{"id":2772,"date":"2020-03-13T17:53:59","date_gmt":"2020-03-13T16:53:59","guid":{"rendered":"https:\/\/www.quantum-bits.org\/?p=2772"},"modified":"2022-08-12T17:13:27","modified_gmt":"2022-08-12T16:13:27","slug":"what-are-forces","status":"publish","type":"post","link":"https:\/\/www.quantum-bits.org\/?p=2772","title":{"rendered":"What are forces ?"},"content":{"rendered":"<p>This question stems from discussions <a href=\"https:\/\/www.dawex.com\" target=\"_blank\" rel=\"noopener\">at work<\/a> about the notion of &#8220;data gravity&#8221;, which, 10 years after its inception, seems to make a comeback and draw some kind of vague buzz within the Data &amp; IT community. It quickly turned out that this concept &#8211; though appealing from afar &#8211; is one of these so many <a href=\"http:\/\/math.ucr.edu\/home\/baez\/crackpot.html\" target=\"_blank\" rel=\"noopener\">crackpot<\/a> concepts that&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Wolfgang_Pauli\" target=\"_blank\" rel=\"noopener\">Wolfgang Paul<\/a> would call &#8220;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Not_even_wrong\" target=\"_blank\" rel=\"noopener\">not even wrong<\/a>&#8220;.<\/p>\n<p>Indeed, the concept relies on misconceptions about sciences &amp; physics in general, and the way (gravity) forces&nbsp;works and behaves in particular.&nbsp;McCrory&#8217;s &#8220;gravity formula&#8221; (which, somehow, tries to mimic Newton&#8217;s law of gravity) reminded me of one of my high school physics teacher&#8217;s favorite saying: &#8220;don&#8217;t mix elephants and wild strawberries in a formula !&#8221; (&#8220;<em>Vous m\u00e9langez les \u00e9l\u00e9phants et les fraises de bois !<\/em>&#8220;). &nbsp;<\/p>\n<p>So, let&#8217;s forget &#8220;data gravity&#8221; and &#8230; let&#8217;s go back to basics: what are forces ?&nbsp;<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1612\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2018\/03\/quantum-physics-formulas-over-blackboard.jpg\" alt=\"\" width=\"850\" height=\"332\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2018\/03\/quantum-physics-formulas-over-blackboard.jpg 768w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2018\/03\/quantum-physics-formulas-over-blackboard-300x117.jpg 300w\" sizes=\"(max-width: 850px) 100vw, 850px\" \/><\/p>\n<p><strong>What are forces ?<\/strong><\/p>\n<p>Let&#8217;s first have a look at the etymology of the word: &#8220;<em>force<\/em>&#8221; comes from Middle English &#8220;<em>force<\/em>&#8220;, which comes from the Old French word &#8220;<em>force<\/em>&#8221; &#8230; which comes for latin &#8220;<em>fortia<\/em>&#8221; : <em>strong<\/em>, <em>brave<\/em>, <em>courageous<\/em>.&nbsp;<\/p>\n<p>By extension, &#8220;<em>force<\/em>&#8221; describe any capacity of exercising an influence or producing an effect. &#8220;<em>Force<\/em>&#8221; is therefore a relatively ill-defined concept. But, at the same time, is also a highly intuitive notion: in this definition, &#8220;<em>force<\/em>&#8221; is related only to <em>strength<\/em>, and strength is something that anybody can immediately <em>feel<\/em>&nbsp;and <em>experience<\/em>.<\/p>\n<p>Historically speaking, it took a long time to clearly define the concept, <i>by relating forces not to&nbsp;strength, but to motion<\/i>.&nbsp;<\/p>\n<p>Following this path, philosophers such as <a title=\"Aristotle\" href=\"https:\/\/en.wikipedia.org\/wiki\/Aristotle\" target=\"_blank\" rel=\"noopener\">Aristotle<\/a> or early scientists such as&nbsp;<a title=\"Archimedes\" href=\"https:\/\/en.wikipedia.org\/wiki\/Archimedes\" target=\"_blank\" rel=\"noopener\">Archimedes<\/a> retained nevertheless fundamental errors in understanding force, due to an inadequate view of frictions and of the nature of <em>natural motion:&nbsp;<\/em>the belief &#8211; at the time &#8211; was that a force is required to <em>maintain<\/em> motion (even at a constant velocity).<\/p>\n<p>Aristotelian physics began facing criticism in medieval science, but its shortcomings would not be fully corrected until the 17th century with&nbsp;physicists like <a title=\"Galileo Galilei\" href=\"https:\/\/en.wikipedia.org\/wiki\/Galileo_Galilei\">Galileo Galilei<\/a> or&nbsp;<a class=\"mw-redirect\" title=\"Sir Isaac Newton\" href=\"https:\/\/en.wikipedia.org\/wiki\/Sir_Isaac_Newton\">Sir Isaac Newton<\/a>: <strong><em>a&nbsp;force is any interaction that will change the motion of an object<\/em><\/strong>. Using mathematics, Newton formulated his <a href=\"https:\/\/en.wikipedia.org\/wiki\/Newton%27s_laws_of_motion\" target=\"_blank\" rel=\"noopener\">laws of motion<\/a>, that were not improved for nearly three hundred years.<\/p>\n<p>This <strong>all changed<\/strong> in the early 20th century, where <strong>observations<\/strong> lead physicists to completely new insights, giving birth to&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Theory_of_relativity\" target=\"_blank\" rel=\"noopener\">relativity<\/a> and <a href=\"https:\/\/en.wikipedia.org\/wiki\/Quantum_mechanics\" target=\"_blank\" rel=\"noopener\">quantum mechanics<\/a>.&nbsp;<\/p>\n<p>Skipping Aristotelian physics, in the next paragraphs, we will explore the notion of force, within the historical framework of Newtonian physics and within the frameworks of today&#8217;s physics.<\/p>\n<p><strong>Newtonian physics<\/strong><\/p>\n<p>Laws of movement were set out in 1687 in Newton&#8217;s masterpiece &#8220;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Philosophi\u00e6_Naturalis_Principia_Mathematica\" target=\"_blank\" rel=\"noopener\">Philosophiae naturalis principia mathematica<\/a>&#8220;. These three laws are the principles underlying the movement of bodies (i.e., what is now called classical mechanics).&nbsp;They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces.&nbsp;They are completed with&nbsp;the law of universal gravitation (i.e. what is now called classical gravity).<\/p>\n<p><strong>Newton&#8217;s first law<\/strong> is the following (inertia principle): &#8220;<em>Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.<\/em>&#8221;<\/p>\n<p>In other terms, a&nbsp;particle not subject to forces moves (related to inertial frame) in a straight line at a constant speed.&nbsp;This is known as <strong>uniform motion<\/strong><i>:<\/i><\/p>\n<ul>\n<li>An object that is at rest will stay at rest unless a force acts upon it.<\/li>\n<li>An object that is in motion will not change its velocity unless a force acts upon it.<\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-2790\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/rect-uniform.png\" alt=\"\" width=\"243\" height=\"40\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/rect-uniform.png 291w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/rect-uniform-285x48.png 285w\" sizes=\"(max-width: 243px) 100vw, 243px\" \/><\/p>\n<p>Newton&#8217;s first law can be mathematically summarized&nbsp;as:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-2792\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/firstnlaw.png\" alt=\"\" width=\"168\" height=\"40\"><\/p>\n<p style=\"text-align: left;\"><strong>Newton&#8217;s second law<\/strong> is the following (law of dynamics): &#8220;<em>The alteration of motion is ever proportional to the motive force impress&#8217;d; and is made in the direction of the right line in which that force is impress&#8217;d<\/em>&#8220;<\/p>\n<p>In other terms, the second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-2797\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/seconnlaw.png\" alt=\"\" width=\"169\" height=\"40\"><\/p>\n<dl>\n<dd><\/dd>\n<\/dl>\n<p>If we are considering a <em>mass-contant<\/em> system, <img src='https:\/\/s0.wp.com\/latex.php?latex=m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m' title='m' class='latex' \/> can be taken out of the differentiation, and the second law can be expressed in terms of <strong>acceleration<\/strong>: &nbsp;<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-2799\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/seconnlaw2.png\" alt=\"\" width=\"303\" height=\"40\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/seconnlaw2.png 394w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/seconnlaw2-300x40.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>The net force applied to a body produces a proportional acceleration:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-2802\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/acceleration.png\" alt=\"\" width=\"191\" height=\"124\"><\/p>\n<p>Newton&#8217;s second law enables one to calculate the <strong>equation of motion<\/strong> <img src='https:\/\/s0.wp.com\/latex.php?latex=x%28t%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='x(t)' title='x(t)' class='latex' \/>, by integration of <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cvec%7Ba%7D%3D%7Bd%5E2%5Cvec%7Bx%7D%7D%2F%7Bdt%5E2%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\displaystyle \\vec{a}={d^2\\vec{x}}\/{dt^2}' title='\\displaystyle \\vec{a}={d^2\\vec{x}}\/{dt^2}' class='latex' \/>.<\/p>\n<p style=\"text-align: left;\"><strong>Newton&#8217;s third law<\/strong> is the following (action-reaction): &#8220;<em>To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.<\/em>&#8220;<\/p>\n<p>All forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first.<\/p>\n<p>Newton&#8217;s laws gives a qualitative definition of the notion of force, and quantitatively relates force to motion via the acceleration of the body (i.e. its change of speed).<\/p>\n<p>Let&#8217;s now introduce <strong>Newton&#8217;s law of universal gravitation<\/strong>:&nbsp;every body attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.<\/p>\n<p>In mathematical terms, the gravitational force between two bodies is<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cvec%7Bf%7D%3D+G+%5Cfrac%7Bm+%5Ctimes+M%7D%7Br%5E2%7D+%5Chat%7Br%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\displaystyle \\vec{f}= G \\frac{m \\times M}{r^2} \\hat{r}' title='\\displaystyle \\vec{f}= G \\frac{m \\times M}{r^2} \\hat{r}' class='latex' \/>,<\/p>\n<p>where <img src='https:\/\/s0.wp.com\/latex.php?latex=m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m' title='m' class='latex' \/> and <img src='https:\/\/s0.wp.com\/latex.php?latex=M&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='M' title='M' class='latex' \/> the messages of the bodies, <img src='https:\/\/s0.wp.com\/latex.php?latex=G&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='G' title='G' class='latex' \/> is the <a title=\"Gravitational constant\" href=\"https:\/\/en.wikipedia.org\/wiki\/Gravitational_constant\" target=\"_blank\" rel=\"noopener\">gravitational constant<\/a>, and <img src='https:\/\/s0.wp.com\/latex.php?latex=r&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='r' title='r' class='latex' \/> the distance between them.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2010\/05\/newton-laws.png\" alt=\"\"><\/p>\n<p>In the case of a N-body problem (N particles each interacting with each other due to gravity), applying the law of universal gravitation and Newton&#8217;s second law leads to a set of N nonlinear coupled second order ODEs:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-2812\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/nbodyodes.png\" alt=\"\" width=\"244\" height=\"51\"><\/p>\n<p>where <img src='https:\/\/s0.wp.com\/latex.php?latex=i+%3D+1%2C+2%2C%5Ccdots%2C+N&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='i = 1, 2,\\cdots, N' title='i = 1, 2,\\cdots, N' class='latex' \/> labels the quantities (mass, position, etc.) associated with each particle.<\/p>\n<p>Solving these ODE&#8217;s leads to amazing trajectories:<\/p>\n<p><center><div style=\"width: 560px;\" class=\"wp-video\"><!--[if lt IE 9]><script>document.createElement('video');<\/script><![endif]-->\n<video class=\"wp-video-shortcode\" id=\"video-2772-1\" width=\"560\" height=\"420\" loop=\"1\" autoplay=\"1\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/rOpM47Lo0VXGFncf.mp4?_=1\" \/><a href=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/rOpM47Lo0VXGFncf.mp4\">https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2020\/03\/rOpM47Lo0VXGFncf.mp4<\/a><\/video><\/div><\/p>\n<p style=\"text-align: left;\">Let&#8217;s pause a moment to think about what we have been able to do: Newton&#8217;s laws enabled us to formulate equations of motion (and trajectories, i.e. solutions of these equations) <strong>through<\/strong> the evaluation of forces, which makes them an extremely practical concept. Now, a question remains: are forces <em>real physical objects<\/em>, or just a <em>tricks that enable calculations<\/em>. As a matter of fact:<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: left;\">When equating both <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cvec%7Bf%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\vec{f}' title='\\vec{f}' class='latex' \/>&#8216;s (the one from the second law and the one from law of universal gravity), <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cvec%7Bf%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\vec{f}' title='\\vec{f}' class='latex' \/> disappears from the resulting equations of motion;<\/li>\n<li style=\"text-align: left;\">We could have formulated the same physics within the framework of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lagrangian_mechanics\" target=\"_blank\" rel=\"noopener\">Lagrangian mechanics<\/a>, resulting of course with the same equations of motion, without ever introducing the concept of force: introducing instead <a title=\"Kinetic energy\" href=\"https:\/\/en.wikipedia.org\/wiki\/Kinetic_energy\">kinetic energy<\/a>&nbsp;<img src='https:\/\/s0.wp.com\/latex.php?latex=T&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='T' title='T' class='latex' \/> and&nbsp; <a title=\"Potential energy\" href=\"https:\/\/en.wikipedia.org\/wiki\/Potential_energy\">potential energy<\/a>&nbsp;<img src='https:\/\/s0.wp.com\/latex.php?latex=V&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='V' title='V' class='latex' \/> to define the Lagrangian, and using the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Principle_of_least_action\" target=\"_blank\" rel=\"noopener\">principle of least action<\/a>&nbsp;to derive the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Euler\u2013Lagrange_equation\" target=\"_blank\" rel=\"noopener\">Euler-Lagrange equations<\/a>:<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+L+%3D+T+-+V%2C%5C+%5C+V+%3D+-+G%5C+%5Cfrac%7BM%5Ctimes+m%7D%7Br%7D%2C%5C+%5C+%5Cfrac+%7B%5Cpartial+%7BL%7D%7D%7B%5Cpartial+q%7D-%7B%5Cfrac+%7B%5Cmathrm+%7Bd%7D+%7D%7B%5Cmathrm+%7Bd%7D+t%7D%7D%5Cleft%28%7B%5Cfrac+%7B%5Cpartial+%7BL%7D%7D%7B%5Cpartial+%7B%5Cdot+%7Bq%7D%7D%7D%7D%5Cright%29%3D0&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\displaystyle L = T - V,\\ \\ V = - G\\ \\frac{M\\times m}{r},\\ \\ \\frac {\\partial {L}}{\\partial q}-{\\frac {\\mathrm {d} }{\\mathrm {d} t}}\\left({\\frac {\\partial {L}}{\\partial {\\dot {q}}}}\\right)=0' title='\\displaystyle L = T - V,\\ \\ V = - G\\ \\frac{M\\times m}{r},\\ \\ \\frac {\\partial {L}}{\\partial q}-{\\frac {\\mathrm {d} }{\\mathrm {d} t}}\\left({\\frac {\\partial {L}}{\\partial {\\dot {q}}}}\\right)=0' class='latex' \/><\/p>\n<p style=\"text-align: left;\">Of course, there is a very strong connection between <a href=\"https:\/\/en.wikipedia.org\/wiki\/Potential_energy#Forces_and_potential_energy\" target=\"_blank\" rel=\"noopener\">forces and potential energy<\/a>, and all this is could be seen as some kind of sleight of hand. Indeed,&nbsp;<strong>both<\/strong> formulations (Newton&#8217;s and Lagrange&#8217;s) are <strong>perfectly adequate<\/strong> when speaking in the words of <strong>classical physics<\/strong>.<\/p>\n<p style=\"text-align: left;\">Trouble is: <strong>Nature is NOT classical<\/strong>. &nbsp;<\/p>\n<p style=\"text-align: left;\">Even if the concept of force is easier to grasp than the one of potential energy (or field) in the conceptual&nbsp;<strong>framework of&nbsp;classical physics<\/strong>, it&#8217;ll be quite <strong>different<\/strong> when dealing with <strong>quantum and relativistic phenomena<\/strong>. &nbsp;<\/p>\n<p style=\"text-align: left;\"><strong>Modern physics (part 1): special and general relativity<\/strong><\/p>\n<p style=\"text-align: left;\">As we have previously seen :&nbsp;<\/p>\n<p><\/center><\/p>\n<ul>\n<li>in absence of external influence, a free body follows a straight line at constant speed<\/li>\n<li>under the influence of gravity, the body follows a trajectory explained by the combination of Newton&#8217;s second law of motion and Newton&#8217;s law of universal gravitation:<\/li>\n<\/ul>\n<div align=\"center\"><img decoding=\"async\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2010\/05\/newton-gravitation.png\" alt=\"\"><\/div>\n<p>But major concerns (experimental and theoretical) lead physicists to seek for a totally new paradigm:<\/p>\n<ul>\n<li>Newton&#8217;s theory cannot cope with today&#8217;s high precision observations. For example, it doesn&#8217;t fully explain the precession of the perihelion of the planet Mercury, or the deflection of light rays by gravity. In simple words: <strong>Newton&#8217;s gravity does not fit experimental observations<\/strong>.<\/li>\n<li>Newton requires forces to be some kind of <strong>action at a distance,&nbsp;<\/strong>transmitted instantaneously, which is known now to be <strong>impossible:&nbsp;no information can travel faster than light.<\/strong><\/li>\n<\/ul>\n<p>To solve these problem, Einstein introduced its General Relativity theory, where effects of <strong>gravitation are ascribed to spacetime curvature instead of a force<\/strong>.<\/p>\n<p>Einstein proposed that <strong>spacetime is curved by matter<\/strong>, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called <a href=\"http:\/\/en.wikipedia.org\/wiki\/Geodesic_%28general_relativity%29\" target=\"_new\" rel=\"noopener\">geodesics<\/a>. In absence of gravity, physics is described by Einstein&#8217;s Special Relativity where geodesics are plain straight lines.<\/p>\n<p>Einstein postulated that spacetime is a (pseudo-riemannian) <a href=\"http:\/\/en.wikipedia.org\/wiki\/Manifold\" target=\"_new\" rel=\"noopener\">manifold<\/a>. Simply speaking, these are curved spaces which can always be locally approximated by flat pseudo-euclidean spaces (Minkowski spacetimes).<\/p>\n<p>To deal with these geometry, one has to introduce new mathematical objects: <a href=\"http:\/\/en.wikipedia.org\/wiki\/Tensor\" target=\"_new\" rel=\"noopener\">tensors<\/a>. Simply speaking, tensors are geometric entities that extend the notion of scalars, vectors and matrices. These are the natural objects to describe quantities in a relativistic way: tensors themselves are independent of a particular choice of coordinate system.<\/p>\n<p>To express his field equations, Einstein introduced a particular tensor, denoted <span style=\"position: relative; top: -2px;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=T%5E%7B%5Cmu%5Cnu%7D+&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='T^{\\mu\\nu} ' title='T^{\\mu\\nu} ' class='latex' \/><\/span> and called <a href=\"http:\/\/en.wikipedia.org\/wiki\/Stress-energy_tensor\" target=\"_new\" rel=\"noopener\">stress-energy tensor<\/a>. It is a quantity that describes the density and flux of energy and momentum in spacetime.<\/p>\n<p>Then, he connected stress-energy tensors to local properties of spacetime (curvatures):<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+G_%7B%5Cmu%5Cnu%7D+%2B+%5CLambda+g_%7B%5Cmu%5Cnu%7D+%3D+%5Cfrac%7B8%5Cpi+G%7D%7Bc%5E4%7D+T_%7B%5Cmu%5Cnu%7D+&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\displaystyle G_{\\mu\\nu} + \\Lambda g_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu} ' title='\\displaystyle G_{\\mu\\nu} + \\Lambda g_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu} ' class='latex' \/> where <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+G_%7B%5Cmu%5Cnu%7D+%3D+R_%7B%5Cmu%5Cnu%7D+-+%5Cfrac%7B1%7D%7B2%7D+Rg_%7B%5Cmu%5Cnu%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\displaystyle G_{\\mu\\nu} = R_{\\mu\\nu} - \\frac{1}{2} Rg_{\\mu\\nu}' title='\\displaystyle G_{\\mu\\nu} = R_{\\mu\\nu} - \\frac{1}{2} Rg_{\\mu\\nu}' class='latex' \/><\/p>\n<p>Theses <strong>field equations<\/strong> mean that <strong>energy \/ mass and momentum proportionally curves spacetime<\/strong>. In absence of gravity (A), spacetime is a flat Minkowskian manifold and free bodies follows straight line. In presence of gravity (B), spacetime is curved and free bodies follow geodesics:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2010\/05\/einstein-gravitation.png\" alt=\"\"><\/p>\n<p>This is a <strong>huge paradigm shift:<\/strong>&nbsp;instead of thinking of gravity as a force pulling or pushing &nbsp;objects (instantaneous action at a distance), hence causing them to travel along curved paths in a 3-dimensional flat space, one has to think of objects traveling along the straightest paths (geodesics) in a 4-dimensional spacetime curved by the presence of energy and momentum.&nbsp;<\/p>\n<p>And here come the unavoidable conclusion: <strong>there is no need for forces<\/strong>. Gravity manifest itself as a geometrical property of spacetime. <strong>When it comes to gravity, the concept of force is a meaningless<\/strong>.<\/p>\n<p><strong>Modern physics (part 2): quantum mechanics and particle physics<\/strong><\/p>\n<p>In <a title=\"Particle physics\" href=\"http:\/\/en.wikipedia.org\/wiki\/Particle_physics\" target=\"_blank\" rel=\"noopener\">particle physics<\/a>, <strong>fundamental interactions<\/strong> are the ways that elementary particles interact with one another. An interaction is fundamental when it cannot be described in terms of other interactions.&nbsp;With the notable exception of gravitation (previously described though the framework of General Relativity), all these fundamental interactions have been expressed according to <a href=\"http:\/\/en.wikipedia.org\/wiki\/Quantum_field_theory\" target=\"_blank\" rel=\"noopener\">quantum field<\/a> formulations, namely:<\/p>\n<ul>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Quantum_electrodynamics\" target=\"_blank\" rel=\"noopener\">Quantum Electrodynamics<\/a> (or QED): the quantum field formulation of electromagnetism, which served as a model for all the other theories<\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics\" target=\"_blank\" rel=\"noopener\">Quantum Chromodynamics<\/a> (or QCD): the quantum field formulation of strong interactions (which used to be my playground in a distant past)<\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Glashow-Weinberg-Salam_model\" target=\"_blank\" rel=\"noopener\">Electroweak model<\/a> (or GWS): <a href=\"http:\/\/en.wikipedia.org\/wiki\/Sheldon_Lee_Glashow\" target=\"_blank\" rel=\"noopener\">Sheldon Glashow<\/a>, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Steven_Weinberg\" target=\"_blank\" rel=\"noopener\">Steven Weinberg<\/a> and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Abdus_Salam\" target=\"_blank\" rel=\"noopener\">Abdus Salam<\/a> have unified both weak and electromagnetism interactions into a single, unified quantum theory, which is now the basis of the standard model of particle physics<\/li>\n<\/ul>\n<p>Modern physical theories describe reality in terms of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Field_%28physics%29\" target=\"_blank\" rel=\"noopener\">fields<\/a>&nbsp;(e.g., the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electromagnetic_field\" target=\"_blank\" rel=\"noopener\">electromagnetic field<\/a>, the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Gravitational_field\" target=\"_blank\" rel=\"noopener\">gravitational field<\/a>). Interactions are mediated by&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/Gauge_boson\" target=\"_blank\" rel=\"noopener\">gauge boson<\/a>, which are bosonic particle that carries any of the fundamental interactions.<\/p>\n<p>Elementary particles interact with each other by the exchange of specific boson carriers:<\/p>\n<ul>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Photons\" target=\"_blank\" rel=\"noopener\">Photons<\/a>: carriers of the electromagnetic force<\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Gluons\" target=\"_blank\" rel=\"noopener\">Gluons<\/a>: the 8 gluons, are bosons that act as the exchange particles for the force between quarks (and actually, between gluons, which makes QCD a fun and tricky theory)<\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/W_and_Z_bosons\" target=\"_blank\" rel=\"noopener\"><img src='https:\/\/s0.wp.com\/latex.php?latex=W%5E%7B%2B%7D%2C+W%5E%7B-%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='W^{+}, W^{-}' title='W^{+}, W^{-}' class='latex' \/> and <img src='https:\/\/s0.wp.com\/latex.php?latex=Z%5E0&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='Z^0' title='Z^0' class='latex' \/> bosons<\/a>: these bosons mediate the weak interaction<\/li>\n<\/ul>\n<div style=\"position: relative; top: +8px;\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-300 aligncenter\" title=\"carriers\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2012\/08\/carriers.png\" alt=\"\" width=\"339\" height=\"114\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2012\/08\/carriers.png 339w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2012\/08\/carriers-300x100.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/div>\n<p>&nbsp;<\/p>\n<p>How can we picture these carriers ? Let&#8217;s forget for a minute fields and particles, and imagine a pair of basketball players (seen from above):<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-304\" title=\"players\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2012\/08\/players.png\" alt=\"\" width=\"475\" height=\"191\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2012\/08\/players.png 475w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2012\/08\/players-300x120.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>At first, let them separately dribble. Each player will follow his path, independently of the another. They are &#8220;non interacting players&#8221;. Now, imagine them exchanging a ball. Both players will now follow correlated path. They are &#8220;interacting players&#8221;. Then, give them an heavier ball. Their paths will get closer, because the range of their interaction will became shorter: exchanging an heavy ball over a long distance is harder than with a lighter one.<\/p>\n<p>That&#8217;s about the same for particles. Electrically charged particle interact with each other by the exchange of virtual photons, quarks (<a href=\"http:\/\/en.wikipedia.org\/wiki\/Color_charge\" target=\"_blank\" rel=\"noopener\">color-charged<\/a> particles) interact with each other by the exchange of virtual gluons, etc.<\/p>\n<p>Instead of images of basketball players, physicists picture these interactions with <a href=\"http:\/\/en.wikipedia.org\/wiki\/Feynman_diagram\" target=\"_blank\" rel=\"noopener\">Feynman diagrams<\/a>&nbsp;(which, actually, are graphical representations of a perturbative contribution to a probability amplitude of a given quantum system):<\/p>\n<div style=\"position: relative; top: -6px;\"><center><img decoding=\"async\" loading=\"lazy\" width=\"458\" height=\"116\" class=\"aligncenter size-full wp-image-306\" title=\"feynman\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2012\/08\/feynman.png\" alt=\"\" srcset=\"https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2012\/08\/feynman.png 458w, https:\/\/www.quantum-bits.org\/wp-content\/uploads\/2012\/08\/feynman-300x75.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/center><\/div>\n<p>&nbsp;<\/p>\n<p>To summarize, quantum field theories describe the exchanges between elementary particles in the form of photons, bosons and gluons.&nbsp;<strong>Neither of these theories uses force<\/strong>.<\/p>\n<p><strong>Modern physics (part 3):&nbsp;symmetries and conservation laws<\/strong><\/p>\n<p><a href=\"http:\/\/en.wikipedia.org\/wiki\/Symmetry_in_physics\" target=\"_new\" rel=\"noopener\">Symmetries<\/a> and laws of physics are deeply connected. There exists an extremely important result called <a href=\"http:\/\/en.wikipedia.org\/wiki\/Noether%27s_theorem\" target=\"_new\" rel=\"noopener\">Noether&#8217;s theorem<\/a>, which states that such symmetries also imply the conservation of physical quantities.<\/p>\n<p>For example, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Energy\" target=\"_new\" rel=\"noopener\">energy<\/a> is conserved if the laws describing a system at a given time are still the same at another time: time-translation invariance of the laws of physics implies the conservation of energy. The same link exists between conservation of (linear)&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/Momentum\" target=\"_new\" rel=\"noopener\">momentum<\/a> and space-translation invariance, or between conservation of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Angular_momentum\" target=\"_new\" rel=\"noopener\">angular momentum<\/a> and rotations.<\/p>\n<div align=\"center\"><img decoding=\"async\" src=\"http:\/\/quantum-bits.org\/wp-content\/uploads\/2010\/05\/noether.png\" alt=\"\"><\/div>\n<p>&nbsp;<\/p>\n<p>Symmetry principles are not just statements about how scientists should write laws. They make testable predictions about how nature behaves. Conversely, they constitute a formidable tool to formulate physical theories from experimental data: <strong>what truly and only characterize a physical system is what doesn&#8217;t change when one changes his point of view of that system<\/strong>.&nbsp;<\/p>\n<p>Force is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in quantum electrodynamics). The conservation of momentum can be directly derived from the homogeneity or symmetry of space and so is considered more fundamental than the concept of a force.<\/p>\n<p><strong>While moments or energy are fundamental quantities of physics, in the sense that they all obey a law of conservation, force can be seen as an artifice of modeling, convenient but not essential.<\/strong>&nbsp;<br \/>\n&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This question stems from discussions at work about the notion of &#8220;data gravity&#8221;, which, 10 years after its inception, seems to make a comeback and draw some kind of vague &#8230;<\/p>\n","protected":false},"author":1,"featured_media":3846,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/posts\/2772"}],"collection":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2772"}],"version-history":[{"count":0,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/posts\/2772\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=\/wp\/v2\/media\/3846"}],"wp:attachment":[{"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.quantum-bits.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}