Explain Multiple Histories & Imaginary Time - Stephen Hawking

[Jack]

In the universe in a nut shell stephen hawking goes on about the universe having multiple histories but I do not feel that he explains it well. Could someone please explain this to me in simple terms?

Also could someone please explain, as simply as possible, the concept of imaginery time?

 

[chroot]

My advice: stop reading anything by Stephen Hawking. At best, he will mislead you.

The idea of multiple histories is best summed up by the Feynman path integral formulation of quantum mechanics. This technique basically says the following:

A particle's actual trajectory is related to the sum of all of its possible trajectories.

Set up two walls, with one hole in each. Fire some particles at the first wall; some of the particles come through, and some of those come all the way through the hole in the second wall, too.

There are a large number of possible trajectories between the first and second holes; all of the particles that emerge from the second hole followed one of those trajectories. The Feynman path integral formulation says that you can integrate (sum) over all of these trajectories (histories) to find the amplitude (i.e. probability) that a particle coming through the first hole will make it to the second.

As far as imaginary time, it's just the extension of the real time coordinate to the complex plane. Quantum mechanics is based on complex quantities, but it is stipulated that the final results of all computations must be real (after all, we believe that all physical quantities are real). Imaginary time is, in my opinion, just mental masturbation: it probably means nothing, but it leads to some interesting stuff. Physicists worry about whether or not a model produces verifiable results; even if you use weird cogs in your machine, your machine is valuable if it works. I don't know if Hawking's complex time models actually produce any falsifiable predictions -- but I don't usually worry much about what he says.

- Warren

 

[E8]

Does everybody in here feel the same way about Hawking? I bought Brief History in Time and Universe in a Nutshell deluxe set on Ebay recently, am I wasting my time and money?

 

[Jack]

Originally posted by E8
Does everybody in here feel the same way about Hawking? I bought Brief History in Time and Universe in a Nutshell deluxe set on Ebay recently, am I wasting my time and money?

I do not feel that he explains stuff well enough and I don't really like him much because he does seem a bit arrogant to me and that is just the impression I have after reading his books. However I have read 'A Brief History of Time and 'The Universe in a Nutshell' because I find the content of his books very interesting even if it is a bit confusing.

 

[chroot]

Originally posted by E8
Does everybody in here feel the same way about Hawking? I bought Brief History in Time and Universe in a Nutshell deluxe set on Ebay recently, am I wasting my time and money?

If you're looking to learn something, yes, they are a waste of time and money. If you're looking for pseudo-fictious and visionary meandering touched with a bit of hubris, they're just want you want.

- Warren

 

[E8]

If you're looking for pseudo-fictious and visionary meandering touched with a bit of hubris, they're just want you want.

Sweet, I am going to get my money's worth.

Seriously though I am going to go ahead and read the books, what specifically in each book should I throw out as pseudo-fictious?

What books in that nature would you recommend(other than Feynman)?

 

[chroot]

Originally posted by E8
Seriously though I am going to go ahead and read the books, what specifically in each book should I throw out as pseudo-fictious?

Pretty much everything between the front cover and the back cover.

What books in that nature would you recommend(other than Feynman)?

Go to your local college bookstore. Look at the texts the professors chose for their classes. Buy those books.

- Warren

 

[Einstiensqd]

multiple histories and imaginary time

The way I interperted imaginary time is the way he explained it in an earlier book. Think of time as a straight line, horizonal. Now add a vertical dimension to time. That led me to the possibility of three-dimensional time.
As for the multiple histories of the universe, I think that it means that there are many possibilities as for the history of the universe, and there are other parralel universes where these different histories occur.

 

[Hurkyl]

Imaginary time is just a mathematical trick. In relativistic formulae, terms with t^2 tend to have opposite sign than terms with x^2, y^2, or z^2. By measuring time as an imaginary number instead of a real number, you flip the sign in those equations. e.g:

s^2 = -t^2 + x^2 + y^2 + z^2 is the usual length formula in special relativity, where t is "real" time. If we write the corresponding equation using "imaginary" time k where k = i * t, this equation becomes:

s^2 = k^2 + x^2 + y^2 + z^2


Basically, the point is to remove the asymmetry from the equations and put it in the representation.

Hurkyl

 

[redtree]

Time question

In considering n-dimensional space-time, can the time axis of the time-space coordinate system be placed anywhere? If not, why?

A plane is defined by any two perpendicular lines, 3-dimensional space by any 3 orthogonal lines, why not-space time by any 4 orthogonal x,y,z,t(time) lines?

 

[selfAdjoint]

The time axis could be numbered any way, but it behaves differently from the space dimensions; there is a sign difference between them. You can set up your math so that when multiplying vectors the space component products pick up a negative sign, or you could set it up so the negative sign went with the time components. This is called the signature, in the first case it would be (+---) and in the second case it would be (-+++). This assumes the time coordinate is numbered first; you could have given it any number but since it has this different behavior it's conventient to put it in first position.

Here's an example, suppose you have two spacetime vectors (a₀,a₁,a₂,a₃) and (b₀,b₁,b₂,b₃) and you take their inner product, using the signature (-+++). The inner product is the product of corresponding component pairs, added up, giving a negative sign to the product of the 0-components (by convention that's time). So -a₀b₀ + a₁b₁ + a₂b₂ + a₃b₃.

This formula for the inner product, with the time products having different signs than space products, is necessary to support the physics of relativity.

A more specific example, suppose you measure the momentum, p, the mass, m, and the energy e of some particle. Then there is a realtivistic vector, the energy-momentum four-vector, that has these components: (e,cp₁,cp₂.cp₃) and its magnitude is known to be mc^2. If you take the inner product of the vector with itself, you get the square of its magnitude. So,
-e^2 + c^2p₁^2 + c^2p₂^2 + c^2p₃^2 = m^2c^4, or e^2 + c^2|p|^2 = m^2c^4. And because this is true for general components, it's true for all observers. Different observers will measure different values for p and e, but the equation will always be true because it's just an identity.

Rearranging the terms we get the covariant law of energy e^2 = c^2p^2 _ m^2c^4.

 

[redtree]

Folow-up question

Thanks for the reply. I understand your point that the time axis can be numbered in any way, and I also understand that the sign of the time axis is opposite the space dimensions. However, my question was really focused on the orientation of time axis.

Think of a movie. A movie is nothing but a series of two-dimensional representations that change over time. Each frame is a snapshot of a given moment. Now, imagine you were to take all those snapshots and stack them on top of each other. Assume you could section that stack of movie frames in a different way, say from one corner to the opposite corner. And then, what if you took these sections and showed them on a projector? What would you be seeing? You'd be seeing the universe of the movie from a different time line. It's just an expansion of the "block universe" view.


The "Block Universe" View
"Physicists prefer to think of time as laid out in its entirety - a timescape, analogous to a landscape - with all past and future events located there together ... Completely absent from this description of nature is anything that singles out a privileged special moment as the present or any process that would systematically turn future events into the present, then past, events. In short, the time of the physicist does not pass or flow." --Paul Davies, "That Mysterious Flow"


What I am asking is an expansion of the "block universe" concept, fron no privileged moments to no privileged time axis in spacetime.