Even more difficult than finding the equations of general relativity is to explain how Einstein did it from almost pure thinking. The historian of science Gerald Holton once remarked, while describing Einstein in the context of the definition of scientific genius, that “there is a mutual mapping of the mind and way of life of this scientist and the laws of nature.” Einstein himself attributed his success to the discovery of the deep relationship between mathematics and the physical world. However, reconciling general relativity with the laws of quantum physics remains a problem, as a self-coherent theory of quantum gravity is lacking. It is not yet known how gravity can be combined with the three non-gravitational forces: strong, weak and electromagnetic. “We now have the technological ability to test theories of gravity in ways we`ve never been able to do before,” said co-author Jessica Lu, an astrophysicist at the University of California, Berkeley. “Einstein`s theory of gravity is definitely in our sights.” A priori, it is not clear whether the new free-falling local frameworks coincide with the reference systems in which the laws of special relativity apply – this theory is based on the propagation of light and thus on electromagnetism, which could have another set of preferred frameworks. But with different assumptions about special relativistic frameworks (such as their terrestrial or free-falling bond), one can derive different predictions for gravitational redshift, i.e. how the frequency of light moves as light propagates through a gravitational field (see below). Actual measurements show that free-falling frames are those in which light propagates as in the theory of special relativity. [35] The generalization of this statement, namely that the laws of special relativity adhere to a good approximation in free-falling (not rotary) reference systems, is called Einstein`s equivalence principle, a crucial guiding principle for the generalization of relativistic physics special to gravity. [36] In 1915, after eight years of sorting through his thoughts, Einstein (literally – he had no experimental precursors) had invented an active ingredient that caused gravity.
And it wasn`t just a strength. According to his theory of general relativity, gravity is much stranger: a natural consequence of the influence of a mass on space. Given the difficulty of finding exact solutions, Einstein`s field equations are also often solved by numerical integration on a computer or by taking into account small disturbances of exact solutions. In the field of numerical relativity, powerful computers are used to simulate the geometry of space-time and solve Einstein`s equations for interesting situations such as two colliding black holes. [57] In principle, such methods can be applied to any system, provided that there are sufficient computing resources and can address fundamental issues such as bare singularities. Approximate solutions can also be found through perturbation theories such as linearized gravity[58] and its generalization, post-Newtonian expansion, both of which were developed by Einstein. The latter offers a systematic approach to the geometry of a space-time that contains a distribution of matter that moves slowly relative to the speed of light. Enlargement includes a number of terms; The first terms represent Newtonian gravity, while the following terms represent smaller and smaller corrections of Newton`s theory due to the theory of general relativity.
[59] An extension of this extension is the parameterized post-Newtonian formalism (PPN), which allows quantitative comparisons between predictions of general relativity and alternative theories. [60] where s {displaystyle s} is a scalar motion parameter (for example, eigentime) and Γ μ α β {displaystyle Gamma ^{mu }{}_{alpha beta }} are Christoffel symbols (sometimes called affine connection coefficients or Levi-Civita connection coefficients) that are symmetric in the lower two indexes. Greek indexes can be 0, 1, 2, 3, and the sum convention is used to repeat the indexes α {displaystyle alpha } and β {displaystyle beta }. The quantity on the left side of this equation is the acceleration of a particle, and therefore this equation is analogous to Newton`s laws of motion, which also provide formulas for the acceleration of a particle. This equation of motion uses Einstein`s notation, which means that repeated indexes are added together (i.e. From zero to three). Christoffel symbols are functions of the four spatio-temporal coordinates and therefore independent of the velocity or acceleration or other properties of a test particle whose motion is described by the geodetic equation. According to the theory of relativity, anything that can happen in a box that gains speed – that is, accelerates – also happens in the presence of gravity.
For example, imagine a horizontal laser in an elevator that accelerates upwards. When the light moves laterally, the elevator rises, causing the beam to hit a place on the wall that is slightly lower than where it started. When the elevator accelerates fast enough, the beam visibly bends towards the ground. If Einstein were right, the black hole would distort space and time in such a way that the wavelength of light would be extended by S0-2. In short, the waves would expand when the intense gravity of the black hole released its energy, changing the color of starlight from blue to red. If the star continued to glow blue, it would lend credibility to Newton`s gravity model, which does not take into account the curvature of space and time. If it had taken on a different color, it would have pointed to a different model of gravity. “It`s very difficult to predict how new discoveries in fundamental physics will affect our daily lives,” Lu said. “But a new theory of gravity could help us understand how our own universe was born and how we got to where we are today 13 and a half billion years later.” Albert Einstein can explain many things, but perhaps not black holes. Scientists believe that in the depths of these massive celestial objects, the laws of the universe integrate on their own, and the elegant model of gravity expounded in Einstein`s theory of general relativity collapses. You can visualize Einstein`s gravity chain by walking on a trampoline. Their mass causes depression in the stretch fabric of the room.
Roll a ball past the chain on your feet and it curves towards your mass. The heavier you are, the more you bend the space. Look at the edges of the trampoline – the chain continues to decrease in relation to your mass. Thus, the same Newtonian relations are explained (and predicted mathematically with better precision), but through a different lens of distorted space. Take that, Newton, Einstein said. With regret. Einstein showed that the same thing happens with a beam in a stationary elevator in a strong gravitational field; Gravity bends light. Similarly, he expected a ray of starlight to bend as it passes through the sun`s gravity. This prediction proved correct when the stars moved during the 1919 solar eclipse.
Another approach begins with the canonical quantization methods of quantum theory. Using the initial value formulation of the theory of general relativity (see Equations of Evolution above) results in the Wheeler-deWitt equation (an analogue of the Schrödinger equation), which unfortunately turns out to be poorly defined without a correct ultraviolet (lattice) limit. [201] However, with the introduction of the variable now known as the Ashtekar variable,[202] this leads to a promising model known as loop quantum gravity. Space is represented by a net-shaped structure called a spin network, which evolves over time in discrete stages. [203] Ordinary quantum field theories, which form the basis of modern elementary particle physics, are defined in Minkowski flat space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields such as those found on Earth. [185] To describe situations where gravity is strong enough to affect (quantum) matter, but not strong enough to require quantification itself, physicists have formulated quantum field theories in curved space-time. These theories rely on general relativity to describe curved background space-time and define a generalized quantum field theory to describe the behavior of quantum matter in this spacetime. [186] With this formalism, it can be shown that black holes emit a spectrum of blackbody particles known as Hawking radiation, which leads to the possibility that they evaporate over time.
[187] As briefly mentioned above, this radiation plays an important role in the thermodynamics of black holes. [188] Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of gravitational force. This suggests the definition of a new class of inertial motions, namely that of objects in free fall under the influence of gravity. This new class of preferred motions also defines a geometry of space and time – mathematically speaking, it is the geodetic motion associated with a particular connection that depends on the gradient of the gravitational potential. The space in this construction still has ordinary Euclidean geometry. However, space-time as a whole is more complicated. As shown by simple thought experiments that follow the free-fall trajectories of different test particles, the result of transporting spatio-temporal vectors, which can indicate the speed of a particle (time vectors), varies with the trajectory of the particle; Mathematically speaking, the Newtonian compound cannot be integrated. We can deduce that space-time is curved. The resulting Newton-Cartan theory is a geometric formulation of Newtonian gravity that uses only covariant concepts, that is, a valid description in any desired coordinate system. [28] In this geometric description, tidal effects – the relative acceleration of bodies in free fall – refer to the derivation of the compound, showing how the modified geometry is caused by the presence of mass. [29] Einstein quickly realized (or knew from the beginning) that his new theory of gravity was in fact a theory of the cosmos.