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    Square Root Of The Universe
    By Johannes Koelman | October 16th 2010 10:48 AM | 75 comments | Print | E-mail | Track Comments
    About Johannes

    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune

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    Is energy conserved? "Of course it is!" anyone with just a rudimentary knowledge of physics will answer. A more pertinent answer would be: "if you can't show me a working perpetual motion machine, shut up and stop wasting my time!" 

    The conservation of energy is an insight that stood the test of time. It was Julius von Mayer who first worded it in its clearest form: "Energy can be neither created nor destroyed". That was nearly 170 years ago. 

    So why question energy conservation?

    The interesting thing about physics is that the deeper you dig, the more you are forced to doubt existing principles. Dig deep into the universe, allow gravity to become a dominant feature, and the conservation of energy becomes much less obvious. 

    Recently, several physics bloggers have tackled the issue of how energy conservation plays out at cosmic scales. You might be surprised to hear that they all seem to conclude that at cosmic scales, total energy can be created and destroyed. Sean Carroll at Cosmic Variance comes to the conclusion:
    "it’s better to [..] just admit that energy is not conserved"
    Sascha Vongehr here at Science 2.0 does not agree with Sean's particular wording, but reaches the same conclusion:
    "Energy conservation just does not hold in general relativity"
    I think they are both wrong. Energy is conserved also at cosmic scales, but one has to look at it from the right perspective. Trying to define the total energy of the universe in the conventional way in terms of a volumetric addition gets you quickly in all kinds of difficulties. The total energy can not be defined as the sum of energies of many small subvolumes. Key to this problem is that there is no such thing as 'the density of gravitational energy'. Gravitational energy is non-local. Or more precisely: it is holographic in nature.  

    To get a handle on the holographic nature of gravitational energy, we first need to understand the concept of space-time horizons.

     
    From black hole horizons to cosmic horizons 
    In a recent post I elaborated on what could be referred to as a Bohr model of black holes. The picture that emerged is the following:

    A black hole can be described purely in terms of its horizon. For an outside observer this horizon can be thought of as a spherical surface along which a large number of photons move at the speed of light. The number of photons is proportional to the surface area of the sphere, and each photon has energy proportional to the curvature of the sphere or, in other words, an energy inversely proportional to the circumference of the sphere. Multiplying the number of photons with the energy per photon, it follows that the total energy of the horizon, and thereby the total mass or energy content of the black hole, is proportional to its circumference. Working in natural units, this proportionality works out as:

    Black Hole Horizon Energy = Horizon Circumference / 4

    The right-hand side, the horizon circumference divided by 4pi, we will refer to as the horizon half-radius, or HHR. 

    Outside observers experience the horizon as a boundary from beyond which light can not emanate. This is what makes a black hole 'black'. Light emitted by an object approaching the horizon, can reach distant observers, but experiences difficulty in doing so. This difficulty manifests itself as a redshift that increases as the object approaches the horizon. The closer to the horizon, the more stretched the light that reaches distant observers. At the horizon the redshift becomes infinite, the light from the object stretches to infinite wavelength, and the object disappears out of sight. 

    So a black hole horizon can be interpreted as a limiting boundary to the region of space that we can observe. The region of space from which photons can reach us with finite redshift.


    A cosmological horizon bounds the universe observable to us. The closer an object is to this horizon, the more red-shifted it will be.

    But we have another such boundary: our cosmic horizon. The boundary that delimits the part of the universe observable to us. The closer galaxies are located to this cosmic horizon, the more they are redshifted. Right at the cosmic horizon, the redshift becomes infinite. This cosmic horizon, just like a black hole horizon is a spherical surface. It encloses our 'look-back universe'. The observable history of the universe. The HHR of the observable universe expressed in natural units measures a whopping 1061 (yes, that's a one followed by sixty-one zeros...). 

    And now comes the key point: if we associate with a black hole horizon an energy equal to its HHR or half-radius, then we have to associate a similar energy to the cosmic horizon. But... this cosmic horizon energy carries a minus sign. There is several ways to make plausible the cosmic horizon energy must have a sign opposite to black hole horizon energies. The easiest way is to recognize that the cosmic horizon is curved towards us rather than away from us like black hole horizons. So the total energy of the cosmic horizon, the horizon area times its curvature, carries a negative sign due to its curvature having a sign opposite to that of black holes.

    Another way of expressing this is by saying that the cosmic horizon is a black hole horizon turned inside-out. Some prefer to refer to such a horizon as a white hole horizon. This all becomes rather vague and suggestive wordplay. For the present purpose you should just accept the fact that the cosmic horizon that we observe 'from the inside' and black hole horizons that we observe 'from the outside' carry opposite signs when it comes to determining their energy.
     
    With this, all cosmic-scale energy conservation issues have all evaporated. It is the energy associated with the cosmological horizon that fixes the bookkeeping of the total cosmic energy. We have already determined the size of the HHR of the universe, so we know the energy of the associated horizon:

    Cosmic Horizon Energy = - HHR = -1061 Plancks 
                  
    The total mass in the observable universe (including non-luminiferous matter) is about 2x1053 kg or 1061 Plancks. So the total energy of the universe adds up to 

    Energy of universe = mass energy + horizon energy = 1061 - 1061 = zero zilch nada...

    Credits and debits add up to zero. That is how it was at the very start, and that is how it is now. Our cosmos has its bookkeeping in perfect balance. 

     
    Expanding baby universes
    The fact that the total energy is not just conserved, but more specifically conserved such that it adds up to zero, is essential when considering the origin of the universe. The universe was born in an infinite flash of light. And it will probably also end in a flash of light. Can we model this evolution based on the above derived horizon description? The answer is "yes", and it is surprisingly easy to do.

    We don't have a theory that describes Planck-scale physics, but we can make an educated guess on some key aspects of the big bang by audaciously extrapolating the above horizon description to the Planck scale origin of the universe. 

    The universe started hot. Imagine an infinite space filled homogeneously with ultra-hot thermal radiation. Infinitely many photons with energy close to the Planck energy. Our early universe constituted a tiny fraction of this infinite space. How tiny? We extrapolate back to a universe containing just a few (say three) photons and a total energy content of one Planck. For this baby universe to have sprung out of nothing without violating total energy conservation, it must have a vanishing total energy and therefore an HHR of one balancing the energy content of one Planck. Only a very tiny three photon universe fits into such a half radius. Notice that another observer at a slightly different location in the infinity of space experiences an entirely different universe, also containing just a few photons. Each of these infinite number of baby universes has total energy zero.


    The all-too-familiar expanding balloon analogy explaining cosmological redshift: radiation stretches to larger wavelengths due to the expansion of the universe.

    How did one of these tiny and dull few photon baby universes grow into the present grandiose display we call our universe? The secret is expansion. Things get more interesting and the number of features grow as soon as the baby universes starts expanding. The wavelengths of the photons as well as their mutual distances increase, and the baby universes grow into larger universes that start to overlap. When the photon wavelengths and inter-photon distances have increased to twice their original sizes, the baby universes have increased their HHR to four times their original value. As a result, each baby universe has grown to 43 = 64 times its original size and now contains 23 = 8 times as many photons. 

    Does energy conservation still hold?

    Let's check this. Each photon has doubled its wavelength and thereby halved its energy. Eight times as many photons at half the energy adds up to four times the energy content in each baby universe. The HHR of each baby universe has quadrupled, and therefore the horizon energy of each baby universe has quadrupled as well into minus four Plancks. Four Plancks of photon energy added to minus four Plancks of horizon energy: the total energy of these baby universes still adds up to zero.

    We conclude that for each factor of two expansion, the universe grows a factor of four. In other words: for a given expansion factor, the boundary of the observable universe must have receded away from it's observer by a factor equal to the square of the expansion factor.  

    A one-third Planck energy baby-universe photon has wavelength equal to 6pi (again in natural units). Expand this wavelength by a Hubble expansion factor of 3 1030, and you get a wavelength of about 6 1031 Planck lengths or about 1 mm. That is the central wavelength of the cosmic microwave background (CMB), the remnant of the big bang. The universe itself is much larger than the Hubble expansion times the size of the baby universe. According to the above, the universe's present HHR should be equal to the size of the baby universe times the square of the Hubble expansion factor. 

    Let's see if that works out OK. An initial HHR of one times 3 1030 times 3 1030 gives a HHR of 1061. You have seen that number before: it is the observed HHR of our current universe.

    Let's recap what we did. We introduced the concept of a horizon energy, a quantity proportional to the circumference of the horizon. With nothing more than this and the law of total energy conservation, we described the Hubble expansion including the redshift of the big bang photons. 

    Impressive? 

    Well, I have to admit that I have somewhat reverse-engineered the above derivation. Would I have started with baby universes containing different numbers of photons, or photons at different energy, things would have worked out less precise. Key point, however, is that using a simple horizon energy picture, one can understand the energy balance that leads to zero total energy, and also grasp the expansion of a radiation-dominated universe. The same horizon picture can be used to also derive the expansion of a matter-dominated universe (the size of which increases with the 3/2th power of the expansion factor).
     
    So when asked "is it possible to build a perpetual motion machine that generates energy?" you know what to answer. You reply: "Such a machine would perhaps be possible, but only if you are able to extend it beyond the cosmic horizon." An answer that will leave them in utter confusion and probably shut them up. If they are witty enough to ask the follow-up question "how far away is that horizon?", you reply "not that far actually, the square root of that distance is roughly the wavelength of the light from the big bang, and that's about a millimeter". Never destroy their hope.

    Comments

    rholley
    What a wonderful title!  I immediately went to read this article.

    As I read, the following came to mind.  It is from “The Nature of the Physical World” by A.S.Eddington, 1928.
    Energy momentum and stress, which we have identified with the ten principal curvatures of site world, are the subject of the famous laws of conservation of energy and momentum.  Granting that the identification is correct, these laws are mathematical identities.  Violation of them is unthinkable.  Perhaps I can best indicate their nature by an analogy.

    An aged college Bursar once dwelt secluded in his rooms devoting himself entirely to accounts.  He realised the intellectual and other activities of the college only as they presented themselves in the bills.  He vaguely conjectured an objective reality at the back of it all — some sort of parallel to the real college — though he could only picture it in terms of the pounds, shillings and pence which made up what he would call “the commonsense college of everyday experience”.  The method of account-keeping had become inveterate habit handed down from generations of hermit-like bursars; he accepted the form of accounts as being part of the nature of things.  But he was of a scientific turn and he wonted to learn more about the college.  One day in looking over his books he discovered a remarkable law.

    For every item on the credit side on equal item appeared somewhere else on the debit side.  “Ha!” said the Bursar, “I have discovered one of the great laws controlling the college.  It is a perfect and exact law of the real world.  Credit must be called plus and debit minus; and so we have the law of conservation of £ s. d.  This is the true way to find out things, and there is no limit to what may ultimately be discovered by this scientific method.  I will pay no more heed to the superstitions held by some of the Fellows as to a beneficent spirit called the King or evil spirits called the University Commissioners.  I have only to go on in this way and I shall succeed in understanding why prices are always going up.”

    I have no quarrel with the Bursar for believing that scientific investigation of the accounts is a road to exact (though necessarily partial) knowledge of the reality behind them.  Things may be discovered by this method which go deeper than the mere truism revealed by his first effort.  In any case his life is especially concerned with accounts and it is proper that he should discover the laws of accounts whatever their nature.  But I would point nut to him that a discovery of the overlapping of the different aspects in which the realities of the college present themselves in the world of accounts, is not a discovery of the laws controlling the college; that he had not even begun to find the controlling laws.  The college may totter but the Bursar’s accounts still balance.

    Hope you enjoy!
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Johannes Koelman
    A thought-provocative analogy, Robert. Thanks.

    Not sure if I fully understand what Edington tries to convey here. The famous Einstein quote "Everything that can be counted does not necessarily count; everything that counts cannot necessarily be counted" seems applicable to the bursar in the story, but I would hesitate to declare this quote equally applicable to the energy-momentum conservation laws.
    The universe expands such that the square root of its size matches the wavelength of the light from the big bang.

    Planck units are wonderful..!

    Aitch
    The significance of Planck’s natural units in a future physical theory of spacetime is only a plausible, yet by no means certain, assumption

    Could it be a flaw in the Math, failing to account for the secret number?

    http://www.strangehorizons.com/2000/20001120/secret_number.shtml#top

    Aitch
    Johannes Koelman
    On Planck units: Verified -- u got it..! Aitch -- I think I have to dedicate a blogpost to Planck units. The math behind them is trivial. Yet, using these we manage to eliminate from the equations the distractions, and to retain what matters.
    Great post, as usual.

    Typo in the 2nd paragraph: "It was Julius von Mayer who first worded it in it's clearest form"

    Johannes Koelman
    Disconcision -- thanks. That's a nasty flaw in the iPad's spellchecker. Can't correct it now, as any edits now would de-feature the article.
    Bonny Bonobo alias Brat
    Johannes, thank you for this great article explaining the inverse black hole and white hole horizon energies and how the total energy of the universe can add up to zero as 'mass energy + horizon energy = 1061 - 1061 = zero'. There is one thing I don't understand though, you say that
    The universe started hot. Imagine an infinite space filled homogeneously
    with ultra-hot thermal radiation. Infinitely many photons with energy
    close to the Planck energy. Our early universe constituted a tiny
    fraction of this infinite space. How tiny? We extrapolate back to a
    universe containing just a few (say three) photons and a total energy
    content of one Planck.


    How could the universe start hot? Surely it would have to start at the equivalent of neutral or zero temperature, if there is such a thing, otherwise immediately, at that point in time the sum total of the energy of the universe would not have been zero?
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    How could the universe start hot? [..] at that point in time the sum total of the energy of the universe would not have been zero?
    Helen -- you have given the answer yourself: the content (radiation) of the starting universe can be very hot, provided there is a white hole horizon energy that offsets the total energy to zero.
    Bonny Bonobo alias Brat
    Thank for your answer Johannes, I was actually trying to imagine the start of the universe just prior to when it was extrapolated to 'containing just a few (say three) photons and a total energy content of one Planck'.

    In my mind, time as a dimension would still have existed because there was a time prior to this universe existing, but wouldn't  there also have been a temperature of nothing, even though that's not really possible according to the third law of thermodynamics? Then suddenly, wouldn't there have been a miniscule amount of heat with a miniscule equivalent white hole horizon energy which somehow then became very hot and contained three photons and and the total one Planck energy? I was  trying to imagine where on the thermodynamic scale (if there is such a thing) between very cold and very hot, that very first temperature after zero, would have appeared?

    The third law of thermodynamics, which concerns the entropy of a perfect crystal at absolute zero temperature, 'implies that it is impossible to cool a system all the way to exactly absolute zero'.

    See http://en.wikipedia.org/wiki/Laws_of_thermodynamics. But what temperature on our thermometer scales is just before or after zero? Is it equivalent to the water freezing point temperature of zero? Anyway, please feel free to delete this comment Johannes if it is going completely off track for this blog. I can keep trying to work this out myself.

    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    Helen -- you tell me where is south of the South Pole and what temperatures prevail over there, and I'll tell you what came before the big bang and how hot that was. You go first...
    Bonny Bonobo alias Brat
    Well maybe there is a South Pole equivalent of this universe, and beyond that is the North Pole equivalent of the next universe, and maybe these are parallel universes with almost nothing in between, with a corresponding almost zero temperature. And just maybe when two such universes occasionally collide their branes or white hole horizons or whatever they are, they create another big bang and a third universe out of that nothing? But you're right, who knows what the initial temperature would be in that situation? Somewhere between zero and very hot, however it does seem that temperature can make a big difference in how the components of the universe behave.

    One of my many problems is I don't understand thermodynamics, I'm on a big learning curve trying to teach myself basic physics. In answer to my question further down Aitch has said that ""Absolute zero" is the coldest temperature possible, occurring at minus  273.16 degrees Celsius, or zero degrees Kelvin. At this temperature, all atoms and molecules stop migrating and vibrating - energyless....yet  full of potential". Thank you for that Aitch. Probably that's also why they cool everything down to such low temperatures at the Large Hadron Particle Collider at CERN?
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    "maybe there is a South Pole equivalent of this universe, and beyond that is the North Pole equivalent of the next universe Could be. What seems to be a consistent scenario is a universe and anti-universe that spring into existence together. The universe evolves and expands forward in time, and the anti-universe does so backward in time. Both universes are infinite and each others mirror images. There would be no beginning and no end to time, but there would be a moment of highest density and maximum temperature. We have a fair idea of what that temperature would be. In terms of the 'South Pole analogy, south of the south pole would be a mirror. In practice such cosmological philosophies have little meaning. There are (as far as I know) no observable consequences associated with them.
    Aitch
    There is a story of a monk, meditating on 'life, the universe, and everything' in a cave, with a small entrance
    Every morning the cave would light at one end and sweep in an arc to the other throughout the day
    He mused for many years as to what was the principle behind this, and finally imagined curved space, ....and became enlightened
    He came down from the mountain to teach his new found wisdom

    "We live in a trumpet!" he declared, in the market place, where people were busy buying food, "and cannot see the edges of our universe because of the curvature of space"

    Everyone knew him to be quite mad.....and blew raspberries at him

    Maybe our [scientific/mathematical] vision of our universe is trumpeted?

    Aitch
    Hank
    As an aside, remind me some time in the new month to institute a forums section.   A lot of these questions may not find a good place in a specific article but readers may want to discuss abstract ideas just the same.    We could make forums a little more 'wide open' than our core science articles.
    Bonny Bonobo alias Brat


    This is a blog for interested lay persons.

    Hank, according to Johannes and maybe Sascha, this is a blog for interested lay persons. I thought my initial lay person question was relevant to what I had just read about the total energy in the universe being zero. If Johannes wants to delete it for being off target or abstract then that's fine by me, but you are making me feel nervous about even asking a lay-person question on what you call a 'core science' article by implying that my question was out of place.

    I was only trying to conceptualize or imagine what Johannes was describing, and asking a related question, well related to me anyway, is there something wrong with me doing that? How can I know beforehand if a question is unanswerable or too abstract, if I'm not an expert in the field? Seems like a bit of a 'Catch22'.

    I guess that what you are proposing is that we should have a separate forum for lay persons and only the PHDs should be discussing 'core science' articles here. I wonder how Johannes, Sascha and everyone else feel about that?
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Hank
    Maybe our [scientific/mathematical] vision of our universe is trumpeted?
    was asked by Henry Cox and I replied to him because it reminded me I had tossed out an idea of forums for introspective/unable-to-be-answered scientifically/philosophical topics.   I certainly appreciate you defending the intent of Science 2.0 but I kinda know it, since I built it.
    Johannes Koelman
    I wonder how Johannes, Sascha and everyone else feel about that? Let's keep the questions coming... (although I can't promise I will answer each and every of them)
    Bonny Bonobo alias Brat
    Johannes, do you agree that extreme temperatures could play an important role in how the universe evolved after or even before it was created? I read this article which described how 'researchers led by Lene Hau at Harvard University had their first success in 1999, when they reduced the speed of light by 20 million fold, to 60kmh by passing it through a cloud of very cold gas (just above minus 273C)'. See http://www.smh.com.au/news/world/scientists-see-the-light-then-make-it-d...

    "In 2001 her team brought light to a dead stop in a similar cloud, known as a Bose-Einstein condensate. For the new study, published overnight in the journal Nature, Professor Hau created two condensates a tiny distance apart. When a laser light pulse was beamed into one it slowed to a halt, as expected. But the light was then completely converted to matter, which travelled over to the second condensate at a leisurely pace of 200 metres an hour".

    "The original light pulse was reincarnated in that condensate, and went on its way. Professor Hau said the fact that the light was momentarily present as matter in the tiny gap between the condensates was very important, because matter was easy to manipulate, unlike light." I find this very difficult to understand and would be grateful if you or someone else could explain how these low temperatures have such a profound effect upon the speed of light.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    Helen -- the article in which Lene Hau et al describe their experiment, you can find here. Nowhere in the article you will find the claim that they have 'slowed down light'. This is misleading pop science talk.

    What Hau did is to lock light in a box, a very special quantum mechanical box. The unique thing about this box is that whilst the light was rattling around, it retained its coherent nature. But the light did rattle around at a speed of about 300,000 km/s.

    Although this might not be the most accurate way to explain the experiment in layman's terms (it is always difficult to describe quantum phenomena in more familiar terms), it certainly is a much better way than what this article presented to you.
    Bonny Bonobo alias Brat
    Nowhere in the article you will find the claim that they have 'slowed down light'. This is misleading pop science talk.

    Thanks Johannes and Jerry for your replies , but I still don’t understand why, even in this paper, they talk about ultraslow light as if it is possible and already exists when they say the following -

    ‘Therefore, methods for reversible transfer of information between light and matter are required, and efficient and coherent mapping of optical states to and from an atomic medium is possible with use of ultraslow light in cold atom clouds under conditions of dark states and electromagnetically induced transparency. Light storage and revival has been demonstrated for light pulses with classical statistics, for single photon pulses, and for entangled states of light with the entanglement preservation determined entirely by the fidelity for classical light storage. Storage times of a few milliseconds were obtained for both classical light and single photon pulses, but for the development of long- distance quantum networks longer storage times are desirable'.

    See the first page at http://arxiv.org/PS_cache/arxiv/pdf/0909/0909.3203v2.pdf
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Amateur Astronomer
    Helen, I believe the item you are referring to is explained on page 2 of the article as a high refractive index in the device on the front end that is used for entangling the wave functions of light with sodium atoms, also the high refractive index in the matching device for untangling wave functions at the far end. Refractive index is a well accepted concept where light travels more slowly in solids, liquids, and gasses, than it does in a vacuum. There is no intent in the article to say that light speed has been slowed down in a vacuum. The energy and momentum of light are not changed when a photon enters a region of high refractive index.
    Amateur Astronomer
    “The light wasn't actually converted into sodium atoms.” http://www.itwire.com/science-news/energy/9352-scientists-convert-light-... Helen, I believe the newspaper article you quoted had a mistake. Here is a different report of the same announcement. The mistake is most evident in the conservation of momentum. People argue about conservation of energy, but no one disputes the conservation of momentum. If light could convert to matter, the matter would have to travel at light speed, a violation of special relativity. For light to convert to matter, two photons gamma radiation have to collide head on from opposite directions. Then you get one electron and one position of antimatter moving off in opposite directions, usually at some angle to the path of the gamma rays. At the cold temperatures of micro degrees, the sodium gas is a super conductor, meaning that it is not transparent to light. The light gets absorbed by electrons in orbit around the sodium nucleus. That gives the atom a boost of momentum that carries it across the gap. Not much diffusion occurs in the condensate. That is a property of condensates. The atoms don’t bump into each other very often. So the boosted atoms have a clear path across the gap and through the other condensate bubble. As the atoms reach the far end of the second bubble, they approach a region where the superconductivity is breaking down. At that point the sodium atoms can unload their excess momentum in the form of visible light. The fact that the light is not dispersed, and emerges as nearly the same beam of light that entered the first bubble, is a way to confirm that the molecules didn’t bump into each other, and the photons were not passed around very often from one atom to another. The important part for Johannes’ article is that momentum is always conserved. There is no person objecting to that. Except for matter that has rest mass, all other energy E travels at light speed c and is directly related to momentum p. E = pc Maybe we are getting closer to the joke that Johannes is having on us. One of Johannes’ previous articles covered something like this. “What’s wrong with E=mc^2?” The answer was that Einstein knew his equation was not relativistically invariant, but was unable to fix it. Dirac fixed it in a way that Einstein accepted. It is called the energy momentum equation or the classical average of the quantum mechanical Dirac Equation. Johannes represented it as a triangle graph. E^2 = (mc^2)^2 + (pc)^2 Now we have figured out the joke. Dirac’s equation is relativistically invariant, although the separate parts of it are not. So it is possible to argue universal conservation of energy, based on this equation. Next we have to guess what book Johannes is reading in his photograph.
    Hank, I have a lot of questions that would find a home in the proposed forum. A much better place than a disturbance in the science that goes on in the individual blog posts.

    I would truly like to see the forums begin.

    Frank

    Aitch
    ....but wouldn't there also have been a temperature of nothing............
    Helen
    Perhaps using nullity instead of nothing makes more sense?
    A use for nullity is in the divide by zero example, here

    http://www.badscience.net/2006/12/maths-professor-divides-by-zero-say-bbc/

    Although that example is to illustrate a problem with computers and integers, a similar problem exists in square roots of negative numbers, and the solution was the invention of the imaginary or '' i "
    Note, title of article: Square root of the Universe

    Tom Disch writes in “The Dot on the i” (in About the Size of It):

    “When it comes to the sense
    Of beauty we are all Pythagoreans,
    Transfixed upon the ineffable and inexplicable
    Significance of a number; for instance
    (Or especially?), i, the square root of minus-one.”

    'i' is regarded as imaginary to the absolute, or real
    The square root of minus one is the geometric mean between opposites: Absolute and imaginary

    "Absolute zero" is the coldest temperature possible, occurring at minus 273.16 degrees Celsius, or zero degrees Kelvin. At this temperature, all atoms and molecules stop migrating and vibrating - energyless....yet full of potential

    However, since entropy is not constant, it does lead to an interesting conclusion – that the universe must have been created with very low entropy, i.e. with an enormous quantity of available energy. Like a clock which was once wound up, but is now relentlessly running down. Energy is running out!.....or so it is said....

    The square root of -1 is a better representation of consciousness than infinity because the square root of -1 has an unsolvable quality while infinity can be visualized as a lot of something.

    Reality is based on paradox (life is full of twists, turns, knowns and unknowns).
    Therefore i (the square root of -1) is an apt representation since i to the third power = -i, and i to the fifth power = i.

    If you find South of South, then you'll need also to find North of North, East of East etc

    Johannes could have said...."its easier to see 'the cow jumped over the moon', ....if you have time"

    OK?

    Aitch
    vongehr
    Baez is also a good source about why energy is not conserved:

    http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html



    “The total energy can not be defined as the sum of energies of many small subvolumes.”     If E is not extensive, then you cannot do thermodynamics, as the latter needs pairs of extensive and intensive quantities like V and P in PV=nRT.








    “The number of photons is proportional to the surface area of the sphere, and each photon has energy proportional to the curvature”      Your assumptions have no justification except that they give you the result you need. Why on earth (on black hole) should the gamma rays and bibles that I throw in arrange in this way?

    “the horizon area times its curvature, carries a negative sign due to its curvature having a sign opposite to that of black holes.”     This is just wrong! You can of course claim that there is a sign, again because you need it, but if you argue with curvature in this way on a science blog, I cannot let you get away with it. The curvature is both times positive! The curvature of a saddle like shape would be negative.



    “I have to admit that I have somewhat reverse-engineered the above derivation.”     He he, thanks – at least you know. It amazes me again and again how much you develop out of one little coincidence (you know which one I am talking about, as we discussed this before) that might be no more than a coincidence after all. But keep it coming - it is very inspiring.
    Johannes Koelman
    "Baez is also a good source about why energy is not conserved" No, John is more thoughtful. He doesn't say energy is not conserved, but rather stresses the fact that within the framework of GR we lack a consistent definition of total energy. It is wrong logic to conclude from this that energy conservation is violated, and I do not see John making that remark anywhere in the text you refer to. His answers to the question "Is Energy Conserved in General Relativity?" is in fact "it depends on what you mean by 'energy', and what you mean by 'conserved'." I think no-one can argue against this remark. To again use the analogy from my post: an accountant who lacks a definition for debits can not claim a balance sheet to be wrong.  “If E is not extensive, then you cannot do thermodynamics." You are mixing up 'non extensive' and 'non local'. Gravitational energy is nonlocal, but that does not make it non-extensive.      "Your assumptions have no justification except that they give you the result you need."   Ok, you are criticizing here my Bohresque model of the Schwarzschild black hole. Fair enough, as long as you realize that such a criticism is purely cosmetic. I am not making really any assumptions here. I merely describe a semiclassical (didactical) model that reproduces *all* black hole features (size, energy and entropy) experienced by outside observers. You are most welcome to replace this Bohr model with any other model of your liking that leads to the same black hole size, energy and entropy. It will not change any of the conclusions.  "if you argue with curvature in this way on a science blog, I cannot let you get away with it." C'mon Sascha! This is a blog for interested lay persons. You may replace the word 'curvature'  with 'Ricci curvature' if that makes you happy.      "He he, thanks – at least you know."  Don't read too much into my reverse-engineering statement. I was solely hinting at the fact that in the derivation of the cosmic expansion behavior I did fine-tune the precise starting point. However, would I have started with one photon rather than three, this would not have changed the derivation of the radiation-dominated (or matter dominated) expansion. Let me conclude by giving you a small challenge. You make the claim that energy is not conserved. You can prove that claim by designing a working perpetual motion machine of the first kind. Note: I don't ask you even to build anything. A conceptual design or gedanken experiment will do. Good luck!
    vongehr
    "lack a consistent definition of total energy."
    One can always, if energy goes missing, just ad hoc postulate a reservoir (potential) where it is supposedly going, and then claim victoriously that holy energy is conserved after all. That is religion, not physics (god also always jumps in yet another place after being kicked out of where ever he was supposed to be before). Baez is more careful in his formulating, true, but he also knows that without the right time symmetry, there just is no energy conservation - it is not even to be expected!
    Classically, space-time is static, and so E is conserved, that means if some is missing, we better find out where it went. However, energy in GR is not even expected to be conserved. If it is missing and we know well why it is missing, then why not? Why insist on traditional thoughts about energy? Why is energy the golden urine of the holy calf? Science is not religion - at least not quite yet.

    "You are most welcome to replace this Bohr model with any other model of your liking that leads to the same black hole size, energy and entropy."
    Exactly! Any artificial model that scales just right to give you the results that you are after.

    "This is a blog for interested lay persons."
    Meaning what? Using sciency sounding explanations (negative curvature) although they are wrong because you know the audience won't get it? They go away from your blog thinking the curvature inside a sphere is negative. Some may discuss this maybe with others and if they do not believe it, they gonna go like "Koelman from Science2.0 said so, and he knows stuff". You started about mass/energy behind a horizon, which was more or less fine, and then with the cosmic horizon it is all of a sudden not the stuff behind the horizon (which is the whole rest of the maybe infinite universe!), but instead the stuff on the side of the observer (horizons are observer dependent!), and since you need it negative, here comes a sign out of nowhere. I am not saying that you cannot postulate such, I just say that maybe we science bloggers should be more careful about how derived ("negative curvature") we let things appear. So, I understood your "reverse-engineering statement" as a necessary disclaimer, which it should be.
    AGAIN, I AM NOT SAYING YOU ARE A BAD PERSON OR A MORON, I AM SAYING WE SHOULD WRITE MORE CAREFULLY! Get it?

    "perpetual motion machine"    Come on - we are talking fundamental physics here, not engineering in your hammock. The universe is a perpetual motion machine, and not just of the benign first kind. And again, why should it not be? There are symmetries that obviously forbid perpetual motion in your hammock. These symmetries do not hold for the universe as a whole, and why should they?
    Johannes Koelman
    Calm down Sascha, and leave your emotions out. There is certainly no need for CAPS LOCK RANTS that display a misplaced and incoherent obsession with religion. You can do much better than that.   "One can always, if energy goes missing, just ad hoc postulate a reservoir (potential) where it is supposedly going, and then claim victoriously that holy energy is conserved after all. That is religion, not physics (god also always jumps in yet another place after being kicked out of where ever he was supposed to be before). " I identified a missing (boundary) term in the definition of the total energy of the universe. That is correct. But that is just the start of the whole argument. More important is that I subsequently demonstrate that the inclusion of this missing term forces the correct description of the Hubble expansion (both for a radiation dominated universe as well as for a matter dominated universe) from total energy conservation alone. Have you entirely missed this point?      "without the right time symmetry, there just is no energy conservation" Wow, Sascha. Are you kidding?  Emmy Noether: "with time symmetry there must be energy conservation". Sascha Vongehr: "ok, let's reverse that, without time symmetry there just is no energy conservation" Apart from generating this non sequitur, you also seem to fail to notice the continuous symmetries relevant to Noether's theorem relate to the Lagrangian description of the evolution, and not to the shape the evolution takes. "Using sciency sounding explanations (negative curvature) although they are wrong because you know the audience won't get it?" That is dangerously close to being offensive. And entirely based on you perceiving an error where in reality you simply fail to understand Ricci curvature.  "Exactly! Any artificial model that gives you the results that you are after; I did not say nothing else." Why are you paraphrasing me incorrectly? Are you again missing the point?  I tell you any model (with the correct energy and entropy behavior) leads to the same cosmic expansion results, and you paraphrase me saying "any model that gives the results you are after".    "The universe is a perpetual motion machine, and not just of the benign first kind. And again, why should it not be? There are symmetries that obviously forbid perpetual motion in your hammock. These symmetries do not hold for the universe as a whole, and why should they?" Who said your magical energy creating device needs to fit into a hammock? I asked for a thought experiment. You can build your fantasies as big as the whole universe.  Short summary of Sascha's position: Energy is not conserved but nature conspires against us to utilize this fact.   Right. And let me guess: in your next post you are going to reveal that light moves relative to an omnipresent ether but nature conspires against us to observe this?  When you find yourself in a hole, it's not a bad idea to stop digging. Well, feel free to continue, but don't expect any further reactions.  Don't take it personally: the simple fact is I am the least interested in spending my valuable time in reaction to confused and/or biased commenters.
    vongehr
    I wrote

    "AGAIN, I AM NOT SAYING YOU ARE A BAD PERSON OR A MORON, I AM SAYING WE
    SHOULD WRITE MORE CAREFULLY! Get it?
    "

    for a reason. You did sadly not get it in spite of all caps (it was not a rant now, was it, just one single line trying to make sure you get it, should I use italics or boldface so you will get it the next time?)

    Anyways, I am too busy to waste time on discussing pseudo science. Sorry, but in my opinion, your answer just jumped the shark or something like that. Don't tell me about Ricci curvature or Noether currents. And I well got your main point that you wanted but in my opinion failed to make a good case for.

    Thank you sincerely for your inspiring articles, please keep them coming, and please consider to maybe be yet more clear about how far out some of your stuff actually is, especially because we indeed do deal with lay people. [I personally for example use straw-man for that, and straw-man has told me many times what a moronically far out crack-pot ether theory my own stuff would be (e.g. in the articles on inflation) if I were to claim them to be more than toy models. THAT is (sorry the caps) why I am not a pseudo-scientist; not because I am not also having the weirdest ideas, but because I am aware of their limitations AND I am careful not to sell it to lay people as the new snake oil. (moreover, I point out the dodgy assumptions rather than hide them)] AGAIN, I AM NOT SAYING YOU ARE A BAD PERSON OR A MORON, I AM SAYING WE SHOULD WRITE MORE CAREFULLY! Get it?
    GR and energy conservation.

    When you turn around an object, We can see that movement creates gravity in this universe.

    Circular movement creates a steady gravitational "field" when standing on the inside as an observer. [Like someone in a rotating spaceship on the inside experiences "artificial" gravity].

    - only requirement: a constant speed.

    Going straight up in a rocket or elevator on the other hand needs an extra boost of energy.

    - requirement: accelerated speed.

    The equivalence principle only deals with positive horizons.

    Standing on Earth we experience a positive horizon, the same person standing in a spaceship turning around experiences a negative horizon.

    In GR there is only room for positive horizons. And that is why it fails in regard to dealing with energy in general. It simply highlights only one aspect of gravity.

    Positive horizon: you need extra energy to account for gravity.
    Negative horizon: you do not have a need for extra energy at all.

    If I may say so, yes GR indeed has a problem regarding energy conservation.

    Always thought the recession of the cosmological horizon is the Hubble expansion. Now I understand the two are not identical. Far from it. It's like climbing up the mast of a ship: your height increase causes the distant horizon to recede. But height above sea level and distance to horizon are not in a 1:1 ratio. That's perfectly obvious. But somehow I always overlooked the same essential fact when it comes to the receding cosmological horizon. Thanks for clarifying!

    Johannes Koelman
    Nice analogy, Hans. Indeed, in terms of its effect on horizon recession, the expansion (redshift) of the radiation is analogous to a sailor climbing the mast of his ship. The error of assuming the cosmic horizon to recede with the Hubble expansion is widespread. Note that the same error is represented in the inflating balloon picture copied above.
    -
    -
    ------------------------------------------------Infinity refutes divinity
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    ----------------------------------------------The Universe is infinite
    -
    -------------------------------------------There NEVER was nothing
    -
    ---------------------------------------------"Beginning" is impossible
    -
    -----------------------------------------Thus "Creator " is superfluous
    -
    -
    -

    Johannes Koelman
    There is no single measurement in contradiction with an infinite universe. So, for all we know the total universe is infinite. But why would this be required to render a creator superfluous?
    -
    -
    --------------------------------------------------"INFINITE Universe" does not 'need' a "Creator"!
    -
    ------------------------------- - -------------------'Infinity" means: "No beginning, no end"!
    -
    -----------'Every' action or "cause" needs an "impetus" thus a 'so-called' "Creation" or "First Cause" is impossible!
    -
    -----------------------------------------------------------There NEVER was "Nothing'!
    -
    -----------------------------------------------------------Mass/ Energy never disappear
    -
    -----------------------------------------------------------------Ever were/ ever here!
    -
    -----------------------------------------The worse form of child abuse is 'corrupting their mind'!
    -
    -

    A blog on the uses (and misuses) of Planck units would be helpful. I like being able to work back in c,G,h at the correct powers to see if I can calculate something in more familiar metric units. (Anyone remember the bank clerk C G H Tompkins?)

    I will go over your article again when time permits. I am more comfortable with horizons being measured in terms of AREA (and bits). Your use of Radius and Circumference is perhaps confusing me. The ratio of volume to surface area of a super dense sphere does not follow the Euclidean formula of {(4/3)piR^3 / 4piR^2} = R/3 (this lower limit is for Flat Space). Then again, maybe you are implying is that space is Flat … or that one could reverse engineer from Flatness and get conservation of energy?

    My apologies for not being clearer … I need to tend to fall projects.

    What about “conservation of information”, unitarity and all that? Where does that fit in?

    Johannes Koelman
    Anon -- a few snippets of information that might eliminate some of the confusion: Circumference = energy Surface = entropy Volume = ? ( doesn't enter the picture) In this particular blogpost I focused entirely on energy. Entropy drives the expansion of the universe (for an intuitive explanation click here).
    What I don't understand, and, it seems to me, the one unjustified assumption you're making, is that of the expansion itself. Given a super-hot and -dense initial state, and given any non-overlapping (I assume) sets of 3, say, photons... first, that's a lot of potential universes... or is it? Just how big is this soup anyway (e.g., why not all the energy in *one* very dense photon)? Second, why should anything expand? What does "expand" even mean in this scenario? To put it another way, what *separates* the three photons from the rest? Perhaps I'm echoing some of Sascha's comments here... but it seems to me that yes, given that we *are* in this universe, probably something like what you're describing happened, but I don't see any reason for it, nor in fact any initial mechanism, given only what you've said above.

    Johannes Koelman
    Steven -- that's a lot of questions. Not sure if the following answers all your questions. Let me know if not: "why not all the energy in *one* very dense photon)?" An initial state with energy per photon close to the Planck energy gives the most compact (highest density) state. photons with much lower energies are poorly localised due to Heisenberg's uncertainty relationship, and much more energetic photons would be poorly localized due to a large horizon forming. "Second, why should anything expand?" Due to entropic acceleration (see the it-from-bit series of blogposts here). "what *separates* the three photons from the rest?" A causal horizon (the 'white horizon' mentioned above). In essence, such a horizon forms whenever N Plancks of energy fit within a circumference of 4 pi N Planck lengths.
    -
    -
    ====================== To: Johannes Koelman; You 'pose' the "QUESTION":
    -
    =========== "----"is it possible to build a perpetual motion machine that generates energy?"
    -
    ---I say: Nikola Tesla Patented (U S Patent # 70) a "Radiant Energy" device' that will provide "Perpetual Energy"!
    -
    There is a U-Tube Video available demonstrating how to build it!
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    It incorporates a Large polished metal plate insulated atop a pole, a capacitor, and a grounding rod.
    -
    The metal plate is wired to one connection of the capacitor, and the other connection goes to the ground rod!
    -
    The "ENERGY" accumulates in the capacitor and is derived therefrom.
    -
    Apparently the "higher" the "metal plate" is, the greater is the energy.
    -
    Type "Tesla's Radiant Energy" at GOOGLE.COM for ALL the info!
    -
    -

    The "baby universe" expanded into what?

    The wavelengths of the photons as well as their "mutual distances" increased how?

    When exactly are you guys going to get out of those freakin' armchairs and tell us something that makes sense without violating the very principles that you are trying to establish?

    Could you please answer this simple, straightforward question? Is everything we know in physics wrong and do we need to start understanding things from scratch completely ignoring what we know?

    “Imagine an infinite space filled homogeneously with ultra-hot thermal radiation. Infinitely many photons with energy close to the Planck energy.”

    I imagine that Jerry (wherever he is) would associate this with Dirac’s Sea.

    And then you have some course grains of this infinite space expanding … stupendously …

    That’s a lot to put on the table for starters. I suppose the expansion comes automatically with some fancy entropy gradients.

    What we need is a time-like evolution equation for these horizons. Something like HHR(t) = Area(t) x 1/R(t).

    Does HHR(t) always equal minus 10^61, or is that just what we observe now.

    Does Total Mass Energy vary with this time parameter? Has it always been 10^61?

    The black hole horizons are also part of the observable universe.

    It is conceivable that each galaxy and galactic cluster could merge into one massive black hole of every increasing area. That would create a lot of Black Hole HR with a plus sign … and take away from the cosmic HHR.

    … assuming we are even correct in the sign conventions for the curvatures which are supposed to be proportional to tidal accelerations.

    (still can’t get my sign-in to work)

    Johannes Koelman
    "What we need is a time-like evolution equation for these horizons. Something like HHR(t) = Area(t) x 1/R(t)." That's right. So far time is missing from the picture. Does HHR(t) always equal minus 10^61, or is that just what we observe now. It started around 1, and now is 10^61. And still accelerating... Does Total Mass Energy vary with this time parameter? Has it always been 10^61? It started around 1, and now is 10^61. And still growing.. It is conceivable that each galaxy and galactic cluster could merge into one massive black hole of every increasing area. That would create a lot of Black Hole HR with a plus sign … and take away from the cosmic HHR. Actually, it would cause the cosmic HHR to grow. Remember, it's all a giant balancing act.
    Amateur Astronomer
    Try signing in on this link. http://www.science20.com/user It has fewer problems than the popup window. You wrote “Infinitely many photons with energy close to the Planck energy” This is not the Dirac Sea of Energy. It is the conventional view of an observer inside the event horizon of a black hole. Such views are possible in the most massive black hole models where the local gravity is not too extreme at the event horizon. A sea of energy outside is not necessary to produce this view. In the popular models ordinary background microwaves get blue shifted enough by the gravity field to appear white hot at the event horizon. They acquire energy approaching the Planck limit, even after x-rays have been given off during angular acceleration. Gravitational blue shift of faint microwaves provides a reason for me to differ from the popular models of black holes and how they evaporate over time. Any massive black hole of conventional description can very quickly receive enough blue shifted energy to reach the limit of Planck temperature and experience a spontaneously unstable event. So the model that allows this is probably wrong. There are ways to fix the standard models. I would like to postpone that to another time and respond to Johannes about the perpetual motion machines. I have two examples of perpetual motion that come from the main stream of science and are supported by experimental data. Before stepping into that bear trap and becoming less popular than I was last week, I should say that I generally subscribe to Johannes’ description of energy expansion except that I apply these topics to an epoch that is much older and much larger than our universe. The first example is an ordinary topic called dark current from electrical engineering of solid state devices. It comes to me from a doctor engineer in a large university decades ago during the early days of solid state physics. A tiny current always flows through a diode in a circuit when there is no power supply connected. Compensation for it is necessary to design devices that work properly. Random action of ambient heat provides a small source of electrons and holes that fall through the diode junction and cannot go backward at the same rate. A forward current occurs in the circuit. The underlying physics of random and non random events is discussed by Schrödinger in his book “What Is Life.” The physical devices are easy to construct and measure. The second device is even easier to understand. It is a parabolic reflector that focuses microwaves from the background radiation to a hot spot target. The temperature difference is sufficient to do all kinds of work. It takes a very big device to get a small amount of power. Efficiency improves when ambient temperatures supply the radiant energy. Anyone can do this experiment. It comes to me from a high school science teacher who was old when I was young. I saw a similar device on display for children in San Francisco. These two examples will not replace conventional energy supplies. They simply disprove a lot of the scientific opinions that are given about energy and conservation laws. The examples are not my creation. They aren’t new or even controversial. Notice that both examples depend on ambient conditions. So they don’t refute Johannes’ description of energy origin and expansion. Time probably had a beginning, and it might have an end. I tend to believe that the science underlying my two examples provides a continual renewal of energy, time, and space. It’s a slow process and takes longer than the age of the universe. Schrödinger gave Boltzmann the credit for it in a discussion about the third law of thermodynamics.
    Jerry's example of an energy creation device: "a parabolic reflector that focuses microwaves from the background radiation to a hot spot target. The temperature difference is sufficient to do all kinds of work."

    No way this is creating energy. It is just converting photon energy into heat. No energy created, no energy destroyed. You can do the same much more efficiently by pointing a parabolic mirror to the sun.

    Energy conservation holds, also in general relativity. Any undergraduate in physics will learn that the Einstein equations are simply an expression of local energy conservation.

    Amateur Astronomer
    The total entropy goes down in the hot spot model, if the temperature difference is used to do net work. All of the energy eventually reaches the original background temperature. That topic was perpetual motion, not net creation of energy. I would argue that the process is perpetual. It does depend on the background energy being available at a lower temperature. With decreasing entropy there is accumulation of potential energy, like an example of the universe living its life time in reverse. Human scale is just a smaller version of the same thing. When entropy goes down in a closed cycle potential energy is being accumulated somewhere in the system.
    It seems you are misled by the term 'perpetual motion'. Perpetual motion machines are "hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not" (from Wikipedia).

    I hope we agree that these don't exist.

    Amateur Astronomer
    I agree the type of perpetual motion machine you described is not operational. It is called Overunity or Overutility. About 20 big names world wide are trying to get money from people to support those projects. A history of 150 years has many promises and no deliveries. At one time it had scientific support, but that was lost by some famous cases of suspected fraud. I feel compelled to oppose the Overunity machines at every opportunity because one of the principal supporters of them is a person named Jerry Decker on Keely Net. My examples were originally developed in opposition to Overunity. If you have to put energy in to start it, then it isn’t the best technology, and there is a history of disappointed investors. There are some related topics of alternative energy like vacuum polarization, zero point, vacuum energy, or the Dirac Sea. I’m a big supporter of those things, except the energy isn’t free and it isn’t a surplus. All of that energy is fully committed to support of the physical laws. Energy can be borrowed from it for a time under the uncertainty principle, but it has to be repaid one way or another. If it looks like I agreed with Sascha on a few points like perpetual motion and conservation of energy, it was not intentional and will probably not happen again. I’m really more in agreement with Johannes, on things like total energy, except I put it in a larger system that allows the total energy to increase very slowly over a long time. Everyone should realize that the examples Johannes gives are very much simplified for the less expert readers. They are really not intended to be a complete technical description. On the contrary, they show fundamental concepts with the smallest possible number of complications. The important reason to use the background radiation is to show that energy moves from low temperature to high temperature without receiving outside help. It is called radiant focusing, and is one of the ways non random processes make exceptions to the familiar laws of energy. The reflector is the non random feature. The decrease of entropy in non random processes is the most important part of my contribution to this page. It would be a complete trilogy of articles all by it’s self. The topic is a bit too complicate to explain exactly how it increases total energy. My example of a universe running backward gives the general concept that most people can understand. A final word about the diodes, it is an experiment everyone can do. Every part can be measured. The diode temperature decreases if energy is removed from it until there is a balance between the flow of heat and the flow of electricity. You can get about 3 millivolts from a good diode, or maybe 15 millivolts from a bad one. So in this case the local energy is conserved in a short time frame, but the entropy decreases slowly over longer time, if some practical use is found for the power. Rather than argue about total energy in distant volumes of the universe where there is a time delay over large distances, I believe it is better to talk about the flow of power across surfaces where a balance can be achieved and measured. That relates to the way Johannes presents the information on holographs and horizons. I’m in favor of the forum Hank wrote about in the planning stage.
    Aitch
    "Random action of ambient heat provides a small source of electrons and holes that fall through the diode junction and cannot go backward at the same rate. A forward current occurs in the circuit"

    Not so random ambient heat from the sun is excellently made available as current by green LEDs, although other colours will work, green seems to give the best results. They generate quite a bit of voltage, about 1.65V, some as much a 1.74V. Not the puny .55 volts of a silicon PV cell. Green LEDs are made from Gallium Phosphide, a semiconductor with a much higher bandgap voltage than a diode.

    scroogle to find suitable circuits

    Aitch
    Bonny Bonobo alias Brat
    The decrease of entropy in non random processes is the most important part of my contribution to this page. It would be a complete trilogy of articles all by it’s self. The topic is a bit too complicate to explain exactly how it increases total energy. My example of a universe running backward gives the general concept that most people can understand.
    Jerry, a trilogy of articles on this subject sounds really interesting.


    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Amateur Astronomer
    My trilogies tend to be mostly mathematics and more than 30 chapters in length. Any publishers can tell you how small the readership is for that type of writing. My view of entropy is not new or especially surprising. It comes from Boltzmann by way of Schrodinger, with a bit of interpretation by others. Boltzmann was the fellow who killed himself because people didn’t like his theory. Then people started liking it. That’s really poor timing. Schrodinger wrote his book in 1944. It has been republished at least 33 times that I am aware of. The new editions are recommended as compulsory reading by Paul Davies. Roger Penrose wrote a forward introduction nearly 20 years ago. Schrodinger gave a view of entropy and the third law of thermodynamics that makes a lot of sense in discussions about cosmology, perpetual renewal of energy, and how order develops in the universe. I’ve never seem any one make an attempt to refute it. The surprising thing is how many young scientists come out of universities with no knowledge of it.
    Bonny Bonobo alias Brat
    Oh, I thought you meant a trilogy of articles here at Science 2.0 about entropy. I suppose that there's no way that you could do a simplified version? How sad that Boltzmann committed suicide because people didn't like his theory. Scientists should have more confidence in their theories being shown to be right one day. According to Wikipedia, Boltzmann and 64 other famous scientists committed suicide, plus 2 social scientists and 14 mathematicians, and that doesn't include Hugh Everett III who's Many Worlds theory was also ridiculed by his peers at the time. Everett drank and smoked himself to death by age 51. See http://en.wikipedia.org/wiki/Category:Scientists_who_committed_suicide and http://en.wikipedia.org/wiki/Hugh_Everett_III
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Amateur Astronomer
    I didn’t intend to write the trilogy for Science 2.0, but maybe some one else would like to write it. I can give some idea of what it might look like. The old fashioned way of defining entropy for one part of a non reversible process is a math expression. dS > dQ*/T Explosions have this type of expression. It says the entropy S increases faster than heat energy Q is added to one part of a system at a temperature T. The term dQ* means that the amount of energy transferred depends on the path though which the energy passes. If the process is reversible then there is an equation. dS = dQ*/T In the parabolic reflector example there are two temperatures and two parts of the process, both of which are reversible. dS1 = dQ1*/T1 dS2 = dQ2*/T2 The two equations make a complete cycle of a reversible process, meaning that the net entropy change is zero. dS2 - dS1 = dQ2*/T2 - dQ1*/T1 = 0 T1 dQ2* = T2 dQ1* Since the temperatures are different, the amounts of energy sent and received are also different. All of this is taught in college, but not explained very well. It is called the second law of thermodynamics. There are better ways to describe it with partial differential equations for those who are technically advanced. Notice that even in conventional science the amount of energy sent and received depends on the temperature at which it is transferred. Also notice that in both parts of the process, the amount of energy transferred depends on the path through which it travels. If my reflector sends 1000 therms of energy to the hot spot from a surface that is 3 degrees Kelvin, the hot spot operating at 300 degrees Kelvin will only measure 10 therms being received and sent back into space. There is a type of conservation, but not the one most people expect to get. The difference is used in changing the temperature. As the universe expands and cools down, the total energy can increase, but only by about the same fraction that the temperature changes. It isn’t a reversible process, or a complete cycle, so the inequalities apply. Sometimes in factories the energy is used more than once in cascade systems where the efficiencies depend on the temperature sequences and the paths through which the energy is transferred. Most of those factories end up with more hot water than they expected, and the cooling towers are too small. There is a first law of thermodynamics that essentially says the energy change in one part of a system is equal to the difference between the energy that came in and the energy that went out. I have no problem with that as long as the system is small enough to avoid relativity in the times and distances. Some people try to extend that law to cover equivalence of energy change in one system to the change in another system. That works well in most ordinary cases where the systems are not large or far apart, such that the systems can be combined and measured simultaneously. When comparing two systems without simultaneity the second law is the one to use. Thermodynamics also has a zero law that was added as an afterthought. It says two systems are in thermal equilibrium if they have the same temperature. My example is an exception. The hot spot is in thermal equilibrium with the cold horizon of background microwaves. The zero law should say it applies to randomly distributed energy states. Schrodinger went a bit further to define entropy of creation in the residual of the third law of thermodynamics. The universal decay of order is described by one process. S = k Ln D Here the entropy is related to the Boltzmann constant k and the logarithm Ln of the number of quantum states D that can be randomly distributed. Schrodinger also described a creation process when the microstates D2 are prevented from being randomly distributed. I add the subscript 2 to show it is not the same process as in the previous equation. S2 = - k Ln (1/D2 ) It is possible to combine the two equations into a more complete third law. (net S) = k Ln (D/D2) Sometimes C is used to represent the non random states in a simplified form, and S implies the net entropy. It is not the science of an explosion. So there may be objections. S = k Ln (D/C) This is not taught in college. I t says there is a chance for a universe to be created by non random processes. This is the only scientific proposal I know of that accounts for the low entropy that occurred in the past. It is the only thermodynamic equation that predicts the possibility of a universe existing at all. There is a lot more to this story, but I will stop here before the physics police come with their flashing blue lights. Not everyone will share these opinions.
    Bonny Bonobo alias Brat
    Thanks Jerry, what you have written here forms a really good foundation for anyone to build upon.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Amateur Astronomer
    Johannes really can find conservation of energy over the whole universe, if he transforms all of the measurements to the same reference temperature and the same space time basis. That is also how factories conserve their energy. For a universe it requires more components in the calculations than are customary in smaller systems. Things like information, time, and space have to be converted to an energy equivalent. If time is money, and money is power, then time has a power conversion over any surface like a horizon or a hologram. Another way to convert time is with the Planck units. Knowledge is also power. So it has a representation on the surfaces, as Johannes pointed out in his previous articles. Gravity arises from the power on surfaces and the entropic information that describes that power. Remember that power crossing a closed surface at light speed is exactly equal to an energy density inside the surface. It is just another way to express curvature of space in general relativity. Curvature represents gravity. The question was asked how we can decide whether we are inside a surface or outside. The answer is that when we are inside a surface we can connect two distant points on the surface by a shorter route than is possible for any route on the surface. Then we have to decide how to measure relativistic distance. Two observers in different reference frames will never agree on how much energy is in the universe, because energy in general is not relativistically invariant. Only the mass conversion to energy with light speed is regarded as invariant energy. It creates the chance to outwit our selves by converting energy from invariant forms to relativistic forma and back again. The more clever we get, the more ridiculous the answers become. I guess Johannes is having a joke on us with conversion factors and equivalent systems. I’m not sure exactly which joke it is, but at least I’ve figured out there is a joke.
    Aitch
    I think the joke maybe: - Q: How do you get 2 Physicists into a hammock? A: Warm one of them up till he's pliable, then slide the other one in while no-one's looking, .............the energy exchange will make for a little light reading Aitch
    Jerry says, "The question was asked how we can decide whether we are inside a surface or outside. The answer is that when we are inside a surface we can connect two distant points on the surface by a shorter route than is possible for any route on the surface. Then we have to decide how to measure relativistic distance."

    Convex versus concave .... I get that much ... but not much else. There is something called intrinsic curvature and another called EXTRINSIC curvature. I'll look it up in a standard book when time permits. Meanwhile, I don't think there is much for us to decide on "how to measure relativistic distance." That's all standard material. Over large intervals, it can depend on the route. Of course, of course, a horse is a horse.

    Many more unanswered questions for sure. The experimental testing mentioned at the bottom of these comments looks very iffy .... controversial and expensive. Farewell to good old-fashioned bench top experiments ....

    ((will work on sign-in later, thanks for the tips ... got to run))

    Well, from my black hole perspective, this energy for free is all double Johannes to me
    How about a low entropy collector, as sascha suggests?

    Anon, Two possible ways to get your sign in to work:
    1. Use your name. as user. The email option doesn't always work. (Never did for me)
    2. Try I.E explorer as sometimes Firefox doesn't work correctly.

    -
    -
    Hello again Johannes Koelman
    -
    You say: "--- The universe was born in an infinite flash of light.---"(?)---- (How do 'you' 'know' this?)
    -
    You also say: "The universe started hot."-------- (If so, 'What' "started" 'it'?)--- (And how do you know this?)
    -
    How do you arrive at such assertions?
    -
    Are You re-inventing "God"?
    -
    Do you actually refer to the REAL "Infinite" "Universe" that has "NO Beginning" and "No End"?
    -
    Even if it were possible to go back to a time of a so-called "Big Bang" that appeared very "hot" with a "blast of light",
    'THIS' would not describe a so-called "BEGINNING", OR, a "START"!
    -
    I say: The "Universe" is "INFINITE"!---'it' has ALWAYS EXISTED!
    -
    There was NEVER a "beginning" nor will there EVER be an end!
    -
    It's 'form' may have changed, or appeared different at times in the distant past, BUT "Universe" never needed a
    so called "beginning" or a so-called "Start"!
    -
    Such a 'thing' would be IMPOSSIBLE!
    -
    There could NEVER have 'ever' been NOTHING!--- 'Something' cannot derive from "NOTHING"!
    -
    You appear to be playing 'MIND GAMES'!
    -
    Why add to the confusion of all those poor souls who are already crazy from mind-controlling religions, the LIES of NASA, and their controlled media companies?
    -
    -

    Aitch
    .....'Something' cannot derive from "NOTHING"!.....
    Where do ideas spring from then, or are we born with them, waiting to be heard on certain days/times?
    One minute, they don't exist, next...."Poof!" an idea is born from nothing

    ...or do you get yours from books?

    Aitch
    -
    -
    Reply to: Henry Cox:
    -
    I say 'EMPHATICALLY': "IDEAS" DO NOT COME FROM "NOTHING"!
    -
    Sir; Why do you refer to: a person, a body, a brain, a mind, a conglomeration of experiences, a memory, an environment, ones immediate surroundings, a feeling, a sense of being, etc, etc, etc,--- as:--- "Poof"---"nothing"!
    -
    I say again for the LITERATE: "something" cannot derive from "nothing"!
    -
    Every 'thing' needs an impetus!------------------ Excluding; our 'INFINITE' UNIVERSE!
    -
    'You' are "read"-ing the wrong "book"s!
    -
    Thanks for asking!
    -
    Cheers!
    -
    -

    Aitch
    OK MR EMPHATIC WITHOUT AN EXPLANATION!
    Sir; Why do you refer to: a person, a body, a brain, a mind, a conglomeration of experiences, a memory, an environment, ones immediate surroundings, a feeling, a sense of being, etc, etc, etc,--- as:--- "Poof"---"nothing"!
    I don't, you did....I said

    One minute, they don't exist, next...."Poof!

    You literate folks lose the art of humour in all that SHOUTING?

    Something deriving from nothing, is both the essence of Eastern Philosophy, and Nature

    Necessity is the mother of Invention

    i.e. where ideas come from, not "a person, a body, a brain, a mind, a conglomeration of experiences, a memory, an environment, ones immediate surroundings, a feeling, a sense of being, etc, etc, etc," - that's just your ego

    Don't feed it so much!

    Aitch
    Hello again Henry Cox;
    Thank you for the note.
    In your prior critique, you quoted me:".....'Something' cannot derive from "NOTHING"!

    Then; you say: "Where do ideas spring from then,
    or are we born with them, waiting to be heard on certain days/times?
    One minute, they don't exist, next...."Poof!" an idea is born from nothing".

    (These are 'your' ---'exact'--- words!)---- "---an idea is born from nothing".--- (Nothing?)

    When you say "an idea is "---born from "nothing" you are denying all the
    factual determinants actually responsible for producing the "idea"!

    I take your statement: "---an idea is born from "nothing"; to mean
    you deny these actual factors: "a person, a body, a brain, a mind,
    a conglomeration of experiences, a memory, an environment, ones
    immediate surroundings, a feeling, a sense of being, etc, etc, etc!

    If you are going to insist you believe "something" can come from "nothing"
    "Philosophically", or otherwise, You may have the very last word!
    Ciao, Jocta

    Aitch
    When you say "an idea is "---born from "nothing" you are denying all the
    factual determinants actually responsible for producing the "idea"!
    Factual determinants - yes; actually responsible, no....emphasis on responsible
    I take your statement: "---an idea is born from "nothing"; to mean
    you deny these actual factors: "a person, a body, a brain, a mind,
    a conglomeration of experiences, a memory, an environment, ones
    immediate surroundings, a feeling, a sense of being, etc, etc, etc!
    Actual factors - no; You assume cause/effect/impetus - I don't
    If you are going to insist you believe "something" can come from "nothing"
    "Philosophically", or otherwise, You may have the very last word!
    Thank you! Most gracious of you, I'm sure ;-)

    I'm sure Johannes will be pleased to hear that his article has given rise to such a stimulating exchange [though he seems to be having one of his own with Sascha]
    Ciao

    Aitch
    In an absolute consideration it is clear that energy is conserved.

    Thank you Johannes for answering some of my questions.
    Below is a quick review of what I think is this holographic way of deriving things.
    My apologies for any misrepresentations. Please correct me where I have gone astray.

    As the edge of the observable universe has expanded, we have a quantity that has progressively increased from 10^0 to 10^61 and continues to increase (monotonically),
    no matter from where in the universe one measures it (although the exact number can depend on the observer). We can let this exponent be a log(t) time parameter. It starts at 1 and runs to 100 over aeons of development from our most distant past to very far into our future. It does not end at 100. It is simply a convenient scale. (It might be related to what is called “enfoldings”).

    To reach our current epoch, The Logarithm of the Half Radius of the cosmic edge of the observable universe has increased from One to its current value of about 61.

    Although the specific edge or horizon we see from Earth is dependent on our position (and velocity), someone else far removed from us will have the same ballpark number. This is why it lends itself to being a type of time parameter. The analogy is that the horizon for someone on a sphere is the same distance out, no matter where you are on the sphere, so long as you perceive it from the same height up the crow’s nest of your ship.

    In addition to the distant cosmic horizon created by the expansion of the universe, there is another variety of horizon which has a number of similarities (yet it’s curvature is “inward” instead of “outward”. These are the horizons of black holes, which are also increasing monotonically. They too are at the edge of the observable universe, yet it is not the same edge as the cosmic one due to the universal expansion.

    The radii of black hole horizons are directly proportional to the Mass they contain.

    Johannes’s blog at top has the following equation:

    Energy of universe = mass energy + horizon energy = 1061 - 1061 = zero zilch nada...

    The “mass energy” term includes the black hole horizon energies. It also includes all ordinary matter and also dark matter. It also includes the 10^80 number baryons that is sometimes used as the number of ordinary particles in cosmology. I could be wrong about this.

    According to Johannes (and others that he is following), the “mass energy” term has increased monotonically from 10^0 to 10^61 and continues to increase.

    I personally have much difficulty in picturing this increase in “mass energy”. It is not obviously happening in my day-to-day world. Nor does it seem to be happening in laboratories. I do not really understand how I am to interpret this “mass energy” term.

    Johannes notes that “Gravitational energy is non-local. Or more precisely: it is holographic in nature.”

    I have tried to pick up on that thought before and have used non-locality and holography as the very basis for “conservation of energy” or more accurately “conservation of information”. I referred to it as an extension of the Copernican Principle.

    One more detail to consider … There is one more zone of physics where one can talk about an “edge of the observable universe”. This is at a micro-micro-micro level much tinier and vastly more energetic than particle physics; it is the Planck scale of quantum geometrodynamics and FOAM that John A. Wheeler starting writing about as early as the late nineteen fifties. He did not call it his original idea. He did popularize it.

    Johannes Koelman
    "I personally have much difficulty in picturing this increase in “mass energy”. It is not obviously happening in my day-to-day world. Nor does it seem to be happening in laboratories. I do not really understand how I am to interpret this “mass energy” term." Anon -- keep in mind that in the above cosmological model the mass-energy term increase is related to the cosmic horizon receding faster than the Hubble expansion. You would have to build a telescope that allows you to look deep into the high-redshift regions of the universe and considerable patience to directly observe the mass-energy increase.
    Sorry about losing the exponent symbol in the 10^61-10^6 1 = 0 equation (and other typos). I have been relegated to a non-editable mode.

    The holographic ideas Johannes is writing about will soon be subjected to experimental tests:

    http://www.symmetrymagazine.org/breaking/2010/10/20/fermilab-scientists-...

    The proposed test will try to detect the space-time blurring that must be exist if the 3D world we observe is no more than a holographic image.

    About the temperature question: remember that temperature is the ratio of energy to entropy and the energy at the cosmic boundary is the negative of that inside. Also, to the surprise of some, there is such a thing as negative temperature. That occurs when the entropy is reduced with an increase of energy or when entropy is increased with an increase of negative energy. This means that the universe could have an “average temperature” of a constant = zero due to the offsetting of the temperatures inside the cosmic boundary with the temperatures at the boundary. The temperature within the boundary can be decreasing while the temperature (increase of negative energy over entropy) is increasing at the cosmic boundary. Another way to say it is that the entropy within the boundary is increasing but the entropy at the boundary is decreasing as it slowly acquires information about what is inside. I think of it as the flip side of the Bekenstein generalized second law of thermo.

    dc, can you give an example of negative temperature? Where does it exist and how can it be measured?

    Mathematics can do things that don't occur in the physical universe.

    Energy is relative to the reference frame. So it can be negative or positive with reference to the reference standard. That doesn't mean it can be negative on an absolute scale. Dirac allowed a negative energy to exist, but he didn't prove it does. Antimatter is postulated as negative energy in theories, but I have to reject them, because in experiments of particles colliding with antiparticles, all of the antimatter comes out as positive energy gamma rays referenced to the center of mass.

    Johannes is suggesting that the total energy in the universe is zero. In one reference frame that will always be true. In other reference frames it might not be. He didn't predict in the big crunch theory for the end of the universe for all of the matter and energy to converge on a point in space and calmly disappear without a trace. Big crunch is out of favor, but the concept is established that there isn't one part of the universe that can collide with another part of the universe and cancel it out completely.

    Sukumar
    Temperature is a statistical concept and defines the ratio of occupancies of states of different energy at equilibrium. As a system gets hotter and hotter, more of the higher energy states are occupied. In the limit of infinite temperature, there is no population difference: lower and higher energy states are occupied equally. In highly non-equilibrium situations, e.g. in an intense laser field or an NMR pulse, one can get a population inversion, such that higher energy states are occupied more than states of lower energy. This corresponds to negative temperature, which is actually considered hotter than infinite temperature. Such non-equilibrium situations are inherently unstable and will soon decay back to a "normal" population distribution.
    Sukumar
    Sukumar
    I have a comment that is rather oblique to the point you are making, but refers to your opening statement: "Is energy conserved? Of course it is!" I would quibble with your claim that "The conservation of energy is an insight that stood the test of time." I would rather maintain that energy is conserved because physicists want it to be conserved. Any time a phenomenon was discovered that violated energy conservation, i.e. where energy was found to appear out of or disappear into "thin air" (so to speak), physicists were quick to invent a new fudge factor, i.e. a new "form of energy" (e.g. "potential energy", "heat", "electromagnetic energy", "mass energy") that made the book-keeping balance out just right. So I would rather say that energy has been conserved by fiat!

    Energy conservation is probably not such a useful concept at the Planck scale due to quantum uncertainties.
    Sukumar