Now for something completely different. I am half way through

reading “Einstein” by Walter Isaacson. At this point I should understand

relativity, although I’m not sure. Here goes: according to my

understanding of special relativity, since a measurement of distance

cannot be made outside time and measurement of time cannot be made

outside space, then all such measurements are relative and there are no

absolute scales of distance or time. In fact, the three dimensions of

space and one of time are not independent and are combined into a four-

dimensional continuum called space-time. Since there are no absolute

measures of time, as for instance imagined in classical Newtonian

physics, there can be no universal clock with a time that started at zero

as there can be no origin of the universe with a distance set to zero.

Therefore, as some friends and I postulated in 1958 when visiting

Brussels for the Exposition (but being poor students we did not have

enough money for the entrance fee) we concluded that this means that

there could be no creation beginning at time zero and point zero (we

dubbed this the “Brussels expostulation”).

But, we know now that there was a “big bang.” In the 1960s, Arno Penzias

and Robert Wilson measured radiation that could only be explained by such

a cataclysmic explosion at the origin of the universe. Then several

people, including Stephen Hawking, made calculations to show that

Einstein’s theory of relativity was consistent with an expanding

universe. In fact, Einstein had realized this in his general theory of

relativity, that included gravity, and had devised a so-

called “cosmological constant” that was included in his equations to keep

the universe static, or balanced, since it was not then realized that the

universe is in fact expanding. Once this was discovered in 1929 by

Edward Hubble the need for such a cosmological constant seemed

unnecessary. However, later theorists have used this constant to show

that the universe is in fact delicately balanced.

So my point is that there seems to be an apparent paradox, according to

the theories of relativity on the one hand there can be no creation point

when the time was zero, but on the other hand there was a big bang and

this fits with the expanding universe. Can any physicist out there

explain this apparent contradiction to me, or am I missing something

obvious?

# Paradox?

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