## Posts Tagged ‘Momentum’

### Relativistic MASS FROM TIME Dilation

March 25, 2016

[Original research to make physics understandable to We The People.]

A reason for the stall of theoretical physics in the last 40 years? Physicists have not enough intuitive understanding of physics (in particular, of what is important in physics). The phenomenon affects both Relativity and Quantum Physics. Both Twentieth Century fields are more philosophically subtle than vulgar physicists think. One needs more context than the usual credo has it.

Here is my intuitive proof of the famous relativistic mass formula. It explains intuitively an observation made late in the Nineteenth Century (19C): when particles are accelerated, they augment in mass, rather than speed.

Buridan contemplated “impetus”, which we now call “momentum” = MV. When A Force Is Applied Indefinitely, V, The Speed, Stalls, While M Keeps On Augmenting.

I reveal that: The basic reason for the augmentation of “relativistic mass” is that FORCE GETS DILUTED BY LOCAL TIME… DILUTION. (This apparent play on words reflects exactly what’s going on!)

The fundamental fact of The Theory of Relativity is TIME DILATION. Time Dilation says that, when something moves fast, time there runs slows. Time Dilation is shocking to those who do not understand where it comes from (I will treat it in another essay). Time Dilation in a moving frame is not an axiom in physics, because it can be easily demonstrated theoretically, or experimentally. It comes from the constancy of the speed of light (locally, in any frame of reference).

Relativity compares physics in the frame at rest R, with physics in the moving frame, M. (So Relativity is relative, but not as relative that some physicists, in particular Einstein, have made it sound. See my future “Time Dilation”.) Say v is the speed of M relative to R (as usual, c denotes the speed of light).

Time in the moving M slows down relative to time in the resting R:

Time of M = (Time of R) [Square Root (1- vv/cc)]. This is Time Dilation.

Basics Theorems Of Relativity. Time Dilation (the middle one) Implies The Other Two. Time Dilation Is Itself A Theorem

The Local Time Equation (Middle) Implies Both the Local Length Contraction Equation, and the “Relativistic Mass: Equation

What is a force? Anything which changes momentum. Say the force F consists into a flow of particles (a bit like quanta, in a way). Let’s call it the STRAFING. The particles have all equal mass, and the same momentum, they arrive at equal intervals, and they travel perpendicularly to the trajectory of the mass m.

If m was standing still, at rest in R (the “rest reference frame”), F would progressively accelerate m (BURIDAN law). Now suppose m is moving at rest in M, that is at v, relative to R. Now in M, time runs slow. This means that m gets hit a lot more by the STRAFING.

Because visualize this: the STRAFFING (= the application of the force F) is launched inside R, the “rest frame”. But it is received in M. So the frequency of hits in M is lower by [Square Root (1- vv/cc)]. That means the force on m, in M, is lower by that amount. In other words, m in M, viewed from R, behaves exactly as if its inertial mass was not m, but m/[Square Root (1 – vv/cc)] .   Here is my little theory in a drawing (the text below will explain the details):

Force Can Be Viewed As Transfer Of Momentum (“Impetus”) By Quanta. Clearly Then It Is Received Slowly Because Time Dilation

The application of force in the moving frame Is DILUTED by Time Dilation. So Inertial Mass appears larger by as much as Local time is dilated.

In the drawing above, I depicted the force as applied transversally. But it could be applied from any direction: the transmission of momentum impulses would still be diluted by slow local time. Also the assumption that momentum would be quantified is no different from, say the Riemann Integral in mathematical analysis: from F = d(mv)/dt, the Buridan equation (a generalization of Newton’s Second Law), one can view the integral of the action of F as the sum of these little impulses (understanding fully may require a familiarity with integral calculus).

Questions are welcome, and let’s recap: time runs slow in the moving frame, so force applies slow. Thus mass appears huge. In the end, time dilation blocks completely the application of force F, so the particle never reaches the speed of light. The explanation is transparent, from first principles.

It could be presented in a cartoon for primary school children, and be understood, the way all fundamental physics should be.

Patrice Ayme’

### BURIDAN: MOMENTUM, FORCE, INERTIA, MIDDLE AGES…

March 20, 2016

Buridan was the real author of the so-called Copernican Revolution… Nearly Two Centuries Prior…

When did mechanics and calculus of the Seventeenth Century originate? Well, around 1350 CE, in Paris, thanks to the genius Buridan, and his many famous and influential students and followers throughout Europe. The first theorems of calculus (say the theorem of the mean) were demonstrated, by students of Buridan, such as bishop Oresme, in the Fourteenth Century, using geometric calculus (which Newton would expertly develop three centuries later).

WHAT’S MASS? It is not an easy question. An answer for inertial mass was given seven centuries ago. Astoundingly, it’s still the foundation of our most modern physics, the relationship between momentum and force. Let me explain. (And the thinker who suggested this, Buridan, used this new mechanics to suggest that the Earth turned around the Sun, and generally planets went into circular orbits; thanks to Catholic terror, most physicists, let alone the Plebs, have any inkling of this: religious terror works!)

Momentum, force, and inertial mass were defined from trajectory deviation, first. This, I will show below, is incredibly modern (the idea is found in Riemann ~ 1860 CE, as I explained within the text of “Quantum Trumps Spacetime”). This was all in Buridan’s work, in the Fourteenth Century (14C).  Jean Buridan postulated the notion of motive force, inventing a notion he named impetus… which is exactly momentum (= mv). Consider this, from Buridan’s Quaestiones super libros De generatione et corruptione Aristotelis:

When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle. The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time. Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomena agree with this one

In 14 C, In The Late Middle Ages, Buridan Defined Momentum And Force By Considering Deviation Of Particle Trajectory

Buridan writes an explicit formula:  impetus = weight x velocity. Just a word of the modernity of it all: the idea translates directly into defining force(s) with changes of distance between geodesics (in differential manifold theory). Also Buridan launches the vector theory of force (the impetus goes in the direction of the force imparted)… and the force of gravity. (Buridan identifies implicitly gravitational and inertial mass, another correct assumption.)

Buridan states that impetus = weight x velocity (modern momentum). All the predecessors of Buridan thought one needed a force to keep on moving, but Buridan did not. Famous predecessors such as Hibat Allah Abu’l-Barakat al-Baghdaadi, who modified Avicenna’s theory, which followed John Philoponus believed in inertia NOT. They all followed Aristotle, who believed all and any motion died away, if no force was applied. (Not to say no Muslim ever invented anything scientific: the Uzbek ibn-Musa al-Khowarizmi crucially put the finishing touch on the zero, which he partly got from India, in the Ninth Century.)

Buridan’s pupil Dominicus de Clavasio in his 1357 De Caelo, pointed out that this extended to gravity:

“When something moves a stone by violence, in addition to imposing on it an actual force, it impresses in it a certain impetus. In the same way gravity not only gives motion itself to a moving body, but also gives it a motive power and an impetus, …”.

Buridan knew celestial bodies were moving from inertia: “God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more…And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.”

By definition, inertial mass is what resists an applied force. The greater the resistance to a force, the greater the inertial mass of what it is applied to.

Buridan invented the tunnel thought experiment (and thus, the idea of thought experiments). If a tunnel were bored through the center of the Earth and a heavy body dropped into it, what would happen to it? Well, Buridan gave the correct answer, repeated as a good parrot by Galileo… nearly three centuries later:

Galileo Galilei expressed this fundamental principle of his dynamics in his 1632 Dialogo:

The heavy falling body acquires sufficient impetus [in falling from a given height] to carry it back to an equal height.

Buridan had many students: Buridan’s thought was pursued up by his pupil Albert of Saxony (1316–1390), by Poles such as John Cantius, and the Oxford Calculators Nicole Oresme pioneered the practice of demonstrating laws of motion in the form of graphs (equations weren’t available yet); some of these are now known as central and basic theorems of calculus (like the theorem of the mean, guessed in Oxford, proven by Oresme)

***

Buridan’s Revolution:

Buridan introduced p = mv, called it “impetus” and stated that it did not change if no force was applied. Thus Buridan buried the complete idiocy known as Aristotle’s physics. (That Aristotle could be a complete idiot at the mental retard level is philosophically, and historically capital, as Aristotle set in place the leadership system through celebrities, which we enjoy to this day).

Buridan’s Inertia Law is known as Newton’s First Law (because Buridan was from Paris, while Newton demonstrates the superiority of the English born three centuries later by attributing to him what Isaac did not discover).

More generally Newton asserted clearly his Second Law: dp/dt = F (where  F is the Force, by definition). It’s an axiom. (Weirdly the Second Law implies the First…)

***

Force = Deviation From Trajectory:

This is Buridan’s idea. It was taken over again by Bernhard Riemann, in the early 1860s (five centuries after Buridan’s death). In modern mathematical parlance, force is depicted by geodesic deviation. It’s this idea which is at the triple core of Einstein’s theory (with the idea that gravitation/spacetime is a field, and that it’s Newton’s theory, in first order).

So this is ultramodern: the idea got carried over in “Gauge Theories”, and, because there are several forces, there are many dimensions.

***

Thought Experiment Often Precedes Experiment:

Yesterday I bought a (2015) book by a (British academic) historian of science. In it, the honorably paid professional asserted modern science started with Tycho in 1572. Tycho, a Count set his student Kepler onto the refined study of the orbit of Mars. Both Tycho and Kepler were 5 star scientists (differently from, say Copernicus or Einstein, both of whom too little inclined to quote their sources). So they were, because, differently from, say, Obama, they had strong personalities. Great ideas come from great emotions. Tycho believed the Ancients had lied. And he was right, they had lied about the orbits of the planets: observations with the same instruments gave different results from the ones the Ancients had claimed.

The preceding shows that this trite notion is profoundly false; the scientific revolution was launched by Buridan and his students (among them Oresme, Albert of Saxony), contemporaries and predecessors (including Gerard de Bruxelles and the Oxford Calculators). Some of their work on basic kinematics, the exponential and the mean theorem of calculus was erroneously attributed to Galileo or Newton, centuries later.

To believe everything got invented around the seventeenth century is not to understand how the human mind works. Experience has to be preceded by thought-experiment (even Einstein understood that). Buridan and his contemporaries did the preliminary thinking (while others were making clocks and hydraulic presses). All of this would become immensely easier after the invention of algebra and Descartes’ analytic geometry, true.

So let’s have a loving and admirative thought for Buridan, the main author of the scientific revolution, whose reputation, and WISDOM was destroyed by the (TERRORIST) CATHOLIC STATE: Buridan’s astronomical reputation was destroyed by the Catho-fascists, more than a century after his death. That’s why the heliocentric system is attributed to an abbot from a rich family (Copernicus), instead of the master physicist said abbot was forced to read as a student.

Studying the history of science, and mathematics uncovers the fundamental axioms, in the natural order given by their obviousness.

Determining which ideas came first, and why is not about determining who is the brightest child, or most impressive bully in the courtyard. In 1907, Einstein made a big deal that he, Albert, was the discoverer of Energy = Mass (“E = mcc”). A careful inspection shows that this either reflects dishonesty, or misunderstanding on his part. Or both. I will address this soon, as I keep on studying mass and momentum.

Buridan put momentum at the core of physics, and thought-measured if dynamically. Momentum is still at the core: photons have momentum, but not mass.

It’s important to realize that many of the latest ideas in physics (all of “Gauge Theories”)  rest on an idea invented in Paris seven centuries ago. Not to slight it, or to heap contempt on all the noble Nobels. But, surely, the time has come for really new ideas!

Patrice Ayme’

### NON-LOCALITY

December 28, 2014

Non-Locality, acting at a distance, without intermediaries, is the stuff of legends in tales for little children. A sorcerer does something somewhere, and something happens, or is felt, somewhere else. Newton himself rejected it. Isaac said the gravitation theory which he had helped to elaborate, was “absurd”, precisely because of it implicitly used “act upon another at a distance”:

“It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.—Isaac Newton, Letters to Bentley, 1692/3.

Du Châtelet Discovered Energy, Infrared Radiation, Correcting Newton On His Confusion Of Momentum (Buridan) and Energy, Which She Established

[Yes, one of civilization’s most important physicists and thinkers was a woman; but don’t ask the French, they never heard of her… because she was a woman.]

However Émilie Du Châtelet pointed out that: “…hypotheses eventually become truths for us if their probability increases to such a point that this probability can morally pass for certainty…. In contrast, an hypothesis becomes improbable in proportion to the number of circumstances found for which the hypothesis does not give a reason. And finally, it becomes false when it is found to contradict a well-established observation.” (Du Châtelet’s Lectures on Physics, 1740. Notice the subtlety of the thinking.)

Every Quantum process contradicts Locality, thus, Émilie Du Châtelet would say, Locality is a false hypothesis.

Gravitation got better described (not much) by making gravitation into a field propagating at the speed of light. It is not a trivial modification: it immediately predicts gravitational waves. If two huge star like objects (such as pulsars) rotate around each other, they should generate such waves, they should carry energy away, and those two objects ought to fall towards each other at a predictable rate. Said rate is indeed observed, thus Einstein’s gravitational equation (obtained by talking a lot with others, such as Hilbert, Grasso, etc.) seems correct.

Einstein’s main motivation for his theory of “General Relativity” was that he wanted to explain inertia (why fast rotating planets develop a bulge at the equator, or more generally an acceleration VV/r). That worry, called Mach’s Principle, actually originated 100% with Newton. Newton put water in a pail, twisted and twisted and twisted a rope from which the pail was suspended, and let go: the pail rotated faster and faster, and the water inside crawled up.

Einstein basic wishful logic was that: gravitation = inertia (he called that the “Principle of Equivalence”). So, by making a theory of gravitation, Einstein would make one of inertia, and become a giant among giants (of Du Châtelet’s caliber, say).

Silly. Silly idea, doomed to fail.

Why silly? Once gravitation was made into a field, Einstein and company made it into curvature in a manifold (called “spacetime”; the basic idea was elaborated by genius Riemann, two generations earlier, although implicitly attributed to Einstein by the ignorant ones).

So gravitation is locally determined: once at a point A, gravitation, that is, curvature of spacetime, is determined in a(ny) neighborhood of A (call it N).

The distant stars do not influence N much, if at all. Yet, inertia is clearly determined by the distant galactic clusters.  Einstein could not understand this.

But now physicists understand better Einstein was deluded, and (Soviet physicist) Fock’s critique that Einstein’s General Relativity is just a theory of gravitation is universally (albeit silently) accepted.

So let me repeat slowly, as I suspect many readers will not understand this either: inertia, as far as present day physics can see, is a Non-Local effect. Inertia has been Non-Local, ever since Buridan discovered it, seven centuries ago (1320 CE; time flies!)

Einstein completely failed at understanding inertia. Einstein even failed to realize that it was a Non-Local effect, although that is completely obvious. So he came out obsessed by Non-Locality, while being angry at it (so he was open to the Non-Local objection of philosopher-physicist Sir Karl Popper! Hence the EPR paper, more or less lifted from Popper.)

All this to say that I am not shocked by Non-Locality: I just have to go out, and look at the stars, move about, and I see Non-Locality.

Many, if not most physicists are horrified by Non-Locality.

Philosophically, though, being afraid of Non-Locality makes no sense. Once I was broaching Quantum Physics with my dad. I explained what I understood of the problem of Non-Locality to him.

My dad did not know much physics, but he was a scientist. Admitted to the famed ENA (the school of conspirators from which the present leaders of France come from), he declined it, and, instead, following the path of his own father, an amateur-professional geologist, he himself became a (highly successful) non-academic geologist (he discovered Algeria’s fortune).

My Dad said: ”Non-Locality is obvious. To think things would get ever smaller, just the same, made no sense.”

With this philosophical perspective, the following arise: physical space is not made of points (although Quantum Field Theory is, one of its many problems).

When physicists talk about Non-Locality, they feel the urge to get into the “Bell Inequality”. But it’s a convoluted, over-specialized, contrived way to get at Non-Locality (I say this, although I respect the late John Bell as much as I despise Feynman when he tried to steal Bell’s work… Although, in general I do respect and love Feynman, especially in light of his appreciation for my own ideas).

Bell theorem says that some Local Hidden Variable theories imply an Inequality that Quantum Physics violate. So Bell’s is a work which predicts that something false is not true.

My approach to Non-Locality is made for Primary School. It goes first through:

• The Uncertainty Principle:

Suppose you want to know where an object is. Suppose all you have is touch. So you kick it. However, if you kick it, it goes somewhere else. That’s the Uncertainty Principle.

Why touch? Because light is touch. It turns out that light carries energy and momentum. Anybody who lays in the sun will agree about the energy. To demonstrate the momentum of light requires a bit more experimental subtlety.

Could you kick the object gently? No. That’s where the Wave Principle kicks in. Waves ignore objects which are smaller than themselves: they just turn around them, as anybody who has seen a twenty meter tsunami wave enter a Japanese port will testify.

So, to detect a small object, one needs a small wavelength, high frequency wave. However the energy of a Quantum wave (at least a light wave) is proportional to its frequency.

So the more precise the determination of (position of) the object, the higher the frequency of the wave, the greater the energy and momentum conferred to the object, etc.

• Conservation of Momentum:

One has axioms, in physics, as in mathematics. Modern physics axioms include the conservation of energy and momentum. Newton knew of the latter, and confused it with the former. A French woman, Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet discovered (kinetic) energy (”force vive”). As she also discovered Infrared radiation, she obviously could have done more when she died from a fever, at age 43, after giving birth to her fourth child. (Her lover Voltaire, also a physicist quipped that:” Émilie du Châtelet was a great man whose only defect was to be a woman”)

Fundamental hypotheses in contemporary physics are conservation of energy and momentum (something the Multiverse violates, thus, into the bin of silly ideas).

• The Non-Local Interaction:

So say two particles, such as a positron-electron pair, are created together and have total momentum zero (a completely realistic situation: machines do this, for medicine).

Knowing the momentum of (say) the electron E, gives that of the positron P (the vector is exactly opposite to that of the electron). Classical and Quantum mechanics say the same.

So, without having disturbed P (it could be next to Beta Centauri, 4 light years away), we know its momentum. Should one measure it later, one will find it as said. (The latter experiment, retrospective checking of entanglement was actually accomplished by the Austrian Zeillinger and his team!)

However, the basic set-up of Quantum Physics says that the measurement create the state (my formulation, you will not read that in textbooks, although it’s clearly what Bohr wanted to say, but he did not dare, lest his academic reputation gets vilified: he had only a Nobel Prize in physics, after all…).

So the state of P, maybe a few light years away, was created by measuring E.

How come?

The basic Quantum set-up was designed for laboratory experiments, not Cosmological Quantum effects. So it did not need to consider all the consequences of this.

Following Du Châtelet, I will say that we are in obvious need of a new hypothesis, the QUANTUM INTERACTION (ex “Collapse of the Wave Packet”). It explains what we observe (instead of trying desperately to say that we cannot possible observe what we observe).

Following Newton, I will say it is absurd to suppose that the effect of E on P is instantaneous. So this Quantum Interaction goes at a speed I call TAU (it’s at least 10^10 the speed of light: 10,000,000,000 times c).

New physics coming to a Quantum Computer near you.

And of course , said new physics will have giant impacts on philosophy (be it only by presenting new models of how things may be done), or Free Will (is it really free if it takes its orders from Andromeda?). This is going to be fun.

Patrice Ayme’

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