Does Mass Have Lasting Gravitational Effect Over Time?

[kyle1320]

I've been thinking about gravity. If mass contracts spacetime, can the warping effects be measured in time as well as spatial distance?

For example -- say you had some matter that suddenly disappeared (please ignore the "how"). Measured in a fixed position, would the gravitational effect drop off instantly, or would it drop off following a curve something like $\frac{1}{t^2}$ (or perhaps $\frac{1}{c^2t^2 + d^2}$ at a spatial distance of $d$), as you got "farther" from the mass in time?

I assume the effect would hardly be measurable, but my thought is that over time this effect would accumulate.

Is there any truth to this line of thought?

 

[PeterDonis]

say you had some matter that suddenly disappeared (please ignore the "how")

You can't. Mass can't just suddenly disappear in General Relativity. So you can't base a scenario on assuming that it can. You can't use the laws of physics to analyze a scenario that violates the laws of physics.

The general concept you appear to be groping toward is how changes in a gravitational field propagate in GR. The short answer is that they propagate at the speed of light; such propagating changes, at least in the linear approximation, are gravitational waves. Heuristically, gravitational waves propagate changes in spacetime curvature that result from masses wiggling around, just as electromagnetic waves propagate changes in the electromagnetic field that result from charges wiggling around. But you can't analyze such things by hypothesizing that mass or charge just disappears.

 

[FactChecker]

When gravitational waves reach the Earth from an event at a great distance, the light from the event can be detected at about the same time as the gravitational wave. Also, the timing difference between gravitational detection sites on Earth can be used to triangulate and (roughly) determine the direction of the event.

 

[kyle1320]

You can't. Mass can't just suddenly disappear in General Relativity. So you can't base a scenario on assuming that it can. You can't use the laws of physics to analyze a scenario that violates the laws of physics.

Fair enough. Then suppose you have some mass in motion. The effect I'm suggesting could be measured as a "trail" left behind by the object, as its gravitational effect propagated through time in its old position.

To be clear, I'm not asking about the propagation in space. I'm asking whether the changes also propagate in the "time" dimension of spacetime.

 

[Orodruin]

To be clear, I'm not asking about the propagation in space. I'm asking whether the changes also propagate in the "time" dimension of spacetime.

They do, but not in the way you are imagining it of leaving any sort of ”trail” behind at the ”place” where it was. There are many many things that are problematic with such an idea in relativity.

 

[kyle1320]

They do, but not in the way you are imagining it of leaving any sort of ”trail” behind at the ”place” where it was. There are many many things that are problematic with such an idea in relativity.

Can you explain more in what ways "they do"? I understand that "the place" isn't absolutely defined, so how would this be resolved?

 

[Orodruin]

Can you explain more in what ways "they do"? I understand that "the place" isn't absolutely defined, so how would this be resolved?

Changes propagate in both space and time. It takes time before the changes are noticable at a different place. Changes where whatever happened that leads to a different scenario are immediate.

As it does not function the way you are probably imagining, there really is no issue here to be resolved.

 

[kyle1320]

So is the warping of "spacetime" really just warping of the spatial dimensions (that propagates outward at the speed of light)? And the effects of warped time only come as a result of something traveling through that warped space?

 

[Orodruin]

So is the warping of "spacetime" really just warping of the spatial dimensions (that propagates outward at the speed of light)? And the effects of warped time only come as a result of something traveling through that warped space?

No and no. The temporal curvature components are particularly important when considering classical approximations of GR.

 

[kyle1320]

Perhaps my confusion is from thinking of the time dimension as similar to the physical dimensions. The concept of four-velocities made a lot of things make sense to me, but I suppose it isn't something that can be generally applied to other concepts like gravity.

 

[Orodruin]

Perhaps my confusion is from thinking of the time dimension as similar to the physical dimensions.

Your problem seems rather the opposite to me, not thinking about spacetime but more about space and time. That the two are intertwined is even more accentuated in GR.

 

[PeroK]

Fair enough. Then suppose you have some mass in motion. The effect I'm suggesting could be measured as a "trail" left behind by the object, as its gravitational effect propagated through time in its old position.

To be clear, I'm not asking about the propagation in space. I'm asking whether the changes also propagate in the "time" dimension of spacetime.

In simple terms, if you have a time-dependent mass distribution, you must have a time-dependent gravitational field.

In classical electromagnetism, when a particle is moving there is the concept of a "retarded potential", which more or less says that the EM field propagates at the speed of light.

You could do some reading on that.

The equations governing EM are linear, but the equations governing GR are non-linear. This means that trying to encapsulate the behaviour of the propagation of gravity is more complicated. As mentioned in post #2 above, in the linear approximation we have gravitational waves.

A general point about your other posts. You can't understand GR (or any physics) just be getting the right words in the right order. You have to describe things in at least a semi-mathematical form for it to make any real sense.

So something like:

Perhaps my confusion is from thinking of the time dimension as similar to the physical dimensions. The concept of four-velocities made a lot of things make sense to me, but I suppose it isn't something that can be generally applied to other concepts like gravity.

Is never going to be precise and unambiguous enough to elicit a good response or help you better understand GR.

 

[kyle1320]

Your problem seems rather the opposite to me, not thinking about spacetime but more about space and time. That the two are intertwined is even more accentuated in GR.

Ok but if it is similar, shouldn't it stand to reason that the gravitational changes will propagate in all dimensions, including orthogonal to the spatial dimensions / in time only? So at a future point in time, the effect can be measured even if the object has since moved?

 

[PeroK]

Ok but if it is similar, shouldn't it stand to reason that the gravitational changes will propagate in all dimensions, including orthogonal to the spatial dimensions / in time only? So at a future point in time, the effect can be measured even if the object has since moved?

You badly need to take a course in classical electromagnetism!

 

[Orodruin]

Ok but if it is similar, shouldn't it stand to reason that the gravitational changes will propagate in all dimensions, including orthogonal to the spatial dimensions / in time only? So at a future point in time, the effect can be measured even if the object has since moved?

As PeroK said, stop trying to do physics by stringing words together. It is not productive. The way you keep talking about gravity is simply not how gravity works.

 

[kyle1320]

As PeroK said, stop trying to do physics by stringing words together. It is not productive. The way you keep talking about gravity is simply not how gravity works.

Oook. I did label this with a [ B] tag. If you want to formalize things to help explain then feel free. I wouldn't really know where to start.

Clearly I'm misunderstanding something fundamental here but it'd be nice to figure out what it is without needing courses in electromagnetics

 

[PeroK]

Oook. I did label this with a [ B] tag. If you want to formalize things to help explain then feel free. I wouldn't really know where to start.

Clearly I'm misunderstanding something fundamental here but it'd be nice to figure out what it is without needing courses in electromagnetics

Although he lived 800 years ago, Roger Bacon was spot on:

"Whoever then has the effrontery to study physics while neglecting mathematics must know from the start that he will never make his entry through the portals of wisdom."

Roger Bacon (1214-84)

 

[Dale]

shouldn't it stand to reason that the gravitational changes will propagate in all dimensions

They do. They propagate at c, so they propagate in space and time at the maximum rate possible.

 

[PeterDonis]

I'm misunderstanding something fundamental here but it'd be nice to figure out what it is without needing courses in electromagnetics

General Relativity is a classical field theory. I don't know of any simpler way to understand how classical field theories work than to first learn how the simplest such theory, classical electromagnetism, works.

 

[PeterDonis]

shouldn't it stand to reason that the gravitational changes will propagate in all dimensions, including orthogonal to the spatial dimensions / in time only? So at a future point in time, the effect can be measured even if the object has since moved?

What does this even mean?

We can't respond usefully to your questions because we have no idea what they mean. They look like word salad to us. They don't correspond to anything that we know of in the actual theory of GR.

Is there any truth to this line of thought?

Given my comments just above, I think the answer is "no".