Posts Tagged ‘GR’

Is All Motion Relative? No!

May 26, 2020

Some Motions Are Relative… Most Are Not.

Fundamental ideas can be simple, yet subtle. Take the “Higgs” Field idea. Dirac’s simple first order PDE for the electron (QED, Quantum ElectroDynamic) had to be modified to incorporate the “weak” nuclear force. But that worked with massless particles. Yet, particles had mass. What to do? The solution was to make the equations even more complicated by introducing a “Higgs” field, which, once it is non-zero on average, can give the electron a mass by interacting with the electron field without messing up the workings of the “electroweak” force. Basically the interaction with the Higgs Field acts like a glue, giving an inertial mass.

Complications on top of complications… Not necessarily a bad thing: after all we got away from the magical world by introducing extremely complex explanations elaborating from a few concepts, sort of all biology from DNA and RNA… A danger, though, is to start from erroneous concepts. As Henri Poincaré put it:

C’est même des hypothèses simples qu’il faut le plus se défier, parce que ce sont celles qui ont le plus de chances de passer inaperçues.

 

  • It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

 

    • Thermodynamique: Leçons professées pendant le premier semestre 1888–1889 (1892), Preface

The principle of relativity, first proposed by Galileo, was stated thus by Newton:

“The motions of bodies included in a given space are

the same among themselves, whether that space is at

rest or moving uniformly forward in a straight line.”

That says nothing about how to define “uniform”, except circularly. Nor does it says all inertial frames are equivalent, just that they “are the same among themselves”…

Quantum Vacuum Fields Radiate Under Acceleration (Un. Chicago 2019 picture).

A great progress attributed to Einstein was the disappearance of any absolute motion. The irony, hidden to the profane, was that Einstein set on developing General Relativity (GR) precisely to explain the “Mach Principle” that he was obsessed with… That thing of Mach was actually discovered by Newton. Put water in a pail hanging from a rope, said Isaac. Twist the rope slowly, rotation after rotation. Release. Pail starts to rotate, water climbs on the side of the pail. Why a rotation relative to the fixed stars would have such an effect is a mystery (Mach observed, Einstein tried to elucidate with GR).  

So the idea of GR, as far as Einstein was concerned, was to find a mechanism to explain absolute motion! Indeed the standard Lambda Cold Dark Matter (LCDM) Big Bang model defines, de facto, an absolute state of motion… the one relative to which the Cosmic Background Radiation looks isotropic… Except, oops, it’s not (latest news).

***

But let’s go back to Relativity. It was named thus by Henri Poincaré, and rested on the notion of LOCAL TIME. In Fast Moving frames, time runs slow. That immediately led to the so-called “Twin Paradox” launched by Paul Langevin in 1911 (Einstein had mentioned the slowing of the moving clock in his 1905 paper). Langevin describes the story of a traveler making a trip at a Lorentz factor of γ = 100 (99.995% the speed of light). The traveler remains in a projectile for one year of his time, and then reverses direction. Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth. Langevin attributed the effect to ABSOLUTE acceleration (that’s reproduced by Richard Feynman, in his Lectures on Physics, but it’s not correct, I feel).

However, looking at the math more carefully, what really matters is how long the world-lines are, not how bent they are. The bending (acceleration) enables the length. The length referred to here is the Lorentz-invariant length or “proper time interval” of a trajectory which corresponds to the elapsed time measured by a clock following that trajectory. Basically the fast frame exchanges time for space: it covers lots of space, thus leaving little energy to spend on time: one can literally see the effect by looking at light wiggling back and forth between two mirrors. If the two mirror assembly goes fast, the wiggling is slow.

A related question is mass (like in “proper mass”). I have argued that it is time which slows down, not mass which goes up (as some texts have it, erroneously). Related to this is the Force-Acceleration law which involves now a (gamma)^3 factor… from multiple divisions by slow infinitesimal time…

All of this will leave some scratching their heads. Am I saying there is a notion of absolute motion? Well, the evidence is overwhelming. It’s time to remember the philosophy of  Henri Poincaré: if it looks like a duck in all ways, it’s a duck. Poincaré was actually saying that if all experiments give a speed of light equal to c then the speed of light c is a constant of nature (ironically, that’s true only locally… that is “infinitesimally”. In GR the speed of light is all over the space and, although locally constant, certainly not nonlocally constant… you see physics can be more subtle than basic logic…)

A notion not usually considered is that any manifold, or pseudomanifold, of dimension n can be embedded in manifold or pseudo manifold, of dimension (2n+1)… If one applies that to the curved spacetime of the LCDM, one gets an absolute reference frame… As de facto observed: the tapestry of galactic clusters is pretty much static…

***

Where am I drifting with these pseudo-idle considerations? Well, I am reinstating in catimini the honorability of space and time absolutism… Comrade Poincaré, a colossal topologist, seems to have been aware of much of this… but he died at 58 in 1912, before GR was finished (Henri had introduced gravitational waves in 1905), and long before De Broglie came up with his ubiquitous Matter Waves. Matter Waves necessitate derivation relative to time… Which local time is that? Differently from Relativity, which starts with a non-accelerated frame, the class of uniformly moving ones, Quantum Physics is indifferent: any time will do. How could that be? Accelerated time is slow time, says General Relativity (this is actually an independent, most simple piece, a building block of GR, which doesn’t require the full theory). Quantum Physics doesn’t care about time as defined by light. It differentiates as if there was one and only one time, as In Newton’s time.

Why? An obvious explanation could be that the architecture of Quantum Physics implicates a much higher speed, the collapse/entanglement/Quantum Interaction speed…  In any case, to go from our class of uniformly moving frames to any others implicates Quantum fireworks, as pictured above… No uniformities are accessible, but for the one we enjoy…

Patrice Ayme


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