1

According to General Relativity and its experimental tests, a clock far above Earth ticks faster than it does on the surface of Earth. Because near the surface of the Earth space-time curvature is deeper. But I don't get why.

G. Smith
  • 51,534
Pərviz Piri
  • 23
  • 4
  • In mechanics, did you learn what a “potential well” is? – G. Smith Oct 25 '20 at 20:34
  • 2
    "Deeper" is not a meaningful comparative adjective for describing curvature. If you want to know why gravitational time dilation happens you'd need to learn some general relativity. – Charlie Oct 25 '20 at 20:45
  • 1
    But gravitational time dilation can be related for weak fields to the Newtonian gravitational potential, for which “deeper” in the potential well is meaningful. – G. Smith Oct 25 '20 at 20:49
  • Yes, where the object has less potential energy than it's surroundings. – Pərviz Piri Oct 26 '20 at 06:05
  • 1
    Time doesn't slow down, because of the curvature. Time slowing down is the curvature. – safesphere Oct 28 '20 at 21:21
  • @safesphere No, time slows in flat spacetime in accelerated frames too. Gravitational time dilation is related to the gravitational potential (where one can be defined), not the curvature. You can have time dilation without curvature and curvature without time dilation. Time slowing is not the same as curvature – Dale Oct 28 '20 at 22:23
  • @Dale I’ve already seen your incorrect answer, no need to repeat your misconceptions in comments. Spacetime curvature is not a scalar. – safesphere Oct 29 '20 at 17:56
  • @safesphere Indeed. Spacetime curvature is a tensor, so time dilation cannot possibly be curvature. You contradict yourself. – Dale Oct 29 '20 at 18:40
  • @Dale Please don't contact me again with your misconceptions and misunderstanding of what is stated. Your intolerance is unwelcome. – safesphere Oct 29 '20 at 19:28
  • 1
    @safesphere I have just as much right to post here as you do. SE is not your personal blog. When you comment in the public part of a forum you are in fact saying that you do welcome responses from the public community of the forum. If you do not wish public responses, then open private chats with the people that you do want responses from. Otherwise public commentary is an inherent part of posting on SE – Dale Oct 29 '20 at 19:38

1 Answers1

7

This is a very common misconception. Although in the Schwarzschild metric there is both more curvature and more time dilation lower down, the two are not directly related. In fact, in other spacetimes they are clearly decoupled. In the Rindler metric there is time dilation but no curvature, and in FLRW spacetime there is curvature but no time dilation.

Instead, time dilation is directly related to the gravitational potential. Locations with a lower gravitational potential have greater gravitational time dilation regardless of the curvature. The reason why the gravitational potential is the key can be understood in terms of gravitational redshift. As light goes up it loses energy and therefore becomes red-shifted. If two objects maintain the same relative distance then the redshift can be attributed to gravitational time dilation.

Dale
  • 99,825