This document contains comments about the article Gravitational time dilation in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass.
Newton predicted the same for pendular clocks.
The higher the gravitational potential (the farther the clock is from the source of gravitation), the faster time passes.
There are two issues: A gravitational mass issue and a speed of light issues.
Both issues can have consequences on the stability of a clock and its capability to show the correct time.
However this has no consequences how fast time i.e. some indication of universal time passes.
This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times.
See above for Newton. When this has been demonstrated by actual experiments you should remove the word: eventually.

### 4. Important features of gravitational time dilation

• According to the general theory of relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame
The first question you have to answer is: what is an accelerated reference frame.
An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly.
Very, very 'strange' sentence.
Additionally, all physical phenomena in similar circumstances undergo time dilation equally according to the equivalence principle used in the general theory of relativity.
First of all you need some experiments.
Part of the problem is that always and everywhere there is mass and gravity.
When you jump from a building, when you fly in an airplane, when you fly to the moon, when you travel in interstellar space, in each and all these places there is gravity. Maybe very very small, but is is there.
• The speed of light in a locale is always equal to c according to the observer who is there.
The next sentence is much easier to understand.
The speed of light in any point p in space is always c.
The question is what does it mean? And: is it true?
That is, every infinitesimal region of space time may be assigned its own proper time and the speed of light according to the proper time at that region is always c.
The proper time is the local time (of a clock) at any point p (in space). Replace the last sentence with:
and the speed of light according to the proper time at that region is always equal to the speed of light
or c = c. What does that mean?
This is the case whether or not a given region is occupied by an observer.
Ofcourse. Observers have nothing to do with the physical processes involved. (At the same part observers should be aware of their limitations)
A time delay can be measured for photons which are emitted from Earth, bend near the Sun, travel to Venus, and then return to Earth along a similar path.
compared to what? When you perform 'the same' experiment, different results are possible because the situation (position of the Sun and planets) can be different.
There is no violation of the constancy of the speed of light here, as any observer observing the speed of photons in their region will find the speed of those photons to be c, while the speed at which we observe light travel finite distances in the vicinity of the Sun will differ from c.
This is easy to write but very difficult to test experimental.
This sentence seems to indicate that locally the speed of light is c, but outside this range it will differ.
• If an observer is able to track the light in a remote, distant locale which intercepts a remote, time dilated observer nearer to a more massive body, that first observer tracks that both the remote light and that remote time dilated observer have a slower time clock than other light which is coming to the first observer at c, like all other light the first observer really can observe (at their own location).
Please call me if you understand.
If the other, remote light eventually intercepts the first observer, it too will be measured at c by the first observer.
Ofcourse.
Simplicity winns.
• Time dilation in a gravitational field is equal to time dilation in far space, due to a speed that is needed to escape that gravitational field.
Here is the proof.
2. Escape velocity from g is 2*G*M / r
3. Time dilation formula per special relativity is t0 = tf*sqr(1 - v^2 / c^2)
4. Substituting escape velocity for v in the above t0 = tf*sqr(1 - 2*G*M / r*c^2)
Proved by comparing 1. and 4.
This definitly does not constitute a proof. The only thing that is true, is that it is mathematically correct.

### Reflection 1 - Gravitational Time Dilation versus the speed of light.

"Gravitational Time Dilation" and "the speed of light is not constant in a gravitational field" are two parts of the same coin. They describe the same physical issues
My understanding is that "Gravitational Time Dilation" 'supports the idea' that two identical clocks at different heights above the earth run at different speeds.
In a gravitational field the speed of light is not constant. This phenomena is important for clocks which use light signals to operate, to tick at different rates.

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Created: 3 November 2017
Modified: 6 July 2018

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