Space-Time is a scientific model in which all the three dimensions of space (x, y, z) and also a fourth dimension were fused together to form a 4d manifold. You might be wondering, what the fourth dimension is. Well, it’s nothing but time. But why is time a dimension? To understand it, we will need to know what a dimension even is.
Dimensions
Dimensions are basically quantities that can describe an event.
So, here as you can see in this image, we can say that X is left/right motion, Y is upward/downward motion and Z is forward/backward motion. Now, imagine an event, let’s say, a car crash. In order to describe this event, we will need X, Y, and Z to pinpoint the location of the event. In addition to that, we need to know the time of the event. So, we need to take time as a Dimension as well, which makes our world a four-dimensional one.
Who discovered it?
Space-time was actually not the idea of Einstein himself, it was first proposed by German mathematician Hermann Minkowski, in 1908, however, it was just a way to reformulate Einstein’s special theory of relativity in 1905. Interestingly, Hermann was one of the professors of Albert Einstein.
Later, Einstein discovered that the curvature in 4-dimensional space was nothing but gravity.
Light cones
The diagram (Fig:5) below shows what’s known as a light cone. But before discussing light cones, let’s take a look at a little more about spacetime. Let’s say that there was a road, spanning all around the earth’s circumference and that you were gonna drive on this road non-stop for 10 months or so. Yes, this is impossible as you’d have to travel 40,075km above water with no sleep for ten months together with a whole host of other problems, but let’s imagine that somehow this happened.
The circle in Fig:2 is a 2D representation of the earth and the dot on the circumference is your car.
Now, we’ve stacked the 2D representations of you going around earth and made it 3D to represent time. And, with this in mind, let’s discuss light cones.
Think of an explosion before we dive into the concept of light cones. When we picture the explosion in 2D, we can see that the object keeps on expanding and increasing in size. The diagram below illustrates exactly this. (Fig:4)
Just like we did last time, let’s stack them up and create a diagram.
All we’ve done so far has to do with only the upper part of the cone. The lower part is a little strange because here, the entire explosion event occurs the other way around.
The cones only show the trajectories light would take, if it were present, so light isn’t necessarily required to be here. This means, our spacetime has a light cone structure even in the dark!
The “A” in this diagram is what the observer calls the present. Nothing can travel faster than light, according to Einstein’s theory of relativity, hence they make up the boundaries of the cone. These light cones can now be used to depict the causal structure of spacetime. The points on and inside the future half of the light cone make up its ‘causal future’. Meanwhile, the points on and inside the lower half will make up the past.
Light cones tell us not only the past, but the possible future events; perplexing I know, but unfortunately, we are beings that evolved to only comprehend the 3 spatial dimensions. Alright, enough of questioning existence, because we will be doing it later while talking about time travel.
How does Space Time interact with Gravity?
As you already know, spacetime is a 4-dimensional model. But we can talk about it in terms of a 2D plane for simplicity’s sake and call it a Spacetime fabric as it will be easier to imagine and understand.
As you can see in the above image (Fig:8), mass bends spacetime. An easier way to imagine this is to take a sheet of paper. And then, if you put some mass(for example, a metal bead or a ball) in the middle of the sheet of paper, you can see that due to the mass of the object, the paper curves/bends around the object. Think of spacetime in terms of such paper. In Einstein’s general theory of relativity, gravity is taken as simply the curvature in spacetime. The greater the mass, the greater the curvature.
When a body (A) with low mass enters the curved spacetime around another body (B) with higher mass, A will be attracted towards B. As the popular saying goes, “Mass tells spacetime how to curve and spacetime tells mass how to move.”
Bending of Light, Time and the Reason Why Black Holes are Black!
We have all learned that light always travels in a straight line. So, you might be wondering how light can bend. Light travels through the spacetime fabric. We learnt that a body with a lot of mass can create a very large curvature in spacetime. And if the spacetime itself is curved, how can light travel in a straight line? Yet, here the light does travel in a straight line but only locally, whereas with respect to space-time we can say it travels on a geodesic. So, very massive objects curve spacetime so much that light cannot escape the curvature. This is also the reason why black holes are Black! Since the escape velocity of the black hole is more than the speed of light(c), even if a black hole emits light, it won’t reach us. Thus they appear black! This also introduces us to a new phenomenon called Gravitational Lensing.
Gravitational lensing is when curvature in space-time or gravity acts as a lens. Here, we can imagine a light source (a star, labelled A) being blocked by a very massive body (the sun) when viewed from the earth (C). As the sun has a lot of mass, it will bend the spacetime fabric. Even though our sun is blocking the light from (A) due to the curved space-time, the light emitted from the star will travel around the curvature of space-time and it will reach (C). This phenomenon is called gravitational lensing.
Now, let’s talk about the bending of time. As you already know, light, as well as time, travels in a straight line. Let’s say that time is travelling from point A to point B. But if spacetime itself is curved, it will take a longer time for it to reach point B as it needs to travel a longer distance due to the curvature in spacetime. So, in short, we can say that time flows slower near a very massive body but you won’t notice it when you are on it, instead, you’ll see everything else away from that body moving at a faster rate.
Red Shift and Blue Shift
We all know that space is expanding. When space expands, the fabric of space-time also stretches. Now, let’s imagine a galaxy, called galaxy A, that is moving away from us, and there is another galaxy that is moving towards us called galaxy B.
Let’s say that galaxy A emits blue light (short wavelength light) and galaxy B emits red light (long wavelength light). When we observe them from a stationary point of view, we will find galaxy A emitting red light, and galaxy B emitting blue light, if they are fast enough. This phenomenon is called red shift and blue shift respectively.
So, why is the light from galaxy A redshifted and the light from galaxy B blueshifted? This is because if a light source is moving away from us at a very high speed, the electromagnetic waves emitted from them will get stretched out along the way. When the waves get stretched out, their wavelength increases. So, the blue light gets redshifted to a red light or infrared or radio depending on the velocity at which it’s moving away from the observer. Similarly, when a light source (galaxy B) is moving towards the observer at a very high velocity, the electromagnetic waves will get compressed. Their wavelength shortens and as a result, red light can get redshifted to blue light, UV, X-rays, etc., depending on the velocity at which the light source is moving towards the observer. A similar effect happens with sound as well, which is known as Doppler Shift.
Apart from the Doppler Redshift, the most interesting type of redshift is the Cosmological Redshift. This phenomenon was observed by Edwin Hubble in 1929. When he observed faraway galaxies, he noticed that the farther the galaxies are, the faster they are moving away from us. Also, another interesting thing he noticed was that the farther away the galaxies were, the redder they got. This later came to be known as Cosmological redshift and led to the formulation of Hubble’s law. Hubble’s law basically states that the universe is expanding and that the farther away the galaxies are, the greater the velocity at which they are moving away. When our universe is expanding, our spacetime expands as well. As a consequence, the light or electromagnetic waves travelling along it also expand and get redshifted. What about a cosmological blueshift then? Cosmological Blueshift has not been observed yet because for it to happen, the universe must contract instead of expanding.
Wormholes, exotic matter and time travel!
In the singularity of a black hole, spacetime bends to a very extreme degree. But there is a possibility that an infinitely dense object can bend space-time to such an extreme that it creates a hole in the fabric of space-time, known as the Einstein-Rosen Bridge or wormholes. Wormholes, if they exist, can allow interstellar travel or even time travel to become a reality. It is easier to visualize this than try to explain it.
In these figures, the orange dot represents matter traveling through a wormhole. As you can see, the wormhole connects two different locations, and by traversing the wormhole you can get there much faster than going there in a straight line. It would even be possible to traverse time in the presence of a closed timelike curve.
But what is a closed time like curve?
In a closed timelike curve, the worldline of an object follows a path through spacetime where it ultimately ends up at the same exact location with coordinates in space and time that it was previously.
Problems
First off, wormholes only exist on paper, as of now. The actual existence of wormholes hasn’t been confirmed just yet. The problems won’t be over, however, even if wormholes do indeed exist. They would be extremely small and would probably close soon after popping into existence, due to gravity. If we somehow manage to find a large wormhole or were able to resize one, how would we hold one open? Exotic matter would be an option. This exotic matter would have properties much different from normal or even dark matter. It would be negative in mass, which is great as it can therefore resist the gravity trying to close the wormhole. But the problems aren’t over yet. Our anti-gravity would have to be tremendously strong in order to withstand any gravitational forces trying to shut a wormhole closed. Besides, where would we even find this exotic matter? The wormhole can be held open with exotic matter sure, but traversing one wouldn’t be so plausible, here’s why.
Positive or ‘normal’ matter would repel the exotic matter. So as beings made up of positive matter, traversing a wormhole held open with negative matter would be a little difficult–and that’s an understatement.
The time travel paradoxes are also going to be an issue. If a plane from New York to Los Angeles took off at just a few degrees off(away from the right direction) southward, it would more likely end up closer to Mexico than Los Angeles. Similarly, a slight change in the past could have very serious consequences. Time travel paradoxes are perplexing to understand for minds that are adapted to perceive a three-dimensional world.
You might also like: What if Einstein was wrong?!
By Arjun Sooraj & Alwin Naveen
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