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Theories in string theory and cosmology lead to an idea that our universe is a single "membrane" (or brane, as it is commonly called) suspended within a higher dimensional "bulk". See Wikipedia.

Is there any way to test and see if this is true?

Here are some ideas:

  1. Use a super-massive (as in a lot of mass) neutron star as a "thimble" to punch a hole in our brane and see the other world (although "seeing it" may be impossible because photons are physically 3-dimensional and the "bulk" has more than 3 spatial dimensions).
  2. Make enough gravitational activity in our universe so that a "bulk being" is tempted to visit us.
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  • $\begingroup$ As stated on the Wiki page: the confinement of Electroweak and strong forces to the brane but lack of confinement of gravity explains gravity's weakness, thus solving the hierarchy problem. This could be taken as indirect empirical evidence. $\endgroup$ – WetSavannaAnimal Apr 29 '15 at 3:57
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    $\begingroup$ Point 2: Hey Bulk Being Creature - who may be aggressive and want to obliterate us but what the heck let's call him over and see whether he wants tea and cake with us - we're over here- yoohoo!: sounds like a line from an Eddie Izzard skit! $\endgroup$ – WetSavannaAnimal Apr 29 '15 at 4:00
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    $\begingroup$ String theory, brane models etc. are, despite some of the names, not even testable hypotheses at this time. I would be careful with using the word "theory" in conjunction with these toy models. $\endgroup$ – CuriousOne Apr 29 '15 at 4:08
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Ha! Some time ago I read an article where they proposed an experiment where they wanted to test exactly what you're asking. Here is the article and here is the paper.

The idea is the following:

Place a shielded neutron detector near a neutron reactor and place a thick wall between them. This wall should be thick enough so that they normally don't reach the detector. In the reactor, the neutrons have a certain probability to transition into a "sterile" state where they exist in another brane. In this brane they are not affected by the wall.

Then, place the detector in different distances from the neutron source. When you see a $1/r^2$ law then this is because the shielded detector detects neutrons that leak from the other brane into ours. They also claim that if the neutrons leak from another brane to ours then you can additionally measure both of the following effects:

  • the detected neutrons flux should not vary if they add extra shielding to the detector and
  • since the coupling between the branes and therefore the rate at which neutrons transition into our brane depends on gravitation on earth, the detected neutron flux should depend on the earth's position on the orbit around the sun.

Referring to the picture below the trajectory of the neutron is then our brane (reactor) $\to$ hidden brane $\to$ our brane (detector).

To do this experiment, they plan to build an additional small $(36cm^3)$ neutron detector near an already existing neutron reactor - the neutron reactor of the institut Laue Langevin in Grenoble, France.

However, this is only a proposed experiment, I don't know if they will build it soon.

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