There is no such thing as negative kinetic energy or negative pressure in a vacuum.
It is difficult to know the answer when one does not understand the question. In this case the question from the OP is two-fold, one being "can pressure in the classical sense be negative?" and the other being "can pressure in the cosmological sense be negative?" Understanding either question requires knowledge of the definition of the word "pressure". Absent such knowledge, one does not understand the question and therefore can hardly be expect to answer reliably.
The negativity of pressure in the classical sense is fairly easy to understand, as long as we realize that negative pressure quite literally
sucks. If a spherical membrane shrinks because it is being pushed in by outside pressure, that is an example of positive pressure applied to the surface. If a spherical membrane shrinks because it is being pulled in from below, that is an example of negative pressure being applied to the surface. One can see that in the general case, any pump works by applying negative pressure to that which is being pumped.
But the cosmological case requires a bit more insight.
Mozina's response above assumes a classical, particle based definition for both "kinetic energy" and "pressure". Given that particular definition, then obviously his conclusion is correct. After all, if we have a true vacuum, then we have no particles and therefore no kinetic energy. And if we have no particles or kinetic energy, then clearly we can have no particle based pressure at all. However, this conclusion is based on the faulty premise that his chosen definition for "pressure" is correct. In fact that is a false assumption, and therefore the conclusions based thereon should be viewed with suspicion, and assumed to be false, in the absence of a strong argument to the contrary.
One must be aware that not all energy is "kinetic" and therefore neither is all pressure "kinetic" or particle based. Fields carry energy, and therefore pressure as well, despite the complete absence of all things "kinetic". Indeed, the pressure from a scalar field is nicely defined for us by Steven Weinberg in his book,
Cosmology (Oxford University Press, 2008), on page 527, equation B.67:
[latex] p = -\dfrac{1}{2}g^\mu^\nu \frac{\partial {\phi}}{\partial {X^\mu}} \frac{\partial {\phi}}{\partial {X^\nu}} - V(\phi) [/latex]
In tis equation, [latex]\phi[/latex] is the scalar field and [latex]V(\phi)[/latex] is the potential for the field. Of course there are ways to simplify this expression by carrying out the indicated operations in the context of a cosmological model. For a general relativistic, expanding universe, we find equivalent formulations in Weinberg's
Cosmology, pages 8-9, and in Scott Dodelson's
Modern Cosmology (Academic Press, 2003), page 151 (section 1.5.1, "Negative Pressure"). Dodelson's equation 6.22 is:
[latex] \dfrac{1}{a} \frac{d^2 a}{dt^2} = -\frac{4\pi G}{3} (\rho + 3P)[/latex]
Quoting from Dodelson: "
Acceleration is defined to mean that d2a/dt2 is positive. For this to happen, the terms in parentheses on the right must be negative. So inflation requires
[latex]P[/latex] < [latex] -\dfrac{\rho}{3}[/latex].
Since the energy density is always positive, the pressure must be negative. This result is perhaps not surprising: we saw back in Chapter 2 that the accelerated expansion which causes supernovae to appear very faint can be caused only by dark energy with negative pressure. Inflation was apparently driven by a similar form of energy, one with P < 0. To reiterate what we emphasized in Chapter 2, negative pressure is not something with which we have any familiarity. Nonrelativistic matter has small positive pressure proportional to temperature divided by mass, while a relativistic gas has [latex]P = +\dfrac{\rho}{3}[/latex], again positive. So whatever it is that drives inflation is not ordinary matter or radiation." (End Quote)
It must be remembered that
observation leads us to the conclusion that the expansion of the universe is accelerating, which is consistent with physics as we know it
only if the pressure of the vacuum is negative, as Dodelson says above. It must also be remembered that
observation leads to the conclusion that physics as we know it and the observed behavior of the universe can be made mutually consistent with each other
only if there is a period of extreme "inflationary" expansion in the very early infancy of the universe, again driven by negative pressure, as Dodelson says above. There is also a nice discussion of negative pressure in Edward Harrison's book
Cosmology: The Science of the Universe (Cambridge University Press, 2000, 2nd edition) on page 369 (section heading: "Universes in Tension: The Strange Worlds of Negative Pressure"), but I will leave that for the reader to pursue.
So, the bottom line for the OP is certainly "yes", pressure can be negative, in both a common practical sense, or a less common cosmological sense. The advent of negative vacuum pressure in cosmology was certainly a surprise but cosmology, like any other scientific pursuit, is dominated by observation (increasingly so in recent decades). We already know that
Mozina rejects dark matter & dark energy, though for no particularly good reason. But then we already know that
Mozina rejects the foundations of science altogether (e.g.,
What is "Empirical" Science? III from 1 Feb 2010 and many a post thereafter). His contrary arguments are thus accompanied only by opinion as a justification, while informed and factual arguments are absent, so his position must be considered without merit.
