That Mysterious Thing Called Gravity
Imagine you are jumping off a high-rise. From your perspective, you are falling straight down to the street below. Einstein, however, would argue that it's relative: the street could be falling to you while you stay suspended in space. If this is the case, then your mass would not matter. You could weigh a ton or be massless and the street would still accelerate toward you at 9.8m/s^2. He would also argue that your spacetime is curved. But you are falling in a straight line toward the street or vice versa. So what is curved spacetime?
Look at the left diagram. There's a circle that represents earth and there's an arrow pointing down. So where's the curve? You are accelerating. That means your change in distance per change in time is changing. If you plot on a graph the total distance you fell for each time period, you end up with a curve. If you know calculus then you know that acceleration is the double derivative of distance, and, when you calculate the double integral of acceleration, you get the curved graph you see at the far left.
The middle diagram shows how a big planet (A) has less spacetime curvature along distance (ds) than planet B. Yet, planet A has more gravity due to its superior mass density. Here is where Einstein's theory of general relativity seems to break down. Data from NASA and some number crunching confirm this lack of correlation between curved spacetime and gravity:
At the previous photo, at the far right diagram, you can see a photon passing by a planet. It goes along a curve. But is it because the space is actually curved? Or is it because it simply gets pulled off its course by a gravitational field? Imagine you have a rubber ball in your hand. You can increase the mass density of the ball by squeezing it. When you do this, you will feel the ball's counter-pressure against your hand. With this pressure and counter-pressure, you are simulating gravity. Anything that gets caught between the ball and your hand will experience the pressure, whether the thing has mass or not. Its mass won't matter. It will experience the same pressure as anything else.
How Mass Density Shrinks Time and Space
A line with unit bars serves as a 1D space to demonstrate how time and space shrink when particles (the two dots) move closer together. The total distance of of the space (s) is 6 units. The total time (t) is the time is takes a photon to go from each point to the other and the time it takes the photon to go from each point to the end of the space closest to each respective point. Actually, just add the number of unit bars and pretend they are time units.
In the first example, the two points are at the extreme ends of the 1D space. s=6 units. t=12 units ([6 units to the right of the left point] + [6 units to the left of the right point] = 12).
As the points move closer together, the distance between them shrinks, so does the time it takes for a photon to traverse between them. But something strange also happens: Notice that the total time (t) shrinks while the total distance (s) remains constant. In the next example, the photon must go 4 units from each point to the other (a total of 8). The right point is 1 unit from the end of s. The left point is 1 unit from the beginning of s. So t = 8 + 1 + 1 = 10.
In the next two examples you can see as the points move closer, time (t) decreases while distance (s) stays constant. Unfortunately, Energy (E) increases. This violates energy conservation. So space (s) must shrink to compensate. But shrinking space only increases the mass density and reduces the time a photon takes to traverse that space, so t shrinks which increases E, so s has to shrink some more!
Hopefully, when a critical minimum distance is reached the electromagnetic force (EM) will prevent a total collapse of time and space. On earth, we feel space pressing down on us, trying to reach an energy equilibrium, but the EM pushes back. We can feel it pressing against our feet as we stand on solid ground.
Is Gravity Fundamental Like the Other Forces?
Imagine a group of scientists riding an elevator. The elevator rises at 9.8 meters per second per second. The acceleration beneath their feet is indistinguishable from gravitational acceleration. They have a theory: This acceleration, they now call gravity, is caused by curved space-time. It is one of the fundamental forces of nature. It is not the electromagnetic force, for instance. But wait! The elevator is powered by electricity!
If it weren’t for the electromagnetic force, this force they call gravity would not be happening.
Gravity would be nowhere if it weren’t for mass and energy. What exactly is mass and energy? They are different forms of the same thing, but if you look at them closely you will note they consist of the strong force, the weak force, the electromagnetic force. The truth is, anything that has energy (that includes all the fields, particles, and forces your physics textbook can offer) can cause acceleration that we interpret as gravity. Heck, the above-mentioned elevator could be powered by a guy pulling on a rope attached to a pulley. Are gravitons produced when he does this? The scientists in the elevator think so.
Here’s a question to ponder: Would the elevator still work if gravitons weren’t involved?
So far the scientists have not found any gravitons. They have discovered bosons for the other forces. This does not surprise me. The electromagnetic force, the strong force, and weak force can all be found inside the atom. At their root, they are very small forces, so finding them at the quantum level is easy. Gravity, on the other hand, is a big force. It requires massive amounts of stuff before we even notice it. And, according to General Relativity theory (GR), it requires curved space--which is a big space.
Quantum space is flat, so why would we find gravitons there? According to GR, you need a big curved space before you can begin to find that elusive graviton--assuming it is there to be found. Scientists have found gravity waves, and why not? They are ripples in space-time. But even gravity waves fail to yield that graviton that is needed to fill that gaping hole in the standard model. Gravity waves are hard to detect and require large orbiting masses just to get a light bulb's worth of gravity-wave energy.
The graviton reminds me of the purple pixel. Suppose you see the color purple on your computer screen and you wonder what it is made of. You decide that purple is made of little, tiny purple pixels, so you get out your microscope and examine some purple you printed. You discover the red, blue and green pixels--they are the fundamental colors. You even create a standard color model. All you need now to complete your model is that elusive purple pixel. You can’t find it anywhere! Yet you see purple!
Hey, maybe the purple you see is really just a collection of the pixels you have already discovered. Maybe gravity is a collection of all the stuff that make up large masses and energy. There is no purple pixel--and maybe there is no graviton.
Gravitational waves suggest that Einstein was right: that gravity is caused by curved space-time. He successfully predicted that light would bend in the presence of a gravitational field. According to our good professor, the light follows a geodesic path, a curve in the fabric of space. But can gravity exist in the absence of curved space-time?
Imagine you are in a rocket flying through space in a straight line. The rocket is accelerating at one g. You experience gravity. Space along your path shrinks and so does time, but these vectors are shrinking, not curving. You are still flying straight. The changes in in time and space are caused by your acceleration you call gravity. They do not power your rocket and cause the acceleration. It is the energy in your fuel tank that is behind your g-force.
Imagine you are skydiving over the equator. You jump out of the plane. You, along with the earth, are spinning, so you don’t fall straight down. Your path is curved. “Ah hah!” you cry out, “there is a correlation between gravity and curved space-time.” Then you skydive over the north pole. The earth spins east; you do not spin with it this time. You fall straight down. You skydive at various locations and find to your amazement that the curvature of your path varies but the pull of gravity remains constant.
Imagine a satellite orbiting the moon at the lowest possible orbit. It follows a steeper curve than if it orbited the earth. The earth-orbit curve is one-tenth the moon’s; yet the earth’s gravity is more than ten times the moon’s.
Gosh! What happened to the correlation between space-time curvature and gravity?
We do have gravity waves, though--so let’s chalk one up to Herr Einstein.
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