Question

Did anyone ever heard about this?I've never seen any serious physicist talk about "mass fluctuations".

Here is the man in his own words: http://www.intalek.com/Index/Projects/Research/woodward1.pdf

And what about this guy: http://aetherwavetheory.blogspot.com/

He claims his theory can explain virtually every unsolved problem in contemporary physics.

Answer 1

No, this paper has nothing to do with serious physics. It has two steps

Mach's principle
bizarre derivation of varying rest masses while accelerating, based on the previous point

The first point is less problematic - Mach's principle has been inspiring even for Albert Einstein when he was looking for general relativity. However, it turned out that Mach's principle is simply wrong and it hasn't become a part of modern physics.

Nevertheless, it's the second step that is much more problematic. Mach's principle couldn't be able to imply conclusions about varying rest masses even if this principle were right. The paper makes no sense and whenever the predictions - which don't really follow from the starting assumptions - were treated seriously and tested, they weren't confirmed experimentally. To make it more amusing, the discoverer proposed the hypothetical effect as motors for spaceships - the kind of context where it shouldn't be hard to see that this is probably not serious research.

To make thing even worse, the blog you mentioned is one by Zephir, a Czech "independent researcher" who is well-known to all physics bloggers in the world, and you don't really want to pay any attention to this stuff.