Causal Relationships and The Light Cone

Discussion in 'Physics & Math' started by Logic101, Feb 19, 2014.

  1. Logic101 Banned Banned

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    Because signals and other causal influences cannot travel faster than light (see special relativity and quantum entanglement), the light cone plays an essential role in defining the concept of causality: for a given event E, the set of events that lie on or inside the past light cone of E would also be the set of all events that could send a signal that would have time to reach E and influence it in some way.

    http://en.wikipedia.org/wiki/Light_cone

    So we see that the light cone play an essential role in all causal relationships.
     
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  3. Logic101 Banned Banned

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    [video=youtube;JXXu6QgCQpQ]http://www.youtube.com/watch?v=JXXu6QgCQpQ[/video]

    As the point moves the light cone moves with it. Is there an equation for causal relationships in conjunction with light signals and information speed?
     
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  5. Logic101 Banned Banned

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    Can someone introduce Light Cone mathematics into this thread please and thank you?
     
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  7. brucep Valued Senior Member

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    Exactly. The lightlike boundary separates all the events in spacetime that we can know about [timelike] from events that we can't know about [spacelike]. I kinda think of the lightlike boundary as representing the boundary of our observable universe. Just something I think about some times.
     
  8. brucep Valued Senior Member

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    I looked around and found this. This comment is revealing. "One nice thing about light cone coordinates is that the causal structure is partially included into the coordinate system itself."
    http://en.wikipedia.org/wiki/Light_cone_coordinates

    I was thinking about the cosmological coordinates. Maybe somebody else is familiar with this?
     
  9. Logic101 Banned Banned

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    Yes. The coordinates are fully included in the coordinate system. Absolutely beautiful.

    [video=youtube;y53hh-LAbLk]http://www.youtube.com/watch?v=y53hh-LAbLk[/video]
     
  10. Logic101 Banned Banned

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    Light is split into two?
     
  11. RJBeery Natural Philosopher Valued Senior Member

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    Technically it isn't really even a cone, it's a sphere. There is an imaginary sphere which grows from you "into the past", representing everything that can could possibly see right now and/or be influenced by; there is also one which grows from you "into the future", representing the volume of things which you could possibly be seen by or influence. It's a natural consequence of the finite speed of light.
     
  12. Logic101 Banned Banned

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    In effect, the system brings itself into existence as a means of atemporal communication between its past and future whereby law and state, syntax and informational content, generate and refine each other across time to maximize total systemic self-utility. This defines a situation in which the true temporal identity of the system is a distributed point of temporal equilibrium that is both between and inclusive of past and future. In this sense, the system is timeless or atemporal. — Chris Langan

    http://ctmublog.wordpress.com/
     
  13. Logic101 Banned Banned

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    I see. Are you able to answer my question to Bruce about light splitting into two? It would be appreciated.
     
  14. RJBeery Natural Philosopher Valued Senior Member

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    No it is not. The light cone isn't a physical thing, it's a HYPOTHETICAL thing which puts a bound on past and future causal relationships. In other words, even a cold dark piece of matter in the dead of space, which emitted no EM radiation of any sort (e.g. light, photons, etc), would still "have" a future light cone because it's just a calculation of points in future spacetime which could in theory have been influenced by the piece of matter.

    Right here, right now you can only affect things within your immediate vicinity. Ten seconds from now your future light cone will actually be a sphere with a radius of 10 light-seconds. This is because there is absolutely nothing you could possibly do right now which would affect an object 11 light-seconds away from your current position at that time. Things outside of that sphere are not able to be influenced by you here and now in any way.

    I think it's actually simpler than you're envisioning.
     
  15. Logic101 Banned Banned

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    I see. So what then is split into past and future (time, reality)? And in that case is the light cone an abstract representation of the speed limit of a signal in a causal relationship?
     
  16. RJBeery Natural Philosopher Valued Senior Member

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    Our past light-cone and future light-cone are really the same thing; they are both light "spheres" extending out into spacetime, except one is mapped into positive time, and the other is mapped into negative time. When two events interact with each other we have chosen to define which one is the cause and which is the effect based on their temporal ordering. Why we do this gets complicated, and it has to do with entropy and the direction of flow of information.
     
  17. brucep Valued Senior Member

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    The light cone is a useful model for describing the natural phenomena it's modeling. A main function of science is building models that describe the natural phenomena in the models domain of applicability. Another main function of science is to test the predictions the models make associated with natural phenomena. Over the history of science the scientists have done a great job. So the lightlike boundary represents a boundary between the timelike and spacelike regions of the light cone model. I'll link metrics which are timelike and spacelike. The discussion about them is very good and easy to understand. The Chapter continues with a derivation for the relativistic energy equation. Awesome presentation.

    Choose Chapter 1 Speeding
    http://www.eftaylor.com/download.html#general_relativity

    Everything inside the lightlike boundary is part of our observable universe. Everything outside the observable universe is in the spacelike region of the light cone model and forever unobservable. To get details about the timelike space it makes sense to understand how we model the observable universe. wiki has a good page on that.

    So is light 'split in two'? No. An example is a 'star' emitting light in the timelike region can be received at our coordinates. A star emitting light in the spacelike region can never reach us. If you want to talk about the metrics let me know.
     
  18. Logic101 Banned Banned

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    RJ Beery,

    When you say the light cone is not a physical thing, are you saying the same thing as the following?

    A light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. If we imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone. The past light cone behaves like the future light cone in reverse, a circle which contracts in radius at the speed of light until it converges to a point at the exact position and time of the event E.

    http://en.wikipedia.org/wiki/Light_cone

    Does the light cone merely represent the path that the light would take and is not an actual bundle of photons?
     
  19. RJBeery Natural Philosopher Valued Senior Member

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    Yes. It says would take through spacetime, but this "light cone" is still the causal bound in spacetime even if no light is being emitted (which is why I mentioned dark cold rocks in space)
     
  20. Farsight

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    If I can offer something here....

    A light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

    The "take through spacetime" is actually wrong. Like a lightcone, spacetime is an abstract thing. Like RJ said, the light takes a spherical path through space. You can "plot" this in spacetime, but the light doesn't move through spacetime. There's no motion through spacetime at all. It's a mathematical model that depicts all times at once. So you have to forget about motion through spacetime.

    If we imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone. The past light cone behaves like the future light cone in reverse, a circle which contracts in radius at the speed of light until it converges to a point at the exact position and time of the event E.

    This is good. See where it says we graph the growing circle. The light moves through space, we limit ourselves to a slice of space, add a vertical axis to represent time, and graph the growing circle to get our cone. This represents the expanding light at all times, so there's no motion associated with the cone.

    Yes, it's a plot, a graph, of the path the light took through space over time.
     
  21. Logic101 Banned Banned

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    Why do you state that light does not move through spacetime?

    This part is the source of my belief that the light cone splits into two, past and future.

    So are you saying the light does not move through neither space nor time?
     
  22. RJBeery Natural Philosopher Valued Senior Member

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    He's saying that motion through spacetime does not exist. Motion through space does...as a function of time. Once we incorporate both concepts together, we no longer get motion, only a persistent 4-D graph. Don't get confused by this, it's perhaps a bit pedantic but Farsight is correct on this point.
     
  23. eram Sciengineer Valued Senior Member

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    @Logic101 what is your question exactly?
     

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