Burning gas generates heat.
If the boiler is generating heat, that heat energy must be constantly transferred to something or else the boiler would quickly fail/catch on fire/explode.
If that heat energy is not being transferred inside your house, it must be being transferred outside of your house.
Your wife is arguing that the boiler is burning gas to generate heat and then continuously dumping that heat outside. Why does she think the boiler is built to routinely work that way in normal circumstances?
Unless something is badly wrong with your central heating or the central heating manufacturer is illegally conspiring with the gas provider to hugely inflate bills, when the boiler is switched on and working it will burn gas only as and when required to maintain the temperature set by the thermostat. The green light will be showing that the boiler is available to use, not that it's currently burning gas. If it's x degrees where the thermosensor is and you set the desired temp to <x degrees, nothing will happen. The boiler will not burn gas because there's no need for additional heat.
If you stand next to the boiler while it's burning gas and someone turns the thermostat temp down below the current temp, what you should hear is this:
1) A short delay (probably just seconds) while the new required temperature is sensed and the system confirms that the current temp is above the required temp.
2) The gas stops burning.
3) The water pump continues functioning for a short period of time, circulating hot water around the system for a while. Probably a minute or two.
This happens all the time unless your central heating system is incapable of heating your house to the desired temperature. That's the only situation in which it would be constantly burning gas when the central heating system is on.
You could also confirm this by looking at the gas meter (listening to it would probably work as well). Gas being used...thermostat turned down below current temp...a few seconds later the gas stops being used.
EDIT: My central heating system is on almost every second of the year. It's only off during power cuts and maybe during part of the annual servicing. Most of the time it uses no gas at all because the master thermostat is set to 8C and my house is above 8C. Or maybe it's 5C, I'm not sure. It's a "just in case" thing to prevent water pipes freezing.
EDIT: Strictly speaking having the central heating on but not supplying heat (because you've turned the thermostat below the current temperature) does increase your bills - it increases your electricity consumption by the amount required to run the boiler control systems. A quick look online shows consumption around 6 ro 7W, which sounds right to me. It's a simple little board. That would increase your electricity bill by about 15p a week. Oh noes!
Thanks Angilion,
To paraphrase Matthew Modine's character, in "Memphis Belle", "You have dropped it straight into the pickle barrel", and succinctly summed it up.
The only part I would take issue with, and then only very, very slightly, is when you said that my wife was arguing that the boiler was burning gas, "and then dumping it outside."
She wasn't saying that per se, but that construction could have been put on it, she was saying, that to her, the fact that the green light was on, was an indication that the boiler was heating gas.
With the benefit of hindsight, and armed with your input, I should have asked her, "If the boiler is generating heat, where is that heat going?"
An uneasy peace reigns chez nous right now, but it met initial resistance, when i handed her the iPad, to read the first batch of replies, backing up my theory, that if the rads had cold water, then no heat was being generated by the boiler, she read maybe 4 or 5, then cast the iPad unceremoniously aside, saying, "I'm not interested, this stuff bores me, I have no inclination to read your puerile Forums, I have more pressing things to do, like check my Facebook page."
I think that a line of posts, proving her theory wrong, had pushed her over the edge, so she had crept back to where a lot of women appear to seek solace, her Facebook pages, pausing only to lash out at my "obsession", looking at Forum pages for perhaps 35-40 minutes per day.