Is it possible to train muscles by doing an exercise without any
weight or resistance?
Yes, in this study they had 16 young men (9 flexing, 7 control) follow a flexing protocol for 3 days a week. After it was over, it was shown that the training group had significantly increased torque as well as muscle thickness. They concluded
"That maximal voluntary co-contraction is applicable as a training modality for increasing the size and strength of antagonistic muscle
pairs without increasing involuntary coactivation level."
Going one step further, there is lots of research out there that shows that thinking about muscle contractions is enough to stimulate muscle growth, and prevent atrophy.
Study 1: Four groups including, mental contractions of little finger abductions, mental contractions of their elbow flexion, physical finger abductions, and a control group. Physical finger abductions increased strength the most, followed by both mental contraction groups, with the control group not changing.
Study 2: Testing the effect of mental imagery in the training of new motor actions. Again, overt action beat out mental, but mental came in a close second, only lacking an increase in reaction time. They still improved on muscle strength, power, and work though.
Study 3: In this one they studied the torque of plantar-flexor muscles of the ankle. Three groups including a imagery training, a low-intensity strength training, and a control group. In this one the mental group actually outperformed the low intensity group. (the low intensity group had results very similar to the control group though.)
- Study: They put casts on 29 healthy individuals wrists. 14 individuals were told to perform mental imagery of strong muscle contractions 5 days per week. At the end of 4 weeks the group who mental contractions had preserved significantly more strength.
I could go on with several more studies, but you get the point. Not only is it possible to gain muscle by contracting your muscles, but simply imagining muscle contractions is enough to stimulate growth or slow down muscle atrophy.