Q:

Is the claim that atheism is the null hypothesis invalid because it applies a physical measurement to the metaphysical?

I've heard several people state that:

Atheism is the null hypothesis. ie that this null hypothesis can be falsified: if one piece of evidence is found to contradict it, the existence is considered proven.
This is the basic mechanism of science itself. One famous example is the old hypothesis that only white swans existed. The null hypothesis then was 'there are no non-white swans', something that can be falsified. When in Australia black swans were found, the null hypothesis was rejected. That is the mechanism of the null hypothesis.

This seemed strange to me from an application point of view. (I'm fine with the swans and the idea of the null hypothesis).
To me science is bound by the limits of repeatable human observation. Can something exist that we cannot observe repeatably? I would say yes.
To me the existence of God is metaphysical, ie it exists outside the realm of human measurement. (If you're a goldfish in a bowl inside, you're not in a position to make observations about astronomy or the biological structure of an ant's nest. These are outside your realm.)
In addition, from my epistemological view - there are categories of things we hold true that are outside the realm of repeatable scientific measurement. Did Julius Caesar walk on the earth? Lots of people wrote down about it, so we agree it is true - but we can't repeatably prove his existence. We hold it as a historical truth, but not a scientific one.
My question is: Is the claim that atheism is the null hypothesis invalid because it applies a physical measurement to the metaphysical?

A:

Atheism is the null hypothesis. ie that this null hypothesis can be falsified: if one piece of evidence is found to contradict it, the existence is considered proven. 

This is a bit of a straw man argument.  Every logical argument meets this requirement: the existence of a contradiction shows the argument to be invalid.  By this definition, "God exists" could also be a null hypothesis, because if one piece of evidence is found to contradict that, the existence is considered disproven.
The real distinction between the null hypothesis and the alternative hypothesis is that the null hypothesis is assumed true until rejected due to contradictory data.  If the null hypothesis is rejected, and the alternative hypothesis is not, the alternative hypothesis can become the next accepted theory, which becomes the null hypothesis for future tests.  It's sort of a "king of the hill" approach, with the current champion serving as the null hypothesis taking on challengers.
A more valid reason for atheism to be the null hypothesis is due to the nature of trying to prove a negative.  It is relatively easy to develop scientific experiments to prove something exists, simply by finding it.  We "prove" gravity waves exist by finding one and measuring it (well, finding several and measuring them all).  Proving a negative is far harder.  If we've never seen an Oompa Loompa, how can we prove they don't exist on some distant exo-planet we've never seen?  Accordingly, it is generally considered unacceptable to demand science prove a negative universally (it is valid to ask science to prove a negative in a bounded case, such as "people don't get injured when you put fences around the crocodile pit").  Scientists will reject demands for science to make such proofs.
An example of this occurring is in the Eastern concept of Chi.  The philosophers and martial artists who claim Chi exists have not had their claims substantiated by science.  However, science can never disprove the existence of Chi, only prove that "in this controlled scenario involving this particular type of punch where the master claims Chi should matter, there was no discernible difference caused by Chi."
This is where the scientific approach gets interesting.  What happens if there are two separate hills, each with their own king?  Each naturally wants to be king of the combined hill, but their approaches may not agree.  In the case of theism, if one starts from the assumption that "God exists," that is the king of your hill.  If another starts from the assumption that "God does not exist," that is the king of their hill.  They cannot develop a scientific challenge to your claim, because such a claim would have to prove a negative.  You, on the other hand, can make a scientific challenge to their claim, by disproving their claim.  This calls for you to prove a positive claim, because you have to prove that something exists that cannot exist if God does not exist.
This is why Atheism is best suited for the null hypothesis, rather than theism.  The evidence which can be found to contradict it is more accessible to scientific inquiry, so a purely scientific process is forced to approach the problem from that particular point of view.  If one uses a process which is not purely scientific, it may be reasonable to approach it from the other direction, with theism being the null hypothesis.
Now as to your question, Metaphysical issues cannot be the null hypothesis in scientific inquiry because science is an empirical approach which can only explore the world which can be explored empirically.  You could find another reason to use the notation of "null hypothesis" and "alternative hypothesis," but science explicitly uses these for exploring hypothesis which provide empirical forms of verification.
However, it is worth noting that science does not prove anything unless you choose to admit their proofs.  Science merely rejects all simpler models until it arrives at one that it has not rejected. That model becomes "king of the hill" until new evidence comes along to dethrone it.  One may choose to accept the current "king of the hill" as truth, through a epistemological process called abduction, but that's up to one's own discretion.

A:

Considering atheism the null-hypothesis seems a nice metaphor, but not a serious characteristics. One can raise the following objections:

In statistics the null-hypothesis is generally assumed to be true. And one looks for a test which contradicts this assumption. But theists would declare just the opposite assumption as null-hypothesis.
Operating with a null-hypothesis H_0 and an alternative hypothesis H_1 presupposes that there are many cases and one is able to collect representative samples. These requirements are not fullfilled in the case of atheism versus theism.
Until today no test exists, which has found consensus from both fractions, to decide between atheism and theism. 

Note. A mathematical model from history which has a certain relatedness to the statistical model from your question is Pascal's Wager.

