Special Relativity (alternative Formulations) - Taiji Relativity

Taiji Relativity

Equivalent to the original ? Yes.

This section is based on the work of Jong-Ping Hsu and Leonardo Hsu. They decided to use the word Taiji which is a Chinese word meaning the ultimate principles that existed before the creation of the world. In SI units, time is measured in seconds, but taiji time is measured in units of metres — the same units used to measure space. Their arguments about choosing what units to measure time in, lead them to say that they can develop a theory of relativity which is experimentally indistinguishable from special relativity, but without using the second postulate in their derivation. Their claims have been disputed. There is a discussion of taiji relativity in the book.

The transformations that they derive involve the factor where β is the velocity measured in metres per metre (a dimensionless quantity). This looks the same as (but should NOT be conceptually confused with) the velocity as a fraction of light v/c that appears in some expressions for the Lorentz transformations. Expressing time in metres has previously been done by other authors: Taylor and Wheeler in Spacetime Physics and Moore in Six Ideas that Shaped Physics.

The transformations are derived using just the principle of relativity and have a maximal speed of 1, which is quite unlike "single postulate" derivations of the Lorentz transformations in which you end up with a parameter that may be zero. So this is not the same as other "single postulate" derivations. However the relationship of taiji time "w" to standard time "t" must still be found, otherwise it would not be clear how an observer would measure taiji time. The taiji transformations are then combined with Maxwell's equations to show that the speed of light is independent of the observer and has the value 1 in taiji speed (i.e. it has the maximal speed). This can be thought of as saying: a time of 1 metre is the time it takes for light to travel 1 metre. Since we can measure the speed of light by experiment in m/s to get the value c, we can use this as a conversion factor. i.e. we have now found an operational definition of taiji time: w=ct.

So we have: w metres = (c m/s) * t seconds

Let r= distance. Then taiji speed = r metres / w metres = r/w dimensionless.

But it is not just due to the choice of units that there is a maximum speed. It is the principle of relativity, that Hsu&Hsu say, when applied to 4d spacetime, implies the invariance of the 4d-spacetime interval and this leads to the coordinate transformations involving the factor where beta is the magnitude of the velocity between two inertial frames. The difference between this and the spacetime interval in Minkowski space is that is invariant purely by the principle of relativity whereas requires both postulates. The "principle of relativity" in spacetime is taken to mean invariance of laws under 4-dimensional transformations.

Hsu&Hsu then explore other relationships between w and t such as w=bt where b is a function. They show that there are versions of relativity which are consistent with experiment but have a definition of time where the "speed" of light is not constant. They develop one such version called common relativity which is more convenient for performing calculations for "relativistic many body problems" than using special relativity.