Natural Science Forum / Physics / Research / March 2008

In the Principia Newton defined time and space for physics:

<quote>
I.  Absolute, true, and mathematical time, of itself, and from its own
nature, flows equably without relation to anything external, and by
another name is called duration:

relative, apparent, and common time, is some sensible and external
(whether accurate or unequable) measure of duration by the means of
motion, which is commonly used instead of true time; such as an hour,
a day, a month, a year.

II. Absolute space, in its own nature, without relation to anything
external, remains always similar and immovable.

Relative space is some movable dimension or measure of the absolute
spaces; which our senses determine by its position to bodies; and
which is commonly taken for immovable space; such is the dimension of
a subterraneous, an aerial, or celestial space, determined by its
position in respect of the earth.
</quote>

We all know that Einstein had something to say on this topic.

He writes in Relativity Chapter 9:

<quote>
Now before the advent of the theory of relativity it had always
tacitly been assumed in physics that the statement of time had an
absolute significance, i.e. that it is independent of the state of
motion of the body of reference. But we have just seen that this
assumption is incompatible with the most natural definition of
simultaneity; if we discard this assumption, then the conflict between
the law of the propagation of light in vacuo and the principle of
relativity (developed in Section VII) disappears."
</quote>

The reason for the assumption could be Newton's description of
absolute time being mathematical rather than relative time.

In Chapter 8, Einstein gives his working definition for time:

<quote>
Under these conditions we understand by the 'time' of an event the
reading (position of the hands) of that one of these clocks which is
in the immediate vicinity (in space) of the event
</quote>

Einstein is defining time in terms of the moving hands of a clock,
which is nearly identical to how Newton defined relative time:

<quote>
Relative, apparent, and common time, is some sensible and external
(whether accurate or unequable) measure of duration by the means of
motion, which is commonly used instead of true time; such as an hour,
a day, a month, a year.
</quote>

While I often hear some claim "Einstein has shown that time is
relative", really, all that he has shown is that our present
mathematics represent relative time, contrary to Newton's definition.

In fact, Einstein had made this point to Heisenberg, I think
demonstrating how easily this subtle point is missed:

<quote>
"But you don't seriously believe," Einstein protested, "that none but
observable magnitudes must go into a physical theory?"

"Isn't that precisely what you have done with relativity?" I asked in
some surprise. "After all, you did stress the fact that it is
impermissible to speak of absolute time, simply because absolute time
cannot be observed; that only clock readings, be it in the moving
reference system or the system at rest, are relevant to the
determination of time."

"Possibly I did use this kind of reasoning," Einstein admitted, "but
it is nonsense all the same. Perhaps I could put it more
diplomatically by saying that it may be heuristically useful to keep
in mind what one has actually observed. But on principle, it is quite
wrong to try founding a theory on observable magnitudes alone. In
reality, the very opposite happens. It is the theory which decides
what we can observe."
</quote>
(In 'Physics and Beyond - Encounters and Conversations', Harper
Torchbooks, 1972, p. 63.)

To summarize all that: in the eyes of both Newton and Einstein, while
absolute space and time are "somewhere out there"; it is relative
space and time that we measure..

Emphasis: RELATIVE SPACE AND TIME ARE MEASURED.

Now.

String theory.

There are visible dimensions of space and time, and there are hidden
dimensions.

These hidden dimensions, I take it, cannot be measured.

Are they still relative?