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> Hitting Absolute Zero Has Been Declared Mathematically Impossible Wait ... wait ... this isn't about mathematics, it's about a mathematical model of physics,
by lutusp 10y ago
> Hitting Absolute Zero Has Been Declared Mathematically Impossible
Wait ... wait ... this isn't about mathematics, it's about a mathematical model of physics, of reality. The title is both confusing and confused. Also, if something is mathematically impossible, declaring it so means nothing (because mathematical truths don't rely on human authority).
There's an interesting scientific finding behind the title, but the title is a disaster.
In any case, there's a simple heat-energy-transfer equation that can be used to show that achieving absolute zero isn't possible for the simplest of reasons:
Q(t) = Δq * e^(-t * f)
Q(t) = temperature at time t
Δq = initial temperature difference
f = a rate-of-heat-transfer factor
t = time, seconds
e = base of natural logarithms, equal to lim n -> ∞, (1+1/n)^n (2.171828....)
If you plot the temperature given by Q(t) over time (the temperature of one body being heated or cooled by another), you see that the temperature never gets to zero, because the rate of heat transfer depends on the remaining temperature difference, and as that difference approaches zero, so does the rate -- and neither becomes zero.
It's simple mathematics, but its meaning is located in reality, in physics. If that were not true, another mathematical relationship could be substituted. So it's not mathematically impossible, it's physically impossible. This kind of mathematics describes reality, it doesn't substitute for it.
- andrepd 10y agoWhere does this expression come from? Proving this is the point.
- lutusp 10y agoThe equation I posted is the solution to a differential equation that expresses the idea that a rate of change depends on the difference between two quantities -- temperature, voltage and so forth. It is a very common solution in physics, describing the rate at which water moves between connected reservoirs, gas moves between connected tanks, current moves between connected circuits in electronics, and many other physical systems. More here: http://arachnoid.com/sage/differential1.html http://arachnoid.com/sage/differential1.html