# Is gravity faster than light?

Short answer: Changes in the gravitational field spread with the vacuum light speed.However, when light passes through a medium, it slows down. There are no such effects for gravity. This means that gravity may be slightly faster than light. In space on the scales where changes in gravity play a role, however, this effect is negligible. It is therefore true that light and gravity are equally fast.

In order to answer this question conscientiously, however, one should first clarify:

1. What is light?
2. What does “faster” mean here?
3. What is gravity?

Let’s start with the first point. To do this, you have to go a little further and start with the concept of electromagnetic interaction.It describes the interaction between electrically charged objects. This means starting with electric charges whose current positions and velocities you know and want to know how accelerations, velocities and positions of these charges develop. To solve this problem, the so-called electromagnetic field is used. This means assigning a vector to each point in space. From the length and direction of this vector it is possible to determine what acceleration a particle would experience, which is located at this point. The Maxwell equations now describe how to determine this field from the distribution of charges and their velocity, and with the help of the Lorentz force one obtains the accelerations from the size of the field and the speed of the charges (and their mass), which experience the charges.

If you look at a situation in which the charges move evenly, you get so-called static solutions, i.e. the size of the field changes from point to point, but remains constant in time.(Caution: the equations look as if they apply to the whole space and for all times. In fact, this solution is only correct from the time when there are no more accelerations and only until the time when accelerations occur and only applies to a finite – albeit spreading – area of space. Only within this space-time section are the fields static.)

But what if the charges are accelerated?Then the field changes not only from place to place, but also in time at every place. It is then called electromagnetic radiation. A special form of acceleration are periodic accelerations, i.e. when the charges move in circles at a constant angular velocity or constantly moving back and forth. It turns out that then the fields (if you go far enough spatially away from the charges) are periodic in space and time, i.e. when one looks at a place, the field strength repeats itself after a fixed time or time. one has a fixed number of repetitions per unit of time – this is called the frequency – and there is a constant distance in the space in which the field strength is repeated – the so-called wavelength. The frequency [mathf[/math and wavelength [math_lambda[/math are now related: [mathf=c/slambda[/math where the speed of light appears for the first time with [mathc[/math

Furthermore, it follows that loads are periodically accelerated by this field.That is, if I periodically accelerate loads in one place, charges with the same period are accelerated in another place. The more energy I use to accelerate the source charges, the higher the frequency of the wave and thus the frequency in the acceleration of the removed charges. So it is transmitted by the wave energy and the size of the energy is related to the frequency. And now we are finally coming to the light! Light is simply such electromagnetic waves in a certain frequency range (approximately 400 to 800 THz – where one THz is equal to [math10-12/math oscillations per second)

OK, that was really quite far-fetched!But we have now done so much preparatory work that the following points are getting a little shorter.

What is the significance of the “speed of light”?Let’s start with the special case of periodic accelerations. We are now changing the period of acceleration at a certain point in time. It turns out that this change is now moving at the speed of light, i.e. at a point that is one second of light (i.e. about 300 000 km) from the source, the frequency of the field change changes after one second. This means that for a charge that is a matter of light from the source, it changes the acceleration after one second. In general, any change in the acceleration of charges at the speed of light propagates.

Let us now turn to gravity and its “speed”.Since Newton, we have known that what keeps us on the ground and what makes the planets orbit around the sun can be described by an interaction, gravity. In Newtonian physics, the gravitational force has no finite propagation velocity, i.e. every change is transmitted instantaneously. Since Einstein, however, we have known that the correct description of gravity is described by much more complicated equations, the Einstein field equations of general relativity. These correspond to Maxwell’s equations for electromagnetic interaction. The mass corresponds to the loads. The fields in the ART are now the metric of the room. The metric of space describes how to determine distances in space-time continuum. But let’s put the details for this certainly somewhat confusing point back. What is important, however, is that, similar to electromagnetism, there are also static solutions here, and for small speeds and small masses, these pass into the Newtonian gravitational equation. Again, the same warning applies as with the static solutions for the EM interaction: even if the equation looks like it lasts for all times and the entire space, it is only valid in a limited range of space and time.

For the consideration of the rate of propagation, we are once again concentrating on a special case, instead of the general solutions of the field equations, which are very difficult to comprehend even for experts.Similar to electromagnetism, we look at the fields at a great distance from masses. In this area, one can assume that the changes in the metric are very small, i.e. you have the metric without any influences of gravity and then small changes on it. This fluctuation of the metric on the otherwise flat space is then called gravitational waves. It now turns out that these also have a frequency and a wavelength at periodic accelerations. Wavelength and frequency are in the same ratio as for electromagnetic waves: [mathf=c/slambda[/math.Furthermore, the following applies again: any change in the acceleration of the masses leads to a change of the fields and spreads at the speed of light.

And how small is this small fluctuation of the metric?In the first direct measurement of gravitational waves in the LIGO experiment, a phenomenon was observed that radiated more energy in the short term than all the stars in the observable universe put together in the form of light – so this was a rather violent event. And this led to a change in length of ten thousandths of the proton diameter of the four-kilometre-long measuring distances.

In short, light and gravity are controlled by the Maxwell equations anddescribed Einstein’s field equations. Both sets of equations result in a propagation speed with vacuum light speed.