Mass and Time Dilation: Causes and Effects

[fishin_kitten]

Any idea why mass slows time down?
More mass more time dialation

 

[Orodruin]

It doesn't, it curves space-time. Time always runs at the same rate locally (1 second per second), but two observers following different paths in space-time may experience that different amount of time has passed. Mathematically this works out very similarly to how to different curves on a sphere can have different length. A geometrical description of this can be found in my Insight blog article for the case of special relativity (flat space-time), but the general concept is the same.

 

[fishin_kitten]

I get all that, gravity exists because things get sucked in by the gradient of time slowing down (I can show a chart of this if you want) I'm more asking why mass curves space-time. It's like Somthing slows the passage of communication more intrinsically than say glass or water.
1 Planck length per Planck time is typical, but it's as if Pt and Pl change in the presence of mass/energy

 

[stevendaryl]

I get all that, gravity exists because things get sucked in by the gradient of time slowing down

That might be your own theory, but that is not what General Relativity says. There is no sense in which mass causes time to slow down.

 

[Orodruin]

I get all that, gravity exists because things get sucked in by the gradient of time slowing down (I can show a chart of this if u want)

I do not need to see a chart to know that this is scientifically inaccurate.

I'm more asking why mass curves space-time.

To be more accurate, energy (of which mass is a type), momentum, and stress curves space-time. There really is no "why" here within GR apart from possibly referring to the action and the derivation of the Einstein Field Equations from there.

It's like Somthing slows the passage of communication more intrinsically than say glass or water.

Again, this is not how things work.

1 Planck length per Planck time is typical, but it's as if Pt and Pl change in the presence of mass/energy

No, they do not.

 

[Ibix]

I get all that, gravity exists because things get sucked in by the gradient of time slowing down

I think you're aiming at an analogy that some people use (the waterfall, or river, model, I think it's called). It's not generally applicable. The actual mathematics are more easily described as curved spacetime. That's what gravity is; that's all it is. Objects tend to move towards large masses because spacetime is curved and their inertial motion (their "natural" motion), which would be a straight line in flat spacetime, is curved towards the mass.

This curvature is responsible also for gravitational time dilation. It turns out that your wristwatch measures "distance" through spacetime in much the same way that your car's odometer measures distance through space. And in curved spacetime there can be inertial paths of different lengths between the same events. So that's why different observers can have different elapsed times between the same events.

Why does mass (or more generally, stress-energy) curve spacetime? No one knows. We expect a theory of quantum gravity will provide some answers, but we don't have one yet. And it'll have different "why" questions that we can't answer.

 

[Nugatory]

I'm more asking why mass curves space-time.

That's a fair question, but you may not be satisfied by the answer: "Because that's the way the universe we live in works." Empirical science is about discovering the laws that govern the behavior of our universe, and using that understanding. It's not so good at telling us why the laws are what they are and not something else.

Newton's theory of gravity has the same limitation. When Newton discovered that there's an inverse-square force between masses - ##F=Gm_1m_2/r^2## - we were suddenly able to explain an amazing range of phenomena, from the motion of planets to the trajectory of a thrown object to the spherical shape of the earth... but you could ask "WHY do masses attract?" and "WHY ##1/r^2## instead of (for example) ##1/r##?" and you'd get no better answer than that that's how the universe we're in works.

 

[pervect]

I get all that, gravity exists because things get sucked in by the gradient of time slowing down (I can show a chart of this if you want) I'm more asking why mass curves space-time. It's like Somthing slows the passage of communication more intrinsically than say glass or water.
1 Planck length per Planck time is typical, but it's as if Pt and Pl change in the presence of mass/energy

One can always ask "why". At some point, one has to stop asking "why", and just say "this is the hypothesis, and it seems to match observation".

However, the full theory of General relativity does not say that "mass slows down time". So the questions multiply. The first question should probalby be - what does general relativity actually say? And the followup question is, can that be interpreted in terms of "gravity slowing down time".

I would agree with Orodruin that what General relativity actually says is given by Einstein's field equations, ##G_{\mu\nu} = 8 \pi T_{\mu\nu}##. In words, this means that the left hand of the side, which represents the curvature of space-time, is proportional to the right hand side, which is the stress energy tensor. The stress energy tensor included "mass", but it also includes other things. Therefore it is better to say that "the stress energy tensor" curves space-time than to say that "mass curves space-time", though often we omit the details for B level posts, as the stress-energy tensor is most likely not familiar to B-level readers. Put into words, though, one can say that energy, momentum, and pressure all contribute to the stress-energy tensor, and that the stress-energy tensor curves space-time.

Given this understanding of what General relativity actually says, it's possible to ask "in what cases can we approximate this by saying that mass slows time?". It's not a totally non-viable way to understand part of the theory, but it's not the whole theory, either. First of all, one needs to ignore the effects of pressure and momentum. Second of all, one needs to simplify the curvature of space-time, which is a rank 2 tensor, to something that can be meaningfully be thought of as "slowing down time". This something is one component of the metric tensor, which is a larger entity. Under sufficiently restricted conditions, with the correct understanding of what the word means, one can approximate General relativity as saying that "mass slows down time", but it's not by any means the full theory.

But let's go back to the "why" quesiton. We note that the correct and full theory is summarized by ##G_{\mu\nu} = 8 \pi T_{\mu\nu}##. Can we ask "why" this is true? The only answer we can really give is that it works. There isn't any theory more fundamental than General Relativity that we currently know that can give us an answer to the "why" question. Perhaps at some date there will be a theory that explains "why" General relativity is true, in terms of some other more basic theory, but at the current time, there is no more basic theory than General relativity.

There was a recent thread on such "why" questions, with a post to a video lecture on Feynman's remarks. It wasn't about gravity, in particular, but it was about the general issue of why questions, and how to stop the infinite regress (that children notice at an early age), that no matter what explanation of events one offers, one can always ask "why" that explanation is true.