An option might be to go Matrix style and extrapolate on the current trends:
Mankind falls in love with virtual reality and technology. By the 2030s, every human was equipped with immersive enhanced reality rigs. Landscape and people are photoshopped in real time, rigs generate a wide range of sensations for their users.
The virtual side of "reality" becomes more attractive while the "real" side become stalled and inhospitable. Pollution and environment degradation push people's lives ever faster towards full virtual reality environment. Life in the "real world" becomes increasingly irrelevant. Work happens exclusively in VR, interaction with the physical world being the purview of specially built robots controlled from a fully distributed VR environment and abstracted away.
People's "real" bodies end up docked in 24/7 in "safe" facilities while they go about their days in a completely virtual environment. Within a couple generations, everyone has forgotten entirely about the existence of the physical universe and of their own bodies. Machines handle the reproduction duties and plug new human units on a regular basis to replace existing worn-out human units.
By the time your story begins, the "real world" is a virtual world and no longer subject to the same laws of physics.
For all we know, it has already happened. ;)
Now, you can have your pockets full of monsters and if you want to store them in some quaint old-fashioned, grapefruit-sized, red-and-white container for the sake nostalgia, who is to tell you different?
Our current reality and its laws of physics didn't account for this perfectly reasonable application, but Reality® Pack Version 3.5b2.08 makes it a breeze.
Think like a manager. If reality isn't consistent with your requirements, reality must be wrong. You just have to upgrade reality.
The scary part is that it's a whole lot more realistic solution than storing genetic information and 3D printing monsters on demand or extracting monsters from a pocket dimension of some kind.
173wait... this sounds vaguely familiar... – Keltari – 2016-07-14T17:46:19.057
46I <3 this question so much – Renan – 2016-07-14T17:55:10.043
9
Perhaps if the 3-ball were in fact a 3-sphere portion of an n-ball (assuming n>3), then you might well have quite a bit of elbow room (as in Pickover's proposal to "stuff a whale into a [10-]sphere the size of a marble": http://sprott.physics.wisc.edu/pickover/fourth_fc.html )?
– Charles Rockafellor – 2016-07-14T19:35:54.80722If your ball is a Tardis, the only problem is getting it past the control console. – Howard Miller – 2016-07-14T20:52:27.933
Drat. Beat me to this question. Of course, mine were focusing on a different part of the problem...
– Frostfyre – 2016-07-14T21:17:48.82044Grapefruit sized is pretty big. When was the last time you fit a couple of grapefruit in your pocket? – Mirror318 – 2016-07-14T23:56:59.900
3The most reasonable way to fit it in your pocket? Pokemon Go. – None – 2016-07-15T01:07:46.233
18Are you saying that the classic bag of holding is offensive to reality? – Separatrix – 2016-07-15T10:10:16.063
Just saying Groudon is way heavier :P – Arcane – 2016-07-15T10:50:51.040
5Sounds like an application of Banach-Tarski to me! – Danu – 2016-07-15T10:52:13.707
5@Mirror318 And, more importantly, are you happy to see me? – David Conrad – 2016-07-15T14:58:59.730
7@Mirror318 yes umm..I've never stuffed a bunch of grapefruit in my pocket for err...questionable reasons before. Anyone who claims otherwise is clearly lying, and also jealous that my grapefruit is so much Juicier then theirs...if you know what I mean. That's my story and I'm sticking to it. STOP JUDGING ME!!! – dsollen – 2016-07-15T16:32:52.137
1Guys! Girls! It's a ... um... small, let's call it right-size grapefruit. Or maybe it grows when you .. uh.. take it out of the pocket. – Serban Tanasa – 2016-07-15T18:27:26.490
If you live in a virtual world with a lot of glitches you'd need to be able to support 2766.5 kg.
– Pharap – 2016-07-16T15:30:34.9705This sounds difficult. You'd have to be good to pull this off. The very best, I'd wager. And I mean, like no one ever was. – Devsman – 2016-07-18T14:28:54.210
4You'd have to travel across the land, searching far and wide to find a way to pull it off. – Xandar The Zenon – 2016-08-03T02:43:42.940