Can I study and obtain two PhDs in different subjects simultaneously?
Check the policies and regulations

Answering to your question hugely depends on the policies of the universities where you want to do PhDs and the country and education system where you are located. Some may allow you and some may not. Even, some universities may not also be interested in students doing simultaneous degrees. Moreover, you need to make sure whether your funding provider (if you are not self-funding) allows you to study for two degrees or not. So, nobody can give you exact information on this part of your question.

However, I have a general advice to you:

Don't run, Walk!

Take a deep breath and answer this question: Why do you want to apply for two PhD degrees simultaneously?  

A PhD degree requires the student to spend most of his time studying and collaborating with his/her advisor. You may need to take some courses in each program, spend your time searching for topics and current papers and books, read them, find an original topic for your dissertation. Put all these huge academic chores besides to your personal life.

It is not a good idea to study two degrees even if the policies allow you to do so.

Don't leave your interests

However, if you are so interested in both subjects, you can apply for one PhD as your major research path and follow the other path as you second or minor research interest. Read papers and books about it. Even, in your free time, you can talk to a professor whose research field is near to your minor research path. Attend conferences, colloquiums and seminars about your favorite subject. Keep in mind that you simply don't need to obtain another PhD to meet your research interests.