Although not directly a question about atheism, this is asked of us quite frequently. It is a question that requires some background information.

First, we need to clarify what it means to "prove" something. Science does not prove anything to an absolute degree - that is not possible outside of mathematics. Instead, "proving" something translates into "demonstration beyond a reasonable doubt". If something can be demonstrated to 98% confidence, that is good enough, as long as we are open to revision down the road.

Science also does not require direct observation to suss out how reality works. It is faster, but not required. The Rutherford Gold Foil Experiment [1], for example, was an experiment that simply was trying to determine whether atoms had distinct nuclei or not. We couldn't "see" the atomic nucleus, but we could still indirectly test for it. Much of science operates in this way. "Unseen" phenomena are not insurmountable problems.

If you go to a park, during a nice summer's day, when lots of people are around, are you able to determine who's in love, or who is angry or sad? Most people can, and it is because the phenomenon of love is giving off evidence. A consistent set of patterns surrounds each emotion.

Love is not in the same category as physical objects. We aren't talking about demonstrating the existence of Bob. It is more like a computer program. Few people dispute that Microsoft Windows exists... but you can't see it, or touch it. All you can do is interact with it through an interface - the monitor, keyboard, mouse, etc. What's displayed on the monitor could be just an illusion by another program.

Yet, we consider interacting through this interface to be sufficient to demonstrate its existence, particularly when we can set up studies, experiments and statistical analyses based on that interface. That brings it into the realm of science (not that many have thought that we needed scientific studies to demonstrate that Microsoft Windows exists).

The same applies to emotions. The person's actions, body language, speech, facial expressions, etc, are all "the interface", and most people are fairly good at accurately detecting another person's mood on a basic level. The scientific field of Psychology has countless studies on love alone, controlling for different variables, setting up blinded trials, etc. [2][3]

Further, when we examine the brain from a biological perspective, we find empirical evidence of altered brain chemistry from love. We've found increased production of Nerve Growth Factor in people who are first in love [4]. Specific regions of the brain have increased activity when people experience love, as CAT/MRI scans demonstrate, to the point that we are learning the specific nuances of the phenomenon, from a biological stance [5][6]

Science has long since moved on from trying to demonstrate that love exists, and is busy figuring out precisely how it works. If the existence of a god were as easy to demonstrate as love, this website wouldn't exist.