Schwarzschild Conference, Frankfurt, July 2017, Summary
In English
August 2, 2017
I’ve just returned from the Karl Schwarzschild Conference, held in Germany at the prestigious FIAS, the Frankfurt Institute for Advanced Studies.
I had hesitated a lot about the content of my poster and ultimately decided to present, in broad terms, my system of coupled field equations.
A text didn’t quite fit the central theme of the conference, focused on "black hole physics." This is a subject I had intended to address, but the paper I published in 2015 in Modern Physics Letters A:
J.P. Petit & G. D’Agostini:
Cancellation of the central singularity of the Schwarzschild solution with natural mass inversion process.
Mo. Phys. Lett. A, vol. 30, n°9 (2015)
was the closest to that theme. Since there was a blackboard next to my poster, I quickly wrote down the main points of that paper:
This immediately attracted attention. Attendees took photos, and a crowd gathered. A man in his sixties, a "senior researcher," immediately expressed skepticism about the idea that all singular aspects of the metric solution found by Schwarzschild in 1916—which serves as the basis for black hole theory—could be eliminated by a single coordinate transformation. Since he wasn’t wearing a badge like others, I concluded he must be part of FIAS, the Frankfurt Institute for Advanced Science, hosting this conference. Here is the coordinate transformation:
Finally, a critique! To make things even clearer, I quickly wrote all the calculation details on a sheet and handed it to my expert, who sat down on a chair and studied it for about fifteen minutes.
Everyone waited for his verdict. He eventually returned my sheet with a nod, marked by deep perplexity. I think he must have thought, "I’ve never seen anything like this before. There must be an error I’m missing. But I’ll look into it later."
I tried to engage him in this issue, which raises the question of interpreting Karl Schwarzschild’s 1916 result (the conference was titled "Karl Schwarzschild Conference"!). I asked if he had read the original paper published in the Annals of the Prussian Academy of Sciences:
K. Schwarzschild:
Über das Gravitational eines Massenpunkets nach der Einsteineschen Theory.
Sitzber. Preuss. Akad. Wiss. Berlin, p. 189–196 (13 Jan. 1916). English version by S. Antoci and A. Loinger at arXiv:physics/9905030 (12 May 1999)
as well as the second article, published a few weeks later, just months before his death:
K. Schwarzschild:
Über das Gravitationsfeld einer Kugel aus incompressibler Flüssigkeit nach Einsteinsechen Theorie.
Preuss. Akad. Wiss. Berlin, p. 189–196 (24 Feb. 1916). English version by S. Antoci at arXiv:physics/9912033 (16 Dec. 1999)
He admitted he had never read them (...) adding:
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You read German?
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No, I just had access to relatively recent English translations (1999), though the documents are now a century old. I have these documents on my laptop. Would you like to go through them together? There’s also a very important text David Hilbert published in December 1916, where he reworks Schwarzschild’s work.
D. Hilbert:
"Die Grundlagen der Physik (Zweite Mitteilung)"
(EN) "The Foundations of Physics (Second Communication)"
(FR) "Les Fondements de la Physique (Seconde Communication)"
He preferred to avoid the topic, adding he didn’t know that other text either (...).
In fact, what I realized in Frankfurt is that black hole researchers simply don’t know the foundational texts from which their own work is derived. During a keynote speech, before the entire audience,
Juan Maldacena,
a "figure" in modern black hole theory, began by saying (as reproduced in the conference brochure):
Juan Maldacena
- The Schwarzschild solution has confused us for over a hundred years and has forced us to sharpen our views on space and time. It has led to a clearer understanding of Einstein’s theory. Experimentally, it explains several astrophysical observations. Its quantum aspects have been a source of theoretical paradoxes that are pushing us to better understand the relationship between spacetime geometry and quantum mechanics.
Translation:
- The Schwarzschild solution has been a source of confusion for over a century and has compelled us to refine our understanding of space and time. This has led to a deeper comprehension of Einstein’s theory. Experimentally, it explains a number of observations. The quantum aspects have generated theoretical paradoxes that are forcing us to better understand the relationship between spacetime geometry and quantum mechanics.
What does this concretely mean?
First came the "discovery" of "Hawking radiation." In fact, all of this rests on the idea of a marriage between General Relativity and Quantum Mechanics. Yet we know that... this union has never been consummated (gravity stubbornly refuses to be quantized, which would lead to the description of a graviton, a spin-2 particle, still absent in the record).
Our modern theorists eventually convinced themselves that this fantasy had real value. Indeed, invoking a quantum phenomenon near the black hole horizon, Hawking "showed" that black holes could lose energy and "radiate." This immediately gave rise to the "cosmological horizon paradox." Indeed, in these objects called black holes, all structure is supposed to disappear, be crushed. Thus, black holes would be "information-destroying machines." Maldacena then presented progress made in "black hole thermodynamics." In particular, he recalled that "it was shown that black hole entropy is proportional to their area."
In short, for the past few decades, theorists have focused on how to circumvent this information paradox. You’ve probably heard of a "firewall" and other such ideas. In his latest work, Maldacena invokes a new "master word": "entanglement" ("Intrication"). A concept from quantum mechanics and the famous Einstein-Podolsky-Rosen paradox (EPR paradox) that I described in my video
JANUS 6
(at 14'04"). In this experiment, the two emitted photons are "entangled." In short, according to Maldacena, "entanglement" provides all the answers. Plus a pinch of string theory.
This speech represents the pinnacle of theory in 2017.
Conference participants clearly referred to the JANUS videos (see the PDF list of their content). Thanks to the enormous effort by Julien Geffray, six videos were equipped with subtitles at the start of the conference: JANUS 14 to JANUS 19. And it’s here that we realize that these high-quality English subtitles are absolutely essential.
It’s impossible to provide mediocrity: internet users would immediately switch off. Geffray, who has followed my work for 20 years and fully masters the language of Shakespeare, was the only one capable of performing this delicate task, requiring three full days of work per video. This amounts to 15,000 to 20,000 characters per video, with a text containing a lot of specific jargon to translate, the difficulty of visually organizing and precisely syncing subtitles to the tenth of a second, as well as creating reference sheets pointing to my papers and comic strips. I paid him 500 euros per video for these six initial works. So 3,000 euros for subtitling these six videos, which I withdrew from the money sent to me by internet users.
Seeing the impact on non-Francophones, I realized I should equip all 19 videos with these (good) English subtitles. We renegotiated the price and agreed on 350 euros per video. Do the math. Six videos at 500 euros, plus thirteen at 350 euros:
Total budget: 7,500 euros.
More than what will be allocated to funding my three first missions to international conferences. Let’s add that I will continue producing these videos at a rate of two per month, i.e., 700 euros per month (one JANUS video and one on quantum mechanics). In my opinion, this is money well spent, because while texts on internet sites often end up forgotten, videos endure without time limits and are the ultimate modern communication tool.
Projected budget, until spring 2018, for subtitles and conferences: 17,000 euros.
Bringing truth to light has a price.
If the money sent by internet users (a huge thanks to them!) is enough to ensure my presence at the upcoming conferences (Frankfurt, then Paris, COSMO 17...) I need urgent additional help to cover these subtitle costs.
Impact of these videos: reactions from young researchers, one of whom, an Italian, eventually told me:
- I’ve seen your papers on your Janus model (he had the expertise to appreciate their content). I’m watching how you’re received here. How can you expect these people to do anything other than turn their backs on you? What you’re bringing undermines the very foundations of their work!
Contact with this young man was established and maintained; he is working in Italy on modified Newtonian laws. This is the first seed planted. If I continue to "engage" at international conferences, there will be more such contacts among the younger generation—and likely not among those who have built their fame on the fantasies I’ve discussed.
Young researchers might think: "I don’t fully believe in this modified Newtonian law. What if I tried to see where these ideas from this Frenchman lead?" These contacts and exchanges will be facilitated by the fact that these young researchers will have had the chance to view the videos, and then read the papers when they meet me.
In Frankfurt, most articles focused on "black hole physics," on "what you could observe, if you observed it..." Adding to this, a trendy new idea: a "holographic universe" (I’ll need to create a video to explain to internet users what a true hologram actually is. I think it will be welcome). A woman explained that "we shouldn’t fear cosmic strings." Another showed how pairs of mini-black holes could form during the inflationary phase of cosmic expansion. We added stories related to string theory, "brane collisions." I was practically the only one standing out by proposing work and results that could potentially be confronted with observations.
If I want to force this scientific community, lost in its dreams, to react, I must target their cherished child, the black hole—something I hadn’t planned to do until much later. But the atmosphere at the Frankfurt conference made me adjust my approach. So the title of my next video will be:
JANUS 21: The Black Hole, Born from a Misinterpretation of the Solution Found by Karl Schwarzschild in 1916
And this will also be the speech I’ll deliver at the COSMO 17 conference in Paris. For now, I won’t be proposing an alternative model, but simply saying:
- As it stands, this model of the object you call a black hole is inconsistent; it doesn’t match the solution found by Schwarzschild in 1916, and I’ll show you why.
The mathematician Karl Schwarzschild, died in Potsdam on May 11, 1916, at age 43, three months after his January 1916 publication.
The solution found by Karl Schwarzschild in 1916 is:
In this article, he perfectly defines a coordinate r as a "polar coordinate":
But he introduces what he calls an auxiliary quantity R, and it is through this that he expresses his famous January 1916 solution:
He died in Potsdam on May 11, 1916, at age 43, three months after his January 1916 publication.
No need to be a math genius to see that, since the r chosen by Schwarzschild (which he defines above) is strictly positive, this intermediate quantity R is not free but has a lower limit, alpha:
Revisiting this work, in a December 1916 article, the great German mathematician David Hilbert, 54 years old in 1916, found this way of expressing the solution uninteresting, as in this case, in his view, "it merely shifts the singularity (at R = alpha) to the origin, at r = 0." He expresses this "personal opinion" in his article of December 23, 1916 (Schwarzschild died in May):
In fact, Hilbert had already been working intensely on this article for years; the title meaning "Foundations of Physics" (!...). We tend to imagine that Einstein was the physicist and Hilbert the pure mathematician. Indeed, we often cite an anecdote where Hilbert was once asked to replace his colleague mathematician Felix Klein, who gave an annual lecture to engineering students at a school. Hilbert began his talk with a quip:
- They say mathematicians and physicists have trouble communicating. In fact, that’s not true. They simply have nothing to do together!
Hilbert’s work in mathematics is indeed considerable, monumental. But if one has the curiosity to refer to this document, one discovers that he attempts to lay the foundations of a highly mathematical physics (in fact, a "mathematical physics"). This means that Hilbert, in contrast to his earlier statement at that engineering school lecture, had completely changed his perspective—perhaps due to his meeting with Einstein, or more generally due to exchanges with the great physicists of the time. Of course, when it came to contributing his own work, he aimed high immediately. This great lord of science could not theorize at a low level, dealing with minor problems. This paper thus lays the groundwork for a "Lagrangian approach" to all of physics, meaning both gravitation and electromagnetism. In this writing, it is clear that Hilbert aims to gather all the physics of the era into this approach, later called a "unified field theory," a work Einstein vainly tried to complete until the end of his life. The attempt failed because these two formalisms cannot be included in just four dimensions, as shown by Souriau in 1954 (in chapter VII of his book "Géométrie et Relativité, Hermann edition"). Five dimensions are needed—just one more: the "Kaluza dimension."
When Hilbert published this 22-page paper on December 23, 1916, it was in no way an improvisation following Schwarzschild’s January and February 1916 papers. Rather, it was the article he had presented in November 1915 (then withdrawn, as he didn’t consider it sufficiently developed), enriched with various developments, including this nonlinear solution of the field equation, mentioning in passing that Schwarzschild had already produced it.
For Hilbert, Schwarzschild’s January solution was merely a minor detail in his vast framework. He was aware of Schwarzschild’s death, which Einstein announced at the Prussian Academy of Sciences on June 18, 1916. Let’s say that, from Hilbert’s perspective, as a funeral oration, this was quite succinct.
Everything is in the following excerpt:
He introduces four coordinates, w1, w2, w3, w4, and immediately specifies that the first three, the spatial coordinates, can be expressed as he does, using "polar coordinates." Since he considers the problem of the gravitational field around a point mass to involve "central symmetry" (zentrischsymmetrisch), this seems obvious to him.
In the final line, he even goes further, writing that his term G(r) is identified with the square of this "radial distance."
Then everything follows, and generations of scientists will reproduce this approach in hundreds of books. In passing, here’s how he handles this time variable.
For Hilbert, time is purely imaginary!
This is his interpretation of Relativity.
In this equation (45), he includes only the "bilinear form," but we discover the origin of his choice of metric signature (+ + + -).
This notation focuses attention on the real, tangible part of spacetime—the space—affected by three plus signs. Time, on the other hand, is imaginary. Thus, squared, it gives a minus sign. In passing, the length element s also becomes imaginary, just like what is called "proper time." Normal: for Hilbert, anything related to time must be imaginary:
He says he then retrieves, modulo sign inversion, Schwarzschild’s result, which should then be written:
Yet there is a difference. For Schwarzschild, this is not written with the letter r but with the letter R.
This is very different. But Hilbert doesn’t dwell on this detail, since under usual astronomical conditions r is always much larger than alpha (a quantity later called the "Schwarzschild radius"). To highlight this difference, let’s explicitly write this solution, as Schwarzschild himself might have done. We obtain:
But he didn’t do so because the previous expression seemed sufficient to him.
This metric is regular for all values of the variable r greater than zero. When this variable becomes zero, the coefficients of the first two terms become zero. We’ll see later the interpretation of this point.
Hilbert’s only comment is a brief footnote:
Translation:
- Transporting the location where r = alpha to the origin, as Schwarzschild does, is, in my own opinion, not something to recommend. Moreover, this Schwarzschild transformation is not the simplest way to achieve such a result.
At the time Hilbert wrote this paper, the location r = alpha was a "true singularity," or "real singularity" for him. But it was later shown to be a "coordinate singularity," which could be removed by a coordinate change.
We know that these metric solutions can be expressed in any choice of coordinate system. This is a fundamental property of solutions to this field equation. Choosing a particular type of coordinate system is a physicist’s gesture: it involves assigning physical meaning to these coordinates. Then comes the task of confronting these theoretical results with observation, i.e., calculating the geodesic trajectories of point masses orbiting in the field created by this "point mass." This is what they all did.
Classically, one equates the variable R with a polar coordinate, which would thus be capable of vanishing. One shows that these geodesic trajectories lie in planes. One can then express the solution as a function and, by comparing the resulting curves with observational data, arrive at the conclusion:
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These trajectories are "quasi-conic" with one focus located at R = 0.
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Under usual planetary astronomy conditions, the elliptical trajectories are very close to ellipses, the deviation representing what is called "perihelion advance."
Note that when R >> alpha, the quantities r and R are practically identical. Schwarzschild makes this remark in his paper: but it’s more readable in the English version:
Thus, except for the choice of a different signature, we can say that Schwarzschild’s and Hilbert’s solutions (as well as Einstein’s linearized solution from 1915) converge, leading to practically identical results in planetary astronomy. Therefore, whether one opts for Hilbert’s radial variable r or Schwarzschild’s R, the theoretical results match "reality."
The radius of the Sun, a sphere, is 700,000 kilometers. As Schwarzschild quickly calculates, its alpha value (the "Schwarzschild radius") is 3 kilometers. Confusing this sphere with a point is merely an error of four millionths.
We should also mention, though I’ll detail this in a future video, that Schwarzschild, besides providing this "external" solution, also constructed the "internal" solution (describing the geometry inside a sphere of constant density).
K. Schwarzschild:
Über das Gravitationsfeld einer Kugel aus incompressibler Flüssigkeit nach Einsteinsechen Theorie.
Preuss. Akad. Wiss. Berlin, p. 189–196 (24 Feb. 1916).
Here is the English translation of this second paper from February 1916 (one month later!). He also noted that for the Sun, alpha (i.e., what would later be called the "Schwarzschild radius," on the order of 3 km) is located deep inside the star.
It is only today, with objects like neutron stars, that we face the problem of the geometric and physical representation of objects where "the distance variable" is no longer negligible compared to the Schwarzschild radius. But then, which variable should we choose? Hilbert’s or Schwarzschild’s?
Theorists then proposed endowing this external solution with physical reality and claimed it described an object they called a "black hole." Geometrically, one must then provide a response:
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In Schwarzschild’s representation, what happens at r = 0
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In Hilbert’s representation, what happens at R < alpha (considered as "the inside of the black hole")
Note that this question does not arise in Schwarzschild’s representation. There’s no need to wonder what happens when point masses fall "inside," since this "inside"... doesn’t exist.
On the other hand, in Hilbert’s representation, if one grants any reality to this "inside," it is indeed strange. The metric signature is altered, leading our theorists to say, "this means that inside, r becomes time and t becomes the radius."
In a 2015 paper:
J.P. Petit & G. D’Agostini:
Cancellation of the central singularity of the Schwarzschild solution with natural mass inversion process.
Mo. Phys. Lett. A, vol. 30, n°9 (2015)
I indicated another choice of coordinates, derived from Schwarzschild’s solution through the coordinate change:
which leads to a presentation of the metric solution in the form:
It is then regular for all values of the variables, except that the first term is zero at the origin, which automatically makes the metric determinant zero. We then interpret the associated geometry by considering that this metric describes a passage connecting two PT-symmetric Minkowski spaces, with the junction occurring through a throat sphere of circumference 2πα. Along this sphere, the determinant is zero, which reflects the double inversion of the time arrow and space direction during the traversal of this surface.
When considering the Schwarzschild geometry, the solution of the field equation expressed in coordinates, one might be tempted to think "the throat sphere is then reduced to a 'point,' the point r = 0." This would attribute a "dimensional" quality to this letter r, whereas in differential geometry, the letters describing coordinates are merely "space markers," simple numbers used to locate points. The only distances, lengths that have meaning are those calculated using the metric, and these lengths, denoted by the letter s, are invariant regardless of the chosen coordinate system, provided we consider identical paths described by different coordinates.
The spherical symmetry property of the solution allows us to consider fixing three of the four coordinates and imagining a 2π turn along the θ coordinate. In Hilbert’s representation, the throat sphere corresponds