"if emotions had no physical basis, such as chemicals, hormones, heat, etc, then how could meditation influence them? "
Emotions cause an effect in the physical world, they measure that effect. It stands to reason that if 'x' emotion produces 'y' effect then inducing 'y' effect artificially will bring about emotion 'x'. Meditation can produce a certain brain-state whereby a certain chemical/ physical reaction takes place in the body. The early LSD experimenters noticed the same effect.
