Grab-bag of questions from dseppala (was Re: Treatment of some posters)

From: Ben Rudiak-Gould (br276deleteme_at_cam.ac.uk)
Date: 02/09/05 

Date: Wed, 09 Feb 2005 19:45:46 +0000

dseppala@austin.rr.com wrote:
> Some posters come back repeatedly over a long span of time because:

Ooh! Ooh! Lots of fun questions to answer. I can never resist posts like this.

> 1. When they ask what the common link is between the speed of light
> and the way matter behaves the response is "unknown", so they wonder
> why.

Are you talking about a question along the lines of "what would the universe
be like if the value of c were different"?

The trouble with this question is that the meter is currently defined to be
the distance that light travels in 1/299792458 second. If you want to
speculate about a different speed of light, you can't do it with that
definition of the meter, so you have to provide a different one. Now are
other constants whose units include a meter also changed to use that new
definition? There's a ripple effect through the theory, and by the time
you're done you haven't really changed the speed of light as such; you've
changed a bunch of things which don't correspond in any obvious way to the
speed of light.

The way to avoid this problem is to tweak a unitless constant instead.
Unitless constants are the only real constants (parameters) in physical
theories; everything else is an artifact of our arbitrary choice of units.
There's no unitless constant which corresponds in an obvious way to the
speed of light. But if you wanted to talk about changing the value of the
fine structure constant, for example, there's a clear-cut answer to that.

> 2. When they post a problem about a rod accelerating from one
> inertial frame to another inertial frame, they are told atoms and
> sub-atomic particles follow the length contraction virtually
> instantaneously whereas molecules adjust at the speed of sound. This
> is stated without any explanation so they wonder why.

First of all, it's really important to understand that things don't go from
one inertial frame to another. They're always "in" every inertial frame,
regardless of their motion. Read through my recent post:

http://groups-beta.google.com/group/sci.physics.relativity/msg/77a649653249add9

As far as "virtually instantaneously" versus "speed of sound", my guess is
that the person writing those words considered the time taken to cross an
atomic diameter at the speed of sound (of some solid) was small enough to be
considered virtually instantaneous. If you push on one end of a rod, there
will be a ripple effect through the rod, traveling at the speed of sound,
which causes each molecule in the rod to "adjust" (i.e. vibrate and
eventually return to an equilibrium state, possibly different from its
previous equilibrium state). Each individual molecule will adjust in a time
which can be treated as negligible (i.e. virtually instantaneous) for many
pusposes.

This is assuming the rod was accelerated by pushing on one end, which is not
necessarily true. In principle you could accelerate it by applying just the
right force to every molecule so that they're always in equilibrium. This is
what happens in maglev (I think). Also, if you keep applying a constant
force to one end, the rod will settle into an equilibrium state which is
different from its inertial equilibrium state. This is the case for any
object at rest on the earth's surface.

> 3. When posters ask about clocks moving from one reference frame into
> another, they are told clocks change rates instanteously when placed
> in the new frame. This is stated without explanation, so they wonder
> why.

See next question.

> 4. When clocks are moved from one reference frame into another, all
> clocks instantaneously behave the same - atomic clocks, electric
> clocks, mechanical clocks. This is stated without explanation, so
> they wonder why.

Again, an essential point is that you can't move something from one
reference frame to another. There are two completely different questions you
might be asking here:

   A. What is the (time-independent) rate of an inertial clock with respect
to two different inertial reference frames?

   B. What is the (time-dependent) rate of a non-inertial clock with respect
to a particular inertial reference frame?

With respect to question A, there is no change of rate going on,
instantaneous or otherwise. In fact there's not much physical content to
this question. Even if the universe didn't exhibit Lorentz invariance (and
in some sense it doesn't -- look at the CMB) you could still ask this from a
purely mathematical standpoint, and answer it using the Lorentz
transformation. This is in fact what Lorentz did.

With respect to question B: In practice, some kinds of mechanical clocks
will not keep accurate time in states of high acceleration, or (in the case
of a pendulum clock) under any acceleration other than g. Nevertheless
there's a well-defined notion in SR (and GR) of an ideal clock which is
unaffected by acceleration. Most non-mechanical clocks approximate the ideal
clock pretty well. Some clocks, such as the decay rate of an ensemble of
muons, approximate the ideal clock so well that no one has ever found a
deviation even at accelerations of, oh, I can't remember but something very
large.

> 5. When calculations of elapsed time are performed for objects going
> from one inertial frame into another, one is told that you must always
> view things as if the entire process happened in the final reference
> frame, and not to consider the view in the initial frame. This is
> stated with explanation, so they wonder why.

This is not true. The only way you can screw up is by considering things
with respect to some mixed-up combination of both reference frames. Every
set of coordinates needs to be explicitly associated with one particular
inertial reference frame. It doesn't matter which one it is, as long as you
always say which one it is.

> 6. When a force is applied to a long rod and to a segmented rod of
> equal length and mass, the long rod moves in the opposite direction of
> the segmented rod at times. This is stated without explanation, so
> they wonder why.

I don't understand what you mean here.

> 7. A rod can be observed to shatter due to stretching when its length
> remains constant. This happens without a stated explanation, so they
> wonder why.

I'm guessing you're talking about a rod whose endpoints have worldlines like
the loci of (cosh alpha, sinh alpha) and (1m + cosh alpha, sinh alpha) with
respect to some SR inertial frame. This rod will indeed eventually break.
You don't need to assume SR to reach this conclusion. You only need to
assume that the rod is held together by electromagnetic forces, and that
electromagnetism follows Maxwell's equations with respect to some Newtonian
inertial frame, and that the rod will break if you pull on it hard enough.
The easiest approach to showing this is to use Lorentz symmetry, which is a
symmetry of Maxwell's equations quite independently of SR.

> 8. A fragile rod can break due to twisting when it has low relative
> velocity, but can undergo extreme twisting when it has high velocity.
> This happens without a stated explanation so they wonder why.

Same answer as the previous question.

> 9. A rod can increase in length, but not be stretched. This happens
> without explanation, so they wonder why.

Not sure what you mean here.

> 10. They are told that they don't understand that SR is about
> differences in measurements only, and not physical properties even
> when everyone agrees that length contraction cannot occur
> instantaneously, so they wonder why.

I would say this is wrong. Again, there's a big difference between (a)
talking about the same phenomenon with respect to two different inertial
reference frames, and (b) changing the motion of a physical object. People
tend to confuse them, even professional physicists.

> 11. It is sacrilegious to state that the simplest explanation of the
> MMX is that the speed of light varies with the velocity of the light
> source, so they wonder why.

Indeed there are other reasonable ways of explaining the null MMX result,
but they all fail to explain other experimental results, e.g. the aberration
of starlight or observations of binary stars. (By observation I mean looking
through a telescope, not SR "observation".) There are ways of explaining the
other results, but they fail on MMX. I think the emission theories all have
problems with binary stars.

> 12. Einstein hypothesizes that the speed of light is independent of
> the velocity of the light source, yet we all know that the direction
> of light propagation is dependent on the velocity of the light source.
> No explanation is given for the underlying reason, so they wonder
> why.

Not sure what you're talking about here -- the headlight effect?

> 12. Pre-emininent physicists like Stephen Hawking state that
> Michelson-Morley discovered that the speed of light is constant, when
> what they measured was phase difference of two interfering light
> beams. Statements like this are never corrected, so they wonder why.

Yes, MMX doesn't prove that the speed of light is constant, nor does
anything else, nor is there any deep ontological sense in which it is
constant. It's impossible to "measure the speed of light" without defining
what you mean by the speed of light, and any such definition is heavily
theory-laden. This is the wrong approach to take (except with regard to
marketing your work in the non-scientific world). The right approach is to
realize that theories are judged, and can only be judged, on how well they
hold together as a whole. You concoct experiments, look at what SR predicts
the result will be, and compare that to the actual result. Sometimes the
predicted result might be the numerical value 299792458 m/s, in which case
people like to say that they've measured the speed of light, but you don't
have to agree with them to be a physicist. You only have to agree with the
process of free theorization constrained by experimental tests.

People make statements like the one you paraphrased because they think that
telling little white lies will help people learn (which is often true), or
because they don't understand how physics actually works.

I don't recommend _A Brief History of Time_. I think most physicists would
agree that it's a lousy book to learn physics from. The reasons for its
popularity are wholly unrelated to any scientific or pedagogical virtues.

> 13. Einstein states in his paper on General Relativity that one
> cannot differentiate between being in a gravitational field or being
> simply accelerated. Everyone knows a simple experiment can
> differentiate between the two, yet no one ever corrects this concept,
> so they wonder why.

The principle of equivalence can be given in a precise mathematical form,
using differentials, in which it's exactly correct of GR. I agree that it's
a bit problematic to use it in handwavy explanations of GR. I think that
this goes in the "little white lie" category.

> 14. All of the experimentally demonstrated consequences of relativity
> are also consequences of matter and light both having wave properties,
> yet this is verboten to think about, so they wonder why.

I don't understand what you mean.

> 15. No one has a clear explanation of how an electrical pulse travels
> down a pair of wires where one wire has a relative velocity wrt the
> other wire, yet we can easily build such a physical device, so they
> wonder why.

I don't know how to solve this problem in a Newtonian setting either (which
is a statement of my ignorance, not of the problem's difficulty). So I can't
help you with the SR case.

> 16. There is not a single source that lists all the axioms and
> hypotheses used by physicists, so they wonder why.

Yeah, this may be true. The famous five postulates of Euclidean geometry are
actually insufficient to generate Euclidean geometry: many of Euclid's
results don't follow from the axioms. Euclid relied heavily on physical
intuition, and modern physicists do too. A complete axiomatization of
Euclidean geometry has 20+ axioms, I think. (Again, I wish I had references
handy.) I don't know how much of modern physics has been properly axiomatized.

> 17. Physicists, including Einstein, use the well-known logic error of
> affirming the consequent as "convincing proof of the correctness of
> the theory", so they wonder why.

That's just the way it is in science. Scientists think of well-confirmed
theories as correct because, well, it's the closest thing to correctness
they're ever going to get. I think that for all their boasting about the
accuracy of their theories, all scientists are nonetheless deeply aware that
any theory can fall to new evidence. In fact, they love it when that happens.

Physicists have great confidence that the SR model expresses *something*
deep about the nature of the universe, not only because it has been directly
confirmed in so many ways, but because it implies all kinds of subtle and
surprising results like the existence of magnetism, antiparticles, and
electron spin. Without SR these all have to be added in phenomenologically.
With SR they're all predicted. And that's just the beginning. I can't begin
to describe how fruitful SR has been as a basis for successful theories.

But I can think of few things that would be more exciting than an
experimental result incompatible with Lorentz invariance. If we discover
that Lorentz invariance is incorrect, we'll know more about the universe,
not less.

-- Ben

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