relativity theory

How time dilation on GPS clocks is induced by static and spinning earth observations.

The image above shows earth at an altitude of 20200 + 9.08 km. The red line I drew is a straight line of 696 km, 3-D straight line — perhaps non-Euclidean, near the CERN – Gran Sasso Baseline, parallel to the latter, which is not straight and about 733 km long.

— Isn’t that a reason to worry?

This altitude is where the GPS satellites are “falling towards earth”.

Why should different baseline ends not introduce any error, to synchronization?

Also if we┬áimagine 13.7 km/s at this altitude, the satellite is almost not moving. It takes 2 minutes for a deviation of 1 degree angle on earth surface — or anywhere, which is “49000 time of flights” of a neutrino bunch from CERN to Gran-Sasso.

That is, 3.54375 E-7 rad / time-of-flight.

The earth spin is 3.000823 E-2 rad / time-of-flight — earth spin being 7.292 E-5 / s.

I have shown that static earth effect is less than 1 pico-sec — special-relativistic-effect is small and negative, compared to general-relativistic-effect.

Spinning earth effect being 1% order of static earth, and earth spinning speed being E-5 orders higher, than satellite angular speed, again the “1% general relativistic effect of 1 pico-sec” will preside over the special relativistic effect, of the satellite.

So, the non-inertial effect of earth, will be ~1% of static earth, which is 1 picosecond. In other words, the total relativistic effect, of the GPS satellite, considering even earth-spin will be, within, about, 1-pico-sec.

We need not worry about this.

The time-energy uncertainty relation.

The time-energy uncertainty relation is a blessing in disguise which comes in handy to check various values that are quoted, so as to see if something is inconsistent or not. It’s very powerful in guiding to check if we are ourselves making something silly or not.

I have described in two recent articles — will link later, why.

1. One must be careful what energy and what time one is relating to, one just does not take any time and any energy and make a relation, in-fact one can see who is a good physicist from one who is a novice, by seeing how this relation is used by him.

This was joked by Landau: I can measure the energy and then look at my watch, time is just a parameter. But Einstein and Niels Bohr argued “during a very short time interval one must be careful what energy is allowed and what is not, there is a constraint on the windows of errors or uncertainties”.

2. Life-times are arbitrary variables as are energies, their means are not necessarily linked inversely as in case of the uncertainty relation itself, the latter gives a relation between the error-window which are linked inversely.

So watch out how much inconsistent description is given in an average article eg in Wikipedia and even in our text-books. These are training the future physicists very wrongly. One needs experience of solving good problems, one is to work in experiments of highest standard and understand them.

Why the neutrino and photon broke up? And why neutrino runs faster than photons?

The photon and neutrino are now separated but they seem to have a chat to their friends and dear ones what was the cause. It turns out that “little thing” was responsible why the neutrino arrived a little faster. They are now happy to be living separated but their boken heart is still singing. And here is a picture how the neutrino and photons look like.