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Name: David M
Status: other
Age: 60s
Location: N/A
Country: N/A
Date: 1999 


Question:
Einstein said that gravity was not a force. Would he, and other scientists, say that gavity was never a force? If someone laid me down and put a five thousand pound weight on my chest, I would think gravity was a force. How would gravity be understood in a situation like this?


Replies:
As a force, of course. The debate about the edges of which you are nibbling is not whether gravity is experienced by masses as a force, but rather on the mechanism by which gravity causes such experiences. Let's explore this a bit, to get a hint at why (a) the issue ain't obvious, and (b) Einstein's resolution is considered so breathtakingly ingenious.

In the case of a 5000 lb weight on your chest, the mechanism of the pressure may seem pretty self evident: the weight ``wants'' to be on the ground, your body is in the way, so the weight (stupidly) tries to go through your body, which resists. The attempt registers to your senses as a pressure -- the force -- and you are also aware of the force, the resistance, your body puts up. All quite simple. An object can only exert a force on another object when the two are in contact, and it does so only when the second object stands between the first object and its ``natural'' state (at rest on the ground for heavy objects, up in the air for light stuff like steam, flame, etc.).

But now Galilean relativity rears its ugly head. Say you're in an airplane and you drop a baseball. The ball falls straight down, seeking its ``natural'' state on the ground. But the ball does NOT also move backward, relative to you standing in the airplane cabin, that is, the ball does NOT seek its natural state of rest. Now we throw a ball the length of the Space Shuttle. The ball slows down (from air friction), seeking its natural state of rest, but it does NOT also fall downward, to seek its natural state on the ground. A couple more experiments like this, and we are forced to abandon the idea of a single ``natural'' state for each object.

The next step is the Newtonian concept of force and inertia. We propose that however a body is moving now (as long as it is in a uniform way) is how it will continue to move in the future. This is inertia. And, if a body is observed starting to move differently, it must be because a force is acting on it. So, a force is something that causes a *change* in state. Objects only seem to have ``natural'' states on Earth because there are large, permanent forces here (e.g. gravity) which are always trying to change the state of things in certain way (e.g. pull them to the ground).

A car slowing down is experiencing a force, as is a car speeding up or a car rounding a bend. In each of these cases, it is the wheels in contact with the ground that are exerting the force. But now the puzzle of action-at-a-distance, or Einsteinian relativity, rears its still uglier head. A rock in free fall or a planet going around the Sun clearly experience acceleration and hence a force: indeed, the force of gravity. But how is this force ``transmitted'' across the empty space in between? If the Sun were to vanish, would the Earth instantly begin traveling in a straight line? *That* can't be, because it violates the principle that there is a maximum speed at which information can be transmitted across distances. (We need the speed limit to preserve ``locality'' in our physics, the idea that far away events are increasingly less likely to influence nearby events, and locality is needed to allow basic physical laws such as energy is conserved or entropy always increases to have meaningful implications.)

We can give up spooky action-at-a-distance by requiring a gravity source, like the Earth, to emit a ``field'' (like a massless fluid) that permeates all of space. Any other matter coming in contact with the field will feel a force exerted by it. Presto, nothing acts at a distance. Also, changes in the field source will result in changes in the field, but these propogate outward at some finite speed below the speed limit.

All right, but what the heck physically is the field? We can touch matter, pick it up and put it in our pockets, and study it by means other than its gravitational effects. Not so for the field. We can't detect it or probe it except by masses, and it has no effects other than gravitational. It seems fake, artificial, very much like the famous aether.

Einstein's solution to this marries the Aristotelian concept of a natural state with the Newtonian concept of inertia. See, inertia means things traveling in straight lines continue to do so unless a reason not to (a force) arises. It's the force that is giving us heebie-jeebies. So what if we ``do without'' it, by assuming that it is the nature of a ``straight'' line that changes when a mass is present? That is Einstein's insight.

The distance between two points dx need not be independent of where you do the measurement x, and near a mass, it isn't. If dx is not a function of x, then space is described by Euclidean geometry, but if dx is a function of x, then space is described by the more general but perfectly logical and consistent Riemannian geometry. To be sure, our usual experience is that space is Euclidean. . . . . .or is it? How do you measure the distance between two points? The simplest way is to take a ruler and measure. The simplest ruler is a beam of light or the path taken by a bullet. You fire one or the other past one point in space, clock how long it takes to pass the second, and multiply by the speed of light or bullet. The bullet or light takes the shortest path (the ``straight line'', or more formally, the geodesic) between the two points.

What happens if we try this near a big mass (say the Earth)? We fire a bullet past the Earth and we see the trajectory bend toward the Earth. If we didn't know about masses and gravity, we'd conclude that this trajectory must be the ``straight line'' between the two points, the shortest distance.

It's only when we compare our geodesic so empirically determined with our preconceptions based on idealized Euclidean geometry that we get surprised. We see that the geodesic isn't a ``straight'' line in the Euclidean sense, and then demand an explanation (a force). Einstein's answer is rather Zen in that we declare the question makes no sense, because a straight line should be defined by direct experiment, and if straight lines (geodesics) so determined do not correspond to Euclidean straight lines, then that is not a priori evidence of a weirdness (a force) but only of the inadequacy of Euclidean geometry to describe reality.

Hence the experience of a gravitational force returns to its ancient simplicity: you experience a gravitational force when you stand in the way of something moving inertially, in a ``straight'' line.

How does matter ``distort'' (render non-Euclidean) space-time? In fact we cannot distinguish (without one of the other 3 forces, which is another sordid story) between the local density of matter and the local degree of non-Euclidean-ness of space-time. We might as well regard bodies of matter interacting gravitationally with each other as simply one non-Euclidean patch of space-time butting up against another.

Grayce



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