Lumens are a way of measuring light density. The units that lumens are actually measured in is equal to the number of candles it would take to light a specific area. It’s pretty old-school, but one lumen actually equals one foot-candle (or, more specifically, it is one candle’s worth of light per square foot of surface when that candle is held one foot away). Similarly, a lux would be one meter-candle (or one candle of light per square meter held one foot away). Saving the math, 1 lumen = 10 lux. However, one important distinction between the two terms needs to made; while lumens are a way to measure light energy leaving the source or bulb (which may also be known as flux), lux is a term generally reserved for indicating the amount of light energy actually reaching a given surface or leaf (and this is also known as illumination).
Basically, if you have one lumen shining on one square foot at a height of one-foot from above, then at two-feet from above that lumen is now only a quarter of a lumen (1/4), because that single lumen will diminish by traveling a greater distance and is now also spread out over a greater area.
Remember, a light bulb shines 360 degrees around. If your HPS puts out 140,000 lumens, that’s 140,000 lumens in all directions. If you manage to get 10 percent of that on your garden, that’s only 14,000 lumens. Then consider the distance of you lamp and the Inverse Square Law, you may only be getting 2,000 of your 140,000 lumens onto your garden!