What is the shiur of a רביעית?

The shiur of a רביעית is used for just about all mitzvos that involve drinking so it is an important shiur. רביעית literally means one quarter, it is defined as one quarter of a לוג. The shiur of a לוג is given as 6 eggs which means a רביעית is 1.5 eggs. In our measurements, eggs are approximately 2 oz (displacement) so a רביעית would be 3oz.

However, the נודע ביהודה in the 1700s raised the following question. The Gemara (Pesachim 109) goves an alternative way of measuring a רביעית. The Gemara says that a box 2x2x2.7 thumb widths holds a רביעית. The נודע ביהודה measured a רביעית both ways and to his surprise saw that a רביעית measured by thumb widths was almost twice as big as one measured by eggs. His conclusion was that eggs must have gotten smaller. This opinion has been popularized by the Chazon Ish in recent times where a רביעית is measured at over 5 oz.

There are a number of problems with this נודע ביהודה.

1. It is based on the idea of נשתנו הטבעים, however, we have absolutely no proof that this happened. In fact, we have proof that the size of eggs didn't change as 2000 year old eggs were discovered by archeologists buried in lava in Pompei and their size was the same size as today's eggs.
2. The Chasam Sofer writes: "איך יצויר בזמן קצר שינוי כזה דווקא בביצים, ולא בשיעורים ולא בקמח ובאדם?!" (שו"ת חתם סופר או"ח א סימן קכז; ועיין שם סימן קפא. How could it be that in such a short time there was such a change specifically in eggs and not in flour or people?
3. The Mishna Berura describes an expirment that he did. The Gemara states that 2 cheekfulls of liquid for an everage person is more then a רביעית. If we double the shiurim like the נודע ביהודה then a רביעית is 3 eggs, yet we see that people today cannot fit more then 2 eggs in their mouth. 

To me, the most fascinating point about all of this is why did it take until the נודע ביהודה, the 1700s for someone to figure this out. This contradiction was around for a long time yet it wasn't discovered by anyone and it certainly wasn't made into a big deal. I believe that the answer is that the נודע ביהודה was influenced by non-Jewish society. The 1700s was after the enlightenment, the start of the industrial revolution and the scientific process had taken hold. People were experimenting, trying to figure out how the world works. The נודע ביהודה was affected by this change and therefore he too started to experiment and came up with his famous contradiction. 

I believe that the answer to this question depends on your view of the Gemara. If you view the Gemara and halacha as an entirely self consistent enterprise then it can't be that Chazal provided 2 contradictory opinions as to the size of a רביעית. However, if you believe הלכה frequently contains contradictions, since it’s a conglomerate of opinions, מנהגים (often of questionable origin), and occasional errors from different פוסקים who didn’t necessarily agree with each other then this is just one among a long list. The contradiction stems from either different shiurim in different places, different ways of measuring, or simply shiurim that were not very exact. People today forget that in the time of Chazal no measurements were exact. The following example illustrates this. I daven vasikin every day. We have a clock that synchronizes with the atomic clock so that the time is exact to the second and we finish גאל ישראל to the second of sunrise. However, when you think about it, this is ridiculous. Chazal had no clocks and had no way of knowing when exactly sunrise was. Sunrise was when they literally saw the sun rise. For us to be מדקדק to the second is certainly not what anyone did until modern times. The same applies to shiurim like a רביעית. It is very possible that Chazal gave approximate shiurim and that they were off by 2 oz.