III. RE-EXAMINATION OF THE FUNDAMENTAL IDEAS.

As Einstein regarded the situation,
the negative result of
the Michelson-Morley experiment,
as well as of other experiments
which seemed to indicate a "conspiracy"
on the part of nature
against man's efforts to obtain
knowledge of the physical world,
these negative results,
according to Einstein,
did not merely demand
explanations of a certain number
of isolated difficulties,
but the situation was so serious
that a complete examination
of fundamental ideas
was necessary.
In other words,
he felt that there was something
fundamentally and radically wrong
in physics,
rather than a mere difficulty.
And so he undertook to re-examine
such fundamental notions as
our ideas of LENGTH and TIME and MASS.
His exceedingly reasonable examination
is most illuminating,
as we shall now see.

But first let us remind the reader
why length, time and mass
are fundamental.
Everyone knows that
VELOCITY depends upon
the distance (or LENGTH)
traversed in a given TIME,
hence the unit of velocity
DEPENDS UPON
the units of LENGTH and TIME.
Similarly,
since acceleration is
the change in velocity in a unit of time,
hence the unit of acceleration
DEPENDS UPON
the units of velocity and time,
and therefore ultimately upon
the units of LENGTH and TIME.
Further,
since force is measured
by the product of
mass and acceleration,
the unit of force
DEPENDS UPON
the units of mass and acceleration,
and hence ultimately upon
the units of
MASS, LENGTH and TIME.
And so on.
In other words,
all measurements in physics
depend primarily on
MASS, LENGTH and TIME.
That is why
the system of units ordinarily used
is called the "C.G.S." system,
where C stands for "centimeter"
(the unit of length),
G stands for "gram" (the unit of mass),
and S stands for "second" (the unit of time),
these being the fundamental units
from which all others are derived.

Let us now return to
Einstein's re-examination of
these fundamental units.
Suppose that two observers
wish to compare their measurements of time.
If they are near each other
they can, of course, look at each other's watches
and compare them.
If they are far apart,
they can still compare each other's readings
BY MEANS OF SIGNALS,
say light signals or radio signals,
that is, any "electromagnetic wave"
which can travel through space.
Let us, therefore, imagine that
one observer, E, is on the earth,
and the other, S, on the sun;
and imagine that signals are sent
as follows:
By his own watch, S sends a message to E
which reads "twelve o'clock;"
E receives this message
say, eight minutes later;
now if his watch agrees with that of S,
it will read "12:08"
when the message arrives.
E then sends back to S
the message "12:08,"
and, of course,
S receives this message 8 minutes later,
namely, at 12:16.
Thus S will conclude,
from this series of signals
that his watch and that of E
are in perfect agreement.

But let us now imagine
that the entire solar system
is moving through space,
so that both the sun and the earth
are moving in the direction
shown in the figure:

without any change in
the distance between them.
Now let the signals again be sent
as before:
S sends his message "12 o'clock,"
but since E is moving away from the message,
the latter will not reach E in 8 minutes,
but will take some longer time
to overtake E,
say, 9 minutes.
If E's watch is in agreement with that of S,
it will read 12:09
when the message reaches him,
and E accordingly sends a return message,
reading "12:09."
Now S is traveling toward this message,
and it will therefore reach him
in LESS than 8 minutes,
say, in 7 minutes.
Thus S receives E's message
at 12:16,
just as before.
Now if S and E are both
UNAWARE of their motion
(and, indeed,
we are undoubtedly moving
in ways that we are entirely unaware of,
so that this assumption
is far from being an imaginary one.)
S will not understand
why E's message reads
"12:09" instead of "12:08,"
and will therefore conclude
that E's watch must be fast.
Of course, this is only
an apparent error in E's watch,
becuase, as we know,
it is really due to the motion,
and not at all
to any error in E's watch.
It must be noted, however,
that this omniscient "we"
who can see exactly
what is "really" going on in this universe,
does not exist,
and that all human observers
are really in the situation
in which S is,
namely,
that of not knowing
about the motion in question,
and therefore
being OBLIGED to conclude
that E's watch is wrong!

And therefore
S sends E the message
telling him that
if E sets his clock back one minute,
then their clocks will agree.

In the same way,
suppose that other observers,
A, B, C, etc.,
all of whom are at rest WITH RESPECT TO
S and E,
all set their clocks to agree with that of S,
by the same method of signals described above.
They would all say then
that all their clocks are in agreement.
Whether this is absolutely true or not,
they cannot tell (see above),
but that is the best they can do.

Now let us see what will happen
when these observers wish
to measure the length of something.
To measure the length of an object,
you can place it,
say, on a piece of paper,
put a mark at one end of the object,
and another mark at the other end,
then, with a ruler,
find out how many units of length there are
between the two marks.
This is quite simple provided that
the object you are measuring and the paper
are at rest (relative to you).
But suppose the object is
say, a fish swimming about in a tank?
to measure its length while it is in motion,
by placing two marks on the walls of the tank,
one at the head, and the other at the tail,
it would obviously e necessary
to make these two marks
SIMULTANEOUSLY--
for otherwise,
if the mark B is made at a certain time.

then the fish allowed to swim
in the direction indicated by the arrow,
and then the mark at the head
is made at some later time,
when it has reached C,
then you would say that
the length of the fish
is the distance BC,
which would be a fish-story indeed!

Now suppose that our observers,
after their clocks are all in agreement
undertake to measure
the length of a train
which is moving through their universe
with a uniform velocity.
They send out orders that
at 12 o'clock sharp,
whichever observer happens to be
at the place where
the front end of the train, A',
arrives at that moment,
to NOTE THE SPOT;
and some other observer,
who happens to be at the place where
the rear end of the train, B',
is at that same moment,
to put a mark at THAT spot.
Thus, after the train has gone,
they can, at their leisure,
measure the distance between the two marks,
this distance being equal to
the length of the train,
since the two marks were made
SIMULTANEOUSLY, namely at 12 o'clock,
their clocks being all
in perfect agreement with each other.

Let us now talk to the people on the train.
Suppose, first,
that they are unaware of their motion,
and that, according to them,
A, B, C, etc., are the ones who are moving, --
a perfectly reasonable assumption.
And suppose that there are two clocks on the train,
one at A', the other at B',
and that these clocks
have been set in agreement with each other
by the method of signals described above.
Obviously the observers A, B, C, etc.,
will NOT admit that the clocks at A' and B'
are in agreement with each other,
since they "know" that the train is in motion,
and therefore the method of signals
used on the moving train
has led to an erroneous setting
of the moving clocks.
Whereas the people on the train,
since they "know" that
A, B, C, etc., are the ones who are moving,
claim that it is the clocks
belonging to A, B, C, etc.,
which were set wrong.

What is the result of this
difference of opinion?
When the clocks of A and B, say,
both read 12 o'clock,
and at that instant A and B
each makes a mark at a certain spot,
then A and B claim, of course,
that these marks were made
simultaneously;
but hte people on the train do not admit
that the clocks of A and B
have been properly set,
and they therefore claim that
the two marks were
NOT made SIMULTANEOUSLY,
and that, therefore,
the measurement of the LENGTH of the train
is NOT correct.
Thus,
when the people of the train
make the marks
simultaneously,
as judged by their own clocks,
the distance between the two marks
will NOT be the same as before.

Hence we see that
MOTION
prevents agreement in the
setting of clocks,
and, as a consequence of this,
prevents agreement in the
measurement of LENGTH!

Similarly,
as we shall see in Chapter 8,
motion also affects
the measurement of mass --
different observers obtaining
different results
when measuring the mass of the same object.

And since,
as we mentioned previously,
all other physical measurements
depend upon
length, mass, and time,
it seems that
therefore there cannot be agreement
in any measurements made
by different observers
who are moving with different velocities!

Now, of course,
observers on the earth
partake of the various motions
to which the earth is subject --
the earth turns on its axis,
it goes around the sun,
and perhaps has other motions as well.
Hence it would seem that
observations made by people on the earth
cannot agree with
those taken from
some other locations in the universe,
and are therefore
not really correct
and consequently worthless!

Thus Einstein's careful and reasonable examination
led to the realization that
Physics was suffering from
no mere single ailment,
as evidenced by the
Michelson-Morley experiment alone,
but was sick from head to foot!

Did he find a remedy?

HE DID!