As you have noted each state in the USA has different requirements. The general requirements are as follows:
- Obtain a Bachelor's in Engineering (BSE) from an ABET accredited engineering program. The disciplines that I am familiar are Electrical, Civil, and Mechanical. I suggest you review the references below for more detailed information.
- Successfully complete the Fundamentals in Engineering exam to obtain Engineering in Training (EIT) status.
- Gain professional experience (typically four years minimum).
- Successfully complete the Principles and Practice of Engineering (PE) exam.
Considering that you have bachelor's and graduate degrees in physics, you have a few options:
- Enroll in a ABET accredited engineering program to obtain a Bachelor's in Engineering. With your physics background you are most likely to get a significant amount of credit. It is likely that you will be able to obtain a Bachelor's in Engineering in about 2 year depending on the University.
- Submit your credential to the licensing authority; hopefully they will accept your credentials and allow you sit for the EIT exam. You will have to do more research on this topic. I suggest that you review the Washington AccordWashington Accord.
- If you are already a licensed, practicing engineer, submit those credentials to the appropriate licensing authority. They may accept your current credentials. I have submitted my USA credentials to Engineers Australia and obtained registration in Australia for an Australia-based engineering project.