Some Basic Conceptual/Philosophical Questions on Special Relativity

Homework Statement

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!)

Imagining one night the idea of making a road trip by car to New York from Los Angeles and back a thought occurred to me, what if we could do the trip quicker, in fact could Einstein’s theory of relativity make it a quicker journey. It was an intriguing thought, and from this grew the idea of applying an actual test case for the journey using Einstein’s paper of 1905. After a little searching on internet the paper “On the electrodynamics of moving bodies 1905” was found. Having falsely anticipated that the mathematics involved would be complex resulting from the many comments concerning advocates of the theory concerning the complexity, I was surprised to see it contained very little mathematics and was basically high school level algebra. So without further ado we can proceed to prepare some rough figures that we can use. To make the calculations easy the distance 2000 miles is used to New York and a speed of 50mph. It may occur to you what about stopping and starting and acceleration when we look through Einstein’s paper he also did not take into account acceleration, so it can be safely ignored and so we can stick to a constant speed of 50mph. One of the things in Einstein’s paper that we have to consider is the speed of light “c”. As this could be considered Einstein’s cosmic “speed limit”, it makes sense also to introduce a motoring “speed limit”. Although a little unrealistic it is convenient to impose an imaginary national speed limit of 30mph for the whole journey, but we still retain the actual speed of 50mph as the velocity of the car. Effectively we are going to break the speed limit by 20mph all the way there and back. The last numbers needed are those of time, with a quick calculation a distance of 2000miles at 50mph this would mean it would take us 40hours going and 40hours to get back.
We now have everything we need to make some calculations using Einstein’s theory. Looking at the paper the first thing that is encountered is the synchronization of clocks this formula is used to determine the conditions when clocks could be considered in sync and interpreted in the context of our road trip is;

t_B- t_A= t'_A- t_B

t_NY - t_LA= t'_LA - t_NY​

This makes complete sense the time of arrival at New York minus the time leaving from Los Angeles is the same as the time returning to Los Angeles minus the time of arrival at New York. Knowing the numbers in advance filling in the formula resulted in;

40hours – 0 = 80hours – 40hours​

The numbers work out just fine at 40 = 40 so any imaginary clocks or watches that we use to time the journey would be synchronous. At this point everything is looking fine. Continuing on the next formula in the paper is a formula for the speed of light, which in our case is the constant velocity of the car;

Einstein’s equation

2AB/t'_A –t_A =50mph

(2 distance of NY to LA)/(Arrival time – Departure Time)=50mph​

In our scenario this really just states that the speed limit is constant throughout at 50mph there and back.

4000miles/(80hours –0)=50mph​

Now we need to address the big part which is the “Relativity of Length and Times”, the title of this section is a little foreboding but it is quite simple in concept. Everything up to now has been based upon a simple formula;

Velocity= Distance/Time​

The crux of the paper is an equation upon which everything else that follows it is based this is the equation to ascertain simultaneity, which will be immediately recognizable by proponents of Einstein’s theory.

t_B- t_A= τAB/(c-v)

And

t'_A-t_B= τAB/(c+v)​

In our case, ascertaining the simultaneity of the two parts of the journey from Los Angeles to New York and the second part from New York back to Los Angeles the formula is expressed as the following;

Arrival time_NY- Departure time_LA= (Distance LA to NY)/(speed limit-speed)

And

Arrival time_LA- Departure time_NY= (Distance LA to NY)/(speed limit+speed)

The results of these two equations should be the same if they weren’t then Einstein claims there would be length contraction. Plugging our numbers in we get;

40hours –0= 2000miles/(30mph-20mph)

Which resolves to “40 = 200”

And

80hours-40hours= 2000miles/(30mph+20mph)

Which resolves to “40 = 40”​

So the numbers as was expected work out exactly as Einstein predicted, there is no simultaneity between the times, the problem is that this is at 50mph in a car. Does this mean that the equations of Einstein allow for us to create a time machine with our car on a road trip, or is there something deeper causing these results.
The answer is not readily apparent, but is obvious if a little thought is put into the process. It can be seen that if a problem exists it has to be in the first equation, as the second one gives the right answer it takes 40 hours for the return journey. There appears to be something going wrong with the first equation giving us a result of 200 hours which is obviously wrong unless we stopped at Las Vegas on the way and wasted over 8 days in the casinos. The mileage is undoubtedly correct at 2000miles and the time it should take at 40hours is also correct, the only remaining element is the speed which is 30mph – 20mph which equals 10mph!, that is why it took so long, but the speed was supposed to be constant! . How did we arrive at this scenario, why did Einstein want to subtract the speed of the car from the speed limit or in his terms the velocity from the speed of light? To understand this we need to think a little about the experiment. If we were to travel from LA to NY the speed is 50mph and upon returning to LA the speed is still 50mph. Einstein made a simple error, he added the speeds for the complete journey. His assumptions in the totals obviously went as follows the distance was twice the distance and also took twice the time so it must be twice the velocity too.
There was no acceleration or deceleration so throughout the journey the speed was always 50mph, without acceleration or deceleration there can be no increase or decrease in speed and the velocity for the experiment was supposed to be constant anyway. The solution to the problem is extremely simple but has drastic implications, replace the “minus” with a “plus” for the velocity component in the first equation, if we do this the equations come out correct for our journey. Upon further observation it will be realized that not only is time and distance variable but also velocity which by the very nature of this fact will permit an infinite number of solutions to any problem, an infinite number of input values will produce an infinite number of solutions everything is variable. It is a classical situation where the results justify the equations and the equations justify the results and can be made to fit any number of situations imagined, with the only requirements being that the end results need to be known.
The implications of this simple action however are enormous, destroying almost the complete theory of Einstein as this identical error is propagated right throughout the paper. The surprising thing is that if this one change is made and propagated through the paper, time dilation, length contraction and all of the paradoxes disappear. It would also appear that his famous equation E=MC² remains intact with the only exception being that the infinities disappear which commonly plague subsequent use of Einstein’s equations, virtually the perfect theory unfortunately it is a theory of nothing.