A Crisped Introduction of Spacetime!!!
Space-Time… I am pretty sure if you have ever watched a ‘Space-Show’ or a ‘Sci-fi film’, then there is a high chance that you have heard this word.
Its sounds cool, isn’t? … And strangely, it’s concept is also cool,
enough to give you a good adrenaline rush to study astrophysics and its related
mathematics.
Okay… enough of the trailer… let’s dive into the movie and enjoy the
climax!!!
Space-time, as it sounds, made up of two critical words, space and
time. Space, as per the traditional physics, represents the 3-dimensional co-ordinate
system of our universe. Scientists before Einstein believed that our universe
is limited to these 3 coordinates (x, y and z axes) and the universe according to
this convention is called Newtonian. But, in 1905, Einstein showed in his
Special Theory of relativity that time is also an integral factor. Well, it was
not before 1908, when one of the Einstein’s own professor and renowned physicist
Herman Minkowski proposed the concept of the union of space and time as a way to reformulate
Special Relativity and in this way the concept of space-time was born.
Well, before going further deep into this, one concept should be
cleared. In a Newtonian Universe, the laws of physics are the same in all inertial frames
and time is absolute. Also, a coordinate is totally dependent on the 3-axes.
Things get a little bit weird in Minkowski universe (now commonly
known as Minkowski Space), where the concept of spacetime comes into the play.
Here, the whole universe is represented a 4-dimensional coordinated system,
which comprises of the traditional coordinate axes (x, y, z axes) and time. But
this concept comes with a critical catch. This time the time is not absolute as
it was in Newtonian Universe. That means that for different objects the time is
running at different speeds depending on a reference frame. I know its hard to
believe as we are not habituated to this type of concept. When we discuss,
space-time, Minkowski universe and special relativity, the concept of the frame of
reference become a critical thing.
The frame of reference refers to a point/object, and with respect to this
point/object, we do our calculations and observations. In the space-time concept, it
becomes critical because here quantities like velocities, time, mass, all are relative
to the observer or frame of reference. Only speed of light is the same in all
inertial frames. Minkowski Spacetime and special relativity obey the Lorentz transformations
which were formulated by H.A. Lorentz.
The concept of Space-time is again used in General Theory of
relativity (1916) and this time is used to describe the gravity. Now after the introduction of this theorem, the gravity is no longer a force as it was described in Newtonian
physics rather it’s the warping of space-time. To understand this, imagine that
ball on stretched tarpaulin, now you should expect a curvature around the ball
and the intensity of curvature is directly proportional to the weight of the
ball. A similar case is with the Spacetime fabric. Einstein described gravity
like this way and he is pretty successful with this as the equations of General
relativity finally solved the mysterious irregular orbit of planet Mercury. But,
till this date no one knows from where this spacetime fabric was created and
why it actually bends, we only know the effects not the reason behind it.
Well, there is a lot in the story but they are outside the scope of
this article and I am planning to write those in my upcoming articles. Topics
like Lorentz Transformation, spacetime interval and how its invariant, 4-vectors,
tensors etc. are very important to understand relativity and cosmology. So, I
will be writing about these gems, very soon…
And a very happy new year 2021 to you and your family. This will be the last article of
this year as well as this decade. Thanks for all the love and support…. See you
in next year…
-Ratnadeep Das Choudhury
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