There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

For a list of all topics discussed, scroll down to the very bottom of the blog, or click here.

Origins of Newton's laws of motion

Non-mathematical introduction to relativity

Three types of waves: traveling waves, standing waves and rotating waves new

History of mechanical clocks with animations
Understanding a mechanical clock with animations
includes pendulum, balance wheel, and quartz clocks

Water waves, Fourier analysis

Sunday, May 29, 2011


All postings by author previous:
confusing aspects
contents of relativity
general relativity

Fig. 12. Several application areas of special relativity
Feymann diagram of electron-positron annihilation. Wikipedia
positron emission tomography, PET, used for medical imaging. Wikipedia
Fermilab accelerator. Wikipedia
Fig. 12a. Feynman diagram for electron-positron annihilation as is used in positron emission tomography (PET), as shown in Fig. 10b. Relativity is central to understanding these diagrams, because all of the rest mass energy of the electron and positron is converted to conventional forms of energy in the annihilation process. Fig. 12b. Some aspects of positron emission tomography. This type of medical imaging is seeing increasing use in such diseases as cancer, strokes, and heart attacks. Fig. 12c. A small section of the Fermilab accelerator in Batavia, Illinois. Accelerators have been used for the past 80 years to further the understanding of sub-atomic particles and nuclear energy. Such accelerators push sub-atomic particles (and in some cases atoms) to speeds approaching that of light. Special relativity plays a key role in understanding the results of experiments done with accelerators.


Special relativity - core ideas - consistent with both Einstein's and Lorentz's views

  • Rapidly moving objects when viewed from a stationary reference frame show length contraction and slowing of physical processes (time dilation).

  • Lorentz transforms are a convenient tool for

    1. Switching from a person's view inside one reference frame to that inside another reference frame having a different velocity.

    2. For calculating characteristics of physical phenomena of high speed objects, especially those of atomic and subatomic particles.

  • The famous equation  E = mc2  can be derived using Lorentz transforms.

  • Modern technology uses relativity to understand nuclear and subatomic phenomena, as well as small relativistic timing effects in spacecraft.

Einstein's view

  • The idea that "physics is the same in all uniformly moving reference frames" is a fundamental truth and requires no derivation or explanation.

  • The fact that light appears to travel at the same rate in all reference frames is a result of the above truth and need not be further explained.

  • Since all objects experience length contraction and time dilation, we should consider these as changes in space itself and as in time itself in rapidly moving reference frames.

  • Neither ether nor a universal stationary reference frame (called an "absolute reference frame") is a useful concept.

  • Electric and magnetic fields need not be explained or are explained in terms of photons.

Lorentz's view

  • The speed of light appears to be unchanged inside a rapidly moving reference frame only because of a quirk in Maxwell's equations which causes length contraction and time dilation in the moving observer's instruments.

  • It is useful to think of a universal stationary reference frame for the purposes of understanding relativistic effects, even though at present we cannot detect our motion with respect to this stationary reference frame. We can call the metric of this stationary reference frame the "ether" if we wish.

  • Electric and magnetic fields are perhaps stresses or distortions of the ether.


Both Einstein's and Lorentz's views are operationally the same. Both involve:
  • Using the Lorentz transformations,

  • Both accept that lengths contract and processes slow down for rapidly moving objects when viewed from a stationary frame, and

  • Both accept Einstein's relativistic equations such as  E = mc2 .

  • At present we have no way of verifying if one view is more valid than the other.

  • The two approaches differ primarily on how the subject of relativity is approached, the starting premises, and what each attempts to explain.

    • For deriving the equations of special relativity, Einstein's approach gets to the results quicker because it just assumes to be true what Lorentz's approach needs to derive.

    • Lorentz's approach offers explanations of what causes the strange relativistic effects. Because of this it may be more acceptable to many people including classically trained scientists and engineers who have problems with Einstein's warping of space and time.

    • Lorentz's approach may prove useful in explaining new discoveries in the future.

    • Both approaches should be preserved for the future by making students aware of both of them.

  • The differences in Einstein's and Lorentz's approaches might be likened to the difference between the axiomatic and statistical approaches to thermodynamics. The axiomatic approach assumes a set of "laws of thermodynamics" and derives many useful equations from these beginning assumptions. The statistical approach uses mathematics of the statistics of very large numbers of atoms to derive the laws of thermodynamics and also to understand other microscopic thermodynamic phenomena. Both are very useful and are universally used and taught. The axiomatic approach is simpler and heavily used for designing engines, refrigerators and other large, macroscopic thermodynamic devices. The statistical approach is more cumbersome to use but offers more insight, especially at the microscopic level.

All postings by author previous:
confusing aspects
contents of relativity
general relativity