08/26/2009
Updated: Condensed Light
Updated article: Condensed Light
"It may also be possible all energy has the same constituents as photons are themselves composed of, which would likewise always have the speed of light. What those may be, however, is highly speculative, as they would be beyond the level even of elementary particles. If all elementary particles have the same basic constituents, however, this would explain how elementary particles can bring others into being. Photons themselves can be converted into any kinds of other particles, for instance. Usually, when two particles interact (read collide) with one another with enough energy, their kinetic energy is converted into other particles. However, if two photons interact with one another with enough energy, they are entirely converted into other particles. This is basically the time reversal transformation of the combination of matter and antimatter particles, which yields photons.
When photons are converted into matter, its energy is transferred into these particles. Thus, it is obvious that the energy in the photons is of the same form of that of the particles, and therefore, has the same particles at some level. That all forms of energy can be converted into one another seems to indicate that all energy fundamentally has the same constituents. Otherwise they could interact, but no more.
All this is, however, mere guesswork."
21:04 Posted in Philosophy, Science | Permalink | Comments (0) | Email this | Tags: light, photons, physics, two-photon physics, quantum mechanics, elementary particles, matter, particle physics
02/25/2009
Condensed Light
Perhaps matter cannot go faster than light because all matter is light.
E=mc^2, meaning that mass is in fact condensed energy; energy in its purest form is light. Perhaps, then, matter in fact consists of photons which have somehow become condensed into more complex structures.
Light moves at a constant speed in vacuum but can slow down in other media because it bounces back and forth from atom to atom. Scientists have even managed to freeze light altogether: firing it through hot rubidium atoms, they locked it in place by trapping it in between two control beams, which interacted with the rubidium atoms to create layers which reflected the photons back and forth. Clearly, it is possible for light to be still. Perhaps, matter is light that constantly rebounds in some kind of subatomic system, a solidified version of photon gas.
In photons, all energy is kinetic, equal to mc^2, while they have no mass-energy. If matter is condensed light, then its mass is actually condensed kinetic energy. In the form of light, all mass-energy is converted into kinetic energy; it is obvious then, that no matter can go faster than light, as for that to happen, more than 100% of its energy would have to be kinetic, meaning that its every photon would have to move in a line. In fact, because of this, matter that would move at the speed of light would necessarily disintegrate.
Since photons have maximum speed, then if all matter consists of photons, one can't really increase its speed; rather, when increasing the net speed of a mass, one employs part of the intrinsic speed of its photons, which is normally almost fully neutralized. This could be compared to the wind, which is caused by a difference in temperature: in this way, the speed of the individual atoms also causes the speed of the air itself, even though the speed of the atoms actually remains unchanged.
If this is true, one could say that the speed of light is absolute for similar reasons that the speed of sound is. Air atoms always move with about the same speed; but usually they move in a random way, so that they do not move on larger scale. When sound waves are produced, however, they collectively move at the speed of sound. This would be very similar to how photons would behave. According to the Bohm Interpretation, photons merely behave like a wave because they move collectively according in a wave function, much like air atoms; in fact, photon waves might actually be no more than an analogy to sound waves.
Remember that air atoms move at a speed of 330 meters per second even though it is more or less still on larger levels, aside from a much slower wind, and that the same counts for the atoms in any matter: all atoms move at their own speed of sound, that is to say, the speed at which sound travels through them. For iron, this is 5 kilometers per second, far higher than in air, and yet it manages to remain solid because of the forces that bind the atoms together, producing energies stronger than those of the atoms' movements. In diamond, this is even as high as 12 kilometers per second, though it is the hardest natural material. Perhaps there is a force that at some level could glue even photons together, despite their speed of 300.000 kilometers per second.
If air atoms were in a closed system, then over time all air atoms would have exactly the same speed, since their kinetic energy would have distributed over the entire system. Without interaction with other systems to cause differences in energy levels, their energy would become evenly spread in accordance to the law of entropy. This is what would have happened for the photons the universe would comprise: they would have exchanged their energy just as air atoms would, but over a period of thirteen billion years, until their speed would become almost perfectly constant. Because everything in the universe is made of the same photons, there was no outward influence to cause gradients in their kinetic energy.
However, like the speed of sound, the speed of light might only be absolute on a small scale. Even though air atoms themselves move at a speed of 300 meters per second, the air itself can move far faster than this speed, for instance, if the air is moved by an airplane, and perhaps photons might themselves move at a speed faster than 300.000 kilometers per second if moved by something larger — such as, for instance, the Big Bang.
The consensus among scientists is that the explanation for the faster-than-light expansion of the universe is that it is not the universe itself, but space which expands. Perhaps it is in fact the universe which expands, because the universe, like the airplane, is so large that the speed of light no longer applies.
Moreover, the Big Bang took place before the speed of light was established, since this happened only later, as the photons exchanged their energy until all had the same speed, at least, on a small level.
It may also be possible that all energy has the same constituents as photons are themselves composed of, which would likewise always have the speed of light. What those may be, however, is highly speculative, as they would be beyond the level even of elementary particles. If all elementary particles have the same basic constituents, however, this would explain how elementary particles can bring others into being. Photons themselves can be converted into any kinds of other particles, for instance. Usually, when two particles interact (read collide) with one another with enough energy, their kinetic energy is converted into other particles. However, if two photons interact with one another with enough energy, they are entirely converted into other particles. This is basically the time reversal transformation of the combination of matter and antimatter particles, which yields photons.
When photons are converted into matter, their energy would be transferred into these particles. Thus, it is obvious that the energy in the photons is of the same form of that of the particles, and therefore, has the same particles at some level. This would also mean that all energy is kinetic, since the energy of photons themselves is also entirely kinetic. That all forms of energy can be converted into one another seems to indicate that all energy is the same, or is comprised of the same. Otherwise, they could interact, but no more than this; they could not be turned into one another.
If matter consists of photons, speed cannot be added to the photons: they can only be brought to move more in the same direction, so that they no longer brake one another as much. The more the matter is sped up, the more the photons move in the same direction. This is much like the wind causes air atoms to move in the same direction, or a supersonic airplane does so: the air atoms are pushed in one direction against one another until they move in that direction, and so are the photons when matter is converted into energy.
At relativistic speeds, however, the matter is moved at such speed that its mechanisms break down; the matter starts to return more to its original state, in the form of a ray of light.
As the movement of the object as a whole increases, the movement of the particles relative to one another decreases, as the latter movement happens in another direction other than that of the movement of the object itself. The kinetic energy of the particles within the object becomes converted into the kinetic energy of the object as a whole.
As the photons are pushed against the light barrier, all particles approach the same speed, that is, the speed of light, and the closer they approach it, the more they slow down. The faster the particles are pushed against this barrier, the more they are slowed down. Particles that travel in the direction opposite to the direction of travel are least changed.
As the particles collide, the collisions in the direction of travel are decreased in force, while the collisions in the direction opposite the direction of travel are increased in force. This causes a net "force" in the direction opposite that of travel, although this force is arguably fictitious. It is another matter with width, since it is only axially, that is, in the direction of travel, that the particles approach the speed of light. Laterally, only the speeds of the particles are changed, while the ratios of speeds remains the same.
The particles of a still body can move freely in all directions, but in a relativistic body, they can barely but move in only one direction, since movement in any other direction would slow the body down, and the only way a body can have such speed is by having all its particles move almost straight in the same direction. The movement of the particles in the object is turned into the movement of the object itself. Because of this, the particles slow down relative to one another, so that their interactions also slow down, and therefore so does their entire physics and chemistry. It is because of this that time dilates as speed increases, since time, as well as speed, is itself but movement, and the former needs to be converted entirely into the latter in order for the speed of light to be achieved.
Time is the result of movement, but the movement that causes time almost ceases at speeds near that of light. In fact, time, as well as space, are both themselves but movement, for if nothing moved, everything would stay exactly where and when it was, so that space and time would become irrelevant: the only time would be now and the only space here, and so they would always stay. It is in this that time and space are one and the same.
Mainstream scientists have another way of explaining time dilation, yet I have come to the same conclusion through other premises, though using the same postulate that the speed of light is absolute. The speed of light is not absolute relative to any frame of reference, but it is nonetheless an absolute property. The speed of light is immanent in all energy, and therefore, the laws of physics are still invariable in any frame of reference and the Theory of Relativity is actually preserved, although reinterpreted. As the speed of light remains invariant, the other normally invariant properties like time and space also become variant at relativistic speeds.
If we base the "velocity" of an object not on how fast it goes relative to other objects but rather base it on its kinetic energy, then velocity is an absolute property rather than one that is relative. Velocity should be measured as how fast it goes relative to how fast it can go (that is, relative to the speed of light). An object can only achieve a certain velocity until all its energy has turned into kinetic energy. The absolute velocity of a non-relativistic object equals the square-root of two times its kinetic energy divided by its mass. Velocity is a property of the object itself, but one that is very hard to measure.
03:37 Posted in Philosophy, Science | Permalink | Comments (0) | Email this | Tags: physics, speed of light, energy
02/24/2009
Causality
Some interpretations in physics dispense with causality; in that these interpretations are no longer scientific, since science is nothing but the investigation of causality, of why things are as they are. Physics without causality is no longer science, but mysticism. Believing something to be as it is without needing any explanation in physics is as unscientific as believing this in religion. Scientists who say that the occurrence of a physical event needs no cause are no better than creationists who say that the existence of God needs no cause, and surely polytheists believed the same in the past about their gods; but we only give up finding the cause of something and say that it "just is" when we are confused about it. Some things about modern physics are very confusing, but that does not give us an excuse to descend into despair to explain them.
16:33 Posted in Philosophy, Science | Permalink | Comments (0) | Email this | Tags: science, logic, causality, physics, quantum mechanics, quantum physics, relativity
02/17/2009
Observed Superluminal Phenomena
Since Special Relativity has become a paradigm of modern physics, any phenomenon of faster-than-light communication has either been ignored or dismissed by physicists. Over the years there have been many experiments in which true superluminal velocities have been observed. Unable to dispute their results, mainstream scientists often represented them in such way that their significance was masked, using cyclical arguments or irrelevant metaphors. Scientists seem to fear that if proven possible, FTL travel would mark the end of Special Relativity.
There is no reason, however, why we should give up Special Relativity if we find that superluminal velocities exist; but perhaps we should nuance it somewhat. Nothing in the universe may be absolute. Natural laws tend to have exceptions. Natural laws are causes of phenomena, but they themselves are phenomena, and so we might assume that they as well have causes. Those causes might be changeable, like anything else in nature appears to be.
We live in a universe that appears to be "fine-tuned" to the possibility of life. For example, should the fine-structure constant (a dimensionless constant equal to 7,29 · 10^-3) be just 4% different, then stellar fusion could not produce carbon, and so life would be impossible. (There is, of course, a possibility of life that need other or less atoms, but the question is what life could do with just two non-inert atoms, hydrogen and lithium!)
This suggests two things.
The first is that there are, or have been, many other universes with other parameters. After all, if there were only one universe (or one region in the universe with distinct physical constants), it would be too much of a coincidence that it is inhabitable. That we live in a universe which happens to be fine-tuned to life because there could be no other universe to live in in the first place.
The second is that physical laws, or at least physical constants (which include the speed of light) are changeable (at least in very extreme circumstances), since they must have formed at some point in time to become what they are now. For our universe, this supposedly happened in the early stages of its birth (although there may be other universes where the laws of nature are still changing constantly). Some of the circumstances of the primeval universe are actually being simulated in particle accelerators, albeit over extremely small spaces. Who knows? Perhaps, one day, we'll get so far as to bend the laws of nature in our own particle accelerators.
In fact, such phenomena have already been observed.
Natural nuclear fission reactors are subterranean deposits of uranium which may undergo spontaneous nuclear reactions; one of the oldest of these nuclear fission reactors lies in Gabon, which has been discontinuously active for about 2 billion years. By analyzing the nuclear decay in these deposits, researchers have discovered that the fine-structure constant, which determines nuclear reaction cycles, has slightly changed over that time.
Phenomena Superluminal Phenomena
1) Inflation Period:
Perhaps the most dramatic instance of superluminal velocity in the history of the universe was at its very beginning: in the "inflation period," a period which lasted for a tiny fraction of the first second after the Big Bang, all the matter in the entire universe exploded at a speed far higher than the speed of light. In 10–33 seconds, the universe increased 1026 times in size. The diameter it had achieved at the end of this period was no more than 10 centimeters, but all this had happened in such a short time that this was by far the most extreme explosion ever. The velocity it involved was 1032 meters per second, or 3 · 1023 times the speed of light.
Many physicists would, as usual, dismiss this phenomenon by pointing out that space and time at this point were distorted by gravity. However, this argument confuses two unrelated frames of reference; from our frame of reference, the speed was faster-than-light. If this would happen again before our eyes and we could somehow observe it, then, supposing that it wouldn't destroy the entire world, we would observe a speed that is undeniably superluminal.
2) Gain-assisted superluminality:
Researchers have achieved faster-than-light communication by sending light pulses through a supercooled gas of exotic cesium atoms. The light pulse travelled so fast that it had actually exited the gas chamber before it had finished entering.
They claim that this leaves Special Relativity intact; the light pulse did not actually travel faster than light, they state, because the light pulse on the other side of the gas chamber was actually a reconstruction of the entering pulse, so that is not actually the same pulse. This interpretation does a poor job hiding the fact that either how, information was nonetheless passed through to the other side of the gas chamber faster than light. This contradicts Special Relativity, which says that under no circumstances information could travel faster than light; it may be that Wang and his colleagues were afraid to openly contradict Special Relativity, for fear of criticism or disregard of their research.
3) EPR paradox:
Observing either of a pair of entangled particles will instantly affect the other particle, no matter how far it is — a fact which has been experimentally verified. No matter how one interprets this, the information that either particle has been observed travels to the other particle instantly, or at least (and perhaps more likely) at a speed faster than we have as yet been able to measure.
It is claimed that this does not allow faster-than-light communication, yet regardless it has been proposed to use this phenomenon in quantum cryptography: by using entangled particles to transmit information, eavesdropping would be instantly detected since it would affect the other particle of the pair. In other words, the information of an instance of eavesdropping would instantly travel to the other particle; this is certainly communication.
The event of the observation of either of the particles has an immediate effect on the other. Einstein mockingly called this "Spokhafte Fernwirkung," and in the formulation of the EPR paradox claimed that this meant that quantum mechanics is incomplete. However, since this "spooky action at a distance" has been confirmed as factual, it would appear that it is rather Special Relativity which is incomplete.
4) Speed of gravity:
Although Einstein dismissed "spooky action at a distance" as impossible, the mainstream interpretation of General Relativity today itself uses "spooky action at a distance" to avoid faster-than-light speed. Tom van Flandern has calculated, based on observation of planets and binary quasars, that the speed of gravity must propagate at no less than 20 billion times the speed of light to accord with their angular momentum.
To avoid this, mainstream physicists interpret gravity as the curvature of space-time rather than an actual force of nature, like electromagnetism. While representing gravity in this way may render the nature of gravity more obscure, however, it does nothing to change the fact that, be it through space-time curvature or through an actual force, gravity propagates at a certain speed. If gravity is represented as space-time curvature, the fact remains, obviously, that mass has an effect on space-time curvature; this effect cannot be random, and therefore requires a signal from the mass that causes it: this signal must be faster than light.
The effect of mass on gravity is such that it can affect the other side of the observable universe in just two seconds. In other words, information is passed at faster-than-light speed, the information of gravity; in the space-time curvature representation, this is the information space-time needs to know just in what way it should curve in accordance to the mass that causes it to do so.
The only way to deny that this is a faster-than-light effect is by detaching the effect from its cause, in which cause one has to give up the entire idea of gravity. In gravity, cause and effect are related at a speed that is faster-than-light, and only through sophistry can one deny this, unless observations are somehow wrong.
5) Virtual particles
Similarly to gravity, electromagnetism appears to propagate at faster-than-light speed through virtual photons. The nature of virtual particles is still unknown, but they are thought by mainstream physicists to be a manifestation of Heisenberg's uncertainty principle. Again, most physicists dismiss the faster-than-light nature of virtual particles because they are virtual; that is, they exist only for a very short time. Outside of their interaction, they do not exist. However, this is irrelevant, as their interaction itself is superluminal; therefore, their interaction might also be used to allow superluminal communication.
6) Opposite or closing speeds:
Special Relativity states that regardless of the frame of reference, nothing can go faster than light. Actually, one doesn't need to think far at all to see that this is plainly impossible: when two photons move on a straight line towards or away from each other, than from our frame of reference they do so twice as fast as the "speed of light." When you tell this to a mainstream physicist, he will say that from the frame of reference of either of the photons themselves, the photons will not move faster than light, thereby changing your question so as to best suit an answer which accords to Special Relativity; the frame of reference of the photons is not very relevant, however. Since all motion is relative and all things in the universe are in motion, it is easy to travel towards something at faster-than-light speed from the frame of reference of the Earth. That is to say, when you have reached your destination which was 200 light years far, it might be that less than 200 light years have passed in the universe.
This is probably the least relevant of all faster-than-light phenomena, since it does little to bring us closer to faster-than-light travel or communication, but it is a faster-than-light phenomenon nonetheless. One can hardly move a star towards a spaceship: while it may be possible to move a star by means of a stellar engine (a type-2 Dyson sphere), it would not be very worthwhile to use this simply to accelerate space traffic.
The least that this means is that we should reformulate the Special Relativity: "Nothing can travel faster towards or away from an object than light would travel towards or away from it." At least, that is how it tends to be.
7) Current cosmic inflation:
The observable universe is 93 billion light years or 28 billion parsecs across in diameter. Every second, the universe expands by 2 trillion kilometers in diameter every second, or 20 million times the speed of light. The matter at one end of the universe moves away from the matter at the other end with the same speed.
Mainstream physicists argue to this that it is not the matter in the universe which is expanding, but rather its space. But be it through the three dimensions we know or through some esoteric "fourth dimension," this expansion of space is in itself a kind of movement, albeit the movement of space. This is, again, nothing but another interpretation of the same thing; but an interpretation which is so abstruse that is hard to find arguments against it. Again, however, matter is moved faster than the speed of light; that is to say, the distance between them grows at a speed faster than light could cover it.
Physicists keep finding new ways of formulating "movement" to mask faster-than-light phenomena. All right, so let's call "movement" "the expansion of space between two objects." In that case, in accordance with this new formulation let me likewise reformulate my question! Is it possible to expand or shrink the space between two objects so that the objects move towards or away from each other faster than light would?
That the observable universe is able to increase the space between its ends faster than light does seem to give us hope that we might ourselves find ways to expand the space between masses faster than light could pass the same space.
Actually, there are plenty of physicists, including Feynman, Dirac, and, earlier mentioned, Tom van Flandern, who did not give credence to the theory that gravity is caused by the curvature of space-time, believing it to be a force of nature just like any other. Either how, it is quite clear that, in whatever way, the space between two objects can expand faster than the speed of light, and it is happening every second. How one interprets this changes little about the fact.
7) Quantum tunneling:
Perhaps the most significant FTL experiment aside from Wang's gain-assisted superluminality was conducted in Köln. Unlike Wang, Mintz was less timid about the results of his experiments, but like Wang's, Mintz' research has not gotten as much credit as it deserved.
Critics found it more difficult to find arguments against Mintz' research, mostly because the experiment was so simple that it was hard to make it seem complicated: the setup of the experiment consisted of an amplifier, a 20 centimeter long tube, and Mozart's 40th symphony in the form of microwaves.
This experiment used quantum tunneling, which is manifested in the earlier mentioned virtual particles, in this case virtual photons. This proves that, despite claims of the opposite, virtual photons can effectively be used as a means of faster-than-light communication.
Quantum tunnelling is a phenomenon in which a particle can spontaneously pass a finite potential barrier in the form of a virtual photon, which is then reconverted into a standard particle. Mintz wave transducer made use of the Hartman effect, the effect that, if a barrier is thick enough, the tunneling time (the time it takes for a particle to get past the barrier through quantum tunneling) becomes independent of the thickness of the barrier and inclines towards a constant value.
The tube, which was called a wave transducer. The wave transducer, which was about 11 centimeters wide, was far too small for microwaves, which start at a wavelength of 30 centimeters, so that normally, they would net be able to get through. Virtual photons, however, could get past the wave transducer through quantum tunneling. On the other side, the tunneled photons went through an amplifier, which then played Mozart; not at very high quality, but enough to be recognizable as Mozart's 40th symphony. In this way, the symphony had been transmitted at 4,7 times the speed of light.
It is often argued that while the group velocity (the speed of the whole of the wave, which may change in dimensions) may exceed the speed of light, the front velocity (the speed of the front of the wave) always remains the same. There are, indeed, phenomena in which some kinds of wave velocities (be it phase velocity, group velocity, energy velocity or signal velocity) are superluminal yet the front velocity remains unchanged, such as negative refractions and atomic coherence effects, but when the wave is observed to have arrived at its destination before light in vacuum would normally have done so, surely this argument is no longer satisfactory. If the wave as a whole has reached at superluminal speed, then obviously so has its front, in violation with Special Relativity.
There have been so many observed FTL phenomena, and many more will follow in future, that we can no longer ignore them. Sooner or later, modern physics will be forced to review its principles, at least insofar as to nuance them. Again, natural laws tend to have exceptions.
19:25 Posted in Futurism, Philosophy, Science | Permalink | Comments (2) | Email this | Tags: physics, relativity, special relativity, quantum physics, quantum mechanics, general relativity, paradigm, paradigm shift, faster-than-light, superluminal
Black Hole Energy
Micro black holes, when no mass is added to them, usually evaporate instantly in the form of Hawking radiation. Since all their energy is converted into photons in this process, creating micro black holes might be a potential source of energy in future. Such energy source would be even more effective than antimatter, since half the converted energy in matter-antimatter reactions is lost in the form of neutrinos.
12:41 Posted in Futurism, Science, Technology | Permalink | Comments (0) | Email this | Tags: black holes, quantum mechanics, hawking radiation, physics, energy, energy source, renewable energy
Particle bundles
Quantum waves are perhaps much like macroscopic bundles of light. These bundles of particles can be at two places at the same time depending on how broad they are. A first pulse in the bundle of particles would leave a gap, which would then be filled in by a second pulse and so on, causing a wave function to arise.
After some research, it turned out I am not quite alone in this position, and a minority of physicists has espoused a similar or identical position known as the Bohm interpretation, rejecting the Copenhagen interpretation of quantum mechanics. Is is also known as the De Broglie-Bohm theory or, originally, as the pilot wave theory.
According to this theory, particles seem to behave like waves because they move together in a wave function, somewhat like air atoms in sound waves. To the critical mind, this theory divests one from a burden of confusion brought about by the Copenhagen interpretation, be it rightly or no. It appears to solve many of its paradoxes, such as indeterminism, acausality and unlocality, that to the intuition are simply unacceptable.
00:32 Posted in Science | Permalink | Comments (0) | Email this | Tags: quantum mechanics, bohm interpretation, wave function, physics, de broglie-bohm theory, pilot wave, pilot wave theory
10/13/2008
Optical battery
Scientists have created a perfect mirror made from layers of dielectrics which, at certain angles, can reflect light without loss of energy (source), for use in optical fibres. Maybe such perfect mirrors could be used for the storage of energy in the form of light, for instance in cyclical optical fibres, so that these could be used to produce optical batteries. This light would preferably of high wavelength, which is colder, as an optical battery would melt or burn if it contained too much light. How much energy could be stored in optical batteries remains an open question, but the concept is, either how, fascinating that we could catch light and put it in a battery.
21:07 Posted in Futurism, Technology | Permalink | Comments (0) | Email this | Tags: optics, physics
06/16/2008
Dimensionless Heat Capacity
Below we come to a number of formulae which relate dimensionless heat capacity to heat in a striking way, showing, notably, that pressure times volume is a constant fraction of heat.
The formula of specific heat capacity is
c = Q/mT
According to the ideal gas law, Q = NkT on a microscopic level, so that
c = Nk/m = k/M
(where M is mass per molecule).
Q = cmT
Now, according to the ideal gas law,
PV = nRT
⇔ T = PV/nR
If we substitute this, we get:
Q = cmPV/nR
As m = nM,
Q = cMPV/R
⇔ PV = Q · (R/cM)
Now, heat capacity is the ability of a substance to store heat with increase of temperature. It is equal to the product of mass and specific heat capacity (the heated needed to heat a kilogram of a substance by one kelvin):
C = cm,
and, according to the heat equation,
Q = cmT,
so that this is equal to
C = Q/T
Now, the dimensionless heat capacity of a substance is equal to its heat capacity divided by the number of moles times the universal gas constant:
C* = C/nR,
the inverse of which is:
1/C* =nR/C
Now, the number of moles equals the total mass divided by the mass of one mole. Substituting m/M in n, we get:
1/C* =mR/MC,
and, as said, C = cm, so that
1/C* = R/cM.
Substituting this in the formula we got earlier, ideally:
PV = Q · (R/cM)
we get:
PV = Q/C*,
This formula may be useful because it relates heat, pressure and volume, showing that pressure times volume is a constant fraction of heat.
Now, according to kinetic theory,
P = ⅓ρv^2
⇔ PV = ⅓mv^2
⇔ PV = ⅔Ek
Thus,
⅔C*Ek = Q
This formula succinctly relates heat to kinetic energy. Note that kinetic energy equals work divided by two, so that
⅓C*W = Q
Also, according to the Dulong-Petit law, any crystal has a dimensionless heat capacity of 3, so that
2Ek = Q
⇔ W = Q
This means that, for any crystal, the heat of a crystal is the total work it may perform. This means that its internal energy twice its heat:
U = W+Q = 2Q = 2W
15:08 Posted in Science | Permalink | Comments (0) | Email this | Tags: thermodynamics, physics, chemistry, heat, kinetic theory, ideal gas law
Distributivity
On the influence of the distribution of charges on the total strength of the forces mediated between them:
Distributivity.rtf
This is of immense importance to the cohesion of all matter. The formula included may be useful someday in foglet technology because foglets would adhere to one another through magnetism, to calculate the required charge to keep their total mass together with a specified strength.
14:09 Posted in Science | Permalink | Comments (0) | Email this | Tags: physics, material science, charge, law of coulomb, electromagnetism, magnetism, electricity
04/28/2008
The Infinity Principle
If either the age, size, energy or complexity of the universe are infinite, so are the others: if the universe is infinite in age, it must be infinite in size because a finite universe would keep expanding, ergo in energy, because it would otherwise be of infinitely low density due to this expansion, ergo in complexity because this energy would be distributed amongst the universe rather than remaining infinitely accumulated.
If the universe is infinite in size, it must be infinite in age because if it had a starting point it would originate from a singularity rather than popping into existence in infinite dimensions, and infinite in energy and complexity because it would otherwise be of infinitely low density as formerly said.
If the universe is infinite in energy, it must be infinite in age because in order to become of finite density it'd otherwise have to expand with infinite speed (this is the most plausible other possibility, as the absolute speed of light might not be absolute), infinite in size for the same reason, and infinite in complexity because of its infinite size.
Infinite complexity basically equals infinite size because size is relative. If the universe is infinite up or down, it makes little difference. Suppose the universe was contained inside a giant atom (which would have an infinitely complex substructure, so that this would be possible!), we'd still say the universe is tens of billions of light years in diameter instead of one and a half femtometer. Relative to an infinitely small world (at an infinitely complex level), everything is infinitely large. As we've said, infinite size and finite density means infinite energy. However, if the universe is infinite in complexity this does not necessarily mean that it is infinite in age.
Thus, we conclude that either:
1) the age, size, energy and complexity of the universe are all infinite,
2) neither the age, size, energy or complexity of the universe are infinite
3) the size, energy and complexity, but not the age, of the universe are infinite, and the Theory of Relativity is incomplete.
You can scratch the latter two possibilities, however, if you can accept the following argument. Existence cannot have had an actual cause, because that cause would itself have to be part of existence, otherwise it could not have existed because it would then not be part of existence. Why would there be a beginning? Where did it come from? What caused it? Now, I'm talking about the whole of existence, not just our own reality, but any reality at all, including hypothetical realities in which our own universe was created. Unless there already existed "something" which had caused the universe to arise, ie there was already something in *existence* (in other words, in the universe), such cause would necessarily have been acausal, and for something to be science it must obey causality. Causality, then, is its own only exception. Everything has a cause, but the chain of causes and consequences itself hasn't.
Following this line of reasoning we conclude that the universe is infinite in age, size, energy and complexity. This also implies a universe of infinite complexity. In such a universe, there would be an infinite number of phenomena; each of these would in some way have to influence each other, as they would otherwise not form one whole. Whatever phenomenon would not influence the rest of the Universe would not really be part of it, and therefore not really exist as far as we are concerned. In this way, all phenomena would be infinitely connected to one another, that is to say, each phenomenon would be influenced, directly or indirectly, by infinitely many others. One of such phenomena is our own will, or consciousness, which would likewise be causally interlinked to all other phenomena, meaning that it as well could influence and therefore control them. Thus, in principle, if one would find one's way through this web of causal connections, one could, in principle, control any phenomenon in the universe, meaning that one could be omnipotent. This appears to follow logically if the universe is of infinite complexity.
18:00 Posted in Mathematics, Philosophy, Science | Permalink | Comments (0) | Email this | Tags: infinity, physics, logic, universe, cosmos
