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An essay in futility, too long to read :)
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An essay in futility, too long to read :)
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yor_on
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An essay in futility, too long to read :)
«
Reply #100 on:
15/12/2010 15:25:32 »
Heh
Nope.
Ever heard about the “delayed-choice experiment”? “In the two-slit experiments, the physicist's choice of apparatus forces the ‘photon/wave’ to choose between going through both slits like a wave or just one slit, like a particle. But what would happen, Wheeler asked, if the researcher could somehow wait until after the light had passed the two slits before deciding how to observe it?”
In the first one it’s your choice of observing, aka equipment, that creates the result, either as a wave interference where photons looks like ‘waves’ or like ‘particles’ aka ‘bullets. But if you make an experiment where you have something ‘forcing’ the light into becoming one or the other, but without yourself knowing what it will be at the time the light ‘propagates’. Will that make a difference?
“Five years after Wheeler outlined what he called the delayed-choice experiment, it was carried out independently by groups at the University of Maryland and the University of Munich. They aimed a laser beam not at a plate with two slits but at a beam splitter, a mirror coated with just enough silver to reflect half of the photons impinging on it and let the other half pass through. After diverging at the beam splitter the two beams were guided back together by mirrors and fed into a detector.
This initial setup provided no way for the investigators to test whether any individual photon had gone right or left at the beam splitter. Consequently, each photon went both ways splitting into two wavelets that ended up interfering with each other at the detector.
Then the workers installed a customized crystal called a Pockels Cell in the middle of one route. When an electric current was applied to the Pockels Cell, it diffracted photons to an auxiliary detector. Otherwise, photons passed through the cell unhindered. A random signal generator made it possible to turn the cell on or off after the photon had already passed the beam splitter but before it reached the detector as Wheeler had specified.
When the Pockels-cell detector was switched on, the photon would behave like a particle and travel one route or the other, triggering either the auxiliary detector or the primary detector, buy not both at once. If the Pockels-cell detector was off, an interference pattern would appear in the detector at the end of both paths, indicating that the photon bad travelled both routes.”
So what’s weird about that one? Well, at first the light behaves as waves, you can ‘split’ waves as much as you like, and when joining them ‘back’ you will find the ‘interference’. That they behaved as waves is because your equipment allowed them to do so, including yourself not ‘knowing’ the ‘path’ taken. What it shows is that to talk about light having a certain property before measuring is impossible. It’s like ‘room time geometries’, you might define a distance as unchanging but when travelling close to light, the Lorentz contraction observed will prove that distances can and will change. But, at the same time as you will find your own ‘frame of reference’ unchanged? Why, shouldn’t it that too ‘change’? The same as those length relations you observe outside your ‘space ship’?
Why didn’t your own ‘room’ contract as the outside did? And if it did, shouldn’t that have made the ‘distances’ outside keep their relative balance versus you, making it impossible to notice? Simple, if they did there couldn’t be any Lorentz contraction from your ‘frame of reference’ and by what would you then define your ‘room time geometry’ changing? As you would know it, finding the journey shorter than it was measured on Earth. The alternative to that would be that it didn’t? Which then would invalidate your ‘time dilation’ too, as measured from Earth. There is the third alternative of course, with a bifurcation taking place every time something moves relative something else, giving me an enormous headache.
Anyway, assuming that we indeed will find it possible to measure this ‘contraction’ from our moving ‘frame of reference’, which I will continue to assume
then there have to be something very special about your own ‘frame of reference’ as it keeps the same ‘properties’ for you, both ‘time’ as well as your own frames ‘distance’ relative what you observe ‘outside’, no matter your velocity or possible mass. Don’t you agree?
To get back to the experiment, it used a laser, right? And lasers ‘shoots’ waves, monochromatic but waves. But you can also say that it ‘shoots’ photons, so would your choice of looking at the beginning make a difference. Nope, not that I know? So in the beginning when we observe it as waves, that’s cool with me.
“When the Pockels-cell detector was switched on, the photon would behave like a particle and travel one route or the other, triggering either the auxiliary detector or the primary detector, buy not both at once. If the Pockels-cell detector was off, an interference pattern would appear in the detector at the end of both paths, indicating that the photon had travelled both routes.”
There are even more advanced experiments existing than this one. Like the one in where you according to the experimenters can wipe out ‘information’ after letting the light wander through a maze ‘transforming’ it from waves to particles. Then to find the ‘wave interference’ of light coming back as you wipe out the ‘quantum information’ it had earlier.
“It has been considered that the general mechanism responsible for the loss of the interference pattern is the uncertainty principle, as no measure can be so delicate not to disturb the system which is measuring. However, in this experiment, the “which-way” information of the particles is found without disturbing their wavefunction. The reason of the interference loss is the quantum information contained in the measuring apparatus, by means of the entanglement correlations between the particles and the path detectors. The experiment shows that if such quantum information is afterwards erased from the system, then the interference reappears (which would be impossible in the case of a perturbation).”
What the experiments says to me is that you as the ‘observer’ didn’t interfere with that first experiment, as the triggering of the Pockels cells were ‘beyond your control’, being a ‘random event’ as far as you were concerned. It also states that each time this Pockels-cell went ‘on’ the wave/photons behaved as a particle. The importance though, to me, is only in your assumption of light propagating inside a ‘arrow of time’. If you do so, assuming that light then will be a wave, (as it have showed itself that way each time before to you), and then randomly turn on this Pockels-cell, why does that turn the light into a particle?
Maybe it’s possible to look at it this way, if we define ‘times arrow’ as something describing ‘changes’. We then arbitrarily define each measurement made by us as ‘events’, or if you like, let a ‘clock’ ticking create a symmetry of equally timed ‘events’ amongst which we measure/pick some as our own observations. Then, according to my definition, what you measure is your ‘reality’. And if you can be a hundred percent certain of an ‘outcome’ you will see it. Nothing strange in that. You see, what all of those clever experiments builds on is the observers arrow of time. When they speak of ‘resurrecting’ the interference, they can only do so inside that arrow, as ‘events’. So to me their logic is strained by ‘time’. The simple truth is that they will have to ‘measure’ before proving it. So I think my idea take care of both of them? Remember that I split ‘reality’ in two. One conceptual where the ‘general rules’ might be seen, the other one being the one we truly can observe, by experimenting. Don’t mix those two.
Why?
If you look at it my way SpaceTime is a ‘game’. Every game builds on rules, if you’re a good gamer you will know/ learn the ‘rules’ and so get ‘your way’ more easily than the person next to you. And assuming that light’s not ‘propagating’ what you have will be more like a ‘mosaic’. Change the ‘mosaic’ according to the rules and you can lock an ‘outcome’. Do it after another ‘locking’ and what you will see is the new configuration. Does this makes the question of a clock ticking (arrow) irrelevant, as everything becomes frozen ‘instants/ configurations’? Not as I know, you will need to show me a way to make an experiment without involving ‘clocks’ before I’ll believe that one, and no, neither of my offerings above is without an arrow. And yes, my view seems to contradict the idea of an ‘arrow’, as well as everything being a ‘flow’. But it’s not at our ‘plateau of observation’ those phenomena takes place. The ‘rules’ we discuss is best thought of as existing at a similar place as my ‘mind-space’ exist, somewhere, just ‘out of reach’ of our observations. In my ‘game’, for light, the rules might state that entangled light are not ‘separated’ by ‘room time geometry’, and if that is the case it’s simple to see why they ‘know’ about what’s happening to their ‘other halfs’ as they (it) in a way are everywhere. Also it seems as all light might be entangled, for example, looking at it as ‘propagating’ it will become ‘monochromatic’ after ‘propagating’ far enough, interacting. And that one doesn’t rule out that the light already was entangled at its ‘source’, as I understands it?
If you assume all light ‘entangled’ in some way, behaving as it does by containing some ‘overall information/ state’ (connected) to all other light in the experiment. Then, when measuring one state you will ‘set’ the rest too. But to me entanglements seems just another way of describing light as ‘unmoving’, as it builds on an ‘instant’ transfer of ‘states’ between them. Also, as the experiment seems to build on you inferring that there have to be a certain ‘ground state’ of the photon/wave, as defined by your previous measurements? Which is a rather stupid thing to do
if you look at it my way, I fully expect light to be able to surprise you. It’s not ‘matter’ after all, it’s ‘light’.
An entanglement differs in that it, even though being instantaneous, can’t present any information faster than light speed can bring it. But, didn’t we also find that ‘entanglements’ transfer ‘energy’? Now, why would it be able to do so? Isn’t energy ‘information’ of a kind too? I’ll be very interested in seeing someone use the idea of instant ‘energy transfer’ as a way of transmitting information faster than light (FTL). Another point worth taking up here is that even if we have a theorem stating that we won’t ever be able to transmit information FTL it then only seem to be true for that first ‘instant’. Imagine two stars communicating, ‘A’ and ‘B’ by entanglements. For that first communication they will need to have a ‘light code’ translated, and that first information ‘A’ only can send at ‘lights speed’ to ‘B’. But if the idea of ‘energy transfer’ is what I think it is then every transmission after that first, theoretically even if not practically, should be able to take place FTL?
Entanglements also bears a uncanny likeness to the idea of the ‘many paths’ your ‘particles’ takes, or if you like, their ‘probability’, in that both are sort of ‘instantaneous’ , taking place simultaneously even though we only find one ‘state’ when measuring. But no matter what experiment you do, however clever, there will always be one ‘state’ measured as you measure, not two simultaneously, as far as I understands it? The rest of that kind of discussion is to me at the same place as ‘time dilation’. Existing on/inside that remarkable ‘mind-space’ where comparisons are made, not ‘reality’, no matter how ‘correct’ it might be. Your ‘reality’ exists in your measurements, not in your comparisons, to me that is.
So, if my way of looking at it is right then it still have rules, although what creating the rules we observe seems more to be on a theoretical plane than observable as direct ‘forces’. And I assume that those rules have to be general ones, valid for different ‘SpaceTimes’. To assume otherwise seems to imply some creator custom-making our ‘SpaceTime’? That might also make those rules easier to see, as we won’t need to find a exact match to our universe. We just need to find enough examples predicting similar universes, and from them try to see what joins them. And what joins them will have to be our general rules too. I know, string theory huh
Maybe their track is the right one, even if I don't agree in all that I've read about it. Then again, I guess they too have have 'fractions' amongst them arguing differently.
«
Last Edit: 16/12/2010 19:25:06 by yor_on
»
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yor_on
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An essay in futility, too long to read :)
«
Reply #101 on:
15/12/2010 15:51:38 »
Let us continue down that never-ending avenue of cogitation, slow grinding wheels accompanied by my trusty companion, ah, headache
You will never prove a time dilation inside your own ‘frame of reference’. It’s a ‘mental space’ in where that happens, as a result of comparing ‘frames of reference’. Never the less it has to be true. Though you will be able to prove a Lorentz contraction inside your own ‘frame’ I believe. That is, if using, and trusting, the ‘history’ you have, you will in ‘real time’ prove to yourself that your distances have ‘contracted’ when moving close to light speed.
‘SpaceTime’ can be split into ‘room time geometries’ aka ‘frames of reference’ and they are what make our ‘SpaceTime’ in where everything existing have its own ‘room time geometry’.
‘Forces’ are our description of certain ‘cause and effects’ that we think us observe inside that ‘room time geometry’. Causality chains created in and from an ‘arrow of time’ never mind its ‘direction’ conceptually.
There is a non-linearity to all of the universe we know, macroscopically as well as at the quantum level. But there is also a strange linearity surrounding and infusing it, as the Feigenbaum constant shows us, both macroscopically and on a quantum level as I understand it.
Now for what’s called ‘scars’ in chaos theory.
“According to Michael Berry, a leading theorist in the study of quantum chaos at the University of Bristol, this issue of linearity is a red herring. "This is one of the biggest misconceptions in the business," he says. His critique rests on the fact that it is possible to recast nonlinear classical equations in a linear form and linear quantum equations in nonlinear form.
Berry's preferred explanation for the difference between what happens in classical and quantum systems as they edge towards chaos is that quantum uncertainty imposes a fundamental limit on the sharpness of the dynamics. The amount of uncertainty in a quantum system is quantified in Heisenberg's uncertainty principle by a fixed value known as Planck's constant. In classical mechanics, objects can move along infinitely many trajectories," says Berry. This makes it easy to set up complicated dynamics in which an object will never retrace its path-the sort of behaviour that leads to chaos. But in quantum mechanics, Planck's constant blurs out the fine detail, smoothing away the chaos."
This raises some interesting questions. What happens if you scale down a classically chaotic system to atomic size? Do you still get chaos or does quantum regularity suddenly prevail? Or does something entirely new happen? And why is it that macroscopic systems can be chaotic given that everything is ultimately built out of atoms and therefore quantum in nature? These questions have been the subject of intense debate for more than a decade. But now a number of experimental approaches have begun to offer answers. …
Quantum billiards
More recently, signs of quantum suppression of chaos have come from another experimental approach to quantum chaos: quantum billiards. On a conventional rectangular table, it is quite common for a player to pot a ball by bouncing the cue ball off the cushion first- In the hands of a skilled player, such shots are often quite repeatable. But if you were to try the same shot on a rounded, stadium-shaped table, the results are far less predictable : the slightest change in starting position alters the ball's trajectory drastically. So what you get if you play stadium billiards is chaos. In 1992, at Boston's Northeastern University, Srinivas Sridhar and colleagues substituted microwaves for billiard balls and a shallow stadium-shaped copper cavity for the table. Sridhar's team then observed how the microwaves settled down inside the cavity. Although their apparatus is not of atomic proportions (a cavity typically measures several millimetres across) , the experiment exploits a precise mathematical similarity between the wave equations of quantum mechanics and the equations of the electromagnetic waves in this two- dimensional situation. If microwaves behaved like billiard balls , you would not expect to see any regular patterns. The experiments, however, reveal structures known as "scars" that suggest the waves concentrate along particular paths.
But where do these paths come from? One answer is provided by theoretical work carried out back in the 1970s by Martin Gutzwiller of the IBM Thomas J. Watson Research Center in Yorktown Heights near New York. He produced a key formula that showed how classical chaos might relate to quantum chaos. Basically, this indicates that the quantum regularities are related to a very limited range of classical orbits. These orbits are ones that are periodic in the classical system. If for example , you placed a ball on the stadium table and hit it along exactly the right path, you could get it to retrace its path ,after only a few bounces off the cushions.However, because the system is chaotic, these paths are unstable. You only need a minuscule error and the ball will move off course within a few bounces. So classically you would not expect to see these orbits stand out. But thanks to the uncertainty in quantum mechanics, which "fuzzes" the trajectories of the balls, tiny errors become less significant and the periodic orbits are reinforced in some strange way so that they predominate.
Sridhar's millimetre-sized stadium was a good analogy for quantum behaviour, but would the same effects occur in a truly quantum-sized system? This question was answered recently by Laurence Eaves from the University of Nottingham, and his colleagues at Nottingham and at Tokyo University. Eaves conducted his game of quantum billiards inside an elaborate semiconductor "sandwich" . He used electrons for balls, and for cushions, he used a combination of quantum barriers and magnetic fields. The quantum barriers are formed by the outer layers of the sandwich, which gives the electrons a couple of straight edges to bounce back and forth between. The other edges of the table are created by the restraining effect of the magnetic field, which curves the electron motion in a complicated way. As in Sridhar's stadium cavity, the resulting dynamics ought to be chaotic.
Number Crunching
To do the experiments, Eaves needed ultraintense magnetic fields, so he took his device to the High Magnetic Field Laboratory at University of Tokyo; which is equipped with some of the most powerful sources of pulsed magnetic fields in the world. Meanwhile his colleagues in Nottingham, Paul Wilkinson, Mark Fromhold, Fred Sheard, squared up to a heroic series of calculations, deducing from purely quantum mechanical principles what the results should look like.In a spectacular paper that made the cover of Nature last month, the team produced the first definitive evidence for quantum scarring, and precisely confirmed the quantum mechanical predictions. Sure enough, the current flowing through the device was predominantly carried by electrons moving along certain "scarred" paths. Quantum regularity was lingering in the chaos rather like the fading smile of the Cheshire Cat in Alice's Adventures in Wonderland. “
So, now we have a little more evidence for it’s not being non-linearity alone ruling, but rather like a intricate mosaic of both ‘linearity’ and ‘non-linearity’ constituting the ‘laws’ creating ‘SpaceTime’. And with it we’re starting to get an idea of what ‘free will’ might be seen as, something actually able to vary in itself, but still falling prey to statistics and probability theory. And with it our universe becoming weirder than ever
.
Now what would that have to do with my thoughts on light not moving? Well, if the universe is becoming a mosaic, as I see it, then ‘moving parts’ just complicates it. But, we see the universe moving, don’t we? Well, maybe we do? But, if it moves, how do ‘shadows’ correspond to a barrier?
Institut d'Optique reported on the direct observation of Anderson localization of matter-waves in a controlled disorder. “From the quantum theory of conduction, in which electrons are described as matter waves, we can draw a naïve picture based on the idea that electrons with certain momenta can travel freely through the crystal, while others cannot as they diffract from the periodic structure played by the lattice. “
Fifty years ago, Philip Anderson, 1977 Physics Nobel Prize winner, worked out that tiny modifications of the lattice, such as the introduction of impurities or defects, can dramatically modify this behavior : the electron that would move freely inside the solid does not simply diffuse on the defects as expected for classical particles but they can be completely stopped.
On a macroscopic scale, that would be like saying that a few blades of grass scattered haphazardly over a golf course could completely stop a full-speed golf ball in its tracks : this would be a surprising situation, since we all know that small perturbations can only slow the movement of material objects, but can never stop them. In the light of fundamental discoveries made in the 1930s about semi-conductors that led to the invention of the transistor and then to integrated circuits, this phenomenon called 'Anderson Localization' created and is still creating strong interests among physicists.”
Did you notice “electrons are described as matter waves” I must admit that I like that, it’s kind of ‘hard’ imagining a golf ball being superimposed in two places simultaneously, on the other hand, it’s almost as hard imagining a wave being it, so?
“In our experiment, ultra-cold atoms play the role of electrons. They are chilled to a temperature close to absolute zero (-459.67 degrees Fahrenheit) to generate a Bose-Einstein condensate (BEC), in which all the atoms can be described as a single wave function. We allowed these BECs to expand from a small starting spot along a single direction imposed by a laser-induced atomic waveguide. To “simulate” the disordered environment, we created a perfectly controlled disorder by shining laser light through finely ground glass onto the expanding atoms — creating then a random distribution of light and dark regions. Without disorder, the atoms propagate freely, but when disorder is present, all atomic movement stop within a fraction of a second. We then observed the atomic density profile. Its exponential form, characteristic of Anderson Localization is the awaited direct proof that random diffusion of matter can hinder the diffusion process.”
Let’s dissect some of the statements first. “In which all the atoms can be described as a single wave function.” Yes they can, but does a statement turn them into waves? Naah, the ‘matter’ still exists, doesn’t it? Even if ‘modified’ it hasn’t turned into ‘waves’? More like some ‘super atom’ it seems? So yes, and no. But the results are weird, and bring us to the question of what a ‘momentum’ is? He wrote “On a macroscopic scale, that would be like saying that a few blades of grass scattered haphazardly over a golf course could completely stop a full-speed golf ball in its tracks : this would be a surprising situation, since we all know that small perturbations can only slow the movement of material objects, but can never stop them.” And here we have those ‘impurities’ created by light and shadows, acting to stop that ‘super atoms’, or ‘wave functions’, momentum, instantly? So, what did the momentum transfer into? And why?
Recoil anyone?
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yor_on
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An essay in futility, too long to read :)
«
Reply #102 on:
15/12/2010 18:18:20 »
So, is ‘action and reaction’ a doomed concept in QM then? Don’t know? Take a look at this experiment “Little Nudges from Light – Measuring the Recoil of Photons” from 2009.
“Prof. Dmitri Petrov in collaboration with colleagues from the Moscow State University were the first to measure this effect. To measure the effect the researchers use a photonic force microscope (PFM) to trap a small metal covered dielectric sphere in a laser beam. The surrounding liquid contains fluorescent molecules that attach to the surface of the sphere. Excited by the light of the laser the molecules themselves start to emit light. Just like a soldier feels the recoil of his gun after firing a projectile, the small molecules pass their momentum they get from light emission on to the sphere. During this process the scientists measure two values: the forces acting on the bead (described by a tiny dithering in the trap) and the intensity of light generated by the molecules coating the bead's surface. As the intensity of the emitted light fades over time due to bleaching the scientists can observe a decline of the recoil as well.
What initially was the set-up for a different experiment turned out to deliver the first direct proof of the correlation between light emission and recoil and also allowed the calculation of the power of light emitted. In their experiment the researches measured a force of 240 femtonewtons, which equals a power coming from the bead of 1 microwatt. "Until now it has been really difficult to say how much light eventually comes off this material", says Dmitri Petrov from ICFO, “but by looking at the recoil we have a completely new approach to quantify light emission by a mechanical force”. Possible applications of the PFM-setup could be to offer a more precise way of measuring the efficiency and intensity of other light-emitting molecules, including the bleaching of fluorescent dyes.”
Ahh, a 'recoil' was it?
Delivered from something without an acceleration, instantly at light speed?
How?
Where does that recoil allow itself to be transmitted inside Planck time from the ‘propagating’ photon? Here is your ‘action and reaction’, and at a quantum plane too, if this is true. Couldn’t it be some sort of ‘sticky phenomena’ instead, no ‘recoil’ at all classically? As if the molecules moves slightly to a change in the rules? Nothing there at all really, but still creating a 'jiggle'. Or should we see a momentum as something existing on its own? A transient created out from a ‘relation’ without needing to be constricted inside ‘times arrow’? If so, does that explain how ‘virtual photons’ can transmit momentum?
And what would that say?
That times arrow is no boundary for causality?
Well, to me it speaks about emergences only, they don’t need to be defined by a clock. An emergence is a transition from one state to another, instantly or not, as we observe it. And if our macroscopic arrow is created through the presence of ‘matter, light and space’ then that arrow is a localized macroscopic phenomenon, not an ‘absolute truth’. But I think that the concept of ‘time’ is different, to me that is an axiom, something needed for all ‘causality’, no matter where those ‘arrows’ point according to us.
“Euclid's familiar geometry of two-dimensional space has the following
axioms,5 which are expressed in terms of operations that can be carried out with a compass and unmarked straightedge:
* E1 Two points determine a line.
* E2 Line segments can be extended.
* E3 A unique circle can be constructed given any point as its center and any line segment as its radius.
* E4 All right angles are equal to one another.
* E5 Parallel postulate: Given a line and a point not on the line, no more than one line
can be drawn through the point and parallel to the given line.6
Here.
The modern style in mathematics is to consider this type of axiomatic system as a self-contained sandbox, with the axioms, and any theorems proved from them, being true or false only in relation to one another. Euclid and his contemporaries, however, believed them to be empirical facts about physical reality. For example, they considered the fifth postulate to be less obvious than the first four, because in order to verify physically that two lines were parallel, one would theoretically have to extend them to an infinite distance and make sure that they never crossed. In the first 28 theorems of the Elements, Euclid restricts himself entirely to propositions that can be proved based on the more secure first four postulates. The more general geometry defined by omitting the parallel postulate is known as absolute geometry.
When stress is equal on all sides then it is no longer a tensor with direction, but a scalar. That scalar is called pressure. As a direct result of Newton's first law: a static fluid undergoes static “geostatic", "hydrostatic", "isotropic" pressure. A fluid cannot support shear stress. While this is demanded for a fluid, it is also a good approximation for layers of rock strata near earth's surface:
The idea that time does not "exist" as an independent quantity would seem to be quite speculative, except for one very interesting fact. We know that Einstein's theory of special relativity (SR) describes the universe using "time". However, special relativity is not the most fundamental theory, as we said, it is derived from Einstein's theory of general relativity (GR). The tools of special relativity give us less generalized solutions that are correct only under a limited set of circumstances. In general relativity the universe is described by solutions to Einstein's field equations. Most physicists believe that a particular description of the universe is correct only if it is a solution to those field equations. The amazing fact is that Einstein's field equations can be solved without any reference whatsoever to a temporal variable of any kind, indeed the field equations may be solved without even defining "time". This astounding fact greatly increases our confidence that we live in an essentially atemporal world. “
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An essay in futility, too long to read :)
«
Reply #103 on:
15/12/2010 18:27:53 »
Let us take a look on non-linearity again. Earlier I said that non-linarity waits in both quantum mechanical ‘systems’ as well as in our macroscopic ‘reality’, didn’t I? But ..
“Where does that leave the problem of how quantum mechanics turns into the classical world on larger scales? One way of looking at the problem is to investigate how a quantum chaos system actually evolves with time. Last December, Mark Raizen and his colleagues at the University of Texas at Austin managed to do just that, using an experimental version of a system called a quantum kicked rotor. The idea is to couple two oscillating systems to produce chaos. Imagine pushing a child's swing. If you time your pushes in rhythm with the swing, then it simply rises higher and higher. If you push at a different frequency, the swing will sometimes be given a boost and sometimes slowed down. If this is done too vigorously, the oscillations become chaotic.
In Raizen's quantum version, ultra cold sodium atoms were subjected to a special kind of pulsed laser light. The laser beam was bounced between mirrors to set up a short-lived standing wave -a periodic lattice of light that remains motionless in space rather like the acoustic nodes on a violin string. Depending on their precise location in the standing waves, the sodium atoms are pushed around by the electromagnetic fields in the lattice. According to classical calculations, the result is that the atoms should be kicked chaotically along an increasingly energetic random walk. Raizen's results confirmed a long standing prediction of the quantum theoretical descriptions of these systems. The atoms did indeed move in a chaotic way to begin with. But after around 100 microseconds (which corresponds to around 50 kicks) the build-up in energy reached a plateau.
Break time
In other words, quantum mechanics does suppress the chaos but only after a certain amount of time known as the "quantum break time". This turns out to be the crucial feature that distinguishes between quantum and classical predictions of chaotic systems. Before the break time, quantum systems are able to mimic the behaviour of classical systems by looking essentially random. But after the break time, the system simply retraces its path. It is no longer random, but stuck in a repeating loop albeit of considerable complexity.
But if this is right, how can classical systems exhibit chaos? Macroscopic objects such as pendulums and planets are, after all, made out of atoms and are therefore, ultimately, quantum systems. It turns out that classical systems are in fact behaving exactly like quantum systems . The only difference is that for classical systems, the quantum break times of macroscopic systems are extraordinarily long-far longer than the age of the Universe. If we could study a classical system for longer than its quantum break time, we would see that the behaviour was not really chaotic but quasi-periodic instead. Thus, quantum and classical realities can be reconciled, with the classical world naturally embedded in a larger quantum reality. Or, as physicist Dan Kleppner of the Massachusetts Institute of Technology puts it, " anything classical mechanics can do, quantum mechanics can do better".”
“Indirect CPV
In 1964, James Cronin, Val Fitch with coworkers provided clear evidence (which was first announced at the 12th ICHEP conference in Dubna) that CP symmetry could be broken, too, winning them the 1980 Nobel Prize. This discovery showed that weak interactions violate not only the charge-conjugation symmetry C between particles and antiparticles and the P or parity, but also their combination. The discovery shocked particle physics and opened the door to questions still at the core of particle physics and of cosmology today. The lack of an exact CP symmetry, but also the fact that it is so nearly a symmetry, created a great puzzle. Only a weaker version of the symmetry could be preserved by physical phenomena, which was CPT symmetry. Besides C and P, there is a third operation, time reversal (T), which corresponds to reversal of motion. Invariance under time reversal implies that whenever a motion is allowed by the laws of physics, the reversed motion is also an allowed one. The combination of CPT is thought to constitute an exact symmetry of all types of fundamental interactions. Because of the CPT symmetry, a violation of the CP symmetry is equivalent to a violation of the T symmetry. CP violation implied nonconservation of T, provided that the long-held CPT theorem was valid. In this theorem, regarded as one of the basic principles of quantum field theory, charge conjugation, parity, and time reversal are applied together.”
From
here.
Okay, what do we learn here? I think that the notion of ‘times arrow’ always will be one defined by your personal frame. If we look at Earth our planets gravity differs depending on where you are, that means that time too will differ, when comparing ‘frames of reference’, but what won’t differ is your own ‘times arrow’. To you the causality chains never get violated. The broken cup never reassembles itself. But can it? Is there some thought up ‘frame’ from where I could watch this cup reassembles itself? I expect not, macroscopically we will always see the cup break, not the other way around. That doesn’t mean that when comparing ‘frames of reference’ you always will agree on what took place at what moment though
“Readers familiar with relativity may be disturbed that this derivation assumed that detector A measured its electron first. According to relativity theory it's meaningless to say which measurement happened first. Some observers will say measurement A happened first while others will say measurement B came first, and they will both be equally valid viewpoints. This doesn't affect the results of this calculation, however. If you redo the calculation from the point of view of an observer that says B came first you will get the same results, namely that if both detectors are pointing the same way they will give the same result every time, whereas if they are pointing different ways they will give the same result 1/4 of the time.
Once again, we find relativity is saved by a technicality; but this one is even more disturbing than the last one. From one point of view the measurement at detector A happens first and instantly changes the state of electron B. From another point of view the measurement at detector B happens first and instantly changes the state of electron A. Physically these descriptions seem completely incompatible. Surely one of them must be the "correct" interpretation of what happened.
Yet experimentally there is no way to distinguish between the two interpretations, so relativity can safely say that either one is a valid description from some particular point of view. Because I find this result so remarkable and incomprehensible, I think it bears repeating. In order to explain the failure of Bell's inequality we had to conclude that one of the measurements (presumably whichever one happened first) affected the state of the other electron. Yet relativity tells us it is a matter of perspective which measurement was the cause and which the effect. Although we can't ever distinguish these two perspectives experimentally, the idea that they should both be valid seems to bring into question some of our most fundamental views about causality. Issues such as these which arise in trying to reconcile relativity and quantum mechanics are, in my opinion, among the most fascinating aspects of physics.” From “spooky action at a distance” by Gary Felder.
So does causality lie? If you can see either one of those two happenings coming before the other? Depending on your choice of ‘frame of reference’? If you think so you’re bicycling in my great yonder methinks
There is no way for you to observe it from those two frames simultaneously, and even if you did, you would still find the cup break, not reassemble itself, as I see it that is. You could imagine me standing on one asteroid throwing that cup at another, where it would break according to me. But to question causality’s temporal flow you would need to find the frame wherefrom the cup reassembles, and that frame doesn’t exist macroscopically. And neither do I expect it to exist anywhere we see an ‘arrow of time’, whatever 'temporal direction' you might interpret it to be pointing, well, except conceptually possibly
So does this make ‘entropy’ a better description? In a way maybe? I’m not sure on that one. But the arrow, or entropy if you like, would still consist of a ‘flow’ to us, not events.
And what explain it are two things I think. That you have only one real ‘frame of reference’ to yourself, the same everywhere, with one arrow of time ticking unchangingly. And, that you are ‘unique’. It seems as if macroscopic object won’t entangle. You might also state it as ‘Emergences’ restricting entanglements macroscopically as our complexity grows.
Let’s finish with this.
“Berry is excited by what appears to be a deep connection between the problem of finding the energy levels of a quantum system that is classically chaotic and one of the biggest unsolved mysteries in mathematics : the Riemann hypothesis. This concerns the distribution of prime numbers. If you choose a number n and ask how many prime numbers there are less than n it turns out that the answer closely approximates the formula: n/log n. The formula is not exact, though : sometimes it is a little high and sometimes it is a little low. Riemann looked at these deviations and saw that they contained periodicities. Berry likens these to musical harmonies : "The question is what are the harmonies in the music of the primes? Amazingly, these harmonies or magic numbers behave exactly like the energy levels in quantum systems that classically would be chaotic."
Deep connection
This correspondence emerges from statistical correlations between the spacing of the Riemann numbers and the spacing of the energy levels. Berry and his collaborator Jon Keating used them to show how techniques in number theory can be applied to problems in quantum chaos and vice versa. In itself such a connection is very unusual. Although sometimes described as the queen of mathematics, number theory is often thought of as pretty useless , so this deep connection with physics is quite astonishing.
Berry is also convinced that there must be a particular chaotic system which when quantised would have energy levels that exactly duplicate the Riemann numbers. "Finding this system could be the discovery of the century," he says. " It would become a model system for describing chaotic systems in the same way that the simple harmonic oscillator is used as a model for all kinds of complicated oscillators. It could play a fundamental role in describing all kinds of chaos."
The search for this model system could become the Holy Grail of quantum chaos research. Until it is found, we cannot be sure of its properties, but Berry believes the system is likely to be rather simple, and expects it to lead to totally new physics. It is a tantalising thought. Out there is a physical structure waiting to be discovered. If we find it, the remarkable experiments that we have recently witnessed in this discipline would be crowned by an experimental apparatus that could do more than anything to unlock the secrets of quantum chaos.”
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Reply #104 on:
17/12/2010 22:53:49 »
So I got some sort of idea of what I mean, maybe. I'm going to use what I think i understand a little here. Won't say it's correct though, but it makes sense to me.
F=ma is what defines force, right?
And what it refers to is the concept of 'inertia', which is a objects tendency to stay in whatever motion, or position, it has unless acted upon by a change. And to me that finally will come down to the idea of 'energy expended'.
Momentum is a property we use a lot, but to me its primary use is for describing a photons 'force' of 'pushing'. When we talk about parallel light beams converging in deep space we are referring to the beams energy 'stressing space' and 'bending/twisting' it.
Relative mass and 'potential energy' seems to me equivalent descriptions of a similar phenomena, used when introducing the 'motion' of matter.
And, to me, light won't budge
As JP wrote.
"In SR, velocity alone determines time dilation. Mass isn't useful in doing so. Velocity is also determined by the ratio of energy to momentum, so you could determine time dilation if you know energy and momentum. For photons velocity is always c and the energy-momentum ratio is always constant. Of course, there is no mathematical theory for the point-of-view of photons, so no physical theory is going to answer the question of how they experience the universe. happy
In GR, time dilation is also caused by curvature of space-time, so mass does get involved, but as I mentioned elsewhere it gets involved through the stress-energy tensor, so the fundamental quantities are still energy and momentum. I don't know the details as well in GR, though."
==
Now I'm going to wave my magic wand and declare both 'relative mass' and 'potential energy' unnecessary. I don't think I need those concepts to see why 'energy' raises with 'motion'.
If you now imagine SpaceTime as consisting of a variety of different 'room time geometry's'. Each one belonging to, and unique for, the 'object', ah, projecting itself on SpaceTime, exchangeables to the concept of 'frames of references' if you like. Then when you accelerate your room time geometry by 'speeding up' relative some reference frame, like Earth, you will observe a Lorentz contraction in your frame of reference, aka your 'personal SpaceTime'.
That Lorentz contraction will 'shrink' your distances. If we now assume that you didn't pop out of normal SpaceTime into something 'else' the 'energy that space contained in form of vacuum fluctuations, foam, virtual photons, gluons and, whatever, still have to be there, but now possibly, from your 'frame of reference' as a compressed state. If you also want to count in the 'time dilation' that you will observe as a 'speeded up' universe, due to your acceleration, then that might be seen as equivalent to a 'blue shift' from your moving 'frame of reference', as I think of it. Still, both of those statements speak of the same, namely that the 'SpaceTime' you observe will, relative you, contain a 'higher energy density' due to 'motion'.
And that is your 'potential energy' as I naievly think of it
But it's not 'potential', it's real. And when two 'frames of reference meet in SpaceTime, like if colliding, the energy released will be a combination of both 'room time geometry's'. Stop looking at it as if there was whole 'SpaceTime' for this example. You need to use the 'mind-space' to see how I see it.
So I don't need to call it potential, because it's there at all times, and what creates different 'energies' observed is your 'room time geometry' contracting and blue-shifting, or the opposite, expanding and red-shifting relative your 'motion' and 'proper mass' aka 'matter'. And that means that we only have one description left to wonder over, lights momentum?
Both 'relative mass' ('momentum' for matter, as I think of it) and 'potential energy' is gone from my efforts to understand motion and 'Einsteins relativity'.
What I have left is a, ah, field maybe? But as I see it as something under Plank size, anyway impossible for us to measure, without extreme acceleration,I think of it as being 'somewhere outside our arrow of time'. But with acceleration it will become visible energy, 'emerging' as I call it, inside that I can observe in my moving 'frame of reference', which now also can be seen as a 'detector' due to its acceleration.
Unruh radiation comes from two effects. The first is that you accelerating will force some particles to chase you, some never catching up depending on acceleration. That will create a 'event horizon' in your 'room time geometry', meaning that the light you use, and all other particles carrying 'information' about your 'SpaceTime' now will become restricted and twisted to your accelerating velocity. The other is that, depending on acceleration, you will find the light blue-shifting gaining energy, together with all other 'energy quanta' you meet accelerating. A blue-shift means that the 'energy' you see coming 'at you' will be compressed in time and of a shorter frequency, 'spikier waves' so to speak.
"These two facts are combined into surprising relation of gravity (because accelerated frame of reference is equivalent to the presence of constant gravitational field!) and thermodynamics (see for example recent paper by Brustein and Hadad), that can be formulated as follows. The presence of apparent horizon means that there are regions of the global spacetime which will never be observer by us, so there should be a certain entropy. If we calculate the energy flux dE from the horizon, we find that
i.e., the second law of thermodynamics that appears in a rather interesting context: we need a) a curved spacetime (or an accelerated observer) and b) quantum fields living in this curved spacetime."
And to that you can add the Rindler effect in where you will see a radiation bath. Read this and ponder. "The Unruh effect tells us that an accelerated observer will detect particles in the Minkowski vacuum state. An inertial observer, of course, would describe the same state as being completely empty; indeed, the expectation value of the energy-momentum tensor would be (unreadable equation here, sorry).
But if there is no energy-momentum, how can the Rindler observers detect particles? This is a subtle issue, but by no means a contradiction. If the Rindler observer is to detect background particles, she must carry a detector - some sort of apparatus coupled to the particles being detected. But if a detector is being maintained at constant acceleration, energy is not conserved; we need to do work constantly on the detector to keep it accelerating.
From the point of view of the Minkowski observer, the Rindler detector emits as well as absorbs particles; once the coupling is introduced, the possibility of emission is unavoidable. When the detector registers a particle, the inertial observer would say that it had emitted a particle and felt a radiation-reaction force in response.
Ultimately, then, the energy needed to excite the Rindler detector does not come from the background energy-momentum tensor, but from the energy we put into the detector to keep it accelerating."
However one present it it will be a radiation existing only as a relation to your acceleration. And if I allow for 'something', reminding me of 'energy', to exist under our limits of observation but in a very real sense becoming part of your 'room time geometry' as radiation/energy then I also will expect that this 'energy' can 'do work'. If it now deliver more energy than the 'energy expended' by you as you measure, what will you call this surplus?
I know what I will call it
an 'Emergence' created out of motion. there are more things to it too, but I need to sleep now, been awake all too long this time.. Hopefully I will remember it when I wake up.
But yeah, I like it
In a totally unscientific way I surely do.
Heh.
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Reply #105 on:
18/12/2010 12:31:53 »
I wrote "If it now deliver more energy than the 'energy expended' by you as you measure, what will you call this surplus?" above didn't I
That's a preposterous statement if we are to believe the laws of conservation and transforming. As if that was right you would all of a sudden get more energy out of our universe than what you put into it. Think of it as a 'system' in where you watch the transformation of energy, then consider what will happen with it as you fill it with 'new energy' from outside the defined 'system'... And maybe I should have wrote the above as ...'As if that was right you would all of a sudden get more energy out of our universe than what you use creating the relation'.. Well, that depends on whose 'room time geometry' we are talking about maybe? I'm not sure on that one, you can have several 'explanations' there I guess.
One is that you never will be able to 'lift' more energy out of a 'room time geometry' than you expend, keeping in terms with how we think of 'SpaceTime' today.
But then we have 'Singularities'? Tell me, if they really are 'Singularities' what happened with their amount of 'energy', no longer a part of our SpaceTime? We can't count that energy as belonging to SpaceTime rigorously speaking, can we? Not if its gone into a different 'Space continuum' like a singularity is seen to be. And so we come into a position where we do have 'energy' disappearing from SpaceTime.
Then on the other hand we have Hawking radiation. That's about the normal pair production under which a particle is thought to be able to come into existence under certain circumstances, like under high 'energies'. And what would the 'room time geometry' be surrounding a black hole? If you look at it my way?
Yeah, extremely well filled with 'energy' wouldn't it? So we should have a lot of 'pair productions' around and at the event horizon of a black hole. Then we come to the statement that this pair production lifts 'information' from that black hole. Nope, not if we are thinking of a particle and its anti particle separating at that boundary (EV), The idea is that instead of taking out each other one particle, the anti one falls in to the Black hole. Well, inside it will take out a 'ordinary' particle as itself is a 'anti', or 'Emo' as some say
and so diminish the 'states' possible inside that black hole. Whilst the particle left outside the Event horizon goes on, smiling and uncaring of its twins sudden disappearance, and so adding to the 'states' existing 'inside' our SpaceTime. Can you see the symmetry presented here, it's a nice one with one exception, 'Information'
The idea is that we have an entanglement created by this 'pair production' where the death of our 'anti particle' will put its stamp on the other still existing particle 'informing' us. There is a lot of subtleties to that statement. First of all, if we shrink all states to 'information', then look at entanglements, creating new 'entanglements' trough splitting 'photons' in mirrors and prisms. Have we really created something? Not if you assume that it's all about 'information', then you have one 'dollar' of information. And just as you can split that 'dollar' into smaller denominations you can split 'information' into smaller denominations too. There is one dissimilarity to the concept though. The dollar when split contain no information of its 'brethren' whilst our 'photon' split (as we see it) in a very real sense always will be the 'whole dollar', no matter what we do to it. Accepting this you get another confirmation of what I'm trying to argue, distance doesn't exist.
There are more stuff I'm thinking and wondering about, but my fingers complain here
We'll see where it will take me. But it's starting to make more sense to me now.
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Reply #106 on:
18/12/2010 12:49:33 »
There is one simple way around this discussion though, accepting that 'times arrow' also is a 'illusion'. Then you can have the whole "SpaceTime' with singularities and all existing. And although we will, inside our arrow of time, find that SpaceTime unsymmetrical at times
with all right too. It still will when looking at it from my 'mind-space' conceptually be a symmetric 'bubble' in equilibrium. but to get to that 'state' of existence there is some things we need to accept first. Distance is an illusion (Conceptually speaking now, remember that mind-space I 'constructed') And the 'times arrow' is also an 'illusion.
So, what would that concept do to our ideas of 'forces'?
==
In a way it all seems to come back to 'entropy' doesn't it? If 'entropy' is a definition of our 'times arrow' then it shouldn't be able to reverse should it? But the fact is that entropy can 'reverse' as well as it can keep 'islands' where the entropy won't act from 'usable' to 'unusable energy' in the same manner as outside those 'islands'. That one you better take on faith for a while as it will take me some time to proof the idea, but as far as I know this is true.
And if you use that definition I present for 'entropy' here, you can have more 'energy' lifted out of 'SpaceTime' than what you expend, 'locally' that is, and by 'locally I mean under one segment of 'time' as well as 'room' now, the 'bubble' won't mind that. Remember that entropy talks about 'transformations' from 'usable' energy into 'unusable'. It does not talk about annihilating the 'energy'. and looked at that way we come to a new, to me that is
, definition of what constitutes 'living'. 'Living' is only possible under this transformation, from usable energy into unusable energy.
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Reply #107 on:
18/12/2010 13:25:20 »
And that's it, really
In my universe you might find it possible to get more energy out, locally, than what you would expect looking at a whole 'objectively existing SpaceTime'. But not when looking at the unique 'room time geometry' you created by 'matter' or motion/acceleration. And that I expect to be proven by experiments soon enough. But it may also be so that we have constants regulating it. In fact, there has to be constants regulating it as we otherwise would have had a chaotic universe making 'life' highly unpredictable. So I expect this to be possible only under highly localized circumstances and not as a 'general rule' of 'SpaceTime'.
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Reply #108 on:
18/12/2010 14:06:44 »
So, have I changed my mind when it comes to entropy then? Before I said it was enclosed by our 'arrow of time' only able to exist inside it? I don't think I have, it's about conceptual space and your real 'room time geometry', they are complementary. In conceptual space (mind-space) entropy rule, but in our 'room time geometry' we will always have an unchanging arrow of time, as checked by comparing your heartbeats to your wristwatch for example, as well as finding that a 'meter' always will be a 'meter' as checked by your personal 'meter stick'. We need to 'split' those ideas to make the world make sense. Your 'mind-space' and your 'room time geometry'.
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Reply #109 on:
18/12/2010 14:27:58 »
I'm looking for the proofs for my statements about 'Entropy'. Eric Verlinde is the one inspiring my comment about 'entropy's reversibility' but not about the 'islands' existing. Smolin finds Verlinde's ideas working for his 'loop quantum gravity' as you can check out here.
We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting.
=
Don't find the exact paper by him that I read, in where he states his idea about 'reversebility'
But what inspired Eric's ideas I understand to be 'entropy' as studied from the viewpoint of biology. Now you might to ask what that have to do with physics
But, if you do you're lost in the clouds.. All things experimentally verifiable inside SpaceTime must become the results we build 'SpaceTime' on. You can if you like 'hypothesize only' but when doing so you need to remind yourself in what 'sphere of pure imagination' you exist as you do, or 'system' if you like.
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Reply #110 on:
18/12/2010 14:45:30 »
So where do I differ?
Well, my 'SpaceTime' I expect to be one of 'relations'. Those relations 'together' are your 'discrete events'. If I apply my view on a particle I can present it like this. It have a 'confinement' defined by the 'forces' of its relations but when inside that confinement there will be 'nothing' to be found. What we call spin polarization, charge etc, is all relations coming to bear by the 'emergence' of that 'confinement' as decided by the 'game rules'. Our arrow of time is also a 'emergence' coming to bear as 'matter' 'space' and 'motion' emerges out of the transitions of those 'rules'. And that we talk about 'forces' is a direct effect from the 'arrow of time' creating the causality chains we take for given.
==
So, is 'forces' wrong?
No, they exist inside our 'arrow of time'.
And they are what made all other ideas come to bear too. I don't like to speak of them myself as I find them too 'jittery' having so many 'causes and effects', but that has to do with where I look at SpaceTime from too. In our real 'room time geometry' they can't readily be ignored, and they will decide what happens. But I still expect us to find 'systems' in where we can bypass them 'locally', although not at the energies (and sizes) normally 'lived in' by us. And that goes both ways, from BEC's to CERN.
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Reply #111 on:
18/12/2010 15:53:05 »
So why do I use 'size' if I don't expect 'distance'?
That's a hard one, but it has a direct relation to how I look at 'distance'. As some sort of 'magnifying' relation. And that it can 'magnify' and 'shrink' we already have seen. To me it seems that 'size' is a description of 'room time geometries' and that it is inside those that we will find our 'distances'.
And I truly don't know what other definition I can use? There is mathematics describing the relations, but they don't convey the mystery of it. Maybe we will invent a new vocabulary to describe it that will make more sense to us, in the 'future'?
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Reply #112 on:
18/12/2010 18:32:18 »
Here is Erik's paper
On the Origin of Gravity and the Laws of Newton.
And here is his response to some, criticizing his approach.
"Entropic forces and the 2nd law of thermodynamics
15/01/10 02:21
Let me address some other confusions in the blog discussion. The fact that a force in entropic does not mean it should be irreversible. This is a complete misunderstanding of what it means to have an entropic force. This is why I added section 2 on the entropic force. For a polymer the force obeys Hooke's law, which is conservative. No doubt about that.
Just last week we had a seminar in Amsterdam on DNA. Precisely the situation described in section two was performed in lab experiments, using optical tweezers. The speaker, Gijs Wuite from the Free University in Amsterdam, showed movies of DNA being stretched and again released. These biophysicist know very well that these forces are purely entropic, and also reversible. The movies clearly showed reversibility, to a very high degree. In fact, I asked the speaker specifically about this, and he confirmed it. They test this in the lab, so it is an experimental fact that entropic forces can be conservative.
So please read section 2, study it and read it again, and think about it for a little longer. When the heat bath is infinite, the force is perfectly conservative. For the case of gravity the speed of light determines the size of the heat bath, since its energy content is given by E=Mc^2. So in the non relativistic limit the heat bath is infinite. Indeed, Newton's laws are perfectly conservative. When one includes relativistic effects, the heat bath is no longer infinite. Here one could expect some irreversibility. In fact, I suspect that the production of gravity waves is causing this. Indeed, a binary system will eventually coalesce. This is irreversible, indeed. This all fits very well. Extremely well, actually. Of course, when I first got these ideas, I worried about too much irreversiblity too. I knew about the polymer example, but had to study it again to convince myself that entropic forces can indeed be reversible.
Another useful point to know is that when a system is slightly out of equilibrium, it will indeed generate some entropy. But a theorem by Prigogine states that the dynamics of the system will adapt itself so that entropy production is minimized. Yes, really minimized. This may appear counterintuitive, but I like to look at it as that it seeks the path of least resistance. So this means that there will in general not be a lot of entropy generated. At least, the system will do whatever it can to minimize it.
By the way, it is true that the total energy of a system of two masses is given by the total mass. But if one then takes the entropy gradient to be proportional to the reduced mass, one again recovers the right force. I thought of putting that in the paper, but I think it is kind of trivial. This confusion was not to difficult to solve.
Another point that may not be appreciated is that the system is actually taken out of equilibrium. If everything would be in equilibrium, the universe would be a big black hole, or be described by pure de Sitter space. Only horizons, no visible matter. If a system is out of equilibrium, there is not a very precise definition of temperature. In fact, different parts of the system may have different temperatures. There is no problem also with neutron stars. In fact, physical neutron stars do not have exact zero temperature. But the temperature I use in the paper is one that is associated with the microscopic degrees of freedom, which because there is no equilibrium, is not necessarily equal to the macroscopic temperature.
In fact, the microscopic degrees of freedom on the holographic screens should not be seen as being associated with local degrees of freedom in actual space. They are very non local states. This is what holography tells us. In fact, they can also not be only related to the part of space contained in the screen, because this would mean we can count micro states independently for every part of space, and in this way we would violate the holographic principle. There is non locality in the microstates.
Another point: gravitons do not exist when gravity is emergent. Gravitons are like phonons. In fact, to make that analogy clear consider two pistons that close of a gas container at opposite ends. Not that the force on the pistons due to the pressure is also an example of an entropic force. We keep the pistons in place by an external force. When we gradually move one of the pistons inwards by increasing the force, the pressure will become larger. Therefore the other piston will also experience a larger force. We can also do this in an abrupt way. We then cause a sound wave to go from one piston to the other. The quantization of this sound wave leads to phonons. We know that phonons are quite useful concepts, which even themselves are often used to understand other emergent phenomena.
Similarly, gravitons can be useful, and in that sense exist as effective "quasi" particles. But they do not exist as fundamental particles."
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Reply #113 on:
18/12/2010 18:50:11 »
And.
"
13/01/10 07:39
THE ESSENTIAL NEW POINTS OF THE PAPER
I have noticed another point of the paper that is not appreciated in blog discussions. For many years, there have been previous works in the literature that discuss the similarity between gravity and thermodynamics. In particular in Jacobson's work there is a clear statement that if one assumes the first law of thermodynamics, the holographic principle, and identifies the temperature with the Unruh temperature, that one can derive the Einstein equations. This is a remarkable result. Yet it is already 12 years old, and still up to this day, gravity is seen as a fundamental force. Clearly, we have to take these analogies seriously, but somehow no one does.
I studied the previous papers very well, and know about them for years. Many people have. We have seen a recent increase in papers following Jacobson, and extending his work to higher derivative gravity, and so. But from all of these papers, I did not pick up the insights I presented in this paper. What was missing from those papers is the answer to questions like: why does gravity have anything to do with entropy? Why do particles follow geodesics? What has entropy to do with geometry?
The derivation of Jacobson does not take in to account the fact that the mass of an object and therefore its energy can change due to the displacement of matter far away from it. There is action at a distance hidden in gravity, even relativistically. The ADM and Komar definitions of mass make this non-local aspect of gravity very clear. This non local aspect of gravity is precisely what the holographic principle is about.
Jacobson's argument is ultra local, and assumes the presence of stress energy crossing the horizon. But there is no statement about an entropic force that is influencing particles far away from the horizon. My point of view is an attempt to take a much more global view, and map out the information over a bigger part of space, even though initially I can only do that for static space times.
The statement that gravity is an entropic force is more then just saying that "it has something to do with thermodynamics". It says that motion and forces are the consequence of entropy differences. My idea is that in a theory in which space is emergent forces are based on differences in the information content, and that very general random microscopic processes cause inertia and motion. The starting point from which this all can be derived can be very, very general. In fact we don't need to know what the micro-scopic degrees of freedom really are. We only need a few basic properties.
For me this was an "eye opener", it made it from obscure to obvious. It is clear to me know that it has to be this way. There is no way to avoid it: if one does not keep track of the amount of information, one ignores the origin of motion and forces. It clarifies why gravity has something to do with entropy. It has to, it can not do otherwise.
When I got the idea that gravity and inertia emerge in this way, which is close to half a year ago, I was really excited. I felt I had an insight that makes clear what gravity is. But I decided not to publish too quickly, also to allow time to make it more precise. But also to see if the idea that gravity is entropic would still appear to me as new as exciting as my first feeling about it. And it does. Now, almost half a year later, I still feel that way.
For instance, the similarity between the entropic force for a polymer and gravity is a real clue to something important. The fact that it fits in well with an adapted version of the work of Jacobson gives additional support. The derivation of the Einstein equations is not really knew, in my mind, since it technically is very similar to the previous works. And I agree that the other line of the paper that discusses inertia is heuristic, and leaves some important gaps. But nevertheless I decided to publish it anyway, because I think this approach to gravity is the right one, it is different, very different from everything that is done today.
Everyone who does not appreciate that this view is different from previous papers are missing an essential point. If space is emergent, a lot more has to be explained than just the Einstein equations. Geodesic motion, or if you wish, the laws of Newton have to be re-derived. They are not fundamental. This has not been discussed anywhere, not even noted that it is the case.
If the previous papers had made the emergence of gravity so clear, why are people still regarding string theory as the final theory of quantum gravity? Somehow, not everyone was convinced that these similarities mean something, or at least, people had no clear idea of what they mean.
Some people may think that when we develop string theory further that eventually we will learn about this. I am not sure that string theory will necessarily take us in the right direction, if we keep regarding the definition in terms of closed strings as being microscopically defined, or may be equivalent to some other formulation. And not if we keep our eyes closed for emergent phenomena. Gravitons can not be fundamental particles in a theory of emergent space time and gravity.
So what is the role of string theory, if gravity is emergent? I discussed this at some level in the paper. It should also be emergent, and it is nothing but a framework like quantum field theory. In fact, I think of string theory as the way to make QFT in to a UV complete but still effective framework. It is based on universality. Many microscopic systems can lead to the same string theory. The string theory landscape is just the space of all universality classes of this framework. I have more to say about it, but will keep that for a publication, or I will post that some other time.
Of course, I would have liked to make things even more clear or convincing. In this paper, I use heuristic and you might say handwaving arguments. The issue of motion: why is the acceleration a that I introduced equal to the second time derivative of the position? If one assumes the equivalence principle, it is clear. Also coordinate invariance would be enough. But I do not have a very precise way of seeing how that emerges. How to go from just information to a Lorentzian geometry in which general coordinate invariance is manifest. Some assumptions have to be made.
But again, this are questions that others have not been even started to think about. These are questions that have not been even addressed by previous works. But they are essential. When one really understands this well, there should be no doubt that gravity is emergent and forces are driven by entropy.
This is the essential idea, which is really new and important, and which in my view justifies this level of reasoning, certainly in a first paper. It is clear that this is not the final paper on this subject. This is also my own view. I clearly did not answer all of the questions. In fact, my approach probably raises more questions than it answers. But it should be obvious that these questions are important, very fundamental and their answers should lead us in a completely new direction. Our theories will have to based on new paradigms.
I find all this still very exciting and will continue to work in this direction.
And remember, quantum mechanics was also not developed in one paper. Do you think de Broglie knew exactly what he was talking about? Leaps based on intuition are sometimes necessary. They are an important part of progress in science, even if they do not immediately give complete finished theories of Nature."
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Reply #114 on:
18/12/2010 18:51:16 »
And finally..
" Logic of the paper
12/01/10 00:50
The paper is not technical, but some background is needed, more than just being able to read the text and the equations. The text explains the logic, but apparently some important points are misunderstood. Clearly, I should do a better job in making them more clear. But it is my impression that the misunderstanding is partly due to a lack of background or a difference in reference frame. Because the logic of the paper is being misrepresented in some reports, I add here some clarifications.
So here is an attempt to address some of the points that I think are not appreciated or generally understood.
The starting point is a microscopic theory that knows about time, energy and number of states. That is all, nothing more. This is sufficient to introduce thermodynamics. From the number of states one can construct a canonical partition function, and the 1st law of thermodynamics can be derived. No other input is needed, certainly not Newtonian mechanics. TIme translation symmetry gives by Noether's theorem a conserved quantity. This defines energy. Hence, the notion of energy is already there when there is just time, no space is needed.
Temperature is defined as the conjugate variable to energy. Geometrically it can be identified with the periodicity of euclidean time that is obtained after analytic continuation. Again there is nothing needed about space. Temperature exists if there is only time.
It is possible to introduce other macroscopic variables that are associated with a finite but still large subset of the microstates. Let us denote such a variable by x, at this point this is just some arbitrary choice. It can be any macroscopic variable that singles out a collection of the microscopic states. So specifying x in addition the to energy gives more detailed description of the microscopic states, but nothing more. So it is not even necessary to think about x as a space coordinate. Nevertheless one can define a number of microstates denoted by Omega(E,x) for given energy E and for a given value x for this macroscopic variable x.
Next one can introduce a formal variable called F and introduce in the partition function as the thermodynamical dual to x. Following just standard statistical physics (I avoid the word mechanics, since Newton's law is not necessary) one can obtain the 1st law of thermodynamics. dE=TdS -Fdx. This makes clear that F is a generalized "force", but it has nothing to do with Newton's law yet. It is defined in terms of entropy differences. The macroscopic force that is obtained in this way has no microscopic origin in terms of microscopic field. The force is entirely a consequence of the amount of configuration space and not mediated by anything. There is no space yet.
The meaning of the statement that space is emergent is that the space coordinates x can be viewed as examples of such macroscopic variables. They are not microscopically defined, but just introduced as a way of singling out part of the available micro states. It is my impression that not all readers have understood or appreciated this essential point. Hence, if the number of states depend on x there can be an entropic force, when there is a finite temperature. This is all, nothing more. Again, for this point I don't need to assume Newtonian mechanics. It does not exist yet in this framework.
The other central point paper is that if one chooses a macroscopic coordinate x that corresponds to a fixed position in a non-inertial frame, that Newton's law of inertia F=ma will be the consequence of such an entropic force. It has to be. There is no other way it can arise, simply because x is not a microscopic variable. It is obvious. Nevertheless, it is a fundamental new insight that has not been noted before. This is not an empty or circular statement. It says something about the way that the function Omega(E,x) should behave as a function of x. All this can be derived and defined without the input of Newtonian mechanics.
The other formulas presented in the paper are just there to illustrate that indeed it is possible to get gravity from this kind of reasoning, and that it is consistent with the ideas of holography. But the main point concerns the law of inertia. The derivation of the Einstein equations (and of Newton's law in the earlier sections) follows very similar reasonings that exist in the literature, in particular Jacobson's. The connection with entropy and thermodynamics is made also there. But in those previous works it is not clear WHY gravity has anything to do with entropy. No explanation for this apparent connection between gravity and entropy has been given anywhere in the literature. I mean not the precise details, even the reason why there should be such a connection in the first place was not understood.
My paper is the first that gives a reason why. Inertia, and hence motion, is due to an entropic force when space is emergent. This is new, and the essential point. This means one HAS TO keep track of the amount of information. Differences in this amount of information is precisely what makes one frame an inertial frame, and another a non-inertial frame. Information causes motion.
This can be derived without assuming Newtonian mechanics.
So the logic of the part of the paper dealing with inertia is:
microscopic theory without space or laws of newton-> thermodynamics -> entropic force -> inertia.
The part that deals with gravity assumes holography as additional input. But this is just like what has been done before. It is also not the main point of the paper. Gravity in a way does not exist in Einstein's theory either. But one would like to recover the gravity equations. The logic here is
thermodynamics + holographic principle -> gravity.
The obvious question is: where does the holographic principle come from? Of course, it was extracted from the physics of black holes. But the holographic principle can be formulated without reference to black holes or gravity. Hence, it can be taken as a starting point, from which one then subsequently derive gravity. Again, this part is in essence not new. Jacobson followed exaclty the same logic.
This way of turning the logic of an existing argument around is done more often in physics, and it is known to lead to much more clear formulations of a theory. One example that comes to mind is the way that Dirac used the result of Heisenberg that p and q do not commute, which was obtained in some roundabout way, and made it in to the starting point for quantum mechanics. This is how it is being taught today. Another is how Einstein changed the logic used by Lorentz and used the constancy of light as a postulate. Lorentz tried to explain why it was constant by using concepts like Lorentz contraction. In fact, Lorentz theory and Einsteins are equivalent. The only difference is in the chosen starting point. The reason we give credit to Einstein is because everything follows in a much more simple fashion from his postulated starting point.
In my paper I claim that gravity follows in a very simply fashion from holography, but that the direction the other way is much more complicated. One has to be able to switch one's perspective, and then the logic becomes more clear. So don't use your usual reference frame with Newtonian mechanics in the back of your mind, but let it go first.
Anyhow, I hope this clarifies some points, and removes some of the misunderstandings ."
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Reply #115 on:
18/12/2010 19:18:28 »
Reading him I find that he seems to have the same idea
Well, I think at least it's similar? And no, I did write about him when the paper came out, but then other things came inbetween and I sort of forgot it. But I'm pleased to see that we agree, I think?
Maybe not agree then, but we have the same sort of idea of a universe coming out of 'relations'. I still don't know just how the 'holographic universe' is thought to come to be, but the same can be said about my simplified 'relational universe' I guess.
But I'm sure i will learn more as I read about people and their ideas, physics must be the best game, ever
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Reply #116 on:
18/12/2010 22:23:13 »
So under what circumstances can we expect a room time geometry to be able to behave like this? Shrinking and expanding? Does it state something about the 'information amount' available. I imagined the 'states' of SpaceTime getting compressed when you accelerated. But can you see it other ways too? Yes I think you can, you can also think of it as that 'screen' hanging in front of us all. You know, the one with the movie featuring you and 'SpaceTime. That screen contains all information reaching you, and it is called the Bekenstein bound. If we look at it from the 'screen', I don't know if I can assume a 'compressed state' of energy relative you when you're accelerating?
It depends, let us put it this way, will I, if accelerating, get more or less information?
"Bekenstein has long argued that the bound should not apply to such wavepacket states (which will eventually spread out in space), but only to `complete systems' which are truly connected to a finite region and that one should include contributions from the energy of any `walls' used to hold the system together.
It is here that some cleverness is needed to make this statement precise since in flat spacetime, even if walls are introduced, the full system (including the walls) will necessarily possess an overall center of mass degree of freedom which will be unconfined and will eventually spread out across all of space."
What does that mean? What is a 'complete system' and what do he mean by 'finite region'? Does he mean that this bound only will work when you twist the 'room time geometry' by expending energy. No that can't be right can it? a black hole will 'twist' the 'room time geometry' too won't it? But it does so from its proper mass, not from expending energy? Is a black hole a 'complete system in a finite region'?
==
In a way it is, one of the few I guess that actually can be defined that way?
But an acceleration then? Is that too a 'complete system in a finite region'?
Depends on how you interpret the 'information' reaching you I think?
Does it contain the same amount you started with, being 'still' relative Earth, or not?
Read this
Information in the Holographic Universe by Jacob D. Bekenstein. 2003
I need to learn more about this one. And so, I guess, do you
While your at it, take a look at this one too
Note on bound states and the Bekenstein bound
And this one perhaps?
Presenting
Bekenstein-Hawking entropy
===
(Tippler goes slightly, ah, wild(?) discussing it. Well, from where I stand
From 2100 to the End of Time.
But he's interesting, I liked his idea of AI:s although, I don't share his beliefs)
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Reply #117 on:
18/12/2010 23:18:36 »
One guy that seems interesting here is Gerard ′t Hooft at the Institute for Theoretical Physics in Utrecht. I especially like when he write
" The Hierarchy Problem.
Now − December 2010 − I can report further progress. To improve our theoretical description of matter going in and out of a black hole, we need a description that works both for observers inside (or near) a black hole, as for observers far away. This is the complementarity principle. It is more important than the holographic principle, even if that is also often ascribed to me. To make complementarity work, I now propose a relativity of scale. In itself, this idea has been proposed many times earlier, but I am giving it a special twist. Local scale invariance is expressed in a field called the dilaton field. What is needed is that the dilaton must be treated as an independent dynamical scalar field. In conventional treatments of gravity the interactions are singular when this field tends to zero. This, I claim, should not be.
The nice thing about this observation is that it generates a new constraint on the way particles may interact: all interaction strengths, all masses and even the cosmological constant are now completely determined by algebraic relations, while they used to be freely adjustable quantities. An important problem can now be addressed: the hierarchy problem, which is the question why particle masses are 20 orders of magnitude smaller than the Planck mass, and the cosmological constant even more than 120 orders of magnitude. Could my theory explain this? I have been studying some intriguing ideas. Could the coefficients that relate to the cosmological constant and the mass terms be due to instantons? They are known for generating exponentially suppressed amplitudes.
My present theory allows me to investigate such approaches, but as yet without success. At this moment, only one firm prediction stands out: constants of nature are truly constant. Attempts to observe space and/or time dependence will yield negative results.
Because of this prediction I strongly support experimental searches for space-time dependence of natural constants, in particular the searches using the "frequency comb" for high precision comparisons between different spectral frequencies in atoms and molecules." From
Here.
Ahh, those constants
I couldn't agree more to that suggestion. They are weird, but here, if we only find out how to see them.
===
Now, he seems to be arguing against an 'emergent SpaceTime'.
Due to quantum effects, a black hole emits particles of all sorts. Thus, if left entirely by itself, a black hole gradually looses mass, eventually ending its life with a gigantic explosion. This is the Hawking effect. For an intuitive understanding of our world, the Hawking effect seems to be quite welcome. It appears to imply that black holes are just like ordinary forms of matter: they absorb and emit things, they have a finite temperature, and they have a finite lifetime.
One would have to admit that there are still important aspects of their internal dynamics that are not yet quite understood, but this could perhaps be considered to be of later concern. Important conclusions could already be drawn: the Hawking effect implies that black holes come in a denumerable set of distinct quantum states. This also adds to a useful and attractive picture of what the dynamical properties of space, time and matter may be like at the Planck scale: black holes seem to be a natural extension of the spectrum of elementary physical objects, which starts from photons, neutrinos, electrons and all other elementary particles. In such a picture, however, what happens to the horizon and the space-time singularities?
An answer sometimes suggested by string theorists, as well as others, is that all of space-time is just “emergent” the theory should first be formulated without space-time altogether. Or, perhaps, time alone is an emergent concept. It was argued that, at least, locality would have to be abandoned. In this paper, however, we dismiss all such options. In particular, we insist that any satisfactory theory should have built in a strong form of causality, as well as locality, in order to explain why cause precedes effect, and why events separated at some distance from one another appear to evolve independently. For this, space-time appears to be indispensable. Something has to give, and in this paper we claim to have found a good candidate for that: the definition of scales in space-time....
We suspect that, eventually, scales enter into our world in the following way. Information is now strictly limited to move along the light cones, since only light like geodesics are well-defined, not the time like or space like ones. It is generally believed that the amount of information moving around in Nature is limited to exactly one bit in each surface element of size 4 ln 2 Planck lengths squared. Turning this observation around, one might assume that, whatever the equations are, they define information to flow around. The density of this information flow may well define the Planck length locally, and with that all scales in Nature. Obviously, this leaves us with the problem of defining what exactly information is, and how it links with the equations of motion. The notion of information might not be observer-independent, as the scale factor ω isn’t. Quantum mechanics will probably require that all these bits of information form distinct elements of a basis for Hilbert space." From
Quantum gravity without space-time singularities or horizons.
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Reply #118 on:
19/12/2010 00:41:10 »
I especially like the way he discuss the question of what a Planck length should be seen as in a accelerated 'room time geometry' at least that is how I read it? "The density of this information flow may well define the Planck length locally, and with that all scales in Nature." Can we use that one? I wondered about that one too when I started to wonder about 'distance'. My conclusion was that it would be 'the same'. That is, just as your 'time' and 'meter stick' locally will be the same for you in whatever frame you exist so will that Plank length be. But when it comes to the 'information received'?
Would that informations Plank length necessarily be yours too?
In my 'contracted universe' I don't think it would. But this introduces a new problem. Suddenly we need two definitions, the one for your 'room time geometry' that always stays the same locally, and then one for the 'information' received?
That we know it to be so we already have defined, you will measure a meter by your meter stick, you will measure the same heartbeats by your wristwatch. But you will also measure a 'contraction' of SpaceTime, and if you like, a speeded up universe, aka a 'time dilation'.
So how do one put that together?
==
Maybe that idea of a 'screen' can help us with that one?
Another thing, talking about 'equivalences'. If you look at it you can see a clear equivalence in the way you observe a time dilation to what the 'earthly observer' will. From your 'frame' the universe 'speeds up'. From his 'frame' you have slowed down.
But when it comes to 'distance'? From your 'frame' distance shrinks. But from his frame distance is unchanging. That's not the same, is it? It's like there is something missing here, what?
What one can argue against that interpretation is that a 'time dilation' only will be 'noticed' if you return to your 'original frame of reference' and that nowhere whilst you 'travel' will you, or your earthly observer, notice a 'time dilation'.
So okay, let's turn it around. Is there anywhere you notice a change? For the earthly observer the answer is 'no' but for you traveling it will be 'yes', on both counts.
And if we accept that for you both effects exist, although not for the earthly observer, that will age so much more than you, then what did you do?
The only thing I can see is that you expended a lot of energy, transforming it into motion.
So expending energy will create a time dilation? and a Lorentz contraction too?
But where? Not in your own frame, wait, the time dilation is still real for you as you reach the star faster than you should, isn't it? Nope, that was the length contraction..
So we're left with the length contraction.
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Reply #119 on:
19/12/2010 01:39:35 »
You know, I think I'm wrong seeing it as only a 'contraction'. I should in reality see it as a shrunk 'room time geometry'. And saying that muons only notice a length contraction isn't true. That example is all wrong, the muon will notice a new 'room time geometry' looking out the 'window'. To her both length and time have changed for the objects she study, their movements will be faster as well as the 'distance' closer.
But her own time and length will be the same. And that is what phreaks me out somewhat. As it states that its not her, its the universe changing. And that is not possible if we look at it from a 'energy expended' perspective. The universe is 'massive', and so big. To expect to be able to change the universes 'room time geometry' just by expending a finite amount of energy is not reasonable, the equivalence is slanted.
So where do I go wrong?
=
It has to be 'energy expended', but does it have to be motion?
Can I introduce a new 'room time geometry' just by expending a lot of energy in a unmoving coordinate system? If we assume that there is a equivalence between 'proper mass' and energy we can use 'matter' as a proof of that concept. But it is a slanted one too as they are not the exact same, very near but as I understands it, not the exact same.
But maybe the 'difference' is in the condensed state matter is found to be, matters 'density' so to speak? I think I can accept that one.
==
So I will simplify, with the risk of becoming too simplistic here.
'Expending energy' will change a 'room time geometry'. And seen as 'entropy' what do I do when expending energy? I speed it up, don't I? But in my own frame of reference then? Seen from Earths frame I must have 'slowed down' my entropy? And in my own 'frame' my entropy is unchanged whilst the universes 'usable energy' is burning up.
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