Imaginary Time

[WinePusher]

Stephen Hawking coined this term in "A Brief History Of Time" and I am no expert on this, I know only what I've read from his exerpts.

Establishing the fact the Hawking believes a singuarlity occured, and space and time began to exist as well, he creates the notion of imaginary time to provide a possible explanation. He argues that imaginary time runs perpendicular to actual time, and any singularity is only a singularity in actual time, not imaginary.

Now, somebody looking at the word "imaginary time" would probably write it off as bogus, for they see the word "imaginary." Is imaginary time a legitamate proposal, or is it all in Hawkings Imagination.

[McCulloch]

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

The imaginary axis running perpendicular to the real one, in time or in numbers is merely a visualization technique. The real guts of the matter is that using imaginary numbers √-1 provides solutions to actual mathematical problems in the real world. The imaginary numbers must cancel themselves out, for the solution to have any real meaning.
Hawking's proposed imaginary time is similar.

[WinePusher]

The imaginary axis running perpendicular to the real one, in time or in numbers is merely a visualization technique. The real guts of the matter is that using imaginary numbers √-1 provides solutions to actual mathematical problems in the real world. The imaginary numbers must cancel themselves out, for the solution to have any real meaning.
Hawking's proposed imaginary time is similar.

The objection I have to this is imaginary numbers have no bearing on actual reality. In reality, it is possible to substract 2 dollars from 4 dollars, however, it is impossible to take the square root of a negative and get a real number. You get i, representating the imaginary. I was always taught in school, when solving complex equations, to distinguished between the real part of the equations and the imaginary part including i. Such as a+bi, the variables a and b are real, i is imaginary.

[Miles]

As explained on Wiki.

• "Imaginary time τ is obtained from real time via a Wick rotation by \scriptstyle\pi/2 in the complex plane: τ =\ it. It can be shown that at finite temperature T, the Green's functions are periodic in imaginary time with a period of \scriptstyle 2\beta\ =\ 2/T. Therefore their Fourier transforms contain only a discrete set of frequencies called Matsubara frequencies. Another way to see the connection between statistical mechanics and quantum field is to consider the transition amplitude \scriptstyle\langle F\,|\,e^{-itH}|I\rangle between an initial state I and a final state F. H is the Hamiltonian of the system. If we compare this with the partition function \scriptstyle Z\ =\ \operatorname{Tr}\ e^{-\beta H} we see that to get the partition function from the transition amplitudes we can replace \scriptstyle t\,=\,\beta/i, set F = I = n and sum over n. This way we don't have to do twice the work by evaluating both the statistical properties and the transition amplitudes. Finally by using a Wick rotation one can show that the Euclidean quantum field theory in (D + 1)-dimensional spacetime is nothing but quantum statistical mechanics in D-dimensional space."

To read it without all the unicode scriptings see HERE

[LiamOS]

The objection I have to this is imaginary numbers have no bearing on actual reality. In reality, it is possible to substract 2 dollars from 4 dollars, however, it is impossible to take the square root of a negative and get a real number. You get i, representating the imaginary. I was always taught in school, when solving complex equations, to distinguished between the real part of the equations and the imaginary part including i. Such as a+bi, the variables a and b are real, i is imaginary.

To say that they have no basis in reality is a bold atatement.
Would you consider irrational numbers to have basis in reality?

And a delightful example of how the imaginary unit interacts in a useful manner is in natural logarithms.
Namely, the fact that:
e^ιπ = -1


I do not necessarily agree that Hawkins' theory is valid, but given the history of mathematical models in theoretical physics, I'm more than happy to entertain it as a possibility.

[WinePusher]

To say that they have no basis in reality is a bold atatement.
Would you consider irrational numbers to have basis in reality?

Yes, irrational numbers (along with rational numbers) are considered to be real numbers. Numbers, in general, would be considered immaterial abstract objects that exist by neccesity to describe seen objects. The number 2 cannot exist on its own, its simply a description of one or more seen physical things. Time, in the same way, exists only to describe the changes in sequence between events. Without any physical space, time cannot exist.

I do not necessarily agree that Hawkins' theory is valid, but given the history of mathematical models in theoretical physics, I'm more than happy to entertain it as a possibility.

It's certainly an intriguing topic, but IMO, it shows the extreme lengths scientists of the atheist persuasion will go to in order to avoid any type of theistic explanation or implication.

[Grumpy]

winepusher

Yes, irrational numbers (along with rational numbers) are considered to be real numbers. Numbers, in general, would be considered immaterial abstract objects that exist by neccesity to describe seen objects. The number 2 cannot exist on its own, its simply a description of one or more seen physical things. Time, in the same way, exists only to describe the changes in sequence between events. Without any physical space, time cannot exist.

Learn some real physics, ok? Time and space are simply parts of the same thing. Our DESCRIPTION of time is not time any more than a yardstick is space. The measurement is not the thing being measured, it is mearly the metric that represents the the thing in our thoughts and calculations.

It's certainly an intriguing topic, but IMO, it shows the extreme lengths scientists of the atheist persuasion will go to in order to avoid any type of theistic explanation or implication.

Believe it or not, disproving god is not a goal of science, nor will scientists lie to do so. If any valid evidence for any god exists scientists would not ignore it, the discoverer would win the Nobel. So your statement is simply slander, not fact.

Grumpy

[WinePusher]

Learn some real physics, ok?

Ahh......Of course because we differ on opinion I must be wrong because the physics I have learned is not real. This may be the so called "toxic rhetoric" we have heard so much about from some forum members. But because a non-theist engages in it, no condemnation will be seen.

Believe it or not, disproving god is not a goal of science, nor will scientists lie to do so. If any valid evidence for any god exists scientists would not ignore it, the discoverer would win the Nobel. So your statement is simply slander, not fact.

If you read my post, you will see I said IMO. That means IN MY OPINION. Not in my FACT, I never claimed to be stating a fact so you are raising a false topic. And, again, because my opinion differs from yours it must also be Slander? It is possible to debate someone on the merits of their opinions without using such incivility and condescention.

[LiamOS]

Time, in the same way, exists only to describe the changes in sequence between events. Without any physical space, time cannot exist.

Is this conjecture, or would you care to support this?
I can find numerous examples of time being interpreted successfully as a dimension, and as a result, rendering large explanatory power.

it shows the extreme lengths scientists of the atheist persuasion will go to in order to avoid any type of theistic explanation or implication.

You know, you're right. We all go to extreme lengths to avoid a theistic explanation.
Accepting a theistic explanation leaves us none the wiser, and still leaves us with the problem of choosing between an infinite number of possible deities.

You don't seem to understand the fact that your view of the universe makes you absolutely none the wiser about anything.

[Abraxas]

Learn some real physics, ok?

Ahh......Of course because we differ on opinion I must be wrong because the physics I have learned is not real. This may be the so called "toxic rhetoric" we have heard so much about from some forum members. But because a non-theist engages in it, no condemnation will be seen.

Believe it or not, disproving god is not a goal of science, nor will scientists lie to do so. If any valid evidence for any god exists scientists would not ignore it, the discoverer would win the Nobel. So your statement is simply slander, not fact.

If you read my post, you will see I said IMO. That means IN MY OPINION. Not in my FACT, I never claimed to be stating a fact so you are raising a false topic. And, again, because my opinion differs from yours it must also be Slander? It is possible to debate someone on the merits of their opinions without using such incivility and condescention.

Without meaning to sound rude, on what basis do you have an opinion? Do you have a background in physics? Have you studied space and time and the mathematical models used to describe them by scientists, understanding why they used the models they use? Do you have data from your own experiments that countermands their data or shows it to be incomplete? For what reason is your opinion different then their opinion?

Now, I am not a total novice in physics, I understand many of the principles and not quite as many of the formulae used in their study. With that said, I haven't even a sliver of a shadow of the total sum knowledge necessary to form an independent opinion, let alone an independent opinion that runs counter to everything the greatest minds in the field hold to be true. This holds true of concepts like spacetime or imaginary time, I simply lack the requisite knowledge and skillset to offer a meaningful evaluation of it, certainly not to the degree that I would accuse Stephen Hawking of Bad science or making stuff up.

So, as I consider myself wholly unqualified to even attempt to run the mathematical models and applied knowledge necessary to offer an opinion and I daresay I have greater understanding in the field than yourself (though by no means would I claim to be the best here), on what basis do you have an opinion on the topic?