A friend and I were discussing the possibility of wireless video cables and we quickly realized that the bottleneck is the current data transfer rate of wireless technology. The average wireless router seems to output at roughly 300 Mbps while a standard HDMI cable puts out roughly 10 Gbps. Does radio frequency interference, distance, and material interference (such as walls) really account for this huge difference in max data transfer rate? Or is there other hardware limiting factors?
Specifically the Shannon Information Theorem, which (loosely) states that the amount of information you can encode in a signal is limited by the bandwidth of the signal. In wireless channels bandwidth is constrained (see below). In wired systems, bandwidth is almost unconstrained (being limited only by manufacturing and cost issues up to 10's of gHz).
A wireless signal is regulated by the government
Government restrictions put severe limitations on how much (contiguous) bandwidth is available for unlicensed commercial use. With licensing (billions of dollars) the situation gets marginally better, but still no where near the free (almost unlimited) bandwidth available in a cable.
Wireless channels are noise/error prone
At a high level, it's like having a conversation across a room with other talkative people in it (wireless), versus holding a cup with a tight string to your ear while your partner speaks into the cup at the other end (wired).
Wireless channels lose information. To counter-act this problem, wireless channels use encoding schemes that enable error detection and (in some cases) recovery. In general, error coding schemes require sparsity (gaps) in the data sequence possibilities so that one valid value isn't undetectably turned into a different valid value. This necessarily hurts throughput (more redundancy = less unique information).
Overcoming errors, noise, and interference takes power
Wireless microchips, like all microchips are limited by the amount of power they can consume in a particular area -- a metric known as power density. Wire-line channels are less noisy, less lossy, and, therefore, way more efficient to transmit and receive into.
All things equal, you could run a wired microchip at much lower power levels for the same bandwidth. Conversely, for the same power level, the wired transceiver could be clocked much faster.