Time-Like Curves, Light Cones & Void Explained in Detail

[Lakshya]

What are all these time-like and space-like things? Are these considered with light cones? Can anybody explain me in full detail the light cone because the more I read about it the more I get confused. I don't want basic information and can anybody also explain me void?

 

[JesseM]

Every event E in spacetime has a past light cone and a future light cone. The future light cone is the set of all points in spacetime with the property that a signal emitted from E moving at the speed of light or slower could reach them. The past light cone is the set of all points in spacetime with the property that a signal emitted from the past event and moving at the speed of light or slower would have time to reach E. Basically, if one event is in the other's light cone (a timelike separation between the two events), that means the first event could have a causal influence on the other; if two events are outside one another's light cones (a spacelike separation), that means there's no way either could influence the other without faster-than-light influences being involved. For instance, information about an event happening on Earth in 2007 would take 4 years to reach Alpha Centauri, so the event on Earth could have a causal influence on an event taking place on Alpha Centauri in 2015, but it could not have any influence on an event taking place on Alpha Centauri in 2008, so the 2015 AC-event lies in the future light cone of the 2007 Earth-event and there's a timelike separation between them, but there is a spacelike separation between the 2008 Ac-event and the 2007 Earth-event, and neither lies within the other's past or future light cones.

The name "light cone" arises if from depictions of spacetime with only two spatial dimensions and one time dimension. In this case, with space a 2D plane, if light goes out in all directions from some initial event then you'll see a steadily-increasing circle of light around the event, with the edge of the circle being the maximum distance the light can have traveled from the initial event at a given moment. If you represent time as the vertical axis then this gives you a cone, with each cross-section of the cone showing the size of the circle at a given moment.

 

[Lakshya]

I am still not getting how we can show it on a graph like time-like separation and space-like seperation. What about void and closed time-like curves?

 

[neutrino]

I am still not getting how we can show it on a graph like time-like separation and space-like seperation.

Do you know how to draw a light-cone? [Or a light-"triangle" with just x and t]. Mark any point, say A, within the future or past light-cone of the origin event O. These two points (O and A) are separated by a time-like interval. Mark any point (B) outside the light-cone, and these two events (O and B) are separated by a space-like interval.

 

[JesseM]

I am still not getting how we can show it on a graph like time-like separation and space-like seperation. What about void and closed time-like curves?

To show it on a graph, just draw the past and future light cones of one of the two events, if the second event lies inside the first event's past or future light cone there's a timelike separation, if it's outside of the light cones there's a spacelike separation (and if it's right on the edge of a light cone there's a lightlike separation). A closed timelike curve is something unusual that only arises in weird situations in general relativity, if you're just learning about special relativity you don't have to worry about it. It basically indicates a spacetime that allows time travel into the past--a particle traveling on a closed timelike curve would have a worldline that forms a loop, so the particle goes back in time and becomes its own younger self. And I haven't seen the word "void" used as a technical term in physics, in ordinary speech it means basically the same thing as "empty space"--what was the context you saw this word used in?

 

[Lakshya]

I have read on the net that there's another universe across light barrier which is a complete converse of our universe. In our universe the maximum speed attainable is that of light but in that universe the minimum speed attainable is of light. The tachyon is a particle of that universe and we will surely find many other particles of that universe with the help of string theory.
Also I didn't understand closed-time like curves that how can a worldline be bent?
I am using void in the context umm... let me quote "The universe is separated by a void". In this line what does void means? And also I have read this term in many discussions.

 

[JesseM]

I have read on the net that there's another universe across light barrier which is a complete converse of our universe. In our universe the maximum speed attainable is that of light but in that universe the minimum speed attainable is of light. The tachyon is a particle of that universe and we will surely find many other particles of that universe with the help of string theory.

Where did you read this? Can you give a link? A tachyon is a hypothesized particle that moves faster than light, so it could connect events that lie outside one another's light cones, but it wouldn't be in "another universe", it would just be a faster-than-light particle in our universe. Also, there is no evidence that tachyons exist, and I think most versions of string theory (along with other models of particle physics) don't predict that they should.

Also I didn't understand closed-time like curves that how can a worldline be bent?

Are you familiar with the basic idea of general relativity, namely that spacetime is curved by mass/energy, and particles follow "geodesics" in curved spacetime? If not you can read http://io.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/general_relativity.htm or this or the articles in the "fundamentals" section of this page. A closed timelike curve could only exist in a spacetime that was curved in a very unusual way that would allow geodesics to form closed loops...it's uncertain whether such a spacetime is actually possible.

For a book which goes into more detail on general relativity and closed timelike curves but which is still aimed at a general audience, I recommend the book "Black Holes and Time Warps" by Kip Thorne.

I am using void in the context umm... let me quote "The universe is separated by a void". In this line what does void means? And also I have read this term in many discussions.

I still don't really understand the context--what parts of the universe are being "separated" here? Can you give a link to the page if it's online, or else the name of the book/article if it's not? It's possible you're referring to something like the giant void described in http://www.time.com/time/health/article/0,8599,1656529,00.html, if so "void" is just a non-technical term for a region of space that's relatively empty of matter, at least compared with the rest of the universe.