onsdag 9 oktober 2013

Slinky as Alternative to Higgs Mechanism of Giving Mass to a Body

The popular description of Higgs' mechanism supplying mass to a body awarded the 2013 Noble Prize in Physics, goes as follows:  Imagine a celebrity (e.g. Brad Pitt) moving through a crowd of people drawing attention from inescapable interaction with the crowd, which can be imagined to generate some kind of resistance to the motion of the celebrity connecting to the amount of fame, or mass, of the star:

A more technical description from Wikipedia goes as follows:

The idea is evidently that a body acquires mass from interaction with some form of background field or crowd.Is this credible? Maybe. Maybe not. 

In any case, here is a reprint of a different mechanism that I reflected on some time ago as a possible resolution of Zeno's paradox of the impossibility of motion with a Slinky as mental image:

The basic idea is that the slinky moves so to speak by itself and not by interacting with a background field. The kinetic energy of the slinky = 1/2 x mass x velocity^2 equals the energy invested to compress or extend the slinky before letting it go. Mass can then be defined in terms of velocity and invested energy stored as kinetic energy through the motion. Mass is then something carried by the slinky through motion related to the stored energy, which can be released by letting the slinky run into a wall. Is this credible? Maybe. Maybe not.  Will Slinky get a Nobel Prize? Maybe not. 

The motion of a slinky suggests a resolution of Zeno’s Arrow Paradox as a combination of compression-release and switch of stability, where the the slinky appears as a soliton wave, which itself generates the medium through which it propagates.

Zeno of Elea (490-430 BC), member of the pre-Socratic Eliatic School founded by Parmenides, questioned the concept of change and motion in his famous arrow paradoxHow can it be that an arrow is moving, when at each time instant it is still?

In Resolution of Zeno’s Paradox of Particle Motion I argued that the paradox still after 2.500 years lacks a convincing resolution, and suggested a resolution based on wave motion.

A fundamental question of wave propagation is the nature of the medium through which the wave propagates: Is it material as in the case of sound waves in air, or is it immaterial as in the case of light waves in vacuum? If the flying arrow is a wave, which is the medium through which it propagates? It is not enough to say that it is air, because an arrow can fly also in vacuum.

We are led to the following basic question: can a wave itself act as the medium through which it propagates?

It turns out that a slinky can serve as an answer! To see this take a look at this movie . We see that the motion of a slinky can be described as follows:
  • oscillation between two forms of energy: elastic energy and kinetic energy compression stores elastic energy 
  • elastic energy is transformed into kinetic energy when the slinky expands
  • there is a critical moment with the slinky fully compressed in which the downward forward motion of the top ring is reflected in upward forward (and not upward backward motion which would lead to motion on the spot) 
  • the slinky forms itself the medium through which it as a wave propagates
  • the slinky acts like a soliton wave.
We understand that the slinky offers a model for resolution Zeno’s paradox as a wave which itself generates the medium through which it propagates.

What is Mass?

You can take this model one step further, and view the work required to compress the slinky from an uncompressed rest state, as an investment into kinetic energy of motion, just as a body can be accellerated from rest by the action of a force and gain kinetic energy.

This would mean that the slinky has inertial mass and that it can move with different velocities depending on the amount of work invested in the initial compression. We may compare with the propagation of massless electromagnetic waves with given fixed speed of light. This connects to the question Does the Earth Rotate? suggesting to define mass as inertial mass M in terms of kinetic energy K and velocity V from the formula K = 1/2 x M x V x V.

PS1 The difference between Higgs and Slinky is a bit like the difference between environment and genetics for living body, with Higgs only exterior environment and Slinky only interior genetics.

PS2 There is a connection to Wittengenstein's ladder which the user successively pulls up behind as the  climbing advances.

PS3 The Higgs mechanism is described in the above picture to "slow down" the motion of an electron as an effect of some kind of viscosity. This seems strange since electrons are not "slowed down" by the mere fact that they have mass. Acceleration is "slowed down" by mass but not velocity.

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