  We consider the quantisation of scalar fields on a Lifshitz background,
exploring the possibility of alternative boundary conditions, allowing the slow
falloff mode to fluctuate. We show that the scalar field with alternative
boundary conditions is normalizable for a larger range of masses than in the
AdS case. However, we then find a new instability for alternative boundary
conditions, implying that the range of masses where alternative boundary
conditions define a well-behaved dual theory is $m_{BF}^2 < m^2 < m^2_{BF} +1$,
analogously to the AdS case. The instability is of a novel type, with modes of
arbitrarily large momentum which grow exponentially in time; it is therefore
essentially a UV effect, and implies that the dual field theory is simply not
defined where it appears. We discuss the interpretation in the dual field
theory, and give a proposed lower bound on the dimension of scalar operators.
