Newton's Space and Time

A changing with the time means that the conditions for A depend on the conditions for B.

The vibrations of a pendulum happen in time when its excursion depends on the earth’s position.

We usually do not take into account the pendulum’s dependence on the earth’s position.

This makes time appear to be a particular and independent thing.

• The position of the pendulum depends on the progress of time

But all things are connected with one another and depend on one another.

We ourselves and all our thoughts are also a part of Nature.

It is utterly beyond our power to measure the changes of things by time.

Quite the contrary, time is an abstraction that we get through the changes of things.

We make time because we are not restricted to one definite measure since all are interconnected.

A uniform motion has equal increments of space corresponding to equal increments of space described by some motion with which we form a comparison.

• An example is the rotation of the earth.

A motion may, with respect to another motion, be uniform.

The following are senseless:

• a question whether a motion is in itself uniform, is
• an “absolute time” independent of change

This absolute time can be measured by comparison with no motion.

It:

• has therefore neither a practical nor a scientific value.
• is an idle metaphysical conception

We get our ideas of time in and through the interdependence of things on one another.

A motion that takes place in time depends on the motion of the earth.

This is not refuted by the fact that mechanical motions can be reversed.

Variable quantities may be so related that one set can change without the others being affected by it. Nature behaves like a machine.

The individual parts reciprocally determine one another.

In a machine, the position of one part determines the position of all the other parts.*

Superphysics Note

This is similar to Descartes’ no void rule

In nature, more complicated relations obtain.

These relations are best represented as a number n of quantities that satisfy a lesser number n' of equations.

• nn' means nature is invariable
• n'n — 1 means one quantity controls all the rest
  • If this is true, then time could be reversed

But the true state of things is represented by a different relation between n and n'.

The quantities in question are partially determined by one another.

But they retain a greater indeterminateness, or freedom, than in the case last cited.

We feel that we, an element of nature, are:

• partially determined
• partially undetermined

Time appears to us as irreversible because:

• the changes of nature depends on us and can be reversed by us
• the time that is past as irrevocably gone

We get the idea of time by the connection of what is in our memory with what we can sense.

Time flowing in a definite direction means that physical events generally and physiological events happen only in a definite sense.*

Differences of temperature, electrical differences, differences of level generally, if left to themselves, all grow less and not greater.

Assume there are 2 bodies of different temperatures.

• They are in contact and left wholly to themselves

We shall find that it is possible only for greater differences of tempe rature in the field of memory to exist with lesser ones in the field of sense-perception, and not the reverse.

In all this, there is simply expressed a peculiar and profound connection of things.

To demand at the present time a full elucidation of this matter, is to anticipate, in the manner of speculative philosophy, the results of all future special investigation, that is a perfect physical science.

3. Newton’s concept of time are in respect to space and motion.

4. Newton has again acted contrary to his expressed intention only to investigate actual facts.

No one is competent to predicate things about absolute space and absolute motion. They are pure things of thought, pure mental constructs, that cannot be produced in experience.

All our principles of mechanics are experimental knowledge concerning the relative positions and motions of bodies.

No one is warranted in extending these principles beyond the boundaries of experience.

In fact, such an extension is meaningless, as no one possesses the requisite knowledge to make use of it.

Assume body K changes direction and speed solely through the influence of another body K'.

This asserts a conception that it is impossible to come at unless other bodies A, B, C… . are present with reference to which the motion of the body K has been estimated. In reality, therefore, we are simply cognisant of a relation of the body K to A, B, C….

If now we suddenly neglect A, B, C…. and attempt to speak of the deportment of the body K in absolute space, we implicate ourselves in a twofold error.

1. We cannot know how K would act in the ab- sence of A, B, C… .;

2. Every means would be wanting of forming a judgment of the behaviour of K and of putting to the test what we had predicated,-which latter therefore would be bereft of all scientific significance.

Two bodies K and K’, which gravitate toward each other, impart to each other in the direction of their line of junction accelerations inversely proportional to their masses m, m'.

This proposition has:

• a relation of the bodies K and K’ to one another
• a relation of them to other bodies

For the proposition asserts, not only that K and K’ suffer with respect to one another the acceleration designated by u (m + m’ /r2), but also that K experiences the acceleration -xm’ /r2 and K’ the acceleration + um/r2 in the direction of the line of junction; facts which can be ascertained only by the presence of other bodies.

The motion of a body K can only be estimated by reference to other bodies A, B, C…. But since we always have at our disposal a sufficient number of bodies, that are as respects each other relatively fixed, or only slowly change their positions, we are, in such reference, restricted to no one definite body and can alternately leave out of account now this one and now that one.

In this way the conviction arose that these bodies are indifferent generally.

The isolated bodies A, B, C… might play merely a collateral rôle in the determination of the motion of the body K.

• This motion might be determined by a medium in which K exists.

In such a case, we should have to substitute this medium for Newton’s absolute space.

Newton certainly did not entertain this idea. Moreover, it is easily demonstrable that the atmosphere is not this motion-determinative medium.

We should, therefore, have to picture to ourselves some other medium filling all space, with respect to the constitution of which and its kinetic relations to the bodies placed in it we have at present no adequate knowledge.

In itself such a state of things would not belong to the impossibilities.

Recent hydrodynamical investigations have shown that a rigid body experiences resistance in a frictionless fluid only when its velocity changes.

This result is derived theoretically from the notion of inertia.

But it might, conversely, also be regarded as the primitive starting point.

What is this hypothetical medium that replaces absolute space?

We cannot abolish the isolated bodies A, B, C… We cannot determine by experiment whether the part they play is fundamental or collateral.