Visualizing 'Past Light Cones' in 'Closed' Space-Time?

Lovely.

Nice visuals man...

I wouldn't lie, this is pretty confusing....

http://upload.wikimedia.org/wikipedia/commons/thumb/5/57/E8PetrieFull.svg/2000px-E8PetrieFull.svg.png

My kids once had a 'Spirograph' which produces these nice geometries with the aid of coloured pencils....I have difficulty believing that someone imagined this form to result from a theorem.

What balls you have!

Are you advocating one of these as the right one? And, if so, which one and why?

It's important enough that he wants to discuss it at least twice.

Tesseract

Minkowski Space:

At last, something that even I can grasp.

Me too.

The tequila goes in the future light cone, I grasp it in the future...

Tequila makes me invisible.

I headed to the Indian casino to take my revenge on them.

This 2-1/2 min yewtoob video seems a pretty good illustration.

It is more of an illustration of reference frames than past light cone; interesting nonetheless.

Mmmm....Time has 2 opposite and simultaneous directions in your sketch (y-axis) ?

Explain please, since cause-and-effect must be linear and uni-directional. Time is not just about light...

The above visualization, of flat space-time, is "dimensionally reduced", i.e. represents a (2+1)D "projection", of full-fledged (3+1)D space-time. Therefore, the "time slices", of the "light-cone" are visualized as circles. But, those circles are "stand-ins", for spheres. Therefore, a full-fledged "light-cone", in full-fledged (3+1)D space-time, is a hyper-spatial "stack" of spheres, even as an actual cone, is a "stack" of circles, i.e. rings. Again, a full-fledged "light-cone" is like the spherical layers of an onion, that has been "pulled and strung out", through the extra hyper dimension.

It seems as if you happened onto some paper or blog that is sporting some new or different theory and find it intriguing.

However, there is no grounding context provided for the theory, only the small slice you have presented here.

Can you provide a supporting link on this so that I can at least try to understand the grounding theories behind the claim?

Well... I probably don't belong in this thread, but I must admit I find it hard to get past the one labeled "flat" spacetime, which is a decent match for the diagrams and examples given here.

It doesn't make sense to me, that the "spheres" in the other two illustrations are out of order - instead of the regular expansion of light from a source. The circle of light gets larger in an orderly fashion which describes over time the shape of a cone.

The "closed-but-static" and "closed-and-expanding" description that the "shells" both grow and shrink, and the image which puts them out of size order, does not seem to have much relevance to the behaviour of light, as far as I can understand it. Please explain - or kick me off your thread if you like, with a rude epithet.

I also unwittingly learned _{while eating my dinner and trying to find explanations}, that dolphins have cone shaped teeth, whereas porpoise teeth are spatulate.... Just wondering whether the term "porpoising" was chosen.. on porpoise.

An observer's "light cone" is, in actual fact, some sort of "hyper-cone", whose "time-slices" are spheres (not circles).

In flat-and-static space-time, those spheres would continuously grow, with increasing "look-back-and-out-time".

In a curved-and-closed space-time, the space-time fabric is finite in size. Thus, a sight-line projected "far enough" in any given direction, would "wrap around" and impinge back upon the observer "from behind". As such, the "spherical time slices", of "light hyper-cones", at first grow; and, then shrink, in size.

In a reduced-dimensional analogy, the circular shock-wave, from the 1960 Soviet "Czar Bomba" super-nuclear explosion, propagated away from the blast-site, increasing in size, until the rings reached "half way around the world"; then, they started to shrink in size, until they converged, at the anti-podal point; then, they re-emerged, growing again, back up until they were "half way back to the blast-site"; then, they started to re-shrink in size, until they re-converged, at the blast site. (This process repeated half-a-dozen times, AFAIK.)

Wow! Thanks for explaining.

I'm back. They won.

From that and this thread I have learned new meanings for 'general custard' and 'little big horns'.

Think I'll stick to helping diagnose no-start Cavaliers. This here stuff is a bit much for my simple brain.

I am currently reading a book entitled "From Eternity to Here" a good read so far. a little slow as there is almost as much reference material a there is basic text!

The book has almost everything, time, entropy,light speed and other stuff which I have yet to reach on Light Cones. The book also addreses time direction.

Good Luck

Sleepy

Light is a wave. No, light is a particle, no light is a wave, no light is a particle, no light is a wave. Ok, light is a wave and a particle. No light is a particle. Is light a multi-dimensional phenomenon exhibiting it's multi-dimensional behavior in a third dimension?

If we have proof that the speed of light barrier is broken, how do we look at electro-magnetic wave morphology with respect to geometry dimension?

If we pass a cone through a flat plane the observer in the plane sees a point and then a curve that grows larger.

What can we build physically in a third dimension that will prove that a fourth dimension exists? Can a flat plane person build a flat plane device that will prove the existence of a third dimension?

Could the behavior of light be as simple as just a energy (wave/particle frequency thingy) doing it's thing in another dimension in the same physical space and time and we are just that third dimension people that need to build a third dimension device that will prove the existence of a fourth (hyperspace) dimension?

or should we just worry about why bank CEO's are still making 20 million dollars or more a year while the rest of us are starving, out of work and losing our homes?

Gizmo,

You seem concerned about the "visualization" of a 4 D space from a 3D environment. I view this as impossible - but that is just my view.

When I was a lot younger, I used to visit libraries and often found books on the 4th dimension, fascinating stuff to an 11 yr old - but that was over 60 years ago!

If these books are still avaialable there were as I recall testswere postulated that one could do to determine whether an object that transientally occupied part of our 3D environment then one could surmise that it was a 4D object temporarily occupying part of our 3D space.

In those books, Light Cones had not been invented and as I recall we did not question the speed of light.

However my memory is not perfect!

Sleepy

I'm not a theoretical physicist by any stretch of the imagination, so I'm probably not even qualified to respond to this thread. However, it seems paradoxically incorrect to be speaking about a "light cone" converging to a future event from past space time. How can a future event (cause) come after the effect (converging light cone)?

Essentially the light cone is a schematic representation of a light flash event and its previous, future, and now characteristics of the event.

The upper cone represents the future.

The lower cone is the past.

The intersection of the two is the now-time.

Typically the cones are drawn with side angles of 45° to represent time in seconds (vertical) and distance in light seconds (horizontal). The intersect is the now-time when the event takes place.

The representative figure depicts that the motion of the source does not impact the direction of the light cone, just the event that emits the light flash.

Do a search on Einstein and light cones if you want to learn more.