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With or Without You (Newton)

Let us for a moment imagine a world in which Newton’s Law of Gravity was not replaced by Einstein’s General Theory of Relativity over a hundred years ago. In this world, when you drop a rock from your boat, the force of gravity pulls it down to the bottom of a shallow lake. In this world, when you dive down to go look at it, you release some bubbles. The bubbles rise to the surface, because the force of gravity causes the water to give the bubbles a buoyant force, quickly propelling them upwards. Sound familiar?

In this same world we might ask, what causes the rock to fall? Well, gravity, obviously. And then we’d want to know, since we are curious beings, what makes gravity do this? According to Newton’s Law of Gravity, it has to do with how much mass is present, and how close those masses are to each other. The more mass, and the closer the masses are to each other, the harder the pull. 

Well that’s great, masses act this way over a distance. But then, a middle school student walks up and asks, “How? How does one mass pull on another mass?” And a high school student says, “Yeah, what’s the mechanism behind this?” The answer is, no one knows. And when we don’t really know, we invent things like gravitational fields, just to make

us feel better about how we could possibly be transmitting forces across empty space. They are a convenient way of thinking about how the forces somehow are there, and since they act this way, well then, it must somehow be true, right? Right?

Well, yes and no. Yes, they act this way. Yes, we can measure the forces and calculate them as if there were a gravitational field there in that space, where the masses are. If we use Newton’s Law, we can calculate a force which is almost exactly equal to the measured force in our experiments. Does this make it useful? Yes. Does this make it correct? No.

Newton’s calculations helped humans predict and then find the planet Neptune. Using Newton’s Laws, we performed calculations to send humans to the Moon and back. That is extremely useful. His Laws are faithful under many circumstances. But there are also circumstances in which they were found to fail. In the same way that the planet Uranus was found to wobble due to Neptune’s pull on it, the planet Mercury had an unexplained motion in its orbit. Long story short, using Newton’s Laws, scientists predicted the existence of the planet Vulcan, which was simply not there, did not exist. No one understood how this could be.

Enter Einstein. In 1915, using his General Theory of Relativity, he showed the world that there is no need for the planet Vulcan. Mercury’s orbit is strange because, as close as it is to the Sun, spacetime itself is warped! Ok, enough of the history lesson, let’s now go back to our rock and bubbles and see what the new answer is, using gravitational science which modern scientists agree is the best current model of our universe. (Warning: most people have not been taught this science, so be prepared for new thinking.)

It’s 2024, one hundred and nine years after Einstein’s theory replaced Newton’s. In this world, when you drop a rock, the rock sees the water and the bottom of the lake accelerating up toward it as it falls. 

Three things you might ask: 

1. Why is the rock falling? 

2. Why do you say the rock “sees” when it has no eyes? 

3. Wait, what? The water and the bottom of the lake are accelerating toward the rock? That’s a bit backward, isn’t it?  

Let’s tackle these: Numbers 1 and 3 first. Ok, Einstein would say, look, it’s not the rock that is accelerating here in the traditional sense. Spacetime is warped around objects with mass. Earth is one of those objects, and it warps spacetime enough to cause all objects near Earth to appear to accelerate toward it. We say appear, because hey, let’s think about what’s truly accelerating. Newton said, in his second Law of Motion, when an object has a force on it, it accelerates in the direction of the force. This is still true today. In this case, as Einstein observed, a “falling” object has no force on it; it’s truly weightless. What does have a force on it is the ground. The ground you say? Yes, the ground. Think about it. The ground is being pushed up from below it by all the atoms stacked all the way to the center of the

Earth (Electromagnetic forces; electron repulsion, if you must know). If the ground were not being pushed up, just like you, without support, it too would fall to the center of the Earth. 

“Ok smartypants,” you say, “if this is all true, then why would I fall? Why does the rock appear to fall?” Good question and one that Newton had no answer for. Einstein explains that spacetime is warped, curved around objects with mass. Earth is massive and so bends spacetime near it. Objects that are not supported, follow the curvature of spacetime and appear to “fall” while doing this. You can think of space as flowing downward at an acceleration of 9.8m/s/s (or 32ft/s/s) at all times near Earth’s surface. Falling then, is simply going with the flow. In order to avoid going with this flow, objects on the surface therefore must experience an upward acceleration of 9.8m/s/s just to stand still. Einstein says a force must act on them (in an upward direction!) in order for them to avoid moving with the spacetime curvature.

What about question 2? Well, you got me there, rocks have no eyes. But seriously, Einstein said there are no privileged reference frames. This means that if you are in the boat watching the rock fall, you see it accelerate away from you. From the point of view of the rock, it is the water and the bottom of the lake that are accelerating toward it. Which is correct? Both, Einstein would say. Which has a true force acting on it? The water and the lake bed have an upwards force on them, Einstein would say (electron repulsion). The rock has an upward force on it too as it is “falling”, first due to the air, and then the water, when it enters the lake and sinks. 

How do the bubbles work in this scenario? Because the ground and the water are accelerating upward, pressure builds up at the bottom due to inertia, and the deeper in the water you are the higher the pressure, just as you would suspect. The buoyancy force on the bubbles causes them to rise. 

Einstein’s Equivalence Principle helps us understand that the conditions on Earth’s surface at a local level are indistinguishable from being in a rocket in deep space and accelerating that rocket at 1g. Everything in the rocket would fall down when you drop it and you would feel pinned to the floor just as if you were on Earth’s surface. The key to understanding this is grokking that the ground underneath your feet is currently accelerating upward in order to support you!

Here’s a machine I invented in order to help you with this concept. Inside two upside down glass jars are water, bobbers (floating upward) and lead fishing weights (hanging downward). When I give the machine a spin, centripetal force is introduced to the system. A reminder here that centripetal force is the fancy name given to the inward force that pulls the water, bobber, and weight toward the center of the system causing them to accelerate by constantly changing their direction (as opposed to their inertia, which would have them flying off in straight lines, away from the center). Watch the video of what happens to the parts of the system when the spin is introduced. What causes the weight to fly off away from the center of the system? What causes the bobber to move toward the center of the system? Think about it a bit. Come back. I’ll wait. 

It looks like density separation, doesn’t it? The lead weight, being more dense than the water, moves to the outside of the system, while at the same time, the less dense bobber moves toward the center. Two causes: centripetal force (leading to acceleration), and inertia. Thinking about direction a bit here, the force is from the outside pushing in (centripetal), which means the acceleration is in the same direction.

Ok, now stop the system from spinning. It goes back to the bobber floating (upward), and the weight hanging (downward). If you cut the fishing lines attaching them, they would perform the same density separation you just saw, the bobber floating to the top, while the weight sinks to the bottom. Same cause, different direction: force (leading to acceleration), and inertia. But be careful here, the cause is not the force of gravity (wrong direction), it is the upward force from the ground, causing the density separation! 

Start the system spinning again and the outside of the jar becomes the new bottom to which the weight “gravitates”. The inside of the jar becomes the new top, to which the bobber floats. This is not happenstance, it’s plain physics. The inward force dictates density separation in that direction. 

Imagine if Newton had thought about this three hundred years ago. He was so close on this one. He introduced the three Laws of Motion. He knew about inertia. He knew that if you put a force on an object it would accelerate. He viewed the orbiting of planets as centripetal acceleration, and invoked the force of gravity as the mechanism behind that acceleration. He was deeply troubled by how this could actually work, and knew this was a shortcoming in his theory. He didn’t believe that some unseeable force could grab planets across the vast distances in space and cause these orbits, and yet, he could find no other way. Here’s what Newton wrote:

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers.”

All readers were just as stumped as Newton, until Einstein developed his General Theory of Relativity. It is the shape of spacetime itself which is the constantly-acting agent. Flat spacetime does not cause objects to fall. Flat spacetime near a star would have no orbiting planets. Curvature alone can explain this. Curvature explains not only the orbits of all the planets, but also predicts black holes, gravity waves, and the relativity of time itself when close to massive objects. All of these predictions have been verified many times over by countless experiments over many decades. 

Ok, still curious? A final question then: What causes matter/energy/momentum to curve spacetime? Great question. Go get your doctorate and answer it. Let me know when you do, I’m curious too!


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