Because the stones in stone henge are MASSIVE!
You couldn't "knock them up" in an hour or two...
The older things are, the more difficult it is to date them - and the more likely it is that carbon dating will be the only truly definitive method. However 1877 is (relatiely) recent, and photographic technology is always advancing, so it is probably fairly easy to date the photo based on what photographic technology was used.
I didn't say an hour or two, I said it could be done over the course of a night!
I'm not saying that - like I say, I'm keeping an open mind. It COULD be 4,000 years old, but I think it's just as likely that it was cobbled together in the early 1800s.
All these old maps and that are all very well, and great for forming a
belief as to how old stone henge really is, and it's fine to base your belief on things like that. However, they're no basis for establishing definite fact.
No, because they were never living, duh...

You can only carbon date things that were once alive but that are now dead.
Carbon has two isotopes, most of it is C-12 which is stable, but some is C-14 which is radioactive. When you are alive,
your body regulates the amount of C-14*, but when you die - the C-14 gradually decays radioactively (into C-12 and helium? at a guess...) and such the percentage of it gradually drops
logarithmically, and at a predictable (known) rate. So more precisely, what carbon dating actuallys tell us is not how OLD an organism is, but specifically how long ago since it died.
However, when we're dealing with thousands of years, and most animals live for less than a century, that's normally good enough. Interestingly enough however, you could carbon date a piece of tree back to 4,000 years ago, but it could have been a giant redwood and been alive for 4,000 years before that.
a. 3 actually, C13 is another isotope - far commoner than C14
b. No it doesn't, the C14 decays to Nitrogen under its own steam
c. Inverse log actually
and finally, C14 is formed by cosmic rays interacting with C13, deep underground, the C14 would all have decayed and no new C14 would be able to form.
And finally, finally, you are obviously hard of reading 'cos I explained all this yesterday afternoon whilst I should have been working.
*
because of the constant 'throughput' of carbon, due to you eating new food, shedding skin, shitting, etc. so no molecule of carbon that you've got in your body stays in you for years on end.