Kat P, I agree, I just started using trekking poles, and there is nothing like almost running down mountains without slips, without worries. I view it more as a crab walking, but agree on the four legged feeling, that's absolutely the case going up or down, but that feeling grows the faster you go, so I find myself going faster almost every outing.
I'm giving my knees veto power over any decision I make re these poles, and they vote firmly on using them, and won't hear about anything else now. If your knees are at all weak from use/abuse, these are a no brainer, but I think, far more important, is if your knees are still in youthful good shape, trekking poles are going to keep them that way. Every time I see someone running downhill, especially with weight, I think to myself, you'll be in surgery in your 40s or 50s, unless you are really lucky.
I believe the physics of these poles, ie, their cumulative weights, are totally unrelated to what Nick said above, it's far more complex than suggested, and I'd have to discuss that with someone who really took the time to examine all the physics of the motion before making any statement about that, but my initial feeling is that ignoring the forward momentum and other forces (think starting a weight suspended from a string in motion, which is what you are basically doing if you are using these right, re the straps). It took me precisely one hike to give up on my decades long attachment to my home made hiking staffs, it was that obvious re the difference in performance.
I bought a friend with bad knees a pair after seeing how good they are, and after our first hike I mentioned the weight question, and he noted that in his opinion, they have a negative weight, because you are pushing yourself with them, using your upper body muscles as well as your leg groups to move forward. Estimating I would say I am going at a very minimum 1/2 a mile per hour faster with them. Maybe more, it's hard to tell. Far more going up and down hill, I'd say there it's almost 2x faster.
The key knee action I believe that ruins knees is the braking motion where the knee hits full extension going downhill, and particularly, that special moment when you have to decide if you go beyond that motion and avoid death by falling down a ravine etc, or you fall. Trekking poles remove that brake and put it onto solid aluminum, to me it's instantly obvious the difference each and every hike I do. Not only that, I'd strongly suspect that if your knees are weak or damaged, using these will allow the tissues to regenerate, since you are not continuously reinjuring the tissues on every downhill.
I have to wonder if growing up cross country skiing as I did has something to do with it, almost the first day I tried them, I found myself falling into a very familiar cadence, without thinking about it at all, then I realized, oh, this is the same exact motion I did as a cross country skier. However, I find that on more flat areas, I have to be going really fast to really get into this cadence, and, oddly, the more I use these trekking poles, the faster and further I go. There's something about taking 20 or so percent of each stride and adding upper body muscle strength to that. Might also matter that bicycles are my primary mode of transport, and the upper body muscle groups are quite similar in terms of what is used. My friend noted as well after his first two hour hike that his upper body ached for days after, which gives an idea of how much you use those muscles.
The one place I'm not sold on them is flats, but even there, if I go fast enough to really hit a true cross country stride, they work almost exactly the same way that cross country ski poles do in terms of using upper body to move you.
I'm sold, no doubts, if I had started using these 20 years ago I have no doubt whatsoever that my knees would be in substantially better shape, at least the hiking parts, can't do anything about the mountain biking issues.
Seeing real physics studies on the actual weights re work carried out (work in the physics sense) would be interesting though. I've also grown to suspect, for the same reasons, that classic formula that a pound on your foot is worth 5 on your back, for similar reasons, though I think there's less pendulum like action with feet than swinging trekking poles. My initial intuition is that using your upper body strength to boost your stride so radically outweighs any small loss re the work related to lifting them a few inches via a swinging motion that that work is not really worth thinking about much. Not to mention I have zero interest in using a pole that is going to be prone to snapping the moment I need it most, putting weight before critical functionality is foolhardy as far as I'm concerned. I've seen how carbon fiber cracks under the wrong pressure.