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 = mc2, 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/s2. 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 1011 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)
Every mass point is either in an inertial (unaccelerated) frame or accelerated frame. If a rigid homogeneous cuboid is in free-falling, every mass point is in accelerated frame. In this cuboid, there can be no inertial frame, even locally.
P.S. This difference is not fictitious but absolute.
Correction (on today’s post : on the third note)
A starlight > A light source
Two Formulas for Speed of Light (in vacuum)
First formula, v=fλ: It is speed of light relative to aether, and v is constant. Area is where light follows aether frame. That is, more than a few light seconds away from light source.
Second formula, c=fλ; It is speed of light relative to light source, and c is constant. Area is where light follows emission theory. That is, within a few light seconds from light source.
Note) First formula is the same as formula for the speed of sound in air (depending on f and λ).
Note) In outer space, a starlight is passing through a tube. In the center of the tube, a plate of glass is placed. In front of the glass, the starlight follows aether frame, and in back of it, starlight follows emission theory.
Note) A starlight is moving in aether. It is possible that v and c move at the same speed. Usually, v will be below c.
Note) For a moving observer, speed of light must be reconsidered (starting with the Doppler effect).
Speed of Light Varies
On the Moon’s surface, plane waves of Sunlight are arriving horizontally from above to two passenger cars. There is a small pinhole at the center of ceiling of two passenger cars, and on the floor, there is a spot of light that passed through pinhole.
Two passenger cars are moving on the Moon’s surface at different speeds (in x direction). For an observer inside the passenger car, position of light spot on the floor will be different. This difference in position will be the same for an observer stands on the Moon’s surface.
Gravity (gravitational field) and Time
There is optical path of triangle ABC with top A of tall tower and mirror BC placed on the ground (as vertices). Laser light emitted from light source set at A (frequency is constant) is reflected by BC and returns to A. Frequencies of laser light at ABC will be the same. Time dilation due to gravity will be impossible.
In outer space, a starlight is coming from the right. This ray enters the pinhole of a pinhole camera and is reflected upward by a mirror set at 45 degrees upwards in the camera.
When the camera moves to the right or left (at a uniform speed), the position where reflected light hits the upper inner wall of the camera will move. Incident light is propagated in aether, and reflected light follows emission theory.
Note: Speed of lincident light and rleflected light relative to the mirror are generally different. So, angle of the two are also. λ are also).
Apology and Cancellation
My recent posts April 29 seem to be invalid. Sorry.
In outer space, three pinhole cameras are pointed in X, Y and Z directions (these are in uniform linear motion, the same as Sun). Cameras are pretty large. In the camera, on the inner wall, on the opposite side of the pinhole, disks rotate once and receiving position of star lights are recorded.
Recorded position of star lights on three disks will not be true circle. These may indicate motion of the pinhole cameras relative to aether.
Mars & Aether
Annual aberration of Mars is based on its revolution period of 1.881 years and average orbital speed of 28.07 km/sec. That is, aberration is mainly caused by motion of observer relative to the aether. Qualitatively and quantitatively. Needless to explain.
Other aberrations of Mars are also.