A Mathematical Proof The Universe Could Have Formed Spontaneously From Nothing

Started by stromboli, November 07, 2014, 08:53:35 AM

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Baruch

SGOS - what you said, in other words, is exactly what St Augustine said 1600 years ago.  "I know what time is, when I don't think about it ... but when I think about it, I don't know what time is".

Josephpalazzo - the Minkowski model was an option, to represent the results of Einstein's SR analysis in geometric form.  This was then crucial for GR, because GR is a geometry theory.  After the fact, it was necessary for space and time to be linked, before GR was invented, because it turns out that Newtonian gravity allows gravitational lensing, but incorrect by a factor of two ... because in Newtonian gravity, only space is bent (rescaled inhomogenously), not time.  In Einstein gravity, both space and time are bent equally (hence the restoration by 2x) in the case of light, because with light, space and time contribute equally.
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Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
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Don't do that.

SGOS

I can imagine time as a coordinate in space... Kind of.  When I picture a point moving through space, I see a line of coordinates tracing a path, and of course, that path would be impossible without time.  We also hear, mostly in science fiction, about the space-time continuum.  I suspect that nomenclature exists with in the actual scientific community as well.  But even the name, "space-time" suggest two entities 1)space composed of dimensions and 2)time composed of whatever it is.  It sounds like distinct parts with separate characteristics making up a whole.  I get the relationships and I can kind of understand the inevitability of the two existing simultaneously.

Using Baruch's analogy of an electron moving, but not ever being at an exact coordinate, I can imagine time as a rather nebulous concept.  I'm not convinced that it is that nebulous, but I can go in that direction too.  But I don't see space, and specifically, the special dimensions in it as nebulous.  They seem much more precise and defined as coordinates. 

OK, the coordinates are somewhat malleable.  They  do bend and warp in the presence of matter, so the precision they imply might be more nebulous than I think.  It's all fascinating to think about, but then my mind kind of goes blank.

Baruch

SGOS - makes my mind go blank too ... been studying modern physics for 50 years now (I was a smart whippersnapper once).  The problem with exactness, runs into the problem of the Heisenberg Uncertainty Principle.  In ordinary non-relativistic physics ... you have to trade exact energy against exact time.  You can't have both, there is a minimum of DeltaE*DeltaT=>Hbar/2.  This also applies to space as well, there is a minimum of DeltaP*DeltaX=>Hbar/2.  You have to trade exact momentum against exact position.  Our naive notion of a particle moving thru space and time, is just an approximation for non-relativitistic, non-quantum situations.  See, in most cases, Schroedinger's Equation can't even be solved ... so it is fortunate that Newton could approximate the Sun as a point particle and the Earth as a point particle, and could use that assumption to make a computable celestial mechanics.  BTW ... the uncertainty principle as a general math problem, exists in classical mechanics too.  For example in control theory, you have position, velocity and acceleration.  You can design a stable control system if you control just two of those ... if you try to control all three ... there is no stable control system possible (it is out of control).  This limits what a robot or human can do mechanically.

Coordinates were only exact for Descartes.

PS - photons are really very different from electrons (the two most common extra-atomic particles).  One of these differences is that while an electron and a positron are different, and are anti-particles ... the photon it its own anti-particle.
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Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
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Don't do that.

josephpalazzo

Quote from: Baruch on September 06, 2015, 10:24:46 AM
SGOS - what you said, in other words, is exactly what St Augustine said 1600 years ago.  "I know what time is, when I don't think about it ... but when I think about it, I don't know what time is".

Josephpalazzo - the Minkowski model was an option, to represent the results of Einstein's SR analysis in geometric form.  This was then crucial for GR, because GR is a geometry theory.  After the fact, it was necessary for space and time to be linked, before GR was invented, because it turns out that Newtonian gravity allows gravitational lensing, but incorrect by a factor of two ... because in Newtonian gravity, only space is bent (rescaled inhomogenously), not time.  In Einstein gravity, both space and time are bent equally (hence the restoration by 2x) in the case of light, because with light, space and time contribute equally.
Sorry, that's incorrect. Space is flat, and numerous experiments have confirmed this over and over. The bending is always, and always, in terms of space-time. Secondly, the factor of two comes from the equation:

(1/2)m(dr/dt) 2 + (1- r*/r)(l2/(2mr2) - GmM/r  = E

The extra term r* is the additional term that is NOT in Newtonian physics. It is strictly a relativistic effect that gives the recession of Mercury's  perihelion  its correct value. That it turns out to give a value of  around twice that of the Newtonian calculation is coincidental.

( r* is the Schwarzschild radius = 2GM/c 2)

Baruch

The geodesic of a photon is null, but the geodesic of Mercury is time-like.  I was using gravitational lensing in my example, not precession of a planetary orbit.  Also space is flat only globally, locally it is curved, as is time.

Please kindly see p32 and p290 et al in Gravitation (1973) by Misner, Thorne and Wheeler.

The precession may be strictly relativistic, but Newtonian gravity plus Newtonian light particles with momentum such as we know from Einstein in 1905 ... does predict deflection of light by massive astronomical bodies.  And the same idea lies behind Laplace and black holes ... only of course his version was also non-relativistic, and he didn't know about photons either.
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Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
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Don't do that.

josephpalazzo

Quote from: Baruch on September 06, 2015, 03:08:17 PM
The geodesic of a photon is null, but the geodesic of Mercury is time-like.  I was using gravitational lensing in my example, not precession of a planetary orbit.

Sorry about that mixed-up. I should have highlighted the part of your post I was addressing, which was,  "In Einstein gravity, both space and time are bent equally (hence the restoration by 2x) in the case of light, because with light, space and time contribute equally."
Quote
Also space is flat only globally, locally it is curved, as is time.

Please kindly see p32 and p290 et al in Gravitation (1973) by Misner, Thorne and Wheeler.


Sorry but on page 32, they are talking about how Riemann was thinking of the curvature of space, and how wrong that was! The real deal is curvature of spacetime. On page 290, there is no mention of space being curved. But they do mention Newtonian spacetime. So no, space is not curved, not globally, and neither locally.


QuoteThe precession may be strictly relativistic, but Newtonian gravity plus Newtonian light particles with momentum such as we know from Einstein in 1905 ... does predict deflection of light by massive astronomical bodies.  And the same idea lies behind Laplace and black holes ... only of course his version was also non-relativistic, and he didn't know about photons either.

Ok, but that doesn't address the issue that you claimed, "In Einstein gravity, both space and time are bent equally (hence the restoration by 2x) in the case of light, because with light, space and time contribute equally." That is wrong in every which way you want to look at this. Space doesn't bend, and in spacetime, it doesn't bend equally with time. The Lorentz transformation shows that space and time get mixed up, but not necessarily on equal terms, and the mixed up is not about bending in the first place. It's just that the transformation equations are non-linear, and so we need to approximate in any calculation - usually to (v/c)2 is good enough.




Baruch

Right ... you are forgiven ;-)  But the 2x factor is only for the deflection of light ... not for all geodesics.  You know a lot, but you don't have to try so hard.  We are on the same side here ;-)
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
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Don't do that.

josephpalazzo

Quote from: Baruch on September 06, 2015, 04:33:23 PM
Right ... you are forgiven ;-)  But the 2x factor is only for the deflection of light ... not for all geodesics.  You know a lot, but you don't have to try so hard.  We are on the same side here ;-)

Ok, but ONLY if you refrain from saying that space and time bend equally...:-)

Baruch

Well, they will bend, if not orthonormally, at least orthogonally ;-)
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Azee’ Å,a’ish nanídį́į́h?
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Don't do that.

SGOS


Baruch

You can learn origami, but only in Japan under the most severe discipline of a sensei who never smiles ... and only if your origami can kill an opponent when they strike a vulnerable part.
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
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Don't do that.

josephpalazzo

Quote from: Baruch on September 06, 2015, 05:49:01 PM
Well, they will bend, if not orthonormally, at least orthogonally ;-)

No they're not. Stop spewing nonsense, :-)

Baruch

Yes ... the devil is in the details.  The light cone is skewed relative to a fast moving observer ... then it is skew-gonal ;-)
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Azee’ Å,a’ish nanídį́į́h?
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Solitary

Quote from: josephpalazzo on September 05, 2015, 12:01:29 PM
I agree with your feelings. I just went over the calculations @ (http://arxiv.org/pdf/1404.1207v1.pdf). Equation (1) is your standard Einstein-Hilbert Action - you'll find that in every standard book on GR. Equation (2) is a slight take on the Robertson-Walker metric (sometimes referred as the Friedmannâ€"Lemaîtreâ€"Robertsonâ€"Walker (FLRW) metric). They plug that into the  Wheeler-DeWitt equation (WDWE) and get equation (4), and  how-do-you-do-do, they get a solution with an exponential, (last equation, first column, page3), and then claim they have the equation of an expansionary bubble. After discussing the different scenarios of an open, closed and flat universe,  they claim that" the vacuum bubble will stop accelerating when it becomes very large, no matter whether it is closed, ï¬,at, or open". Big Yawn. They celebrate their great achievement with  "Thus, we can conclude that the birth of the early universe is completely determined by quantum mechanism." Phew...

You can safely say that sensationalism has overtaken too many in the sciences, must make many theists gleefully snivelling, but that's my take...

Thank you JP! Your mind is as sharp as ever.
There is nothing more frightful than ignorance in action.

josephpalazzo

Quote from: Baruch on September 07, 2015, 09:43:18 AM
Yes ... the devil is in the details.  The light cone is skewed relative to a fast moving observer ... then it is skew-gonal ;-)

Skewness (about a measure of an asymmetry) and orthogonality (about non-overlapping, independent objects) are like apples and oranges, and you know the proverbial saying, don't mix your apples with...