Gravity and the Theory of Relativity

According to the Theory of Relativity, gravity does not exist in the same way as Sir Isaac Newton believed it did. Newton believed that gravity was a force between two objects that attracted them together whereas Albert Einstein and his Theory of Relativity says that gravity is just a matter of curved space-time (I write “space-time” because the Theory of Relativity now blends space with time to give four dimensions). That is, an object bends and “curves” space around the object itself with the more massive the object, the greater the bend in space-time. This would mean that the Moon orbiting our Earth is following a curved path in space that is invisible to our eyes.

This also means that “gravity” bends our three dimensional space into a two dimensional invisible “curve” in space.

Since both the Moon and the Earth are quite massive, under the Theory of Relativity they must each “curve” space-time around each object but since the Earth is more massive, the Moon orbits it. At least, that is how I understand it. The more massive object wins and its “curve” in space-time is the one that is used. This raises a lot of questions.

If a massive object curves space-time then why don’t all of the planets orbiting the Sun orbit in the same path? According to the Theory of Relativity an object can create one curved path as its mass doesn’t change, so how do multiple objects in different sized orbits occur? Why don’t the moons of Jupiter, for example, break away from their orbit of Jupiter and follow the Sun’s orbit instead? Why does Jupiter’s “curve” override the Sun’s when it comes to its moons? What curve in space-time are humans following when they obey the laws of gravity by walking across the Earth?

If you think about gravity as “curved space-time” and only think very simplistically of one object’s gravity and its effect on another object (for example, the Earth’s gravity effect on the Moon), then it is very easy to see how the Theory of Relativity can apply. However, life is not that simplistic and there are many more objects in the universe than that and many different combinations that Relativity cannot seem to address.

Also, what allows objects to breakout of that curve? Are you punching a hole in the curve or riding over the curve? That would indicate a two dimensional curve and changing three dimensional space into a two dimensional curve is not possible. You can’t throw one of our three dimensions away because it is more mathematically pleasing.

I have seen a lot of people try and explain this phenomenon of gravity being “curved space-time” by having four people hold a flat bed sheet at the corners. A fifth person takes a heavy ball like a shot-put and drops it on the bed sheet. If the people at the corners of the bed sheet keep pulling on the edges to keep the bed sheet near as flat as they can, the ball rolls to the middle of the sheet where it has made a dent or curve in the bed sheet. This is how, the presenter would say, that an object “curves” space. Then they would take another ball, this time a much smaller, lighter one and drop it on the bed sheet only to see the second ball make its way to the first. The presenter would say that this is how gravity works. The second ball is just following the “curve” and doesn’t need to be attracted to the large ball in the centre of the bed sheet.

There are two major problems with this presentation. One is that you need gravity to pull on the shot-put to cause the curve in th efirst place and also to cause the second ball to move towards the first. If you tried this presentation in space, there would be no gravity to aid you, causing the balls to do not much of anything. The second is that you are trying to show three dimensional space as a two dimensional field (the bed sheet is the representation of two dimensional space). Again, there are three dimensions, so you can’t get around that one. Plus the ball is in three dimensions, so how can can you have a three dimensional object and a two dimensional object interact? You can't!   

If you believe that the bed sheet presentation is a true representation of how gravity works under the Theory of Relativity, then how do objects circling another object like a satellite circling the Earth, fall from its orbit? In the presentation the bed sheet has a downward plane caused by the first ball and this downward plane is what causes the second ball to move towards the first. In the presentation, Earth’s gravity is actually working on the second ball and forcing it down the plane of the bed sheet. If this was reality, there is no gravity to force an object down the plane of the “curved space-time” because “curved space-time” is gravity, so how does the curve force a satellite towards Earth? It doesn’t.

The simple truth is that the Theory of Relativity does not explain gravity but Newton’s theory of gravity does.

Two Dimensional (2D) Objects

Two Dimensional Objects; do they really exist?

My answer is no; two dimensional (2D) objects cannot exist in the real world, only in mathematical calculations and in theoretical scenarios.

In order to exist, an object must be made of three dimensions; length, width and height. If you can see it or detect it, it must be a three dimensional object.

Now you may be thinking, aren’t the very words written on paper or even in this blog an example of 2D objects? Again, the answer is no.

If you take a piece of paper with writing on it and look at it from the edge, you probably won’t see the height of the ink as it rises above the paper, but it is there. The ink has height and rises from the paper, if it didn’t you wouldn’t be reading this sentence right now. Take that paper and place it under an electron microscope and the ink on the page will look like a mountain range.

Electronically, the words on your screen have a depth to them. You can't really see the depth by moving the moniter, but the depth is there.

Even though there is no possible way a 2D universe can exist with the current laws of physics, this hasn’t stopped people from thinking about a theoretical 2D universe. For example, an author by the name of Edwin A. Abbott wrote a book in 1884 named Flatland. This book introduced characters that lived in a two dimensional universe. In this universe the rain came from one direction, north, since there was no “up” for it to rain down on and people were triangles, squares, circles and straight lines. Somehow light exists in Flatland from somewhere as the residents actually view other residents and things happening around them. Since there is no “up”, the author cannot say the light comes from a sun or another light source so he never answers that question. Since people in three dimensions actually see things (and colours for that matter) after light reflects off of the surface of an object, the author doesn’t say how objects without a surface facing them (that is, without height) can be seen. The author also doesn’t say how anyone can tell a triangle from a square.  If the “person” can only see its edge, how can a figure be discerned? In fact, if a triangle person doesn’t have an edge, that is it doesn’t have any height at all, how can it see? The only place for the eyes would be in the centre of the object facing “up”. However, since there is no “up” or third dimension, how can eyes be placed there? If they could, they still couldn’t look all the way to what is beside it as this requires height. Also, in order for an object to move freely like the people described in Flatland, they would need to be independent of the ground; that is, they must be unattached or untethered. In order to be unattached, there must be space between the two objects and in order to have space this requires a third dimension; height. Finally, if 2D objects did become “people”, like in Flatland, how do they interact? Sound needs three dimensions in order to work, light wouldn’t work as it too needs three dimensions to work and sexual intercourse and general interaction would be impossible as each “person” has no height and therefore would pass through each other because there is no thickness to stop them from doing so. Things may be incredibly flat in Flatland, but they are not two dimensional.

However, for some reason, even great scientists have not figured out these problems with two dimensional objects. Even Albert Einstein used 2D objects in some of his “thought experiments.” For example, in a lecture before the Prussian Academy of Sciences on January 27, 1921, Einstein talked about how you could take a “disc” and put it on a spherical surface and then push that disc across the spherical surface forever as you would not reach anything to obstruct you. He calls this, “two-dimensional continuum that is finite, but unbounded.” Einstein then takes the disc that is on the sphere and, using an outside light source and a flat object below the sphere like a giant piece of paper, manages to create a shadow of the disc on the object below. His theory was that by manipulating the disc on the surface of the sphere, one changes the size and shape of the shadow formed by the disk. Einstein then goes on to say that this can be translated into the, “three-dimensional case.”

Huh?

By using the three dimensional sphere, a light source shining down on the sphere from above and an object below the sphere, you are actually already in three dimensions! Just because the main focus of your concept was on the sphere’s surface, does not negate the three dimensional objects you were using.

Today scientists use the concept of 2D objects to help them understand a three dimensional universe better. Scientists and those without a scientific background seem to like the idea of two dimensional objects as it ‘simplifies things’ when trying to deal with complex ideas. For example, how would gravity work in a two dimensional universe? There isn’t a “down”, so gravity cannot pull from below an object, so would there even be gravity? If there isn't an "up" and a "down", does gravity matters? Some scientists believe that gravity could still exist but that it can warp the universe like someone taking a piece of paper and rolling it into a torus or doughnut-shaped object. The creatures of this “two dimensional” universe would live on the surface.

Now first of all, paper is not two dimensional, it is three dimensional but if you start “curling” a two dimensional universe, it is no longer two dimensional, it is now three dimensional. Second of all, how can you step out of the two dimensional universe in order to curl it? You can only move in two directions, if you moved outside the universe to curl it, you automatically have another dimension.

Also, two dimensional brains would, by their very limited nature of just two dimensions, find thinking much more difficult as a third dimension adds volume and extra space for a brain to exist. I mean, if you took a three dimensional brain and pulled it apart molecule by molecule, took those molecules an formed a "sheet" or one incredibly thin layer, the sheer size would take up the size of a football field! Two dimensional “people” would have to be huge in order to incorporate the brain alone or suffer a vast lack of intelligence!

While scientists may be able to mathematically create a 2D universe, the reality is that it just doesn’t work. As I have shown above, there are far too many problems with a universe limited to two dimensions so much so that it is not truly two dimensional.

It might be fun to think up a two dimensional universe as a concept but like thinking of pigs that spontaneously sprout wings and fly to the moon, it is just not possible.