Slow days

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marcus

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Hi selfAdjoint, I wonder if anyone else is having the same trouble that I do reading LaTex.
When LaTex is typed in line there is sometimes overwriting. So this from your last post should be perfectly legible but is not because part of the algebraic expression is typed overtop the other. And it doesnt happen with complete consistency every time I view the post! Now it is not doing it. This passage comes through perfectly:

selfAdjoint said:
...And that's what the Wick Rotation does with time. Defining [tex]t = i\tau[/tex], a pure imaginary, we have [tex]-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2[/tex], so you go from [tex]-c^2t^2 + x^2 + y^2 + z^2[/tex] to [tex]+c^2\tau^2 + x^2 + y^2 + z^2[/tex] with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever [tex]\tau[/tex] appears, because that smooth transition is guaranteed.
But earlier today, to make this readable I needed to insert carriage-returns after some of the LaTex to avoid having two Tex expressions on the same line. Like this:


<<...And that's what the Wick Rotation does with time. Defining [tex]t = i\tau[/tex], a pure imaginary, we have [tex]-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2[/tex],
so you go from [tex]-c^2t^2 + x^2 + y^2 + z^2[/tex]
to [tex]+c^2\tau^2 + x^2 + y^2 + z^2[/tex] with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever [tex]\tau[/tex] appears, because that smooth transition is guaranteed>>
 
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nightcleaner

marcus said:
Hi selfAdjoint, I wonder if anyone else is having the same trouble that I do reading LaTex.
When LaTex is typed in line there is sometimes overwriting. So this from your last post should be perfectly legible but is not because part of the algebraic expression is typed overtop the other. And it doesnt happen with complete consistency every time I view the post! Now it is not doing it. This passage comes through perfectly:



But earlier today, to make this readable I needed to insert carriage-returns after some of the LaTex to avoid having two Tex expressions on the same line. Like this:


<<...And that's what the Wick Rotation does with time. Defining [tex]t = i\tau[/tex], a pure imaginary, we have [tex]-t^2 = -(i\tau)^2 = - ((-1)\tau^2) = +\tau^2[/tex],
so you go from [tex]-c^2t^2 + x^2 + y^2 + z^2[/tex]
to [tex]+c^2\tau^2 + x^2 + y^2 + z^2[/tex] with all positive signs, which allows the path integrals to converge. Then after you get the result you know you can just plug in t in it wherever [tex]\tau[/tex] appears, because that smooth transition is guaranteed>>
Marcus, I am not experiencing the difficulty you mention, but it sounds like a problem I had with my previous computer. I am afraid you may be having a hardware difficulty. I hope you can resolve this difficulty quickly and easily!

Richard
 

marcus

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nightcleaner said:
Marcus, I am not experiencing the difficulty you mention, ...
that's good. then hopefully it is not a general problem just something
my system does on occasion
not to worry about further
 
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I'm going to stick my neck out a bit and try out some ideas.

Next to one of thread titles here, 'Relativity' I think, it is written that time and space are relative concepts, not absolute things. My impression is that there no agreement about this in current physics, but the statement has been there a long time and it seems true to me. If so then it follows that this spacetime universe reduces to, or emerges from, something that is unextended in spacetime, something that is absolute, for common sense says that there must be something that is absolute. This something would have to be like an infinitely curled up dimension (or number of them) perhaps, not so much at right angles to the usual four and innaccessible to us, but rather just unextended so unobservable and immaterial. If anything like this is the case then it's small wonder then that we are confused about where the BB happened and when it did, for it didn't.

I liked Hawking's idea when I thought he meant time was imaginary. It made sense, even if he didn't bite the bullet and considered only the beginning and end of the universe, leaving out the bit in between. However, to say that time (at the beginning and end) turns into an imaginary number seems meaningless to me, even if it is necessary to represent it by such a number in a mathematical formalism. Why not just say it's imaginary, as this seems to be generally accepted? (I'm still not quite convinced that Hawking didn't mean imaginary literally. If not then the writer I read on this was being very sloppy).

To use the sphere metaphor, which is misleading but helpful, this would mean that the spacetime universe could be represented as being on the surface of the sphere, and all points in spacetime would be directly and uniquely connected to the focus of the sphere, which would represent the unextended but paradoxically co-extensive-with-spacetime dimension curled up into an unextended singularity. If spacetime is not fundamental then the singularity is fundamental. If spacetime is conceptual/imaginary then the singularity remains fundamental and unchanged and there was no BB, or, rather, we are still experiencing the BB, a continuous creation or emergence of virtual particles and waves from another dimension into their conceptually-extended spacetime, causing the appearance of an expanding universe and a uniform background radiation. (Yes, I know this sounds crazy, perhaps it is).

So, conceptually, from one perspective the sphere can be thought of as a singularity, for if there is nothing outside of the sphere it doesn't make sense to assign it a size, although we have to give it a size to conceive of it. Or it can be thought of as infinitely extended, for the same reason, but only in the minds of its observers.

Is that lunacy? Perhaps. But if there is a fifth dimension or 'hyperspace' as suggested by some then I would have thought it'd have to be something like this, topologically-speaking. It's only a rough and metaphorical picture, however it seems to tie in with the paradoxical results we obtain from quantum cosmology and micro-physics. But I'll expect one or two objections. :smile:

Tying this in with the Higgs fied, which is where we started, is beyond me. It might suggest that the Higgs field is unextended in spacetime, which might bear on some of the properties of gravity and our inabilty to find the Higgs field (or is it just Higgs bosuns we can't find?) but this is where it all gets far too technical for me.

The key test of this idea is whether or not it is possible to explain the cosmic background radiation as generated uniformly over time and not just all at once at the "beginning" of time. I have no idea whether it is possible to do this, or possible to show that it cannot be done. I'm hoping someone here will know.
 
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it's the return of the space cowboy just to say...

...imagine Canute, being not on the outside surface or the inside surface of a sphere/bubble but trapped in the membrane itself ???


Imagine, if you will bubbles...
expanding as they float around
bumping into other bubbles
and inside of these bubbles
is another bubble expanding
and so on...

...and if all these bubbles
made a musical note,
as they bumped and merged
and expanded,
they created chords and melodies
and so on...

if you look at the swirling effects on a bubble skin/membrane and took note of different points on the bubble you'll see patterns of points seemingly moving towards and away from each other while still maintaing surface tension...

...then it pops and you have to blow another one

equate that to gravity, redshifting and inflation then scale it up or down, throw in some blackholes/wormholes to connect the bubbles and allow for energy exchange then VOILA...

bye for now...
 
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Yes, this is more or less what I'm suggesting, but taking a broader view and going a little deeper.
 

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