# Is gravity 'weak' because it leaks into higher dimensions?

1. Apr 9, 2012

### B.Spinoza

I seem to have read something once that suggested that gravity may be leaking into other dimensions/branes, this could explain why this force is so weak.
I've been left thinking that it makes sense as a possibility. If it turns out to be the case, could Dark Energy then be leaked gravitational energy from other dimensions leaking into our Universe? I realise that Dark Energy has the opposite effect to gravity, but somehow I think that makes sense, just like when you move a figure from one side of an = sign to another, the sign flips.

Ideas anybody? Thanks

2. Apr 9, 2012

### Mark M

Hi B.Spinoza, welcome to the forum!

The idea you're speaking of comes out of non-perturbative string theory, called M-theory. In M-Theory, strings are not the only ingredient. Rather, multidimensional strings, called branes, are fundamental along with ordinary one dimensional strings. M-Theory explains string tension, the variable that determines string oscillations and hence particle values, can be explained in terms of how tightly the branes hold the ends of open strings, the strings that make up everything except gravity. Gravity, in string theory, is represented by a closed loop string. Since a brane cannot hold onto a closed loop, since it has no ends, it will occasionally float off of the brane.

The problem with supposing dark energy is truly gravity from other branes is it doesn't explain the constancy of the acceleration of the expansion of the universe. But I can't say for sure, considering M-theory is still in its infancy. I did a search on arxiv for a paper on the topic, but I couldn't find anything.

But, some string theorists have proposed that dark matter may be gravity from other branes.

The idea may be a source of experimental testing of M-Theory in the future. If particle collisions could produce less mass than was originally started with, that would be a sign of strings being 'knocked off' of our brane.

3. Apr 9, 2012

### B.Spinoza

Hi Mark

Thanks for the welcome and reply. It all makes sense (so much as these things can)

re: 'doesn't explain the constancy of the acceleration of the expansion of the universe'... OK, but I thought that the Universe hasn't expanded constantly, I was under the impression that after 'inflation' the expansion slowed considerably and then kinda kept coasting on and that the expansion rate is actually increasing as the binding force of gravity is diluted throughout the increasing volume of the Universe.

If the Universe has a finite mass/energy and is a closed system (I know it wouldn't be if gravitational energy was leaking across branes) then the amount of gravitational energy that leaks out would be constant. The energy leaking in to our Universe from other branes would be constant too as the other Universes have a finite/fixed mass, if that is the source of the Dark Energy and associated expansion then it would a constant force.

Is that convoluted b.s. or does it make sense?

4. Apr 9, 2012

### Mark M

Remember, inflation was not caused by dark energy. Inflation occurred because a scalar field, known as the inflaton field, decayed into a false vacuum. A false vacuum is essentially a state that a field can get 'stuck' in, while trying to decay to it's ground state, a true vacuum. In order for the inflaton field to reach a true vacuum, it had to exert an enormous negative pressure, resulting in repulsive gravity. This repulsive gravity drove the expansion of the universe until the inflaton field decayed.

The rate of expansion is increasing, yes. But it is most likely doing so at a fixed rate. Once inflation ended, the universe underwent the normal expansion, decelerating over time. The gravity of the totality of everything in the universe out weighed that of dark energy, causing the universe to slow down over time. But as the volume of the universe diluted, dark energy began to have a more prominent role. About 7 billion years ago, the force of dark energy overcame that of gravity, and began to accelerate the expansion of the universe. The important point to remember is that, as far as we know, dark energy's value seems to remain constant, or at least, very close to it. It may lose some density through expansion, but nothing like the amount lost by matter/dark matter.

So, in short, yes, the universe is accelerating. But it is doing so according to a fixed rate. If gravitons from other branes were the case, we should see fluctuations in this rate of expansion, not a constant acceleration.
Good point, but you are relying on the fact that the other branes are identical to ours. Say another brane came floating by through the bulk of space, and dropped off some repulsive gravitons. We would detect this as an abnormality in the rate of expansion.

5. Apr 9, 2012

### B.Spinoza

Super. I like that answer, I need to read up for the first sentence a little; the rest made sense. I get the history of Universal expansion a little more, not that I can picture 7 billion.

I'm guessing 'Inflatons' are hypothetical particles that carry the inflation force? (a kinda anti-Higgs?) Anti-gravity? Maybe one day all this atom smashing will come up with something useful! ;-)

Branes shouldn't be symmetrical to ours, from what I understand that most of the concept relies on each brane having different qualities.

I'm gonna keep thinking... thanks again.

6. Apr 9, 2012

### Mark M

Exactly. Originally, when Alan Guth proposed inflation in the 1970's, he assumed that the Higgs Field played the role of the inflaton field. Later, with the dawn of new inflation pioneered by physicists such as Paul Steinhardt and Andrei Linde, it was realized the inflaton had to be its own particle.

There isn't an inflation force, but it is repulsive gravity. Here's how it works:

In general relativity, mass, energy, and pressure produce the attractive gravity that we are familiar with. This causes a positive curvature in spacetime. Negative pressure, the force that is exerted by a tense rubber band, has the opposite effect - it gives spacetime a hyperbolic shape, resulting in repulsive gravity. Since gravity is just the shape of spacetime, a negative pressure will drive expansion.

The inflaton field is a scalar field, meaning it takes a value at every point in space. Essentially, when it was trying to reach it's ground state, it super-cooled. This is similar to how purified water can be lowered below 0 degrees Celsius without freezing. The inflaton field would react by filling the universe with large amounts of energy, and as Guth found, a negative pressure. This enormous negative pressure would allow for the inflaton field to reach its true vacuum, and in the process, expand the universe by a huge amount. After reaching this ground state, it would decay into a hot bath of radiation, which would soon give birth to the matter in the universe.

7. Apr 9, 2012

### Chronos

Gravity leaking into other dimensions is not a satisfying solution. Were this true, should we not expect gravity from 'other universes' to leak into our universe?

8. Apr 9, 2012

### rbj

gravity is neither weak nor strong in comparison to, say, EM because it acts on mass while EM acts on charge and the two quantities are incommensurable, so they cannot be directly compared. it is true that the attractive gravitational force between two protons is much much less than the electrostatic repulsive force between the same two protons (both fields are inverse-square, so it doesn't matter what the spacing is), and that is because the charge on the protons is in the same ballpark as the Planck charge, but the mass of the protons is far, far less than the Planck mass.

quoting Frank Wilczek:

9. Apr 10, 2012

### Chronos

er, and your point is ...

10. Apr 10, 2012

### Dickfore

This is from Anthony Zee's "QFT in a Nutshell", chapter I.6.

In a $D = (3 + n)$-dimensional world, the potential energy goes as:
$$V(r) \propto \int{d^{3 + n} k \, \frac{e^{i \mathbf{k} \cdot \mathbf{x}}}{k^2}} \propto \frac{1}{r^{1 + n}}$$
If the gravitational force is proportional to the masses of the interacting particles regardless of the number of spatial dimensions, we may write:
$$V(r) = G_{3 + n + 1} \, \frac{m_1 \, m_2}{r^{1 + n}}$$

In natural units ($\hbar = c = 1$), the dimensions of mass, length, and time satisfy $\mathrm{T} = \mathrm{L} = \mathrm{M}^{-1}$, and every physical quantity has only a mass dimension. For example:
$$\left[ V(r) \right] = [E] = \mathrm{M} \, \mathrm{L}^2 \, \mathrm{T}^{-2} \stackrel{\mathrm{n.u.}}{\rightarrow} \mathrm{M}$$
Then, the "Universal Gravitational Constant" in $3 + n + 1$ space-time dimensions has a mass dimension:
$$\left[ G_{3 + n + 1}\right] = \frac{[E] \, [r]^{1 + n}}{[m]^2} = \mathrm{M}^{-2 - n}$$
Indeed, this constant defines a Planck mass in $3 + n + 1$ space-time dimensions:
$$G_{3 + n + 1} = \frac{1}{M_{\mathrm{Pl}, 2 + n}}$$
Indeed, in (3 + 1)-space-time, $M_{\mathrm{Pl},4} = 1/\sqrt{G_{4}} \sim 10^{19} \, \mathrm{GeV}$. This is a HUGE energy scale (energy and mass have the same dimension in natural units), a fact we interpret as the reason why gravity is so weak.

But, suppose the extra n spatial dimensions are "curled up" to linear dimensions of the size R. This need not be a microscopic length scale, but is small enough that it had not been detected by gravitational experiments performed on such a small length scale. For distances $r \gg R$, the gravitational flux spreads only in the 3 unfolded linear dimensions, and the gravitational potential energy goes as:
$$V(r) = \frac{m_1 \, m_2}{M^{2 + n}_{\mathrm{Pl}, 3 + n +1}} \, \frac{1}{R^n} \, \frac{1}{r}$$
If we interpret:
$$\frac{1}{M^2_{\mathrm{Pl},4}} \equiv \frac{1}{M^{2 + n}_{\mathrm{Pl}, 3 + n +1} R^{n}}$$
$$\frac{M_{\mathrm{Pl},4}}{M_{\mathrm{Pl},3 + n + 1}} = \left( M_{\mathrm{Pl},3 + n + 1} R \right)^\frac{n}{2}$$

Now, the Planck mass in $3 + n + 1$ space-time dimensions may as well be of the order of magnitude of ordinary particle masses (let us choose a range of values 10 eV - 100 GeV). This would put the dimensioless ratio of masses:
$$\frac{M_{\mathrm{Pl}, 4}}{M_{\mathrm{Pl}, 3 + n + 1}} = 10^{17} - 10^{27}$$
Then, the distance R, should be:
$$R = \frac{1}{M_{\mathrm{Pl},3 + n + 1}} \, \left( \frac{M_{\mathrm{Pl}, 4}}{M_{\mathrm{Pl}, 3 + n + 1}} \right)^\frac{2}{n} = \frac{1}{M_{\mathrm{Pl}, 4}} \, \left( \frac{M_{\mathrm{Pl}, 4}}{M_{\mathrm{Pl}, 3 + n + 1}} \right)^{1 + \frac{2}{n}}$$
This is a monotonically rising function of the dimensionless ratio (the smaller the mass of the Planck particle, the bigger the ratio). For a popular choice $n = 6$, we would have:
$$R = (10^{19} - 10^{31}) \, M^{-1}_{\mathrm{Pl},4} = (10^{-16} - 10^{-4}) \, \mathrm{m}$$

11. Apr 10, 2012

### Physgeek123

Dangit People! What inflation really was.

THIS AND EVERYTHING ELSE can be explained by the standard model if you look a little closer. Problem?

It goes like this: After a fraction of a second after the big bang (brane collision, whatever) there were only TWO fundamental forces instead of four. They were the Electromagetism force and the Weak-nuclear force. The amalgam of these two forces formed the Electro-weak force.

This is the "inflaton" field you speak about (apparently). Anyway back to the Big Bang timeline, this super-force somehow caused inflation, spreading and recycling (yes recycling not creating as stated by E=mc^2) matter in an incredibly short amount of time. We now call this inflation.

But why do we not see the super weak force now? Think of each force as a spinner with two outputs. When you spin the spinner, it gains energy and then soon it looses it and lands on one of the possible outputs. Now apply that to the electro-weak force. It had a MASSIVE effect and quickly exhausted it's available energy thus forcing the spinner to land on something. But unlike spinners in real life, forces (when they stop "spinning") land on all the outcomes at the same time. The electro-weak superforce has now split into The Weak nuclear force, the strong nuclear force and the Electromagnetic force. But where's gravity?

Scientists believe that gravity was the result of the same superforce which spawned dark energy. The balancing scale of gravity vs. dark energy was tipping toward gravity and then for some reason reversed giving dark energy the upper hand.

So the answer to the question "Is gravity 'weak' because it leaks into higher dimensions?" is a big no no. Gravity is the same thing as everything else. It just seems to be weaker because there is not much concentration and quantity of the things it has control over (matter).

Hope that helped.

- Physgeek123

12. Apr 10, 2012

### rbj

dunno whom you were addressing, but if it was me, the point is that the premise of "weak gravity" that the question of this thread is based on is flawed. gravity is not weak, but protons (and other elementary particles) have very, very small mass, while their charge (if they are not neutral) is not particularly small. it is because of this fact that it appears to some that gravity is weak but they are considering the wrong quantities.

13. Apr 10, 2012

### Mark M

An idea in brane cosmology is that dark matter is composed of gravitons from other branes. This would explain why it's proved difficult to find it's constituents. Since the prospect of two 3-branes hovering near each other in a ten dimensional space seem slim to none, it would be unlikely that we would get a steady flow from these other branes.

As usual with all cosmological models based off of M-theory, it's interesting, but there is no evidence.

This is incorrect. A grand unified theory supposes that there was one unified forces, which then broke symmetry when the Higgs mechanism was activated.

Also incorrect. Grand unified theories do not claim any role in inflation, that is the sole purpose of the inflaton field. I suggest you do some research on inflation, that's not how it occurs. You should read this:

http://arxiv.org/abs/astro-ph/0101507

I don't know where you got this information. The breaking of symmetry of the forces was caused by the Higgs field. Once again, read this:

http://en.wikipedia.org/wiki/Higgs_mechanism

Gravity is not a force. It is a curvature in spacetime, altering the geodesic of objects traveling through it. No scientist believes in a 'superforce' that spawned it, it is an intrinsic property of spacetime.

Once again, you're mistaken. Gravity is not the same. Gravity is not a force.

Great post DF, that would seem to solve the problem better than gravitons 'leaking' off of our brane.

Last edited: Apr 10, 2012
14. Apr 10, 2012

### alexg

The idea is not that there are 'other universes'. It's that unlike electroweak and strong force, gravity is able to propagate into the additional dimensions called for by M-theory. All those dimensions are part of our universe, but only gravity can move in those 'directions'. It would explain why gravity is so weak relative to the other forces. It's diluted through out the other 10 dimensions.

15. Apr 10, 2012

### DaveC426913

That wasn't in jest. Crackpottery and crackpottery link reported. And he may get more than just a warning.

16. Apr 11, 2012

### TheTechNoir

Also if I remember correctly another way of possibly testing both the gravity leaking into other dimensions hypothesis as well as the upper limit of and the actual size of the extra dimensions is by testing gravity on smaller and smaller scales and seeing if it's strength suddenly increases. If for example we were able to test gravity's strength at a scale of 0.001 mm and it was the same, we'd know that the extra dimensions must be smaller than that if the idea is correct. And of course if we found gravity suddenly increased at x size scale then that would be one explanation, it was leaking off into the tiny dimensions, ones that we were detecting the signature of.

17. Apr 12, 2012

### B.Spinoza

Yeah, what he said is the kind of concept that spawned my initial question.

18. Apr 12, 2012

### B.Spinoza

Yes. I suggested that Dark Energy may be gravity leaking in. Its all guessing...

19. Apr 12, 2012

### TheTechNoir

Although that makes no sense, as was already pointed out it has a far far far far greater likelihood of explaining dark matter than dark energy. And even for dark matter it's 100% speculation.

20. Apr 13, 2012

### B.Spinoza

Was that directed at my previous?

Dark Matter is unlikely to be gravity leaking in from other dimensions or similar. Dark Matter is lumpy in its Universal distribution, it is clustered around matter.

Dark Energy seems to come from space as a whole.

Why would it make no sense that gravity leaks? If gravity leaks out from our Universe/brane/whatever then maybe it leaks in from other places too?

It is all 100% speculation. We know something out there is making the Universe expand and that there is more gravity than can be accounted for from the observable matter. 'We' hope there is a Higgs particle and that this is Dark Matter. Correct me if I'm wrong, but I don't think there is much else to it? It really is a true unknown, something very exciting in this age of science.