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As I was going through some work of my college level courses of fundamental physics, the formula caught my attention $F={G}\frac{Mm}{r^s}$. "r" seems can be any value; there would still be an output for F. Does that mean when r (the distance between two objects) changed from $6*10^9$ m to $6.1*10^9$ (assuming the object moved), the corresponding forces between the two object will also change instantly (as the instance when the object moved)? Or will there be a lag/delay, after the object was further taken apart?

The same question applies to $F_E={k}\frac{Qq}{r^s}$

I know there must be some answer if I dig deep enough into Einstein's relativity theories, but I simply do not have the mathematics knowledge backing me up to understand his points nor someone trying to explain it.

Qmechanic
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Joe
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    Does this answer your question? How fast does gravity propagate? – Sandejo Dec 06 '20 at 05:17
  • Yes, thank you. – Joe Dec 06 '20 at 05:20
  • When you ask how the same question applies to Coulomb's law, you should be aware this force is describing the effect of an electric field from a point source charge. If that point source charge accelerates, the electric field (and induced magnetic field) will vary in time. That IS light. – zh1 Dec 06 '20 at 05:20
  • Just note that distance of two objects cannot be changed instantly as $c$ is the maximal velocity. As you change the distance also gravitationall force will change, however, the change will not be instanant. Information about change in distance will travel at speed of light. – Martin Vesely Dec 06 '20 at 07:00

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The effects of force fields do not travel faster than light; nothing in the current model of physics travels faster than light. However, some do travel at the speed of light.

There are a number of fundamental forces in the universe, including the electromagnetic force (which light is a phenomenon of), gravity and the strong and weak nuclear forces. The effects of the electromagnetic force travel at the speed of light and are mediated by the force carrying particle of photons (i.e. light). The effects of a force such as gravity also travel at the speed of light and are speculated by the scientific community to be mediated by the force carrying particle of gravitons (analogous to photons, but for gravity). The strong and weak nuclear forces also have respective force mediating particles.

Edit:

To further answer your question, there is a "lag" between an object with mass being moved and its changed gravitational force on a distant object being felt, as there equally is for an object with charge being moved and its changed electric force being felt at a distance. Both produce waves (which are equivalent to particles in physics) that travel at the speed of light to reach and impact other objects. You have heard of light waves and may also have heard of gravitational waves.

It can be useful to consider the analogy of waves in the sea arising from a disturbance caused by a ship moving, but the wave taking time to reach the shore and exert a force on beach-goers. Something similar happens when electromagnetic or gravitational disturbances occur, but the speed of the force-carrying waves/particles is at the speed of light.

Alexander Kalian
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  • The effects of a force such as gravity also travel at the speed of light Does that mean the fields travels in the same respect of speed of light? – Joe Dec 06 '20 at 05:18
  • Fields don't travel per say; they just exist and cover what is often an infinite distance. However the forces produced by interacting fields (such as two gravitational fields interacting, produced by two objects with mass, or two electric fields produced by two objects with charge) are mediated by force-carrying particles which travel at the speed of light. – Alexander Kalian Dec 06 '20 at 05:21
  • You're wrong. If a lag existed, planets would not maintain their orbits. This is trivial math. – AjaxLeung May 30 '22 at 05:47
  • Incorrect - gravitational waves travel at the speed of light and the planets still maintain their orbits. I would be interested to see your "trivial math". https://en.wikipedia.org/wiki/Speed_of_gravity?wprov=sfla1 – Alexander Kalian Jun 04 '22 at 00:21
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The fields actually surround the gravitating/electrostatic objects. Any change in the gravitational/electrostatic field will propagate at the speed of light $c$. It does not matter by how much the distances between objects are changed, this speed will always be $c$. So the change never travels instantaneously, rather it is governed by $c$.

In electromagnetism, the speed of light emerges naturally from Maxwells equations. In gravity, the speed at which gravitational effects propagate, also $c$, emerge from the Einstein field equations.

joseph h
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