<p>An exact answer would require a rather specific and mathematical formulation of the multiverse in consideration.</p>

<p>As a simple approximating example, suppose we have a countably infinite number of (observable) universes of the same mass $M$.  Suppose the dimension of the full multiverse is one higher than each individual universe, and suppose the universes are all separated by the same minimum distance $\epsilon&gt;0$ from each other.  In a 2-D picture, this would just look like a bunch of parallel lines all separated by the same distance.</p>

<p>Pick your home universe and put an observer.  Another universe of distance $n\epsilon$ away (meaning they're $n$ universes up or down from you in the 2-D picture) exerts a gravitational force on the observer in its direction approximately proportional to $\displaystyle{\frac{M}{n^2\epsilon^2}}.$  With the right units, we can just say "approximately".</p>

<p>The maximum gravitational force occurs when the observer is at the bottom (or top) of the picture, and all over universes are above it (or below): universes on each side will pull in opposing directions and so lead to cancellations.  So the net gravitational force from the other universes (in the right units) is at most 
$$\sum_{n=1}^\infty \frac{M}{n^2\epsilon^2} = \frac{M}{\epsilon^2}\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2 M}{6\epsilon^2}&lt;\infty.$$</p>

<p>If the observer was "in the middle"&mdash;infinitely many universes above and below, with the distribution identical in either direction&mdash; the net gravitational force from the other universes is exactly 0.</p>

CC BY-SA 3.0
2015-06-26T05:29:14.027Z
2015-06-26T05:29:14.027Z
zibadawa timmy
<p>The answer to your question for brane cosmology is simply that gravity follows the inverse-square law. We don't feel the gravitational pull of, say, Mars because it's so far away. Any other universes are so unimaginably (all right, that's hyperbole) far away in comparison that any gravitational effects by the matter in them would be very, very, very, tiny.</p>

<p>A similar argument might be to say that an infinite series always goes to infinity because you keep adding on terms. But this is often not the case, as with the series
$$\sum_{n=0}^{\infty}2^{-n}=2$$
It is infinite, but it converges.</p>

CC BY-SA 3.0
2015-06-24T18:21:18.857Z
2015-06-25T20:32:20.340Z
2015-06-25T20:32:20.340Z
HDE 226868
<p>As I understand it, one theory of the multiverse is that there are an infinite number of universes separated by small distances in other (than our observable 3/4) dimensions and that gravity is weak because it permeates these other dimensions.</p>

<p>But if there are an infinite number of these universes then surely the gravitational force we would feel would be infinite?</p>

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2015-06-15T14:04:16.913Z
If our "plain vanilla" universe is topologically flat then it is infinite. And if matter is large-scale homogeneously distributed, which seems to be the best and simplest  model today, then it already contains infinitely much mass. So the key part of the question is maybe "short distance in another dimension".
LocalFluff
CC BY-SA 3.0
2015-06-24T23:16:35.100Z
Just because there's an infinite number of something doesn't mean that those somethings need to be tightly packed in next to each other. There could be a football field and a half worth of something else between each universe. That'd act to weaken trans-brane gravitational interactions.
Wayfaring Stranger
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2014-07-02T21:04:39.617Z
Perhaps you can link to the sources of your information, so we can better explain them to you.
Jeremy
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2014-08-06T18:26:42.540Z
Do multiverse theories say that there must be an infinite number of universes?
HDE 226868
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2014-08-09T19:47:41.230Z
Some do, certainly
adrianmcmenamin
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2014-08-09T20:25:52.870Z
Right, but not necessarily all. What specific theories say that there must be an infinite number of universes?
HDE 226868
CC BY-SA 3.0
2014-08-10T18:06:46.347Z
Well, eternal inflation is one, infinite brane cosmologies are another
adrianmcmenamin
<cosmology><space-time><multiverse>
Why doesn't this paradox disprove (some) multiverse quantum gravitational theories?
adrianmcmenamin
# Why doesn't this paradox disprove (some) multiverse quantum gravitational theories?

(Asked by: username_0 on 2014-07-02)

As I understand it, one theory of the multiverse is that there are an infinite number of universes separated by small distances in other (than our observable 3/4) dimensions and that gravity is weak because it permeates these other dimensions.

But if there are an infinite number of these universes then surely the gravitational force we would feel would be infinite?

**Tags:** cosmology, space-time, multiverse
> **Comments:**
> **username_3**: Perhaps you can link to the sources of your information, so we can better explain them to you.  
> **username_4**: Do multiverse theories say that there must be an infinite number of universes?  
> **username_0**: Some do, certainly  
> **username_4**: Right, but not necessarily all. What specific theories say that there must be an infinite number of universes?  
> **username_0**: Well, eternal inflation is one, infinite brane cosmologies are another  
> **username_1**: If our "plain vanilla" universe is topologically flat then it is infinite. And if matter is large-scale homogeneously distributed, which seems to be the best and simplest  model today, then it already contains infinitely much mass. So the key part of the question is maybe "short distance in another dimension".  
> **username_2**: Just because there's an infinite number of something doesn't mean that those somethings need to be tightly packed in next to each other. There could be a football field and a half worth of something else between each universe. That'd act to weaken trans-brane gravitational interactions.  

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## 2 answers

### Answer by username_5 on 2015-06-26. Score: 3 | Accepted answer

An exact answer would require a rather specific and mathematical formulation of the multiverse in consideration.

As a simple approximating example, suppose we have a countably infinite number of (observable) universes of the same mass $M$. Suppose the dimension of the full multiverse is one higher than each individual universe, and suppose the universes are all separated by the same minimum distance $\epsilon>0$ from each other. In a 2-D picture, this would just look like a bunch of parallel lines all separated by the same distance.

Pick your home universe and put an observer. Another universe of distance $n\epsilon$ away (meaning they're $n$ universes up or down from you in the 2-D picture) exerts a gravitational force on the observer in its direction approximately proportional to $\displaystyle{\frac{M}{n^2\epsilon^2}}.$ With the right units, we can just say "approximately".

The maximum gravitational force occurs when the observer is at the bottom (or top) of the picture, and all over universes are above it (or below): universes on each side will pull in opposing directions and so lead to cancellations. So the net gravitational force from the other universes (in the right units) is at most
$$\sum\_{n=1}^\infty \frac{M}{n^2\epsilon^2} = \frac{M}{\epsilon^2}\sum\_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2 M}{6\epsilon^2}<\infty.$$

If the observer was "in the middle"—infinitely many universes above and below, with the distribution identical in either direction— the net gravitational force from the other universes is exactly 0.


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### Answer by username_4 on 2015-06-24. Score: 3

The answer to your question for brane cosmology is simply that gravity follows the inverse-square law. We don't feel the gravitational pull of, say, Mars because it's so far away. Any other universes are so unimaginably (all right, that's hyperbole) far away in comparison that any gravitational effects by the matter in them would be very, very, very, tiny.

A similar argument might be to say that an infinite series always goes to infinity because you keep adding on terms. But this is often not the case, as with the series
$$\sum\_{n=0}^{\infty}2^{-n}=2$$
It is infinite, but it converges.


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