Fourth dimension

I have to confess that the movie ‘Interstellar’ renewed my interest in astrophysics and understanding fourth dimension. It was in 2008 that I used to have discussions about fourth dimension after reading Hawking’s ‘Brief History of Time’ and ‘Theory of everything’. These two books showed a way to search answers for the countless questions we ask ourselves – who are we? where are we? etc. Then, I felt it was very complex to understand it. My recent rag picking of information on space-time from Youtube videos, articles made me understand how complex it is to understand the fourth dimension. And the intention of this blog is NOT to make the reader understand fourth dimension, but to understand its complexity and how we are ‘trapped’ in a 3-dimensional space.

Mathematical fourth-dimension

Let’s begin with understanding the mathematical fourth dimension. The above picture illustrates the 4th dimension in the euclidean space. The question – why is it not a still image? We’ll answer. Before that, let us understand 1-Dimension (1-D). Space with 1-D is a single line. There will be a single coordinate axis, alone, say x. An object in 1-D can either move forward or backward. To point out an object X in a 1-D, an example of a tuple looks like {2}. Which translates to, position of object X is 2. Object X looks either like a dot or line (connection of dots). Moving to 2-dimensional (2-D) space. It will have two coordinate axes, say x and y. The axes are orthogonal to each other. To point out an object Y in a 2-D, an example of tuple looks like {2,3}. Object Y can move forward, backward, left and right. Y can be a circle, triangle, rectangle etc. – so any plane figures. Now imagine, an object Y from 2 dimensional space comes to meet an object X in 1-D. Since, the intersection of 1-D and 2-D space gives us only a 1-D space, all that the object in 1-D can view is either a line or dot. X from 1-D with its limitation of being in a 1-D is not able to get the complete picture of Y. Extending the scenario to 3-dimensional space – add z-axis to already present x & y – orthogonally – Object Z. Tuple example – {2,3,5}. Z can move forward, backward, left, right, up and down. Z can be a sphere, cube, cuboid etc. Consider the intersection between 2-D and 3-D. We get a 2-D space. Now, when Z comes to meet Y. Y can see Z only as a circle or square or rectangle. Since, Y is struck in 2-D space. Moving to 4-D – we can observe that x,y and z are perpendicular to each other in 3-D. To envision a 4-Dimension, we should be able to show an axis, that is perpendicular to x, y and z. Showing such an axis in 3-D space is impossible and hence, we see it in the gif image (motion picture) put before the paragraph.

Understanding the boundless universe

Universe is expanding. We came to this conclusion from knowing that distances between galaxies are increasing. But, the question remains, is universe infinite? Applying our limitations in higher dimensions, we may get an answer. From above we can understand that an object is not able to comprehend object/information that belongs to a step above its dimensional space. Consider object Y (Object in 2D. Limitation – it cannot comprehend 3-D). Let the plane that Y moves on, be a surface area of sphere. Y being from 2-D space believes the surface area of sphere as plane. Now, with enthusiasm to explore, Y embarks on a voyage to see the ends of the plane. Will Y ever find an end? Y (with its limitation of 2D understanding) comes to believe that the plane is infinite and boundless. But actually, the sphere is finite and boundless. Similarly, universe also may be a boundless but finite space. It is the object Z (or read humans) that is not able to comprehend its higher dimension (i.e. the fourth dimension), completely. Interestingly, this higher dimension is part of our everyday life. We use it everyday, every hour, every minute, every second. We visit it when we want give the complete coordinates of meeting place or a dating place. It is every where. It is all around us. It is TIME.

Fourth dimension & physics

It is interesting to note that the phrase “time is precious” has altogether a different meaning. But, even in daily sense, when we plan to meet someone, we share the details of spatial coordinates and also time. Not sharing time leaves the plan incomplete. In physics, after the 3 spatial dimensions (x, y and z) 4th dimension is a temporal dimension – time. Understanding time implicitly means understanding time dilation i.e. relativity in time. In our daily routine, too, we see time is relative to GMT. But, when we speak about time dilation it is not the relativity with respect to GMT that we talk about, but, the relativity with object from another space-time dynamics. Time dilation is observed (not caused) in two different situations. One, when observers are moving relative to each other. Two, when observers are situated on different gravitational masses (Eg. read two different planets). This is not any hypothesis. This is part of daily routine for space scientists. The satellites moving in space run slow in time than us on earth, by a few seconds.

What should we do

We are a rare species. We haven’t yet found anyone of our kind (at least, with whom we can have an intelligent conversation and solve the mysteries of our universe). Hawking believes there is no such species in a billion light years from earth while Neil degrasse quirks that aliens might have visited us only to find intelligence absent on earth (we not being sufficiently intelligent for them. As in, what do you find when you see an insect or an ant? intelligence?). Sun is halfway through its lifetime. Before sun starts exploding into a giant redstar earth would have already burst. To escape from that certain catastrophe understanding the fourth dimension and above is essential. Hawking or his friends’ combine cannot do this alone. We need to think and move as a species. For all of the mankind to be as one, we need to quickly get to such a political arrangement, too. Observe our lives and politics, today. Every moment is governed by profit, power and pride. United States’s NASA is given a budget of $18.4 billion while its Corporate Banks were given a bailout of $1.4 trillion. As individuals we are not just locked in 3-D space but also trapped in consumerism & elitism. With such conduct of affairs and politics we would lose much prior to the certain catastrophe. All those working for an egalitarian society now have a new reason. Working for such a society is not just an option for us, but a necessity.