Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000Bird, J. Malcolm (James Malcolm)
Philosophy
Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000
Bird, J. Malcolm (James Malcolm)
Relativity (Physics)
Imagine an observer so dominated by his coordinate system that he
knows no way of relating $P$ with $Q$ save by their horizontal and
vertical separation. His whole scheme of things would be shattered
by the suggestion that other observers on other reference frames find
different horizontal and vertical components. We have to show him the
line $PQ$. We have to convince him that this length is the absolute
property enjoyed by his pair of points; that horizontals and verticals
are merely relations between the points and the observer, result of
the observer's having analyzed the distance $PQ$ into two components;
that different observers effect this decomposition differently; that
this seems not to make sense to him only because of his erroneous
concept of a fundamental difference between verticals and horizontals.
THE FOUR-DIMENSIONAL WORLD OF EVENTS
We too have created a distinction in our minds corresponding to no
sufficient reality. Our minds seize on time as inherently separable
from space. We see the world made up of things in a continuum of three
space dimensions; to make this dead world live there runs through it
a one-dimensional time continuum, imposed from without, unrelated.
But did you ever observe anything suggesting the presence of time
in the absence of space, or vice versa? No; these vessels of the
universe always occur together. Association of the space dimensions
into a manifold from which time is excluded is purely a phenomenon
of the mind. The space continuum cannot begin to exist until the time
dimension is supplied, nor can time exist without a place to exist in.
The external world that we observe is composed, not of points,
but of events. If a point lacks position in time it does not exist;
give it this position and it becomes an event. This world of events
is four-dimensional--which means nothing more terrifying than that
you must make four measures to locate an event. It does not mean,
at all, that you must visualize four mutually perpendicular lines in
your accustomed three-space or in a four-space analogous to it. If
this world of four dimensions seems to lack reality you will be
able to exhibit no better reality for your old ideas. Time belongs,
without question; and not as an afterthought, but as part of the
world of events.
To locate an event we use four measures: $X$, $Y$ and $Z$ for space,
$T$ for time. Using the same reference frame for time and space, we
locate a second event by the measures $x$, $y$, $z$, $t$. Minkowski
showed that the quantity
$$\sqrt{(X-x)^2 + (Y-y)^2 + (Z-z)^2 - (CT-Ct)^2}$$
is the same for all observers, no matter how different their $x$'s,
$y$'s, $z$'s and $t$'s; just as in the plane the quantity
$$\sqrt{(X-x)^2 + (Y-y)^2}$$
is the same for all observers, no matter how different their $x$'s
and $y$'s.
Public-domain text, read in full here on John Shaqi.
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