acceptable p-level for scientific studies

I have a statistical question, that doesn't belong to this list, and I
apologise for that in advance but I would appreciate your help very much.
Is there some convention for selecting the a level for significance 
testing in scientific (e.g. chemical processes) studies? Most people use
the 0.05 level but I could not find a reference to justify this. Why not 
0.01 or 0.1? Montgomery in his book "Design and Analysis of Experiments" 
disagrees with setting a priori acceptable levels at all. Is it 
necessary to set a limit for significance testing since R can provide 
exact probability levels for the significance of each effect?

In general, setting arbitrary criteria for statistical significance seems 
to be based upon a compromise between apparent progress (maximal 
discovery) and theoretical durability (minimal disconfirmation). If we are 
to build knowledge from ignorance or misapprehension, it is best to choose 
methods and criteria that lead to an optimal compromise. Statistical 
evaluation of data has done a much better job than rhetorical contention 
as a method. 
Criteria range from the apparently slack alpha=0.1 in fields where is it 
difficult to discover any regularity to approximately 0.000000001 for 
establishing an effect at "six sigma" where variables are apparently well 
described and measurement is correspondingly precise.
In fact, what seems to happen is that researchers and reviewers find 
criteria that allow them to advance, at least apparently, at a certain 
rate. Thus my opinion is that a certain level of apparent progress is 
psychologically necessary in research, and those in the messier areas are 
willing to look a bit more foolish.

Jim