Imaginary Time

[Gibsense]

This is denoted by adding "i" to the numbers. It is the square root of -1 (multiplied by your number I suppose)

It is considered to be a mathematical tool that as it turns out justifies the universe having NO beginning. It also smoothes out issues re Black Holes.

It has been explored conceptually/ mathematically by Hawking and er (I must look up the name of the other person) concerning their main interest - Black Holes. It also removes the need for a Singularity.

As many posters debate the origin of the universe and the singularity in Black Holes I thought I really should post something on the subject - especially as Time itself is of considerable interest to me. I confess to knowing next to nothing about Imaginary Time except it is supposed to be perpendicular to space as a spatial dimension. I am not sure if it is mathematically used as a substitute for 'normal' time or as an additional time.
Maybe there are people here that know what they are talking about on imaginary time (?)

 

[promytius]

"Perpendicular to time" now that's going to take some explanation, because first you would have to deal with things like: what is perpendicular to an inch? or an ounce?
Right now, I'm thinking that's ridiculous. Staying tuned to learn.

 

[Gibsense]

There are 3 spatial dimensions - up down and across. The idea is that another spatial dimension can be added at right angles to those three. Look up Tesseract. A tesseract is a four-dimensional cube. Although spatial this additional dimension enables us to experience Time.
In the case above Hawking and Co used this extra dimension to calculate the effect of Imaginary Time

 

[Atlan0001]

There are 3 spatial dimensions - up down and across. The idea is that another spatial dimension can be added at right angles to those three. Look up Tesseract. A tesseract is a four-dimensional cube. Although spatial this additional dimension enables us to experience Time.
In the case above Hawking and Co used this extra dimension to calculate the effect of Imaginary Time

"Imaginary time": Light's holographical coordinate points past-future histories (p(t=+1) f(t=-1)) SPACETIME (the "observable universe").

 

[billslugg]

The biggest step loss in EE students occurs at the point "i" is introduced. It happens around beginning of Junior year.

 

[promytius]

i i i...

 

[Gibsense]

The biggest step loss in EE students occurs at the point "i" is introduced. It happens around beginning of Junior year.

THIS POST OF MINE IS NONSENSE SO FAR AS COMPLEX NUMBERS ARE CONCERNED (I DISCOVER)
Instead of deleting it, I think the logic may be OK in discussing the nature of time but not complex numbers certainly as to my surprise the square root of -4 is not 2i but is -√2 + √2i.

The reason for leaving the text below is that it may well be relevant in challenging the nature of time itself - hopefully on another post in this thread. Apologies to all


That made me wonder what explanations are given to students regarding' i' numbers. I am trying to remember what I was told, but it is so long ago! Those here might contribute if we have some 'anchor' from which to stand and debate/argue.

So anyway I thought I would take a crack at it using my favourite subject: Time

Time has a strange property that might prove revealing: It is always positive
Time can however progress in an opposite direction (as in a spherical expanding universe's opposing sides and positrons/antiparticles)

If time is always positive and yet can be opposite (as in antiparticles) we must invent a number system that can cope with having a positive value and yet be opposite to a 'normal number'. Like it or not we have committed the negative sign to denote the 'Opposite' but the opposite numbers we have lumbered with a negative sign are nevertheless positive (and can be treated that way (the square root of a negative number)

That will do for starters except to comment that Spherelander springs to mind (looking forward to getting the book!

 

[Gibsense]

"Imaginary time": Light's holographical coordinate points past-future histories (p(t=+1) f(t=-1)) SPACETIME (the "observable universe").

Hawking in his book: "The Universe in a Nutshell", refers to this. He considers we may be living on the surface (of a four-dimensional brane) of a 5 dimensional something. This surface, He suggested, may be the surface of a black hole and might contain all the information of what lies beyond much like a holograph.

I have had this book a couple of years but only skimmed it. I decided to read properly the parts on Imaginary Time. There are surprises:

Vacuum energy he says has an influence opposite to that of Gravity. He says it causes inflation. Is this Dark Energy?
He says that Imaginary Time is Spherical and Small whereas Real-time is open and he draws it as rings getting larger and that they influence each other

I suppose I need to read it about a further 30 times to get a useful understanding.