Are there places in the Universe without gravity?

Question

Not sure if that is possible as I couldn't find an answer about it.

Are there places in the Universe where there are no gravitational forces?

Answer 1

In two dimensions I think I can infer in a lame, unconvincing and rigorless numerical way that there are likely to be zeros in gravity from a random distribution of objects there can be points of zero gravity.

I create a space with 20 randomly distributed point sources, calculate and plot the force field on a 2000 x 2000 grid then choose the smallest grid point and through a minimization routine find a point with arbitrarily small scalar force.

I've done everything on a log10 scale, the max, min values are of order +8 and -1 but I can easily find log10(force_magnitude) around -14 by specifying that tolerance in the minimization routine.

I can't prove this extends to 3 dimensions nor arbitrarily large space and numbers, but I have a hunch this can be addressed mathematically, so I have just asked in Math SE: What is the relative density and dimensionality of zeros in inverse square force fields to density of sources in (at least) 1, 2 and 3 dimensions?

Here are six cases for flavor:

There be zeros here!

import numpy as np
from scipy.optimize import minimize
import matplotlib.pyplot as plt
https://astronomy.stackexchange.com/questions/44184/are-there-places-in-the-universe-without-gravity
def mini_me(xy, positions):
    return np.log10(get_force_magnitudes(positions, xy))
def get_force_magnitudes(positions, XY):
    r = positions[:, None, None, :] - XY
    forces = r * (((r2).sum(axis=-1))[..., None]-1.5) # all vectors
    force_field = forces.sum(axis=0)  # vector field
    return np.sqrt(force_field**2).sum(axis=-1)
N = 20
positions = np.random.random((N, 2))
x = np.linspace(0, 1, 2000)
X, Y = np.meshgrid(x, x, indexing='xy')
XY = np.stack((X, Y), axis=2)
force_magnitude = get_force_magnitudes(positions, XY)
indices = np.unravel_index(np.argmax(-force_magnitude), force_magnitude.shape) # find the smallest one on the grid
xy0 = XY[indices] # starting point for minimization
result = minimize(mini_me, xy0, args=(positions, ),
                  method='Nelder-Mead', tol=1E-08)
if True:
    fix, ax = plt.subplots(1, 1)
    extent = 2*[0, 1]
    thing = ax.imshow(np.log10(force_magnitude), origin='lower',
               extent=extent, vmax=2)
    x, y = positions.T
    ax.plot(x, y, '.r')
    x, y = result.x
    label = str(round(result.fun, 2))
    ax.plot([x], [y], 'o', color='none', markeredgecolor='red',
            markersize=14, markeredgewidth=2)
    ax.text(x+0.02, y, label, color='red', fontsize=14)
    plt.colorbar(thing, ax=ax)
    plt.title('log10 normalized scalar force')
    plt.show()

Answer 2

This answer just amplifies on the correct answer by Barbierium.

Are there places in the Universe where there are no gravitational forces?

The answer to this question is that there is no answer to the question. To define whether or not a gravitational force would act on a test particle at a certain point in space, we have to define some frame of reference. But in fact there is no globally preferred frame of reference. The only preferred frame of reference is a local one, which is a free-falling frame of reference, and in such a frame the gravitational force on a test particle is zero.

This is known as the equivalence principle.

Answer 3

Gravity extends to infinity, so no, strictly theoretically speaking there is always some gravity present. In theory, even in this case we could have points in space where gravitational forces cancel out, but given the complexity of our universe, this just won't happen in practice.

As a more relaxed viewpoint - there are special points around orbiting objects called Lagrange points, where gravitational forces of the two objects (eg a star and a planet) sum up to zero. Those points do receive gravitational forces from other objects however (eg from Jupiter in case of the Sun and Earth). Also, as the two objects in question are also moving, these points are moving with them (otoh, there's also simply no absolute positions in space anyways, but that's a title for another story)

Answer 4

I think we must be a bit careful what we are discussing here. General relativity states that when an observer is on a geodesic, i.e. in freefall, they are not experiencing gravity. That's Einstein's famous falling elevator gedankenexperiment. It's not that gravity is there but cannot be measured, or that it is there but canceled out by the equivalent acceleration; it is not there period in the frame of reference of the observer on the geodesic.

In this sense, for every spot in the universe there is a reference frame in which no gravitation is present, namely the one moving along the geodesic. An example would be a beam of light. In its own frame of reference it's moving perfectly straight through space time. (Or rather, sitting perfectly still in an immutable, flat universe.)

Now admittedly, there are no point-shaped observers; what the man in the elevator as well as any other observer with finite size can observe is a gradient causing inner forces within the observer (more precisely, within the observed finite volume of space). The reason is that the geodesics for the different space time locations within the observed volume are not quite parallel in an inhomogeneous gravitational field. A gravity gradient is perfectly well measurable within an extended object in freefall; an example is the ISS. Only some points on it are in perfect freefall, namely those on the orbital trajectory of its center of mass; the others are pulled or pushed along.

Now the effect is already fairly small even in the comparatively steep gradient close to Earth; if you choose a location with very little gravity to begin with, and choose an inflection point at the right distance from the closest mass clusters, the effect will be extremely small. A good spot might be in an intergalactic void. My gut feeling is that it will be indistinguishable from background noise like photons from the the microwave background radiation, or general vacuum quantum fluctuations. Oh, and the gedankenexperiment also necessitates a massless observer because any local masses would create much stronger gradients, due to their proximity, than even very large masses at large distances, thus drowning out any subtle global gradients.

Answer 5

It depends on what your definition of the Universe. As long as there's mass, there's gravity. Gravity acts infinitely at causality speed, also known as speed of light. Some data suggests that there's a tiny, but everywhere present force that pulls very far away objects in opposite directions, essentially adding more space in between matter, but only where there is very little mass. Since the universe has a lot of low mass bits of space, very far objects would need to travel faster than light to reach us, but we know that's not going to happen. Each moment, some bits of matter far away fall beyond this limit after which their influence cannot influence us.

Now imagine a photon, which is of course massless, traveling into a direction that is empty, apart from objects that are so far away that space is added in between the photon and those objects, at a rate faster than the photon's speed. Once the photon reaches a distance from the source, so that space behind it is added at a higher rate than the speed of the photon, that bit of space where the photon exists would have no theoretical gravitation.

This is more of a thought experiment than anything else. Not only that a massless observer of a gravity free space cannot be created, but by definition, that bit of space would be causally disconnected from everything else. In other words, you asked whether there can be a place that is not related to a force that relates everything, and I'm telling you that yes, but only if we define that space as a space that doesn't relate to anything. You might as well consider that a no.

On top of it, if we have a single traveling photon and nothing else around it, not only that time loses any meaning, but also space. Is it even correct to say that space expands if there is no space? And if a space has no spacetime, is it a universe. Also would you consider that no-space-space, containing a single photon, originating from our universe, as being part of our universe, since they cannot ever interact with each other? They are linked to each other through their past, but surely not through their future.

I'm not an astrophysicist, but I believe that the essence is that the maths and physics that we generally use to describe reality don't forbid the existence of a gravitation-less place, but given the same maths and physics that we use, it's a very boring place void of any meaningful property. A gravitation-less place seems like a fun place to explore, even if only in your mind, but it's about as fun as being forever stranded on a deserted island, where you are the island.

Answer 6

If I understand Einstein's theory (and if it actually is correct) then gravity is the shape of space. That shape is imposed on it by mass. Thus if there is mass in the universe, there must be gravity.

Since (per the Big Bang theory) all of space & mass was once a single point (or something really small) which expanded at less than the speed of light, all of space must be affected by that mass, hence gravity must exist everywhere.

Answer 7

Suppose the universe consists of only a hollow sphere. The diameter of the sphere doesn't matter, but we require that the shell of the sphere be uniform thickness.

The sphere will have finite mass, therefore, if an observer at any distance from the sphere were to measure the resulting gravitational field, he would find a non-zero field, and hence, a force in the direction of the sphere. That being said, there is no place outside the sphere that doesn't have gravitational forces.

However, inside the sphere is another matter. There will be no force on a object within the shell of the sphere. All of the force contributions from the mass of the sphere will cancel out. In this make-believe universe, there is no gravitational force within the hollow part of the sphere.

Someone mentioned that the Space Station, being in orbit, caused the interior to have no gravity. This isn't quite correct: there are measurable microgravity forces. These are due to the fact that the real world doesn't consist of only the earth and the orbiting vehicle. Gravitational forces from tides, mass concentrations in the earth, drag on the Station from residual atmosphere at it's orbital height: all contribute to a very small gravitational forces inside.

Answer 8

I can think of one place. Inside the ISS gravity is zero! If you go up and enter the station you will experience this. No gravitational force will pull you down.

So, inside the ISS, there are certainly places (points) where there is no gravity. There exists a very very tiny tidal force at these points, but for all practical purposes, this can be completely ignored. Theoretically, there are tidal forces, so there is gravity, but from an experimentalist point of view, these can be ignored.

Only if the ISS were orbiting a black hole, the astronauts would be able to sit on the floor of the ISS. They would probably be stretched beyond comfort...

So two particles in the ISS, initially at rest wrt each other, will always stay at rest wrt each other. In the very far future will they have a small observable velocity. It would be a nice problem to find out how long it takes...

While gravity in the universe can be zero, the potential due to gravity is non-zero everywhere. Even between the most distant galaxies, the potential is non-zero, while the force of gravity between the galaxies can be positive, zero, or negative.