Posted by: Aba Cohen | April 10, 2009

Understanding what Gravity is: Time Expansion & Space Contraction

text in English

Understanding what Gravity is:

Time Expansion  & Space Contraction

by Aba Cohen Persiano

Physics Department, Federal University of Minas Gerais-Brazil

 Click here and see also

 why the concepts of INERTIA and GRAVITY are  UNIVOCAL

 As I said in the EasyPhysics twitter´s sentence, “gravity of a given mass M comes from Time Expansions associated with transverse (to g) Space Contractions”. The whole effect corresponds to Energy Gradients (you can understand this as “tidal forces”) drawing m towards M, where m is a second mass  set in such a deformed spacetime tissue. We can see below two distinct approaches where gravity (that is not a “force” but just an acceleration or a kind of “surfing wind”, according to Einstein´s General Theory of Relativity – GTR) is present:

To understand its mechanism you don´t have to know, a priori, anything about  the GTR to get the thing. You just need to know (have heard) from the Special Theory of Relativity -STR- that space shrinks and time expands with increasing velocities, when a given phenomenon is described by an inertial observer.

At first I use a MATERIAL spinning disc to explain what follows: Suppose a situation where the disc´s external edge moves at a given constant angular velocity, e.g. at relativistic speed (v < ~c), but NOTE, this huge velocity is not necessary at all. An observer from outside the disc (see the figure below) observes, relative to his/her clock, a time expansion, proportional to gamma, and a space contraction of the disc’s perimeter, proportional to 1/gamma, where gamma is the Lorentz Factor [1/ square root (1 – v2/c2)]; no change is observed in the disc’s radius as it is not material or it does not move (or, if you are not yet convinced, assume that “the radius moves” transversally to v and, from the STR, space shrinks only in the direction parallel to v – so “r gets thinner” conserving its length). As the internal concentric circumferences rotate with the same angular speed (ω), the respective tangential velocities (v´ = ω.r´) are progressively smaller than v as you get closer to the center, where v´= 0. Being so, the internal circumferences shrink regressively less and less. The same happens to the centripetal accelerations (a = v2/r´ = ω2 r´) as they also drop with r, when described by the external observer. gravity-of-a-spinning-material-disc-and-of-a-huge-mass-m-a3

The consequence of progressivelly shrunk circumferences and lethargic clocks along fixed radii is a bend in space-time as you can see in the figure above. An internal rotating observer lying still on the disc’s surface feels the action  of his feet (i.e. the reaction to the centripetal force, that keeps him in rotation) pulling the “floor” radially outwards –consider this floor as a step fixed on the external circumference, to avoid the internal observer being spit out form the disc– keeping him in rotation. He designates this as the “force of gravity”. Actually it is a strugle between his feet and the floor reaction to keep its inertial body in the accelerated system. For the external observer, this is also gravity and is described by the GTR as a consequence of the time expansion and transverse (to g) space contraction. From the Newtonian (Classical Physics) point of view, such a “centrifugal force” is called “inertial force” and neither time-expansions nor space-contractions exist to justify its existence. In the GTR inertial-mass is synonym of gravitational-mass: The “inertial feeling” of m, opposing acceleration, is exactly what we call gravity, where time “flows” slowly.

In the second approach a given mass M distorts the space-time tissue with stronger time expansions and space contractions as you get closer to M (increase g):  Similarly, the gravity created by M comes from the time expansion and the transverse (to g) space contraction (I see inertia -space contraction- as a kind of “belt fastening” to stick M into the Universe’s space-time tissue, like a stamp sticker fixes itself on the album’s tissue) that creates tidal forces (observe the dragging gradient) pulling (accelerating) m towards M.

 Click here and see also why the concepts of inertia ana gravity  are  identical

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  1. It is hard to get bored in your class.
    Since I was supposed to “hit the road” late in the night last Thursday, I had to leave earlier, so I probably missed something interesting from your lecture.
    Although you have an exceedingly interesting way of approach to the matters of physics, I still having some trouble understanding the growth of matter under light-year velocity. Hopefully it’ll be a “piece of a cake” at the end of the course.
    See’ya in class.

    • O aumento da massa M=GAMA*Mo veio de uma expressão deduzida por Einstein para o momentum linear P=GAMA*Mo*V. A interpretação de Einstein era que (GAMA*Mo)=”massa relativistica” e assim haveria um aumento da massa, já que o momentum clássico é dado por P=M*V.´Além do próprio Einstein, diversos físicos de renome como Richard Feynman (premio Nobel de fisica de 1965) adotaram essa expansão da massa (Mas não com o acréscimo de novos átomos… quem pensa assim está completamernte enganado) associada ao aumento da inércia do corpo. Essa concepção mudou e hoje, considera-se a massa como uma invariante da Física. o termo M = Mo para qualquer velocidade é adotado, sem invalidar, logicamente, a expressão P=GAMA*M*V; quem aumenta do fator de Lorentz, GAMA, é o produto (M*V). É uma discussão puramente conceitual, mas esta nova postura evita confusões, como a sua.

  2. Como não estive presente na aula passada(n°5), gostaria de ter a oportunidade de ainda assim receber a aposila da mesma.

    Luiz Carlos

  3. Caro Professor Abba,
    Estou gostando muito do curso e gostaria de continuar a fazer a fase seguinte. Gostaria de entrar na questão da “gravidade quantica” e na questão da seta do tempo. Se o espaço tempo se encurva dentro de sí o tempo também encurva, certo? E se for uma curvatura tão grande que a seta tome sentido inverso? E mais ainda, não poderiamos tratar o tempo como uma grandeza vetorial. Pode ser uma heresia já que é escalar, mas e se o tempo também não tiver sentido e direção?

  4. Time is a consequence of expansion.
    Look at the problem of inflation.
    Universal speed of light is determined by distance and time.

    • Hi Peter, I agree with you regarding the expansion, as time is a consequence of (was triggered by) the big bang, “the navel of matter-space-time”; I do not understand what you mean with the second affirmative.

  5. […] building something more complex: the General TR, valid for accelerated referentials. In my post “Understanding What Gravity Is” you can read about the relation between gravity/acceleration and both space contraction and time […]

  6. very very good so i wold like to ask its post in portuguese please

    • Raul, me manda seu email. O meu é
      Moro em Belo Horizonte/Brasil. Se você morar por perto poderá fazer um dos cursos sobre temas correlatos.


      Aba Cohen

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