Posts Tagged ‘Spacetime’

Relativistic Philosophy Beyond Consensus

August 4, 2017

It’s good to focus on “General Relativity” and Cosmology without the cloak of mathematics gone wild and unsupervised, indeed.

Anything having to do with “General Relativity” has a lot of extremely debatable philosophy hidden below a thick carpet of computations. Abuse of philosophically unsupervised spacetime leads one to believe in time machines, wormholes, and similar absurdities. A recent discovery such as Dark Energy (ever expanding space faster than previously anticipated), and a not so recent one, Dark Matter, show one has to be extremely careful.

Einstein equation of “General Relativity” (GR) is basically Curvature = Mass-Energy. Einstein long observed that the left hand side of the equation was built of mathematical beauty, and the right hand side of a murky mud of a mess. The discovery of Dark Matter proved him prophetic about that. (BTW, I know perfectly well that, stricto sensu, it’s the Ricci tensor, derived from the full Curvature tensor on the left…)

First a philosophical trap: “General Relativity” (GR) is a misnomer. It’s not clear what’s being generalized. GR is certainly a theory of the relationship between gravity and local space-times (the Theory of Relativity of space and time which Poincaré named that way in 1904).

Einstein was initially motivated to explain inertia according to the Newton-Mach observation that the distant stars seemed to endow matter with inertia (because if matter rotates relative to distant stars, a centrifugal force appears).

That way, he failed, as Kurt Goedel produced spacetime models which rotated wildly without local consequences. Frame dragging exists nevertheless, and is crucial to GPS. So GR has local consequences.

Neither Poincaré nor Einstein liked the concept of “spacetime”.

There are massive galaxy cluster, such as Abell 370 (shown here). They can be made up of thousands of Milky Way-sized galaxies. This is beyond anything we can presently have a feeling for. The space inside this cluster is not expanding, that’s a fact, but the space between this cluster and other, unbound, galaxies and clusters, is viewed by today’s Main Stream Cosmology, as expanding. I’m robustly skeptical. Image credit: NASA, ESA/Hubble, HST Frontier Fields.

A question has naturally come up: if space expands, how come we don’t? An answer to this has been the raisin bread model of the expanding universe.

As Sabine Hossenfelder, a theoretical physicist in Quantum Gravity and High energy physics  puts it: “In cosmology, too, it helps to first clarify what it is we measure. We don’t measure the size of space between galaxies — how would we do that? We measure the light that comes from distant galaxies. And it turns out to be systematically red-shifted regardless of where we look. A simple way to describe this — a space-time slicing that makes calculations and interpretations easy — is that space between the galaxies expands.”

However, the entire area is contentious. The usual snap-back of haughty physicist keen to deny any brains worth noticing to the Commons, is to say that all those who don’t understand the mathematics at hand should shut up.

That’s a disingenuous answer, as NOBODY understands fully the mathematics at hand (those with snappy rejoinders know this, but they enjoy their power maliciously).

An example of the non-universality of the notion of expanding space is the following exact quote from Physics Nobel Laureate Steven Weinberg, author, among many other things, such as the Weinberg-Salam model of the electroweak interaction, of the most famous textbook on the subject, “Gravitation and Cosmology”: “…how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better”

Well, they don’t.

Reference https://www.physicsforums.com/threads/raisin-bread-model-of-space-time.901290/

Personally, I think that both space and time are local concepts (as long as one does not add to consideration the Quantum theory, as it was created, post 1923, by De Broglie, and after 1924, by the Copenhagen School). Local space and local time are united by the speed of light, c, through naturally ubiquitous light clocks. Space and time are measured locally (although Poincaré proposed a slow motion to move synchronized clocks around, and Einstein copied and published that mechanism, verbatim, as he had with E = m c²).

It has been proposed that the redshift of cosmological photons, and its attribution, 100%, to the expansion of spacetime, is a proof of the expanding “spacetime”. One must say that this statement is the core of present cosmology. And anybody looking down on the idea will not be viewed as serious by famous physicists. However just saying something does not prove it. Especially when the conclusion seems to be the hypothesis.

Lorentz- Poincaré Local Space and Time theory was experimentally provable (electromagnetism proved it).

But where is the proof that the universe is like an expanding dough, spacetime, with galactic raisin grains in it? Just waving the notion that the atomic force is 10⁴⁰ the gravitation force at a small scale does not seem compelling to me. It’s rather a question of range: gravitation is much longer range, although, much weaker. Thus the geodesic deviations due to gravitation show up at a very great distance, whereas those due to atomic and molecular force cause enormous geodesic deviations, but only at very short range. We are these enormous local deviations, larger by 10⁴⁰ locally.

Yet, even this more precise argument smacks of hand waving.  Why? Because a theory of local forces as curvatures, although posited by Riemann in 1865, and the foundation of GR, still does not exist (that’s one thing string theory was trying to achieve, and failed). Gravitation remains the only force that is tautologically equivalent to a curved space theory.

Quantum Physics has provided that theoretical spacetime with a nonlocal causal architecture (through Quantum Entanglement). However that “causality” although geometric, is non metric (and thus manifests itself with no geodesic deviation, no force).

Einstein, after a debate on nonlocality imparted by the Quantum, with the Austrian philosopher Karl Popper, attracted the world’s attention on that problem in 1935, with his famous EPR paper. There Einstein denounced the way the “spooky action at a distance” affected distant “elements of reality”. Since then, the spookiness at a distance has been amply confirmed (and enables to encrypt space communications while knowing 100% whether they have been breached, as a Chinese satellite recently showed). Nonlocal effects show unambiguously that the metric (of “spacetime”) does not capture all the geometry (an notion which may surprise physicists, but not those mathematicians who have studied the foundations of their field).

This Quantum architecture has led, so far, to no prophecy, let alone theory, by established physicist. Entangled Quantum architecture is actually not part of the General Relativistic raisin cake model (or any GR model). However, I will venture to say one can view it as predicting Dark matter, at the very least. It’s just a question of baking something more sophisticated than raisin bread.

Patrice Ayme

Gravitational Waves Directly Detected

February 11, 2016

How Were Gravitational Waves detected?

By two detectors in the USA, one in Washington State, the other in Louisiana (detecting in one place would have been enough; in two places at the same time, the finding is overwhelming certain; the National Science Foundation of the USA had spent $1.1 billion, over 40 years, on that research). The detectors were simplicity themselves in concept: just a light interferometer to measure the distance between mirrors: light is split, sent in two perpendicular directions, and then re-united with itself. If one of the branches vary slightly in length relative to the other as a gravitational waves passes, an interference will show up. However mirrors hanging from pendulum hanging from pendulums five times, the whole thing in an anti-vibration machine had to be realized in half a dozen places in a chain of reflections and interference.

What are these Gravitational Waves?

As far as existing gravitation theory has it, distortion in space (and, thus time: time and space are related by the speed of light, c).

A Field Carries Away A Wave Just As A Whip Does

A Field Carries Away A Wave Just As A Whip Does

What Was Detected:

Einstein’s Gravitation Theory says that gravitation “is” the deformation of space(time) it brings. It is this deformation which was directly detected: a part of space in one direction was made shorter than in another direction. That meant a huge gravitational wave had passed.

The formidable event that caused it was the crash and collapse of two black holes into each other, each around 30 solar masses (much more details are known).

Gravitational Waves Were Certain Theoretically, & Already Detected:

We already had evidence for the existence of gravitational waves, both theoretical and experimental. Einstein’s name was rolled out, naturally enough. Because Einstein contributed to the present Theory of Gravitation (I am not anti-Einstein, far from it, but he closely worked with a number of other people, including the towering mathematician David Hilbert, who published his own approach to gravity within weeks of Einstein).

Einstein tends to appear as the cherry on many a cake. Those who celebrate the photogenic cherry, and ignore the cake, will go hungry.

WAVES ARE PREDICTED BY FINITE SPEED FIELD THEORY:

Actually, once one has hypothesized that gravitation is a field propagating at a finite speed, the apparition of waves is automatic.

The reasoning was made first by British and French Eighteenth Century physicists, in the framework of electromagnetic force; the mathematics is exactly the same with gravitation, as both fields vary with the inverse square of the distance. This is what happens in a radio antenna, with electrons going back and forth: the electric field that those electrons create is deformed in such a way that it moves other electron at a distance, back and forth.

The Gravitational Energy Loss Detection Method:

Thus, how do the waves show up? By shaking things at a distance. Using conservation of energy, it means that the field creating system, by moving just so, loses energy to its waves. An obvious case is two neutron stars (“pulsars”) rotating around each other: as they move back and forth, because of said rotation, they create gravitational waves which carry energy away from their system, As this happens, their system loses energy, the two stars should spiral into each other, thus rotate ever faster, and this should be observable, and computable exactly. This, indeed, was thoroughly observed, so we knew the waves were there.

Einstein’s Gravitation Theory is a sleight of hand:

It affects to identify space(time) deformations with gravitation. The idea actually originated with the awesome German mathematician Bernard Riemann, who invented manifold theory in part to point out that any force could be viewed as convergence, or divergence of geodesics (this is an idea that physics has been milking ever since).

This, though, does not answer Newton’s deeper query about the nature of gravitation (see below). It’s a bit as if a creature asked:’What is an arm?’ And one answered:’An arm is what pushes things, and we can detect the deformation the arm brought.’

What is the discovery good for?

Well, first, one has to make sure. Science is about making 100% sure. The present experiment improved some technology far out what anything else required (but then it does open some possibilities!) Just an importantly, now we will be able to check the details of the Gravitation Theory (the big picture was not in doubt; the details are). Ultimately it may be possible to communicate through gravitational waves, etc (although right now the deformation are only of the size of the fraction of a nucleus, and we could detect them!)

Who were the originators of that idea? First Newton himself pointed out that his own theory of gravitation was grotesque (I am paraphrasing). Newton:

“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.”

There were actually two problems: that the action was instantaneous, and that it was at a distance without intermediaries. Newton paid attention to the second one, physics, in the last two centuries, solved the first (which was implicit in Newton’s observations).

As I mentioned in passing above, part of Newton’s worries were addressed by the invention of the concept of field. And then by the realization that fields carried energy away in waves. At that point, gravitational waves were automatic… Riemann’s introduction of manifolds, and how to conceptualize forces in them gave the manifestation of its nature to gravitation we presently have, a distortion of space metric (once again, time follows automatically).

It’s important to know who invented what, and contributed most. Because it unveils how ideas appear and evolve. Then, in turn, one can make theories of that, accelerating innovation (don’t forget there is a horse race between innovation and oblivion, on the scale of the entire biosphere!)

Curiously, this is all very useful; GPS with a precision of 30 centimeters has allowed to find out that baboon society is more democratic than ours, in fundamental ways. “General Relativistic” effects (the fact clocks run slow in a gravitational field) make crucial corrections to the GPS computations (otherwise GPS would be pretty useless). So this is not all academic. GPS will soon allow robotic agriculture… among other things.

We still don’t know what gravitation is. However, we can predict more things than Newton did… Even if he did not suspect they were there. This is just the beginning of what could be revealed, if our satanic impulses are kept in check.

Patrice Ayme’

Is “Spacetime” Important?

November 3, 2015

Revolutions spawn from, and contributes to, the revolutionary mood. It is no coincidence that many revolutionary ideas in science: Chemistry (Lavoisier), Biological Evolution (Lamarck), Lagrangians, Black Holes,, Fourier Analysis, Thermodynamics (Carnot), Wave Optics, (Young, Poisson), Ampere’s Electrodynamics spawned roughly at the same time and place, around the French Revolution.

In the Encyclopedie, under the term dimension Jean le Rond d’Alembert speculated that time might be considered a fourth dimension… if the idea was not too novel. Joseph Louis Lagrange in his ), wrote that: “One may view mechanics as a geometry of four dimensions…” (Theory of Analytic Functions, 1797.) The idea of spacetime is to view reality as a four dimensional manifold, something measured by the “Real Line” going in four directions.

There is, it turns out a huge problem with this: R, the real line, has what is called a separated topology: points have distinct neighborhoods. However, the QUANTUM world is not like that, not at all. Countless experiments, and the most basic logic, show this:

Reality Does Not Care About Speed, & The Relativity It Brings

Reality Does Not Care About Speed, & The Relativity It Brings

Manifolds were defined by Bernhard Riemann in 1866 (shortly before he died, still young, of tuberculosis). A manifold is made of chunks (technically: neighborhoods), each of them diffeomorphic to a neighborhood in R^n (thus a deformed piece of R^n, see tech annex).

Einstein admitted that there was a huge problem with the “now” in physics (even if one confines oneself to his own set-ups in Relativity theories). Worse: the Quantum changes completely the problem of the “now”… Let alone the “here”.

In 1905, Henri Poincaré showed that by taking time to be an imaginary fourth spacetime coordinate (√−1 c t), a Lorentz transformation can be regarded as a rotation of coordinates in a four-dimensional Euclidean space with three real coordinates representing space, and one imaginary coordinate, representing time, as the fourth dimension.

— Hermann Minkowski, 1907, Einstein’s professor in Zurich concluded: “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”

This remark rests on Lorentz’s work, how to go from coordinates (x, t) to (x’, t’). In the simplest case:

C is the speed of light. Lorentz found one needed such transformations to respect electrodynamics. If v/c is zero (as it is if one suppose the speed v to be negligible  relative to c, the speed of light infinite), one gets:

t = t’

x’ = x – vt

The first equation exhibits universal time: time does not depend upon the frame of reference. But notice that the second equation mixes space and time already. Thus, philosophically speaking, proclaiming “spacetime” could have been done before. Now, in so-called “General Relativity”, there are problems with “time-like” geodesics (but they would surface long after Minkowski’s death).

Another problem with conceptually equating time and space is that time is not space: space dimensions have a plus sign, time a minus sign (something Quantum Field Theory often ignores by putting pluses everywhere in computations)

In any case, I hope this makes clear that, philosophically, just looking at the equations, “spacetime” does not have to be an important concept.

And Quantum Physics seems to say that it is not: the QUANTUM INTERACTION (QI; my neologism) is (apparently, so far) INSTANTANEOUS (like old fashion time).

As we saw precedingly (“Can Space Be Faster Than Light“), the top cosmologists are arguing whether the speed of space can be viewed as faster than light. Call that the Cosmic Inflation Interaction (CII; it has its own hypothesized exchange particle, the “Inflaton”). We see that c, the speed of light is less than CII, and may, or may not be related to QI (standard Quantum Physics implicitly assumes that the speed of the Quantum Interaction QI is infinite).

One thing is sure: we are very far from TOE, the “Theory Of Everything”, which physicists anxious to appear as the world’s smartest organisms, with all the power and wealth to go with it, taunted for decades.

Patrice Ayme’

Tech Annex: R is the real line, RxR = R^2, the plane, RxRxR = R^3 the usual three dimensional space, etc. Spacetime was initially viewed as just RxRxRxR = R^4.]What does diffeomorphic mean? It means a copy which can be shrunk or dilated somewhat in all imaginable ways, perhaps (but without breaks, and so that all points can be tracked; a diffeomorphism does this, and so do all its derivatives).