Was Trayvon Martin aggressive and paranoid from smoking marijuana, and did that lead him to attack George Zimmerman? That’s what lawyers for Mr. Zimmerman are arguing. He is on trial for killing Mr. Martin, but claims he acted in self-defense, and the judge in the racially charged, nationally followed case decided earlier this week that the jury could be presented with Mr. Martin’s toxicology report, which shows that he had marijuana in his system.

As a neuropsychopharmacologist who has spent 15 years studying the neurophysiological, psychological and behavioral effects of marijuana, I find this line of reasoning laughable. The toxicology exam, which was conducted the morning after Mr. Martin was killed, found a mere 1.5 nanograms per milliliter of blood of tetrahydrocannabinol, or THC, in his body. This strongly suggests he had not ingested marijuana for at least 24 hours. This is also far below the THC levels that I have found necessary, in my experimental research on dozens of subjects, to induce intoxication: between 40 and 400 nanograms per milliliter. In fact, his THC levels were significantly lower than the sober, baseline levels of about 14 nanograms per milliliter of many of my patients, who are daily users. Mr. Martin could not have been intoxicated with marijuana at the time of the shooting; the amount of THC found in his system was too low for it to have had any meaningful effect on him.

Some observers of the case note that the toxicology test also found 7.3 nanograms per milliliter of THC-COOH, one of the main metabolic byproducts formed as the liver breaks down THC. But these metabolites of marijuana have no psychoactive properties, and they have no effect on behavior. They can also remain in the body, like THC itself, for up to four weeks. This is why their presence does not reveal when — or exactly how much of — the drug was used.

For argument’s sake, though, suppose that the tiny amount of THC found in Mr. Martin’s blood somehow managed to mildly intoxicate him that night. The scientific studies, including my own research, on the short-term effects of the drug on cognitive functioning show how unlikely it is that marijuana could have caused him to behave erratically or have difficulty following instructions.