The Mechanism of Space and Time (Theory of Relativity)
By Punyae Bhatia
Cosmofluencer (Season 03)
Einstein put forth his Theory of Relativity to try and explain how one’s motion in space results in a motion through time.
BASIC CONCEPTS OF COORDINATES AND REFERENCE BODIES
We all are familiar with the 3 spacial coordinates (x,y,z), which we often use to describe the position of an object in space. These are perpendicular to each other and are attached at a common point called the ‘origin’, which also acts as a point, relative to which the coordinate values are used.
For example;- Consider a point at coordinates (4,9,2). We can say that this point is:
● 4 units far from the origin along x
● 9 units far from the origin along y
● 2 units far from the origin along z
The origin acts as a reference body,also called an ‘inertial reference
frame.’
The x, y, and z dimensionsconstitute the 3 dimensions of space i,e position. This is known as the CARTESIAN SYSTEM Of COORDINATES.
Image credits: www.wikipedia.com
SPACE AND TIME IN CLASSICAL MECHANICS
Einstein told us to imagine ourselves travelling in a railway carriage moving along a straight embankment at a uniform velocity. Now imagine you drop a stone (not throw) from the carriage window.
Now, if we neglect the effects of air resistance, we will observe the stone falling straight downward since it retains most of the horizontal velocity it had while on the carriage.
To an observer standing on the embankment and watching you drop the stone, the stone will appear to fall in a parabolic path as it moves horizontally, as well as vertically, relative to that observer.
Image credits: InterNext.co.za
So we can say that; the stone traverses a straight line relative to a system of coordinates rigidly attached (relative) to the carriage, but relative to a system of coordinates rigidly attached to the ground, it describes a parabola.
It can be clearly observed that there is no such thing as an independently existing trajectory, but only a trajectory relative to a particular body of reference.
● In order to have a complete description of the motion, we must specify how a body alters its position with time.
Hence we highlight the need for the time coordinate i.e. a 4th dimension. These 4 dimensions; x, y, z, and time (t) can be used to describe any motion or event. Einstein termed this four-dimensional arrangement as the ‘space-time continuum.’
Can you think of other everyday examples where different observers would see different paths for the same object?
EFFECTS ON RELATIVE BODIES
You may be familiar with Newton’s Law Of Inertia. It states that:-
● A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line. A system of coordinates, relative to which the law of inertia holds (objects move in a straight line) is known as the Galilean System of Coordinates.
Hence, the basic PRINCIPLE OF RELATIVITY forms itself as;
“All natural phenomenon run their course with the same general laws in two bodies relative to each other when one is in uniform motion relative to the other.”
The most important and basic example of such is the constant nature of the speed of light in a vacuum (approx. 3 x 10^8 m/s). The Principle of Relativity implies that the speed of light is the same for all bodies, regardless of their relative motion.
These basic laws that we discussed are what were brought together by Einstein to create his first theory.
THEORY OF SPECIAL RELATIVITY
The THEORY OF SPECIAL RELATIVITY simply says that:
- The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.
- The speed of light c is a universal constant, independent of the relative motion of the source emitting the light.
CONSEQUENCES OF SPECIAL RELATIVITY
● E = mc2
It says that energy (E) equals mass (m) times the speed of light (c) squared. It means that mass and energy are related and can be converted from one to the other.
Another result of SR is that as an object moves faster, its observed mass increases. As an object approaches the speed of light, its mass becomes infinitely large. As a result, an infinite amount of energy is required to make an object move at the speed of light, which is not possible.
● Time-Dilation
Time dilation is the difference in time measured by two different bodies relative to each other. The faster you move through space, the slower you move through the fourth dimension – time (relative to the other body). The faster you move, the greater the effects.
Imagine you leave Earth today and travel in a spaceship at 99.99% the speed of light. When you return after what seemed like 24 hours to you, 193 years would have passed on Earth!
Your time simply moved a lot slower than the time on Earth because of how fast you were moving. Everyone on Earth would experience time normally, but would actually be moving slower/faster relative to the other. The time difference between you and Earth would simply depend on how fast you were travelling.
This leads us to the final topic;
GENERAL THEORY OF RELATIVITY
We know from Newton’s laws that the higher mass a body has, the more gravity it exerts. Einstein told us to imagine space-time as a fabric. He said that massive objects can warp this space-time ‘fabric’, causing other objects to follow that curved path. The deviation of this path solely depends on the mass of the bigger body.
Massive Bodies Warp Space-Time!
Image
credits: www.ligo.caltech.edu
Light also follows this curved path in a warped space-time. The more warped space-time is, the longer path light has to travel around it, and thus longer it will take. This is why staying near a massive object can slow down time relative to someone else. A person on Earth will experience time relatively slower than someone just floating in space.
Conclusion
In conclusion, the theory describes the relative nature of time. It also explains gravity based on the warping of space-time and the relations between space, time, velocity, energy, mass, and gravity, and how a change in one would affect the others.
The theory’s implications extend beyond theoretical physics, influencing technologies such as GPS and enhancing our understanding of cosmic phenomena like black holes. As we continue to explore the universe, the principles of relativity will remain fundamental to finding the mysteries of space and time.
We will keep looking for new theories and cosmic objects that defy everything we know. What we may find is still unknown, but that’s the best part about it, isn’t it?