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#Relativity requires different values for the inertia of a moving object: in its direction of motion, and perpendicular to that direction.  This contradicts the logical principle that the laws of physics are the same in all directions.

#Relativity requires different values for the inertia of a moving object: in its direction of motion, and perpendicular to that direction.  This contradicts the logical principle that the laws of physics are the same in all directions.

#Relativity requires that anything traveling at the speed of light must have mass zero, so it must have momentum zero.  But the laws of electrodynamics require that light have nonzero momentum.

#Relativity requires that anything traveling at the speed of light must have mass zero, so it must have momentum zero.  But the laws of electrodynamics require that light have nonzero momentum.

#Unlike most well-tested fundamental physical theories, the theory of relativity violates conditions of a conservative field.  Path independence, for example, is lacking under the theory of relativity.<ref>In defense of the theory, it is noted that it mandates conservation of the matter-stress-energy tensor (the only way to get ''real'' conservation, since matter and energy are interchangeable.)  This follows from the "contracted Bianchi identity".  [http://www.mth.uct.ac.za/omei/gr/chap6/node14.html]  Also, the curl of the "gravitational field vector" is exactly zero in the absence of moving sources, due to symmetries of [[Riemann]]'s tensor.  It follows, from [[Stokes' Theorem]], that the gravitational field is conservative and has a potential function.  Energy is conserved.</ref>

#Unlike most well-tested fundamental physical theories, the theory of relativity violates conditions of a conservative field.  Path independence, for example, is lacking under the theory of relativity, as in the "twin paradox" whereby the age of each twin under the theory is dependent on the path he traveled.<ref>In defense of the theory, it is noted that it mandates conservation of the matter-stress-energy tensor (the only way to get ''real'' conservation, since matter and energy are interchangeable.)  This follows from the "contracted Bianchi identity".  [http://www.mth.uct.ac.za/omei/gr/chap6/node14.html]  Also, the curl of the "gravitational field vector" is exactly zero in the absence of moving sources, due to symmetries of [[Riemann]]'s tensor.  It follows, from [[Stokes' Theorem]], that the gravitational field is conservative and has a potential function.  Energy is conserved.</ref>

#The Ehrenfest Paradox: Consider a spinning hoop, where the tangential velocity is near the speed of light. In this case, the circumference (<math>2 \pi R</math>) is length-contracted. However, since <math>R</math> is always perpendicular to the motion, it is not contracted. This leads to a paradox: does the radius of the accelerating hoop equal <math>R</math>, or is it less than <math>R</math>?

#The Ehrenfest Paradox: Consider a spinning hoop, where the tangential velocity is near the speed of light. In this case, the circumference (<math>2 \pi R</math>) is length-contracted. However, since <math>R</math> is always perpendicular to the motion, it is not contracted. This leads to a paradox: does the radius of the accelerating hoop equal <math>R</math>, or is it less than <math>R</math>?