B Does the gravitational distortion of mass still exist in the past?

[Giblet]

As our space rock hurtles through the infinite void. Acting under the assumption that the fabric of spacetime is a 4 dimensional space if one were to travel to a point on that fabric for a value of time that our 3 dimensional planet has already been to given that we're traveling "through" time and don't constantly occupy all values of it. Would the 4 dimensional fabric remain distorted in our absence as if it were a paused snapshot of what was, is, or ever will distort it for that value of time? I imagine it like moving a finger through the sand and even after the hand has passed the hole remains. The 4d fabric at Time=x was distorted by the earth when it reached Time=x. And so even when the Earth reaches Time=Y the distortion at Time=x will always remain

 

[Ibix]

You seem to be asking if masses leave some sort of trail in spacetime. The short answer is no, and the easy way to see it is to remember that this is relativity: it is equally valid to consider the a body as at rest or in motion, so there is no single true definition of "where it was in the past". So there can be no trail.

There are some slight exceptions to that. Orbiting bodies usually produce gravitational radiation. You can use the detected waves to deduce the motion of the emitting bodies, but it's more like ripples on a pond than a trail. It's also an indetectably tiny effect for anything except the final moments of colliding black holes - the Earth/Sun system emits around 100W of gravitational radiation, which is simply too small to be detectable.

 

[Giblet]

I'm very sorry but I believe this is an error in imagery. I'm not asking if mass leaves a trail that distorts the points in spacetime we currently occupy. But the points in spacetime we've left behind. If i were to delete the sun it would take 8.5 minutes roughly for the "ripple" to propagate to us but if i were to visit the value for T(time) where the sun were deleted and pause it by not varying the value for T that i occupy.

My understanding is that the gravitational distortion would appear to remain for that value of T until the value of T was changed. Even though the sun no longer occupies the space. And I'm curious to believe that simply because the sun has changed points in 3d space... If i were to move to the physical space it was and also change my value of T to match the *when* that it occupied.

Even though the 3d object making the distortion is no longer present the 4d fabric would still hold that distortion for that value of T regardless of where on the axis the 3d object currently is. Almost as if you were capable of rewinding a replay of a video but a single prop in that video continued to move forward in it even though you've rewound the scene. The effects the prop had would remain present though it would no longer be on screen.

 

[javisot]

As our space rock hurtles through the infinite void. Acting under the assumption that the fabric of spacetime is a 4 dimensional space if one were to travel to a point on that fabric for a value of time that our 3 dimensional planet has already been to given that we're traveling "through" time and don't constantly occupy all values of it. Would the 4 dimensional fabric remain distorted in our absence as if it were a paused snapshot of what was, is, or ever will distort it for that value of time? I imagine it like moving a finger through the sand and even after the hand has passed the hole remains. The 4d fabric at Time=x was distorted by the earth when it reached Time=x. And so even when the Earth reaches Time=Y the distortion at Time=x will always remain

Suppose you start with a flat spacetime (Minkoswki, for example) and add things to it—that is, we produce a certain curvature by adding some matter.

Now suppose you want to remove the things you've added; you should recover Minkoswki. If that doesn't happen, that is, if some trace like the one you described remains, it means the energy conditions have been violated.

In informal terms, space-time can be deformed elastically if all energy conditions are respected, or plastically if the energy conditions are violated.

 

[Giblet]

It still feels to me like the passage of time is required for elasticity to apply in this sense but I lack the education necessary to refute it. Thank you for your responses I appreciate it.

 

[Dale]

our 3 dimensional planet

Our planet is 4 dimensional, not 3 dimensional.

In spacetime, the earth is not a 3D sphere with a diameter of $13 \ 10^6\mathrm{\ m}$. It is a 4D cylinder with that diameter and a length of at least $4.3 \ 10^{25} \mathrm{\ m}$

I imagine it like moving a finger through the sand

It is more like a garden hose laid on the sand.

 

[256bits]

if one were to travel to a point on that fabric for a value of time that our 3 dimensional planet has already been

Are you asking if the Block Universe is a valid concept. That is what it seems you are describing, where all past, present, future 'points' in spacetime exist.
https://plus.maths.org/content/what-block-time


https://en.wikipedia.org/wiki/Growing_block_universe
This would be an analogy to the growing Block Universe. where past, present exist, but the future evolves.
https://en.wikipedia.org/wiki/Growing_block_universe

 

[phinds]

@Giblet just to be sure you are clear on this, space-time is NOT a "fabric" that can be stretched, bent, twisted, or otherwise acted on as though it had physical substance. Space-time is geometry. Period.

 

[Jaime Rudas]

As our space rock hurtles through the infinite void. Acting under the assumption that the fabric of spacetime is a 4 dimensional space if one were to travel to a point on that fabric for a value of time that our 3 dimensional planet has already been to given that we're traveling "through" time and don't constantly occupy all values of it. Would the 4 dimensional fabric remain distorted in our absence as if it were a paused snapshot of what was, is, or ever will distort it for that value of time?

As @Dale rightly points out, our planet is 4 dimensional, not 3 dimensional. The above implies that if at time $t_1$ the Earth is located at the coordinates $x_1$, $y_1$, and $z_1$, then at the coordinates $(t_1,x_1,y_1,z_1)$ of spacetime you will "always" find the Earth and its corresponding spacetime distortion.

 

[PeterDonis]

Would the 4 dimensional fabric remain distorted in our absence

The question doesn't make sense. In the 4 dimensional fabric, a massive object does not "move". It just is. It occupies a "world tube" within the 4 dimensional fabric, and the geometry of the 4 dimensional fabric, which also doesn't "change", it just is, takes into account the mass that's present inside that world tube.

 

[PeterDonis]

You seem to be asking if masses leave some sort of trail in spacetime. The short answer is no,

I would say that the short answer is that the question doesn't make sense. But if you consider the object's world tube as a "trail in spacetime", then the short answer is yes, not no.

 

[PeterDonis]

the points in spacetime we've left behind.

There is no such thing. A massive object doesn't "leave behind points in spacetime". It's a 4-dimensional "world tube" within the 4-d geometry of spacetime.

If i were to delete the sun

You can't. This violates the laws of physics. Asking what would happen if the laws of physics were violated is pointless, because the laws of physics are what we use to predict what would happen.

 

[PeterDonis]

Suppose you start with a flat spacetime (Minkoswki, for example) and add things to it

You can't; this would violate the laws of physics.

Again, it's pointless to hypothesize what would happen if the laws of physics were violated.

 

[PeterDonis]

In informal terms, space-time can be deformed elastically if all energy conditions are respected, or plastically if the energy conditions are violated.

Do you have a reference that supports this? It looks like personal theory to me, which is off limits here.

 

[Giblet]

The answer i needed was einsteins block space. Thank you. The communicational error was that I was unfamiliar with the concept and that my current idea of it is that the mass is itself 3 dimensional where the block is 4 dimensional. Rather than the mass being 4 dimensional. The block in space at certain values of t would distort to accommodate a 3d object when that specific object occupies that value of t independent when other 3d masses occupy that value of t in their path along the block. In this assumption my idea seems correct. In the idea that it's 4 dimensional then it's also correct but with an incorrect visual of space.

 

[PeroK]

The answer i needed was einsteins block space. Thank you. The communicational error was that I was unfamiliar with the concept and that my current idea of it is that the mass is itself 3 dimensional where the block is 4 dimensional. Rather than the mass being 4 dimensional. The block in space at certain values of t would distort to accommodate a 3d object when that specific object occupies that value of t independent when other 3d masses occupy that value of t in their path along the block. In this assumption my idea seems correct. In the idea that it's 4 dimensional then it's also correct but with an incorrect visual of space.

Whatever words you choose to string together, the physics is clear and unambiguous and is encapsulated in the Schwarzschild metric for the geometry around a spherically symmetric mass:$$ds^2 = \left(1-\frac{2GM}{rc^2}\right)c^2dt^2 -\left(1-\frac{2GM}{rc^2}\right)^{-1}dr^2-r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$

 

[Giblet]

This is an accurate response to how it would distort at that value of t but I don't believe it answers the question of whether it would. Its my feeling that The block shares a value of t with the mass within it even if the mass doesn't share that value with eachother. Such is the direction of my question.

 

[PeroK]

This is an accurate response to how it would distort at that value of t but I don't believe it answers the question of whether it would. Its my feeling that The block shares a value of t with the mass within it even if the mass doesn't share that value with eachother. Such is the direction of my question.

That's a complete description of the spacetime geometry - hence, a complete description of gravitation in this case. You must add, of course, the relevant extremal principle to define how to calculate the trajectory of a test mass in curved spacetime.

That's the physics of General Relativity in a nutshell. Something like:

As our space rock hurtles through the infinite void ...

is more poetry than physics, IMO.

 

[PeterDonis]

This is an accurate response to how it would distort at that value of t

No, it isn't. It is the metric of a 4-dimensional spacetime manifold that describes it at any value of the four coordinates. It is not a "snapshot" at a single value of t.

Its my feeling that The block shares a value of t with the mass within it even if the mass doesn't share that value with eachother.

This doesn't even make sense. I don't think you have fully grasped what it means to say that spacetime is a 4-dimensional manifold.

 

[Ibix]

I would say that the short answer is that the question doesn't make sense.

I would say we're disagreeing about whether he's wrong or even wronger.

But if you consider the object's world tube as a "trail in spacetime", then the short answer is yes, not no.

I was absolutely not considering the object's world tube as a trail. That is the object.

 

[Dale]

The block in space at certain values of t would distort to accommodate a 3d object when that specific object occupies that value of t independent when other 3d masses occupy that value of t in their path along the block.

Again, objects are not 3D, they are 4D. And in 4D every object occupies every t from the object’s creation to its destruction.

 

[Dale]

This thread was briefly closed and some feedback posts were moved to the feedback section. The thread is reopened

 

[PeterDonis]

I was absolutely not considering the object's world tube as a trail. That is the object.

I agree. But I think the OP has not grasped this fact--that what he is thinking of as a "trail" is actually the object itself, when you take a spacetime viewpoint.

 

[Ibix]

I agree. But I think the OP has not grasped this fact--that what he is thinking of as a "trail" is actually the object itself, when you take a spacetime viewpoint.

Ah - so (dropping a dimension for ease of visualisation) you (and @Dale) think the OP's mental model is that spacetime is a 3d block through which the Earth, a 2d disc, floats upwards like a flattened bubble rising up through lemonade?

If that's the case, @Giblet, then the problem with your understanding is that the Earth looks like a rod in that model. It appears circular to us because we only see the cross-section of it that's in the present (or, more precisely, on our past lightcone), but it is extended in time. It doesn't just exist now, it always existed (well, for the last 4bn years). So the geometry of space around the Earth one second ago never changes because the Earth never changes. We just look at cross-sections of it at different times and interpret that as motion through space.

 

[PeroK]

I personally believe that the earth being itself a 4dimensional object is closer to personal conjecture and currently subscribe myself to the belief that it is 3 dimensional in nature.

The Earth is physically a 3D object in space, but it's a 4D object in spacetime. In Newtonian (Classical) physics, vectors are generally 3D: displacement or momentum vectors, for example. In special and general relativity, vectors become 4D objects and are called four-vectors:

https://en.wikipedia.org/wiki/Four-vector

You posted this thread in the Relativity Forum, so we are generally talking about 4D spacetime - and not classical 3D space, with time as a separate and distinct dimension.

 

[Ibix]

I personally believe that the earth being itself a 4dimensional object is closer to personal conjecture

Unfortunately, the maths disagrees with you.

My question inherently sought opinion on whether the "trail" would remain.

Whether there would be a trail behind a 3d object moving in a 4d spacetime is unanswerable because it is not a situation you can describe in general relativity.

I am not a 4 dimensional being.

Yes you are, at least as modelled in general relativity. You may not want to believe that, and that's fine, but then you can't discuss general relativity because you are refusing to accept the model on its terms. It's like trying to understand how a light switch works while rejecting the notion of electric current. The theory will never make sense to you, even though everyone else is able to use it to make accurate predictions.

 

[Ibix]

After all 2 dimensional objects can move through a 3 dimensional space without themselves turning 3 dimensional.

If time is something other than one of those three dimensions, sure. But that's not the case in relativity. Time is one of the dimensions. When you imagine watching a 2d object move through the 3d object you are imagining the model changing with respect to another time parameter (the one in the real universe, in fact) that is external to the model.

So you aren't thinking about relativity. You're thinking about relativity (or some misconception thereof) plus a second concept of time for which there is no evidence.

 

[weirdoguy]

Unfortunately i am very sorry but I haven't been capable of finding anything on this particular idea that has caused me to change my view.

So I wonder why did you come to scientific forum then. Universe doesn't care about your views, it works the way it does, we can't pick and choose what we like.

 

[PeterDonis]

I personally believe that the earth being itself a 4dimensional object is closer to personal conjecture and currently subscribe myself to the belief that it is 3 dimensional in nature.

Sorry, but the Earth being 4-dimensional is not "personal conjecture". It's what our best current theory of gravity, General Relativity, says. You don't get to just ignore parts of our best current theories that you don't like or can't understand. You've been given very good responses on how that theory works. If you don't want to listen, there's no point in further discussion. There is certainly no point in you posting your own personal speculations (which is off limits here in any case).

Thread closed.