How did Einstein know that gravity alters time? - by Rick McGeer - Quora Question review

This document contains a review of the answer by Rick McGeer on the question in Quora: "How did Einstein know that gravity alters time?"
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• The text in italics is copied from the article.
  
• Immediate followed by some comments
  

Contents

• 1. Answer Review

Reflection

• Reflection 1 - Question Review

1. Answer Review

The Equivalence Principle. https://en.wikipedia.org/wiki/Equivalence_principle

You cann't use any principle to answer the question.

The equivalence principle says that a person in a closed laboratory cannot, even in principle, run an experiment that will tell him whether he is on the surface of the Earth or in a rocket ship accelerating at 1 g.

In order to understand what you write, you must perform experiments.

So now let’s do a thought experiment. Consider two observers, Nancy and Tom. Nancy is in the nose of an accelerating spaceship of length r , Tom is in the tail. They agree to send flashes of light to each other, one per second (this is the standard way that separated observers compare clocks). The spaceship is accelerating at g

You can also not use a thought experiment to demonstrate any physical phenomena.

Let’s examine the situation from Tom’s perspective. Nancy emits a flash of light, and it takes time r/c to travel the length of the ship to Tom. But in that time, Tom has acquired a velocity of gr/c with respect to the frame in which the flash was emitted. Since this is independent of the flash, Tom is always traveling towards the light source with velocity gr/c . Thus, due to the Doppler Effect, he sees the flashes have a frequency of √(1+β)/(1−β)
Where β=v/c=grc^2 . Given g,r we could do the numerical calculation, but as soon as we see β>0 we know that Tom receives flashes faster than once per second: 1+β1−β>1 . Hence he concludes that Nancy’s clock is running faster than his.

Now let’s look at the situation from Nancy’s perspective. She acquires a velocity of −gr/c from the frame in which Tom emitted the light, and so Nancy is always traveling away from the light source with velocity gr/c . Again according to the Doppler Effect, she receives flashes with a frequency of Sqrt(1−β/1+β)

Since β>0 we know that Nancy receives flashes slower than once per second: 1−β/1+β<1 . Hence she concludes that Tom’s clock is running slower than hers. Note that the rates are exactly symmetric here: if Tom thinks that Nancy’s clock is running at f ticks per second, Nancy thinks that Tom’s clock is running at 1/f ticks per second.

Now let’s put Tom and Nancy in a lab on the surface of the Earth, at exactly r apart, with Tom below Nancy. Once again, they exchange flashes.
By the equivalence principle, the results must be exactly the same as the results in the rocket ship: Tom must receive flashes at Sqrt(1+β/1−β) ticks per second, and Nancy must receive flashes at √(1−β/1+β) ticks per second.

Just for fun, let’s do the numerical calculation. Assume r=10 , g=9.8 ; we are using meters for our unit of distance and seconds for time, so c=3×10^8 . So β=98/9×10^16 = 1.09×10−15 . if we plug this in, and take the Taylor expansion of √(1+x)/(1−x)=1+x+O(x2) we see that Nancy’s clock runs faster than Tom’s by 1+1.09×10^−15 ; about a quadrillionth of a second per second faster. This is tiny, of course — Nancy will gain about 34 nanoseconds per year. But it’s detectable using precision clocks, and this was done in the Hafele–Keating experiment https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment. And, of course, the results of the experiment were in full agreement with GR.

The Hafele-Keating experiment is an experiment in its own right. To mention this experiment is the 'simple' answer on the question.

To answer the question "How did Einstein know that gravity alters time?" the Hafele–Keating experiment can be mentioned. https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment. The most important part is the physical reasoning about this experiment.
In simple reasoning: The lightpath of a vertical lightsignal in a clock at rest is shorter than a vertical lightsignal in a horizontal moving clock. That means if the moving clock also is moved backwards to its original position and both clocks can be compared than the clock at rest will show more ticks than the moving clock. Implying that the moving clock runs slower.
However and now comes the most important point: That does not mean that this has any influence on what you could call the age of universe or universal time
The time in the question: "How did Einstein know that gravity alters time?" is in fact the time of a clock. In fact to do physics you should use universal time.

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