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**Franklin, "Lorentz contraction, Bell's spaceships, and ..."**

In the discussion of a new FAQ entry on the Bell spaceship paradox, the following paper came up:

Jerrold Franklin, "Lorentz contraction, Bell's spaceships, and rigid body motion in special relativity," Eur. J. Phys. 31 (2010) 291, http://arxiv.org/abs/0906.1919

Since the paper contains some serious mistakes, I thought it would be helpful to start a thread here about it in order to collect some discussion and keep it publicly available for people who might otherwise be in danger of being misled by some of Franklin's claims. I initially thought, "Oh, nice, a detailed discussion of the Bell spaceship paradox that isn't behind a paywall." Then PAllen pointed out serious problems with it. The following two quotes, with my added labels [A] and

**, are both on p. 2:**

[A] The measured length of a moving object depends on the ‘particular way’ in which it is measured.

It should also be pointed out that another classically reasonable method of

measuring the length is to take a photograph of a moving object and compare

it with a photograph of the same object at rest. As Terrell[3] showed some time

ago, the photograph would show an object that is somewhat rotated, but of

the same shape and dimensions as it had at rest. Indeed, the photograph of a

moving sphere would show a sphere of the same size.

A is a general claim, and B appears to be intended as an example that demonstrates it to be true.

B is simply wrong. There is a group at ANU, for example, that has made a series of educational videos such as this one http://youtube.com/watch?v=JQnHTKZBTI4 , which I often show to my classes. In it, you can see very clearly that a shape such as a cube does not retain "the same shape and dimensions." I have a treatment of the cube as an example in section 6.5 of my SR book, http://www.lightandmatter.com/sr/ . The calculations are summarized and explained there, and anyone who's interested in the details of the calculation can examine my computer code here https://github.com/bcrowell/special_relativity/tree/master/ch06/figs/cube-sources . I'm pretty sure my calculations are right, since the resulting shape looks just like the one seen in the ANU video. Franklin has mischaracterized Terrell's work.

A could be argued to be true in the sense that optical measurements do not simply show the longitudinal length contraction by 1/γ. But the fact that Franklin supports it using a completely incorrect statement suggests that he thinks it is true in some broader sense, which is false. When we talk about the length of an extended body in relativity, we mean, simply as a matter of definition, the distance between two events on that body's world-sheet, with the two events being simultaneous. This definition gives a consistent result, longitudinal contraction by 1/γ, regardless of the details of the procedure used for carrying out the measurement. Optical measurements simply don't implement the definition, since the observer receives light rays simultaneously that were not emitted simultaneously in his frame.A is a general claim, and B appears to be intended as an example that demonstrates it to be true.

B is simply wrong. There is a group at ANU, for example, that has made a series of educational videos such as this one http://youtube.com/watch?v=JQnHTKZBTI4 , which I often show to my classes. In it, you can see very clearly that a shape such as a cube does not retain "the same shape and dimensions." I have a treatment of the cube as an example in section 6.5 of my SR book, http://www.lightandmatter.com/sr/ . The calculations are summarized and explained there, and anyone who's interested in the details of the calculation can examine my computer code here https://github.com/bcrowell/special_relativity/tree/master/ch06/figs/cube-sources . I'm pretty sure my calculations are right, since the resulting shape looks just like the one seen in the ANU video. Franklin has mischaracterized Terrell's work.

A could be argued to be true in the sense that optical measurements do not simply show the longitudinal length contraction by 1/γ. But the fact that Franklin supports it using a completely incorrect statement suggests that he thinks it is true in some broader sense, which is false. When we talk about the length of an extended body in relativity, we mean, simply as a matter of definition, the distance between two events on that body's world-sheet, with the two events being simultaneous. This definition gives a consistent result, longitudinal contraction by 1/γ, regardless of the details of the procedure used for carrying out the measurement. Optical measurements simply don't implement the definition, since the observer receives light rays simultaneously that were not emitted simultaneously in his frame.

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