## The different kinds of time dilation, invariance of proper-time and principle of equivalence

November 5, 2011

Mohan, mdashf

this is a featured blog on wordpress “Physics”

NOTE: this blog will be majorly updated to reflect the latest ideas I have made elsewhere reg. this. and a diagram that will make the situation clear. Basically it will show you why all Doppler effects are time dilations and contractions (red and violet/blue shift) and gravitational effects are also either contracted or dilated times, depending on the exact situation.

Just how many kinds of time dilations are there permitted by Theory of Relativity. The answer is for a recession of source from observer there are 3 types. i. time dilation ii. time dilation due to Dopler effect iii. time dilation due to gravitational field. SO 1st two of these are special relativistic and the 3rd one is a general relativistic effect. We are considering only source receding away from observer or from center of gravitational potential. For the reverse motion that is source approaching the observer the 1st effect is same but the 2nd (Doppler effect) and 3rd effects change. Interestingly this means 1st effect is always a red-shift, **increase of time period, decrease of frequency, increase of wavelength**. The 2nd effect is Doppler effect which for recession that is positive velocity or velocity that takes the source away from observer the effect is red-shift. **increase of time period, decrease of frequency, increase of wavelength** This can occur in an angle between the source-observer line and line of sight. Hence it’s an angular distribution of frequency shift but all of them are red shifted. For 2nd effect if the speed is negative that is source and observer are in relative approach the effect will always be anti-red shifted or as is known violet-shifted, again a distribution in angle which is extended towards translational vantage and line of sight vantage. (perpendicular to line of sight that is) The 3rd effect for positive speed or recession takes us away from the gravitational potential hence increases the potential energy and decreases time dilation. This means it’s a blue or violet shift for speed of recession. If the speed is negative that is source and observer (observer at center of potential) are in relative approach the potential energy decreases SO this produces a red-shift just. Note that the last effect does not produce additional shift if there is no relative speed, such as a satelite in orbit, here there is only a time-offset because of the relative strength of the gravitational potential at point of source and observer. This was a casual description. In the more suitable description you can consider 3 things, i. the speed of recession in a gravity potential itself gives Doppler effect time dilation. ii. It’s the position in the gravity potential that determines the gravitational or general relativistic time dilation. From principle of equivalence you have accelerations, rotations and perturbations in the gravity potential that gives to time dilation, also temperature to a very high degree such as 3000 deg. K can produce large time-shifts. It’s for this reason that radiation pressure of Sun is calculated in GPS satelite clocks. iii. The speed of satelites such as lower altitude GPS clocks can also be taken into consideration for time-dilation. The points ii and iii are the type 3 effects here.

You can call the 1st effect Lorentzian time dilation to avoid ambiguities …

The most important thing to remember in special theory of relativity, apart from it’s basis concepts i. speed of light invariance and ii. invariance of physical laws or Lorentz invariance is this: proper-time intervals are the same in all frames of references moving inertially wrt each other. That is propertime is a Lorentz invariant quantity. A square of any proper-time is a squared difference between the space and time length of any two events in their respective frame. When you change frames this quantity will again be the same for the same two events, that is the square of the propertime as is propertime itself, being defined as a square difference of space and time separation of two events are the same for these two events for all sorts of inertial observer no matter what their speed is wrt each other …