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

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.

The details of the above statements have been published as a paper in various archives: here is the link [https://mdashf.org/2012/01/17/article-doppler-shift-and-time-dilation-binomial-analysis/]

Article: Doppler Shift and Time Dilation, binomial analysis
mdashf.org
1. Dash, M. & Franzén, M. (2012). Time dilation have opposite signs in hemispheres of recession and approach. PHILICA.COM Article number 312.  2.University of Texas, Mathematical Physics, Mathe …

so I will not update this article for above promises of adding diagrams. etc The paper has the diagrams.

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 Doppler effect

iii. time dilation due to gravitational field.

In-fact effect-i is a special case of effect-ii as shown in the paper above.

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,

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. 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. (Needs to be reviewed >> this statement:  perpendicular to line of sight that is)

A nomenclature issue: Yes violet-shift is a legitimate use synonimous with blue-shift. One can refer Weinberg’s text where violet-shift is widely used. I read somewhere in the wild alleyes of internet that violet-shift is an illegitimate usage which is nothing but incorrect and imature thinking. There is nothing that stops us to name it violet-shift if there is time contraction. It need not be blue and there can not be a strict reason physically that physical phenomena must appear blue now. It depends on the amount of time contraction that is occuring. In-fact one can also use IR-shift for time contractions. It just denoted the sign of time dilation is -ve or positive.

An interesting issue: The candles on ISS [international space stations] appear blue and is sphericalized due to lesser gravity. Again the lesser gravity means lesser time-dilation which is what blue-shifts are in a relative way. So one needs to study the detail of the candle phenomena on ISS to confim this.

A conceptual issue: Yes time is contracted as is it is dilated. In-fact if it were not so Relativity would lose some of its meaning. This has been worked out in the above paper. Also in space/distance there is both contracted and dilated effects. Conceptually time dilation is an energy-dilation-contraction and through equivalence of physical quantities could mean contraction-dilation. The basic idea is its energy which causes time dilation-contraction whether kinetic energy, potential energy, gravitational energy or heat energy. I mention contraction-dilation because from time-dilation or time-contraction alone its not clear which way enrgy pr momentum will be dilaed or contracted. Its just 4-vector formulation. So anyone can write an outstanding paper on these conceptual notes to show how energy is dilated-contracted based either on time-dilation or on time-contraction. I have worked out in the paper only different situations leading to dilation or contractions of time. I hope my paper will be useful in this regard as it rests on a powerful method of binomial analysis.  

[I wrote this with Mikael Franzen and he helped it reaching wider audience. I would like this paper to be published in a regular Journal, as I have mentioned the “Invariance Publishing House of MDashFoundation” copy, that is, the mdashf.org copy linked above is the correct and further reviewed copy of the paper which is correct in relation to a few errors in the archive cop(y/ies)]

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. Note that the last effect does not produce additional shift if there is no relative speed, such as a satelite in circular orbit, here there is only a time-offset because of the relative strength of the gravitational potential at point of source and observer. Actually the circular orbit means a transverse Doppler shift which accumulates gradually as time passesby.

This was the reason OPERA anomaly was considered to be coming from effect of time-measurement due to GPS satellite. The OPERA anomaly has been greatly dealt in this web-journal and the details were worked out why GPS satellite does not add any significant proportion of error. In-fact the error the GPS satellite adds to OPERA-baseline of 2.43 ms was calculated to be thousands of time smaller than the ns level accuracy. 

The above description of types of dilations and contractions were 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. [SR-theory]

ii. It’s the position in the gravity potential that determines the gravitational or general relativistic time dilation. [GR-theory]

From principle of equivalence you have accelerations, rotations and perturbations in the gravity potential that leads 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.

Not sure why I wrote the following and I have striked this out, needs further review

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 proper-time 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 proper-time as is proper-time 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. …

If you ask any undergrad in Physics or even many in the advance level (I would have said the same thing as these referred people) what is principle of equivalence?: the answer will be invariably “it says the gravitational mass and the inertial masses are the same”.
But that is in addition to what implication it has for the laws of Physics.
If and when a gravitational force is involved and no generality is lost and the laws of physics are the same in addition to the two types of masses being equivalent
**as is observed experimentally to certain degree for elementary particles
i. for individual particles almost to 1 part per million
ii. with binding energy of these particles considered to 100 parts per million**
The above is called a “principle of equivalence” or a “strong principle of equivalence”. Under such equivalence all laws of physics known are supposed to be valid.
If only the gravitational force laws are exempted from such considerations and this is extended to encompass all other force laws such as special relativistic and electromagnetic and other such laws it is called a “medium strong principle of equivalence”.
If the laws of physics that are encompassed only as far as the simple kinematical laws (as is known in the Newtonian scheme?) but the statement of equivalence of gravitational and inertial masses are used it is called a weaker principle of equivalence. Most people would state only this weaker form of equivalence which is what Newtonian or Galilean Physics is all about. This is like saying the Galilean principle of Relativity when asked about principle of relativity [of Einstein].

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