Your core without your pelvic floor, is not your core.

There are a wide variety of ideas about which muscles grouped together form “the core” and help to stabilise the hips and pelvis against the ribs above. Some definitions seem to want to include muscles that move and support the spine, and whilst yes, those muscles are important for delivering stability, they also contribute strongly to movement, whilst ‘the core’ to me, is more about anti-movement. Resisting things other than movement in the direction you’d like to move in. Some definitions also add glutes as part of the core, and yes they form an important part of movement and stability, but to me, muscles that cross the hip joints are hip muscles. Like the spinal muscles, hip muscles rely on that stability of the core to work well, but they’re not ‘the core.’
Which is not to say that you want your core to be stable like rock. A solid, immovable torso, that isn’t the goal. In fact, I have seen rock hard abs and not moving much from the spine as a result, account for a large part of some problems- that’s also not how it works best!
Being strong enough with your back in different positions is pretty helpful in life, of course- being in a posture where you already weren’t overly strong and then something silly happens, is a common cause of injury. To me, ‘the core’ is about resisting movement which the spinal muscles can’t reasonably be asked to do by themselves while they also move you. The muscles doing the moving have an important role, and the muscles doing the stabilising have an important role, and that’s an important distinction.

If we then look at other overly-simplistic definitions of ‘the core’ to some people it seems it can be pretty much just abs, and that’s not really the case either.
Working on your abs for a stronger core is almost as pointless as things get.
Sit ups honestly have to be one of the most pointless exercises known to man. Unless you want a 6 pack there is absolutely no reason to do them. Having a 6 pack itself is pretty pointless unless people can see it, and that’s probably 80% hardcore weight management for very low body fat, and 20% hardcore workout.
Ain’t nobody with back pain got the time for vanity abs.
There are better things to do with your time if your back is sore, guaranteed.

Abs that are actually really weak are actually quite rare. I don’t think I have seen people with weak rectus abdominus or obliques very often at all in the last 20 years of bodywork. Sure, it happens with some crazy injuries, but it’s not common for those muscles to be a bit useless, unless other things are even more useless! Sometimes transversus abdominis seems really weak, in fact it’s quite common, without needing crazy injuries. Again, there’s other things at play there.

If you consider ‘the core’ as the muscles that form a cylinder where the walls of the cylinder are the abs, and then the diaphragm and the pelvic floor muscles close either end, it’s being able to hold a bit of tension in all those things, all together, which increases the pressure inside your abdomen, and that’s what supports your back so it can do what it’s designed to do and move you around the place.

The diaphragm as part of the core can very much feel like an issue at times.
If you’re doing core work at the gym, and then collapse and take a bunch of gasping breaths, then your diaphragm isn’t working quite the way it should as part of the core. Which, if you’re picking the theme here, isn’t necessarily the diaphragm’s fault.
Ideally, breathing somewhat normally with a really strongly engaged core should be possible, but, speaking as someone who’s been working on core for 20 something years, it’s not an easy skill. Is it worthwhile working towards? Absolutely, it’s not like that needs to be perfect before you can do anything else, although the better you can use your diaphragm with a well engaged core, the easier all sorts of other things get.

So it’s not your diaphragms fault it can’t work? And usually the abs aren’t weak? You probably won’t need many guesses what’s left as the culprit.
Pelvic floor dysfunction unfortunately seems like ‘the norm’ when it comes to lower back pain. I don’t think anyone really understands the physiology of how being in pain switches the pelvic floor muscles off, but it does. Somehow if you’re experiencing pain, particularly around your lower back, hips or trunk, the body decides you can move all weird and not use your core and that alleviates some of the pain, so it does that, and then after a while it just forgets to start trying to work properly. Then, years and years of back pain.
Ask me how I know.

One of the most unfortunate developments in advice around the core is not to worry about pelvic floor and just focus on the lower transversus because that’s the important bit.
Good function in the lower transversus is huge. If you can’t get that going, yeah, getting all the bits of the core to pressurise and support the way it should ain’t happening. The way to get transversus doing what it needs to is rarely to focus like hell on transversus, it’s the pelvic floor.
Ask me how I know.

It frustrates me how much of that sort of advice abounds, and it is also frustrating that people will often think they’re engaging their pelvic floor, and they’re not. I see this regularly. The ideas used in pilates and elsewhere of taking elevators to 5th floors and then back down to the 3rd, or zipping to 100% and then back to 70 or whatever are just unfortunately too abstract, if people cannot find their pelvic floor, then it doesn’t matter what they’re trying to zip, it’ll maybe feel like they’re getting it and still be everything else but. Then you’re basically back to battling with the diaphragm and building stronger abs and that’s never going to pressurise a cylinder with one end that’s not really doing its fair share!
I do suspect that this sort of advice has come through studies showing that you shouldn’t need to consciously engage from the pelvic floor, and that it should just happen. And I don’t disagree, it should! It does for many people. Lucky them. Yet, for people with lower back pain particularly, it doesn’t.
Ask me how I know.

I know, because I had years (and years and years and years) of back pain. I know, because my pelvic floor didn’t work. I know, because sorting out my understanding of core and pelvic floor had a profound effect on my pain. Not like a magic bullet, but things changed quite a lot first of all, and with growing better at it, the persistent pain resolved. Yeah I still get a sore back sometimes, but it’s transient and still usually when I’m doing something just a bit taxing, and not being aware- these are fairly understandable factors.

I know, because if I’m working with athletes who perform at a high level and have some weird thing going on, that nobody seems to be able to help them correct, and they’re strong enough to ‘pass’ most of the core testing that I do, so that it looks like that’s not an issue. We address other aspects of what’s going on and the weird thing goes on and on and on…….. on closer assessment, so many times, it’s pelvic floor.
How did these people otherwise highly capable people get to that state? Often it’s hard to pick, often it’s injury and a painful recovery, and in many respects it doesn’t matter how it got like that, if pelvic floor dysfunction is part of the issue, sorting it out is always helpful.
I have certainly also seen people who have been told by other presumably experienced practitioners that whatever is causing the pain it’s seemingly not an issue with their core, and discovered that, actually, yep, pelvic floor isn’t doing what it should.

So, guess what. Even if you thought you were doing a good job of it, I’ve talked to lots of people like that. If you have been told you you’re doing a good job, and lower back or whatever is still not happy, it’s possible your pelvic floor is stopping your core being your core. This is one thing I am always mindful of being involved in a number of complaints, for many reasons but very much as a result of my own personal experiences in my own body. The answers for getting to less lower back pain or better function or better range of movement can be varied and take some figuring, but it all starts with the core. And the core starts with pelvic floor.