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Is time a geometric property of space? No need for a fourth dimension?

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File:Wooden hourglass 3.jpg
passage of time, imaged/S. Sepp

From James M. Chappell et al. at Frontiers in Physics:

The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which “flows equably without relation to anything external.” In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that he could provide a unified representation of space and time. With the publishing of Einstein’s theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation of 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein’s relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension. More.

One thing is for certain: Time is intrinsically more mysterious than the other dimensions. There are hardly any controversies worth mentioning about length or width, but it is easy to start one about time.

See also: Economist: Can time go backwards?

New theory links flow of time with Big Bang

Time is all in our heads?

Atlantic asks, is time real?


Can physics tell us if time had a beginning?

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2 Replies to “Is time a geometric property of space? No need for a fourth dimension?

  1. 1
    bornagain77 says:

    Actually, with advances in quantum mechanics, the ‘psychological time’ of philosophers, i.e. ‘the now’, is shown to take precedence over Einstein’s ‘physical time’.

    Einstein’s encounter with Bergson over the proper definition of time, and the heated disagreement that ensued between the two men over that proper definition, was one of the primary reasons that Einstein failed to receive a Nobel prize for relativity: (Nov. 2016)

    LIVING IN A QUANTUM WORLD – Vlatko Vedral – 2011
    Excerpt: Thus, the fact that quantum mechanics applies on all scales forces us to confront the theory’s deepest mysteries. We cannot simply write them off as mere details that matter only on the very smallest scales. For instance, space and time are two of the most fundamental classical concepts, but according to quantum mechanics they are secondary. The entanglements are primary. They interconnect quantum systems without reference to space and time. If there were a dividing line between the quantum and the classical worlds, we could use the space and time of the classical world to provide a framework for describing quantum processes. But without such a dividing line—and, indeed, with­out a truly classical world—we lose this framework. We must explain space and time (4D space-time) as somehow emerging from fundamentally spaceless and timeless physics.

  2. 2
    mw says:

    “The proper description of time remains a key unsolved problem in science.”

    Perhaps that is because in God we live and move and have our being (Acts 17:28).

    Therefore, does God live in space and time; that is. eternal space and time, or is God somewhat space and time? “I am that I am” (Exodus 3:14).

    It seems to me that out of the eternal space and time of the eternal spirit of God our material beginning came. It appears God exists, as a function of spirit, in or is part of eternal space and time.

    Human calculations of the beginning cannot calculate spirit and cannot calculate a miracle or understand miracles, therefore cannot disprove God created a mature universe when he cast matter created from the spirit into the vaults of heaven. We have no idea, if we are honest, on the maturing effects of miracles on data.

    We have the Judaeo-Christian God’s personal word on how long it took the Holy Trinity to create. God could have created instantly out of eternal time and space but for humans’ sake, he took six days.

    Calculations have not identified God or spirit down a black hole or behind a singularity. Thus, we are dealing with human philosophy, limited observations, limited calculations and a very limited faith when we only consider the Big Bang Theory and origins of space and time only from then.

    Our Origins come through the word of God.

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