No, that's wrong. As I stated previously, lumens have only to do with human perception, not with photosynthetic activity. This is not to say that there is no overlap, only that you cannot predict the photosynthetic potential of a light source using Lumens.
The human visual cortex is optimized around the green and yellow frequencies. That means we have very good response to these wavelengths, in the neighborhood of 500 nanometers. It also means that we do not have a very good response to red (700 nm) or to blue/violet (400 nm).
Therefore, it is entirely possible for a bulb that has a lot of blue/violet and that does not have a lot of green/yellow to have a higher PAR but that will look dimmer to us. Because lumens is essentially a measure of how much green/yellow the bulb contains then that same blue/violet bulb will have a low Lumen rating but will have a very high PAR value.
On the contrary, you can have a bulb that has high green/yellow content which will produce a higher Lumen rating than the first bulb but this bulb could easily have a lower PAR.
PAR grows plants, not Lumens. So when you need a light that will be bright to your eyes, say a bulb for lighting your driveway, then yes, you want as high a Lumen rating as you can get for the given wattage. But blue light has higher energy than green or red so that bulbs with blue, although they will look dimmer to us and would not do as good a job of lighting the driveway, may actually deliver more energy to the leaf.
One of the things that the energy saver bulbs will claim is that they have a lower wattage but that they produce light of a higher wattage bulb. One way they can do this is to tailor the bulb to emit more of it's energy in the 500nm region which your eyes will be more sensitive to, thereby giving the illusion that they are as strong as a higher wattage bulb. The bulb that they are comparing themselves to will be bulbs that emit in wavelengths further in the red or blue part of the spectrum.
Lumens, Lux, Kelvin and CRI are only relevant to our perception of light and are measurements of this perception. Again, this does not mean that any given bulb with a higher Lumen rating than another given bulb is necessarily weaker, only that you cannot predict the effect of photosynthesis using this measurement alone. PAR means Photosynthetically Active Radiation. Iit absolutely does not mean Lumens per watt. It is a direct measurement of the number of photons crossing a unit area per unit time - and this is exactly the measurement that counts for plants. If the Lumen value of a bulb happens to be higher than an lesser PAR rated bulb then this is a coincidence based on the wavelength distribution of that bulb but it can never be a correlation across bulb types. The Lumen value will have an effect on your perception of the light in the tank. A bulb vendor can design the emission spectrum of the bulb such that there is a high green/yellow content. The bulb will therefore appear to have better penetration, again, because your eyes will be more sensitive to that part of the emission. Plants and algae do not care what looks brighter to you, or what appears to have better penetration to you. They care about the total spectral energy. They care about PAR.
The technology of the bulb also determines how much of the bulbs energy is PAR energy. An incandescent bulb only has about 5%-10% of it's energy as PAR energy. The remainder of it's emissions is as infrared. That means a 400 watt incandescent bulb only has about 25 watts of useful PAR. Fluorescent and halide bulbs emit a much higher percentage of useful PAR, somewhere around 30%-40%. A typical 400 watt Metal Halide bulb will emit somewhere in the neighborhood of 150 watts of PAR energy. This is one of the reasons that fluorescent bulbs run much cooler than incandescent bulbs, because they emit more of the input energy in the visible spectrum and not as infrared (heat).
That's why it's very difficult to compare bulbs of different types. You cannot directly compare a halide bulb with a T-12 bulb unless you measure their relative PAR values. It's even difficult to compare bulbs of the same technology simply because the the emission spectrum of the bulbs may differ vastly. Therefore, if you want to compare bulbs for human activities such as photography or aesthetics or driveway lighting, then measurements such as Lumens, Lux, CRI and so forth are relevant. If you want to compare bulbs for the purpose of photosynthetic organisms, and specifically for plants, then you have to limit your comparisons to Photosynthetically Active Radiation measurements.
Cheers,
