The judge questioned the juror about his research, which included evidence that the judge had specifically excluded. Mr. Raben recalls thinking that if the juror had not broadly communicated his information with the rest of the jury, the trial could continue and the eight weeks would not be wasted. “We can just kick this juror off and go,” he said.

But then the judge found that eight other jurors had done the same thing  conducting Google searches on the lawyers and the defendant, looking up news articles about the case, checking definitions on Wikipedia and searching for evidence that had been specifically excluded by the judge. One juror, asked by the judge about the research, said, “Well, I was curious,” according to Mr. Raben.

“It was a heartbreak,” Mr. Raben added.

Information flowing out of the jury box can be nearly as much trouble as the information flowing in; jurors accustomed to posting regular updates on their day-to-day experiences and thoughts can find themselves on a collision course with the law.

In the Arkansas case, Stoam Holdings, the company trying to overturn the $12.6 million judgment, said a juror, Johnathan Powell, had sent Twitter messages during the trial. Mr. Powell’s messages included “oh and nobody buy Stoam. Its bad mojo and they’ll probably cease to Exist, now that their wallet is 12m lighter” and “So Johnathan, what did you do today? Oh nothing really, I just gave away TWELVE MILLION DOLLARS of somebody else’s money.”

Mr. Powell, 29, the manager of a one-hour photo booth at a Wal-Mart in Fayetteville, Ark., insisted in an interview that he had not sent any substantive messages about the case until the verdict had been delivered and he was released from his obligation not to discuss the case. “I was done when I mentioned the trial at all,” he said. “They’re welcome to pull my phone records.”

But juror research is a more troublesome issue than sending Twitter messages or blogging, Mr. Keene said, and it raises new issues for judges in giving instructions.

“It’s important that they don’t know what’s excluded, and it’s important that they don’t know why it’s excluded,” Mr. Keene said. The court cannot even give a full explanation to jurors about research  say, to tell them what not to look for  so instructions are usually delivered as blanket admonitions, he said.