Exactly 100 hundred years ago from today, on the 25 November 1915, Einstein published a paper entitled *The field equations of gravitation*. This paper was responsible for introducing his field theories in the form of General Relativity. Since its conception, Einstein’s General Theory of Relativity has been excruciatingly tested for flaws – of which none have come to fruition. The theory has passed every single test which has been thrown at it. But it is not completely out of the woods yet, for their is one last prediction General Relativity makes which has evaded for decades – gravitational waves.

To celebrate the centenary of advancements Einstein’s greatest theory has offered, I will take you through a brief history of how it all started as well as some of the aches and pains plaguing the theory, some of which perplexed even Einstein himself.

**— Special Relativity–**

During Einstein’s free time working at the Swiss patent office, he was able to daydream about what it would be like to ride alongside a light beam. Einstein’s thought experiments led to his 1905 ‘miracle year’, where he would go on to publish 4 amazing papers. Amongst proving that light exists as a particle (the photon), providing clear evidence for the existence of atoms through Brownian motion, as well as a paper on his most famous equation E = mc^{2}, Einstein postulated a very radical theory – a theory known as the Special Theory of Relativity.

The notion of relativity has been explored since the times of Galileo. Before Einstein transformed the landscape, Newton and Galileo before him had proposed a common sense view of space and time. That was, that time was absolute and separate from space. This means that an event which takes place at a particular time, say the turning on of a light bulb inside a moving train, occurs at the same time for a person observing the light bulb who is on the train as well as for a person who is on the platform watching the train power by.

Einstein’s little thought experiment however shook this idea to its very core. If the train were to (hypothetically) be moving at the speed of light, then something very strange would happen. Ask yourself, if you were on a train moving at the speed of light and held up a mirror in front of your face, would you see your reflection?

The answer is YES. This flash of inspiration came from a discovery made by James Clerk Maxwell in 1865, which was that the speed of light was constant (moving at 300,000 km/s). If the speed of light were to remain constant in any frame of reference (whether that be a stationary frame such as the man on the platform or a frame moving at some constant velocity such as that of the train passenger), then Einstein realised that the faster you move through space the slower you must move through time.

This radical idea married the ideas of time and space into a single four dimensional ‘space-time’, with the consequences involving time dilation and length contraction. This also meant that events no longer needed to happen simultaneously for observers in alternate frame of reference. One persons past could be another’s future.

**— General Relativity —**

Despite Einstein’s earlier successes, he realised that Special Relativity only applied to non-accelerating frames of reference. He knew that in order to correct for this he had to incorporate gravity in – the only problem was that he didn’t know how.

“In all my life I have laboured not nearly as hard; compared with this problem, the original relativity is child’s play”. –

Einstein

200 Years prior, Sir Isaac Newton had been sitting outside his lodge when he saw an apple fall from its tree. This led him to formulate his law of gravity – an objects falls towards the Earth because there exists a mysterious force pulling it down. However even Newton himself was not satisfied with this explanation – objects move because they are pushed, not because they are pulled. Einstein also knew that Newton’s theory couldn’t be right and he decided to devote the next decade of his life to solving the mystery surrounding gravity.

Einstein had no idea of where to even begin. The problem had no clear boundaries. But as always, Einstein placed his faith into his thought experiments. Sitting at his office in Bern, he began to imagine what a person would feel if they were to fall off of a roof. That is when it hit him, a flash of inspiration for the ages. If you were in an elevator at the top floor, you would feel your weight as you would normally do so on the ground. This is because gravity is pulling you towards the centre of the Earth whereas the Elevator is being held up by a series of large cables. Now if those cables were to suddenly disappear, you would have a very big problem. The elevator would not begin falling towards the ground at the same rate as you would at 9.8 m/s^{2}. However this is where Einstein’s inspiration kicked in – as you fell with the elevator, you would be weightless! It would be as though gravity had been switched off. So what is really going on here?

The Earth has curved the space around it, and it is the space which is pushing things downwards. Not only that, but it is space-time which is curved, so that the curvature of space also means we have some warping of time. One way to visualise this is to imagine placing a bowling ball on a trampoline. In this case we can treat the bowling ball as our Sun and the trampoline as space*. The bowling ball will sink the trampoline at its location, which directly translates to the gravitational well that is produced by any sort of mass residing in the space-time continuum. Throwing a marble onto the trampoline with some velocity parallel to the sinking of the trampoline will cause it to roll around the bowling ball – in other words the Earth in orbit around the Sun.

In essence, anything with mass or energy warps space-time, creating a gravitational field.

*The catch here is that the trampoline representation is one spacial dimension smaller than our space-time reality. This means for an accurate representation you would have to imagine a bowling ball inside a three-dimensional trampoline. If you’re having trouble visualising this don’t fret, the top scientists are in the same position as you are!

**— Confirming General Relativity — **

Just prior to publishing his theory, Einstein used a long known problem regarding the orbit of mercury to self-check General Relativity. At that point, it had been known for quite a while that Mercury’s orbit around the Sun deviates from Newton’s Laws of Motion. Rather than having an elliptical orbit around the Sun, it tilts a little which causes it to trace out an orbit reminisce of the petals of a flower. After painstakingly calculating the orbit of Mercury using his own General Theory of Relativity, he observes a near perfect match.

The first confirmation came in 1919. One of the predictions which arose from General Theory was that a gravitational field bends passing light rays, a phenomenon known as gravitational lensing. This provided the perfect way to test his theory – light coming in from stars in a distant galaxy would be bent as it travels passed the curved space around our Sun. The problem then becomes how to see this light when the Sun produces its own blinding light via the processes of nuclear fusion. Fortunately for Einstein, this problem is solved momentarily during a total solar eclipse.

“Light only knows straight lines – what’s bent is space.” –

Neil deGrasse Tyson

British Astronomer Sir Arthur Eddington succeeded in photographing the Hyades star cluster which was visible during the total solar eclipse. The relative position of the stars was compared to how they looked several months before (where they were well out of the Sun’s path) and what they observed was a bending by the amount Einstein had predicted!

It took almost half a century for the next crucial verification of Einstein’s theory. General Relativity predicted that radiation (including light) would become stretched in a gravitational field – an effect known as ‘gravitational redshift’. It was at Harvard University where physicists placed a radioactive source in the basement of a tall building with a detector on the roof. The idea was that due to the difference in gravity at the top and bottom of the building would reveal this gravitational redshift. After taking measurements, they flipped the experiment so that the source was on the roof and the detector in the basement. Just as expected, the radiation that came from the basement had a wavelength that was slightly longer than that emitted from the roof. Gravity had stretched the electromagnetic waves.

One final verification came when dealing with the time aspect of space-time. Not only was spaced altered, but time itself was also stretched in a gravitational field. This indicated that the further inside a gravitational well you are (or more simply closer to Earth’s surface), then the slower time ticks for you. This was none more apparent when engineers launched satellites for our Global Positioning System (GPS) devices to work. Initially the engineers who launched these satellites didn’t believe in the non-sense that is time dilation, yet after a couple of hours in orbit our navigations systems were offset by a number of kilometres. Luckily they were able to correct for this effect as they had taken measures ‘just in case’ Einstein was right. Seems like they should have had a little more faith in him!

**— Problems in General Relativity —**

Despite all of its successes, there are still a couple of major issues surrounding General Relativity.

The last piece in completing the General theory of Relativity lies in finding gravitational waves. Einstein predicted that when any sufficiently large scale masses are accelerated then little ripples in space-time should radiate outwards. However Einstein predicted that even the most calamitous events in the cosmic realm would produce only the feeblest of waves. While we haven’t detected gravitational waves yet*, there is speculation that pulsars (rotating neutron stars) could hold the key. Except for black holes, neutron stars are the densest objects in the cosmos. The gravity on its surface would be about 10^{11} times the strength than what we experience here on Earth, with a teaspoon of the stuff weighing in at about a billion tonnes. If a pulsar happened to link up with an ordinary star, then in theory their oscillations should emit disturbances in the form of radioactive waves.

The only worry at this stage is with how to detect these tiny waves. Several detectors have been built around the world, with the most notable being the Laser Interferometer Gravitational Wave Observatory, or LIGO for short. LIGO consists of two large L shaped detectors which pick up small disturbances via a method of laser interferometry. Two sets of these detectors are crucial to verify that the source is indeed a gravitational wave and not a rogue signal, such as the rumble of a truck in the distance. As you would imagine they are extremely sensitive, with upgrades in progress to increase the sensitivity 10-fold.

*The big stir caused by the BICEP2 data taken in the Antarctic last year turned out to be a false flag. What looked to match the expected signals for gravitational waves was actually the signals due to cosmic dust which was not accounted for, as verified by the Planck data.

The final issue with General Relativity is its refusal to talk with Quantum Mechanics. Einstein himself wrestled with the idea of merging the two theories but was unsuccessful. Quantum mechanics basically deals with quantised energies – that is, small packets of energy in the form of photons or other ‘messenger’ particles. In order to complete the standard model of particle physics, physicists are searching far and wide for the hypothesised messenger particle of gravity – the graviton. Many believe that if the graviton is discovered, then a grand unification theory may actually be possible – something that Einstein had been working on up until his death in 1955.

**— Something Extra —**

One of the more exotic predictions from General Relativity was the existence of an object so dense that it curved space-time to the point where it became isolated from the rest of the universe. Black holes warp the space-time around them to such an extent that at its centre, the singularity, the equations governing space and time break down. The results which yield infinite density and time dilation indicates that the General theory of Relativity is incomplete.

If you have seen the film Interstellar then you may have some notion of what happened towards the end of the film where they went into orbit around the black hole, Gargantua. When Cooper refers to the Quantum data inside the black hole, he is specifically referring to the data that will help reconcile General Relativity with Quantum Mechanics. Additionally it explores the idea that time ticks more slowly in regions of very high gravitational fields (or more explicitly the greater warping of space-time) when they visit Miller’s planet and go into orbit around Gargantua.

Local Inertial Frame ? (again)

A homogenous disk is rotating vertically. Gravity from below. Therefore, inertial force (centrifugal force) and gravity act on each mass point of the disk. When the rotation speed of the disk exceeds a certain magnitude, a mass point appears where vector of inertial force and gravity are canceled (as total). But it is only natural. It seems to not be note worthy.

In free falling elevator, mass point where vector of inertial force and gravity are canceled (as total) also. Physically, it would be the same phenomenon as a rotating disk.

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Free Fall (Monologue)

A large number of particles are floating in vacuum space. To our eyes, these are visible as a cube or an elevator cabin. Suddenly, a gravity source appears below and the elevator-like thing starts free-falling. As time passes, the elevator-like thing gradually changes its shape.

The above can be explained by Newtonian mechanics.

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2Inertial Resistance is not Fictitious (rephrase)

Not a few explanations of law of action and reaction begins with two bodies. Misleading explanation. This law is the law at point of action of force. And, it is the law that action and reaction are equal, and direction of force is opposite.

A body is pulled by a string. At every point on the string, tension is the same. That is, action and reaction have the same magnitude and opposite directions. This is the same when the body is uniformly accelerated by the string. Both forces are true forces. It is Impossible that one (inertial resistance) is fictitious.

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Inertial Resistance is not Fictitious (again).

Let’s review formulas, F = ma and F = mg.

Dividing both sides by m gives a = F/m and g = F/m. Therefore, a = g.

Thus, mass acting as gravity and mass acting as inertial force are (assumed to be) the same. Also, quantitatively as m. This is also guaranteed by Newton’s third law of motion.

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Inertial Force is not Fictitious (Continued)

In previous post (Jan 17), both sides of formula F = ma are divided by m. Now, alternatively, F = ma are divided by a. Then, formula F/a = m is given. This will also show that a and ma will not be fictitious.

Also, two formulas F = ma and F = mg may not be compatible with the assertion of gravitational mass and inertial mass (“Both are completely different phenomena” on Wikipedia “mass” in Japanese. Also, not be compatible with existence of two idioms).

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Inertial force is not fictitious (is something wrong ?)

Formula, F = ma, is well-known formula. Now, dividing both sides by m. It gives F/m = a. F on the left side is the force (external force) in “Newton”. Both F and m are physical quantities. Both will not be fictitious. Therefore, a and inertial force ma will not be fictitious also. Is there anything wrong with the above ?

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Inertial force is not fictitious (monologue)

On a plane (no friction), there is a body mass 3m. It is pulled by a string from the left and is accelerated. Tension of the string F is 3ma. Now, suppose there is another body to the right of this body. Two bodies are tied with a string. Also suppose the mass of the left body be 2m and the mass of the right body be m. The force F that pulls the left string is the same. So, tension on the left string will be 3ma and tension on the right string will be ma.

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Newton’s Third Law of Motion

A body of mass m is suspended from ceiling by a string. From below, this body is pulled by another string. Tension of this string is 2 mg. So, the tension of upper string is 3 mg. That is, action-reaction of upper string is both 3 mg. Mass of the body is basically irrelevant.

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Inertial Force is not Fictitious (partially reposted)

Gravity acts on everything equally. And if there is action, there is reaction. As stated by Newton’s third law of motion. Below are some examples.

F = mg (free fall)

F = normal reaction

F = air resistance (falling at terminal speed)

F = air resistance + inertial force (falling before terminal speed)

Is F in F = mg fictitious ? The claim of fictitious will not hold.

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Motions Relative to Aether (monologue)

1) Rotary motion: Two same disks are rotating. If the rotary speed is the same, the same inertial force will appear. Regardless of the direction of plane of rotation. It must be because of aether (homogeneous and isotropic).

2) Curvilinear motion: Two same spheres move in curvilinear motion. Two curves are the same in size and shape. If two spheres move at the same uniform speed (from the same starting point), the same inertial force will appear. Regardless of the direction of curve. It must be because of aether (homogeneous and isotropic).

3) Accelerated motion on straight lines: Two same spheres move on two straight lines. If motions are the same accelerated motion, the same inertial force will appear. Regardless of the direction of the straight line. It must be because of aether (homogeneous and isotropic).

4) Uniform linear motion: Two same spheres move in uniform linear motion. Inertial forces do not appear. Regardless of the direction of straight line. It must be because of aether (homogeneous and isotropic)…

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Local Inertial Frame (Monologue)

In all areas of a free-falling elevator, formula F ≒ ma ≠ 0, or F = ma ≠ 0 will consist. So, there will be no inertial frame, even locally.

In a free-falling elevator (assumed to be a rigid body), coexistence of inertial frame and accelerated frame will be impossible, even locally.

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Aberration on the Moon

Major aberrations observable on the moon’s surface are four. Two are corresponding to daily, annual aberrations of earth. Two are annual, secular aberrations of earth themselves (in common). These four aberrations show that aberration are caused by the motion of the telescope on the moon’s surface relative to aether. Qualitatively, quantitatively. Motion of telescope is motion relative to aether.

On the moon’s surface, a water-filled telescope will show what Airy imaged (but if light receiving surface is glass, it will follow the refractive index of the glass). Also on the moon’s surface, picture of tilted umbrella and rain drops (raindrops are photons) will be valid.(invalid on earth).

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Gravity and Time Dilation

There are two mirrors. One is on the ground, one is 22.6m above. These are facing each other. A laser beam is emitted downward from the left end of the upper mirror, forming letter W, and is coming to the upper right (beam is in vacuum). Frequency at five points will be the same. There will be no time dilation due to difference of gravity.

Note) A few translated books say that (outline), when the distance between two points on the light path remains the same, the frequency of two points are the same (assuming frequency of the light source is constant).

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About the speed of light (supplement to Dec 19)

Plane waves and rays (photons) of light from the first-magnitude star, Sirius are propagating through outer space. An observer is moving in various motions. Speed of plane waves and light rays (photons) to the observer will be different (usually).

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About the Speed of Light

For light that is propagated in aether, speed of light waves and ray (photons) relative to an observer will be different (usually). And, for light that is propagated according to emission theory, above will be the same (different also, usually).

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About the speed of light

As for speed of light, constancy of speed of light, and the formula c = f λ seem to be all. But is it so simple ?

A ray of light is propagating through aether. An observer is moving in a uniform linear motion lerative to this ray at various angle. The speed of the observer relative to aether is also varies. And, the observer’s motion can be accelerated motion, jerk (on a straight line), or can be curvilinear motion. Besides, there will be areas where the propagation of light follows emission theory.

In short, there will be no reason to treat light specially. It’s so simple.

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Inertial Force

◎ Inertial force is reaction of Newton’s law of action-reaction (the third law of motion). It is not a fictitious force.

◎ In the entire elevator cabin in free-falling, gravity and inertial force are action and reaction. And the two are equal. So, it is not surprising that in this cabin, there is a local area where the magnitude of gravity and inertial force are equal. In this local area, magnitude of inertial force is not zero. That is, this local area is not an inertial frame.

◎ There are two points that are not in relative motion. It is impossible to say for one to be an inertial frame and for the other an accelerated frame. There can be no such thing as a local inertial frame.

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Equivalence Principle

When a mass point is accelerated, inertial force appears. Its vector can be at our will. On the other hand, gravity acting on a mass point is unrelated to the accelerated motion of this mass point. And, the vector is not at our will. In summary, inertial force and gravity are two different things, like water and oil (even if the vector of the two acting on a mass point happen to cancel each other out).

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Equivalence Principle

In free-falling elevator cabin, and at the specific local area, gravity and inertial force are equal in magnitude. This seems to be the reason for the equivalence principle. However, at many local area, gravity and inertial force are not equal in magnitude. Is it possible that the principle is based on this specific local area ?

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Inertial Force is not Fictitious Force

Inertial force is not fictitious force. See, Newton’s third law of motion (law of action and reaction). Also see, formula F = ma in the second law of motion. This is a big problem.

P.S. There are two types of motion: uniform linear motion and all other motions. In the latter, inertial forces appear during the motion, and corresponding to the motion.

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Gleaning (wavenumber, invariant)

In outer space, a starlight is coming. When an observer moves in the direction of light path, frequency varies. But, according to this, in the formula c = f λ, does wavelength λ vary ? Unbelievable !

There is a word “wavenumber”. It is the number of waves in a unit length (1 cm or 1 m) and is called Kayser. Like 25,000 K (visible red). This wavenumber and wavelength are reciprocals of each other. Therefore, since the wavenumber is an invariant, the wavelength will also be an invariant. That is, the wavelength cannot be varied with the motion of an observer. It is the speed of light that varies.

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Light is Propagated in Two Ways (supplement to the 15th post)

◎ Statings on the formula: c = f λ are from the view point of the mirror (stationery or in uniform linear motion).

◎ Light will follow the emission theory for a few seconds only, after leaving light source. And then light follows aether.

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PLight is Propagated in Two Ways

In outer space, a starlight is reflected by a mirror. There is a formula c = f λ. Now, the mirror is stationary. In comparing of incident light and reflected light, f is the same. And usually, c & λ are different.

Now, the mirror moves in the direction of the light path of incident light. In the formula on incident light, λ is constant. And c & f will be variables. And in the formula on reflected light, c is constant. And f & λ will be variables.

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Binary Star & Aether

Speed of light coming from approaching and receding stars of binary star is the same. This will be one of evidence of the existence of aether.

Note: However, as for evidence, aberrations (caused by motions of Earth relative to aether) will be more definite.

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Murmur, Again

Starlight is coming from outer space. When an observer moves in the direction of the light path, frequency of the starlight varies. For light, there is a formula c = f λ. Which one, c or λ, varies with the above frequency varying ?

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An Intermittent Ray of Light

Imagine that an incoming star light is intermittent (on and off: by human work). An observer is observing this ray of light. It will be certain that observer’s motion (in the light ray direction) does not affect anything of coming ray (intermittency, wavelength, amplitude, waveform, etc). So, in the equation c = f λ, it is f and c that vary for the moving observer.

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A Light clock

A light clock is working in a moving passenger car. Light path of light clock is illustrated vertically (in drawings). But this light clock leans somewhat to the right (or to left). So, to an observer stands on the ground, zigzag of light path (saw-tooth like) warps. Two kinds of dilation ? And if two clocks work, and these lean differs ?

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