In far mode we should feel more distant from folks around us. So since happy is far, happy folks should feel more lonely. And they do:

The more people value happiness, the lonelier they feel on a daily basis (assessed over 2 weeks with diaries). … An experimental manipulation of valuing happiness … demonstrates that inducing people to value happiness leads to relatively greater loneliness, as measured by self-reports and a hormonal index (progesterone). In each study, key potential confounds, such as positive and negative affect, were ruled out. (more)