Bootstrap, contact_php und contact.js nicht E-Mails senden

Ich bin mit Bootstrap und nutzen wollen, eine E-Mail-Kontakt-Formular. Ich habe setup eine test-Seite - http://www.beatrootonline.co.uk/test.html. Wie Sie sehen können, überprüfen Sie ok (jqBootstrapValidation.js) und scheint eine E-Mail senden. Ich bin jedoch nicht erhalten eine E-Mail über dieses Formular.

Hier ist der html -

<div class="row">
<div class="col-lg-12">
<form name="sentMessage" id="contactForm" novalidate>
<div class="row">
<div class="col-md-6">
<div class="form-group">
<input type="text" class="form-control" placeholder="Your Name *" id="name" required data-validation-required-message="Please enter your name.">
<p class="help-block text-danger"></p>
</div>
<div class="form-group">
<input type="email" class="form-control" placeholder="Your Email *" id="email" required data-validation-required-message="Please enter your email address.">
<p class="help-block text-danger"></p>
</div>
<div class="form-group">
<input type="tel" class="form-control" placeholder="Your Phone *" id="phone" required data-validation-required-message="Please enter your phone number.">
</div>
</div>
<div class="col-md-6">
<div class="form-group">
 <textarea class="form-control" placeholder="Your Message *" id="message" required data-validation-required-message="Please enter a message."></textarea>
</div>
</div>
<div class="clearfix"></div>
<div class="col-lg-12 text-center">
<div id="success"></div>
<button type="submit" class="btn btn-xl">Send Message</button>
</div></div>
</form>
</div>
</div>

und die contact_me.js
$(function() {

$("input,textarea").jqBootstrapValidation({
    preventSubmit: true,
    submitError: function($form, event, errors) {
        //additional error messages or events
    },
    submitSuccess: function($form, event) {
        event.preventDefault(); //prevent default submit behaviour
        //get values from FORM
        var name = $("input#name").val();
        var email = $("input#email").val();
        var phone = $("input#phone").val();
        var message = $("textarea#message").val();
        var firstName = name; //For Success/Failure Message
        //Check for white space in name for Success/Fail message
        if (firstName.indexOf(' ') >= 0) {
            firstName = name.split(' ').slice(0, -1).join(' ');
        }
        $.ajax({
            url: "bin/contact_me.php",
            type: "POST",
            data: {
                name: name,
                phone: phone,
                email: email,
                message: message
            },
            cache: false,
            success: function() {
                //Success message
                $('#success').html("<div class='alert alert-success'>");
                $('#success > .alert-success').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                    .append("</button>");
                $('#success > .alert-success')
                    .append("<strong>Your message has been sent. </strong>");
                $('#success > .alert-success')
                    .append('</div>');

                //clear all fields
                $('#contactForm').trigger("reset");
            },
            error: function() {
                //Fail message
                $('#success').html("<div class='alert alert-danger'>");
                $('#success > .alert-danger').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                    .append("</button>");
                $('#success > .alert-danger').append("<strong>Sorry " + firstName + ", it seems that my mail server is not responding. Please try again later!");
                $('#success > .alert-danger').append('</div>');
                //clear all fields
                $('#contactForm').trigger("reset");
            },
        })
    },
    filter: function() {
        return $(this).is(":visible");
    },
});

$("a[data-toggle=\"tab\"]").click(function(e) {
    e.preventDefault();
    $(this).tab("show");
});
});


/*When clicking on Full hide fail/success boxes */
$('#name').focus(function() {
$('#success').html('');

und meine contact_me.php

    <?php
    //check if fields passed are empty
    if(empty($_POST['name'])        ||
    empty($_POST['email'])      ||
    empty($_POST['message'])    ||
   !filter_var($_POST['email'],FILTER_VALIDATE_EMAIL))
   {
    echo "No arguments Provided!";
    return false;
   }

$name = $_POST['name'];
$email_address = $_POST['email'];
$message = $_POST['message'];

//create email body and send it    
$to = '[email protected]'; //put your email
$email_subject = "Contact form submitted by:  $name";
$email_body = "You have received a new message. \n\n".
                  " Here are the details:\n \nName: $name \n ".
                  "Email: $email_address\n Message \n $message";
$headers = "From: [email protected]\n";


$headers .= "Reply-To: $email_address"; 
mail($to,$email_subject,$email_body,$headers);
return true;            
?>

Bekomme ich eine Meldung auf dem Bildschirm, die sagen, dass die E-Mail wurde gesendet, aber keine E-Mail ankommt (ich ersetzte meine echte E-Mail-Adresse für einen fake auf die php -)