When there is no normal matter present (with T = 0), the curvature R of space-time is balanced in the following equation in which the scalar curvature R of space-time obeys: R =8πG/c3 T + (theta) Consequently, when there is no normal matter present (with T = 0), the curvature R of space-time is balanced by R = (theta) . Therefore, there is no real vacuum in the universe.
This is from a paper by Ma and Wang mathematically speculating on gravitational field equations and dark energy and dark matter. Their new theory suggests that the curvature R is always balanced by "theta" (can't print the symbol) in the entire space-time and the space-time is no longer flat. Entire space-time is curved and is filled with dark energy and dark matter. In particular, the discontinuities of R induced by the discontinuities of the energy- momentum density T , dictated by the Einstein field equations, are no longer present thanks to the balance of "theta". On Mar 5, 10:19 pm, archytas <nwte...@gmail.com> wrote: > The electron now seems to "split" to three identifiable 'bits' - > spinon, orbiton and holon - described as > quasi-particleshttp://www.nature.com/nature/journal/v485/n7396/full/nature10974.html > > Maybe the photon splits too. The say the last thing fish notice is > water and maybe 'nothing' is much more active than we yet know. > The term ‘incommensurable’ means ‘no common measure’, having its > origins in Ancient Greek mathematics, where it meant no common measure > between magnitudes. For example, there is no common measure between > the length of the leg and the length of the hypotenuse of an > isosceles, right triangle. Such incommensurable relations are > represented by irrational numbers. Irrational and complex numbers > form systems in which we work stuff out - odd they arise in the > incommensurable. We have sets of equations that are incommensurable, > but their harmonics turn out not to be- and we have Wiles' proof re > Fermat's last theorem bridging eliptic and modular equations (I forget > the Japanese name of the bridge). The question of what mathematics > is, really, remains. > > On Mar 5, 8:53 pm, sadovnik socratus <socra...@bezeqint.net> wrote: > > > > > > > > > Euler's Equation Crackpottery > > Feb 18 2013 Published by MarkCC under Bad Math, Bad Physics > > > One of my twitter followers sent me an interesting piece of > > crackpottery. > > I debated whether to do anything with it. The thing about > > crackpottery > > is that it really needs to have some content. > > Total incoherence isn't amusing. This bit is, frankly, right on the > > line. > > ==. > > Euler's Equation and the Reality of Nature. > > a) Euler's Equation as a mathematical reality. > > Euler's identity is "the gold standard for mathematical beauty'. > > Euler's identity is "the most famous formula in all mathematics". > > ‘ . . . this equation is the mathematical analogue of Leonardo > > da Vinci’s Mona Lisa painting or Michelangelo’s statue of David’ > > ‘It is God’s equation’, ‘our jewel ‘, ‘ It is a mathematical icon’. > > . . . . etc. > > b) Euler's Equation as a physical reality. > > "it is absolutely paradoxical; we cannot understand it, > > and we don't know what it means, . . . . .’ > > ‘ Euler's Equation reaches down into the very depths of existence’ > > ‘ Is Euler's Equation about fundamental matters?’ > > ‘It would be nice to understand Euler's Identity as a physical process > > using physics.‘ > > ‘ Is it possible to unite Euler's Identity with physics, quantum > > physics ?’ > > My aim is to understand the reality of nature. > > Can Euler's equation explain me something about reality? > > To give the answer to this. question I need to bind Euler's equation > > with an object – particle. Can it be math- point or string- particle > > or triangle-particle? No, Euler's formula has quantity (pi) which > > says me that the particle must be only a circle . > > Now I want to understand the behavior of circle - particle and > > therefore I need to use spatial relativity and quantum theories. > > These two theories say me that the reason of circle – particle’s > > movement is its own inner impulse (h) or (h*=h/2pi). > > a) Using its own inner impulse (h) circle - particle moves > > ( as a wheel) in a straight line with constant speed c = 1. > > We call such particle - ‘photon’. > > From Earth – gravity point of view this speed is maximally > > . From Vacuum point of view this speed is minimally. > > In this movement quantum of light behave as a corpuscular (no > > charge). > > b) Using its own inner impulse / intrinsic angular momentum > > ( h* = h / 2pi ) circle - particle rotates around its axis. > > In such movement particle has charge, produce electric waves > > ( waves property of particle) and its speed ( frequency) is : c. > > 1. We call such particle - ‘ electron’ and its energy is: E=h*f. > > In this way I can understand the reality of nature. > > ==. > > Best wishes. > > Israel Sadovnik Socratus. > > > ==. > > Euler's equation says that . It's an amazingly profound equation. > > The way that it draws together fundamental concepts is beautiful > > and surprising. > > But it's not nearly as mysterious as our loonie-toon makes it out to > > be. > > The natural logarithm-base is deeply embedded in the structure of > > numbers, and we've known that, and we've known how it works > > for a long time. > > What Euler did was show the relationship between e and the > > fundamental rotation group of the complex numbers. > > There are a couple of ways of restating the definition of that > > make the meaning of that relationship clearer. > > For example: > > > That's an alternative definition of what e is. If we use that, and we > > plug into it, we get: > > > If you work out that limit, it's -1. Also, if you take values of N, > > and plot , , , and , ... on the complex plane, as N gets larger, > > the resulting curve gets closer and closer to a semicircle. > > An equivalent way of seeing it is that exponents of are rotations > > in the complex number plane. The reason that is because if you take > > the complex number (1 + 0i), and rotate it by radians, you get -1: . > > That's what Euler's equation means. > > It's amazing and beautiful, but it's not all that difficult to > > understand. > > It's not mysterious in the sense that our crackpot friend thinks it > > is. > > But what really sets me off is the idea that it must have some > > meaning in physics. That's silly. > > It doesn't matter what the physical laws of the universe are: > > the values of and e will not change. > > It's like trying to say that there must be something special about > > our universe that makes 1 + 1 = 2 - or, conversely, that the fact > > that > > 1+1=2 means something special about the universe we live in > > . These things are facts of numbers, which are independent > > of physical reality. Create a universe with different values for all > > of the fundamental constants - e and π will be exactly the same. > > Create a universe with less matter - e and π will still be the same. > > Create a universe with no matter, a universe with different kinds > > of matter, a universe with 300 forces instead of the four that > > we see - and e and π won't change. > > What things like e and π, and their relationship via Euler's equation > > tell us is that there's a fundamental relationship between numbers > > and shapes on a two-dimensional plane which does not and cannot > > really exist in the world we live in. > > Beyond that, what he's saying is utter rubbish. > > For example: > > These two theories say me that the reason of circle – particle’s > > movement is its own inner impulse (h) or (h*=h/2pi). > > Using its own inner impulse (h) circle - particle moves ( as a wheel) > > in a straight line with constant speed c = 1. > > We call such particle - ‘photon’. > > From Earth – gravity point of view this speed is maximally. > > From Vacuum point of view this speed is minimally. > > In this movement quantum of light behave as a corpuscular (no > > charge). > > > This is utterly meaningless. > > It's a jumble of words that pretends to be meaningful and > > mathematical, > > when in fact it's just a string of syllables strung together > > nonsensical ways. > > There's a lot that we know about how photons behave. > > There's also a lot that we don't know about photons. > > This word salad tells us exactly nothing about photons. > > In the classic phrase, it's not even wrong: what it says doesn't have > > enough meaning to be wrong. What is the "inner impulse" > > of a photon according to this crackpot? > > We can't know: the term isn't defined. > > We are pretty certain that a photon is not a wheel rolling along. > > Is that what the crank is saying? We can't be sure. > > And that's the problem with this kind of crankery. > > As I always say: the very worst math is no math. > > This is a perfect example. > > He starts with a beautiful mathematical fact. > > He uses it to jump to a completely non-mathematical conclusion. > > But he writes a couple of mathematical symbols, > > to pretend that he's using > > math.http://scientopia.org/blogs/goodmath/2013/02/18/eulers-equation-crack... > > > ==. > > > On Feb 14, 8:46 am, sadovnik socratus <socra...@bezeqint.net> wrote: > > > > Euler's Equation and the Reality of Nature. > > > =. > > > Mr. Dexter Sinister wrote: > > > ‘ I understand Euler's Identity, > > > and I know what it means, and I know how to prove it, > > > there's nothing particularly mystical about it, > > > it just demonstrates that exponential, trigonometric, > > > and complex functions are related. > > > Given what we know of mathematics it shouldn't surprise > > > anyone that its various bits are connected. > > > It would be much more surprising if they weren't, that would > > > almost certainly mean something was badly wrong somewhere.’ > > > > Mr. Gary wrote: > > > Mathematics is NOT science. > > > Science is knowledge of the REAL world. > > > Mathematics is an invention of the mind. > > > Many aspects of mathematics have found application > > > in the real world, but there is no guarantee. > > > Any correlation must meet the ultimate test: > > > does it explain something about the real world? > > > As an electrical engineer I used the generalized > > > Euler's equation all the time in circuit analysis: > > > > exp(j*theta) = cos(theta) + j*sin(theta). > > > > So it works at that particular level in electricity. > > > Does it work at other levels, too? > > > Logic cannot prove it. > > > It must be determined by experiment, not by philosophizing. > > > ====.. > > > Thinking about theirs posts I wrote brief article: > > > Euler's Equation and Reality. > > > =. > > > a) > > > Euler's Equation as a mathematical reality. > > > Euler's identity is "the gold standard for mathematical beauty'. > > > Euler's identity is "the most famous formula in all mathematics". > > > ‘ . . . this equation is the > > ... > > read more » -- You received this message because you are subscribed to the Google Groups "Epistemology" group. 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