I have a 'grasp' of quantum mechanics and of general rel. I am having BIG problems with imaginary time.

Question

I can sometimes 'see' what is meant by the term. Mostly I am befuddled. It seems like a masterly piece of trickery. Is there such a 'thing' as the cosmological constant, unless of course it suits us to believe in one ??

Answer 1

Its no more a piece of trickery than the math that leads people to speculate over multiple universes. Its not that theory predicts these, its that the mathematical trick to do the sums in much of physics is to "sum over paths" turns them up.

For instance, to discover the path a stone takes under gravity (we know the answer to that one) you would sum over all the paths it could take in the whole universe. The probability of most would vanish.

The problem with sums over paths like this is that, if the space being summed over is "lumpy", like real space is, then you get infinities. This is not nice. The usual mathematical trick here is to divide by infinity in the right places (renormalisation), but this fails in a lot of cosmological theory.

Phrasing the sum over paths in imaginary time gets rid of this problem. It allows you to create a framework with a single set of rules that includes the singularity of the big bang rather than breaking down at it.

Its a bit like going to the north pole by walking on the apparently flat Earth. Its a singular point, but the rules do not break down there. The secret is to realise there is a third dimension - space is not flat.

Answer 2

Cosmological constant was introduced by Einstein to give a result that matched a steady state universe, one where Newtonian physics still applied, He called it his greatest blunder.
Time is better thought of as a dimension, not separate from space but being part of a four as opposed to a three dimensional continuum. Time should also be considered as non local having some of the shared properties of distance considered without location, not easy to express in words,

Answer 3

BIG problems usually result from trying to interpret the mathematical features of an algorithm as if they represented aspects of the real world. Quantum mechanics provides us with algorithms for assigning probabilities to the possible outcomes of measurements on the basis of actual measurement outcomes. Transmogrify the mathematical features of such an algorithm into features of the physical world, and you have a BIG problem.

Answer 4

imaginary time is a way of looking at the time dimension as if it were a dimension of space: you can move forward and backward along imaginary time, just like you can move right and left in space.