## ‘Unveiling the Astronomical Layers of Our Universe’

The greatest mysteries of our universe have often troubled the greatest minds to ever live on our earth. But what happens when one can resolve the unsolvable? In the field of physics, the era-defining genius Albert Einstein has made breakthrough discoveries after breakthrough discoveries. To this day, the legacies and works of this mastermind continue to play a major role in unraveling the mysteries of the world. Einstein’s Theory of General Relativity and the discovery of black holes have truly inspired many physicists and have truly shaped our perception of the world.

## General Relativity:

Firstly, what is Einstein’s Theory of General Relativity? In 1905, Einstein determined that the laws of physics are the same for all non-accelerating observers, and in a vacuum, the speed of light is independent of the motion of its observers. This was known as the theory of special relativity and was the new framework in the fields of physics that proposed new concepts of space and time. Einstein then spent the next 10 years attempting to include acceleration in this theory. In 1915, Einstein’s Theory of general relativity was finally published and he determined that huge objects cause a distortion in space-time and are felt as gravity. After discovering that the speed of light in a vacuum is the same regardless of the which the observer travels, Einstein deduced that space and time are interwoven into a single continuum known as space-time. Imagine a bowling ball in the center of a trampoline, the ball would compress into the fabric causing it to dimple. A marble is placed onto the trampoline rolls around the edge and spirals inwards towards the ball, pulling in similarly to the way gravity pulls at rocks in space. [image: ] This theory of gravitation also generalizes Einstein’s special theory of relativity and replaces Newton’s standard theory of Gravitation. Considered to be perhaps ‘the most elegant and beautiful example of a physical theory ever constructed’, the radical theory relates the structure of time and space to the distribution of matter and energy. The amount of matter and energy that space-time contains is a direct function of the geometry of space-time – to put it simply, massive objects distort space-time.

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## The Principle of Equivalence:

The foundations of general relativity are significantly old as they date back to the equivalent principle of Galileo and Newton. According to Newton, the principle of equivalence states that ‘all objects accelerate at the same rate in a gravitational field regardless of their mass or composition’. His theory was proven on numerous occasions over the years, notably by Hungarian physicist Baron Lorand von Eotvos. However, Einstein’s principle of equivalence states that: ‘No observer can determine by experiment whether are in an acceleration frame of reference or gravitational field.’ To prove this, let’s propose a hypothetical situation. As shown in Figure x, one box is sitting on Earth whilst another is accelerating at 9.81ms-2 in space. All experiments must be done in the box and it's not allowed to look out the window however no matter what actions the two observers take, they will ultimately see the same result: The dropped red ball will fall with an acceleration g.

To further explain this experiment, in a reference frame where gravity is felt, the effects of gravitation on physical laws can be obtained simply by mathematically transforming laws from a freely falling frame to the laboratory frame. According to differential geometry, this is insinuating that space-time is curved or as per Einstein’s Equivalence Principle, the effects of gravity are indistinguishable from the effects of being in curved space-time.

## The Speed of Light:

When the principle of Equivalence occurs, there are immediate consequences. The first consequence is that the speed of light in a gravitational field is the same as in any inertial frame of reference. As shown in Figure X, An observer in A would measure the speed of light as 3 x 108 for the speed of light. An observer in the free frame of B also would reach the same conclusion since both frames are equivalent.

## Inertial and Gravitational Mass:

The second consequence is that inertial mass and gravitational mass are the same. The inertial mass is the ratio of the net force on a body to the body’s acceleration and the gravitational mass is the ratio of the gravitational force on a body to the acceleration due to gravity. In Frame A of Figure X, the mass measurements are also the inertial mass measurements. However, in frame B at rest in a gravitational, mass measurements are gravitational mass measurements. Since the two frames are equivalent, the equality of the two masses follows.

## The Bending of Light:

Another consequence of the equivalence principle is that light bends toward a massive body. Imagine a spacecraft orbiting a massive object. A ray of light is emitted from the back of the spacecraft toward the front. The frame of the spacecraft is freely falling and so equivalent to a frame moving at constant velocity in a straight line. In this frame, there is no doubt that the light will hit point F in the spacecraft in orbit since the two frames are equivalent. Hence, massive objects can act as a kind of gravitational lens.

## Time slowing down:

A final consequence of the equivalence principle is that time slows down near a massive body. As shown in Figure X, two rays on a wavefront AB are bent as they pass near a massive object, Points A and B are in phase.

The ray at B moves onto the point at D and the ray at point A moves onto point C. The wavefront AB has bent because the rays bend towards the massive object. If points C and D are to be in phase, the rays from Points A and B must take the same time to get to C and D. However, as ray BD will cover a shorter distance than rays AC, BD will continue to travel at the same speed. The problem can be avoided if time runs slower for Ray BD.

## Gravitational Redshift:

Einstein’s theory of general relativity predicts that the wavelength of electromagnetic radiation will lengthen as it climbs out of a gravitational well. Photons must expend energy to escape, but at the same time must always travel at the speed of light, so this energy must be lost through a change of frequency rather than a change in speed. If the energy of the photon decreases, the frequency also decreases. This corresponds to an increase in the wavelength of the photon, or a shift to the red end of the electromagnetic spectrum – hence the name: gravitational redshift. This effect was confirmed in laboratory experiments conducted in the 1960s.

## The Pound-Rebka Experiment:

In this experiment, which was conducted at Harvard University in 1960, a beam of gamma rays of energy (14.4 keV) from a nuclear transition in iron-57 was emitted from the top of a tower 22.6m high and detected at ground level.

Let Fembe the emitted frequency at the top of the tower and Fo the observed frequency at ground level.

The energy of the emitted photon is hfem. This photon is received at a position lower than the emission point and energy conservation demands that:

Hfem + mgH = fo

‘Mass here stands for the gravitational mass of the photon, that is its energy divided by c2. This mass is thus (hf/c2). Hence

Hfem + hfem/c2 x gH = fo

· Fo= fem(1 + gH/c2)

This means that the frequency shift Δf= f0-fem Δf/f = gH/c2

(Here, f stands for either the emitted or the observed frequency since they are almost equal)