No, it's pure science fiction.
First of all, handwriting on a piece of paper is digital. It's composed of discrete, digital symbols. A burnt match could be a piece of digital information...
Second, copying from chips such as flash storage, generally requires powering them and addressing them. This can not be done remotely for general chips. Exceptions, such as RFID, are exceptions that carry a large antenna to harvest enough energy, and adhere to specific protocols.
And when it comes to spinning disks... what physics would that be? Information is stored as magnetic information on a set of spinning platters. The disk is a pretty good faradays cage by design, and it requires large amounts of power to spin up the disk and actuate reading head voice coils...
Furthermore, there's no logic, if this was possible, that it would have to start over from the beginning if interrupted. Especially not from the beginning of the file, not the block device. If you're able to jump to the start of the file on a block device, there's no reason why you can't jump to an arbitrary point within the file as well.
The closest we have is TEMPEST attacks which try to catch the electromagnetic noise created by computers. Some components, such as CRT monitors, created fairly strong signals, that gave a quite clear representation of what was presented on the screen. But it requires the device in question to be powered on, and access the data you want to see. It doesn't allow you to grab non-accessed content from for instance a flash device or a hard drive.