{"id":11405,"date":"2025-07-05T23:13:20","date_gmt":"2025-07-05T20:13:20","guid":{"rendered":"https:\/\/uni-mag.gr\/?p=11405"},"modified":"2025-07-28T18:51:56","modified_gmt":"2025-07-28T15:51:56","slug":"the-geometry-of-gravity","status":"publish","type":"post","link":"https:\/\/www.uni-mag.gr\/en\/the-geometry-of-gravity\/","title":{"rendered":"Alternative Gravity Theories"},"content":{"rendered":"\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">Alternative Gravity Theories<em><span style=\"color: red;\"> <\/span><\/em><\/h2>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<p><em><span style=\"color: #6f0000;\"><strong>By Vasiliki Karanasou, PhD Candidate, Laboratory of Theoretical Physics, University of Tartu<\/strong><\/span><\/em><\/p>\n\n<p>We all remember the schoolbook story of Newton, who was supposedly sitting idly under an apple tree when an apple fell on his head, leading him to discover the law of gravity. Things probably didn\u2019t happen exactly that way, but according to Newton, gravity is a force that one body exerts on another, causing attraction between them. This force is responsible for apples falling from trees, for people being held to the ground instead of floating away, and for planets orbiting the Sun. Newton\u2019s theory managed to describe our world very effectively\u2014or did it?    <\/p>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.uni-mag.gr\/wp-content\/uploads\/2025\/07\/1&#x395;&#x3BD;&#x3B1;&#x3BB;&#x3BB;&#x3B1;&#x3BA;&#x3C4;&#x3B9;&#x3BA;&#x3AD;&#x3C2;-&#x3B8;&#x3B5;&#x3C9;&#x3C1;&#x3AF;&#x3B5;&#x3C2;-&#x3B2;&#x3B1;&#x3C1;&#x3CD;&#x3C4;&#x3B7;&#x3C4;&#x3B1;&#x3C2;.png\" alt=\"\" class=\"wp-image-11383\"\/><figcaption class=\"wp-element-caption\"><em> Illustration of Newton under an apple tree discovering the law of gravity. (Credit: Freepik) <\/em><\/figcaption><\/figure>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<p>Although Newtonian gravity explains many macroscopic phenomena, an early sign that it is incomplete is its inability to fully describe Mercury\u2019s orbit around the Sun. Moreover, when studying phenomena involving speeds close to that of light, Newtonian theory proves to be entirely inadequate. In 1915, Einstein introduced a new theory\u2014general relativity\u2014which radically reshaped our understanding of space, time, and gravity.  <\/p>\n\n<p>Space is no longer a passive backdrop where events unfold and time flows uniformly. In relativity, space and time are combined into a four-dimensional entity known as spacetime. We can imagine this entity like a stretched-out sheet held taut at the corners. If we place a ball on this sheet\u2014or, analogously, planets, stars, or galaxies in spacetime\u2014their mass causes the sheet to bend. The greater the mass, the deeper the curvature.    <\/p>\n\n<p>Since objects in the universe are not stationary, they don\u2019t simply fall into heavier bodies but instead move along curved paths around them. That\u2019s why planets in a solar system orbit their star. So gravity is no longer considered a force, but rather the curvature of spacetime caused by the presence of mass.  <\/p>\n\n<p>Gravity is geometry. But what kind of geometry? Our first thought might be Euclidean geometry\u2014the kind we learned in school\u2014where the shortest distance between two points on a plane is a straight line. But what if spacetime isn\u2019t flat? What if it\u2019s curved like a sphere?<br\/>Imagine the Earth and suppose we want to travel from Estonia to Argentina. Even if we follow the shortest path, it won\u2019t be a straight line but a curve due to the Earth\u2019s shape. The type of geometry Einstein proposes for spacetime is called Riemannian geometry.        <\/p>\n\n<p>Although general relativity has successfully explained many phenomena that classical Newtonian theory could not, it may still not be the final answer.<\/p>\n\n<p>Observations indicate that the universe is expanding. If we could observe the night sky with the naked eye in enough detail, we would see all other galaxies moving away from ours at a uniform speed. This expansion is not yet fully understood, and several hypotheses have been proposed.  <\/p>\n\n<p>One of the most well-known theories involves dark matter and dark energy. If there is something that doesn\u2019t interact with light\u2014hence \u201cdark\u201d\u2014it might explain the universe\u2019s accelerating expansion. <\/p>\n\n<p>Another approach is to modify the theory of gravity itself. But what does that mean? As we\u2019ve said, gravity is geometry. So can we assume a different geometry?   <\/p>\n\n<p>Mathematically speaking, besides curvature, we can define two more properties of spacetime: torsion and non-metricity. In Einstein\u2019s theory, only curvature is non-zero; torsion and non-metricity are assumed to be zero. But if we allow all three to coexist\u2014or at least two of them\u2014then spacetime no longer follows Riemannian geometry, and the theory of gravity must change as well.  <\/p>\n\n<p>The following diagram illustrates what happens to a vector (an oriented line) when it is subjected separately to curvature, torsion, and non-metricity while being parallel transported in spacetime\u2014that is, moved without changing it deliberately.<\/p>\n\n<p>So, could an alternative theory of gravity be the final answer?<br\/>Although such a theory might explain the expansion of the universe, that is not the only phenomenon we must account for. <\/p>\n\n<p>Many alternative theories of gravity have already been developed. Some have been ruled out based on experimental data, and among those that remain, each one explains certain phenomena but fails to account for others\u2014none stands out as the most likely. <\/p>\n\n<p>Maybe none of them are correct because we\u2019re still missing something fundamental. <strong>Perhaps we need a radical shift in how we perceive gravity. Perhaps we need a new relativity.<\/strong><\/p>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.uni-mag.gr\/wp-content\/uploads\/2025\/07\/2&#x395;&#x3BD;&#x3B1;&#x3BB;&#x3BB;&#x3B1;&#x3BA;&#x3C4;&#x3B9;&#x3BA;&#x3AD;&#x3C2;-&#x3B8;&#x3B5;&#x3C9;&#x3C1;&#x3AF;&#x3B5;&#x3C2;-&#x3B2;&#x3B1;&#x3C1;&#x3CD;&#x3C4;&#x3B7;&#x3C4;&#x3B1;&#x3C2;.png\" alt=\"\" class=\"wp-image-11387\"\/><figcaption class=\"wp-element-caption\"><em>The curvature of spacetime. The more massive an object is, the greater the curvature it causes. (Credit: ESA\u2013C. Carreau)  <\/em><\/figcaption><\/figure>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.uni-mag.gr\/wp-content\/uploads\/2025\/07\/3&#x395;&#x3BD;&#x3B1;&#x3BB;&#x3BB;&#x3B1;&#x3BA;&#x3C4;&#x3B9;&#x3BA;&#x3AD;&#x3C2;-&#x3B8;&#x3B5;&#x3C9;&#x3C1;&#x3AF;&#x3B5;&#x3C2;-&#x3B2;&#x3B1;&#x3C1;&#x3CD;&#x3C4;&#x3B7;&#x3C4;&#x3B1;&#x3C2;.png\" alt=\"\" class=\"wp-image-11391\"\/><figcaption class=\"wp-element-caption\"><em>In the first case, a vector is parallel transported in a geometry with curvature. This changes the direction of the vector.<br\/>In the second case, two vectors are parallel transported in a geometry with torsion. The result is that the parallelogram we would expect them to form does not &#8220;close.&#8221;<br\/>In the third case, a vector is parallel transported in a geometry with non-metricity. The result is that the length of the vector changes.     <\/em><\/figcaption><\/figure>\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<p><strong>References<\/strong><\/p>\n\n<ol class=\"wp-block-list\">\n<li><a class=\"\" href=\"https:\/\/en.wikipedia.org\/wiki\/Newton%27s_law_of_universal_gravitation\">https:\/\/en.wikipedia.org\/wiki\/Newton%27s_law_of_universal_gravitation<\/a><\/li>\n\n\n\n<li><a class=\"\" href=\"https:\/\/en.wikipedia.org\/wiki\/General_relativity\">https:\/\/en.wikipedia.org\/wiki\/General_relativity<\/a><\/li>\n\n\n\n<li>E. Albert, \u201cKosmologische Betrachtungen zur allgemeinen Relativit\u00e4tstheorie\u201d, <em>Sitzungsberichte der Preu\u00dfischen Akademie der Wissenschaften: 142 (1917)<\/em><\/li>\n\n\n\n<li>Supernova Search Team Collaboration, A. G. Riess et al., \u201cObservational evidence from supernovae for an accelerating universe and a cosmological constant,\u201d <em>Astron. J. 116 (1998) <\/em> 1009\u20131038<\/li>\n\n\n\n<li>E. J. Copeland, M. Sami, and S. Tsujikawa, \u201cDynamics of dark energy,\u201d <em>Int. J. Mod. Phys. D 15 (2006)   <\/em> 1753\u20131936<\/li>\n\n\n\n<li>J. Beltr\u00e1n Jim\u00e9nez, L. Heisenberg, and T. S. Koivisto, \u201cThe Geometrical Trinity of Gravity,\u201d <em>Universe 5 (2019) no. 7, 173<\/em><\/li>\n<\/ol>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p class=\"card-text\">Is gravity really just a force\u2014or is it geometry? From Newton and Einstein to the most radical alternative theories, explore how the shape of spacetime may hold the key to understanding our expanding universe.  [&#8230;]<\/p>\n<p class=\"m-0\"><a class=\"btn btn-outline-secondary btn-read-more\" href=\"https:\/\/www.uni-mag.gr\/en\/the-geometry-of-gravity\/\">Read More<\/a><\/p>\n","protected":false},"author":4,"featured_media":11528,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2887,139,116],"tags":[2679,2964,1914,2970,2963,1216,2540,2968,2965,2969,2966,2967,311],"class_list":["post-11405","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-issue-13-en","category-issues-en","category-news-en","tag-albert-einstein","tag-alternative-gravity-theories","tag-astronomy-en","tag-expansion-of-universe","tag-general-relativity","tag-gravity-en","tag-newton-en","tag-non-metricity","tag-space-time","tag-theoretical-physics","tag-torsion","tag-torsion-en","tag---en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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