Re: Relativity in the rough

From: Uncle Al (UncleAl0_at_hate.spam.net)
Date: 03/02/05 

Date: Wed, 02 Mar 2005 11:18:22 -0800

Alan Boyle wrote:
>
> Howdy to the group: I'm Alan Boyle, science editor at MSNBC.com... We're in
> the midst of putting together a graphic introduction to relativity in honor
> of the Einstein centenary, and I thought I would try to put out a first
> rough draft of the "script" so that if there are glaring problems, we can
> fix them *before* we do all the Flash magic and publish it.

WHOA! Careful. Improved numerical methods are divergent with old
touchie-feelie approximations. Consider a relativistic sphere. If it
comes right at your nose it flattens into a pancake SOP. If it
whizzes by your head (best done in vacuum!) it undergoes Terrell
rotation instead.

Google
"Terrell rotation" 191 hits

http://bkocay.cs.umanitoba.ca/Students/Theory.html
 The distorted cube

The rubber *** demo of gravitation and spacetime curvature is
actually rather piss-poor.

> This is just a
> rough outline, and there may be incomplete references to things that would
> be included in the app... but if you see anything glaringly miscast, please
> write alan.boyle@msnbc.comBUTNOSPAM ... Probably should put "Rough
> Relativity" in the subject line so I can distinguish it from the Nigerian
> investment opportunities. Many thanks...
>
> The roots of relativity
>
> I. Introduction: Einstein's relativity theories predict
> some weird effects, such as black holes, a kind of time travel

I'd be real careful with "time travel."

> and bending
> light waves. But Einstein didn't go out looking for the weirdness; rather,
> the grand achievement of his theories was to demonstrate that the laws of
> physics work the way we think they should, even in weird circumstances.
> Einstein's view of the world is actually the one that best fits our everyday
> experience. Click through this graphic to find out why.

Einstein created a math model, Special Relativity, to reconcile
physics with Maxwell's equations. He postulated the Equivalence
Principle (all local bodies fall identically in vacuum) to add
gravitation in General Relativity. GR uses tensor mathematics free of
a coordinate background (no location or directional bias). Everything
else kinda appeared on its own.

 
> II. Before Einstein.
>
> a. Galilean relativity: The idea of relativity goes back to Galileo's
> day in the mid-1500s.

Cf: Stevin, Simon. "De Beghinselen der Weeghconst" ("Principles of the
Art of Weighing") (Leyden, 1586) Dijksterhuis, EJ. "The Principal
Works of Simon Stevin" (Amsterdam 1955)

> If you're playing a game of tennis on the deck of a
> smoothly sailing cruise ship, would you have to change your game completely
> just because you're traveling across a calm ocean at 25 mph? Of course not.
> That illustrates the Galilean concept of relativity, that the laws of
> physics work equally well in any reference frame, even if one frame is
> moving with respect to another frame. By adding together forces and
> velocities, you could figure out exactly how that tennis ball would move, on
> land or on the cruise ship.

INERTIAL reference frame. If the ship is linearly accelerating or
angularly turning, "fictitious forces" appear, e.g., Coriolis forces
and spinning weather systems.
 
> b. The problem of electrodynamics: What about light waves? In the
> mid-1800s, physicist James Clark Maxwell determined that electromagnetism -
> including electricity, magnetism and even light - propagated through space
> as waves. These waves were thought to ripple through a substance that filled
> the universe, known as the ether, just as sound waves propagated though air.
> That implied that the speed of those electromagnetic waves through a vacuum*
> would vary, depending on whether you were at rest with respect to the ether,
> or moving through the ether, just as the speed of sound waves varied. And
> that, in turn, implied that not all reference frames would be the same when
> it came to light and other electromagnetic waves. Physicists conducted
> increasingly precise experiments to look for variations in the speed of
> light that could reveal how fast Earth was moving through this universal
> ether - but every time they looked, the speed of light was exactly the same.
> (Climax came with the 1887 Michelson-Morley experiment, one of the most
> famous experiments in physics)

Michelson-Morley in 1887 ws good to detecting 10^(-8) anomaly; now
good to detecting 1.7x10^(-15),
Phys. Rev. Lett. 88(1) 010401 (2002)
Phys. Rev. Lett. 90 060403 (2003)
Phys. Rev. Lett. 42(9) 549 (1979)
Phys. Bull. 21 255 (1970)
Europhysics Lett. 56(2) 170 (2001)
Gen. Rel. Grav. 34(9) 1371 (2002)

Kennedy-Thorndike experiments
Ives-Stilwell experiments
Hughes-Drever experiments

Physics Today 57(7) 40 (2004)
http://physicstoday.org/vol-57/iss-7/p40.shtml
 No aether

http://fsweb.berry.edu/academic/mans/clane/
http://physicsweb.org/articles/world/17/3/7
 No Lorentz violation
 
> (* When we're talking about speed of light, we're always talking about its
> maximum speed in a vacuum. Light waves can always move more slowly in a
> medium such as water or glass. In fact, physicists have designed some
> ultra-cold environments where light seems to stop altogether.)
>
> III. Special relativity: Clocks and yardsticks
>
> a. Einstein instinctively knew there was something wrong with the way
> physicists were thinking about the problem. Even at the age of 16, he
> daydreamed about matching the speed of a light wave and seeing it frozen in
> space. Such an idea would lead to bizarre effects: For example, if you held
> a mirror in front of your face, the light reflected from your face could
> never catch up with the mirror, meaning the glass would be blank.
>
> b. A decade later, in 1905, Einstein put forth the claim that
> electromagnetic waves obeyed the same principle of relativity Galileo put
> forth for the motion of objects more than three centuries earlier: The laws
> of physics are the same in all smoothly moving reference fields. Einstein
> said that also meant that the speed of light was constant, even if that idea
> might seem "apparently irreconcilable" with the principle of relativity.
>
> c. How did Einstein reconcile those two ideas? He made the radical
> assertion that because the speed of light the same in all reference frames,
> it must be our measurements of distance and time that vary between reference
> frames.

INERTIAL reference frames (INERTIAL coordinate backgrounds).

> d. Light clock illustration:
[snip]

> IV. General relativity: Warps in spacetime
>
> a. In the world of clocks and yardsticks, we've been talking about
> reference frames that move uniformly in relation to each other. But that's
> actually a very rare and special scenario - that's why the theory is called
> "special" relativity. Einstein realized that if he was going to have a
> coherent explanation for how the electromagnetic realm worked, he'd have to
> account for scenarios in which there was acceleration, including the force
> of gravity. And that meant he'd have to take on an even bigger challenge:
> the Newtonian view of the universe.
>
> b. Problem for Einstein: Newton's claims that there was an "absolute
> time," and that gravity acted instantaneously on distant objects. Both those
> claims contradict special relativity.
>
> c. In 1907, Einstein had what he later called the "happiest thought in
> my life": that gravity and powered acceleration were equivalent for any
> local reference frame. Nine years later, the insight yielded what is now
> known as the general theory of relativity, Einstein's crowning achievement.
>
> d. In thinking about the Principle of Equivalence, Einstein visualized
> the experience of a man falling off a roof. But for our purposes, let's
> consider a sealed elevator car in Earth's gravity field, as well as a rocket
> ship in zero-gravity:

Einstein's elevator Gedankenexperiment,

Jahrbuch der Radioaktivität u. Electronik 4 411 (1907)
"The Collected Papers of Albert Einstein," Vol. 2 English translation,
A. Beck, trans. (Princeton University Press: Princeton, NJ, 1989) p.
252.
 
> 1. Elevator car in free fall (left) (Newton in the left car, Einstein
> in the right)
>
> 2. Rocket ship in zero-gravity (right)
>
> 3. Elevator car comes to rest (left)
>
> 4. Rocket ship accelerates at 32 ft/sec2 (right)
>
> 5. Laser light (another Einstein-based innovation) turns on in rocket
> ship (right)
>
> 6. Lantern with focused beam turns on in elevator car (left)
>
> 7. Conclusion: Light bends in a gravity field! (Einstein smiles,
> Newton frowns)

The Equivalence Principle is a postulate. It is only valid until a
counter-example is demonstrated (if ever).

http://www.mazepath.com/uncleal/eotvos.htm#b22

The Equivalence Principle has no exceptions for all compositions of
matter including binding energy mass-equivalent,

<http://wugrav.wustl.edu/people/CMW/update98.pdf>
<http://www.astro.northwestern.edu/AspenW04/Papers/lorimer1.pdf>
 Equivalence Principle testing

<http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf>
http://arXiv.org/abs/gr-qc/0301024
Phys. Rev. Lett. 93 261101 (2004)
 Nordtvedt Effect

HOWEVER, nobody knows whether whether a left hand falls identically to
a right hand - test mass geometry as a challenge to spacetime
geometry. The three defining experiments are in serial execution in
mainland China as you read this. Results by end of 2005.

http://www.mazepath.com/uncleal/qz.pdf

> e. Newton's theories did not account for the bending of light waves,
> which have no mass. The bending of light led Einstein to propose that
> gravity was not a mysterious "action-at-a-distance" force that acted on
> mass. Rather, gravity arose from the way concentrations of mass warped the
> fabric of spacetime itself, and objects as well as light waves simply
> followed the path of least resistance through those warps. Physicist Richard
> Wolfson calls this a case of "cosmic laziness."

http://arXiv.org/abs/gr-qc/9909014
Amer. J. Phys. 71 770 (2003)
Phys. Rev. Lett. 92 121101 (2004)
 falling light
 
> f. The greater the mass, the more curvature there is.

That is sloppy as stated. Density matters (e.g., Schwarzschild
radius), as does distance from the center of mass and external to the
stuff. Cf: Hipparcos-observed displacement of star positions up to 90
degrees from the solar limb.

> One way to
> measure that curvature would be to have a setup of three powerful lasers and
> light sensors around a huge star. If the star is relatively light, the
> angles of this cosmic triangle would add up to about 180 degrees. The more
> massive it is, the higher the sum would be. Add or subtract mass to this
> star to see how space curves. (The ball-on-rubber-*** model. In the
> extreme case of a black hole, the sum would go up to 1,080 degrees . three
> times 360.)

All you need is one laser and two mirrors. Cf: LISA.

http://www.esa.int/science/lisa/
 
[snip] 

-- 
Uncle Al
http://www.mazepath.com/uncleal/
 (Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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