Retina displays, high-res background images

Do I need to double the size of the .box div to 400px by 400px to
match the new high res background image

No, but you do need to set the background-size property to match the original dimensions:

@media (-webkit-min-device-pixel-ratio: 2), 
(min-resolution: 192dpi) { 

    .box{
        background:url('images/box-bg@2x.png') no-repeat top left;
        background-size: 200px 200px;
    }
}

EDIT

To add a little more to this answer, here is the retina detection query I tend to use:

@media
only screen and (-webkit-min-device-pixel-ratio: 2),
only screen and (   min--moz-device-pixel-ratio: 2),
only screen and (     -o-min-device-pixel-ratio: 2/1),
only screen and (        min-device-pixel-ratio: 2),
only screen and (                min-resolution: 192dpi),
only screen and (                min-resolution: 2dppx) { 

}

– Source

NB. This min--moz-device-pixel-ratio: is not a typo. It is a well documented bug in certain versions of Firefox and should be written like this in order to support older versions (prior to Firefox 16).
– Source


As @LiamNewmarch mentioned in the comments below, you can include the background-size in your shorthand background declaration like so:

.box{
    background:url('images/box-bg@2x.png') no-repeat top left / 200px 200px;
}

However, I personally would not advise using the shorthand form as it is not supported in iOS <= 6 or Android making it unreliable in most situations.

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