lengthcontractions

This section is going to explore some of the claims of relativity regarding length contraction. Length contractions are used to explain many phenomena; for example the results of the Micheson-Morley experiment. Earth is supposed to experience a small length contraction in the directions of its motion around the sun and this is just enough to justify the results of the experiment. On the other hand, relativity also claims, that for two observers moving relative to each other, they “appear” to length contract from each other’s perspective. Length contractions have to either be real or apparent, Can they be both? If we assume that contractions are ‘real’ for the Michelson-Morley experiment (MMX), then Earth motion through space also has to be ‘real’; that is, Earth’s motion in space around the sun is not relative.

For the MMX, the time that it takes light to travel the path parallel to the motion depends on the actual length of the path; not on an apparent length. If length contractions are real and the true explanation for the results of MMX; then defeating length contractions is not very difficult, and there are multiple ways.

One way of defeating length contractions is by the figure shown below.

A laser source is aimed at a mirror at an angle from the direction of motion. The mirror reflects the light back to the laser source where is detected by sensor. If the system is length contracted as in the next figure, then the mirror will not receive the light perpendicular to the surface and it will not be reflected back to the source.

If length contractions are appearances, then this will not apply; but then that does not explain the MMX.

Many explanations given for relativity use the concepts of “appearances”, and are presented just as different realities for different observers. This is not the way science works. Reality and appearances are not the same thing, and just because something appears a certain way, it does not make it a ‘reality’.

Consider the animation below for an object traveling at one-half the speed of light. In one case, the object may “seem” longer and the other case shorter.

This appearance is because the camera cannot take a picture of both ends at the same time. It is just an optical illusion. These type of explanation about relativity have nothing to do with relativity at all, they are only optical illusions.

Let's look at length contractions effects and their ramifications.

Let’s say that a solid object is subjected to a constant acceleration from a dead stop to a relativistic speed, to where length contractions effects are apparent. This is illustrated in the image below.

To the left is the initial position of the object, and, to the right, at the time acceleration stops and where the object is moving at a speed where length contraction has taken place.

Distance A is the distance traveled by the leading edge and B is the distance traveled by the trailing edge. It should be obvious that distance A is shorter than distance B, that is, the leading edge has traveled less than the trailing edge.

From the formulas for motion we have

d = d₀ + v₀t + ½ at²

Because we assume that d₀ and v₀ (initial distance and velocity) are zero, then the equation is reduced to:

d = ½ at²

Since the time of acceleration for both leading and trailing edges is the same, this implies that the acceleration is not the same for leading and trailing edge. This also implies that the trailing edge is moving faster than the leading edge when acceleration stops. Because acceleration stops, and therefore, length contraction effects stop, the object will experience a shock at this time, to balance out the difference in speeds at both ends. Being a solid it may very well survive, but this is a very strange effect if we accept that length contraction effects are real.

Let’s say we cut the object in half and place the two pieces end to end and then subject both to the same acceleration as before. What do we get now? Does length contraction affects only the total length, meaning they remain close to each other? Or do they experience length contraction effects individually and they separate? Both cases have serious problems. See illustrations below.

In case A, where length contraction occurs around a common Center of Gravity, the trailing object is moving faster than the leading object (it experiences higher acceleration) and they will crash into each other when acceleration stops.

In case B, where length contraction occurs around their individual Centers of Gravity, the objects are no longer end to end, they have now separated. Length contraction is supposed to be perceived by those in the same frame of reference as their original frame of reference, before they were accelerated. From that perspective, the objects have separated. From the objects own frame of reference, they both underwent the exact same acceleration and they are now in a new common frame of reference. From their own perspective, they should maintain the same position with respect to each other, that is, they are not length contracted and are still end to end and not separated. These two perceptions are obviously not the same and cannot both be true.

So, Are length contractions real?

Length contractions were invented to explain the Michelson-Morley Experiment as a real event; but then were later incorporated into the Theory of Special Relativity as an ‘apparent’ effect. They are not necessary. Doing away with length contractions has unusual consequences. For the muon in section 2.1 moving at near the speed of light towards Earth, Earth may seem to have length contracted, but at the same time, Earth’s objects may seem to move at hundreds of times the speed of light. The key word here is “seem”. This is again, just a temporal illusion. It is also important to note that no experiment has ever measured length contraction effects directly with any accuracy, empirical data are only “indications”, “the data seems to point in that direction”, “the effect can only be explained by”, etc. The accuracy of the Lorentz transformation for length contractions has never been verified. The only real length contractions are caused by acceleration. These length contractions vary for different materials depending of their modulus of elasticity; but this is a different subject related to the field of Mechanics.