The careers of Fleischmann and Pons were destroyed as quickly as a nuclear flash - names once linked to a Nobel Prize were forgotten by nearly everyone. And most of the scientific world today is happy to leave it that way.
"I'm still waiting for the water heaters. I'm still waiting for the thing that will produce heat on demand," Richard Garwin, one of the most respected physicists in the world, told Pelley.
In the 1950s, he helped design the most successful fusion experiment of all time: the hydrogen bomb.
"It was unfortunately, a very successful experiment," Garwin told Pelley.
Garwin was a critic of Martin Fleischmann back in 1989. And he has seen reports on the research that's been done since.
He thinks McKubre is mistaken.
Asked why, Garwin said, "I think probably he measures the input power wrong."
It's one of the most common criticisms of cold fusion experiments - that the amount of electricity going in and the heat coming out are simply mismeasured.
"It's possible, it is possible, that I have been mismeasuring energy for 20 years, but I think it extremely unlikely. A very large number of people have been making these measurements and measurements of current, voltage, temperature, resistance they're some of the simplest measurements that a physicist or a physical scientist will measure," McKubre said.
But there's another problem that critics point out: the experiments produce excess heat at best 70 percent of the time; it can take days or weeks for the excess heat to show up. And it's never the same amount of energy twice.
"I require that you be able to make one of these things, replicate it, put it here. It heats up the cup of tea. I'll drink the tea. Then you make me another cup of tea. And I'll drink that too. That's not it," Garwin said.
He told Pelley that for him to become a believer, the process would have to work 100 percent of the time.
But McKubre said, "Our critics often complain that we can't boil water to make tea. We could have, in fact, boiled 64 gallons of water and made 1,000 cups of tea, had we chosen to do so."
No one's sure why the experiments can't be consistently reproduced. McKubre thinks it has something to do with how the palladium is prepared. He's working with an Italian government lab called ENEA where some of the most reliable palladium is made.