rectly observe a fourth spatial dimension, because the process of observ-
ing a fourth dimension involves the use of the electromagnetic spectrum,
and current theories do not allow the electromagnetic force to probe a
fourth dimension. However, the gravitational force can leak into other
dimensions—as we mentioned, this is one way that we might be able to
discern the existence of those other spatial dimensions.^6 If this does in-
deed prove to be the case, the first law of thermodynamics would no
longer hold; but it would open up an extremely appealing possibility. If
gravitational energy from our three dimensions could leak out elsewhere,
why couldn’t gravitational energy from other dimensions leak into ours?
This might enable us to obtain free lunches from extra-dimensional ca-
terers, and at the same time necessitate a new first law of thermodynam-
ics: in the universe as a whole, energy cannot be created or destroyed.
There have been other instances in which the Law of Conservation of
Energy has been restructured. Einstein’s classic equation Emc^2 gives
the “exchange rate” for matter and energy; 1 unit of matter is converted
into c^2 units of energy. This necessitated a restatement of the law of con-
servation of energy: the totality of matter and energy are conserved ac-
cording to Einstein’s formula, much as the total value of cash remains the
same even if some of it is in dollars and some in euros. Given this history
for the law of conservation of energy, it would not be completely surpris-
ing if yet another change lurked in its future.
Why Entropy Increases
In order to know why entropy increases, we have to know how to calculate
entropy. The symbol �x, which appears frequently in mathematics, rep-
resents the change in the quantity x—if, at the end of the month, x repre-
sents my bank balance, �x is the amount of money that the state of
California, which employs me, deposits directly to that account. In ther-
modynamics, S represents the amount of entropy in the system. The
symbol �S, the change in the entropy of the system, is the sum of all the
quantities �Q/T in a system, where T is a temperature at which a compo-
nent of the system resides and �Q is the heat change in that component
at the temperature T. For those who have had calculus, it’s more formally
defined as the integral of dQ/T—for those who haven’t had calculus, an
integral is simply the sum of lots of very small things.
I’ll borrow an example from Brian Greene’s The Fabric of the Cosmos^7
and imagine that we have a glass of water with some ice cubes in it. Heat
f lows from hotter to colder because heat is a measure of how fast mole-
cules are moving; when fast-moving molecules collide with slow-moving
The Raw Materials 189