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The Ladder Paradox

The ladder paradox, also called "the long ladder in the short garage" paradox has given virtually endless trouble to technical people for over a century now. The ladder paradox has also given the "anti-relativity" fraternity a good number of arguments in their quest to prove Einstein wrong.

The paradox goes like this: let a long ladder fly lengthwise at great velocity past a normal garage. The proper length of the ladder is more than the length of the garage. Due to the length contraction of special relativity, the passing ladder can for an instant (or two) fit into the garage, as observed by the garage owner.


However, for an observer riding on the ladder, it is the garage that moves at high speed and is length contracted. For the ladder observer there is no way that the ladder can fit into the garage, even for the briefest of moments. Hence, the whole idea seems paradoxical.


Once the problem is fully understood in terms of the relativity of simultaneity, the ladder paradox is reduced to common sense, but it is not always easy to understand how. This page and the Blog will help you bridge that gap (if you haven't done so already ;-)

Relativity 4 Engineers has a Blog going on the ladder paradox, as will be linked to below. There you can read the short articles, the comments of others and you can also comment on any entry. But, before you go there, please read the next two paragraphs. It will make the Blog entries much easier to follow.

Units: In the Blog the units of feet (ft) for distance and nanoseconds (ns) for time have been used. This because of the fortunate coincidence that the speed of light is very, very close to 1 ft/ns, meaning in such units, the speed of light is unity. This is particularly handy in space-time diagrams.

Space-propertime: In the second half of the articles on the Blog, space-propertime diagrams are used for clarity. It is defined more fully in the Blog, but they differ from normal Minkowski spacetime diagrams in that it is the moving observer's time plotted against the stationary observer's space on one diagram.

Space-propertime diagrams are also called Brehme- or Loedel-diagrams and make comprehension of special relativity much easier. Here is the link to the Ladder Paradox Blog.

The above images are from Wikipedia, where you can compare the clarity of the Blog's space-propertime diagrams with Wikipedia's Minkowski spacetime diagrams.


Return from the Ladder Paradox page to the Paradoxes page



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