The following story contains a MAJOR SPOILER for Joker. If you haven't seen the film, go check it out, and then come back to read the details.
When we first meet the character of Thomas Wayne in Joker, it feels like's meant to only help reinforce the comic book world of Gotham City. The man is rich and running for mayor, about as far removed from the world that Arthur Fleck (Joaquin Phoenix) lives in as possible.
While there is a connection between the two, Arthur's mother once worked for the Wayne family, the movie takes a pretty significant change in direction when Arthur learns that he might actually be the illegitimate son of Thomas Wayne. Brett Cullen, the actor who plays Wayne was just as surprised to see that twist when he read the script as any in the audience were this weekend when they saw it.
Cullen says that director Todd Philips, saw the connection between the Joker and the Wayne family as a way to explain Joker's hatred, but in a way that the audience can sympathize with. According to Cullen...
I was very surprised when I read the twist. I went to Todd and asked, ‘Are we playing this the way I think we’re playing this’ Todd responded with, ‘What would be a compelling reason for the Joker to hate Batman so much?’ The idea that the Joker is an illegitimate child that didn’t get anything from the Wayne family is a very compelling motivation for his character’s hatred. This movie makes you feel for Arthur, when you see him struggling with his mother. And she’s saying, ‘Go see Thomas Wayne, he’ll help us. He’s a good man.’ It’s gut-wrenching.
Of course, the twist that Arthur is actually a Wayne isn't the only twist the movie has in store. Later, we learn that Arthur's mother may have been suffering from mental illness. Her credibility on the claims she had an affair with Thomas Wayne is called into question, and evidence is presented that Arthur was actually adopted.
The question of the truth of Arthur's parentage, like many other questions about Joker, is left open for the audience to debate. Although, Brett Cullen does tell THR that he approached his performance believing that the affair was real. He thinks Thomas Wayne was also responsible for having Arthur's mother committed.
Even if we believe the affair did happen, it doesn't mean necessarily that Arthur is Thomas Wayne's son, though the odds of that certainly do go up.
The decision to link Joker and Bruce Wayne as half-siblings is certainly an interesting one. Todd Philips apparently felt this would help explain Joker's hatred of Batman, which makes sense if you assume that Joker eventually discovers that Batman is Bruce Wayne, which, at least traditionally, is not how that is handled.
Of course, while Joker is yet another movie that gives us the Batman origin story, there's no indication that it plans to ever go beyond that. We'll have to simply imagine how the battle between this Batman and this Joker will go.