Curved spacetime
In physics, curved spacetime is the mathematical model in which, with Einstein's theory of general relativity, gravity naturally arises, as opposed to being described as a fundamental force in Newton's static Euclidean reference frame.
These principles laid the groundwork for a deeper understanding of gravity through the geometry of spacetime, as formalized in Einstein's field equations.
Newton's theories assumed that motion takes place against the backdrop of a rigid Euclidean reference frame that extends throughout all space and all time.
Gravity is mediated by a mysterious force, acting instantaneously across a distance, whose actions are independent of the intervening space.
[note 1] In contrast, Einstein denied that there is any background Euclidean reference frame that extends throughout space.
[1]: 175–190 In any analysis of spacetime, evidence of gravitation requires that one observe the relative accelerations of two bodies or two separated particles.
It is the cumulative total effect of many local manifestations of curvature that result in the appearance of a gravitational force acting at a long range from Earth.
[4]: 118–126 Years before publication of the general theory in 1916, Einstein used the equivalence principle to predict the existence of gravitational redshift in the following thought experiment: (i) Assume that a tower of height h (Fig.
(iv) At the top of the tower, an energy-mass converter transforms the energy of the photon E' back into a particle of rest mass m'.
But the theoretical arguments predicting gravitational time dilation do not depend on the details of general relativity at all.
But general relativity is a theory of curved space and curved time, so if there are terms modifying the spatial components of the spacetime interval presented above, should not their effects be seen on, say, planetary and satellite orbits due to curvature correction factors applied to the spatial terms?
The reason is that planetary velocities are extremely small compared to the speed of light, so that for planets and satellites of the solar system, the
As the astronomer who had earlier discovered the existence of Neptune "at the tip of his pen" by analyzing irregularities in the orbit of Uranus, Le Verrier's announcement triggered a two-decades long period of "Vulcan-mania", as professional and amateur astronomers alike hunted for the hypothetical new planet.
[9] In 1916, Einstein was to show that this anomalous precession of Mercury is explained by the spatial terms in the curvature of spacetime.
Curvature in the temporal term, being simply an expression of Newtonian gravitation, has no part in explaining this anomalous precession.
The success of his calculation was a powerful indication to Einstein's peers that the general theory of relativity could be correct.
The most spectacular of Einstein's predictions was his calculation that the curvature terms in the spatial components of the spacetime interval could be measured in the bending of light around a massive body.
For the weak field expression of the invariant interval, Einstein calculated an exactly equal but opposite sign curvature in its spatial components.
(3) Another contribution to the active gravitational mass of the bottom stream comes from an additional pressure term which, at this point, we do not have sufficient background to discuss.
[6]: 245–253 Matter in motion through a gravitomagnetic field is hence subject to so-called frame-dragging effects analogous to electromagnetic induction.
[14][15] Quantities that are directly related to energy and momentum should be sources of gravity as well, namely internal pressure and stress.
Taken together, mass-energy, momentum, pressure and stress all serve as sources of gravity: Collectively, they are what tells spacetime how to curve.
The inclusion of pressure as a source of gravity leads to dramatic differences between the predictions of general relativity versus those of Newtonian gravitation.
In regards to pressure, the early universe was radiation dominated,[17] and it is highly unlikely that any of the relevant cosmological data (e.g. nucleosynthesis abundances, etc.)
Likewise, the mathematical consistency of the Einstein field equations would be broken if the stress terms did not contribute as a source of gravity.
[18] In Newtonian theory, In general relativity, The classic experiment to measure the strength of a gravitational source (i.e. its active mass) was first conducted in 1797 by Henry Cavendish (Fig. 5-9a).
However, the repulsive electromagnetic pressures resulting from protons being tightly squeezed inside atomic nuclei are typically on the order of 1028 atm ≈ 1033 Pa ≈ 1033 kg·s−2m−1.
[22] With decades of additional lunar laser ranging data, Singh et al. (2023) reported improvement on these limits by a factor of about 100.
Initial results confirmed the relatively large geodetic effect (which is due to simple spacetime curvature, and is also known as de Sitter precession) to an accuracy of about 1%.
[29] Another effort, the Gyroscopes in General Relativity (GINGER) experiment, seeks to use three 6 m ring lasers mounted at right angles to each other 1400 m below the Earth's surface to measure this effect.
