Spacetime Curvature

We have seen that the union between space and time is evident within relativity.  By travelling fast "in" space, one travels fast "in" time.  The farther you are from something, the greater the time delay due to the increasing distance light must traverse through.  

So we can think of the universe as a huge spacetime continuum, where space and time are intrinsically intertwined.  We have the three dimensional space we are familiar with plus time, the supposed fourth dimension.  Together, we have a four-dimensional fabric.  Instead of a landscape where all material objects are layed out and exist all at once, we have a timescape, where space and time are all layed out, all existing.  The past and the present as well as the future are all equally existent. There is no illusionary "flow" of time that is on track for everyone.  Each observer will have his or her own time and his own location and standpoint from this world.

Gravity can be thought was a warp or curvature of this spacetime.  Obviously, however, we cannot see the curvature since it is a four-dimensional curvature (remember gravity also warps time).  However, by using one dimension lower analogies with which we can correlate, we can conceive of a somewhat analogous scenario.

If you place a heavy ball on say a rubber mat, the ball's mass will create a depression in that mat.  The greater the mass of the ball, the greater the depression.  Roll a marble across the mat, and this dent will "pull" on the linear path of the marble, causing it to swirl and swirl.  If the marble was close enough or if the curvature of the mat was great enough, then the pertubation of the marble's path might even cause it to spiral into and eventually collide with the heavy ball.

(Note: The above curved path is an arbitrary curve with no mathematical accuracy.
It was made simply to somewhat "fit" the warp.)

This is exactly the same behavior we see in nature.  The closer an object is and the more massive, say a planet is, the greater the attraction between them.  And, as the object nears the planet, the curvature becomes greater, and the object speeds up, falling faster and faster.   However, in space, there is no friction, since it is a vacuum.  Thus, the Earth will not slow down and plummet into the sun, unlike the rubber mat scenario, where the rubber mat will eventually stop the marble.  

So we can imagine this four dimensional spacetime to be dentured, warped, and curved in a wild array due to all the matter occupying the universe.  If there were no curvature, as in the left-hand side of the above image, there would be, in effect, no gravity.  Objects would travel in straight lines and motion would be perfectly uniform.  

This curvature also explains the tidal effect, which, as its name suggests, makes the ocean tides. In the classical explanation of gravity (Newton's formula), gravity is inversely proportionally to the square of the distance, which means that if two objects double their distance, the gravity is now one-fourth as strong; triple the distance, the gravity is one-ninth as strong; quadruple the distance, the gravity is one-sixteenth as strong, and so forth.  Therefore, an object of considerable height will have different pulls on different areas of itself.  Your head is slightly farther away from the Earth than your feet.  Thus, your feet feels a stronger pull, and your head feels a less strong pull, and so you are slightly stretched.  However, since your relative height is so minimal compared to the Earth's radius, this effect is infinitesimal.  

However, a relativity large being would feel the pull.  The distance between his head and feet, when squared would produce a large result and therefore make a huge difference in force.  

Now, the moon is what causes the ocean tides here on Earth.  The side facing the moon is attracted the most, and bulges out to make a high tide. On the opposite side of the Earth, the tides, which feel sufficiently less gravity, are pulled away and thus also protrude and make a high tide.  The left side of the Earth is attracted and moves slightly to the right, while the right side of the Earth is attracted and moves slightly to the left.  This draws the water inward and makes two low tides.  

(from BlackHoles & Time Warps by  Kip Thorne (c) 1994)

Translating this into curved space, we can envision the tidal effect as the result of the different "intensities" of the curvature. As we can see, only a tall enough entity could feel the different strains, since a small being would be more or less "on" the same curvature.  The part farthest away from the massive object would feel less a tug and be stretched away, while the closer parts would be pulled inward.  Since the Earth is an extremely wide object, the distance between the side closest to the moon and the side furthest away will yield quite a coniderable difference in gravity.

A very giant astronaut feeling the pull:


(from Black Holes & Time Warps by Kip Thorne (c) 1994)

We can envision the spacetime curvature and how it moves things closer or stretches things apart by looking at the below two diagrams:

In this case, the curvature is negative, since it pulls objects away from each other:


(from Black Holes & Time Warps by Kip Thorne (c) 1994)

In this case, the curvature is positive, since it pulls objects together:


(from Black Holes & Time Warps by Kip Thorne (c) 1994)

In the first picture, the spacetime curvature is like the effect that takes place on the side of Earth opposite the moon.  In this case the curvature forces the two objects (water) to move apart and separate.  This causes the buldge of the tides. In the second picture, this is exactly what happens to lines of longitude on a globe.  The curvature of spaces forces, what apparently seems to be parallel lines at the equators, to converge at the poles.

Conclusion:

In fact, gravity is still a mystery today.  It is hypothesized that there is a graviton, a particle with hardly, if any mass, that is supposed to cause the force of gravity.  They are the messengers of gravity so to speak.  However, they are very weak and so have not been detected.

However, we can see that gravity is at least no longer a funny and mysterious "force acting at a distance" as Newton had thought.  It simply is a curvature of space and time.  Yet, since we cannot see this curvature, we depict space and time as continuous.  The above diagrams pretend that you are a higher dimensional creature looking down upon a curved smaller universe.  In this case, the figures were supposed two-dimensional figures curved in third dimension.

Translate that with our universe and we have our three-dimensional space curved into the fourth dimension.  We cannot see this fourth dimension, and we cannot see this curvature, since we cannot see light from the fourth dimension.  Everything is confined in three dimensions so no matter how warped or curved space might be, it would still seem smooth, as if it was a vastly hollow box.  

Gravity, we have seen, also has the same physical effects as acceleration.  A constant acceleration produces an artificial gravity while free fall makes the reference frame appear as if there was no gravity.

However, there are still many difficulties with gravity that prevent it from being unified with the strange world of quantum mechanics. 

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