Why Is The Tardis Bigger On The Inside?

To the uninitiated the Tardis is just a blue box with the warm, friendly, and official looking sign “Police Call Box” emblazoned, in lights, on all sides. To the fan, The Tardis is short for “Time and Relative Dimension in Space” and its way,way more than just a Blue Box. Today we will explore the most obvious and endearing quality of this most peculiar object.
The very first words uttered, muttered or mouthed by stupefied first time visitors to Dr Who’s box are, invariably, “Its bigger on the inside” to which the Doctor or a random Companion (assistant is no longer PC enough for the BBC) responds, invariably, “it’s dimensionally transcendental.”
Dimensionally Transcendental indeed. But what does that mean and is it possible? Do the laws of physics allow for that particular conceit. Well, Yes. The ridiculously Weird Science of Modern Physics allows even this far fetched premise. There are many ways to achieve this. We will explore but a few.
First, and easiest for our trusty Time Lord to achieve would be a simple, Space-Time projection. The Tardis’ interior might just be in a distant part of the universe and the doorway that connects the police box exterior might just be a straight forward, yet impossibly difficult to achieve, Einstein-Rosen Bridge, better known as a wormhole. This means that when the Tardis Materializes and dematerializes, in fact the only thing changing location, not necesarily moving, is the access point. This acces point in Space (and time) is the wormhole’s entrance in disguise as a Blue, circa 1954, Police Box. The interior of the Tardis is safely stowed away at that “undisclosed location” far, far away. The Physics of wormholes is well known and all that the Galifreyans need wrestle up is just a bit of exotic matter to keep the portal from collapsing. That should not be difficult even for the most daft of Rassilon’s brood.
Even more Tardis speculation AFTER THE JUMP!
Another method by which the Timelords could construct their conveyances is by compressing Spacetime itself within a Blue Police Box shaped containment field. Think of it as a black hole without the black hole trapped inside magic blue cellophane. Within the Tardis all space dimensions contain more “Stuff” than without. The way this would work is that the interior would have more volume and thus way more mass than the outside. Its similar to pushing a silk handkerchief into a palm, it is still there,just compressed into a tiny almost invisible speck. Presumably,a culture that could time travel and manipulate exotic matter to create a wormholes could also use it to compress spacetime. Thus the rectangular time machine could contain the additional parcel of Space and Time needed for the pool, library and all those white corridors. There is evidence that this extra “Stuff” could be jettisoned to make the total vehicle mass lower, in case of an emergency, for instance.
Finally, my favorite. The simplest, most elegant solution is that the Tardis is actually not a three dimensional object at all. If the Tardis were four dimensional it would react just like in the series. The previous answers require strong force fields or exotic matter non of which are ever mentioned. On the other hand, the phrase dimensionally transcendental is continuously used. Allow me to entretain the notion that the Tardis is akin to an Escher painting and that it is actually a Four dimensional Object. This Tesseract like thing protrudes into 3Space exclusively through the Blue Box shaped entry way.

An easy way to think of this is to imagine that the world is a 2D sheet of paper and its citizens are flat. In this scenario the Tardis would be like a strip of paper or ticker tape attached with glue to a tiny flat square. Flatlanders could walk around the square but if they enter it they could get off the page, as it were, into the third dimension within the flat Tardis. The flat people could go all the way inside for miles and miles as long as there was paper on the strip.
If you take the same principle and apply it to 3D Space (our world) you could imagine a three dimensional box with an opening that connects to a 3d tube into the fourth space dimension. In other words the interior of the Tardis is mathematically besides reality. In mathematical terms, the region within the Tardis is purely “imaginary”, intersecting with the “real” world only when It is needed. You know, that suits me just fine.
Now, if you think I’m full of it, you might like to look up these books on the subject: “Hyperspace” by Michiu Kaku, “Spacetime Physics” by Archibald Wheeler and the wonderful “Flatland: A Romance of Many Dimensions” by the English schoolmaster Edwin Abbott Abbott.