Rutabagas of a quiet past in a stormy present
May 2, 2010 § 1 Comment
The law of inertia
Bodies when removed from interaction with other bodies will continue in their states of rest or straight line uniform motion. In other words, the motion of such bodies is unaccelerated.
Supposedly, the laws of mechanics take the same form in all inertial systems, that is, in all those coordinate systems which can be obtained by subjecting any one inertial system to arbitrary Galilean transformations.
All mechanistic branches, such as the theory of elastic bodies and hydrodynamics, or the mechanics of rigid bodies, can be deduced from the mechanics of free mass points by introducing suitable energies and by carrying out certain limiting processes.
But during the nineteenth century, a new branch of physics had developed that could not be brought into the realm of mechanics: electrodynamics.
Maxwell formulated laws of electromagnetism by introducing the concept of fields. In mechanics a system is completely described when the locations of all of its mass points are known as functions of time. In Maxwell’s theory a number of field variables are used. These are not functions of the time coordinate alone, but are defined for all values both of the time and three space coordinates. Functions of four independent variables.
Here comes trouble
In short, the hunt was on for inertia! For there must exist one frame of reference, presumably and preferably an inertial system, with respect to which the field equations take their standard form.
What followed were lots of attempts. Pretty much like bailouts: Corpuscular hypothesis, or maybe the transmitting medium is the frame of reference, experiments (Michelson and Morley became famous), and as a last resort to hold on to the trustworthy Galilean transformations, Ether.
The idea of ether suggests that it might be the coordinate system in which the ether is at rest. It doesn’t solve the fundamental problem. All it does is reword it, because to find out what the state of motion of the earth through the ether is, we would have to measure the speed of light. Circular reasoning if I ever did see one.
Yet intuition …
… was screaming (all the evidence pointed toward) the existence of a “relativity principle” in optics and electrodynamics, even with the Galilean transformations ruling that out entirely.
Start on the transformation
What if the evidence can be trusted and we can conclude a relativity principle exists (is valid). We just haven’t found it yet. Now that’s a serious case of proper systems thinking (and timing)!
Analyse and modify Galilean transformations so that they become compatible with optics and electrodynamics, is what Einstein did.
Undoing the assumptions
The next step is finding the assumptions and undoing them:
- A universal time t exists which is defined independently of the coordinate system or frame of reference
- The distance between two simultaneous events is an invariant quantity, with a value independent of the coordinate system.
And that’s whenwhere the scientific group mind started to move out of its cognitive dissonance. With Lorentz transformations.
Suddenly clocks appear to go at their fastest rate and every rigid body appears longest when at rest relatively to the observer.
Space-time intervals are imagined to exist between events: When it is real (tau12) it is time-like, and when it is imaginary (meaning the sequence of two events is such that a light ray from either arrives at the other only after it has occurred) we simply use a little trickery and we name it a space-like interval (rho12) and declare it real.
Whether the interval is time or space like is an invariant property of the two events of course, and the law of inertia is invariant with respect to Lorentz transformations.
New rutabagas, of course
- The equations of classical mechanics are covariant with respect to Galilean transformations, but not with respect to Lorentz transformations. Not a real problem. We will simply have to develop a Lorentz invariant formalism so that our statements may be independent of the coordinate system used.
- In classical mechanics the force which acts on a body at a given time is determined by the positions of the other interacting bodies at the same time. Meaning, the “same time” is independent of the frame of reference. Try that one on for size!!! Totally counter theory of relativity.
Never a dull moment in a storm eh?
Conservation laws enter. Relations between mass and energy, Compton effect, … equivalence, curvature tensors, field equations, rigorous solutions, experimental tests, equations of motion, gauge-invariant geometry, projections, closed five dimensional worlds … and alternative methods that are simply a neutral transformation, containing no physical significance. (pdf)
But the biggest mistake would be if science stopped making mistakes
And whatever you do,
don’t think about bananas!
- Cosmic Log: How to spot quantum quackery (cosmiclog.msnbc.msn.com)
- Geocentrism? Seriously? (blogs.discovermagazine.com)
- Time-Reversal [Built on Facts] (scienceblogs.com)