Is the Twin Paradox a Misinterpretation of Relativity?

[Grimble]

It is said that Relativity proves that if one travels near the speed of light that time slows down, i.e. that the twin who travels ages less than the twin who stays behind (Twin Paradox) and that distances/lengths contract, but only in the direction of travel.

Yet a simple look at these two findings shews they are misinterpretations.

The speed of light, c, is the same wherever and however it is measured.
and speed is calculated by dividing the distance traveled by the time elapsed on the journey.

So if c = d/t and time is dilated (increases) while lengths contract (decrease) then the speed of light will change. > c would equal >d/t< which must be greater than d/t

Closer examination reveals that where a length contracts it is the units that contract or decrease (in Einstein's illustration of the metre rod it is the length of a metre that shortens not the length of the rod); while it is the total elapsed time or quantity of units that dilates or increases.

In fact the only way this can be reconciled is if both effects are applied to each quantity. So each has a greater number of smaller units.

The duration (quantity x unit size) of the Twin's journey is the same, but the measure (quantity of units) is dilated; while the size of those units is contracted.

So, in conclusion, the traveling Twin does not experience more time pass for each year aged as is implied in the traditional view, but rather, they experience LESS time pass for each year counted and consequently they age QUICKER than the stay-at-home twin, as each year is shorter and so more pass.

What is measured, the total time (unit quantity x unit size) and the total distance (unit quantity x unit size) don't change. It is the way that they are measured that changes to cater for the observer's motion.

 

[TumblingDice]

You've miss-interpreted the meaning of time dilation. Time dilation is the "stretching" of time. Clocks in a reference frame that's moving relative to another reference frame will tick slower. The decreased rate of time combined with contracted lengths support the consistency of c in all inertial reference frames.

 

[Dale]

In addition to Tumbling Dice's point, you also forgot the relativity of simultaneity. You have to use all of the Lorentz transform, not just pick and choose the parts that suit you.

It takes about two minutes worth of algebra to show that c is in fact invariant under the Lorentz transform, contrary to your claim.