As others have suggested, you are not clearly explaining your problem, what you are trying to do, or what your expectations are as to what this function is actually supposed to do.
If I have understood correctly, then you are expecting this function to refresh the page for you (you actually use the term "reloads the browser").
But this function is not intended to reload the browser.
All the function does, is to add (push) a new "state" onto the browser history, so that in future, the user will be able to return to this state that the web-page is now in.
Normally, this is used in conjunction with AJAX calls (which refresh only a part of the page).
For example, if a user does a search "CATS" in one of your search boxes, and the results of the search (presumably cute pictures of cats) are loaded back via AJAX, into the lower-right of your page -- then your page state will not be changed. In other words, in the near future, when the user decides that he wants to go back to his search for "CATS", he won't be able to, because the state doesn't exist in his history. He will only be able to click back to your blank search box.
Hence the need for the function
history.pushState({},"Results for `Cats`",'url.html?s=cats');
It is intended as a way to allow the programmer to specifically define his search into the user's history trail. That's all it is intended to do.
When the function is working properly, the only thing you should expect to see, is the address in your browser's address-bar change to whatever you specify in your URL.
If you already understand this, then sorry for this long preamble. But it sounds from the way you pose the question, that you have not.
As an aside, I have also found some contradictions between the way that the function is described in the documentation, and the way it works in reality. I find that it is not a good idea to use blank or empty values as parameters.
See my answer to this SO question. So I would recommend putting a description in your second parameter. From memory, this is the description that the user sees in the drop-down, when he clicks-and-holds his mouse over "back" button.