How could it be possible to exert gravity without mass?

Some of what I read in How could a 4D organism influence events in our world made me think in a different direction about a question I asked before.

I'm trying to create a large sphere shaped field of gravity, without a physical mass at it's center, that floats in space. Inside the field would exist a habitat that humans could live in. Basically a massive ball of air held together by this force in what I imagine would be a microgravity situation. I already assume this couldn't be found in nature. I guess it would have to be some kind of super science.

How could the physical mass be "elsewhere" but it's gravity be felt "here"? Could something exist in another dimension or reality but exert its effects in our reality?

EDIT:

"One leading hypothesis is that dark matter consists of exotic particles that don't interact with normal (baryonic) matter or light but that still exert a gravitational pull." Does that help with ideas?

Adding onto edit 1:

https://www.space.com/33850-weird-galaxy-is-mostly-dark-matter.html

From the article: “Motions of the stars tell you how much matter there is," van Dokkum said in a statement. “They don’t care what form the matter is, they just tell you that it’s there. In the Dragonfly galaxy stars move very fast. So there was a huge discrepancy: using Keck Observatory, we found many times more mass indicated by the motions of the stars, than there is mass in the stars themselves.” In other words, van Dokkum and his team found evidence of way more mass than they could actually see.

OR EDIT 2: Could the use of massless particles lead to an answer?

https://en.wikipedia.org/wiki/Massless_particle

EDIT 3: A version of String Theory known as M Theory suggests that separate "branes" interact through gravity (The central idea is that the visible, three-dimensional universe is restricted to a brane inside a higher-dimensional space, called the "bulk"). Could something along these lines be an answer?

• Not scientifically. We can use acceleration/rotation to simulate gravity, but that's it. – Alexander Feb 6 '18 at 18:05
• You mean that there is no meaningful mass anywhere in the bubble, or that there must be a gap at the exact center? What does "another dimension" mean? – user25818 Feb 6 '18 at 18:16
• Massless black hole? – PyRulez Feb 6 '18 at 19:26
• Note that as far as we know, Dark Matter does have mass (which is why it has gravity). However, because it does not interact with the electromagnetic force (or possibly any others), it can not be see or felt or be interacted with in any other way. – RBarryYoung Feb 6 '18 at 22:12
• @Len In any way except gravity. Have a look at concepts like "gravity tractor"; it'd need a lot of patience and precision engineering, but it's doable. The main problem with manipulating something that only interacts through gravity is that it's very hard to dissipate energy - that's why matter coalesces to stars and planets (it loses energy through EM radiation), but dark matter doesn't (the only energy loss is through gravitational radiation, which is absurdly low-energy in most conditions). – Luaan Feb 7 '18 at 9:38

1. You could have the gravity produced by a big wad of dark matter

Dark matter is a hypothetical type of matter distinct from ordinary matter such as protons, neutrons, electrons, and neutrinos.

Dark matter has never been directly observed; however its existence would explain a number of otherwise puzzling astronomical observations. The name refers to the fact that it does not emit or interact with observable electromagnetic radiation, such as light, and is thus invisible to the entire electromagnetic spectrum.

Although dark matter has not been directly observed, its existence and properties are inferred from unexplained mass in gravitational lensing calculations, which affects the motions of baryonic matter and light.

Given that light and radiation pass through dark matter (but the path of radiation can be bent by the gravity of dark matter) it may be that other things pass right through also - like people. Dark matter might only have gravity.

2. Gravitational mass not in 3D plane.

Consider a 2D world. I am a flatlander and there is a large 2D mass as well - perhaps a big circle. The gravitational forces between us can be expressed as a vector. The vector can be considered a sum of X and Y vectors.

Now a 3D world. I am here, and so is Earth. The gravity between me and Earth can be expressed as the sum of X, Y and Z vectors.

Depending on how you want to make gravity work, you could have extraplanar objects exert gravity. In the 2D world, if a 3D sphere intersected it the flatlander would perceive it as a circle. You could have gravity exerted along X and Y vectors by only the mass of the sphere that was within that 2D plane. In this case it would not be possible for me to experience gravity from something which was not in the same plane as me.

Or - you could have extraplanar objects exert gravity on things not in their plane. The entirety of the mass exerts gravity as is the case between me and Earth. For the Flatlander the entire 3D mass could pull, but only the X and Y vectors would be relevant. A Flatlander cannot be pulled out of its 2D plane and so the Z vector is irrelevant. To calculate the pull of a 3D object out of plane of the 2D object one would calculate X Y and Z vectors then drop Z.

So too your 4D object. If you have gravity work this way an extraplanar 4D center of mass can exert gravity on a 3d object via X,Y and Z vectors but not "A", which would pull me out of my 3D plane.

It does not have to be a 4D object exerting gravity on me. It could be an ordinary 3D object but not in my 3d plane. An interesting speculation: perhaps dark matter (that has only gravity) is actually normal matter which is not in the same 3D plane as us, but can exert gravitation influence on objects in our plane. A 3d star in a 3d plane "adjacent" to mine via the 4th dimension could exert gravity on me but I would not see its light or feel its heat.

3. Bent space.

There are actually two different parts of general relativity. They're often stated as

1. Spacetime tells matter how to move
2. Matter tells spacetime how to curve

Gravity is actually a product of locally warped spacetime. Spacetime warps because of matter in it. I recommend the linked article on the physics stack for those interested. Could spacetime get warped absent any matter? I am thinking of the dent a cat leaves on a pillow. When the cat leaves the dent stays. Of course curved spacetime is kept curved by the presence of matter and uncurves as the matter moves on. But what if there were a piece of spacetime that like the pillow stayed curved even though the cat has left? This "bent" would produce gravitational effects despite there being no mass - it would only be spacetime telling matter how to move.

Sort of spooky but maybe appropriate for concept-driven high SF.

• DARK MATTER! I was thinking of that, but since dark matter has not actually been observed I thought I'd get a lot of nays. Now, how to manipulate something that has never been observed... – Len Feb 6 '18 at 18:25
• Although dark matter has not been directly observed, its existence and properties are inferred from unexplained mass in gravitational lensing calculations Dark matter has mass. The OP wants gravity without mass, which isn't going to happen. – kingledion Feb 6 '18 at 18:26
• No, it was stated that the mass could be "elsewhere" but the gravity is "here". Dark matter, as some theories have it, fits. It doesn't interact with normal matter or energy except through gravity, so for all practical purposes it's "elsewhere" even if physically present. – Keith Morrison Feb 6 '18 at 18:41
• One theory that competes with dark matter is that gravity interacts between multiple dimensions. So, nearby dimensions have gravitational influence on ours. That explains why gravity is so weak compared to the other forces. – ShadoCat Feb 6 '18 at 19:09
• @Len it hasn't been observed, but it's been hypothesized, and that's Good Enough For Fiction... – RonJohn Feb 6 '18 at 23:13

What you're proposing can't work. If you contain the sphere of air via gravity as you are thinking, the gravity will necessarily pull on all matter equally at any given range. As a result, denser things (like, say the human inhabitants) will be pulled toward the center and the air will not provide sufficient resistance for them to stop themselves. Therefore you would either need a physical mass for them to stand on or have them constantly expending energy fighting gravity via some kind of personal propulsion system... Or, I suppose, just live with the writhing ball of flesh at the centerpoint... Perhaps they take turns being the floor...

If your goal is for humans to be able to fly, there are two approaches that come to mind:

1. Some kind of membrane or forcefield to hold the air in without providing gravity. Given that you don't like the idea of a solid barrier, probably the latter. Maybe some kind of gravitational lensing effect heretofore unobserved? Make the gravity that holds stuff in only be in effect at the periphery of the sphere. Probably wouldn't do good things to anyone passing through it though.

2. An environment similar to the one in Larry Niven's "The Integral Trees" where the cloud of atmosphere takes the place of the rings of a gas giant. That gets you a source of sufficiently strong gravity to hold the air in, but puts it in orbit so the inhabitants don't all pile up in the center. Such a system would not be stable in the long-run, but long-run on celestial timescales is plenty long enough for humans to live in for quite a while.

• Perkins, thanks. I was already aware of your #2 option and have explored similar options with other questions. Your #1 option is better and closer to what I'm thinking, but it's problematic too, because when I did some research on Force Fields it seemed like they're just not possible. As far as the micro-gravity - yeah that's what I want. My characters have the means to self propel. What did you mean when you wrote: "Make the gravity that holds stuff in only be in effect at the periphery of the sphere. Probably wouldn't do good things to anyone passing through it though." What would happen? – Len Feb 6 '18 at 22:07
• @Len it's called "gravitational shear" and it's why the Roche Limit is a thing. In order to wrap a "bubble" of gravity around the air that would grab any that tried to escape until sufficient back pressure built up to contain the rest you would need to focus a large amount of gravity into a small area. Assuming it's only 1G (which seems low to me) there will be a point where the force applied on any solid object passing through will be 9.8m/s^2*(mass of whatever portion is passing through) Concentrating force like that into a small area tends to break solid objects into non-solid objects. – Perkins Feb 6 '18 at 22:25
• Oh I get that part. But if the sphere of gravity is a field wouldn't the outer edges be thinner like when entering a planets atmosphere? Strong enough to contain the atmosphere but not such a contrast that shear comes into effect? – Len Feb 6 '18 at 22:32
• You can decrease the shear by making the boundary layer wider, but that will also increase the total amount of energy required due to larger area. You should be able to calculate how much force is required to contain a bubble based on the internal desired pressure and then calculate how wide your gravity bubble needs to be based on the shear equations and the tensile strength of your creatures. I'm not sure what it will come out to. Might have to be really big if you want full Earth sealevel pressure. And all this depends on being able to "focus" gravity, which is theoretical at best. – Perkins Feb 6 '18 at 22:46

Space habitats meant for humans to live in may well have artificial gravity without any mass whatsoever in the center. All you need to do is spin the habitat - the faster it rotates, the greater the centripeal force generated by this will be. So as long as you have an habitat with a hollow center, you're good - after all, your humans will need rooms and restrooms and everything, right? They are not just going to float in space.

If you don't like the idea above, and you want to generate gravity without mass... You can do that, but you are going to need an humongous amount of energy. In general relativity, gravitational fields are generated by the stress-energy tensor, which is a property not exclusive to matter - radiation also has it.

Therefore, energy has its own gravity as well. Get enough energy on a point (through concentrated radiation, i.e.: visible light lasers) and you may start feeling the pull.

The problem is how much is enough, really. The equation you are looking for is the famous E = MC2 one. So, to feel a pull equal to Earth's surface gravity, from a point that is one Earth radius away from you, you would need approximately...

M = Earth's mass = approx. 6 x 1024 kilograms
C = Speed of light = approx. 3 x 108 meters per second
E = Energy required = MC2 = approx. 6 x 1024 x (3 x 108)2 joules

A back-of-the-napkin calculation suggests an energy amount of 3.6 x 1041 joules. That is 8 orders of magnitude greater than the power output of our sun's core for one Earth year, so a set of lasers with a total power of a one hundred billion sun cores aimed and focused at a small region in space for a whole year will give you the energy amount you need. I think it is reasonable to expect that any civilization capable of such a feat would have the means to keep the energy contained in that point.

Edit: see Daffy's answer. If the region in space holding the energy is small enough (30 cm radius or less), you will generate a black hole. That will not bode well for the habitat, as anything that crosses the hole's horizon (including air) is practically lost forever.

• @Len the only thing that could do the trick for you is gravity. Unfortunately, the amounts of energy involved are just the way our universe works. We might as well complain that the noon sky is blue... – Renan Feb 6 '18 at 18:52
• @Len by the way, the calculation is for a habitat the size of the Earth. That would bring along a whole other set of problems. You may reduce the amount of energy required (and problems) by going with a smaller radius. It's just that I don't know how to calculate that right now. – Renan Feb 6 '18 at 18:54
• You also need to keep the energy contained, or replace it if it leaks. – PyRulez Feb 6 '18 at 19:24
• @Len a space habitat without a hard cap would be called a planet. – John Feb 16 '18 at 17:38
• @John... without mass, John. WITHOUT mass. :) – Len Feb 16 '18 at 19:14

You could have your pocket of gravity be created by energy instead of mass. Photons have no mass, but are affected by gravity, and they create their own gravitational field. The energy of a photon is $E = \frac{hc}{\lambda}$. $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the photon's wavelength. So a single ultraviolet (Extreme ultraviolet, 100nm) photon has the energy of about 2 nanojoules. We can rearrange $E=mc^2$ to be $m = \frac{E}{c^2}$. So each photon has a relativistic mass of 2.2 * 10^-26 kilograms. That means it creates the same gravitational field that a particle of that mass would create. So to create earth-like gravity, you need to match 6*10^24 kg. That will take about 2.73*10^52 particles.

So great, we have an earth-like gravity with no mass. But the photons will fly off in all directions right now. So you have two options. 1) Sci-fi a way of containing them. (magnetic fields, strange technology that's unknown to your charactors, etc) or 2) collapse it into a kugelblitz black hole.

The Schwarzschild radius is the "radius of no return" for black holes. If you collapse a mass to be smaller than its Schwarzschild radius, it'll become a black hole. The Schwarzschild radius is given by the equation $r = \frac{2mG}{c^2}$ where $G$ is the gravitational constant. Given a mass of 6*10^24 kg, your photon planet will become a black hole if you crush it into a ball with a radius of about 30 centimeters. Keep in mind, it'll still have earth's gravity, and getting too close to the center will spaghettify you, but at earth-surface-like distances, it'll feel identical. Except for, you know, the lack of anything to stand on and all.

• Holy... that's awesome. – Len Feb 7 '18 at 0:10
• @Len Not gonna lie, those calculations were fun. :) – Daffy Feb 7 '18 at 0:20
• I love this answer. I have to nitpick, though... Things will fall towards the hole, including air. The habitat would soon be no more. – Renan Feb 7 '18 at 3:24
• "Magnetic Fields? Would that work or is that handwavey?" Super super handwavey. Photons don't react to magnetic fields anyway, since they have no charge. (Don't quote me on that). You'd have better luck doing this with electrons, but electrons have mass, so you'd be back to square one. Or you can sci-fi it away :) Like @Renan said, "You only have to explain things up to a certain point before it becomes overthinking" – Daffy Feb 7 '18 at 19:45
• @Daffy, Though I LOVE your answer I feel like the another answer above would be more useful or applicable to others inquiries. But Thank you so much. – Len Feb 17 '18 at 17:47

Make it a bubble of Time.

Time and Gravity go together. If you slow down time just a tiny bit, you will create a gravity field.

Gravitational Time Dilation is part of Einstein's theory of Relativity. The closer you get to an object of mass, the slower time moves for you.

Want to have the effects of mass? Find a way to slow down time.

• Time and Gravity go together...what? – kingledion Feb 6 '18 at 18:25
• @James, can you elaborate please? Thanks. – Len Feb 6 '18 at 18:26
• I see where he's coming from, and he's technically correct... However: If you slow down time you'll end up with two problems. Firstly the fact that the bubble of air lasts for centuries for the outside observer doesn't mean that the inhabitants won't subjectively be losing their air in an explosive decompression event at what seems like normal speed. Second the chronometric shear at the boundary layer will do horrible things to anything passing in or out of the environment, so you might as well have a solid barrier. (In fact it will become one as mass accretes upon the boundary.) – Perkins Feb 6 '18 at 22:05
• @Perkins, You wrote: "It will become a solid barrier as mass accretes upon the boundary". That is unless the inhabitants have a means to clear it(?) – Len Feb 7 '18 at 0:21
• @Len Given the amount of time dilation required the inhabitants are highly unlikely to be able to clear it fast enough. Remember, time runs more slowly for them. – Perkins Feb 7 '18 at 18:48

If you're looking to create an air-planet, have you thought about setting it in a nebula, and part of it just happens to meet Goldilocks conditions?

Or what's wrong with having a nitrogen-oxygen gas giant?