Uncertainty and the Question of Time Scale

If you have ever tried to take a photograph of a moving object, you know that the shutter speed of the camera must be adjusted to avoid blurring the image. And, of course, the faster the object is moving, the shorter must be the exposure time to freeze the motion. We have very similar considerations in spectroscopy. 

Suppose you owned a collection of very extraordinary chameleons that were able to change colors instantaneously from white to black or black to white every 1 s. If you took a picture of them with a shutter speed of 10 s, each of the little critters would appear to be gray. But if you decreased the exposure time to 0.01 s, the photograph would show black ones and white ones in roughly equal numbers but no gray ones Thus, to capture the individual colors, your exposure time must be significantly shorter than the lifetimes of the species, in this case the 1-s lifetime of each colored form. 

There are many types of molecular chameleons, that is, molecules that constantly undergo some sort of reversible reorganization of their structures. If absorption of the photon is fast enough, we will detect both the black and white forms of the molecule. But if the absorption process is slower than the interconversion, we will detect only some sort of time-averaged structure. The situation therefore boils down to the question How long does it take for a particle to absorb a photon Unfortunately, such a question is impossible to answer with complete precision. 

In 1927, W. Heisenberg, a pioneer of quantum mechanics, stated his uncertainty principle There will always be a limit to the precision with which we can simultaneously determine the energy and time scale of an event. Stated mathematically, the product of the uncertainties of energy (AE) and time (Ar) can never be less than h (our old friend, Planck s constant)  

if we know the energy of a given photon to a high order of precision, we would be unable to measure precisely how long it takes for the photon to be absorbed. Nonetheless, there is a useful generalization we can make. Using Eq. (1.3), we can substitute h Av for the AE in Eq. (1.6), giving 

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Recently, two basic questions of chemical dynamics have attracted much attention first, is it possible to detect ( film ) the nuclear dynamics directly on the femtosecond time scale and second, is it possible to direct (control) the nuclear dynamics directly as it unfolds These efforts of real-time detection and control of molecular dynamics are also known as femtosecond chemistry. Most of the work on the detection and control of chemical dynamics has focused on unimolecular reactions where the internuclear distances of the initial state are well defined within, of course, the quantum mechanical uncertainty of the initial vibrational state. The discussion in the following builds on Section 7.2.2, and we will in particular focus on the real-time control of chemical dynamics. It should be emphasized that the general concepts discussed in the present section are not limited to reactions in the gas phase. 

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