Four-dimensional space

<p>Four-dimensional space (4D) is the mathematical extension of the concept of <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a> (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called <i><a href="/facts/Dimension/0ktmUyac">dimensions</a></i>, to describe the <a href="/facts/Size/brTWIYNF">sizes</a> or <a href="/facts/Location/fXux5RaJ">locations</a> of objects in the everyday world.  This concept of ordinary space is called <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a> because it corresponds to <a href="/facts/Euclid/dHpVyL4R">Euclid</a><a href="/facts/Euclidean_geometry/V6cTcoCy">'s geometry</a>, which was originally abstracted from the spatial experiences of everyday life.
</p><p>Single locations in Euclidean 4D space can be given as <a href="/facts/Vector_space/M1pxMLx2">vectors</a> or <i><a href="/facts/N-tuples/BI1HIxL8">4-tuples</a></i>, i.e., as ordered lists of numbers such as (<i>x</i>, <i>y</i>, <i>z</i>, <i>w</i>). For example, the <a href="/facts/Volume/aeAXCBUd">volume</a> of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z). It is only when such locations are linked together into more complicated shapes that the full richness and geometric complexity of 4D spaces emerge. A hint of that complexity can be seen in the accompanying 2D animation of one of the simplest possible <a href="/facts/Regular_4-polytope/lFf8IH1C">regular 4D objects</a>, the <a href="/facts/Tesseract/tlqouBoU">tesseract</a>, which is <a href="/facts/Hypercube/q2mRPbIz">analogous</a> to the 3D <a href="/facts/Cube/65lUaAqN">cube</a>.
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<h3>Entropion Field (Theoretical Physics)</h3>
<p>The Entropion Field is a proposed scalar field in <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a> introduced as part of the 4D Quantum Projection Hypothesis. It is designed to unify <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, <a href="/facts/Thermodynamics/q4hIx3yP">thermodynamics</a>, and <a href="/facts/General_relativity/jVsoIg8X">general relativity</a> by providing a mechanism for <a href="/facts/Wave_function/KgM5ykjY">wave function</a> <a href="/facts/Quantum_decoherence/mngM3rxy">decoherence</a> and the <a href="/facts/Arrow_of_time/U5Hjl9lf">arrow of time</a> within a four-dimensional spatial framework.
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<h4>Overview</h4>
<p>The Entropion Field is theorized as a fundamental component of spacetime dynamics, responsible for:
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<ul><li>Driving <a href="/facts/Quantum_decoherence/mngM3rxy">decoherence</a> in quantum systems via interaction with the 4D projection of matter</li>
<li>Governing <a href="/facts/Entropy/s52IXeFz">entropy</a> increase, giving rise to the thermodynamic arrow of time</li>
<li>Coupling to standard model fields, affecting quantum behavior at small scales and macroscopic classicality</li></ul>
<p>It operates as a self-interacting scalar field, denoted by ϕₑ(x⁰, x¹, x², x³, x⁴), where x⁴ represents the hypothesized fourth <a href="/facts/Dimension/0ktmUyac">spatial dimension</a>. Its potential function V(ϕₑ) is responsible for the non-linear feedback between <a href="/facts/Entropy/s52IXeFz">entropy</a> and curvature, forming part of a modified action in the unified 4D field equations.
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<h4>Role in 4D Theory</h4>
<p>In the 4D framework, the Entropion Field plays three central roles:
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<ol><li><a href="/facts/Quantum_decoherence/mngM3rxy">Decoherence</a> Engine: It regulates the collapse of quantum superpositions by dynamically interacting with the projected wave function in 3D space.</li>
<li><a href="/facts/Entropy/s52IXeFz">Entropy</a> Carrier: It propagates entropy spatially, enforcing time-asymmetry without relying solely on probabilistic thermodynamics.</li>
<li><a href="/facts/Cosmology/yM19zM7Y">Cosmological Function</a>: On large scales, it contributes to spacetime geometry modifications, possibly explaining <a href="/facts/Dark_energy/6bWIYewA">dark energy</a> or entropy gradients in cosmology.</li></ol>

Four-dimensional space open-in-new

Four-dimensional space