You can't observe an experience. You experience conciseness, you don't observe it.
How can science work with something that you can't observe, and therefore can't measure?
The religious person is the one claiming something without and reasoning or evidence. Therefore the onus is on them to prove that God exists, rather than the atheist to prove he doesn't.
There is no evidence to suggest that science will be able to observe an experience, so the onus is on you to prove that its a reasonable suggestion.
We may one day be able to measure experience, but we don't know yet. Until then science is the best tool we have.
This reasoning is nothing at all like being asked to prove there is no god, the history of science shows that we are able to untangle the mechanisms of the natural world, and there are no evidence to the contrary.
Now, in the eyes of science it is not the responsibility of a religious person to prove that god exists or does not exist, it is as much the responsibility of science - it's just very much a non-topic in science since no evidence have been found either way.
(And there are a lot of evidence that science will be able observe an experience - we already can do very basic recognition of patterns in brain waves based on what the subject is experiencing, we are starting to map, understand and simulate a human brain. Eventually that might turn into an engineering problem of hooking up the proper equipment to neurological pathways.)
This is a bold claim. You might as well say that science can't prove electrons exist or that water is wet.
What do you mean by 'proof', and why is that what you choose to mean by it?
What we call measurement is a mental model that we invented to help us think about reality. We don't have a measurement model for consciousness yet, but that doesn't necessarily mean we never will.
Technically though, when someone takes an MRI of your brain, that means your consciousness is being observed.
Interesting study though.