LV11903.

Hotter than infinitely hot

Nothing can be colder than the absolute minimum of temperature located at -273.15 degrees of Celsius or -459.67 degrees of Fahrenheit. Absolute temperatures, measured in Kelvin with T=0 Kelvin at the minimum of temperature, are therefore usually positive. However, the laws of thermodynamics can also be extended to negative absolute temperatures, T < 0. They describe states which have a higher energy than an infinitely hot system: they are hotter than infinitely hot. Such states have first been realized with nuclear spins and are also important to understand lasers. Systems with negative T show many counter-intuitive phenomena. For example, to hold together a cloud of atoms at negative temperatures, one needs external forces which try to pull the cloud apart. In Physical Review Letters ???, we show theoretically how such states can be realized using ultraslow atoms captured in a lattice made out of light. We suggest that an exotic type of superfluidity can be used to identify experimentally negative temperatures using a simple imaging technique.


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AV10556

Quantum algorithms know in advance 50% of the solution of the problem

Since Deutsch’s 1985 work, it is known that quantum algorithms produce the solution of the problem with fewer computation steps than their classical counterparts. However, the exact reason for this “quantum speed up” has never been explained. The explanation propounded in this paper is that quantum algorithms know, before starting, 50% of the solution of the problem. How? Let Bob be the problem setter, Alice the problem solver. In classical problem solving, there is of course correlation between the selection of the problem on the part of Bob – for example choosing the number of the drawer to hide a ball in – and the selection of the solution on the part of Alice – finding the number of the drawer with the ball by opening different drawers. Correlation between the two numbers means that they depend on one another – of course they must be the same in the present case. In quantum problem solving, this correlation becomes quantum. Quantum correlation is the “spooky action at a distance” (in Einstein’s words): doing something to one thing here, instantly affects another thing there, possibly light years away, and vice-versa. With quantum correlation between the drawer number chosen by Bob and that found by Alice, all is like Alice contributed to 50% of Bob’s choice. No wonder she knows in advance 50% of the solution. Which 50%? Anyone, in fact the quantum algorithm turns out to be the quantum superposition of all the possible ways of taking 50% of the bits of the solution and, given the advanced knowledge of these bits, classically computing the missing bits. A practical consequence of this finding is that the quantum speed up comes from comparing two classical algorithms, with and without this advanced knowledge. The fact that quantum algorithms know in advance 50% of the bits of the solution they will produce in the future, and use this knowledge to reach the solution with fewer computations, is of course an intriguing philosophical consequence.


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LU12425

Future may influence the present

What happens at the present has influence from what
happened in the past but not from what will happen
in the future. Is it right? Well, if an absolutely
sharp distinction between present, past and future
can be made, this statement should be right and is
known as causality principle. We showed in a simple
model containing a fundamental scale of time and
length that influence in the present from an immediate
future time interval may occur. Far from absurd, this
influence appears as natural because this interval is
of the order of the fundamental time scale at which it
is expected that the concept of a sharp instant of
time must be substituted by a blurred interval of time.
Such matters, daily business in sophisticated theories
as quantum gravity or superstrings, are described in our
work in terms of a dispersion relation and a retarded
Green function, both concepts discussed at undergraduate
level. We believe that our work may be of interest for
the general public because it touches the very fundamental
issues of time and causality from the sole consideration
of such simple concepts.