**Speculations on Physics
VI**

**Chris Cole**

This is the sixth installment of my
speculations about physics, which occur sporadically in *Noesis*. For the record, the
previous installments have been:

*Noesis* 43 (Nov 89): Schrödinger’s Cat and

*Noesis* 75 (Nov 92): Causality (with

*Noesis* 137 (Mar 98): Duality between Space,
Objects, and Interactions

*Noesis* 138 (Sep 98): Octonions (with Robert Low)

*Noesis* 150 (Oct 00): Approximate Continuity

It is not well known outside of certain
specialties in physics, but the major conservation laws are consequences of the
major invariances. For example,
conservation of energy is a consequence of the invariance of nature under time
translation. Momentum conservation is a
consequence of invariance under space translation. Angular momentum conservation is a
consequence of invariance under rotation.
In fact, it is possible to show that a continuous invariance leads to a
conservation law. This is called
Noether's Theorem.

To see how this works, let's consider time
translation invariance. Time translation
means moving the origin of time. Let's
say we change coordinate systems from the old system with time t to the new
system with time t'. The energy E of the
system cannot change just because we changed coordinate systems, so we have

E(t') = E(t)

Now let's look at an translation d(t) for each moment t in the old coordinate system, such
that

t' = t + d(t)

Then we have

E(t') = E(t + d(t))

If we take the limit of d(t)
very small at all times t (a continuous invariance), then we have

E(t') = E(t + d(t)) = E(t) + (dE/dt) * d(t) = E(t)

Therefore

(dE/dt) * d(t) = 0

for all possible forms of the infinitesimal d(t). From the calculus of variations we know that
this is sufficient to conclude that

dE/dt = 0

for all values of t, or equivalently, that
energy is conserved. QED.

If the universe is very large, then all
points in it are nearly indistinguishable.
Similarly, if the universe is very old, then all times are nearly
indistinguishable. If the universe is
nearly homogeneous, then all directions are nearly indistinguishable. This would seem to imply logically that if
the universe is very large, then the laws of physics would be invariant under
the time and space translation and rotation.

Consider the alternative. Suppose that the laws of nature were such
that it is possible to detect a space transformation. This would seem to imply that there is some
preferred location in space. Presumably
this preferred location would be special in some way; perhaps it would be the
"center" of the universe. But
since the universe is very large, it should be very hard to detect this
"center." And indeed the laws
of nature as we know them now do not allow us to find any evidence of such a
special place.

Thus it is possible that the invariance
under time and space translation and rotation is a consequence of the universe
being very large. Then by the theorems
mentioned above, this implies that the various conservation laws will be
observed in any universe that is sufficiently large.

This then suggests a line of inquiry. What would the universe be like if it were
smaller? How would the departure from
invariance show up in the laws of physics?

One way the universe could be smaller was
discussed in the last installment. It
may be that the universe is not composed of infinitely many points. If this were true, then perhaps this lack of
scale invariance shows up as a needed change to the laws of physics. One would expect the new terms in the laws to
be proportional to the fixed scale.
Could this be the origin of the laws of quantum mechanics?