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Einstein and Gravity
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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Update: June 2012
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