homogeneous model of the Earth (when its density does not change with depth), and also performed a calculation for a preliminary reference model of the Earth. The results differ significantly from each other and from Feynman's estimate. Also, calculations were carried out showing the difference in the ages of the center and the surface of the Sun.
In the case of a homogeneous Earth, the gravitational potential of the planet is described by two formulas: one - for a point outside the celestial body, the other - inside it. The gravitational redshift between the center and the surface of the planet is determined through the potential difference at the corresponding points, the radius and mass of the planet. Result: the center of the Earth is 1.58 years younger than its surface.
A more realistic preliminary reference model of the Earth's internal structure takes into account the change in gravitational potential due to different densities at different depths of the planet. In this case, the core of the planet is 2.49 years younger than its surface. Scientists also gave an estimate according to which the relativistic time dilation caused by the Earth's rotation around its axis can be neglected (the contribution of the effect does not exceed two days).
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Danish physicists conclude their article with reasoning about the reasons why Feynman's conclusions have not been tested earlier. The lectures of the American scientist were stenographed by postdocs, proofread by editors, they were reprinted several times and served as a textbook for several generations of physics students. According to the Danes, here we are faced with an example of Aristotelian proof of ethos.
That is, when the authority and status of a scientist is high, his conclusions are taken for granted by colleagues. One of the authors of the article (Ulrik Uggerhoy) admitted that he also considered Feynman's estimate of the difference in the age of the center and core of the Earth to be correct.
Meanwhile, Feynman himself, while working on the theory of beta decay, somehow in one of the old articles (not his own), devoted to the interpretation of experimental data, discovered inaccuracies. This led to many other articles that turned out to be incorrect, because they were based on initially incorrect data. “Since then, I have not paid attention to what the experts say. I figure it out myself,”he said about this. This episode is described in the autobiographical collection "You, of course, are kidding, Mr. Feynman!"
Ksenia Kruger