The whole concept of higher dimensions has always been a fascinating one, but I have to ask if anyone has found anything, like a popular science article or something, that suggests a useful way of interacting with them. One of the big problems with the idea of interacting with them or going to them is that doing so suggests a loss of energy from our dimension. At this point, there isn't any evidence of energy being literally lost from the universe as far as I know (discounting any zero point energy stuff). There is the suggestion that black holes could exist in higher dimensions or that dark matter could, but other than that there isn't much. The only way that I've heard about for going to other dimensions is by using an extremely huge amount of energy like the energy in particle accelerators. Is there any lower energy way someone or something could interact with a higher dimension that has some science behind it?
I regret the answer is no. I don't know where you heard about the energy thing, but it suggests the speaker had little understanding of what science believes are the higher dimensions. Science Fiction, alternate realities, and new age thought have all unintentionally conspired to suggest that higher dimensions are someplace we can "be." You must remember that a dimension is a "dimension of measurement."
It is assumed (because science has declared it to be so, and it's not an unreasonable assumption) that time is the 4th dimension. Thus, if you think of a patch of ground as the 2nd dimension, a building constructed on that ground as the 3rd dimension, then the decay of the building and it's possible replacement over time is the 4th dimension.
To get an idea of what science thinks about multiple dimensions, view this youtube video (allow me to apologize for the narrator in advance).
It's worth noting that, perceptively, our understanding of dimensions suggests that you can always look (observe) "down" into the lower dimensions, but cannot look (observe) "up" into the higher dimensions. You certainly can't exist in lower dimensions, QED, you can't exist in higher dimensions, either, other than to experience it one-piece-at-a-time (e.g., second-by-second, you can't "enter" the 4th dimension such that you can "observe" time as you would "observe" a landscape).
You might want to consider parallel universes. Scientists are investigating a spot in our universe that might represent the collision between two such universes. If this proves to be true, then it would be theoretically possible to move between them.
EDIT: @Tom, as you can see, I needed more space to respond to your comment.
Remember that "dimensions" are an arbitrary form of catagorizing observable measurement, not universal constants (and certainly not places to visit). Time happens to be something measurable, that's all. Therefore, there is nothing gravitons can escape "into."
Perhaps the best way to say it is, could there exist a creature who can observe more than three dimensions of measurement? If so, how would gravitons affect such a creature? Such a creature doesn't "exist" in a "4th dimension." Said creature would exist in our universe just as we do. It's passage before us would, perhaps, be perceived as a 3D "flicker" as our passage through time happens to coinside momentarily with his (oohhh... ghosts...). This reflects the example from the video I suggested where passing your hand before a 2D being would result in its seeing a series of modulating edges as the 3D hand passed through its 2D vision.
The reason, perhaps, there is so much confusion in the world about this is the tesseract. A tesseract is a "four-dimensional" cube where the fourth dimension is NOT time. It's a theoretical geometric construct that works like this:
If you start with a one-dimensional point, creating a 2D line is done by drawing a line from that point in any direction to a second point (doubling the number of points). A shadow cast by light shining along the line's angle of protrusion is a point.
Creating a square means drawing equal length (that's important) lines at 90-degree angles from the first two points to encompass a total of four points (doubling the number of points). A shadow cast by light shining along the square's angle of protrusion is a line.
Creating a cube means drawing equal length (remember, this is important) lines at 90-degree angles from the existing four points to encompass a total of eight points (doubling the number of points). A shadow cast by light shining along the cube's angle of protrusion is a square.
Creating a tesseract means drawing equal length lines at 90-degree angles from the existing eight points to encompass a total of sixteen points (doubling the number of points). A shadow cast by light shining along the tesseract's angle of protrusion is a cube (and we just ran out of reality as there is no evidence of an emissive source that could do this).
Can you see the problem? You can model it mathematically, but you can't build it because there isn't a way to spatially align more equal length lines at 90-degree angles. The "space" doesn't exist. It's only a mathematical concept as it cannot be measured (like time).
That's why "inter-dimensional travel" is (at least at this time) a nonsensical concept. With the exception of the mathematical and geometric exercise of a tesseract, "dimensions" are identified as things that can be measured... even by us in a "lower" dimension.