Archive for the ‘Wave’ Category

WHY LIGHT & GRAVITATION GO AT SAME SPEED

November 2, 2017

As long as one does not have a simple explanation, and, or description, of a subject, one does not understand it fully.

The present essay presents a direct proof, found by me, from basic principles, that gravitational waves go at the speed of light.

The essay also presents the direct experimental proof of the same fact that we got a few days ago, when the explosion of a “kilonova” was observed (kilonovae are very rare, but crucial in the apparition of life as we know it, details below).

A consequence of the preceding is that the MOND theories are false. MOND was a philosophical horror, something full of ad hoc hypotheses, so I am happy it’s out of the window. MOND eschewed the simplest description of gravity, the basics of which, the 1/d^2 law preceded the birth of Newton himself.   

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First things first: WHY GRAVITATIONAL WAVES?

When two sources of a field of type 1/d2 (such as gravitation or electromagnetism) rotate around each other, they generate waves which go to infinity (even if I don’t believe in infinity, as an absolute, it works fine as a figure of speech…)  

That’s simply because the field changes, as sometimes the charges are aligned, sometimes sideways. As the field changes it moves the objects it acts on. Now the point is that this disturbance of the field propagates indefinitely.

At this point, a philosophical question may arise: do the disturbances of the field carry away energy? Well, in a way, it’s an idiotic question, because we know it does, that’s an experimental fact.

This experimental fact shows fields are real.

Now, let’s slow down a bit: one century of experimentation with electromagnetic fields had shown, by 1900 CE, that, electromagnetic fields carried away energy.

What about gravitation? Well,  theories were made in which a waving gravitational field carried away energy, such as Poincaré’s theories of gravitation, and, in particular, Einstein’s.

The experimental proof came when closely rotating stars, which should have been emitting copious amounts of gravitational field energy, were observed to lose energy just as predicted. But first the theory:

Orbiting Masses Generate Gravitational Waves (on top). If the gravitational waves were left behind the light, many references frames would observe non-conservation of energy after a collision event (bottom) between aforesaid masses. This is my thought experiment, and it’s also what happened 130 million years ago in a galaxy not that far away.

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HERE IS WHY GRAVITATIONAL WAVES GO AS FAST AS LIGHT WAVES:

Patrice Thought Experiment Demonstrating Gravitation & Electromagnetic Waves Go At the Same Speed:

So now visualize this. Say, to simplify, that two equal masses rotate around each other. Call them M1 and M2. Say M1 is matter, and M2 antimatter, each of mass m The system M1-M2, emits more and more gravitational energy as the two masses approach each other. Finally they collide. At this point, the system M1-M2 becomes pure electromagnetic radiation, of energy E = 2 (mc^2).

Now what does one see at a distance?

Suppose the electromagnetic energy E going at the speed of light, c, travelled faster than the gravitational wave of energy G, travelling at speed g.

Then suppose also one is in a reference frame R travelling at uniform speed V, away from the M1-M2 collision event. As g is less than c, V can be more than g.

And then what?

The gravitational wave of energy G going at speed g, CANNOT catch up with the reference frame R.

However, before the collision, some of the energy of the system was inside G. And it’s easy to compute how much: it’s equal to the potential energy of the rotating system before the collision. In the scenario we constructed, that energy is never seen again, from the point of view of R. Let me repeat slowly: before the collision, M1  and M2 can be seen, orbiting each other. The potential energy of the system P, can be computed, using this VISUAL information (visual, hence travelling at the speed of light, c). So then the energy of the system is 2Mc^2 + P.

All of P is transformed into G, the energy of the gravitational wave. If the speed g of the wave is less than the speed of light, c, there are reference frames, namely those with V > g, where P will be seen to have disappear.

Thus if the speed of gravitational waves was less than the speed of light, there would be frames in which one could observe distant events where energy would not be conserved. 

Now let’s make it realistic.  The preceding situation is not just possible, but common:

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Closely Orbiting Annihilating Stars Were Just Observed:

Instead of making the preceding M2 out of antimatter, one can simply make M1 and M2 into neutron stars. That’s exactly what happened 130 million years ago, when dinosaurs roamed the Earth, in a galaxy far away—NGC 4993, to be exact—two neutron stars spiraled into each other, from emitting gravitational radiation, and emitting more, the more they spiraled (the waves got converted in sound). The stars then went into a frantic dance, and collided.

Had this happened inside our own Milky Way, the present gravitational waves detectors the U.S.-built LIGO and European-built Virgo observatories, would have detected the gravitational waves for minutes, or maybe hours. But the gravitational waves we got were diluted by a factor of 10^10 (!) relative to what they would have been if the collision had been just 10,000 light years away, inside the Milky Way.

After billions of years spent slowly circling each other, in their last moments the two neutron-degenerate stars spiraled around each other thousands of times in a frenzy before finally smashing together at a significant fraction of light-speed, likely creating a black hole (typically neutron stars are remnants of sun like stars, two of those packed in a small volume makes a black hole).

Such an event is called a “kilonova” (because it has the energy of 1,000 novas). Kilonovae are rare cosmic events, once every 10,000 years in a giant galaxy like the Milky Way. That’s because neutron stars are produced by supernovae. To boot, supernovae explode asymmetrically, giving hefty “kick” to those remnants, strong enough to eject a neutron star entirely from its galaxy (the Crab Nebula remnant goes at 375 km/s relative to the explosion nebula.

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Exit MOND:

MOND, or MOdified Newton Dynamics is a somewhat ridiculous class of theories invented in the last few decades to deny the existence of DARK MATTER. Instead, the MOND monkeys devised an ad hoc theory, which basically claim that gravity is stronger at low speeds (whatever), as was more or less observed (sort of) inside galaxies (didn’t work so good, or not at all, for clusters).

You see, gravitation basic behavior is simple. Kepler thought it was an attractive force in 1/d. However Bullialdus suggested the law was 1/d2 in analogy with the behavior of… light (however Bullialdus didn’t understand that, in combination with Buridan’s mechanics from 1350 CE, one could explain Kepler’s laws; but Hooke and then Newton did)

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The collision of the two neutrons stars, and the black hole they created, also emitted electromagnetic radiation. That light comes from the fact materials fall at enormous speeds. Thus both gravitational waves and electromagnetic waves were captured from a single source. The first light from the merger was a brief, brilliant burst of gamma rays, the birth scream of the black hole. The gamma ray flash was picked up by NASA’s Fermi Gamma-Ray Space Telescope, 1.7 second after the arrival of the gravitational waves (dust would have delayed the light a bit at the onset, but not the gravitational waves). Hours later astronomers using ground-based telescopes detected more light from the merger, the “kilonova” produced by the expansion of debris. The kilonova faded from view over the following weeks.

As expected, astronomers saw in the aftermath various wavelengths of corresponding to the many heavy elements formed instantly during the collision (it was an old prediction that merging neutron stars would form the heaviest elements such as gold and titanium, neutron-rich metals that are not known to form in (normal) stars.

(Caveat: I hold that star theory is incomplete for super hyper giant stars with hundreds of solar masses, and a very reduced lifetime; that has been one of my argument against standard Big bang theory.) But let’s go back to my thought experiment. What about the other aspect I envisioned, being on a frame R travelling at a very large speed?It’s very realistic, actually for its other aspect, frames moving at near light speed.

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Frames Travelling At Close To Speed Of Light Are Common:

… Not jut a figment of my imagination. That’s also very realistic: as one approaches the event-horizon, entire galaxies recess ever closer to the speed of light, here is the V I was talking about above.   

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Simple science is deep science

All treaties on Gravitation tend to be the same: hundreds of pages of computation, and one wrong equation could well sink the ship (Quantum Field Theory is worse, as few fundamental hypotheses therein make any sense. Hence the famous prediction from QFT that the energy of the vacuum should be 10120 greater than observed…)

I believe instead in a modular approach: from incontrovertible facts, quick reasonings give striking conclusions. This makes science logically compartmentalized, avoiding thus that any subfield of science follow the Titanic down the abyss, from a single breach. It also make science easier to teach, and even easier to think about. For example the reality of Quantum Waves comes not just from all sorts of variants of the 2-slit experiments, but also from the Casimir Effect, a direct evidence for the reality of Quantum waves in empty space, which is observed so much that it has to be taken into account in the engineering of any nano-machinery (I also suggested a device to extract energy from this “vacuum”).

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Conclusion: Just from the necessity of apparent conservation of energy in all inertial frames, rather simple physics show that the speed of gravitational waves has to be exactly the speed of light. No need for hundreds of pages of obscure computations and devious logics. No need even for Relativity, just basic kinematics from 1800 CE.

Patrice Ayme’

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Not An Infinity Of Angels On Pinheads

July 1, 2016

Thomas Aquinas and other ludicrous pseudo-philosophers (in contradistinction with real philosophers such as Abelard) used to ponder questions about angels, such as whether they can interpenetrate (as bosons do).

Are today’s mathematicians just as ridiculous? The assumption of infinity has been “proven” by the simplest reasoning ever: if n is the largest number, clearly, (n+1) is larger. I have long disagreed with that hare-brained sort of certainty, and it’s not a matter of shooting the breeze. (My point of view has been spreading in recent years!) Just saying something exists, does not make it so (or then one would believe Hitler and Brexiters). If I say:”I am emperor of the galaxy known as the Milky Way!” that has a nice ring to it, but it does not make it so (too bad, that would be fun).

Given n symbols, each labelled by something, can one always find a new something to label (n+1) with? I say: no. Why? Because reality prevents it. Somebody (see below) objected that I confused “map” and “territory”. But I am a differential geometer, and the essential idea there, from the genius B. Riemann, is that maps allow to define “territory”:

Fundamental Idea Of Riemann: the Maps At the Bottom Are Differentiable

Fundamental Idea Of Riemann: the Maps At the Bottom Are Differentiable

The reason has to do with discoveries made between 1600 and 1923. Around 1600 Kepler tried to concretize that attraction of planets to the sun (with a 1/d law). Ishmael Boulliau (or Bullialdius) loved the eclipses (a top astronomer, a crater on the Moon is named after him). But Boulliau strongly disagreed with 1/d and gave a simple, but strong reasoning to explain it should be 1/dd, the famous inverse square law.

Newton later (supposedly) established the equivalence between the 1/dd law and Kepler’s three laws of orbital motion, thus demonstrating the former (there is some controversy as whether Newton fully demonstrated that he could assume planets were point-masses, what’s now known as Gauss’ law).

I insist upon the 1/dd law, because we have no better (roll over Einstein…), on a small-scale.

Laplace (and some British thinker) pointed out in the late 18C that this 1/dd law implied Black Holes.

In 1900, Jules Henri Poincaré demonstrated that energy had inertial mass. That’s the famous E = mcc.

So famous, it could only be attributed to a member of the superior Prussian race.

The third ingredient in the annihilation of infinity was De Broglie’s assertion that to every particle a wave should be associated. The simple fact that, in some sense a particle was a wave (or “wave-packet”), made the particle delocalized, thus attached to a neighborhood, not a point. At this point, points exited reality.

Moreover, the frequency of the wave is given by its momentum-energy, said De Broglie (and that was promptly demonstrated in various ways). That latter fact prevents to make a particle too much into a point. Because, to have short wave, it needs a high frequency, thus a high energy, and if that’s high enough, it becomes a Black Hole, and, even worse a Whole Hole (gravity falls out of sight, physics implodes).

To a variant of the preceding, in: Solution: ‘Is Infinity Real?’  Pradeep Mutalik says:

July 1, 2016 at 12:31 pm

@Patrice Ayme: It seems that you are making the exact same conflation of “the map” and “the territory” that I’ve recommended should be avoided. There is no such thing as the largest number in our conceptual model of numbers, but there is at any given point, a limit on the number of particles in the physical universe. If tomorrow we find that each fermion consists of a million vibrating strings, we can easily accommodate the new limit because of the flexible conceptual structure provided by the infinite assumption in our mathematics.

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I know very well the difference between “maps” and territory: all of post-Riemann mathematics rests on it: abstract manifolds (the “territories”) are defined by “maps Fi” (such that, Fi composed with Fj is itself a differential map from an open set in Rx…xR to another, the number of Real lines R being the dimension… Instead of arrogantly pointing out that I have all the angles covered, I replied:

Dear Pradeep Mutalik:

Thanks for the answer. What limits the number of particles in a (small enough) neighborhood is density: if mass-energy density gets too high, according to (generally admitted) gravity theory, not even a graviton could come out (that’s even worse than having a Black Hole!)

According to Quantum Theory, to each particle is associated a wave, itself computed from, and expressing, the momentum-energy of said particle.

Each neighborhood could be of (barely more than) Planck radius. Tessellate the entire visible universe this way. If too each distinct wave one attaches an integer, it is clear that one will run out of waves, at some point, to label integers with. My view does not depend upon strings, super or not: I just incorporated the simplest model of strings.

Another mathematician just told me: ‘Ah, but the idea of infinity is like that of God’. Well, right. Precisely the point. Mathematics, ultimately, is abstract physics. We don’t need god in physics, as Laplace pointed out to Napoleon (“Sire, je n’ai pas besoin de cette hypothese”). (I know well that Plato and his elite, tyrant friendly friends and students replied to all of this, that they were not of this world, a view known as “Platonism”, generally embraced by mathematicians, especially if they are from plutocratic Harvard University… And I also know why this sort of self-serving, ludicrous opinion, similar to those of so-called “Saint” Thomas, a friend of the Inquisition, and various variants of Satanism, have been widely advocated for those who call for self-respect for their class of haughty persons…) 

The presence of God, aka infinity, in mathematics, is not innocuous. Many mathematical brain teasers become easier, or solvable if one assumes only a largest number (this is also how computers compute, nota bene). Assuming infinity, aka God, has diverted mathematical innovation away from the real world (say fluid flow, plasma physics, nonlinear PDEs, nonlinear waves, etc.) and into questions akin to assuming that an infinity of angels can hold on a pinhead. Well, sorry, but modern physics has an answer: only a finite number.

Patrice Ayme’