Is “Spacetime” Important?

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

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).

Neurons, Axons, Axioms

(Second Part of “Causality Explained”)

Axiomatic Systems Are Fragile:

Frege was one of the founders of mathematical logic and analytic philosophy. Frege wrote the Grundgesetze der Arithmetik [Basic Laws of Arithmetic], in three volumes. He published the first volume in 1894 (paying for it himself). Just before the second volume was going to press, in 1903, a young Bertrand Russell informed Frege of a dangerous contradiction, Russell’s paradox (a variant of the Cretan Liar Paradox). Frege was thrown in total confusion: a remedy he tried to apply reduced the number of objects his system could be applied to, to just ONE. Oops.

Frege was no dummy: he invented quantifiers (Second Order Logic, crucial to all of mathematics). It is just that logic can be pitiless.

If Those Neurons Evolved Independently From Ours, Neurons Solve Thinking

Neurons are (part of) the solution to the problem of thinking, a problem so deep, we cannot conceive of it. A second independent evolution of neuronicity would certainly prove that.

Truer Axiomatics Is Simpler, More Powerful:

Russell and Whitehead, colossal mathematicians and philosophers, decided to demonstrate 1 + 1 = 2. Without making “Cretan Liar” self-contradictions.

They wrote a book to do so. In the second volume, around page 200, they succeeded.

I prefer simpler axioms to get to 1 + 1 =2.

(Just define the right hand side with the left.)

It would be interesting that philsophers define what “causing” means, and what “causality” is, for us. Say with explicit examples.

I want to know what cause causes. It’s a bit like pondering what is is.

Some creatures paid as philosophers by employers know 17th century physics, something about billiards balls taught in first year undergraduate physics. (I know it well, I have taught it more than once.) Then they think they know science. All they know is Middle-Ages physics.

These first year undergraduates then to explain the entire world with the nail and hammer they know so well.

They never made it to Statistical Mechanics, Thermodynamics, etc. And the associated “Causality” of these realms of knowledge.

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Axiomatics Of Causality With The Quantum:

How does “causality” work in the Quantum Mechanics we have?

You consider an experiment, analyze its eigenstates, set-up the corresponding Hilbert space, and then compute.

“Billiard Balls” is what seems to happen when the associated De Broglie wave has such high frequency that the eigenstates seem continuous.

So Classical Mechanical “causality” is an asymptote.

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Know How To Dream… To Bring Up New Axiomatics

Human beings communicate digitally (words and their letters or ideograms), and through programs (aka languages, including logic and mathematics).

All of this used conventions, “rules”, truths I call axioms, to simplify… the language (this is not traditional, as many of these axioms have had names for 25 centuries).

So for example, I view the “modus ponens” (if P implies Q and P happens, then Q) as an axiom (instead of just a “logical form” or “rule of inference”).

The reason to call basic “logic forms” “axioms” is that they are more fragile than they look. One can do with, or without them. All sorts of non-classical logics do without the “excluded third law” (for example fuzzy set theory).

With such a semantic, one realizes that all great advances in understanding have to do with setting up more appropriate axioms.

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Buridan’s Revolution, Or An Axiomatics Revolution:

In the Fourteenth Century, the intellectual movement launched by Buridan, included Oresme and the Oxford Calculators. They discovered inertia, momentum (“impetus”), graphs, the law of falling bodies, the heliocentric system (undistinguishable from the geocentric system, said Buridan, but we may as well stick to the latter, as it is in Scripture, said Buridan, wryly).

Buridan’s revolution is little known. But was no accident: Buridan refused to become a theologian, he stuck to the faculty of arts (so Buridan did not have to waste time in sterile debates with god cretins… differently from nearly all intellectuals of the time). Much of Buridan is still in untranslated Medieval Latin, that may explain it, after centuries of Catholic war against him.

http://www.encyclopedia.com/topic/Jean_Buridan.aspx

These breakthroughs were major, and consisted in a number of new axioms (now often attributed to Galileo, Descartes, Newton). The axioms had a tremendous psychological effect. At the time, Buridan, adviser to no less than four Kings, head of the University of Paris, was untouchable.

The philosopher cum mathematician, physicist and politician, died in 1360. In 1473, the pope and king Louis XI conspired to try to stop the blossoming Renaissance.

More than a century after his death, Buridan’s works, his new axioms, were made unlawful to read. (However Buridan was mandatory reading in Cracow, and Copernic re-published the work, as soon as he was safely ensconced within the safety of his death bed).

The mind, the brain, is quite fuzzy (in the sense of fuzzy set theory; the dreaming part; think of dendrites, prominences within synapses, starfish-like astrocytes, neurotransmitters, etc.). Axioms, and axons enable to code it digitally. So mathematization, and programmation are intrinsic human mental activities.

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We Are All Theoretical Scientists Of The Mathematical Type:

Human beings continually draw consequences from the axioms they have, through the intermediary of giant systems of thought, and systems of mood (mentality for short).

When reality comes to drastically contradict expected consequences, mentality is modified, typically in the easiest way, with what I call an ANTI-IDEA.

For example when a number of physics Nobel laureates (Lenard, Stark) were anxious to rise in the Nazi Party, they had to reconcile the supposed inferiority of the Jews with the fact that Einstein was a Jew. They could not admit either that Poincare’ invented Relativity, as he was also of the most hated nation (and of the most anti-German fascism family in France!).

So they simply claimed that it was all “Jewish Science” (this way they did not have to wax lyrically about why they had collaborated with Einstein before anti-Judaism).

When brute force anti-ideas don’t work after all (as became clear to Germans in 1945), then a full re-organization of the axiomatics is in order.

An example, as I said, is fuzzy set theory. It violates the Excluded-Third Law.

But sometimes the reconsideration may be temporary. (Whether A and Non-A holds in the LOGIC of Quantum Mechanics, the Einstein-Schrodinger Cat, is a matter of heated debate.)

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 Quantum Logic:,Both In & Out Of This World:

The removal of old logical axioms can be definitive. For example the Distributive Law of Propositional Calculus fails in Quantum Logic. That has to do with the Uncertainty Principle, a wave effect that would be etched in stone, were it not even more fundamental.

http://en.wikipedia.org/wiki/Quantum_logic

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Verdict? Neurons, Axons, And Axioms Make One System:

We have been playing with axioms for millions of years: they reflect the hierarchical, axon dominated, neuron originated most basic structure of the nervous system.

Why?

Well, the neuronal-axonal skeleton of minds is probably the lowest energy solution to the problem of thinking in the appropriate space. It has just been proposed neurons evolved twice:

https://www.quantamagazine.org/20150325-did-neurons-evolve-twice/

We do not just think axiomatically, but we certainly communicate axiomatically, even with ourselves. And the axiomatics are dynamical. Thus causes learn to fit effects.

The fact this work is subjective, in part, does not mean it does not have to do with nature. Just the opposite: causality is nature answering the call of nature, with a flourish.

Human mentality is a continual dialogue between nature inside (Claude Bernard) and nature outside.

Changing axioms is hard work: it involves brain re-wiring. Not just connecting different neurons, but also probably modifying them inside.

Mathematicians have plenty of occasions to ponder what a proof (thus an explanation) is. The situation is worse than ever, with immense proofs only the author gets (Fermat’s Last Theorem was just an appetizer), or then computer-assisted proofs (nobody can check what happened, and it’s going to get worse with full Quantum Computers).

Not all and any reasoning is made to be understood by everybody. (Mathematicians have to use alien math they don’t really understand, quite often.)

Yes, thinking is hard. And not always nice. But somebody has to do it. Just remember this essence, when trying to communicate with the stars: hard, and not always nice.

Patrice Ayme’

Quantum Expands Causality

CAUSALITY HAS EXPANDED:

Having a notion of when something causes something else is paramount. We have evolved some subtle notions since Shamanism (or David Hume).

Two things struck me:

1. a) The paucity of the imagination of many pillars of intellect. In 2008, there was a huge spike in the price of crude oil, followed by an equally impressive crash.

What caused it? Nobody in the economic establishment had a public answer. However, I had an obvious one: crude oil futures, a type of financial derivatives which can be manipulated, thanks to the gigantic leverage in the futures’ market.

Through a psychological mechanism I explained at the time, the price of real crude oil  spiked up (as a consequence of the spike in the futures; something similar just happened). Paul Krugman obstinately denied, loud and clear that this could ever happen, because he stridently proclaimed, he saw NO causal link between futures and the price of the underlying commodity. (Thus, according to Krugman, oil futures are OK, whereas I see them as a plague, waste, blot on humanity, and a major prop for plutocracy.)

From my point of view, Krugman was not smart: he just looked in his little corner of economy he knew, and not the big picture. (Please don’t tell he was friendly from some crude oil future guy, that would be so crude, besides being the correct explanation.)

In general, correct reasoning and causality means looking at the wholeness of the spatially implicated order.

Do we have a physical model for this? Yes, Quantum Physics.

1. b) Many thinkers claimed, especially generations ago, that Quantum Physics destroyed causality. The exact opposite is true: the Quantum has expanded the notion of causality (to the implicate order).

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SO WHAT’S CAUSALITY? A CAUSES B WHEN A LOGOS GOES FROM A TO B.

Old fashion causality involves forces. A force points from a point to another point (it’s called a “vector”; forces actually gave the mathematical concept of vector).

However, there are no points in Quantum Physics.

(That there are points in Quantum Field Theory is a problem: string theory tried to get around it. That was perhaps its main motivation.)

But before I get to the Quantum, let me explain my philosophical concept of causality.

What’s causality? An event A is said to cause an event B if whenever A occurs, so does B, and a logos, a discourse, goes from A to B. (That logos is, in precise science, an evolution equation and its attached notions).

Thus one needs a definition of A, B, and of the implication itself. All come from statistic ensembles. (I am saying that probabilities are hidden in plain sight in classical mechanics and arguments; they are not something reserved to Quantum Physics.)

Does that mean all causality arise directly from statistics, and only from statistics? Not really: a differential equation E predicts (if well behaved!) the evolution of a system S. Then knowing S(t) one can get S(t+1). In this case one says that the initial conditions S(t), plus the law E, cause S(t+1).

Some make a big deal that equation of physics are reversible, they see that as indication of time travel, or something weird. However, whether the equation E is time reversible, or not, is irrelevant: one plugs in (t+1), not (t-1).

Differential equations or, more generally, evolution equations, are all over physics and nature. Those who declare something as strange as “causation has disappeared from physics” should come up, with just one example of physics without an evolution equation. It will not be found, as physics is about predicting the future. (Better than predicting the past as all too many do.)

THE QUANTUM EXPANDED CAUSALITY:

The Quantum, some who know it all too little, was said to have destroyed causality.

In truth, Quantum Physics is all about Non-Commutative Geometry (and not just in Alain Connes’ restricted sense; this is the main argument for Super Symmetry). In clear language; no more points. Then old fashion, point to point causality does not apply.

In Quantum Physics, is waves writ large. Quantum guidance is all about waves. According to De Broglie’s Wave Principle, all and any particle is guided by a wave. Yes, that would be true even for trucks. It was recently confirmed at a larger scale than atoms and molecules.

Hitting a wave with another wave is messy. Causal, but messy. Thus causality in Quantum Physics tends to be probabilistic.

Models of De Broglie’s Pilot Wave theory have recently appeared in labs (starting in Paris, where De Broglie’s ideas long pursued a subterranean existence; after all, De Broglie, who lived to nearly 100, was Perpetual Secretary of the Academie des Sciences). Even in the good old USA, these ideas are gaining traction:

http://www.wired.com/2014/06/the-new-quantum-reality/

The wave guiding proceeds at a speed much higher than the speed of light (at least 10^10 c). Call it TAU. Thus any Quantum Process embraces the totality of accessible space. Moreover that space is a Hilbert space (not just 3 dimensional space).

This means that the causality (the set of causes) in any Quantum process involves not just a Cauchy data set, the classical way, and an evolution equation (Schrodinger, Dirac, Klein-Gordon, etc., but an entire space “visualized” by the Pilot Wave at speed TAU (> 10^10).

Notice that many of the preceding is not part of the conceptology of those who claim that Quantum Physics is not causal. Most of them probably do not know what a Hilbert space is (that the Pilot Wave proceeds in a Hilbert was an early objection against it; it’s as intelligent as protesting that the sky is blue).

Once all the ingredients are in, including CAUSAL SPACE, Quantum Physics is completely causal. Conceptually speaking.

QUANTUM COMPUTER CAUSES MORE:

Those who are elaborating, as we speak, Quantum Computers are trying to make Quantum Physics so incredibly causal, that it will be able to easily make CAUSAL relationships that traditional classical computers cannot do (and cannot check!). One has to understand that classical computers work, indeed, according to classical mechanics. They are glorified water clocks (with electrons flowing).

The Quantum Computer will convince the Commons that Quantum Physics is more causal than pathetically precise classical physics. Ultra pathetic precision leads classical physics to arbitrarily large errors. Whereas computing with waves is forgiving, hence more precise in the long run.

Time to get causal in the wavy way, people, embracing wholeness and the implicate (spatial) order famed physicist David Bohm was speaking (more or less) about. The real truth is going to be even more subtle (to simplify this essay, I neglected Quantum Entanglement).

Conclusion? Whenever there is a logic, there is a context, and the logic implicates the context. This is true in pure logic (from introspection, and writing logic down), but also in the Quantum world (from experimenting in the real world).

Logic without context is nothing. Physics without space is nothing. Nature without the implicate spatial order is nothing either. Thinking globally is the only thinking there is.

Patrice Ayme’