...all.
By now, this phrase should alert you to the likelihood of error.
...little.
Recall the image of the pebble-thrower walking along the dock and watching the ripples propagate in the pond.
...originators!
Poor FitzGerald gets less press these days, alas.
...upon),
Mach would have had apoplexy over today's quarks -- but that's another story!
...motion.
An inertial reference frame is one that is not accelerated -- at rest or moving at constant velocity.
...named.
It is perhaps unfortunate that the theory was called ``Relativity'' when in fact it expresses the principle that the ``Laws of Physics'' are not relative; they are the same for all reference frames, moving or not! It is the transformations between measurements by different observers in relative motion that give weird results. When someone says, ``Yeah, Einstein showed that everything is relative,'' every Physicist within earshot winces. On the other hand, the does explicitly rule out any absolute reference frame with respect to which all motion must be measured -- thus elevating the negative result of the Michelson-Morley experiment to the status of a First Principle -- and does imply that certain phenomena that we always thought were absolute, like simultaneity, are not! So the name ``Relativity'' does stimulate appropriate debate.
...appears
The term ``appears'' may suggest some sort of illusion; this is not the case. The clock aboard the spaceship actually does run slower in the Earth's rest frame, and vice versa.
...later.
The one thing we left out of the original analysis was that you can't get from rest to near light speed without rather impressive accelerations, and there is no ambiguity about which twin gets accelerated! This breaks the symmetry between their experiences and resolves the paradox, at least conceptually. Inasmuch as GENERAL RELATIVITY deals with the effects of non-inertial reference frames (those under acceleration and/or in gravitational fields), it is often asserted that GENERAL RELATIVITY is needed to resolve the Twin Paradox. This is not really true; it can be done within , if we are careful.
...trouble
I haven't shown all the false starts in which I got the wrong answer using what seemed like perfectly logical arguments.... Here's a good one:

Refer to Fig. gif: let x be the distance between the flash bulb and the forward detector, as measured by the observer O on the ground, and let 94#94 be the same distance as measured by the observer 95#95 aboard the spaceship. Assume that O stretches out a tape measure from the place where the flash bulb is set off (say, by a toggle switch on the outer hull of the spaceship which gets hit by a stick held up by O as 96#96 flies by) to the position of the detector in the O frame at the instant of the flash. That way we don't need to worry about the position of the detector in the O frame when the light pulse actually arrives there some time later; we are only comparing the length of the spaceship in one frame with the same length in the other. [It may take a few passes of the spaceship to get this right; but hey, this is a Gedankenexperiment, where resources are cheap!] Then the time light takes to traverse distance 97#97, according to 98#98, is 99#99, whereas the time t for the same process in the rest frame is 100#100. Therefore, if (from TIME DILATION) t is longer than 101#101 by a factor 102#102, then x must also be longer than 103#103 by the same factor if both observers are using the same c.

Simple, eh? Unfortunately, I got the wrong answer! Can you figure out why?
...then
It takes about 3.4 ns [nanoseconds, 121#121 s] to go 2 feet at a velocity of 122#122.
...different.
If the door were at the far end of the barn (where the pole hits), there could be no such disagreement, since two events at the same place and the same time are for all intents and purposes part of the same event. It is only events separated in space about which such differences of opinion can arise.
...time''
Time measured aboard the spaceship is no more ``subjective'' than time on Earth, of course; this terminology suggests that the experience of the traveller is somehow bogus, which is not the case. Time actually does travel more slowly for the moving observer and the distance between origin and destination actually does get shorter.
...animation
The idea of suspended animation is a good one and I find it plausible that we may one day learn to use it safely; but it does not quite fall into the category of a simple extrapolation from known technology -- yet.
...technologies.
Except for the ``ramscoop'' technology and the requisite shields against the thin wisp of ambient matter (protons, electrons,...) inhabiting interstellar space, which is converted into high-energy radiation by virtue of our ship's relative motion. Minor details.
...system.
This situation might arise if an architect suddely discovered that his new plaza had been drawn from coordinates laid out by a surveyor who had aligned his transit to magnetic North while standing next to a large industrial electromagnet. The measurements are all OK but they have to be converted to true latitude and longitude!
...terms.
We wouldn't want the left hemisphere to feel ``left out," heh, heh!
...dimensions.
The sensory input upon which we base depth perception, and thus 3D vision, is actually pretty flimsy! All we have is the feedback from the muscles that point our eyeballs and focus their lenses. That is why we are so easily fooled by various ``3D" gimmicks.
...WORLDLINE.
In CLASSICAL MECHANICS the locus of a particle's motion is usually represented as a graph of position x (vertical axis = dependent variable) as a function of time t (horizontal axis = independent variable). The convention for Minkowski space (as in Fig. gif) is reversed, with x horizontal and ct vertical, mainly to signal a shift in our way of looking at time and space when thinking about the : both x and ct are now independent variables of equal status!
...times.
Turning the second part of the statement around, if both obervers were timing the bombs with identical clocks, 193#193 would measure a shorter interval than O, which O would interpret as the 194#194 clock itself running slower -- , time dilation.

Jess Brewer
Fri Aug 16 17:01:55 PDT 1996