Oliver in Quantum-Gravity-land

By Alessio Rocci

[Note: highlighted words link to the Glossary at the end of the post.]

Historically, the term Quantum Gravity (QG) has had many meanings. Today it is often associated with the idea that the gravitational field must be quantized, but we do not know how to construct this theory in a consistent way. From the birth of General Relativity (GR) in 1915 until today, many approaches have tried to face, in a broad sense, the problem of harmonizing the quantum principles that govern the microscopic world. GR is actually our best theory describing the gravitational field.

In 1916, Albert Einstein was the first to argue that quantum effects must modify his general theory.1 In fact, he had in mind Bohr’s principle of stationary orbits, which had already modified the classical idea of the atomic collapse in the case of the energy loss due to electromagnetic wave emission, and that seemed to suggest that a similar solution was needed to avoid the energy loss caused by gravitational wave emission. Presumably he did not know, at that time, that this kind of atomic collapse is characterized by a time of the order of 1037s, that is an enormous lack of time compared with the life of our Universe: recent results give approximately (4,354±0,012)x1017s.2 The first attempt to quantize the gravitational field appeared in 1930, in two papers published by Léon Rosenfeld. For this reason, the years running from 1916 to 1930 are often referred to as the prehistory era of QG, a period that collects all attempts to harmonize the microscopic world with GR, or with others theories of gravity.

The prehistory era is divided in two half-periods by a wall: the birth of Quantum Mechanics (QM) in 1925-1926. We are interested in the ambien first half-period, when one of the big problems was the origin of Bohr’s stationary orbits and when the application of GR to the microscopic world was not broadly accepted. In fact, in the first four years after the birth of GR, the only experimental test of Einstein’s theory was the amazing calculation of Mercury’s perihelion time-precession. Things started to change in UK after Sir Frank Watson Dyson announced, in 1919, Sir Arthur Eddington’s results of the eclipse expedition: starlight was deflected in the sun’s gravitational field by the exact amount predicted by Einstein.3 At this point Sir Oliver Lodge enters our story. In fact, he was very active in the field of Relativity during those years.4 As the general interest of the scholars for GR suddenly rose exponentially, Lodge also started to consider the new theory of gravitation and its connection with the microscopic world. In fact, even if Lodge is famous for his hard defense of the aether concept, he always looked at the scientific world with a very open mind and tried to face all of the popular problems of his time. He started to consider various problems connected with GR. Here we arrive at the year 1921, a very special year for Lodge production. Maintaining his old-fashioned vocabulary, Lodge writes a Letter to Nature, strongly impressed by a George B. Jeffery’s paper, where GR is applied to the microscopic world, as all pioneers of QG tried to do.5 Referring to the electrical theory of matter and GR, Lodge uses Jeffery’s results in order to infer something new about the origin of the gravitational field of an electron and he speculates about its interior. For this reason, we included Sir Oliver Lodge in the prehistory of QG.

Peter Rowlands writes that ‘Lodge’s analyses of contemporary work were frequently accompanied by brilliant speculations’.6 Indeed, many brilliant speculations are raised in the letter to Nature and would become prevalent in the whole production of the year. In the brief communication, Lodge notes some inconsistencies connected with the electrical theory of matter, which in fact contradict Einstein’s equivalence principle, as it would be pointed out e. g. by Enrico Fermi two years later.7 In the letter, Lodge also discusses how GR tells us that the origin of the electron mass should not have an electromagnetic origin. Last, but not least, he rightly points out that the new Jeffery’s result ‘does not apply in the interior of an electron, if an electron has any interior’, putting the old idea of composite electron and the modern concept of elementary particle on equal footing. With these comments, Lodge ends his incursion into the history of QG, but we can continue to track the other ideas that he developed in this period. Lodge himself attracts attention in his papers, published in the Philosophical Magazine.8 In ‘On the supposed weight and ultimate fate of radiation’, Lodge introduces the idea of refractive index of light in a gravitational field that he uses to correctly describe what happens to the light-cone, approaching the Schwarzschild radius.9 He poses the following questions: ‘What happens to light when, in free modified ether, it is stopped relatively to a gravitational mass? Does it retain its energy…tie itself into electrons and add to the mass of the body?’10 Lodge’s idea is amazing: doesn’t it resemble the modern concept of Black Hole accretion? In ‘Ether, Light and Matter’, Lodge associates the idea of the quantum with closed curves of magnetic lines, and has in mind the electromagnetic nature of the mass as he writes: ‘I ventured on a speculation that matter is a sink as well as a source of radiation… Annulling of the electric component in a ether wave… may also liberate the magnetic component…’.11 Lodge’s imagination goes further: ‘the problem is whether part of the magnetic circulation, left stranded, could not cease to be oscillatory and become continuous and permanent; and whether the synchronous electric pulses of myriads successive waves could not accumulate as a separated pair of opposite electric charges’.12 Doesn’t it resemble the modern idea of pair creation? In his successive paper, Lodge tries to go deeper and deeper with this idea: ‘Referring to previous papers… if it is ever possible to separate … a positive and a negative electron bringing them into practical existence from absolute neutrality … the uniting force must … follow the law: [here Lodge inserts a mathematical formula for the force, that mixes the gravitational force with an elastic force] The opposite charges may be thought of as initially united by an elastic thread of zero length… till it snaps.’13 The idea, exposed by Lodge, resembles the quark anti-quark string model of the seventies!

To summarize, I would like to express my opinion on ativan Lodge’s idea about the distinction between pure and applied science, emerging from the papers that we discussed briefly. Lodge’s speculations are very abstract models and could be thought as an incursion into pure science. But every speculation he did was always followed by a precise calculation, as if to try to connect it with reality, as requested by applied science. As an example, I mention that Lodge calculated the temperature at which the pair creation should take place. Finding too big a number, he comments: ‘I confess I had hoped that this ebullition temperature would not have been so high, so that there might have a chance of reaching it, at least locally, in the sun or some of the stars’.15 It is my opinion that Lodge never tried to distinguish between pure and applied science and I think that Lodge’s philosophy is well described by the following sentence:

For undoubtedly general relativity, not as a philosophic theory but as a powerful and comprehensive method, is a remarkable achievement […] but, notwithstanding any temptation to idolatry, a physicist […] must remember that his real aim and object is absolute truth […] that his function is to discover rather than to create […[ and that beneath and above and around all appearances there exists a universe of full-bodied, concrete, absolute, Reality.16

On 31 of October 1921, Lodge was in Liverpool, lecturing on ‘Relativity’ to the Literary and Philosophical Society and, on the same day in 2014, we were in Liverpool to give honor to this great scholar, at the third workshop of ‘Making Waves’.

Glossary

quantized: the terms quantum, quantization, quantized always refer to the fact that atomic world follows new laws, discovered from the beginning of last 20th century, often referred as quantum laws, that are deeply different from the laws of the macroscopic world, usually referred as classic laws. Gravity governs the microscopic and the macroscopic world. This fact implies that, at least for this reason, we need some synthesis between gravity and quantum laws. [back]

Bohr’s principle of stationary orbits: Bohr’s model of atom is the most popular image of quantum world (see the logo of the sitcom The Big Bang Theory). In this model electrons move around a nucleus made of protons and neutrons, like Earth and other planets do around the sun. But due to classic laws, an electron should emit electromagnetic waves, like a mobile do while ringing, loose its energy and fall towards the nucleus. Bohr postulated the existence of stationary orbits, where the electron does not irradiate, in order to let the atom live!. [back]

gravitational wave: Einstein discovered that his famous equations, describing the dynamic of a gravitational field produced by a body, also describe the process of emission of waves, called gravitational waves. Phentermine weight loss by gravitational wave emission by the Pulsars has become another important test for GR. [back]

Mercury’s perihelion time-precession: lets something have a fixed direction into the sky, like polar star for the sailors. The perihelion of a planet is the point occupied by the planet when it is closest to the Sun. The position of a perihelion is not fixed with respect to direction you choose: it rotates with a time that, in the case of Mercury, is about 43 seconds of arc per century. The Mercury’s time-precession puzzled the physicists from the birth of Newton’s theory of gravity and was correctly explained for the first time by GR. [back]

Electrical theory of matter: due to this theory the origin of mass should emerge from Maxwell’s electromagnetic theory applied to a rigid sphere electron model. The idea started with a Thomson’s formula, that express electron mass using the electric charge, the sphere radius and some fundamental constants of Maxwell’s theory. [back]

Einstein’s equivalence principle: Einstein defined it as like the most beautiful idea he ever had. Let suppose you are falling freely with a heavy ball in your hands. If you open your arms, the ball will fall with you. Now let’s imagine that you and your heavy ball shut in an elevator. If you don’t know that you’re falling, what you see is the absence of gravity, exactly like astronauts of the International Space Station do. If you reverse this idea you get the equivalence principle: gravity is due to an acceleration field that in GR is created by a curved geometry, exactly like roller coaster’s rails, generated by a mass. [back]

refractive index of light: like every mass does, light follows the curved geometry created by a big mass (see the Einstein’s equivalence principle in this dictionary). This phenomenon is called light bending and it could be described throughout the analogy with the phenomenon of refraction, where the bending of light is due to the change of the medium’s density that the light is traveling through. [back]

Light-cone: In Relativity this is an imaginary doubled-cone, whose edges are made of light rays, where we live, and that separates, in a certain sense, the past-cone from the future-cone. [back]

Schwarzschild radius: when the nuclear reactions inside a star end, gravity wins among all exploding forces and the star begins to implode. In some cases the radius of the star can approach the Schwarzschild radius. In this case we could say that a Black Hole has been born, because at the Schwarzschild radius the gravitational force is so strong that even the light cannot escape any more. [back]

Notes

1 Albert Einstein,‘Naerungsweise Integration der Feldgleichungen der Gravitation’, Preussische Akademien der Wissenschaften. Sitzungsberichte (1916), 688-696. [back]

2 Planck Collaboration (Ade P. A. R. et al.),‘2013 Planck 2013 results. I. Overview of products and scientific results’, Preprint: astro-ph.CO/1303.5062. [back]

3 Peter Rowlands, Oliver Lodge and the Liverpool Physical Society (Liverpool: Liverpool University Press, 1990). [back]

4 Oliver Lodge, ‘The Gravitational field of an Electron’, Nature, 107 (1921), 392-392. [back]

5 Ibid. [back]

6 Rowlands, p.259. [back]

7 Enrico Fermi, ‘Correzione di una contraddizione tra la teoria elettrodinamica e quella relativistica delle masse elettromagnetiche’, Nuovo Cimento, 25 (1923), 159. [back]

8 Oliver Lodge, ‘On the supposed weight and ultimate fate of radiation’, Philosophical Magazine, 6.41 (1921), 549; Oliver Lodge, ‘Ether, Light and Matter’, Philosophical Magazine, 6.41 (1921), 940; Oliver Lodge, ‘Light and Electron’, Philosophical Magazine, 6.42 (1921), 177. [back]

9 Lodge, ‘On the supposed weight and ultimate fate of radiation’. [back]

10 Ibid., 555. [back]

11 Lodge, ‘Ether, Light and Matter’, 942. [back]

12 Ibid., 943. [back]

13 Lodge, ‘Light and Electron’, 177. [back]

14 Ibid., 183. [back]

15 Oliver Lodge, ‘The Geometrisation of Physics, and Its Supposed Basis on the Michelson-Morley Experiment’, Nature, 106.2677 (1921). [back]

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