Newton's First Law stated that:
"Every body continues in its state of rest, or of uniform motion in a
right line, unless it is compelled to change that state by forces impressed
upon it." -- Ibid
This is often called the Principle of Inertia.
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Is this "Law" always true? Of course not. Imagine you a sitting in
a car at a red stoplight. A pair of dice is hanging from the rear-view mirror;
it is optional for the dice to be fuzzy. As you sit there, the dice are at rest
relative to you. The only forces acting on the dice are the force of gravity
pulling them down and the string pulling them up. These two forces are equal in
magnitude, so the total force on the dice is exactly zero. We imagine that the
car is facing to the right. |
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The light turns green and the driver steps on the gas. The dice
swing towards the back of the car. So Newton's First Law is not true: at one
moment the dice are stationary and at the next moment they begin to swing
towards the back of the car although no net forces are acting on them.
Now imagine that you are standing on the sidewalk watching the
car. As it sits at the red light the dice are stationary relative to you. When
the light turns green and the car begins to accelerate to the right, the dice
remain stationary relative to you until the force exerted on them by the string
forces them to follow the motion of the car. So Newton's First Law is true when
you stand on the sidewalk, but is not true when you are sitting in the
car. |
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Thus we see that to use Newton's analysis of motion, we must restrict
ourselves to only certain viewpoints, certain frames of reference.
Frames of reference where Newton's analysis works are called inertial
frames. They are frames where the Principle of Inertia is true.
For Newton, there was a "master" inertial frame: a frame stationary
relative to absolute space. And any reference frame that is moving at a uniform
velocity in a straight line relative to this master inertial frame will also be
an inertial frame in the Newtonian analysis. Any reference frame which is
accelerating with respect to absolute space, such as the car's frame when the
light turns green and the driver steps on the gas, will not be inertial.
Now imagine that you are riding in the car at, say, 100 km/hr down a
straight highway. The dice are hanging motionless from the rear view mirror.
The principle of inertia is true for you. A second observer is standing beside
the highway, watching the car go by. For her the dice are moving in uniform
motion in a straight line. So the second observer is also in an inertial
frame.
In this case, a good question is: who is moving? And the answer is that you
are moving relative to the observer beside the highway, but the observer beside
the highway is moving relative to you. So you are both moving relative to each
other.
Both your inertial frame and her inertial frame are equally "valid."
This realisation is often called Galilean relativity. A classic
illustration is a cannonball dropped from the mast of a moving ship. From the
point of view of an observer on shore, the ball falls with a uniform
acceleration downwards while moving with constant speed in the horizontal
direction. For a sailor on the ship, however, the cannonball appears to fall
straight down. For both observers the cannonball lands at the base of the
mast.
If you are riding in the car at 100 km/hr and the driver puts on the
brakes, the dice will swing towards the front of the car. Thus during the
deceleration you are not in an inertial frame. The observer beside the road
will see the dice continue to move at constant speed in a straight line until
the string forces them to slow down with the car.
Similarly, if the car keeps moving at 100 km/hr but goes around a right
hand turn, the dice will swing to the left. So during the turn you are again
not in an inertial frame. Again for an observer beside the road the Principle
of Inertia remains true for the dice.
When it was proved by Young in the early nineteenth century that light
was a wave, the question arose as to exactly what was waving? For other waves
there is a medium that is waving. For sound waves the medium is the air;
for water waves the medium is the water. It was postulated that there was a
medium for light waves, which was called the luminiferous ether. This
substance was believed to be massless and homogeneous everywhere in the
universe. It seems natural to associate this luminiferous ether with the
absolute space that Newton had proposed much earlier.
The Newtonian analysis then, and all the Physics that followed from it,
works in a frame fixed in absolute space, or equivalently fixed relative to the
ether, and also in any frame moving in uniform motion in a straight line
relative to this absolute space. The upshot is: We can only do Physics in
these inertial reference frames.
In 1905 Einstein's Special Theory of Relativity dropped a bomb on
the Newtonian view. He made the concept of the ether, and the related idea of
absolute space, "superfluous."
We know that there are frames in which the Principle of Inertia
is true, and that we can only do Physics in such a frame. But without an
absolute "master" inertial frame we are reduced to a circular argument:
- We can only do Physics in inertial reference frames.
- Inertial reference frames are frames in which the Principle of
Inertia is true.
But the Principle of Inertia is itself one of the law of Physics. So
essentially we are saying that the laws of Physics are true in frames where the
laws of Physics are true. It is perhaps amazing that Physics, based on this
tautology, works at all. But it does work very well.
You may wish to muse about the fact that post-1905 we can say that not
only is uniform motion relative, but so is acceleration. If two observers are
accelerating with respect to each other we can not say which one is "really"
accelerating because there is no absolute frame to which we can compare the two
observers' motions. However, we do know that if one of these observers is in an
inertial frame of reference, then the other is not.
Considerations of relative acceleration is one topic of Einstein's
General Theory of Relativity of 1916.
Why did the chicken cross the road?
- Aristotle:
- It is the nature of chickens to cross the road.
- Newton:
- Because no force caused the chicken's state of uniform road crossing
to change.
- Einstein:
- Is the chicken crossing the road or is the road moving under the
chicken?