Visible crew/equipment: When Angier goes to Tesla's laboratory and walks to the gate, on the far right side of the fence a figure can be seen, apparently holding something ahead. It seems to be one of the film crew holding a boom mike upright. (00:09:59)
Visible crew/equipment: When Angier and Tesla have their first talk on the balcony, take a closer look at the moment where Alley pours the tea into Angier's cup, and you can see two stage lights and a boom microphone reflected on the teapot. (00:50:30)
Visible crew/equipment: In the final shot where Angier lies dead on the ground with the theatre on fire, the camera can be slightly seen reflected on the glass box with one of many Angier's doubles inside once it does a tracking shot. (02:04:52)
Answer: They were twins. Tesla didn't make a matching machine for Borden - all he made for the twins was a machine that made some light and noise to enhance their trick. The Borden brothers sent Angier off to see Tesla on what they thought would be a wild goose chase, just to get him out of the way for a while - they would never actually give away the real secret to their trick. They never anticipated that Tesla could actually have built the machine in question.
Tailkinker ★