During my PhD, there were times when I felt I shouldn't be there. Some of the other students in the research group were ridiculously smart, and while I was struggling to get even the roughest of results, they were publishing article after article and presenting their work at international conferences. Many of them had done their undergraduate degrees at the same university, so their supervisors had known who they were recruiting, but I had moved from Sheffield to Nottingham and always had the slight feeling that I had bluffed my way in and would, eventually, be found out. This is the impostor syndrome, and is a common problem among PhD students.
If you're working day after day in pursuit of a goal, part of you must believe it's possible. But the contradiction between the belief and the doubt—the forces pulling in two opposite directions—creates a stress that can stop you working to the best of your ability, which in turn reinforces the doubt.
Because impostor-like feelings are so common, it's easy to dismiss them as just something that everyone goes through. I don't think it's enough to say "everybody goes through this, just believe in yourself, keep going and it will be OK". I think it's better to examine the ideas behind the impostor syndrome and how they affect your work, then think about whether there's a more effective way of approaching it.
Although I present some ideas for dealing with impostor syndrome below, I want to make very clear that persistent feelings of unworthyness (or worthlessness) can be a sign of depression, and it would be deeply irresponsible to pretend that I have a solution to this other than seeking qualified help (speak to your doctor or your university counselling service).
If you feel like you aren't good enough, how good do you think you should be? At a recent talk I gave in Sheffield, one student said that "to get a PhD means you are the world's leading expert in your topic." While that's a kind of almost true, in that nobody else knows your project like you do, if taken literally it's a near-impossible expectation to live up to.
It's healthier, and more accurate, to think of a PhD as a beginner's qualification. It is during your PhD that you develop basic research skills, which you can then develop further should you continue in academia. Maybe you can become the world's leading expert in something, but it's going to take a hell of a lot of work and a hell of a lot longer than your PhD to build that experience and reputation.
Even when you graduate you will still be a relative beginner, so what matters is not how good you are now, but how your skills develop over time.
Ability is not fixed—it is almost always possible to improve upon whatever talents you have, but in order to do so you have to consciously work on the uncomfortable boundaries of your skills. This is only possible if you acknowledge where those limits are.
Impostor syndrome vs beginner mindset
Impostors, by definition, hide their identity. In the context of a PhD, this means hiding any insecurity or weakness in knowledge; avoiding asking the "stupid question", avoiding mistakes, avoiding risk and avoiding difficulty. It is a state motivated by fear, by the avoidance of a negative outcome, but it actually makes the negative outcome more likely.
Sometimes it's worth embracing the very thing you fear the most. Rather than avoiding being found out, why not be open about what you don't know?
If you think of yourself as a beginner, the question is no longer whether you are good enough, but how to get better. If you embrace the beginner mindset by being enthusiastically open about your weaknesses, it frees you to ask questions, to make mistakes and to learn. This is a much more positive outlook.
Really, it's about identifying problems you can do something about. If you can specify a skill that you need to strengthen, and specific actions to strengthen that skill, this is something you can focus on instead of the vague and destructive sense of unbelonging.