Additionally, it can be shown that any massless spin-2 field would be indistinguishable from gravitation, because a massless spin-2 field must couple to the stress-energy tensor in the same way that the gravitational field does.

— Wikipedia on Graviton

2010.08.15 Sunday ACHK

The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power.

Solution

Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. Planck postulated that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to the frequency, as given by Planck’s law. This has the effect of reducing the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy at those frequencies by application of the equipartition theorem.

Historical inaccuracies

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In this version, the “catastrophe” was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental – his motivation for introducing “quanta” was entirely different. That Planck’s proposal happened to provide a solution for it was realized much later, as stated above.

Though this has been known by historians for many decades, the historically incorrect version persists, in part because Planck’s actual motivations for the proposal of the quantum are complicated and difficult to summarize to a modern audience.

— Wikipedia on Ultraviolet catastrophe

2010.08.14 Saturday ACHK

Uncertainty principle and observer effect

The uncertainty principle is often stated this way:

The measurement of position necessarily disturbs a particle’s momentum, and vice versa.

This makes the uncertainty principle a kind of observer effect.

This explanation is not incorrect, and was used by both Heisenberg and Bohr. But they were working within the philosophical framework of logical positivism. In this way of looking at the world, the true nature of a physical system, inasmuch as it exists, is defined by the answers to the best-possible measurements which can be made in principle. To state this differently, if a certain property of a system cannot be measured beyond a certain level of accuracy (in principle), then this limitation is a limitation of the system and not the limitation of the devices used to make this measurements. So when they made arguments about unavoidable disturbances in any conceivable measurement, it was obvious to them that this uncertainty was a property of the system, not of the devices.

Today, logical positivism has become unfashionable in many cases, so the explanation of the uncertainty principle in terms of observer effect can be misleading.

— Wikipedia on Uncertainty principle

2010.08.12 Thursday ACHK

I think biology without mathematics is like physics before Newton: you could observe a star’s position yesterday and today, but you could not predict where it would be tomorrow. Biology without mathematics is phenomenological – we are merely collecting data, but we cannot make useful predictions or obtain a quantitative understanding. Biomathematics is still in its infancy, but has already and will make important contributions to biology (Hodgkin-Huxley etc.).

— Franziska Michor: math of cancer

— Lubos Motl

2010.08.11 Wednesday ACHK

The generators of symmetries are nothing else than the observables that are conserved if these symmetries are respected.

— Why and how energy is not conserved in cosmology

— Lubos Motl

2010.08.10 Tuesday ACHK