Most Powerful Equation?

Discussion in 'Physics & Math' started by Reiku, Oct 19, 2007.

  1. Reiku Banned Banned

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    What is the most powerful equation?
    I like the schrodinger wave function.

    (ßMc^2+\sum_{k=1}^3a_kP_kc)psi(x,t)=i’planckcon x partial’psi/partial’t(x,t)

    I was goind to choose Einsteins energy equivalance principle, but that looked to obvious. Then i was going to choose Eulers equation, when i finally gave up to this bitch of an equation...

    What equation do you think is most powerful in physics? - Or ofcourse, simply like?
     
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  3. spidergoat pubic diorama Valued Senior Member

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    I like the ones where you can turn them upside down and they spell naughty words.
     
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  5. draqon Banned Banned

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    all equations are equally important and unimportant.
     
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  7. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    draqon is equally stupid and ignorant
     
  8. fmonroy Registered Senior Member

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    btw, powerful?:m:
     
  9. superluminal I am MalcomR Valued Senior Member

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    Cauchy's integral:


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    http://en.wikipedia.org/wiki/Cauchy's_integral_formula

    I'm no mathemetician (just a lowly engineer) but when I lerarned of this, I thought it was the coolest thing.

    The description I was first given was that it was like being able to trace out the letters around the perimiter of a newspage and from that, knowing the contents of the entire page (not that the contents of a newspage are holomorphic in nature...)
     
  10. Yorda Registered Senior Member

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    The most powerful equation is the equation of creation, it actually explains how and why the universe came from nothing:

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    If you turn it backwards it explains that the universe is an illusion, nothing: 1/∞=0
     
  11. fmonroy Registered Senior Member

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    how you got that eq?
     
  12. superluminal I am MalcomR Valued Senior Member

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    MJ. :m:
     
  13. Reiku Banned Banned

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    I like the reality equation. I'm converted.

    You know its true. Everything (E=Mc^2+E=-Mc^2=0) totals to nothing.
     
  14. superluminal I am MalcomR Valued Senior Member

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    Me too. That's pretty profound. I'm convinced because +1 - 1 totals to zero also. Amazing.
     
  15. andbna Registered Senior Member

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    So, how did you come up with that equation for everything?
    Einstien's mass/energy equivilence simply means that an amount of energy has a proportional amount of mass, and conversly that any mass is 'worth' a proportional amount of energy. It tells us nothing about how much energy or mass exists.

    -Andrew
     
  16. Reiku Banned Banned

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    Positive matter/energy = (E= -Mc^2) Yes?
    > Then
    The negative energy vacuum (E=Mc^2) + (E=Mc^2) = 0

    This goes for all the matter and energy in the vacuum.
     
  17. Reiku Banned Banned

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    In fact, its the same equation when you add spin.

    In double fact, this is what is called, 'renormalization.'
     
  18. andbna Registered Senior Member

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    wait, where did that negative before the mass variable come into the picture?

    Never heard of a "negative energy vacuum" got a link?

    -Andrew
     
  19. Reiku Banned Banned

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    Sorry... the negative was displaced.

    Yes, many links. Take the Cosmological Constant; which is a negative energy filling the vacuum of space and time. There is also the hypothetical quintessence. You'll find plenty links on them, then, concerning the equation:

    E=Mc^2+E=-Mc^2=0

    of renormalization, you will find plenty links on that also. But if you want to cut the links, i'll provide some work i did in the past, if you want to hold on.
     
  20. Reiku Banned Banned

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    Also, here is another big contributer to the negative energy in the vacuum:

    The Zero-Point Energy Field
    You know, according to Einstein, there was no such thing as matter. Just energy. Strange this isn’t it. Just energy… In fact, all this energy had to come from somewhere, and according to physics, we call this source the Zero-Point Energy Field. It is an electromagnetic sea, and has strong correlations with the Dirac Sea of negatively spinning virtual particles.
    A ‘’thing’’ has a lot of energy. Even a small particle contains a whopping amount of energy for its size. Take a marble. It contains something like 10^99 grams of energy! That’s a lot of energy. But if you were to extract every bit of matter and energy from the vacuum, you would still have a massive amount of energy left over. This is the electromagnetic virtual sea of the Zero-Point Energy Field.
    Inertial mass appears to be the resistance an object has when being accelerated; when it is inexorably subjected to a force. In Newton's equation of motion, the application of a force begins to stop, the acceleration goes down, all the way to zero, and the object remains in a uniformal motion. Physical objects are thus assumed to resist acceleration, because that resistance is, or at least appears to be an intrinsic property of matter. F=ma is obviously the equation that states that the change of velocity is proportional to the force F, where the constant is the inertial mass m of the object.
    The work i am studying right now suggests inertia is a property, or shadow at best of a property arising out of all-pervading electromagnetic field of the Zero-Point Energy Field... I like this study, because i have thoughts that even consciousness might arise out of this vacuum, just like matter and energy does.
    From what i have learned, is that the Zero-Point Energy Field (should be) a background temperature of electromagnetic radiation that is uniform and isotropic... Recent results interestingly showed that as a moving observer accelerates through the Zero-Point Field, the spectrum of the Zero-Point Field becomes distorted, just like acceleration in spacetime causes natural distortions, and the distortions increase with an ascending value of acceleration.
    It turns out that there is no longer need to suppose that there is something called mass having an ''innate property'', inertia, that resists acceleration; the really interesting thing that is really happening, is that an electromagnetic force acts on the inner charge of matter which ultimately creates the effect of inertia!
    The Vacuum
    The vacuum is a continuum of both space and time. They simultaneously came into existence, and with them they brought energy and gas. Matter which was nothing but creases in the spacetime fabric; in fact, matter is somehow space and time. It turned out that ordinary matter, the ‘’heavy elements’’ we see around us, wasn’t the only type of matter we could contemplate, and indeed turned out necessary for quantum physics.
    And in came antimatter. This stuff is said to be the time reversed entity of ordinary matter. The antielectron, (the positron), like all antiparticles, are the exact symmetry of their partners in appearance and attitude, but they have slight differences in age. The positron, unlike the electron, had a positive energy. Because of this, inside atoms, if an electron pops out of the Dirac Sea, accompanied with a positron, it will be forced to rush away from the nucleus, because it will come too close to the proton, which also has a positive charge. They would act like magnets, repelling each other.
    Dark matter as well came into the picture, to answer some galactic problems in gravity distribution in relation to observation of galaxy formation. Some of these particles where very strange; they do not interact with the electromagnetic forces, so they did not reflect or emit photons. Some will have very strange substances, a type of energy allowing it move through matter such as mountains and forests. This particle is called the ‘Axion.’ It is hypothetical, but is taken seriously. Neutrino’s are also a Dark Matter candidate.
    Then there was Dark Energy. What is annoying about these theories is that we don’t really know anything about them. What we do know is that Dark energy is a hypothetical form of energy with a negative pressure that is thought to permeate spacetime. According to Einstien’s theory of relativity, the effect of negative pressure is in opposition to gravitational force on massive and strong scales. It is believed by some that such a force maybe responsible for the universes evident accelerated expansion; which is ultimately indicating that our universe is dying!
    Dark energy would make up the lions share of missing matter, making up about 74% of all matter in the vast universe. Two forms of dark energy are proposed as the 'cosmological constant,' a constant energy density filling spacetime homogeneously and there is 'quintessence', a dynamic field which has an energy density that can vary in space and time. It requires high-precision measurements to determine the exact speed of expansion.
    During the 1990's, observations of type 'la supernovae' by the 'Supernova Cosmology Project' and the 'High-Z Supernova Search Team' have provided the suggestion that the universe is indeed accelerating - being backed up with several pieces of observable evidences which include measurements of the 'background microwaves', 'gravitational lensing' and improved measurements on observable supernovae have been consistent with something called the 'Lambda-Chromodynamics Model.’
    But the vacuum has more surprises. It turns out that some calculations made on the hydrogen atom would never have made sense without virtual negative and positive particles spontaneously popping in and out of reality. They contribute to a small value, but it is large on massive scales.

    Then for the Renormalizable theories of GUT

    Renormalization
    In the 1920’s, quantum mechanics worked well with molecules and atoms… this was because they had a finite number of degrees of freedom. However, whenever we worked with the electromagnetic force, all that was result was erroneous calculations, because the electromagnetic field was infinite within its own degrees of freedom; in other words, two degrees of freedom in any point in spacetime. We envision these points as being oscillators, each with its own position and momentum.
    It turned out that the oscillators could never be at rest because that would defy the Uncertainty Principle… Instead, the oscillators where assigned with zero-point fluctuations and even a non-zero energy! Whenever the little electron [wasn’t] being observed, the energies of all the infinite degrees of freedom would make the little bugger’s mass and charge to become infinite…
    This was settled eventually in the late 1940’s with a simple procedure called ‘Renormalization.’ It in simple extracted large numbers by subtracting them with other large numbers; infinities minus infinities. But the main goal was to leave a finite sum – a non-zero remainder.


    Then Dark Energy: a negative energy filling spacetime:

    Dark energy is a hypothetical form of energy with a negative pressure that is thought to permeate spacetime. According to Einstien’s theory of relativity, the effect of negative pressure is in opposition to gravitational force on massive and strong scales. It is believed by some that such a force maybe responsible for the universes evident accelerated expansion; which is ultimately indicating that our universe is dying!
    Dark energy would make up the lions share of missing matter, making up about 74% of all matter in the vast universe. Two forms of dark energy are proposed as the 'cosmological constant,' a constant energy density filling spacetime homogeneously and there is 'quintessence', a dynamic field which has an energy density that can vary in space and time. It requires high-precision measurements to determine the exact speed of expansion.
    During the 1990's, observations of type 'la supernovae' by the 'Supernova Cosmology Project' and the 'High-Z Supernova Search Team' have provided the suggestion that the universe is indeed accelerating - being backed up with several pieces of observable evidences which include measurements of the 'background microwaves', 'gravitational lensing' and improved measurements on observable supernovae have been consistent with something called the 'Lambda-Chromodynamics Model,' (but i will not explain this as it is not germane to the argument.)
    The most direct evidence we have for dark energy comes from the la supernovae - the Hubble red-shift, a way of measuring 'time warps' from the light of receding objects - measuring how distant a thing is, is more difficult to say the least. Thus, it is necessary to find 'standard candles' - these universal candles actually help us in determining certain distances and magnitudes with good accuracy. Without standard candles, it is relatively impossible for us to measure red-shift distances without us making a wild guess, which is really not acceptable in the realms of science. Type la supernovae are the best known candles in our cosmos for our observations - simply because they are extremely bright and thus visible at distances of billions of light years.
    The la supernovae is explained by the favored example of an old 'white dwarf,' which gains mass from a counterpart star and grows until it reaches the 'Chandrasekhar limit' - at this limit, the white dwarf is unstable to thermonuclear runaway and the result is that it explodes with a tremendous brightness, flaring ever outward with energy. It is this brightness that makes observing the Hubble red-shift possible - and it is our observations that indicate the universe isn't decelerating, but is in fact accelerating, at an alarming rate... and it is these observations that the acceleration in universal expansion might be caused by dark energy with negative pressure.
    The presence of dark energy is really needed in physics, to reconcile with the measured geometry of spacetime with the total matter in our universe. Measurements of the cosmic background radiation made recently the 'Wilkinson Microwave Anisotropy Probe,' indicates that the universe is nearly flat - a big leap i must say from Einstien’s highly curved universe. For a universe to be flat, the mass-energy density of the universe must be proportional to the 'critical density.'
    'Baryons' and 'dark matter' is thought to cover only about 30% of the universes critical density matter (more on dark matter later.) Thus, it implies the existence of an additional form of energy to account for the missing 70%. Before we continue, baryons are in the family of 'hadrons.' We have seen two types of baryons in this book - they being protons and neutrons that make up the nucleus of atoms.
    The very nature of dark energy is a matter of speculation. It is thought to be extremely homogeneous, not very dense and doesn't interact with electromagnetic, strong or weak forces; only gravity. Since it is not very dense, around 10^-29 grams per cubic centimeter, it is very hard to comprehend dark energy being detected in the laboratory - with it making at least 70-74% of universal matter would have as you can imagine a drastic impact on expansion. Two leading models as we have seen, concerning dark energy are quintessence and the cosmological constant.
    The simplest explanation for dark matter is that it is the 'cost of having space.' Thus a volume of spacetime has some kind of intrinsic, fundamental energy. This is the cosmological constant. It is sometimes called 'Lambda' after the Greek letter, which is used as a mathematical symbol to represent this quantity. The cosmological constant is estimated to be on the order of 10^-29g/cm3 or 10^120 in reduced 'Plank Units.'
    The cosmological constant might be well known by the reader. It was first proposed by Einstein himself as a mechanism to proclaim a solution to the gravitational field equation, that would lead to Einstien’s strange dream; a static universe. Though, his calculations proved to be quite unstable, and that a static universe would be unpredictable due to local inhomogeneties which would result in a universe that contracts or accelerates - this means that the universe, if it expands only a tiny fraction will continue to expand due to a release of energy from the vacuum, and if it decelerates a tiny fraction, again it will continue to contract. Thus, we now know that the universe is accelerating, and Hubble red shift proved this fact - Einstien’s mistake went past history, as nothing but a curious flaw, as he himself said, it was his biggest blunder.
    Dark energy might arise from the particle-like excitations in a dynamical field called quintessence. Quintessence can vary in spacetime, so it differs from the cosmological constant. Some scientists believe quintessence might be found in violation of Einstien’s 'Equivalence Principle.'
    The 'cosmic coincidence,' theory asks the problem to why the universe accelerated when it did. If acceleration began earlier than it did, planets stars and galaxies would not have had time to form life - we ultimately would not have been here if it had started earlier. Promoters of the 'anthropic principle,' use this to support evidence of the universes means to create us - possibly by superintelligence, like God.
    However, the 'tracker behavior' of quintessence solves this paradox. The tracker behavior model of quintessence has a density which closely tracks (but less than) the radiation density until the matter-radiation is equal, which ultimately triggers the 'quintessence field' to act as dark energy to dominate the universe. One case of quintessence which is thought to exist is called 'phantom energy,' where the energy density can increase in time. As weird and wonderful phantom energy sounds, it might actually result the universe in a 'Big Rip,' as we shall see later. I truly hope not.



    And here is quintessence, and how it is currently used:

    Cosmology estimates that the cosmos did in fact begin acceleration about 5 billion years ago, give or take a billion years - before that, it was thought that dark matter and baryons where decelerating the universe. However, the density of dark matter disappears quickly in an expanding universe and will inexorably disappear, leaving dark energy to become the dominant matter in the universe.
    When the volume of the universe doubles, the density of dark matter is halved, but the density of dark matter is, as i am sure you could guess, halved, and according to the cosmological constant, dark energy is almost unchanged. Though, here is where Armageddon raises its ugly head, and informs us, if acceleration continues, then our universe will probably face a 'Big Rip'. The hypothesis focuses on the quintessence, phantom energy, spoke of in part one, and a steady balance in the equation of state (w), which resembles the ratio between the dark energy pressure and its energy density.
    When we reach in mathematics w<-1, the universe will be violently ripped apart. In a universe that expands at this alarming rate would mean that the observable universe is shrinking (which is around 14 billion light years away - note, that it is an estimated 40 billion light years away to the edge of the universe). This means that all of those galaxies and stars out on the observable edge of our universe are being whisked away at the speed of light - dragged by space and time itself, (this is not in violation of relativity).
    You can imagine, as the observable universe (a matter dominated region) produces a lot of gravity - and as they are pulled away from each other, interaction of the forces will be strained - and eventually when it reaches a certain critical value, absolutely no interaction will occur - no gravitational pulls, no electromagnetic, no influence of strong or weak forces... the result is a catastrophic rip. Not one particle will survive the rip.
    The authors of this doomsday vision say that the first evidences would be that the galaxies are separated from each other - some scientists argue hauntingly that this is what is happening right now. 60 million years before the end, gravity will not be able to support our galaxy, the Milky Way, and other individual galaxies. In the very last three minutes, our planet will be ripped apart by the destructive forces of acceleration. Not to worry though - by then our sun will have turned into a Red Giant, and we will have all been cindered alive - then all that would be left to rip apart would be a barren earth and a star that was now a black dwarf; and i don't like the thought of that. Perhaps this 'civilized' race will blow itself up first using nuclear weapons...
     
  21. andbna Registered Senior Member

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    Egad! Il read that tommrow...
    Now Zero-Point energy and the Cosmological constant ring bells, however it was my understanding that zero point energy is positive, which should cause a large cosmological constant given all the vacuum there is for it to exist in...

    Anyway, goodnight for now.
    -Andrew
     
  22. Reiku Banned Banned

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    Goodnight to you too Andrew. Good dreams. God bless.
     
  23. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    By being ignorant of how math actually works.

    My favorite equaiton is this:

    \(\mathcal{S}_{YM} = \int d^Dx\,\, Tr\,\, F\wedge *F\).

    Pure gauge Yang Mills in D dimensions.
     

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