**A brief tour on a weighty subject**

**Anthony Zee**

**University of California, Santa Barbara, CA, USA**

**https://www.physics.ucsb.edu/people/anthony-zee**

**https://en.wikipedia.org/wiki/Anthony_Zee**

**About the speaker**

Anthony Zee (b. 1945) is a physicist, writer, and currently a professor at the Kavli Institute for Theoretical Physics and the physics department of the University of California, Santa Barbara.

After graduating from Princeton, Zee obtained his PhD from Harvard in 1970, supervised by Sidney Coleman. During 1970–72 and 1977–78, he was at the Institute for Advanced Study. From 1973 to 1978, he was an Alfred P. Sloan Fellow. In his first year as assistant professor at Princeton, Zee had Ed Witten as his teaching assistant and grader.

Prof Zee has authored or co-authored more than 200 scientific publications and several books. He has written on particle physics, condensed matter physics, anomalies in physics, random matrix theory, superconductivity, the quantum Hall effect, and other topics in theoretical physics and evolutionary biology, as well as their various interrelations.

His latest book ‘On Gravity‘ is available now on Amazon and in all good book stores.

**The Royal Insitution July 28 ^{th} 2020**

Of the four fundamental forces of nature, gravity might be the least understood and yet the one we are most intimate

In this talk, Physicist, Professor Zee started at the discovery of gravity waves and gave us an original and compelling tour of Einstein’s general theory of relativity, leaving us with hints of future mysteries such as quantum gravity, and dark matter and energy.

The following are notes from the on-line lecture. Even though I could stop the video and go back over things there are likely to be mistakes because I haven’t heard things correctly or not understood them. I hope Professor Zee and my readers will forgive any mistakes and let me know what I got wrong.

Any talk on gravity has to start with Newton. In professor Zee’s opinion textbooks have been unfair on Newton – that forces act at a distance is weird. Newton was aware of the problem of action at a distance – like the Earth exerting a force on the Moon through the vastness of space.

Newton’s 1693 letter to his friend Richard Bentley:

“That gravity should be …. [such] that one body may act upon another at a distance through a vacuum without the mediation of anything else by and through which their action or force may be conveyed from one to another is to me so great an absurdity that I believe no man [who] has in philosophical matters any competent faculty of thinking can ever fall into it”

Professor Zee did wonder if his audience found the idea of action at a distance bizarre. My answer to his question was no.

Would Newton have described you us as lacking in “faculty of thinking”?

Who solved Newton’s conundrum for him?

https://en.wikipedia.org/wiki/Isaac_Newton

Sir Isaac Newton PRS (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a “natural philosopher”) who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, laid the foundations of classical mechanics.

Michael Faraday’s ideas about electric charges and electric fields gives us some idea how gravity can act at a distance.

https://en.wikipedia.org/wiki/Michael_Faraday

Michael Faraday FRS (22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry.

Albert Einstein (along with the professor and myself) regarded Michael Faraday as a hero “For us, who took in Faraday’s ideas so to speak with our mother’s milk, it is hard to appreciate their greatness and audacity.”

https://en.wikipedia.org/wiki/Albert_Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

Professor Zee thinks that Faraday’s ideas are vitally important to theoretical physics. He introduced the concept of electric field.

https://www.newworldencyclopedia.org/entry/Electric_field

An electric charge produces an electric field. This electric field exerts a force on other electrically charged objects.

The discrete nature of electric charge was proposed by Michael Faraday in his electrolysis experiments.

A moving charge has not just an electric field but also a magnetic field, and in general the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. For this reason, one speaks of “electromagnetism” or “electromagnetic fields.”

https://www.toppr.com/guides/physics/electric-charges-and-fields/electric-field-lines/

An electric field can be used in the pictorial form to describe the overall intensity of the field around it. This pictorial representation is called the electric field lines. There are certain properties, rules, and applications of electric field lines. Electric Field Lines can be easily defined as a curve which shows the direction of an electric field when we draw a tangent at its point.

The concept of electric field was first proposed by Michael Faraday, in the 19th century. Faraday always thought of electric field lines as ones which can be used to describe and interpret the invisible electric field. Instead of using complex vector diagram each time, electric field lines can be used to describe the electric field around a system of charges in an easier way. They** **point in the direction that a positive test charge would accelerate if placed upon the line.

The strength of electric fields is usually directly proportional to the lengths of electric field lines. Also, since the electric field is inversely proportional to the square of the distance, the electric field strength decreases, as we move away from the charge. The direction of arrows of field lines depicts the direction of the electric field, which is pointing outwards in case of positive charge and pointing inwards in case of a negative charge. Unlike charges attract and like charges repel.

Further, the magnitude of an electric field is well described by the density of charges. The lines closer to the charge represent a strong electric field and the lines away from charge correspond to the weak electric field. This is because the strength of the electric field decreases as we move away from the charge.

https://www.britannica.com/science/magnetic-field

Magnetic fields can also be represented by continuous lines of force or magnetic flux, that emerge from north-seeking magnetic poles and enter south-seeking magnetic poles. The density of the lines indicates the magnitude of the magnetic field. At the poles of a magnet, for example, where the magnetic field is strong, the field lines are crowded together, or denser. Farther away, where the magnetic field is weak, they fan out, becoming less dense. A uniform magnetic field is represented by equally spaced parallel straight lines. The direction of the flux is the direction in which the north-seeking pole of a small magnet points. The lines of flux are continuous, forming closed loops. For a bar magnet, they emerge from the north-seeking pole, fan out and around, enter the magnet at the south-seeking pole, and continue through the magnet to the north pole, where they again emerge.

The similarity with electric fields is that unlike poles attract and like poles repel.

The real content of Faraday’s picture: the electromagnetic field not only can be thought of as a separate entity, it is a separate physical entity.

Faraday knew very little mathematics and when Maxwell became interested in this field of work, he vowed not to use any until he had mastered what Faraday had to say.

https://en.wikipedia.org/wiki/James_Clerk_Maxwell

James Clerk Maxwell FRSE FRS (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics. His most notable achievement was to formulate the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism, and light as different manifestations of the same phenomenon. Maxwell’s equations for electromagnetism have been called the “second great unification in physics” after the first one realised by Isaac Newton.

Faraday and Maxwell couldn’t have more different backgrounds. Faraday grew up in poverty and Maxwell came from an extremely wealthy family (he eventually gave up a university position to look after his large estates in Scotland, although he later returned to Cambridge to become the first Cavendish Professor of Physics.).

Maxwell realised the importance of Faraday’s work and also realised that electromagnetic fields could “leave home, take off and live independently of the charges and currents that generated them”.

https://en.wikipedia.org/wiki/Electromagnetic_spectrum

The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.

The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 10^{25} hertz, corresponding to wavelengths from thousands of kilometres down to a fraction of the size of an atomic nucleus. This frequency range is divided into separate bands, and the electromagnetic waves within each frequency band are called by different names; beginning at the low frequency (long wavelength) end of the spectrum these are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays at the high-frequency (short wavelength) end.

Electromagnetic radiation was first linked to electromagnetism in 1845, when Michael Faraday noticed that the polarization of light traveling through a transparent material responded to a magnetic field. During the 1860s James Maxwell developed four partial differential equations for the electromagnetic field. Two of these equations predicted the possibility and behaviour of waves in the field. Analysing the speed of these theoretical waves, Maxwell realized that they must travel at a speed that was about the known speed of light. This startling coincidence in value led Maxwell to make the inference that light itself is a type of electromagnetic wave.

Maxwell’s equations predicted an infinite number of frequencies of electromagnetic waves, all traveling at the speed of light. This was the first indication of the existence of the entire electromagnetic spectrum.

https://en.wikipedia.org/wiki/Electromagnetic_radiation

https://en.wikipedia.org/wiki/Electromagnetic_radiation#Maxwell%E2%80%99s_equations

Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave

According to Maxwell’s equations, a spatially varying electric field is always associated with a magnetic field that changes over time. Likewise, a spatially varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the electric field are always accompanied by a wave in the magnetic field in one direction, and vice versa. This relationship between the two occurs without either type of field causing the other; rather, they occur together in the same way that time and space changes occur together and are interlinked in special relativity. In fact, magnetic fields can be viewed as electric fields in another frame of reference, and electric fields can be viewed as magnetic fields in another frame of reference, but they have equal significance as physics is the same in all frames of reference, so the close relationship between space and time changes here is more than an analogy. Together, these fields form a propagating electromagnetic wave, which moves out into space and need never again interact with the source. The distant EM field formed in this way by the acceleration of a charge carries energy with it that “radiates” away through space, hence the term.

A linearly polarized sinusoidal electromagnetic wave, propagating in the direction +z through a homogeneous, isotropic, dissipationless medium, such as vacuum. The electric field (blue arrows) oscillates in the ±x-direction, and the orthogonal magnetic field (red arrows) oscillates in phase with the electric field, but in the ±y-direction.

A moving charge can produce a magnetic field which in turn can cause charges to move forming a current (electromagnetic induction).

Maxwell realised that light (em waves/spectrum) was caused by oscillating electromagnetic fields.

Maxwell’s equations

Prior to Einstein the idea of gravitational fields followed on from electric and magnetic fields (they all obey the inverse square law)

https://en.wikipedia.org/wiki/Inverse-square_law

If you double the distance the field strength halves

https://en.wikipedia.org/wiki/Oliver_Heaviside

Oliver Heaviside FRS (18 May 1850 – 3 February 1925) was an English self-taught electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques for the solution of differential equations (equivalent to Laplace transforms), reformulated Maxwell’s field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science

If electric/magnetic fields have associated waves then it was natural to consider that gravitational fields would have associated gravitational waves (the gravitational analogue of light). Of course, in 2019 the first gravity wave was detected.

Newton had wanted to know what the mediation was between the Earth and the Moon.

**Thought experiment**

When you hit one end of an infinitely rigid rod, then by definition the whole thing moves as a whole, and the information that the rod is being hit at one end is transmitted to the other instantaneously.

Hater by Newton and forbidden by Einstein as nothing can travel faster than the speed of light.

In Newtonian physics space-time is rigid. In Einsteinian physics it isn’t and can move about. It is curved and leads to the overwhelming belief that there are gravity waves.

Rigidity no, waves yes

As soon as rigidity falls, we have waves: electromagnetic waves and gravity waves.

That waves and rigidity clash is readily understood in everyday terms. Undulation is all about flexibility and if you suffer from a stiff arm it is difficult to wave.

Spacetime is the last rigid entity in classical physics to fall: spacetime undulates!

Once Einstein declared that spacetime is elastic, that it is curved and can be bent and not absolutely rigid, then the existence of gravity waves became inevitable!

That is why the majority of theoretical physicists had long been convinced of the existence of gravity waves.

When quantised, gravity waves are made up of gravitons just like electromagnetic waves consist of photons.

Einstein’s theory of gravity, proposed in 1915, has withstood the tests of time

https://en.wikipedia.org/wiki/Tests_of_general_relativity

Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the “anomalous” precession of the perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory.

**The deflection of light and a dramatic factor of 2**

Newton himself wondered, “Do not bodies act upon light at a distance, and by their action bend its rays?”. In 1801, Johann Soldner used Newton’s corpuscular theory supposing light to consist of a stream of miniscule particles and calculated the deflection of light by astronomical objects, thus obtaining the Newtonian value against which we now compare. The mass of the particles of light cancel out.

https://en.wikipedia.org/wiki/Johann_Georg_von_Soldner

Johann Georg von Soldner (16 July 1776 in Feuchtwangen, Ansbach – 13 May 1833 in Bogenhausen, Munich) was a German physicist, mathematician and astronomer, first in Berlin and later in 1808 in Munich.

As the wave nature of light and Maxwell’s work on electromagnetic waves became accepted in the 19^{th} century Soldner’s ideas were ignored and he sank into obscurity.

History often takes curious turns. In 1911, Einstein, unaware of Soldner’s calculation, predicted that light would bend in a gravitational field in his still-evolving theory of gravity.

Einstein made a computational error, and reproduced the Soldner-Newton result which he did not know about and which would have disagreed with observation.

As a naive theorist, Einstein wrote to George Hale, the director of Mount Wilson Observatory, wanting to know “how close to the Sun fixed stars could be seen in daylight”. Hale explained that exploiting a solar eclipse would be more promising.

https://en.wikipedia.org/wiki/George_Ellery_Hale

George Ellery Hale (June 29, 1868 – February 21, 1938) was an American solar astronomer, best known for his discovery of magnetic fields in sunspots, and as the leader or key figure in the planning or construction of several world-leading telescopes; namely, the 40-inch refracting telescope at Yerkes Observatory, 60-inch Hale reflecting telescope at Mount Wilson Observatory, 100-inch Hooker reflecting telescope at Mount Wilson, and the 200-inch Hale reflecting telescope at Palomar Observatory. He also played a key role in the foundation of the International Union for Cooperation in Solar Research and the National Research Council, and in developing the California Institute of Technology into a leading research university.

In later years the Nazis accused Einstein of stealing the work from a “pure” German.

**Einstein’s luck**

An expedition was mounted in 1912 for the next eclipse in Argentina but this encountered bad weather. The next eclipse was due on the 21^{st} August 1914 in Crimea. Unfortunately, WW1 started the month before and as the Crimea was part of the Russian empire, and enemy of the Germans, any German astronomers “sneaking around”, talking about curved spacetime, with telescope would likely be arrested as spies.

Meanwhile, Einstein found his mistake, that he was off by a factor of 2.

The year after world war 1 ended there was another total solar eclipse that was visible throughout most of South America and Africa as a partial eclipse.

https://en.wikipedia.org/wiki/Solar_eclipse_of_May_29,_1919

https://en.wikipedia.org/wiki/Eddington_experiment

The Eddington experiment was an observational test of General Relativity, organised by the British astronomers Frank Watson Dyson and Arthur Stanley Eddington in 1919. The observations were of the total solar eclipse of 29 May 1919 and were carried out by two expeditions, one to the West African island of Príncipe, and the other to the Brazilian town of Sobral. The aim of the expeditions was to measure the gravitational deflection of starlight passing near the Sun. The value of this deflection had been predicted by Albert Einstein in a 1911 paper, and was one of the tests proposed for his 1915 theory of General Relativity. Following the return of the expeditions, the results were presented by Eddington to the Royal Society of London, and, after some deliberation, were accepted. Widespread newspaper coverage of the results led to worldwide fame for Einstein and his theories.

The 29 May 1919 solar eclipse.

https://en.wikipedia.org/wiki/Frank_Watson_Dyson (below left)

Sir Frank Watson Dyson, KBE, FRS, FRSE (8 January 1868 – 25 May 1939) was an English astronomer and Astronomer Royal who is remembered today largely for introducing time signals (“pips”) from Greenwich, England, and for the role he played in proving Einstein’s theory of general relativity.

https://en.wikipedia.org/wiki/Arthur_Eddington (above right)

Sir Arthur Stanley Eddington OM FRS (28 December 1882 – 22 November 1944) was an English astronomer, physicist, pacifist, and mathematician. He conducted an expedition to observe the solar eclipse of 29 May 1919 that provided one of the earliest confirmations of general relativity, and he became known for his popular expositions and interpretations of the theory.

Arthur Eddington made it his personal mission to show that good physics transcended national boundaries and overnight, despite his German background, Einstein became a world celebrity.

People certainly found the idea of curved spacetime more interesting than the precession of Mercury.

Eddington wrote a popular book which included a humorous puzzle “How many pounds of light does a pound buy you?” (140 million pounds per pound).

Where does the factor of 2 come from?

Factor of 2 (not something more complicated?) between the two masters of gravity, the undisputed greatest among the greats, could be summarized somewhat mysteriously as follows:

Somewhere in the Universe’

Newton: “I curved time”

Einstein “I curved space also”

Arthur Eddington wasn’t the only one who went looking for the solar eclipse. There was also an expedition to Brazil led by Andrew Crommelin.

https://en.wikipedia.org/wiki/Andrew_Claude_de_la_Cherois_Crommelin

Andrew Claude de la Cherois Crommelin (6 February 1865 – 20 September 1939) was an astronomer of French and Huguenot descent who was born in Cushendun, County Antrim, Ireland. In 1919 he participated in the solar eclipse expedition to the city of Sobral, in Brazil, which aimed to determine the amount of the deflection of light caused by the gravitational field of the Sun. The results from these observations were crucial in providing confirmation of the General Theory of Relativity, which Albert Einstein had proposed in 1916.

The Royal Society funded all the expeditions.

Below is a newspaper report (Monday 10^{th} November 1919)

“More or less agog – but nobody need worry”

“Efforts made to put in words intelligible to the non-scientific public … so far have not been very successful.”

The other big news that day:

French government to open cheap national restaurants

**Einstein’s motivation for curving spacetime – where did he get the weird idea from**

https://en.wikipedia.org/wiki/Apollo_15

Apollo 15 astronauts repeated Galileo’s leaning tower experiment (3^{rd} August 1971) showing the universality of gravity. A hammer and a feather were dropped at the same time from the same height, reaching the ground at the same time because of gravity and no air resistance

https://moon.nasa.gov/resources/331/the-apollo-15-hammer-feather-drop/

Einstein gravity in a nutshell. Gravity is actually a consequence of curved spacetime. Curved spacetime masquerading as gravity!

The flightpath shown below shows how a straight line can look curved bcause spacetime is curved.

Caution: excessive curving of spacetime leads to black holes

If an object is too massive for its size, it becomes a black hole

The Schwarzschild radius is given as

https://en.wikipedia.org/wiki/Schwarzschild_radius

where G is the gravitational constant, M is the object mass, and c is the speed of light.

An obesity index for the Universe

Even light cannot escape once it gets inside the event horizon of the black hole

**How do we measure the curvature of spacetime?**

Think of a creature living on a curved surface. When we think of a curved surface, we naturally think of it as contained (embedded) in the 3-dimensional space we live in. We can easily see whether the surface is curved. But the creature cannot get off the surface and look at his world any more than we can get out of our Universe to take a look. What can the creature do?

“Walk in the same direction” is called parallel transport of vectors in mathematics. The relevant mathematics was developed by the German mathematician Bernard Riemann: Parallel transport vector over a closed loop.

https://en.wikipedia.org/wiki/Bernhard_Riemann

Georg Friedrich Bernhard Riemann (September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series.

https://en.wikipedia.org/wiki/South-pointing_chariot

The south-pointing chariot (or carriage) was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretched arm. The chariot was supposedly used as a compass for navigation and may also have had other purposes.

The square of physics without gravity, with gravity and the cube of physics

Horizontal axis: size, vertical axis: speed

Quantum mechanics: Quantum Field Theory! The upper right-hand box is where research is being done. The holy grail is to marry Relativity and quantum mechanics

Quantum fluctuations can’t do very much

Special relativity shows there is a relationship between energy and mass

Leads to new physics which will now be explained

https://en.wikipedia.org/wiki/Uncertainty_principle

In quantum mechanics, the uncertainty principle (also known as Heisenberg’s uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions.

ħ is the reduced Planck constant, h/(2π), Dt is a time interval and DE is the energy change/energy fluctuation

Consider an embezzling analogy. The larger the accounting error, the sooner it would be detected and set right. In contrast, a tiny accounting error might last for a long time. In this respect, the quantum world actually accords with the everyday world: a sure-fire embezzling scheme that might not be detected for a long time is to skim off a penny from each customer over a long period of time. DE represents the accounting error. Energy is fluctuating.

Students learn to deal with these fluctuating uncertainties. But what can these fluctuating uncertainties in energy over a short duration do? Actually, nothing all that much. Imagine having the students in a quantum mechanics exam calculate the behaviour of 2 electrons in a box. They could calculate until they are blue in the face, but there will still be 2 electrons in the box, not one more, not one less.

Energy = mass x (speed of light)^{2}

Energy could be converted into mass and hence particles according to Einstein. The embezzler could turn an accounting error into an expensive car. But only in his dreams if the world is classical, not quantum. There is no accounting error.

Two separate strange worlds, but not strange enough!

The fun really begins when physicists combine the two

Quantum mechanics + special relativity = Quantum field theory

**When Dr Heisenberg (quantum) meets Professor Einstein (relativity)**

In quantum field theory, a state of nothingness is known as the vacuum. But nothingness does not merely contain nothing; to the contrary, in some sense it contains everything.

The vacuum is a rolling sea of quantum fluctuations, boiling with particles and their corresponding antiparticles, coming into existence from nothing, and after a short while, poof, the particles and its antiparticle vanish into thin air! Physicists say that they have annihilated each other.

How long they last is determined by the energy of the particle/antiparticle pair in accordance with the uncertainty principle.

So, this magic could last for only a short time, before the expensive car turns into an old banger, so to speak.

**How to avoid this? Two possibilities**

In our analogy: what could our embezzler do?

1) Build some high energy accelerator so that there is a lot of energy flying around

A zillion dollar account lying around

2) Curve spacetime: go near a black hole and hide stuff there

An accounting error could last and be turned into stuff if a slush fund is hidden in some dark corner of the bank where no inspector has ever ventured. Or, if an inspector did venture there, he is trapped and cannot escape to tell a tale.

The first possibility is kind of obvious, but the second …..

The second possibility was realised by Professor Stephen Hawking (seen below with Professor Zee)

**Hawking radiation **

A quantum fluctuation near the horizon produces a particle and its antiparticle. Due to the uncertainty principle, we can’t be sure whether both are inside the horizon, both are outside, or one is outside but the other is inside the event horizon.

Suppose the antiparticle is inside the event horizon and falls to its doom while the particle outside escapes.

An observer far away from the black hole sees the particle coming from the black hole and concludes that the black hole is radiating particles. (Equally well, we could have the particle being inside the horizon and falling to its doom while the antiparticle escapes.)

Therefore, the observer far away would see the black hole radiating equal streams of particles and antiparticles.

A child asks a panel of experts “Why do we all fall down?”

Aristotle said “Well, the Earth is the natural home for rocks and men. Rocks fall faster because they want to go home. As rocks fall, they go faster and faster. When fall down you are expressing your inner desire to go home”

https://en.wikipedia.org/wiki/Aristotle

Aristotle (384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece.

Newton said “Aristotle is talking a load of rubbish. I have interviewed plenty of rocks, and they never said anything about going home. Rocks and apples fall because they and the Earth and every other object in the Universe exert an attractive force on each other. By the way, as you fall down, you are actually also pulling the Earth up.”

Einstein said “Newton is correct, but there is more to the story. The force Newton talks about results from the curvature of spacetime. The Earth warps the spacetime around you so that when you fall down, you are actually “looking” for the best path to get through space and time.”

The quantum theorist of gravity said “Einstein somehow finds the quantum world distasteful, even though he was one of the founders of quantum physics. If he hadn’t been so stubborn, he might have realised that his curved spacetime is due the incredible number of gravitons moving about. When you fall down, gravitons move back and forth between you and the Earth.

If Darwin had been asked, he might have said “I can’t explain why rocks fall down however some apples would have fallen down and others would have flown up into outer space. Those that went into space wouldn’t have been able to reproduce so apples evolved to fall down.”

**Questions and answers**

1) Does light have mass?

Mass is a constant between energy and momentum

When energy is zero momentum is equal to its mass

Photons have zero mass so energy equals momentum

So massless but has momentum

Einstein said mass and energy are equivalent, E = mc^{2}

Black holes are “impossible” in Newtonian physics.

In Einsteinian physics, with black holes pressure generates energy which produces mass – a runaway process.

2) Two black holes. Two people – one falling into one and the other falling into the other. Would they be aware of each other if the two black holes merge?

No. A Rosen bridge is pure science fiction

https://en.wikipedia.org/wiki/Wormhole

A wormhole (or Einstein–Rosen bridge or Einstein–Rosen wormhole) is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations.

3) Where did all the antimatter go at the start of the Universe?

https://en.wikipedia.org/wiki/CP_violation

In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry (parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C symmetry) while its spatial coordinates are inverted (“mirror” or P symmetry). The discovery of CP violation in 1964 in the decays of neutral kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch.

It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present universe, and in the study of weak interactions in particle physics.

https://en.wikipedia.org/wiki/James_Cronin (below left)

James Watson Cronin (September 29, 1931 – August 25, 2016) was an American particle physicist

https://en.wikipedia.org/wiki/Val_Logsdon_Fitch (above right)

Val Logsdon Fitch (March 10, 1923 – February 5, 2015) was an American nuclear physicist who, with co-researcher James Cronin, was awarded the 1980 Nobel Prize in Physics for a 1964 experiment using the Alternating Gradient Synchrotron at Brookhaven National Laboratory that proved that certain subatomic reactions do not adhere to fundamental symmetry principles. Specifically, they proved, by examining the decay of K-mesons, that a reaction run in reverse does not retrace the path of the original reaction, which showed that the reactions of subatomic particles are not indifferent to time. Thus, the phenomenon of CP violation was discovered. This demolished the faith that physicists had that natural laws were governed by symmetry.

https://en.wikipedia.org/wiki/Baryon_asymmetry

In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem, is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antibaryonic matter in the observable universe. Neither the standard model of particle physics, nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges. The Big Bang should have produced equal amounts of matter and antimatter. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and antimatter. Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon. As remarked in a 2012 research paper, “The origin of matter remains one of the great mysteries in physics”.

4) What is the speed of an electron in atom?

It’s better to talk about momentum

In every atom, electrons orbit the nucleus with a certain characteristic velocity known as the Fermi-Thomas velocity, equal to

where Z is the number of protons in the nucleus and c is the speed of light.

5) Do gravitational waves behave in the same way as normal waves?

Yes, but they are a bit more complicated.

https://en.wikipedia.org/wiki/Poynting_vector

In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m^{2}). It is named after its discoverer John Henry Poynting who first derived it in 1884. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition.

https://en.wikipedia.org/wiki/Gravitoelectromagnetism

Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell’s field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.

The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton’s law.

The GEM Poynting vector compared to the electromagnetic Poynting vector is given by

E_{g} is the gravitoelectric field (conventional gravitational field), with SI unit m⋅s^{−}^{2}

E is the electric field

B_{g} is the gravitomagnetic field, with SI unit s^{−1};

B is the magnetic field;

G is the gravitational constant;

c is the speed of propagation of gravity (which is equal to the speed of light according to general relativity)

ε_{0} is the vacuum permittivity

6) Hawking radiation

Mass/energy is not lost. As the black radiates its mass decreases but the temperature increases.

https://en.wikipedia.org/wiki/Micro_black_hole

Micro black holes, also called quantum mechanical black holes or mini black holes, are hypothetical tiny black holes, for which quantum mechanical effects play an important role. The concept that black holes may exist that are smaller than stellar mass was introduced in 1971 by Stephen Hawking

https://en.wikipedia.org/wiki/Black_hole_information_paradox

The black hole information paradox is a puzzle resulting from the combination of quantum mechanics and general relativity. Calculations suggest that physical information could permanently disappear in a black hole, allowing many physical states to devolve into the same state. This is controversial because it violates a core precept of modern physics—that in principle the value of a wave function of a physical system at one point in time should determine its value at any other time.

Information is stored in a Planck-sized remnant –

Advantage: No mechanism for information escape is needed.

Disadvantage: To contain the information from any evaporated black hole, the remnants would need to have an infinite number of internal states. It has been argued that it would be possible to produce an infinite number of pairs of these remnants since they are small and indistinguishable from the perspective of the low-energy effective theory.

7) How will we prove that gravitons exist?

Dyson raised this question. He said gravity shouldn’t be quantised – so gravitons won’t be discovered. Professor Zee disagrees.

8) Why did Professor Zee write popular science books.

He had an interest in writing

**Anthony Zee videos**