Hi guys, this question is from Taylor and Wheeler's Spacetime Physics, problem 3-6 on page 79. It is a multi-part conceptual/philosophical question on the basic ideas of special relativity. Here goes:
Mr. Van Dam is an intelligent and reasonable man with a knowledge of high school physics. He has the following objections to the theory of relativity. Answer each of Mr. Van Dam's objections decisively - without criticizing him.
(a) Observer A says that B's clock goes slow, and observer B says that A's clock goes slow. This is a logical contradiction. Therefore relativity should be abandoned.
(b) Observer A says that B's meter sticks are contracted along their direction of relative motion, and observer B says that A's meter sticks are contracted. This is a logical contradiction. Therefore relativity should be abandoned.
(c) Relativity does not even have a unique way to define space and time coordinates for the instantaneous position of an object. Laboratory and rocket observers typically record different coordinates for this position and time. Therefore anything relativity says about the velocity of the object (and hence about its motion) is without meaning.
(d) Relativity postulates that light travels with a standard speed regardless of the free-float frame from which its progress is measured. This postulate is certainly wrong. Anybody with common sense knows that travel at high speed in the direction of a receding light pulse will decrease the speed with which the pulse recedes. Hence a flash of light cannot have the same speed for observers in relative motion. With this disproof of the basic postulate, all of relativity collapses.
(e) There isn't a single experimental test of the results of special relativity.
(f) Relativity offers no way to describe an event without coordinates - and no way to speak about coordinates without referring to one or another particular reference frame. However, physical events have an existence independent of all choice of coordinates and all choice of reference frame. Hence relativity - with its coordinates and reference frames - cannot provide a valid description of these events.
(g) Relativity is preoccupied with how we observe things, not what is really happening. Hence it is not a scientific theory, since science deals with reality.
The Attempt at a Solution
Here are my thoughts on the critiques. I would like to know if they sufficiently answer the objections, or if I need to say something deeper.
(a) First, let's agree on the definition of a clock, as there are (from what I read in this book) two. Definition 1: a clock could be part of a huge lattice of clocks and metersticks that perform all measurements in a free-float frame and beat every second. In this definition, a clock is an imaginary human construct. Definition 2: a clock could be a physical thing that beats every second, but only with respect to a particular free-float frame.
If we take the first definition, then this guy is wrong, since all measuring kits (lattices of clocks and metersticks) work the same way for all free-float frames, hence nothing goes slower.
If we take the second definition, then "B's clock" really means a physical clock at rest in frame B; the same thing goes for "A's clock." Here, I would argue that if A saw B's clock go slow while B saw A's clock go fast, then there would be a method to determine absolute velocity, for the form of the laws of physics could not be the same in both reference frames. Hence, the principle of relativity would be violated. In fact, if A saw B's clock go slow by a certain factor, then B must see A's go slow by the same factor, in order for the principle of relativity to hold.
(b) It seems that the discussion is the same here, only replace the word 'clock' with 'meterstick.'
(c), (f) I would say this: in Newtonian physics, the space coordinates of events are not the same, so why should the spacetime coordinates of events in special relativity be the same? The important thing is the invariance of the spacetime interval. This gives events existence without a coordinate system.
(d) If one holds firm that time is absolute, that is, that the time of an event is independent of free-float frame, then it is impossible for there to be a speed that is invariant. This is because if one assumes absolute time, the Galilean transformations necessairly follow. And in the Galilean transformations, speed cannot be invariant with respect to a change of free-float frame. Therefore, if we give up the idea of absolute time, the invariant speed c is definitely possible.
(e) This is an easy one. Just look at particle accelerators where speeds never exceed c, or an experiment I heard about where they took a clock into an airplane and got a measureable time-dilation effect.
(g) In special relativity, the word 'observe' means that the lattice of clocks and metersticks detect an event. They describe what is really happening. It does not mean that one sees something in the literal sense, for that means we would have a delay by the speed of light of the information getting to you.
Are these statements correct and do they answer the objections? Thanks for the help.
(By the way, it might have been more appropriate to post this question on the relativity thread. If so, then to the all-powerful rulers of the forum: please move it!)