Spacetime curvature

at the center of a planet/star/etc

Study matter and its motion through spacetime...

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Re: Spacetime curvature

#61  Postby hackenslash » Mar 05, 2011 8:48 am

[youtube]http://www.youtube.com/watch?v=08s7ygL5GYQ[/youtube]
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Re: Spacetime curvature

#62  Postby Animavore » Mar 05, 2011 9:16 am

How is he making a hyperbola with only one point? How does he know the shape of the hyperbola with just one point? And I still don't get why a hyperbola and why it goes away from the centre?
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Re: Spacetime curvature

#63  Postby twistor59 » Mar 05, 2011 9:33 am

Animavore wrote:How is he making a hyperbola with only one point? How does he know the shape of the hyperbola with just one point? And I still don't get why a hyperbola and why it goes away from the centre?


ETA Not referring to the video here, just to the hyperbola that appears in special relativity:

Using t for time and x for space, take t2 - x2 = 1 for example

rewrite as t2 = 1 + x2

rewrite again as t = sqrt(1 + x2)

Let's just take positive square roots for now:

if x = 0, shoving it in that last equation gives t = 1
Letting x start to go positive, say x = 0.0001, gives t just a titchy bit greater than 1, and as x increases t goes even greater than one. It never gets closer. Letting x go negative, say x = -0.0001, ALSO gives t just a titchy bit greater than 1, since x gets squared, in the formula, so again as x goes negative t increases and stays greater than 1.

So 1 is the smallest t ever gets, and you get the hyperbola-in-the-top-half shape.

But of course when you take the square root of a number, you can take the negative square root as well as the positive one, so the hyperbola in the top half gets mirrored in the bottom half.
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Re: Spacetime curvature

#64  Postby Animavore » Mar 05, 2011 9:42 am

So you're using 't' for 'y' here?
That makes sense.
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Re: Spacetime curvature

#65  Postby twistor59 » Mar 05, 2011 9:50 am

Animavore wrote:So you're using 't' for 'y' here?
That makes sense.


Yeah.

In relativity, a common convention is that you give the t2 term the positive sign and x2, y2, and z2 the negative signs when you're constructing the hyperbolas
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Re: Spacetime curvature

#66  Postby Animavore » Mar 05, 2011 2:18 pm

Ok. I just want to make sure I have this right before I move on (or even read the chapter again).

As per the equation above the line of the hyperbola can be seen as an infinite series of points depending on the value of x, correct?

and;

Each of those points represents a distance from the event with none of the observers on any point, obviously seeing the event before it happens, or do the points represent people at different speeds or is it either?
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Re: Spacetime curvature

#67  Postby hackenslash » Mar 05, 2011 2:30 pm

A) Correct.

B) The former. The hyperbola represents a continuum of all the points at which the distance in spacetime between event O and event A is equal to s, as per the diagram in this post.
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Re: Spacetime curvature

#68  Postby twistor59 » Mar 05, 2011 2:38 pm

Yes, for the example I gave, the distance, s, in hack's post, was equal to 1. So the hyperbola is the set of all events with "distance" 1 from the orgin. In Hack's the distance was a generic number, s.
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Re: Spacetime curvature

#69  Postby Animavore » Mar 05, 2011 2:54 pm

:thumbup:
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Re: Spacetime curvature

#70  Postby Animavore » Mar 06, 2011 9:43 am

Here's a very recent lecture from Brian Cox filmed by an amateur. You might need to turn it.

[youtube]http://www.youtube.com/watch?v=WM4c96y9VkI[/youtube]
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Re: Spacetime curvature

#71  Postby hackenslash » Mar 06, 2011 10:06 am

OK, so I turned it, but that just meant that I couldn't read the captions... :P
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Re: Spacetime curvature

#72  Postby Animavore » Mar 06, 2011 10:44 am

*up*
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Re: Spacetime curvature

#73  Postby hackenslash » Mar 06, 2011 11:22 pm

Watched that lecture now. Excellent stuff.
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Re: Spacetime curvature

#74  Postby Dov Henis » Oct 14, 2011 3:19 pm

Spacetime???

EOTOE, Some Implications (2)

This equation describes the presently expanding universe:

E=Total[m(1 + D)] D = distance travelled by mass since singularity

This equation describes the future contracting universe:

E=Total[m(1 - D)] D = distance travelled by mass since end of expansion

Implications:

The base units of mass - may be designated gravitons but MUST have mass - are not temporal,
they never disappear.

In the present expanding universe they are in motion as mD away from the singularity point.
Those of them that hit a whatever mass format and move it become inert. This will go on until
all or nearly all of them cease moving forward, i.e. until D ceases growing.

When D ceases growing gravitation will overcome the inertial motion away from the singularity
point and will start pulling them back towards it. It is then that -D will replace +D , to maintain
the equation’s equality…

And MORE, MUCH MORE:

The rational commonsensical, and therefore scientifically probable, implication is that Space is
Imbued with these massed gravitons that are continuously left behind during Expansion…

Dov Henis (comments from 22nd century)
http://universe-life.com/
http://universe-life.com/2011/10/07/eot ... cations-i/
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