Stephen Hawking and Maya

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Hello All,

 

In Sahaja Yoga, which is based in large part on the Hindu/Buddhist

world-view, we look upon the world and existence as unreal or

imaginary - Maya, to use the appropriate Sanskrit term.

 

Stephen Hawking, in his book, A Brief History of Time, may have

chanced upon the mathematical indication or evidence of this view of

existence; though it cannot be called a proof because this was not

what he had set out to do in the first place.

 

In his attempt to make sense of his mathematical model he had to

resort to using imaginary time in his space-time equations for them

to hold. In mathematical parlance, unreal or imaginary quantities

involve the square root of a negative number. To put it in another

way then, the universe exists in the imaginary or unreal part of the

equation. As a corollary to this, we therefore exist in an unreal or

imaginary universe, at least mathematically. Could this then be a

mathematical indication or hint of Maya, perhaps?

 

It is interesting to note that the mathematical terms, unreal and

imaginary, invented by French mathematician René Descartes in 1637,

coincide exactly with the meaning of Maya. Even if Descartes had

used different terminology for this mathematical phenomenon, the

discovery by Hawking would have been no less fascinating.

 

As Hawking puts it, " This might suggest that the so-called imaginary

time is the real time, and that what we call real time is just a

figment of our imaginations. " He then avers, " So maybe what we call

imaginary time is really more basic, and what we call real is just

an idea that we invent to help us describe what we think the

universe is like. " However, Hawking was quick to add, almost

apologetically, that this might all just be games mathematicians

play, in case anybody should lose sleep over being deemed

unreal: " We may regard our use of imaginary time and Euclidean space-

time as merely a mathematical device (or trick) to calculate answers

about real space-time. (...) a scientific theory is just a

mathematical model we make to describe our observations: it exists

only in our minds. So it is meaningless to ask: Which is

real, " real " or " imaginary " time? It is simply a matter of which is

the more useful description. "

 

C.

 

 

Extract from A Brief History of Time

(Bantam Books Edition)

 

Page141

We don't yet have a complete and consistent theory that combines

quantum mechanics and gravity. However, we are fairly certain of

some features that such a unified theory shouId have. One is that it

should incorporate Feynman's proposal to formulate quantum theory in

terms of a sum over histories. In this approach, a particle does not

have just a single history, as it would in a classical theory.

Instead, it is supposed to follow every possible path in space-time,

and with each of these histories there are associated a couple of

numbers, one representing the size of a wave and the other

representing its position in the cycle (its phase). The probability

that the particle, say, passes through some particular point is

found by adding up the waves associated with every possible history

that passes through that point. When one actually tries to perform

these sums, however, one runs into severe technical problems. The

only way around these is the following peculiar prescription: One

must add up the waves for particle histories that are not in

the " real " time that you and I experience but take place in what is

called imaginary time. Imaginary time may sound like science fiction

but it is in fact a well-defined mathematical concept. If we take

any ordinary (or " real " ) number and multiply it by itself, the

result is a positive number. (For example, 2 times 2 is 4, but so

is -2 times -2.) There are, however, special numbers (called

imaginary) that give negative numbers when multiplied by themselves.

(The one called i, when multiplied by itself, gives - 1, 2i

multiplied by itself gives - 4, and so on.) To avoid the technical

difficulties with Feynman's sum over histories, one must use

imaginary time. That is to say, for the purposes of the calculation

one must measure time using imaginary numbers, rather than real

ones. This has an interesting effect on space-time: the distinction

between time and space disappears completely. A space-time in which

events have imaginary values of the time coordinate is said to be

Euclidean, after the ancient Greek Euclid, who founded the study of

geometry of two-dimensional surfaces. What we now call Euclidean

space-time is very similar except that it has four dimensions

instead of two. In Euclidean space-time there is no difference

between the time direction and directions in space. On the other

hand, in real space-time, in which events are labeled by ordinary,

real values of the time coordinate, it is easy to tell the

difference - the time direction at all points lies within the light

cone, and space directions lie outside. In any case, as far as

everyday quantum mechanics is concerned, we may regard our use of

imaginary time and Euclidean space-time as merely a mathematical

device (or trick) to calculate answers about real space-time.

..

Page147

If the universe really is in such a quantum state, there would be no

singularities in the history of the universe in imaginary time. It

might seem therefore that my more recent work had completely undone

the results of my earlier work on singularities. But, as indicated

above, the real importance of the singularity theorems was that they

showed that the gravitational field must become so strong that

quantum gravitational effects could not be ignored. This in turn led

to the idea that the universe could be finite in imaginary time but

without boundaries or singularities. When one goes back to the real

time in which we live, however, there will still appear to be

singularities. The poor astronaut who falls into a black hole will

still come to a sticky end; only if he lived in imaginary time would

he encounter no singularities.

 

This might suggest that the so-called imaginary time is the real

time, and that what we call real time is just a figment of our

imaginations. In real time, the universe has a beginning and an end

at singularities that form a boundary to space-time and at which the

laws of science break down. But in imaginary time, there are no

singularities or boundaries. So maybe what we call imaginary time is

really more basic, and what we call real is just an idea that we

invent to help us describe what we think the universe is like. But

according to the approach I described in Chapter 1, a scientific

theory is just a mathematical model we make to describe our

observations: it exists only in our minds. So it is meaningless to

ask: Which is real, " real " or " imaginary " time? It is simply a

matter of which is the more useful description.