Distortion of Space Time

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Summary:

Does mass draw space-time in to it?

Main Question or Discussion Point

Presume we look at a two-dimensional view of space time, with no local masses, and we draw a grid of equidistance spaced lines. The intent is to look at space but not time.
As we begin, we look in all directions and the grid lines are evenly spaced.
Begin adding mass to the center of the grid. To my understanding, so far, the mass will draw the lines of space in towards it. They become closer together in closer to the mass.
We might also draw those grid lines as circles about a point in space. As we add mass, space is distorted and the lines are closer to the mass. They are closer together.

Here is the question:
Looking some distance from the mass, and as we add mass, are the circles drawn in towards the mass?
That means that space time is compressed within some distance from the mass.
It also indicates that space, some greater distance from the mass, is stretched. The circles are further apart.
Are these valid conclusions?


Thank you for your time.
 

Answers and Replies

  • #2
Ibix
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The intent is to look at space but not time.
You can't really do that. Particularly if you want to add mass, since that's something that happens over a period of time.
Begin adding mass to the center of the grid. To my understanding, so far, the mass will draw the lines of space in towards it.
How are these lines drawn? You can't make marks in spacetime. All you can do is put out a grid of buoys or something, but once you start adding significant mass they will, of course, fall towards it.

Also, how are you planning to add the mass? You can't just wave a magic wand and add the mass - that would violate local energy conservation and the Einstein field equations cannot describe that situation. You'd have to bring the mass in from somewhere.
Looking some distance from the mass, and as we add mass, are the circles drawn in towards the mass?
That depends on how you draw the circles, I'm afraid. And since the spacetime you are describing is non-stationary there's a degree of subjectivity in the answer anyway, since there isn't necessarily a clear candidate for how to divide spacetime into space and time.

I must say you've picked a horribly complicated problem to investigate. Can I ask why you're asking?
 
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Ibix wrote: You really can't do that.
That is similar to saying that I cannot make a drawing in only two dimensions. The claim is not to pretend the other dimensions do not exist, rather to provide limits to the scope of thought. A narrower scope often leads to better thinking.

Ibix wrote: How are these lines drawn?

This is an imaginary thought process. Lines may be drawn in any manner desired. Start with them equidistance apart, some number of millions of kilometers. If you want something more concrete, I create a magical marker that can leave a mark upon space time that can be seen. If space time can be distorted, then I can draw imaginary lines upon it.

Since Einstein could imagine running along side a light beam, then I can imagine drawing lines in space. No, I do not compare myself to him, but I do presume the ability to imagine things.

For this mental exercise, our observation point is detached. As we observe our perceptions are not changed by the effects of the added mass.

This is an imaginary exercise. Presume I use magic and just create the mass there. Presume also that we allow sufficient time for our imaginary system to stabilize. The concept to examine is not how the mass got there, but the effect it has upon nearby and far away space.

Ibix wrote: Why?

I am neither mathematician nor physicist, but am curious and think about many things. Back in the year 2000 or so I derived a concept that a black hole might have an upper limit to its size. (Others have probably occasioned upon that thought, but it was original to me.) I wrote about that and a few other topics on my web site www.bkelly.net.
 
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Ibix
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Ibix wrote: You really can't do that.
No I didn't. You can just highlight text and click Reply in the popup menu that appears in order to get correct quotes.
That is similar to saying that I cannot make a drawing in only two dimensions.
That's not the point. The point is:
since the spacetime you are describing is non-stationary there's a degree of subjectivity in the answer anyway, since there isn't necessarily a clear candidate for how to divide spacetime into space and time.
...which is to say that you first need to define what you mean by "space". Then, since you want to consider changing mass you need to consider space at multiple times. Which is spacetime.
I create a magical marker that can leave a mark upon space time that can be seen. If space time can be distorted, then I can draw imaginary lines upon it.
You need a physical process. If you can't specify a process for drawing those lines in a physically plausible way then we cannot apply the laws of physics to work out what would happen. If you use magic then what happens obeys the rules of the magic, which you can make up.
If space time can be distorted
It can't. That's a rather inaccurate popsci description of spacetime curvature.
Since Einstein could imagine running along side a light beam, then I can imagine drawing lines in space.
The thing is that he didn't imagine any magic. He just considered an (apparently) reasonable physical scenario and realised that it led to contradiction.
Presume I use magic and just create the mass there.
Then, as I said, you cannot use the Einstein field equations to describe the result. So this presumption is simply asking what the laws of physics say about a scenario they say is impossible. That's easy: this is impossible.
Back in the year 2000 or so I derived a concept that a black hole might have an upper limit to its size.
Given that I haven't said anything you wouldn't know if you'd ever opened a general relativity textbook, I rather doubt that your have the knowledge to do this.
 
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PeterDonis
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Are these valid conclusions?
No.

Since Einstein could imagine running along side a light beam
Only in order to show why doing so was actually impossible. And Einstein did not invoke "magic" as an excuse.

This is an imaginary exercise. Presume I use magic
We don't discuss magic here. We discuss physics. Physics has laws, and we can only discuss scenarios that are consistent with those laws. The laws in question in this particular scenario are the laws of General Relativity, which, as @Ibix has already pointed out, you can learn about from any of a number of textbooks. Or you can look up Sean Carroll's online lecture notes.

Back in the year 2000 or so I derived a concept that a black hole might have an upper limit to its size. (Others have probably occasioned upon that thought, but it was original to me.) I wrote about that and a few other topics on my web site www.bkelly.net.
PF is not for discussion of personal speculation.

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