realpath() returns empty string

Better than to read "somewhere" -- you can read on the official online documentation!
http://us.php.net/manual/en/function.realpath.php

As you can see, your OS and release levels matter.  You might start by printing out the value of __FILE__, next printing the value of dirname(), etc.  Drill down into the function calls to isolate and visualize the return values from these functions one layer at a time.

The issue definitely seems to be the realpath function. If I remove that and output the value of the APPLICATION_PATH, then there's something to output, but if I run the output through the realpath() function, it comes back empty.

... it comes back empty.

Would that mean empty as in the PHP function call empty()? What is the output if you use var_dump() to print out the values of these variables and function calls?

Using var_dump() it just outputs bool(false)

I copied the site files to a server of my own this morning, and I'm still getting the same problem.

I don't understand why it's returning false.

My PHP version is 5.3.4

Just to confirm
------------------------
defined('APPLICATION_PATH')
    || define('APPLICATION_PATH', realpath(dirname(__FILE__) . '/../application'));

var_dump(APPLICATION_PATH);
------------------------

Outputs...
"Bool(false)"

If I remove the realpath() function from the line, I get this..
"/home/webdev/public_html/appdev/salonspy/../application"

I could use a function to replace realpath, but this site uses the Zend framework and I've no idea how often the realpath() function is used within the site.

You might consider using a code scanner to look for other occurrences of realpath().  I have found that Textpad's "Find in Files" functionality is pretty good.  Most editors have something like that.

Just curious... If you're getting this...

"/home/webdev/public_html/appdev/salonspy/../application"

... what is realpath() supposed to do with that string?

I believe it's supposed to convert it to...

"/home/webdev/public_html/appdev/application"

Is this note applicable?
http://us2.php.net/manual/en/function.realpath.php#88964

Problem was not really resolved, but we moved servers which fixed it.