Naturally, you are skeptical of this. So you want to see it for yourself. You want to go into the room and measure some things to see if they have shrunk. The trouble is that your ruler will also have shrunk to half the size. Your metre ruler will be only 50 centimetres long. So if you use it to measure an item that has shrunk to 50 centimetres, then you will mismeasure that as having a length of 1 metre....You cannot get empirical evidence to test my claim of a shrinking room.
As a piece of pedantry I should note there are ways to ascertain if everything else has shrunk in this situation that don't involve a ruler. For example: Light still travels at 300,000km/s. If according to your 'ruler' light travels at 600,000 kms - you know it's because your ruler has shrunk. Acceleration due to gravity would appear to change too in your room.
You need to change time as well as space to make your analogy work
Even then - I think you might still be able to tell via fundamental physics.
As a conventionalist, I see that the omphalist is not following the same conventions I am using, and therefore when the omphalist talks of "age of the earth" that has no relation at all to what I mean by "age of the earth".
I disagree. When an omphalist says the world is 6,000 years old, we agree on what '6,000 years' means. It is not like the shrinking room at all. Omphalists are NOT saying "The earth is 6,000 years old, but it appears to be 4billion years old because we're using different conventions of time recording". They are saying "The earth is 6,000 years old. Not 4billion years old. It appears to be 4billion years old because it was created with the appearance of having been 4billion years (less 6000)"
We all agree on what 6,000 means.
We all agree on what 4billion means.
We all agree on what a year is.
We all agree on what 'age of earth' means.
We all agree on what age the earth appears to be.
This is not a difference of convention. We're in complete agreement on that. The only disagreement is on how much time has passed between the time when the earth was a reasonably solid sphere of heavy elements and now.