It’s an oxymoron to say live rock, or live sand; that is to say both rock and sand themselves are not actually living entities, but are inorganic minerals.  However, the terms live rock and live sand have become ubiquitous in the vocabulary of most aquarists.  It is implicitly understood what is being discussed when the terms live rock or live sand is used; or it is.
If this rock is not alive- then what is alive to grant use of the name?  To fully appreciate the answer, one must consider the type of material being examined.  A granite slab pulled from the shores off North Carolina will undoubtedly have some life on it.  Coating its surface would be species of cyanobacterium, and even some turf algaes.  However, few reef aquarium enthusiasts would consider this live rock suitable for their displays.
We must all converge on a single definition of live when applying the standard to the reef aquarium hobby.  I propose the following list of criteria to describe true live rock for the marine aquarium.  The rock must be primarily of reef origin.  It should be populated by a diverse collection of flora and fauna representing 6 or more Phyla of plants and animals.  Lastly, the rock should be viable and healthy, meaning no species that will never survive transit or the rigors of a closed ecosystem.  Most aquarists will agree that the higher quality live rock available today fits this collection of criteria.
Of foremost importance is the origin of the rock.  It is best to use true reef rock, rubble formed by years of coralline growth and coral fragments, and microorganisms cementing it all into a solid mass.  This rock has been formed by years of growths and organisms cementing calcareous particle together.  It is already populated with many desirable organisms, and provides a suitable habitat for many of the specimens we wish to keep in our closed ecosystems.  Recent studies have shown that corals may favor attachment to rock that has layers of other calcareous organisms present, so the multitude of coralline algaes and encrusting corals is vital to optimal growth in a home system.  Recently, a trend towards ‘fabricated’ live rock has provided some of this material to be commonly available.  This fabricated rock may have a composition similar to that of natural reef rock, but falls short in all other areas.  This type of rock usually has high levels of undesirable chemicals, such as phosphates, or heavy metals.
The dazzling purples, reds, and pinks formed by the coralline algaes are highly desirable.  Couple this with yellow and other colored encrusting corals, and visible macroalgaes and most would call this beautiful and quality live rock.  Beauty is only skin deep, as the best features of live rock are microscopic animals living within the pores and crevices of the rock.  This diversity allows each piece of rock to be its one small biotope. This myriad of living organisms provides the primary denitrification of our closed ecosystems, and maintains the quality of the water such that we can keep animals like the corals.  This diversity should be preserved once the rock is collected.  Every effort should be made to ensure that much of the encrusting animal and plenty life makes the transpacific journey and can be sustained right into your living room aquarium.
Reef tanks are not just piles of rocks, they are should also contain a softer substrate for optimal cultivation of other organisms. Animals have specific habitat requirements, and as responsible aquarists we need to consider these requirements. Body type and feeding modality play a role in organismal specialization to a particular habitat. A living sand bed is one sort of soft sediment biotope. Even if using excellent quality live rock, adding this to a pile of dried, rinsed, and packaged sand, will never create the diversity desired in a home aquarium.  The dead sand will allow some animals to make a shallow home, but the majority of organisms that are desirable to keep, do not live in the rocks, so would not ever be present to invade the sand bed.
Contrary to some popular advice, adding live rock to a dead sand bed will not convert the dead sand into something more. A few of the animals living within the rock will make the transition from rock to sediment bed.  Nevertheless, those were already present in the rock, and in many cases, rocks are collected far from the bottom of a reef, so many sand dwelling organisms cannot be present in live rock.  Many polychaetes, molluscs, and crustaceans that dwell in the deep sands will not be present from live rock. You would loose the diversity from a Terrebellid worm, various small clams, and other critters from your biotope. The only way to get animals specialized for the sandy habitat, is to collect them originally from the same or similar habitat.
Acquiring quality live sand is not as simple as a trip to the local fish store, or a quick call to your favorite mail order vendor.  The problem of how to get a quantity of sand, teeming with life off the reef, and to your home, while keeping the fragile animals alive and intact is the largest obstacle. Many of the organisms that dwelling the sand beds are soft bodied. These delicate worms and thin-shelled molluscs cannot withstand the weight, and the grinding particles of shipping.  By the time the sand has reached the United States, then a wholesalers then a local store, much of the macro life is long since missing.  For example, many bivalves live within the top 4 inches of the sediment.  As the sand is collected, it is placed into bags or buckets, the distinct layers are not preserved and many animals used to life with only three or four inches loose sediment above them now find themselves buried beneath 10 to 12 inches of packed sand.  The weight of the sand and water alone is enough to crush them.  Sand is also an excellent abrasive; all those fine mineral grains are miniature rocks with jagged edges.  Once packed the movement and jostling of transit causes the friction to literally shred the softer organisms.   Fortunately- many of the bacteria and larval forms of these creatures will survive the stresses of transit, and using live sand will provide those beneficial organisms.
In order to add the macrolife that makes the most of your sand bed, it should be done after the sand is in your tank. Some facilities now culture may of the macroorganisms.  These animals are either collected through filters at the point of origin, or cultured in small containers here in the US.  Since they are packaged appropriately, and shipped separately, the animals have a much higher survival rate and can be safely introduced to your existing sand bed. 
This approach also takes away a lot of the guesswork about what you are getting.  A bag of sand is a mystery.  It could be full of everything you want, nothing, or undesirable organisms.  If you purchase selected animals separately, you know exactly what you are adding to your reef aquarium ecosystem. 
To conclude, the origin of your rock and sans it going to determine if it meets the criteria for benefiting your aquarium.  It it’s from a reef in origin, covered with a diverse array of plant ands animal life, its going to contribute to a successful system.  Sand that has been bagged and processed will do little good to any reef for many months, and then only as a natural nitrate reduction center.  The organisms that live in soft sediments on the reef must be collected separately and added after the sand is in place.  This preserves the organisms and allows you the most assured means to add desirable sealife to your system.

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