......
It is theoretically possible to do off-chain transactions totally electronically. Here's one approach :
https://bitcointalksearch.org/topic/m.1578079 The required technology for this particular scheme will be commonplace (ie: in the vast majority of phones and desktops) by the end of the decade. However, it means that the special hardware required is trusted. Some phones appear to already have the most of the basic hardware required such as the Samsung S4 with KNOX.
This only works if everyone uses Trusted Computing, meaning no one has real control over their own systems.
Hate to break it to you, everyone will be using computers with TPM hardware installed soon (in fact if you own a new computer you most likely are).
Just because you have trusted computing hardware installed and available software support doesn't necessarily mean that you lose control. For example, Linux has had support since the 2.6.13 version, yet I'm still free to install anything I like on my machine that I'm typing this on (my computer runs Linux).
Trusted Computing is just a tool, it by itself is neither good or evil but can be used for either. Same as a scalpel is just a tool: a scalpel can be used to take a life by slicing the throat or to save a life in a surgical operation. It's the way that we use trusted computing that matters.
All I ever seem to hear from people is how TC can only be used to weaken your rights and diminish your control. You rarely here the other side of the argument how that it can also be used to give users power and control and strengthen their rights. eg: With TC you could create a social network site like Facebook except that the user has true control over who can view what and when also you would would have the ability to truly delete stuff from you record, even the operators of the site wouldn't have the ability to keep/use your data in ways that you don't approve of (admittedly ignoring out of band breaches such as people photographing the computer screen.) This gives the user power-- not detracts from it!!! Another example, is the bitcoin exchange scheme above-- this scheme gives you true anonymity and instant transfers.
(By-the-way: how are you sure that you have exclusive control of your computer currently regardless of the trusted computing issue. It is extremely easy for the manufactures to add backdoors into the hardware/software- the software situation is even worse because they can add them during upgrades).