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Watsisname
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18 Mar 2019 19:55

What Matt in the PBS Space Time video means by "reversing the direction of your changing spacetime interval" is to change the sign of Δs2.  For allowed (slower than light) motions, Δs2 is negative, while for faster than light motion, it is positive.  Their diagram represents the negative values as being downhill while positive is uphill, which is a nice way to visually distinguish these different regions of spacetime and whether they are accessible or not.  The boundary between them is where Δs2 = 0, which is level (neither up nor down), and can only be followed by photons.  

Some more jargon:  we refer to Δs2 < 0 as "time-like", Δs2 > 0 as "space-like", and Δs2 = 0 as "light-like" or "null".  Everything on the diagram separated by "space-like" intervals is inaccessible since it would require moving faster than light, and we call that region "elsewhere", being outside of our light cone.

The downhill side opposite the direction of our future, is the direction to the past.  It is our "past light cone", showing those events that have had causal influence over us.
 
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19 Mar 2019 07:48

This still doesn't answer what I asked, I said, "if you could SPEED UP TIME", not "if you could go as fast as light".
 
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19 Mar 2019 13:58

Propulsion Disk wrote:
Source of the post This still doesn't answer what I asked, I said, "if you could SPEED UP TIME", not "if you could go as fast as light".

I answered right here. (Post #1455).  The problem with the question is that it's unclear what "speeding up time" means.  Coordinate time, or proper time?
 
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19 Mar 2019 14:05

I was wondering if a person somehow managed to go 13.7 billion light-years from the center of the universe would he be able to see Big Bang itself (with a Hubble). But then came the question of the expansion of the universe that would be faster than light. As space-time is responsible for universal expansion, by the time the boundary of the universe reaches that person he would enter space-time and be carried along with the expansion at a speed faster than light and he would not be able to see the light of the Big Bang. Or is it anyway impossible to see the Big Bang at such a distance since the light would need the space and the time to reach that person?
 
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19 Mar 2019 14:13

Hewerton22 wrote:
Source of the post I was wondering if a person somehow managed to go 13.7 billion light-years from the center of the universe would he be able to see Big Bang itself (with a Hubble).

We can see the Big Bang (or at least very close to it: within about 380,000 years of it, before which the universe was opaque) by looking out with our telescopes from here on Earth.  For each light year out in space that you look, you see back 1 year in time.

The universe also has no absolute center.  Any point in space that you choose is the center of its observable part of the universe, due to the finite age of the universe and the finite speed of light.  For everyone, no matter where they are, the Big Bang is seen at a distance of (current age of universe)x(speed of light) away from them, in terms of light travel time.

Signals from shortly after the Big Bang are extremely stretched out (redshifted) by the expansion as well.  For example, beyond the Cosmic Microwave Background (emitted 380,000 years after Big Bang when the universe became transparent to light), lies the Cosmic Neutrino Background (emitted just a few seconds after Big Bang when the universe became transparent to neutrinos).  The microwave background is stretched out by a factor of about 1100, while the neutrino background is stretched out by a factor of billions, making it extremely difficult to observe even aside from the problem of neutrinos already being hard to detect under normal conditions.

Hewerton22 wrote:
Source of the post As space-time is responsible for universal expansion, by the time the boundary of the universe reaches that person he would enter space-time and be carried along with the expansion

Just as the universe has no absolute center, it also has no absolute edge.  If you could freeze the expansion and fly off in any direction at any arbitrary speed, you will either keep going forever without reaching an edge, or (if the space is curved like the surface of a sphere), you'll eventually wind up back where you started.
 
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19 Mar 2019 20:47

Watsisname wrote:
Source of the post There's a subtle difficulty with this question.  What do we mean by "making time go faster"?  Time can refer to two different things: coordinate time and proper time.  

I meant proper time, both would be good to know, but I would want to know how time is in the "spacetime distorter's" frame of reference, which I believe would be proper time.
Watsisname wrote:
Source of the post  But I feel like this might not be what you have in mind by "making time go faster".

No we're on the same page here, perhaps "make time go faster" wasn't clear enough for any final answer to be made, sorry for the confusion.
 
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19 Mar 2019 22:06

Propulsion Disk wrote:
Source of the post I meant proper time, both would be good to know, but I would want to know how time is in the "spacetime distorter's" frame of reference, which I believe would be proper time.

What we can change is the relationship between proper time and coordinate time.  But this is just what time dilation is.  A moving clock will tick fewer seconds of proper time for a given amount of coordinate time (coordinate time being the time measured in our non-moving frame).

Example:  A ship moves past us at 95% of the speed of light.  We will see clocks on board that ship tick about 3.20 times slower than our own.  In 1 hour of our time, 18.7 minutes passes on the ship.  By symmetry, people on the ship will experience one second per second, but will see our clocks ticking 3.203 times slower than theirs.  

If the ship slows down to 50% of the speed of light, then their clocks tick 1.155 times slower than ours, or 51.9 minutes for them for each hour for us.  We say their clocks are now ticking faster, and by symmetry they say their clocks stay the same and it is our clocks that are now ticking faster.

On the spacetime diagram, if we plot ourselves at rest in space (and thus moving up along the time axis at 1 second per second), then the ship originally follows a path angled about 42° from our time axis (compared to 45° for light).  When it slows down to 50% of c, that slope decreases to 26.6 degrees.   

We can shift to the ship's frame of reference by performing a Lorentz transformation, as described in the PBS Space Time video. The ship's path becomes the new coordinate time axis, the "x axis" of what we called simultaneous events at t=0 shifts by the same angle, and the whole diagram transforms to square things up.
 
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20 Mar 2019 07:15

Watsisname wrote:
Source of the post What we can change is the relationship between proper time and coordinate time.  But this is just what time dilation is.  A moving clock will tick fewer seconds of proper time for a given amount of coordinate time (coordinate time being the time measured in our non-moving frame).Example:  A ship moves past us at 95% of the speed of light.  We will see clocks on board that ship tick about 3.20 times slower than our own.  In 1 hour of our time, 18.7 minutes passes on the ship.  By symmetry, people on the ship will experience one second per second, but will see our clocks ticking 3.203 times slower than theirs.  If the ship slows down to 50% of the speed of light, then their clocks tick 1.155 times slower than ours, or 51.9 minutes for them for each hour for us.  We say their clocks are now ticking faster, and by symmetry they say their clocks stay the same and it is our clocks that are now ticking faster.On the spacetime diagram, if we plot ourselves at rest in space (and thus moving up along the time axis at 1 second per second), then the ship originally follows a path angled about 42° from our time axis (compared to 45° for light).  When it slows down to 50% of c, that slope decreases to 26.6 degrees.   We can shift to the ship's frame of reference by performing a Lorentz transformation, as described in the PBS Space Time video. The ship's path becomes the new coordinate time axis, the "x axis" of what we called simultaneous events at t=0 shifts by the same angle, and the whole diagram transforms to square things up.

Yeah I got all that from the video, I should've gave an example, to show what I'm meaning. Okay, say that we have "something" in a area with little to no energy except for the "something", if the "something" was moving around we would see it going faster than it would in an area with lots of energy (like earth's atmosphere) because all that energy is distorting spacetime and making everything go slower, without it, everything would go faster than usual, like with the "something" in literally empty space, my question is, how would something like this be plotted on the spacetime diagram?
(PS) I actually meant the coordinate time, I was up late making that last post, didn't think enough about which one I wanted to know, sorry for the inconvenience.
(PPS) this subject is kinda hard to explain, so if you are still confused there's nothing more I can really do, sorry, :cry: but don't worry, i'm pretty sure I have it all figured out, but thanks for all the knowledge! 
 
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Watsisname
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20 Mar 2019 18:37

Propulsion Disk wrote:
Source of the post say that we have "something" in a area with little to no energy except for the "something", if the "something" was moving around we would see it going faster than it would in an area with lots of energy (like earth's atmosphere) because all that energy is distorting spacetime and making everything go slower, without it, everything would go faster than usual, like with the "something" in literally empty space, my question is, how would something like this be plotted on the spacetime diagram?

Okay, what you're describing here is the effect of gravitational time dilation, and more specifically what it looks like to take it away.  

The best and simplest example to illustrate this is a black hole, but at the end1 I'll come back to a less extreme example with Earth's surface.  Time passes more slowly close to a black hole according to faraway observers, and comes to a halt at the event horizon.  What does this looks like on a spacetime diagram?  That will depend on our choice of coordinates.  

If we use Schwarzschild coordinates, which are built to describe the locations of events as measured by those faraway observers, then what happens is the edges of light cones collapse on themselves, opening in narrower and narrower angles, closer in to the event horizon.  At the event horizon itself, the light cone is squashed down to a vertical line parallel to the time axis.  This represents that anything at the horizon is "frozen in time" there, again according to the distant observers.  No progress is allowed either inward or outward from there.  Even a photon emitted radially outward will just be seen to hover at the horizon.  Same with a photon emitted radially inward!

This squishing down of the light cones and everything "getting frozen in time at the horizon" is an artifact of the vantage point of the distant observers. If we dive in ourselves, then we don't freeze at the horizon, and instead sail right through it in a very short proper time.  To map this out, our spacetime diagram is transformed into a new coordinate system, such as Eddington-Finkelstein coordinates.  In this coordinate system, light cones don't squash down to zero at the horizon, but instead rotate and face more and more inward.  This shows that you are "forced" to move inward, and cannot move outward.  You pass through the horizon, and your future lies at the singularity.

There are even more ways of representing curved spacetimes like these on a diagram, such as Kruskal-Szekeres coordinates, or even a Penrose Diagram, which is transformed in such a way as to keep the paths of light rays at 45° angles at all times.  PBS Space Time has a great episode all about it with lots of visual examples and explanation.  I highly recommend for you -- this will probably make things more clear than my lengthy explanation would. :)



So, long story short, what a region of slowed time due to gravitational field looks looks like on a spacetime diagram depends on how we draw the diagram, but the main theme is that light cones turn to face in toward the center of that gravitational attraction.  This represents that when in that gravitational field, you lose freedom to move outward, and are "compelled" to move inward instead.  If the gravitation is strong enough, like below the horizon of a black hole, then you can only move inward.

Now then it's probably straightforward to see what moving to a region of "faster flowing time" looks like.  Just move away from the black hole, and into a region of flat spacetime as described by special relativity.  Flat spacetime represents the fastest that time can flow in any meaningful sense.


Example using the Earth's surface:  
In Schwarzschild coordinates, by how much are our light cones squashed inward?  (Warning: bit of math involved).

The Earth's gravitational field is very well described by the Schwarzschild metric, and the Schwarzschild coordinates in the equatorial plane are

Image

As described earlier, the edge of the light cone is defined by a light-like interval where ds2 = 0.  Setting the equation equal to zero and solving for dt,

Image

Plug in the mass and radius of the Earth for M and r, and we get a slope for the edge of the light cone as 

dt/dr = 1.000000001392

which is 44.99999996012° from the time-axis.  A very tiny difference from 45°!  But this just means Earth's surface gravity and its effect on time is very weak by relativistic standards.
 
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21 Mar 2019 17:44

Alright I got it now, thanks for answering WHN! also, ever sense you posted that pbs spacetime video, I've been watching them and been gaining a lot more knowledge from them, so, thanks for introducing me to them too! :lol:
 
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21 Mar 2019 18:48

Great!  Glad this was helpful for you, and that you've been enjoying the PBS series as well. It really is a wonderful channel for all things spacetime and astrophysics related. :)
 
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25 Mar 2019 00:57

I have a question regarding wormholes. Ignoring for the moment the viability of that technology, and assuming that the Einstein-Rosen Bridge interpretation of that possible phenomena is correct, how visible would such a spatial structure be?

If a wormhole was made by an advanced civilization, who somehow mastered the laws of physics and had the required components for that technology, at what distance from Earth would it be invisible to our observations using radio telescopes or other detective instruments?

Additionally, some follow-up questions (in no particular order) are:

  • What wavelengths of electromagnetism would the presence of the wormhole be apparent on?
  • How would it's size (in terms of the physical aperture from which matter and energy comes in and out of) effect visibility?
  • How could an advanced civilization hide this technology, if it is readily visible at a reasonable (~1000lys) distance?
  • Aside from transporting matter or energy, what other effects might the wormhole have on the immediate environment in which it is situated?

Before you answer, I am fully aware that only a fairly advanced interstellar civilization would have the needed technology and resources to make a wormhole or wormholes - and that therefore they would be obvious to us via their energy emissions and territory in space (unless they are very good at hiding).
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25 Mar 2019 01:13

Watsisname wrote:
Great!  Glad this was helpful for you, and that you've been enjoying the PBS series as well. It really is a wonderful channel for all things spacetime and astrophysics related. :)

PBS is awesome for everything!  It is perfect proof why capitalism and education dont (and shouldn't) mix.  I highly enjoyed their series on indigenous vs processed food and how our modern diet is leading to all sorts of health problems!  The lecture was done by a gastroenterologist with degrees from Columbia and Yale.

About unidentified sources of intense energy, wasn't there recently a story about this being observed in a galaxy 5 billion light years away?

I liked the chimp video!  I was recently reading about how human activities are impacting chimp behavior, their usage of tools, etc.
 
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25 Mar 2019 01:19

A-L-E-X wrote:
Source of the post About unidentified sources of intense energy, wasn't there recently a story about this being observed in a galaxy 5 billion light years away?

I think you are thinking about FRBs (Fast Radio Bursts). I'm not sure if wormholes would emit a radio wave like that.
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25 Mar 2019 01:23

Stellarator wrote:
A-L-E-X wrote:
Source of the post About unidentified sources of intense energy, wasn't there recently a story about this being observed in a galaxy 5 billion light years away?

I think you are thinking about FRBs (Fast Radio Bursts). I'm not sure if wormholes would emit a radio wave like that.

Yes that's what it was- 80 had been discovered in a very short time all coming from the same galaxy.  

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