https://medium.com/the-physics-arxiv-blog/a-mathematical-proof-that-the-universe-could-have-formed-spontaneously-from-nothing-ed7ed0f304a3
QuoteOne of the great theories of modern cosmology is that the universe began in a Big Bang. This is not just an idea but a scientific theory backed up by numerous lines of evidence.
For a start, there is the cosmic microwave background, which is a kind of echo of the big bang; then there is the ongoing expansion of the cosmos, which when imagined backwards, hints at a Big Bang-type origin; and the abundance of the primordial elements, such as helium-4, helium-3, deuterium and so on, can all be calculated using the theory.
But that still leaves a huge puzzle. What caused the Big Bang itself? For many years, cosmologists have relied on the idea that the universe formed spontaneously, that the Big Bang was the result of quantum fluctuations in which the Universe came into existence from nothing.
(https://d262ilb51hltx0.cloudfront.net/max/800/1*INtAsuxJF7cMqoCBmesz-w.jpeg)
That’s plausible, given what we know about quantum mechanics. But physicists really need more â€" a mathematical proof to give the idea flesh.
Today they get their wish thanks to the work of Dongshan He and buddies at the Wuhan Institute of Physics and Mathematics in China. These guys have come up with the first rigorous proof that the Big Bang could indeed have occurred spontaneously because of quantum fluctuations.
The new proof is based on a special set of solutions to a mathematical entity known as the Wheeler-DeWitt equation. In the first half of the 20th century, cosmologists struggled to combine the two pillars of modern physicsâ€" quantum mechanics and general relativityâ€"in a way that reasonably described the universe. As far as they could tell, these theories were entirely at odds with each other.
The breakthrough came in the 1960s when the physicists John Wheeler and Bryce DeWitt combined these previously incompatible ideas in a mathematical framework now known as the Wheeler-DeWitt equation. The new work of Dongshan and co explores some new solutions to this equation.
At the heart of their thinking is Heisenberg’s uncertainty principle. This allows a small empty space to come into existence probabilistically due to fluctuations in what physicists call the metastable false vacuum.
When this happens, there are two possibilities. If this bubble of space does not expand rapidly, it disappears again almost instantly. But if the bubble can expand to a large enough size, then a universe is created in a way that is irreversible.
The question is: does the Wheeler-DeWitt equation allow this? “We prove that once a small true vacuum bubble is created, it has the chance to expand exponentially,†say Dongshan and co.
Their approach is to consider a spherical bubble that is entirely described by its radius. They then derive the equation that describes the rate at which this radius can expand. They then consider three scenarios for the geometry of the bubble â€" whether closed, open or flat.
In each of these cases, they find a solution in which the bubble can expand exponentially and thereby reach a size in which a universe can formâ€"a Big Bang.
That’s a result that cosmologists should be able to build on. It also has an interesting corollary.
One important factor in today’s models of the universe is called the cosmological constant. This is a term that describes the energy density of the vacuum of space. It was originally introduced by Einstein in his 1917 general theory of relativity and later abandoned by him after Hubble’s discovery that the universe was expanding.
Until the 1990s, most cosmologists assumed that the cosmological constant was zero. But more recently, cosmologists have found evidence that something is causing the expansion of the universe to accelerate, implying that the cosmological constant cannot be zero. So any new theory of the universe must allow for a non-zero value of the cosmological constant.
What plays the role of the cosmological constant in Dongshan and co’s new theory? Interestingly, these guys say a quantity known as the quantum potential plays the role of cosmological constant in the new solutions.
This potential comes from an idea called pilot-wave theory developed in the mid-20th century by the physicist David Bohm. This theory reproduces all of the conventional predictions of quantum mechanics but at the price of accepting an additional term known as the quantum potential.
The theory has the effect of making quantum mechanics entirely deterministic since the quantum potential can be used to work out things like the actual position of the particle.
However, mainstream physicists have never taken to Bohm’s idea because its predictions are identical to the conventional version of the theory so there is no experimental way of telling them apart. However, it forces physicists to accept a probabilistic explanation for the nature of reality, something they are generally happy to accept.
The fact that the quantum potential is a necessary part of this new mathematical derivation of the origin of the universe is fascinating. Perhaps it’s time to give Bohm’s ideas another spin round the block.
Ref: arxiv.org/abs/1404.1207 : Spontaneous Creation Of The Universe From Nothing
The universe is a humongous spontaneous orgasm.....
(http://s3-ec.buzzfed.com/static/enhanced/webdr02/2013/8/27/12/anigif_enhanced-buzz-27615-1377620530-38.gif)
I've seen a rabbit pulled out of an empty hat too. Does anyone realize how idiotic it is to think something came out of nothing? You might as well say God did it. It may be a proof mathematically just as plane geometry says two parallel lines don't intersect, but they do in solid geometry. Here is what Einstein had to say about such nonsense with mathematics describing reality.
QuoteAs far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
All the evidence in the world is not reliable if it depends on interpretations that may be wrong, or trying to prove something already believed, like religion does. Solitary
Quote from: stromboli on November 07, 2014, 08:53:35 AM
The universe is a humongous spontaneous orgasm.....
Shit, dude. I coulda told you science is sexy....
(http://i59.tinypic.com/21aiqur.jpg)
So, I read the article. Then I started to read the paper... then I got to this point:
QuoteIn quantum cosmology theory, the evolution of the
universe is completely determined by its quantum state
that should satisfy the WDWE. With HΨ = 0 and
...what?
HΨ = EΨ = 0
The energy of the wave function cannot be equal to zero. The wave function can be in the ground state, which is the lowest energy state (zero-point energy), but that is EΨ = â,,ω/2 not 0. If it was zero, then we wouldn't need a wave equation, or uncertainty principal... let alone the Hamiltonian or Schrodinger equation. We could get an electron in it's lowest energy of zero and know the momentum and position of the particle.
Then again, maybe I missed something?
But the bibble Sez goddidit, write They're on the First page! Praise JEJUS!
Also the Grate Mathmaticicician Leonard Euler prooved god With his eqasion "(a+b^n)/n = x, therfor god existes".
Buy the whey, its not WDWE, its WWJD!!!!!!!
As a man who can barely spell math, I agree to everything that has been posted on this topic.
Quote from: Solitary on November 07, 2014, 11:44:18 AM
Here is what Einstein had to say about such nonsense with mathematics describing reality. All the evidence in the world is not reliable if it depends on interpretations that may be wrong, or trying to prove something already believed, like religion does. Solitary
I had a similar thought farkel through my brain when I read (partially read) the article. As soon as I started getting lost, which I knew I would, my attitude was "Well, yeah, whatever," and I quit reading. I'm not denying the line of thinking. And while math is a good way to quantify things in reality, something from nothing using a math proof is just a bit too much to wrap my head around.
Yet almost all cosmologists are math wizzes, and they draw conclusions about some very strange things in reality using math, things that don't even seem mathematical in nature. I sometimes think that everything that ever happens in the universe can be expressed mathematically... albeit in formulas that are so far beyond my knowledge that I can't begin to understand. I mean absolutely can't even begin. I couldn't last 10 seconds before I'd get lost. No, not even one second. I literally couldn't even begin.
Quote from: Solitary on November 07, 2014, 11:44:18 AM
I've seen a rabbit pulled out of an empty hat too. Does anyone realize how idiotic it is to think something came out of nothing? You might as well say God did it. It may be a proof mathematically just as plane geometry says two parallel lines don't intersect, but they do in solid geometry. Here is what Einstein had to say about such nonsense with mathematics describing reality. All the evidence in the world is not reliable if it depends on interpretations that may be wrong, or trying to prove something already believed, like religion does. Solitary
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...
The first issue of Popular Physics was the beginning of the end for physics ;-)
In classical GR ... it is possible for the space-time continuum to have a boundary ... in the Big Bang model the boundary is in the past, and not surrounded with an event horizon. In the Black Hole model the boundary is in the future, at the singularity hiding inside the event horizon. But people are uncomfortable with a universe that has any boundaries.
In GR, the boundary is in a 4th spatial dimension. Add time, and you get 5-D. Note that Lisa Randall has put forward a cosmological theory in 5-D, and the AdS/CFT Correspondence uses 5-D.
Why is time a dimension? It seems more like an aspect of being, but it doesn't seem like a dimension unless we twist the common definition of a dimension. I hate to be pedantic about it, but time just strikes me as something else, a part of the whole, to be sure, but not a dimension. I can imagine a 4th dimension represented by a 3D model, just the way we can use perspective to suggest 3 dimensions on a 2 dimensional sheet of paper. I can extrapolate a 5th, 6th, 7th, on to an infinite number of dimensions using that reasoning, but time plays no part in the representations for me.
In fact, time has properties that normal dimensions don't have, yet we still refer to it as a dimension. That seems like an error to me.
SGOS - it has to do with abstraction in general. For example, in logic, we have the If/Then structure, that is exactly defined. However in human conversation, they aren't using this exact definition, they are also using ordinary language as the variables. The human version of implication came first, then the logicians abstracted out an essential component of the human version, to produce the technical version. The same thing happened with time. Before St Augustine, nobody even tried to think abstractly about time, because exact chronometers hadn't even been imagined yet. Once the earliest mechanical clock was invented, and later the pocket watch (and today we have the AppleWatch) it became possible to imagine time as a separate dimension. This wasn't first done by Einstein or Minkowski ... but by Scholastics in the 15th century. They were simply graphing data in an attempt to quantitatively understand motion. But they were premature, this graphical approach had to await Descartes, Galileo, Stevinus and Kepler. And their mess was clarified by Newton and Leibniz. In an effort to clean up Newton's mess (post Maxwell) Einstein forced ordinary mechanics to be consistent with EM theory ... and Minkowski rediscovered the 4-d model of the 15th century. Or to be more exact, way back then you had two, 2-d models ... space vs space and space vs time. Of course with the advent of proper vector calculus in the 19th century under Gibbs ... 2-d space was expanded to 3-d space (most of Newton's problems all happen in a plane). This of course was necessary so that Maxwell could clean up Faraday's mess. And the idea of 4-d didn't even start with Minkowski ... in fiction, in the book Flatland, by Abbott, in 1884, a generation earlier.
So what of time? It isn't a dimension like the space dimensions. And ordinary matter (say an electron) doesn't move thru the space-time continuum the same as light (say a photon). They are qualitatively different, hence your discomfort. Lots of people have had a emotional problem with SR and GR. But it mostly works anyway. Even I don't like the standard formulation of SR or GR .. I think they can be improved. If even SR were improved, it is possible that the Standard Theory (which relies on the standard formulation of SR) would also be improved ... let alone if GR could be merged with it.
http://www.flatlandthemovie.com ... everything sounds so much more real, with an English accent ;-)
It almost seems like no one ever bothered to define time properly, or more correctly bothered to categorize it:
"Hey Buddy, look at what I found over here; Time. I can't explain it. What is it like? Where should I put it? Do we have a taxonomic classification for classifying it?"
"Nope, not yet. Just group it with the dimensions for now. 200 years from now when we figure out what it is, we can create a new Phylum or something to put it in."
Quote from: SGOS on September 06, 2015, 08:59:47 AM
Why is time a dimension? It seems more like an aspect of being, but it doesn't seem like a dimension unless we twist the common definition of a dimension. I hate to be pedantic about it, but time just strikes me as something else, a part of the whole, to be sure, but not a dimension. I can imagine a 4th dimension represented by a 3D model, just the way we can use perspective to suggest 3 dimensions on a 2 dimensional sheet of paper. I can extrapolate a 5th, 6th, 7th, on to an infinite number of dimensions using that reasoning, but time plays no part in the representations for me.
In fact, time has properties that normal dimensions don't have, yet we still refer to it as a dimension. That seems like an error to me.
Time is a coordinate in GR. Main reason is that time can slow down or speed up and so it behaves like the 3 spatial coordinates. A second reason is that GR wouldn't make much sense if expressed in 3-D. In 4-D, (3 spatial + time), the equations in GR are not only easier to handle but are easier to understand intuitively, though it takes time (pun?) to get that kind of perspective. The other point to make is that though time is a coordinate, it's also treated as an imaginary number, which gets William Lane Craig all up in arms, ;-).
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.
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.
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.
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)(l
2/(2mr
2) - 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)
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.
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.
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 ;-)
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...:-)
Well, they will bend, if not orthonormally, at least orthogonally ;-)
I always wanted to learn origami.
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.
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, :-)
Yes ... the devil is in the details. The light cone is skewed relative to a fast moving observer ... then it is skew-gonal ;-)
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.
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...
God is in the details damn it! He is the Alpha and Omega, the beginning and the end. Dumb atheist infidels. :angel: :lol:
From a human perspective space and time are different : space is visualised whilst time is experienced
In other words you see space but you feel time. One mind bending paradox about time is that its three
arrows [ psychological / thermodynamic / cosmological ] all move forward though everything we see is
in the past. That is because of the time it takes for light to travel from any object to us. For even if that
is as close to us as physically possible we still see it in the past. Of course the time that it takes for light
to travel small distances fools our brain into thinking we are seeing things in the present. The only place
however that the present really exists is in our own minds. Everywhere else it is permanently in the past
Psychological time is also cultural. In Japanese, your POV is assumed to be looking into the past, because you can't see the future (this is the traditional view). Americans would be the exact opposite ... because we are progressive. We choose a goal, and go for it, like archery and Robin Hood.
Quote from: surreptitious57 on September 28, 2015, 02:10:46 AM
From a human perspective space and time are different : space is visualised whilst time is experienced
In other words you see space but you feel time. One mind bending paradox about time is that its three
arrows [ psychological / thermodynamic / cosmological ] all move forward though everything we see is
in the past. That is because of the time it takes for light to travel from any object to us. For even if that
is as close to us as physically possible we still see it in the past. Of course the time that it takes for light
to travel small distances fools our brain into thinking we are seeing things in the present. The only place
however that the present really exists is in our own minds. Everywhere else it is permanently in the past
The physical time in physics is needed to measure velocity. Without motion, time wouldn't exist. What does it mean that you're 20 years old? It means you have travelled twenty times around the sun. You can't define any unit of time without referring to some type of motion. And you're right: "Everywhere else it is permanently in the past." That was made clear with Einstein's theory of relativity with the speed of light being a universal constant and as a limiting factor.