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

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).

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13 Responses to “Is “Spacetime” Important?”

  1. brodix Says:

    Patrice,

    To raise the point I keep trying to make; We experience reality as flashes of cognition and so think of time as this point of the present, the now, moving from past to future. Physics codifies this by treating it as measures of duration, to correlate with measures of distance, thus treating space as the three linear vectors of the xyz coordinate system, which is a mapping device, not the holistic volume being mapped.
    Yet the reality is a changing configuration of what physically exists is creating and dissolving these events we experience and so it is they, by coming into being and dissolving, which go future to past. Tomorrow becomes yesterday because the earth turns.
    What is measured is frequency and duration is simply the state of the present, as these moments come and go. This makes time an effect of activity, much more like temperature, than space. Given that temperature arises from masses of frequency and amplitude.
    So then when we step back and try to wrap our linear thought processes around this non-linear thermal medium, is it any wonder we can’t clarify direct cause from action?
    If “particles” are entangled, isn’t that trying to tell us that connectivity is something more than just between atoms and quanta?
    As for the revolutions which could arise from this, might it lead to visions of society where we are not all atomized individuals, but as connected to our environment and each other, as much as the cells in our bodies are connected to each other, for better or worse?
    We only exist in this state of the present, while that same element of consciousness shines through us all, like light through a multitude of prisms. Is it any wonder that we are both the most highly evolved features of the known universe, but also seemingly extremely expendable, in the tumult of our own efforts.
    A revolution is not more of the same, but a complete change of direction. Now we are ever more focused on the details, as signs of our expertise, yet what does it take to sense the basic dynamics of expanding energy creating and dissolving these seemingly static forms of reality, which precipitate into the past, as the energy moves onto the future, yet always only conserved as the present state?
    It might be that quantum mechanics might seem more sensible than the classic, if we were to see it from another perspective.
    Think of the quantum realm as wood growing/expanding holistically as a tree, while classic reductionistic logic is simply the carpenter cutting it into boards for furniture.
    It is not further into the abstract we need to look, but back into that earth from which we are rising.

    • gmax Says:

      ‘Point of the present’??? What’s this point of the present? Patrice and Einstein seem to have a problem with this point of the present

      • brodix Says:

        Given that rational thought is based on an extension of singular events, points seemingly creating a line, that it is a problem for perception to understand that from which it is emergent.

        Think of the mind/brain duality in terms of two physical objects hitting each other. This creates an event, as the objects continue onto other events. The brain, being a physical object, goes from one event to the next, while the mind is a recording of the events. So we are constantly replaying, rewriting, splicing them, etc. Thus it is natural to think of it as a form of space.
        Yet there is only this non-linear physical state, in which all activity is balanced by the reactivity of its context.

        Energy, like a wave that hasn’t crested, is indeterminate, until it is finalized. While the finalized form has no extension of itself. Like a crested wave, it can only recede into the past, without more energy to propel it, which then blurs it, like the uncrested wave.

        Think of this in terms of complexity theory, as the complex state being that line between order and chaos. Just as the present is that line between the probability of the future and the determination of the past.

        • Patrice Ayme Says:

          I can, and have, made the argument that points are mathematically impossible to define (that infuriated my ex-colleague research mathematicians, but I am right and they are wrong). The argument has been made on this site.
          “Hitting” means nothing in light of the Uncertainty Principle. “ENTANGLING” does, though.

      • Patrice Ayme Says:

        Indeed. Einstein did not know what to do of the problem of the “now” as he called it. In the New Mood, that does not exist.

    • EugenR Says:

      You did not mention the memory as a factor bringing the past to the present. Memory can be blurry, but when recorded clear. The same can be said about visions and planning as representations of future. Information can be from past, present and future, yet its representation only at present.

  2. Gmax Says:

    If I understand well, Patrice is saying that Einstein style reality was made of unsubstantiated ‘points’. Instead QUANTUM REALITY shows that reality is made of non-local blobs.

  3. Paul Handover Says:

    Well this is one post where I won’t be contributing any observation. For the simple reason that I do not understand the proposition.

    • Patrice Ayme Says:

      Well, that, Paul, by itself is a contribution.

      Old mood: Reality, and, in particular its geometry, is made of chunks of 4 dimensional “spacetime”. This predicts a number of (very) subtle effects, some of which have been observed (but can be obtained with… chunks of the theory, not the whole thing)

      New Mood: The real architecture of the universe is not made of points, but of non-local, dynamic entanglements. The effects are not subtle, but drastically massive and omnipresent.

      This is a much bigger revolution than Relativity, or early Quantum Physics.

      Hope that helped a bit.

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