Ask Ethan: If mass bends space-time, how does it straighten back?

The curvature of spacetime near any massive object is determined by a combination of mass and distance to the center of mass. It is necessary to take into account other parameters, such as speed, acceleration and other energy sources.

Matter tells space how to bend, and curved space tells matter how to move. This is the basic principle of Einstein GR, which for the first time connected such a phenomenon as gravity, with space-time and relativity. Place the mass at any point of the Universe, and the space around it will respond by curvature. But if you remove the mass or move it, what causes space-time to “fall into place”, assuming a non-crooked position? This question is asked by our reader:

We are taught that mass deforms space-time, and the curvature of space-time around a mass explains gravity - for example, an object in orbit around the Earth actually moves in a straight line lying in a curved space-time. Suppose it makes sense, but when a mass (like the Earth) moves through space-time and bends it, why does space-time not remain curved? What mechanism straightens this area of ​​space-time when the mass moves on?

There are many interesting things connected with this question, and the answer can actually help you understand how gravity works.


The curvature of space given to it by the planets and the sun in our solar system must be taken into account in the course of any observations that a spacecraft or other observatory can make. The effects of GR, even the smallest, cannot be ignored.

For hundreds of years before Einstein, Newton's best theory of gravity was. The concept of the universe from Newton was simple, straightforward and philosophically did not satisfy many. He stated that any two masses of the Universe, regardless of their location and removal, instantly attract one another with the help of a mutual force, known as gravity. The more massive each body, the greater the force, and the farther they are located, the smaller the force (decreasing with the square of the distance). This applies to all objects of the Universe, and Newton’s law of universal perception , in contrast to all other alternatives that existed, ideally coincided with observations.


Newton's law of the world, replaced by Einstein's theory of relativity, was based on the instantaneous action of forces at a distance

But he introduced an idea that many of the greatest minds of the time could not accept: the concept of action at a distance. How can two objects located at different ends of the Universe suddenly and instantly affect each other? How can they interact at such a large distance that there is nothing between them? Descartes could not accept this concept, and instead formulated another, in which there existed an environment over which gravity was propagated. He argued that space is filled with some matter, and when mass moves through it, it displaces matter and creates whirlwinds - this was an early version of the ether. This theory was the first in a long line of what would later be called mechanical (or kinetic) theories of gravity .


In the version of gravity from Descartes, the space was filled with ether, and only its displacement could explain gravity. This idea did not lead to the formulation of gravity, which coincided with the observations.

Of course, the concept of Descartes was wrong. The usefulness of a physical theory determines the coincidence with experiment, and not our predisposition to certain aesthetic criteria. When the GRT appeared, it fundamentally changed the picture painted by Newton's laws. For example:

• Space and time were not absolute and everywhere the same, but were connected and behaved differently for observers moving at different speeds in different places.
• Gravity does not act instantly, but moves at a limited speed — at the speed of light.
• Gravity is not determined by mass and position directly, but by the curvature of space, which, in turn, is determined by the entire mass and energy in the universe.

The action at a distance did not disappear anywhere, but “the force acting at infinite distance through motionless space” was replaced by Newton with the curvature of space-time.


The curvature of space-time means that clocks that are located deeper in a gravity well — and, therefore, in a more curved space — operate at a speed different from clocks located in a less deep, less curved place of space.

If the Sun had suddenly disappeared from the Universe, we would not have known about it for some time. The earth would not immediately fly away in a straight line; it would continue to rotate around the location of the Sun for another 8 minutes and 20 seconds. Gravity is determined not by mass, but by the curvature of space, which is determined by the sum of all the matter and energy that is in it.

If you removed the Sun, the space would pass from a curved to a flat state, but this transformation does not occur instantaneously. Space-time is a fabric, and the transition should take place in the form of some sudden movement, sending very large waves - gravitational - through the Universe, which spread along it like ripples on the surface of a pond.


Each wave propagating in a medium or in a vacuum has a propagation velocity. There is no infinite speed, and, in theory, the speed of propagation of gravitational waves should coincide with the maximum speed allowed in the Universe: the speed of light.

The speed of wave propagation is determined in the same way that the velocity of everything in the theory of relativity is determined: their energy and mass. Since gravitational waves have no mass, but have finite energy, they must move at the speed of light. And this means that the Earth is not really tied directly to the location of the Sun in space - it is tied to the place where the Sun was a little more than 8 minutes ago.


Gravitational radiation appears every time when one mass moves in orbit around another, therefore, the orbits decrease for quite a long time. Sometime in the future, the Earth will spiral down on what remains of the Sun, if no body has ever ejected it from orbit before. Earth is tied to the place where the Sun was about 8 minutes ago, and not to where it is at the moment.

This is odd, and potentially a problem, since we studied the solar system quite well. If the Earth were tied to the location of the Sun, which it took ≈ 8 minutes ago according to Newton's laws, then the orbits of the planets would not coincide with the observations. However, GR also differs in another aspect. For calculations it is necessary to take into account the speed of a planet moving in orbit around the Sun.

For example, the Earth, since it also moves, in a sense, "rolls" on these waves, going through space, falling not in the place where it raised it to this. In GR, there are two new phenomena that strongly distinguish it from Newtonian: the object’s perception of gravity is influenced by the speed of each object, as well as changes in the gravitational field.


The fabric of space-time, with waves and deformations occurring due to the presence of masses. The fabric of space, of course, is bent, but when mass moves through a changing gravitational field, a lot of interesting things happen.

If you want to calculate the curvature of space-time at any point in space, GR allows you to do this, but you first need to know something. You need to know the location, size and distribution of all the masses of the universe, exactly as Newton demanded. In addition, you need information on the following:

• how these masses move and move,
• how are all the other non-mass forms of energy distributed,
• as an object from which you are observing, moves in a changing gravitational field,
• and how the curvature of space changes over time.

And only with this additional knowledge can one calculate the curvature of space at a certain point in space and time.


The evolution of space-time and the work of gravity are determined not only by the positions and magnitudes of the masses, but also by how they move relative to each other and accelerate in a changing gravitational field.

This curvature and straightening has its costs. The accelerating Earth cannot just move in the changing gravitational field of the Sun without consequences. They exist, albeit small, and can be measured. Unlike Newton's theory, according to which the Earth should describe a closed ellipse, moving around the Sun, GR predicts that this ellipse should experience precession over time, and the orbit will slowly decrease. The time interval for which this will occur may exceed the current age of the Universe, but, nevertheless, the orbit will not remain stable for an arbitrary time.

Even before we measured gravitational waves, this was the main method for measuring the propagation velocity of gravity. Not by the example of the Earth, but by the example of a system with extreme parameters, in which the change in orbit can be easily noticed: a system of two objects in a close orbit, at least one of which is a neutron star.


The easiest way to see this effect is if a massive object moves at a rapidly changing speed in a strong and changing gravitational field. And such conditions give us double star systems of neutron stars! One or two such rotating stars emit pulses that are visible on the Earth each time the star’s axis passes through a line of sight. Predictions of Einstein's theory of gravity are extremely sensitive to the speed of light, so much so that, following the observation of the very first pulsar, the PSR 1913 + 16 dual system, discovered in the 1980s ( the Khals-Taylor binary system ), we put restrictions on the speed of gravity, which coincided with the speed of light within the measurement error of just 0.2%!


The rate of reduction of the orbit of a double pulsar strongly depends on the speed of gravity and the orbital parameters of the binary system. We used data on the binary pulsar to limit the speed of gravity, and equate it to the speed of light with an accuracy of 99.8%

Only by the example of these double pulsars we learned that the gravitational velocity is in the range of 2.993 × 10 ⁸ - 3.003 × 10 ⁸ m / s. This confirms GR and eliminates Newtonian gravity and other alternatives. But a mechanism explaining why space is not bent when the mass, which was in some place, leaves there; GTR is not an explanation for this. A mass moving with acceleration through a changing gravitational field will radiate energy, and this energy will be waves, known as gravitational waves, go through the matter of space-time. A return to a balanced, non-curved state happens naturally. It does not require further explanations, the GRT is everything. [ When Newton was asked about the nature of gravity, he replied: I do not invent hypotheses / approx. trans. ]