JavaScript is strictly client side. PHP is strictly server side. To submit a form, you have to send data from the client to the server. The server processes it (aka: PHP in this case) and then the server has the opportunity to send something back to the browser (if it doesn't, the browser will just time out saying the page couldn't be found).
With this in mind, its kind of tough to do what your asking. It can be done if you're creative. You may decide to use iframes or frames and that could work. Another thought is maybe popup windows. I think with some creative PHP and JavaScript coding you might be able to do something with this, but it depends on how much time you want to spend versus what your ultimate user experience will be.
Another approach is to have JavaScript pre-validate the data before submitting to the web server. That's usually pretty easy to do and it saves the user a round trip of data. But you will also want to have server side validation in this times when the user doesn't have JavaScript enabled.
I personally prefer templates. I've got a template system I use which allows me to easily populate the form fields with minimal amount of code. And if there's a form validation error, I have a message tag that gets swapped out with the error message and I just reshow the template (with all the form data so the user doesn't have to retype it all). If the form was submitted successfully, then I just have the code move onto the next page.