Re: Relativity in the rough

From: Ben Rudiak-Gould (br276deleteme_at_cam.ac.uk)
Date: 03/03/05 

Date: Thu, 03 Mar 2005 02:38:18 +0000
To: Alan Boyle <alan.boyle@msnbc.com>

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.

You might want to post this to sci.physics.research. Despite its name, it's
not just for discussions of current research; it's basically a moderated
version of sci.physics. Lots of smart and well-educated people read that
group who don't bother reading sci.physics. The reverse is not true. :-)

>I. Introduction: Einstein's relativity theories predict
>some weird effects, such as black holes, a kind of 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.

If you're talking about its supposed better compatibility with the principle
of relativity, then I disagree. See below.

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

This is a good example. But you shouldn't be playing on the deck, because
you might well have to alter your game to compensate for the 25 mph
difference in wind speed.

>[...]
>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.

No, it doesn't imply this at all. If it did, the wind on the deck of the
cruise ship would violate the principle of relativity too. There's no
conflict between the principle of relativity and the notion that light is a
wave in a medium.

>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.

It's more complicated than that. There were many different ether theories,
only some of which predicted an ether wind. As far as I know, the M-M
experiment is famous only because it was historically last: it eliminated
all the theories that hadn't already been eliminated by previous
observations. You might mention that ether-dragging theories and emission
theories were consistent with the null result of M-M, but they had already
been eliminated by other data (the aberration of starlight in the former
case, observations of binary stars in the latter case). Standard textbook stuff.

>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.

You wouldn't be able to see the glass either. You wouldn't be able to see at
all, or think, since the nervous system operates by electrical pulses which
are limited by the speed of light. Your body would disintegrate because the
electromagnetic force would no longer operate between electrons and nuclei.

But none of this means that it's impossible to exceed the speed of light!
Falling into a black hole would also be fatal in a weird way, but that
doesn't mean that black holes don't exist.

>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.

This is fine, but it's really important to understand that only the
experimental data could possibly justify this step. It is not justified on
purely philosophical grounds, any more than a similar statement about the
speed of sound would be. We need experiments to tell us that this is true of
light and not true of sound. Einstein was not staying any more true to the
principle of relativity than the etherists were. He just figured out a way
to use it to explain the observations.

>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.

I don't think this is accurate. He didn't assert this to be true: he
demonstrated why it is true. That was the insight which distinguished him
from Lorentz and Poincare', who had previously developed theories which were
mathematically the same as Einstein's. They didn't understand why it made
sense; he did.

>d. Light clock illustration:
>[...]
>5. It gets even stranger: We've shown that from Al's point of view,
>Bert's clock seems to be ticking more slowly. But from Bert's point of
>view, it's Al's clock that's the slow one.

Okay, time for my long pet-peeve rant. Feel free to skip this.

I'd like to see the whole notion of time dilation purged from introductions
to relativity. It only confuses things.

Einstein's insight was that we can't assume a priori that it makes sense to
talk about what happens at the same time in different places. It turns out
that, in the real world, it *doesn't* make sense. Physics is local;
different parts of the universe evolve independently, not in lockstep.
That's the key. Given that physics is local, the twin "paradox" isn't
surprising at all; why should the twins age the same amount, when they're in
different places?

A century later, most people still don't get what he got back then. Standard
introductions to special relativity still talk blithely about what happens
in different places at the same time. They still describe distant systems,
like Al's and Bert's clocks, as though they were evolving in lockstep. All
of the hopeless confusion about observer-dependent reality arises from this
fundamental misconception.

The fact is that there's no such thing as time dilation and length
contraction and the relativity of simultaneity unless we construct reference
frames to refer our measurements to. In order to construct reference frames
we must *synchronize clocks*, and that's where all the trouble arises. You
really cannot talk about time dilation without synchronized clocks, and time
dilation is really a property of synchronization, not of moving clocks.

It's not clear that any of this is necessary or desirable in a popular
introduction to relativity. Who cares about synchronizing clocks? It's
physically meaningless given the locality of physical law. And if we don't
synchronize clocks, we can avoid all the time-dilation nonsense, and
concentrate on physically real effects like the twin paradox and the doppler
shift.

Other than that, I think your light clock example is fine. :-)

>e. This phenomenon has sparked the phrase "moving clocks run slow" .
>but physicists say that phrase can be misleading. As we've just seen,
>either Al's or Bert's clock could be considered the "moving" clock.
>Physicist Richard Wolfson suggests a more "relative" description of the
>relativity in time measurement: "The time between two events is shorter
>when measured by a single clock that's present at both events than it is
>when measured by two separate clocks."

Yes, Wolfson's statement (which I hadn't heard before) is much more accurate
than the statement that "moving clocks run slow".

His point is that to talk about time dilation you need at least three
clocks, one that's being measured and two to measure it by. (He doesn't
mention that the latter two must be comoving and synchronized.) Your
description in part (d) cannot be correct because it only mentions two clocks.

>f. And if time gets "squishy" between reference frames that are
>moving with respect to each other, measurements of distance gets squishy
>also. It turns out that your measurements of objects that are moving
>through your reference frame get shorter in the direction of the motion.
>(Shrinking yardstick.)

If the yardstick shrinks, shouldn't the distances it measures get larger,
not smaller? Again, it's more complicated than this. Synchronization is the
key; everything else is detail.

I object to the use of the word "squishy" here, since the predictions of
special relativity are no less precise and unambiguous than the predictions
of Newtonian dynamics.

>g. Al and Bert twin-paradox calculator (* The fact that Al ages more
>than Bert might seem to contradict relativity theory. From Al's point of
>view, shouldn't it equally be the case that Bert would seem younger? No:
>The reason Al's the one who ages more slowly is because he's in a shifting
>reference frame.

There's no such thing as being "in" a reference frame: everything is in
every frame. And there's no such thing as a shifting reference frame. This
explanation of the twin paradox is basically wrong, as is the later GR
explanation. The only correct statement along these lines is that the fact
that one twin accelerates and the other doesn't *breaks the symmetry* of the
problem, which means that it's *possible* for their ages to differ at the
end. But it doesn't explain why the ages do differ, or which twin will end
up younger.

I don't think there's any way to sensibly explain the twin paradox in terms
of reference frames. But I suppose you're stuck with doing it, because what
kind of popular relativity site wouldn't mention the twin paradox?

>It would take an infinite amount of energy to give the object that
>extra little push to light speed - which is the root of Einstein's most
>famous equation, E=mc2.

This is incorrect. E=mc^2 is not related to the impossibility of
accelerating to light speed.

>i. All this can get confusing: Observers in different frames of
>reference might not agree on what happens when, or even which events come
>first and which come later. (Mishmash of moving clocks, yardsticks, trains,
>rocket ships, etc., on overlapping grids.)

I don't think the illustration should show a "mishmash", since there is
nothing ambiguous or unclear about the predictions of relativity. Like
"squishy", this only seems to reflect confusion in the mind of the writer
and/or reader.

>So does that mean that everything's
>relative? Are we lost in space and time? Thankfully, no. Einstein's special
>theory of relativity includes equations that help physicists work out
>consistent coordinates for events, using measurements that incorporate
>space as well as time - a four-dimensional view of the cosmos known as
>spacetime.

Perhaps I'm misinterpreting this, but it suggests an image of Einstein
bravely showing the way through a bizarre and incomprehensible universe. I
disagree with this image, obviously. It's like tacitly admitting that you
haven't actually explained anything, that only real physicists (or only
Einstein) will ever understand what relativity is about. This shouldn't be
true, and needn't be true.

>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.

General relativity is no better than special relativity at dealing with
acceleration that's not due to gravity. Einstein initially thought that it
was, but this was one of the many occasions on which he was wrong. And even
in those days he understood that SR could deal with acceleration; he just
didn't find the SR approach philosophically satisfying.

>And that meant he'd have to take on an even bigger challenge:
>the Newtonian view of the universe.

Hadn't he already done that?

>[...]
>7. Conclusion: Light bends in a gravity field!

All this looks good.

>(Einstein smiles, Newton frowns)

But Newton also believed that light would be bent by gravity, because he
thought that light was made of particles (corpuscles).

>e. Newton's theories did not account for the bending of light waves,
>which have no mass.

The notion of a massless object makes no sense in Newtonian dynamics. But
even if Newton had believed that light was made of massless particles, he
still would have predicted that it was deflected, because the deflection of
an object by gravity is independent of its mass. It doesn't go away as the
mass goes to zero.

If Newton had believed that light was a wave in a medium, he probably would
have predicted that it was not deflected. But that's not because of a lack
of 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."

I don't think that "cosmic laziness" (better known as the principle of least
action) is really related to GR. It's a general formalism which applies
equally to Newtonian dynamics, special and general relativity, and quantum
theory. And I wouldn't describe light as lazy: like other waves, it takes
*every possible* path, which is about as far from lazy as you can get!

>f. The greater the mass, the more curvature there is. 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.

Whether this is correct depends on the accuracy of your Flash applet. :-)

>(The ball-on-rubber-*** model.

The ball-on-rubber-*** model is a description of *Newtonian* gravity. As a
model of general relativity it's quite wrong. The confusion stems from the
fact that a typical embedding diagram from an introductory GR textbook
happens to look sort of similar to a Newtonian gravitational well. But
that's coincidence.

One example: Suppose you freeze the rubber *** and then turn it upside
down, so it's now a hill instead of a valley. Is that a repulsive force or
an attractive force? It looks like it should be repulsive. If the "***" is
a Newtonian potential, then it is repulsive. But if it's a GR embedding
diagram, it's attractive. The fact that they appear to agree in the valley
case is, as I said, coincidence.

Another example: In ordinary cases, like the orbit of planets around the
sun, the only significant deviation from flatness is in the time direction
(the dt^2 component of the weak-field metric). This curvature is invisible
in the usual embedding diagram. You can ignore the spatial curvature
entirely (so the embedding diagram is precisely flat) and still reproduce
all the predictions of Newtonian gravity. I think you can even derive the
precession of Mercury's orbit in this approximation.

I would love to see an end to this decades-old mistake (originated by
Eddington, I think), and you might as well lead the way. :-)

>g. Remember how outside observations of time and space vary between
>reference frames that are in smooth motion with respect to each other? This
>effect applies to accelerated reference frames as well. For example, if you
>were to send a clock and a yardstick from Earth to Jupiter, the clock would
>seem to tick slower and the yardstick would shrink slightly in the stronger
>gravitational field. When the clock was brought back to Earth, it would
>still be out of sync.

Mm. You don't really need to take it all the way to Jupiter, just to the top
of a tall building on Earth (I think this experiment has been done).

>That provides an alternate explanation for the
>phenomenon in the twin paradox: Al is the one who goes through acceleration
>and deceleration, while Bert isn't subjected to as many forces during Al's
>trip. Thus, Al is the one who ages less.

Nope, sorry. The twin paradox is about path length, not acceleration.

>V. Proving Einstein right: At first, Einstein's theories
>weren't given much credence.

I don't understand this statement. As far as I know they were widely
believed to be correct even before the evidence was in.

>Here are some of the key phenomena
>confirming the theories:
>
>a. Precession of Mercury (check)

This was known long before 1916, but the fact that GR could explain it did
increase Einstein's confidence in the theory.

Also, it isn't the whole precession of the orbit, just a tiny residual
amount that hadn't already been explained by other means.

>b. Bending of light during eclipse (check)

Careful: Eddington's famous experiment is now widely considered to have
proven nothing. His error bars were much larger than his signal.

The idea of gravitational deflection of light dates back to Newton. General
relativity predicts a different amount of deflection (exactly twice what
Newton would have predicted).

I think the best modern evidence for gravitational deflection of light is
the gravitational lensing of distant galaxies.

>d. Spacetime frame dragging (check) . including GPS (cf. Scientific
>American): GPS satellites have to be adjusted by 38 microseconds every day
>to account for the relativity effect.

I don't think the GPS adjustment has anything to do with frame dragging
(also known as the Lense-Thirring effect). The correction is for
gravitational time dilation (based on the height of the satellites) plus a
twin-paradox-like effect from the orbital motion.

>e. Black holes (semi-check)

I think the evidence for the existence of black holes is overwhelming at
this point.

>f. Gravity waves (question mark)

There's strong circumstantial evidence that they exist, from observations of
binary stars.

-- Ben

Quantcast