If you did not show up for the court date and did not make payment by mail, the court would likely enter a "default judgment" on the ticket. In essence, that means you would be convicted of the ticket and a fine would be imposed.
The ticket would go on your driving record and could have insurance consequences. Realistically, the fine would be imposed, but it is unlikely that AZ would start a collection process on someone who lives in VA. However, if in the future you happened to be back in AZ and were stopped by the police, this could present some problems for you.
If you have further questions, I would recommend you speak to a traffic attorney in AZ.
The court must first obtain jurisdiction over you by serving you.
For more details, read my legal guide on photo radar procedures in Arizona.
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