If you aren’t lucky enough to have a physics degree, you might care to keep a wet towel on hand to wrap around your head as you read this. It is a complicated subject, and I must warn you it might even involve use of the word “gigahertz”.

Those of you who feel at home in the world of the gigahertz might be among the 3.24m people who have already installed a high-definition television (HDTV), which is supposed to be the future of broadcasting.

With this technology we will be able to see Jade Goody’s face in much greater detail, and we’ll be able to follow the progress of any beads of sweat that happen to be troubling Maria Sharapova’s thighs. It will be easier to follow ball games: in ice hockey matches, we will actually be able to see the puck.

Now the bad news. If you have been lured into buying a set in expectation of these delights, it looks as if you might be disappointed. Certainly if you were hoping to watch them with an ordinary aerial or on Freeview.

The great digital switchover begins in Cumbria in October, and when all analogue television is finally binned in 2012 it will leave great swatches of empty space on the broadcasting spectrum. Where mighty Ant and mighty Dec once bestrode the airwaves, there will be nothing but tumbleweed.

Supporters of Freeview say that vacant part of the spectrum should be set aside for high-definition television, which needs up to four times as much elbow room as conventional television. But they have reckoned without Gordon Brown.

Ofcom, the industry regulator, says these valuable properties on the spectrum could be worth up to £10 billion. This is money that Gordon badly needs to pay for more health target assessment administrators, education initiative co-ordinators, and diversity outreach team leaders.

So he might prefer to sell the space to the highest bidder, probably the mobile phone companies. Just think: we could soon have live action video of Britney’s latest hairdo beamed straight to our handsets from the salon.

Ofcom has been asking the public which option they would prefer, but — in the usual way of these things — consultation closes on Tuesday, just as many people are waking up to the issue. When I last looked at the Ofcom website, just 49 people had responded.

Ofcom itself has been sniffy about HDTV. “In our research, high-definition television was not identified as a major benefit to society,” it said in its consultation report. “A bigger choice of channels was rated more highly.” I’d venture 3.24m HDTV owners say otherwise, not to mention the 4,917 who have signed an online petition to Downing Street.

I know which side my bread is buttered, so I should mention at this point that you can get HDTV on subscription from Sky, a sister service of The Sunday Times. Well, not really a sister: more of a cousin that we really only see at weddings. You can also get HDTV on Virgin.

But the point is this. We can assume that many of these technology-friendly HDTV owners invested in their sets to watch on Freeview. Now there is a danger that this will not happen. Many of these people are also voters.

Brown would very much like to become prime minister and win an election, but he does not seem popular at the moment.

He will become even more unpopular if he auctions off public property to mobile phone companies.

Your call, Gordon.