The UK made the decision awhile back to delay giving second doses of vaccine in order to spread limited supplies to as many people as possible. Although there is evidence that this would be helpful for the AZ vaccine, presumably because it allows time for the immunity to the vector to die down, I was critical at the time of the decision to do this for Pfizer.
My reasoning was that the RNA vaccines do not give neutralizing antibodies in appreciably amounts until after the second shot. Neutralizing antibodies are a sign that the immune system has had a full-blown adaptive immune response, in which it goes through an iterative process of tailoring the antibodies to the specific pathogen. Those more specific antibodies bind more tightly to the spike protein and therefore are better at blocking the binding of the virus to the receptor. I was worried that the immune system would get locked into weak antibodies if you waited too long between shots.
This study, done in the UK, compares the antibody and T-cell responses to the Pfizer vaccine for those with the standard 3-week spacing, and the long spacing of 11-12 weeks.
Unfortunately, they did not look at neutralizing antibodies, so my question was not answered. They did look at total antibodies, and found that they were higher for the long spacing. But peak T-cells were higher for the normal spacing, and T-cells are necessary for that aforementioned full adaptive immune response. So my question of whether or not neutralizing antibodies are lower with the long spacing is still open.
However, I was encouraged to see (in other studies) that people who have prior infection do make a strong neutralizing antibody response upon vaccination, even with one shot. Many people with infection don't make neutralizing antibodies, possibly because the virus infects and damages T-cells. So this suggests that the long spacing will not be a problem in the long run.
https://www.medrxiv.org/content/10.1101/2021.05.15.21257017v1.full.pdf
And also the study showing neutralizing antibodies after vaccination on top of prior infection.