So, in an unusual experiment, he tricked them.
In their laboratory, Dr. Thompson and his assistant Mark Stone had had the cyclists pedal as hard as they could on a stationary bicycle for the equivalent of 4,000 meters, about 2.5 miles. After they had done this on several occasions, the cyclists thought they knew what their limits were.
Then Dr. Thompson asked the cyclists to race against an avatar, a figure of a cyclist on a computer screen in front them. Each rider was shown two avatars. One was himself, moving along a virtual course at the rate he was actually pedaling the stationary bicycle. The other figure was moving at the pace of the cyclist's own best effort - or so the cyclists were told.
In fact, the second avatar was programmed to ride faster than the cyclist ever had - using 2 percent more power, which translates into a 1 percent increase in speed.
Told to race against what they thought was their own best time, the cyclists ended up matching their avatars on their virtual rides, going significantly faster than they ever had gone before.
While a 2 percent increase in power might seem small, it is enough to make a big difference in a competitive event that lasts four to five minutes, like cycling for 4,000 meters. At the elite level in sports, a 1 percent increase in speed can determine whether an athlete places in a race or comes in somewhere farther back in the pack.
The improved times observed in his experiment, said Dr. Thompson, are "not just day-to-day variability, but a true change in performance." And they give rise to some perplexing questions.
What limits how fast a person can run or swim or cycle or row? Is it just the body - do fatigued muscles just give out at a certain point? Or is the limit set by a mysterious "central governor" in the brain, as Timothy Noakes, professor of exercise and sports science at the University of Cape Town in South Africa, has called it, that determines pacing and effort and, ultimately, performance?
Until recently, exercise physiologists have mostly focused on the muscles, hearts and lungs of athletes, asking whether fatigue comes because the body has reached its limit.
But athletes themselves have long insisted that mental factors are paramount. Roger Bannister, the first runner to break the four-minute mile, once said: "It is the brain, not the heart or lungs that is the critical organ. It's the brain."
Now researchers like Dr. Thompson are designing studies to learn more about the brain's influence over athletic performance.
For example, Jo Corbett, a senior lecturer in applied exercise physiology at the University of Portsmouth in England, wondered how much competition can affect an athlete's speed. To find out, he asked cyclists to ride as hard and as fast as they could on a stationary bicycle for the equivalent of 2,000 meters. As he rode, each rider was shown an on-screen figure representing the cyclist riding the course.
Then Dr. Corbett and his colleagues told each athlete that he would be racing against another rider hidden behind a screen. The researchers projected two figures on the screen, one the outline of the rider and the other the outline of the competitor.
In fact, the competitor on the screen was a computer-generated image of the athlete himself in his own best attempt to ride those 2,000 meters.
The cyclists rode furiously through the on-screen race. And, as happened in Dr. Thompson's experiments, the cyclists beat their best times, finishing with a burst of speed that carried them to virtual victory by a significant length.
Dr. Corbett said the extra effort, above and beyond what the athletes had previously demonstrated, seems to come from the anaerobic energy system, one that is limited by the amount of fuel stored in muscle. The brain appears to conserve the body's limited fuel to a certain degree, not allowing athletes to work too hard.
But in a race, he said, the brain seems to allow athletes to tap more deeply into energy stores than would ordinarily be permitted. "Competition is able to motivate you to dip further," Dr. Corbett said.
In contrast, does not increase individual performance, Dr. Corbett said - at least, not in research experiments. Physiologists have asked athletes to go as fast as they can on a course and then offered money if the athletes could beat their own best times. They could not.
Still, there must be a limit to how fast an athlete can go, even with the most intense competition or even with deception. In a new study, Dr. Thompson tried to find what that limit is.
He used the same method as before: Cyclists on stationary bikes raced an on-screen avatar going a bit faster than the cyclist's own best time. In one group, the only variable was competition. Cyclists were told that the avatar would be going 2 percent faster or 5 percent faster than the cyclist had ever gone.
The other group was deceived. Each cyclist was told to compete against an avatar that would be moving as fast as that athlete had in his best effort. Actually, the avatar was programmed to race 2 percent harder or 5 percent harder. (A 5 percent increase in power translates into a 2 percent increase in speed, Dr. Corbett said.)
The cyclists in the first group gave up from the start when they knew the avatar would be moving faster than they ever had - even when the avatars were going 2 percent harder than the cyclists' own best times. Instead, the athletes matched their own best efforts.
As had been observed in previous experiments, cyclists in the second group, who were deceived, kept up with their avatars when they were programmed to perform 2 percent harder than each athlete at his best. But 5 percent was just too much: The athletes kept up for about half the race, then gave up.
In the end, their overall pace was no better than it had been in their best effort without the avatar. Some seemed to do even worse than their previous best effort.
"It comes back to the belief system within the athlete," Dr. Thompson said. Within limits, if an athlete thinks a certain pace is possible, he or she can draw on an energy reserve that the brain usually holds in abeyance.
One lesson, Dr. Thompson said, is that coaches can eke better performances out of athletes by means of small deceptions.
When an athlete has reached a plateau, a coach might tell an athlete in a training session that the course distance is slightly shorter than it actually is, for example, or that his or her speed at each interval is slightly slower than it is.
The new research suggests that this strategy may bring about an increase in performance, and Dr. Thompson said that it has been used to coach elite middle-distance athletes, although he declined to provide details.
But it is a risky approach, he added: Even small deceptions can erode the trust between athlete and coach.