This bizarre crime was first discovered by Dr. Roy Meadow, a British pediatrician. And ever since, mothers have been prosecuted in Britain and in the United States based on his theories.
But recently, a few of those women have been freed from prison - and there is now reason to believe that some of Meadow's theories are tragically wrong.
In Britain, at least 250 criminal convictions are being reviewed in Britain. But that's not all. It appears that hundreds of other parents have had their children taken away for good because of Meadow's questionable testimony. Correspondent Scott Pelley reports.
It's hard to comprehend the two tragedies that have torn one family apart. The couple asked 60 Minutes II not to use their real names, so we called them Karen and Mark Haynes.
Their hopes of building a family began in 1998 with the birth of their first child, Peter. But from the start, Peter had trouble breathing. There were two trips to the hospital within just the first month. And then at four months, Peter was rushed to the hospital again with massive swelling of the brain caused by a lack of oxygen.
"As far as we were concerned, he had died," says Karen. "He was kept on a life support machine all day on Thursday. We knew that there was no hope for him."
Mark and Karen had Peter christened and then he was removed from his life support. Peter died 30 minutes later.
Doctors couldn't explain why Peter stopped breathing, and the Haynes thought the tragedy was well behind them - until Karen became pregnant again five months later.
They were surprised to receive a letter summoning them to the child welfare department. "We just looked at it and thought there must be some sort of mistake here. We don't understand what's going on," says Mark.
What they didn't know was that Britain's most distinguished pediatrician, Sir Roy Meadow, had been asked by police to review Peter's death. Meadow said Karen probably murdered her son, even though the Haynes says he never met with the family or examined Peter's body.
Meadow only saw the medical records, but he noticed that in one of Peter's earlier trips to the hospital, doctors found cuts on his nose and some blood in his nostrils. Meadow said this was proof that Karen tried to smother Peter, even though Karen says it happened when she tried to resuscitate her son.
Meadow, however, said resuscitation would not leave those kinds of injuries, and based on his word alone, a judge ordered police to take Karen's newborn daughter, Sarah, right in the delivery room.
"I held her for about 20 minutes, if that, about 15-20 minutes, and then she was taken," says Karen. "And then she was taken away. Yes, they left me still on the bed, and they walked out of the room with her."
Karen and Mark were allowed to visit their daughter in a foster home while their case was in Family Court. Seven doctors said Peter's death was natural, but Meadow said Peter was probably murdered by Karen.
The judge gave Sarah to another family for adoption, and Mark and Karen never saw their daughter again. "We have had our child taken away from us for life. We have a life sentence, a true life sentence," says Mark.
How could one man's testimony tear a family apart? 60 Minutes II wanted to talk to Meadow, but he declined an interview request. These days, he's in seclusion at home, a far cry from when he was a celebrated pediatrician.
In 1977, Meadow announced the discovery of a strange new form of child abuse he called Munchausen Syndrome by Proxy, in which women were nearly smothering their babies - just to get attention for themselves.
As Meadow's fame grew, he became president of the Royal College of Pediatrics, and was even knighted by the queen.
"Sir Roy Meadow is undoubtedly one of the foremost experts in child care and child health that the country has seen over the last 30 or 40 years. He is a man of great standing in his profession," says Earl Howe, a member of Parliament's House of Lords, who helps draft health policy for the Conservative Party.
Lord Howe says prosecutors eagerly sought Meadow's testimony because he had clout with judges. Meadow has often lectured judges privately on his theories of child abuse.
"Very often the judge is familiar with him and has met him and has listened to his lectures about Munchausen Syndrome by Proxy," says Howe.
Meadow was so influential that one of his theories came to be known as "Meadow's Law." Meadow wrote that in a single family, "one sudden infant death is a tragedy, two is suspicious and three is murder until proved otherwise."
But this theory would prove a devastating diagnosis. It was Meadow's Law that brought lawyer Sally Clark to trial in 1999. Her two infant boys died without apparent cause. Meadow testified that the odds of two children dying naturally in the same family were astronomical - 73 million to one – and Clark was convicted of murder and sentenced to prison for life.
A few months later, the police came for Angela Cannings after she and her husband, Terry, lost their third infant in 10 years. Cannings was charged with murder. "No, this isn't right. It was just a complete and utter shock because I had absolutely no idea that this was gonna happen," recalls Cannings.
There was no evidence against Cannings, except Meadow's testimony and Meadow's Law - that three sudden deaths is murder.
"I just wanted to stand up in that courtroom and say to the jury, 'Please, please don't believe this man,'" says Cannings.
But the jury believed Meadow, and Cannings was convicted and sentenced to life. The trials were a sensation and brought a lot of attention to Meadow's testimony, including the attention of Dr. Jim Morris.
Morris, a pathologist and a leading authority on sudden infant death syndrome or SIDS, says that Meadow's Law is wrong because one sudden infant death in a family makes it more likely there will be others.
"That tells you there's something in the family, environmental or genetic, that is increasing the risk," says Morris. "So there's bound to be a bigger risk in the next baby."
Meadow has argued that three is murder. But that's wrong, says Morris: "The evidence is that even with three in a majority of cases, it will be natural disease."
Meadow had also told the juries the chances of even two SIDS deaths in a family were 73 million to one.
"Now, this is very powerful evidence for the jury, but it was 100 percent wrong," says Howe, who's become a leading critic of Meadow. "They were wrong by a huge order of magnitude. Statisticians have since said that the chances of two naturally occurring deaths taking place in a family is something like 150 to one."
In fact, scientists now believe families like the Cannings may have a defective gene that increases their chance of SIDS.
Morris was asked to look into Cannings' case and found a family history of sudden infant death. He also reviewed the medical records for one of Sally Clark's sons, Harry.
"There was evidence of overwhelming staphylococcal infection in Harry and that was the most likely cause of death," says Morris, who adds there was no evidence of any kind that would suggest smothering in Harry's case.
On appeal, Meadow's testimony in the Clark case fell apart. The appellate court called his evidence "grossly misleading" and "manifestly wrong." Clark was released after three years in prison.
Five months ago, Angela Cannings was also released after nearly two years. Now, she says she'd like to meet the man who put in prison and say to him: "I am innocent, so tell me why you put us through four years of hell?'"
In freeing Cannings, the appellate court said the genetic evidence was a "realistic explanation" for the deaths of her children.
How could such a distinguished scientist make such errors? "He's an expert in child abuse, but he's not an expert in sudden infant death syndrome," says Morris. "Sudden infant death syndrome is a very complicated area, and I think Professor Meadow made a mistake when he moves from his area of expertise, child abuse, into talking about sudden infant death syndrome."
The British government is now looking at 250 criminal cases to see whether other mothers were wrongly convicted of murder.
And on top of that, the government is trying to figure out what to do about hundreds of other cases that were heard in family court - in which children were taken away from their parents because of the Meadow's testimony.
"To many parents who have undergone this experience of being accused falsely of harming their children, that is exactly the feeling they have, that there is no escape," says Howe. "Nothing they do can convince their accusers that they are innocent."
Mark and Karen Haynes hope to convince the court that they are innocent, and they have new evidence in their case. It turns out that while Peter was in the hospital, doctors gave him a drug that has since been taken off the market because it was linked to deaths in other children.
Still, the Haynes have been told that even if their daughter was taken unjustly, the court won't reverse the adoption now. She's four years old and too many years have gone by.
"We're not resigned, but we can see no other way. We can see no other way," says Mark. "We cannot see a way that those adoptions will be overturned. We don't want it to happen. We want our daughter back with us."
Even after the loss of their daughter and the death of their son, the Haynes are not giving up on having a family. Karen is now five months pregnant. Do they believe that this time, they will be able to keep their baby?
"We live in belief, yes, we live with hope," says Mark. "We have to live with hope."
The Haynes are negotiating with the British authorities over whether they will be allowed to keep their new baby. Karen is due in just three months.
These cases in Britain are being watched closely here in the United States because hundreds of women have been prosecuted under Meadow's theory of Munchausen Syndrome by Proxy.
As for Sir Roy Meadow, he's under investigation by Britain's General Medical Counsel, which later this year is expected to decide whether he will be allowed to keep his medical license.