From: Ronald Wong (ronwong@inreach.com)
Date: Fri Dec 20 2002 - 01:54:03 PST
Message-Id: <l03102800ba0cd4816864@[209.209.19.156]> Date: Fri, 20 Dec 2002 01:54:03 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: gravity
A while ago, Jennie Brotman asked a series of questions regarding gravity.
I've tried to answer some of them recently on Pinhole. This message will
try to address the rest.
Jennie asked:
>are there further theories about where this force comes from or what it is
>more
>precisely? any info on the "why?" i think einstein's ideas about gravity
>dont' call it a force at all, but a curvature in space-time(!)- but are
>there any explanations for the theory that it is a force? or do most
>physicist believe einstein's theory and don't believe its a force of
>attraction at all? any ideas on how to make this very abstract concept more
>concrete would be very helpful!
Ah... Relativity.
It's interesting to note that Aristotle, Newton, and Einstein did one thing
in common - they approached their study of nature from the standpoint of
two conditions. In the case of Aristotle, it was natural motion, which did
not require a force, and violent motion, which did. For Newton, it was
uniform velocity, which did not require a force (that is, no NET force),
and acceleration, which did (the unbalanced force). In the case of Einstein
it was the same event viewed from the standpoint of two observers where, in
the first case, one was in a frame of reference moving with uniform
velocity with respect to the other and, in the second, one was in a frame
of reference accelerating with respect to the other.
Although the initial observations and assumptions of Aristotle and Newton
seem apparent and reasonable to most individuals (see earlier messages),
Einstein's seem to get lost in the course of their presentation.
In retrospect, the initial conditions seem apparent. Between two
independent frames of reference there would seem to be only two
possibilities:
1. One frame of reference is moving with uniform velocity with respect
to the other or
2. ... it isn't.
Einstein's investigation of the first case lead to the Special Theory of
Relativity (STR) in which he was able to show that length, mass, and time
were a function of the observer's frame of reference. Depending on which
frame of reference you were in relative to the frame of reference in which
the event took place, you arrived at a different set of values for these
three quantities. The same investigation also lead to the famous equation,
E=mc^2.
The second case lead him to the development of the General Theory of
Relativity (GTR). It is in this second case that we are able to see in what
way Newton got it wrong.
How we got to this state of affairs is, once again, an example of how
fundamental ideas about nature change. As I mentioned in my earlier post,
"scientists explain how nature works by using models based on observations
and assumptions".
New observations and new assumptions frequently lead to new models and new
ways of thinking about the world we live in.
_______________________________________________________
The New observations:
1. The Michelson-Morley Experiment.
Their experimental setup consisted of a monochromatic light source,
some mirrors (one half-silvered), a plate of glass, and a viewing
device for examining a beam of light. The setup was placed on a
platform which floated on a pool of mercury. The platform was set in
motion so that it slowly rotated about it's center. On the platform,
the setup took a beam of monochromatic light and split it into two
perpendicular beams. Each beam traveled towards a mirror where
it was reflected back on itself. They were then recombined into
a single beam producing an interference pattern that was examined
using the viewing device.
According to the prevailing theory at the time, light was an
electromagnetic wave and, as such, moved through an ether.
Astronomical observations suggested that the earth was plowing through
this ether as opposed to dragging some of it around as it orbited the
sun. That being the case, there would be a point in time when one of
the two light beams in the Michelson-Morley experiment would first be
moving AGAINST (or WITH) the ether as it approached it's mirror and
then returning back WITH (or AGAINST) the ether after it's reflection.
At the same time, the other beam's motion, which was perpendicular to
the ether's apparent motion, would be unaffected. This difference
between the motion of the two beams through the ether would appear
as a shift in the interference pattern as the platform rotated from
one position to another causing each beam to go from one state to the
other and back again. The size of the shift was directly related to
how fast the earth was plowing through the ether.
When they performed the experiment, no shift in the interference pattern
was observed. There was no evidence for the electromagnetic wave's ether.
Explanations were offered to try to explain how this could be by
those who firmly believed in the existence of an ether, but none of
them proved satisfactory.
2. Some well known problems with Maxwell's Electromagnetic Wave Theory
The man who did the most to establish that Maxwell's electromagnetic
waves actually existed, Heinrich Hertz, ran into a problem when he
tried to examine how well Maxwell's theory could explain the
electrodynamics of moving bodies. It lead to problems that he and
his colleagues found insurmountable.
Hendrik Lorentz noticed that Maxwell's Laws - the four mathematical
statements which summarized the EM Theory - did not lend themselves
to simple Galilean transformations. When you transposed them from one
frame of reference to another moving with uniform velocity with
respect to the first, Maxwell's Laws changed! This wasn't supposed
to happen. According to Newton's first law, moving with uniform
velocity was equivalent to being at rest. The laws should have
remained unchanged.
Lorentz did find a way to make the Laws invariant between one frame
of reference and another but it involved a new, more complicated,
set of equations that others dismissed as ad hoc and nothing more
than a mathematical trick.
_______________________________________________________
The New assumptions:
For frames of references moving with uniform velocity:
1. Since one cannot perform an experiment that would establish whether
one's frame of reference is at rest or moving with uniform velocity,
Einstein concluded that ALL the laws of physics must be the same for
all frames of reference which are moving with uniform velocity relative
to one another (he later generalized this statement to include all
forms of motion when he developed the GTR).
This may sound like a piece of logic, but it's an act of faith just
like Aristotle's belief that objects seek their natural place or
Newton's four Rules of Reasoning.
If this is assumed to be true, how does one deal with the fact that
Maxwell's Laws changed when they were transposed from one frame
of reference to another moving with uniform velocity with respect to
the first?
This leads to assumption number...
2. The speed of light in a vacuum is the same in all frames of reference.
One way of seeing how Maxwell might have come to this assumption is to
recognize that the speed of the electromagnetic waves can be determined
from Maxwell's Laws using a pair of constants derived from laboratory
measurements of electrical and magnetic phenomena.
When Maxwell looked at the value prescribed by the laws, he
discovered that it was similar to the speed of light. He then
asked how would light behave if it was indeed an electromagnetic
wave? Using his laws, he was able to explain not only all the
known properties of light but those of electricity and magnetism
as well - a synthesis as grand as Newton's of heaven and earth.
Since all the laws of physics are assumed to be the same for all
frames of reference then the speed of light, a corollary of Maxwell's
Laws, will also be the same for all frames of reference.
For accelerated frames of references:
3. The Principle of Equivalence: Within an accelerated frame of reference,
there is no experiment that one can perform that will allow one to
determine whether they are in an accelerated frame of reference or
in a Newtonian gravitational field. For example: If you were in
an elevator that was accelerating 9.8 m/s/s upwards in empty space,
the effect on you would be the same as if the elevator stood on the
surface of the earth and a Newtonian force of gravity was pulling
down on you.
_______________________________________________________
Using the first two assumptions, Einstein was able to derive the "new, more
complicated, set of equations" of Lorentz thus showing that they weren't "a
mathematical trick". They were indeed the proper way to transpose
Maxwell's Laws from one frame of reference to another. In addition, the
null results of the Michelson-Morley experiment could be explained in light
of these new equations and the problems of Hertz became surmountable.
Length, time and, when conservation laws were considered, mass were shown
to be a function of one's frame of reference.
More can be said but, since we are dealing with gravity, I'm going to skip
to assumption number 3
An important caveat: The fact that one cannot distinguish between
being in an accelerated frame of reference and being in a Newtonian
gravitational field does NOT mean that they are the same.
When Einstein explored the consequences of being in an accelerated
frame of reference from the standpoint of spacetime geometry (not
space AND time - the Newtonian geometry - but spacetime) he
was led to a model that not only allowed scientists to explain
phenomena that could be explained by Newton's Law of
Universal Gravitation (LUG) but phenomena that COULDN'T (the
precession of Mercury's orbit). He and subsequent scientists went
on to predict events that would be unexplainable in terms of
Newton's LUG (gravitational bending of light by matter,
gravitational red shift of light from the sun, black holes, etc.).
Newton's concept of gravitation involved a mysterious,
instantaneous action at a distance with the concomitant element
of absolute simultaneity. Einstein's STR showed that simultaneity
was relative and not absolute and his GTR went on to explain
gravitational effects more completely without the need for a
mysterious force that acted at a distance.
Einstein was able to show that, in the absence of matter, spacetime (the 4
dimensional geometry of relativity) would be "flat". Any object placed in
this state of affairs would behave in a manner consistent with Newton's
first law as it sought the shortest path through this geometry. In this
case, it would move in a straight line with constant speed - if it were
moving at all. This would be it's natural motion under these circumstances
and there would be no unbalanced forces acting on it. If the object were a
box with a ball in it, the ball would float inside the box or, if set in
motion, move with uniform velocity inside the box.
The presence of matter alters spacetime. The spacetime becomes curved in
the region around this mass.
The earth alters spacetime around it so that if a space shuttle has the
right tangential speed for it's altitude it will, as it follows the
shortest path through spacetime, move in a fashion consistent with
Kepler's laws (the same is true for the sun and it's planets). This is it's
natural motion through spacetime and thus no unbalanced force is required
to account for it's orbit around the earth. If the space shuttle was a box
with a ball in it, the ball would float inside the box or, if set in
motion, move with uniform velocity. Anyone who has seen videos of our
astronauts while they were orbiting the earth in the space shuttle know
this is indeed the case.
If the tangential speed of the space shuttle was zero, than the shortest
path through spacetime would be downward along a straight line
perpendicular the earth's surface - so down it would go. Again, this is
it's natural motion through spacetime and thus no unbalanced force acts on
it. If the space shuttle was a box...etc.
You're probably sitting in a chair right now. So your natural motion
through spacetime is also straight down just like in the last example. But
you aren't moving straight down as you should. The fact that you aren't
pursuing your natural motion downwards means that an unbalanced force must
be acting on you in the upward direction. This force has nothing to do with
a gravitational force. It comes about because in trying to seek your
natural place in spacetime you bear down on the chair and, consistent with
Newton's third law, it pushes back. That's a real force and you can
determine it's value by multiplying your mass by the upward acceleration of
your frame of reference (the third assumption + Newton's second law). How
do you get the value for this acceleration? Just release a ball and measure
it's acceleration downward (obviously a bathroom scale is an easier way of
getting the force but releasing a ball is in keeping with the approach I'm
using).
If the concept of "natural motion => NO force" and the "lack of natural
motion => force" sounds vaguely Aristotelian to you, congratulations. We
are not exactly in the same place as Aristotle was 2400 years ago but, in
one sense, Aristotle was right - and so were your students after they
jumped off their chairs and realized that there was nothing pulling them
down (for the same reason there was nothing pulling on the space shuttle in
the previous examples).
There is no need/evidence for a gravitational force.
That's what Einstein said early in the last century. The first evidence
proving that he was right showed up in 1919 - eighty three years ago.
_______________________________________________________
As a bone to those who insist on talking about "the force of gravity" as if
it were there despite ample evidence to the contrary I offer the following:
In the days of Newton - and probably long thereafter (and maybe even today
in many parts of the world - including ours) - Aristotelian physics was
still sufficient for explaining the way nature behaved for many people as
they went about their daily lives. It wasn't complete, couldn't explain in
detail all that was going on, and couldn't predict the outcome of events as
well as the laws of Newton's but it was good enough for them.
Today, the same case can be made for those who continue to talk in terms of
a Newtonian force of gravity. It isn't complete, can't explain in detail
all that is going on, and can't predict the outcome of events as well as
Einstein's GTR but it's good enough for them. This includes a number of
physicists and engineers because, when it comes to the space shuttle, trips
to the moon, sending probes out into our solar system and beyond, the
mathematics of Newton's ULG is quite sufficient (and a lot simpler). But...
- - - - - - -
As science teachers, we have a responsibility for getting it right when it
comes to our science students. This is especially true when their own
experience corresponds to what scientist have found to be true. The reason
you don't see a force pulling down on an eraser as it falls to the ground
is because there isn't any. To leave our students with the idea that there
IS such a force is tantamount to brainwashing. What compounds this error is
that an opportunity to give our students a deeper understanding of what
science is has been lost.
More important than all the facts and problems that can be found in our
students' science books is the message that science is a human endeavor
where people are continuously engaged in a process, involving observations
and analysis based on reasonable assumptions, that has led to testable
models which have benefited us greatly in our attempts to understand the
nature of the world we live in. The process is not perfect and every
"successful" model has had it's strengths and weaknesses - even the GTR,
but we have come a long way since the days of Aristotle by being creative
in the way we have implemented this process and it continues to prove it's
usefulness to us every day.
If we can combine this message with the fact that this process is similar
to one that students engage in all the time as they go about their daily
activities, they will begin to understand why studying science is important
to them - even when their major interests lie elsewhere. In this way not
only will our students become more knowledgeable due to our efforts but
they'll be more educated as well.
Isn't that what it's all about?
ron
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