Light Cone Explanation

Question

Not sure if this question belongs here, or on Physics. Would someone please describe the "anatomy" of a light cone and provide an intuitive example?

I have read the Wikipedia article (http://en.wikipedia.org/wiki/Light_cone) and I think I have a basic grasp of the concept. However, I still have questions: is a cone emitted every time there is a disturbance in the electromagnetic spectrum? Does every electron changing energy states emit a light cone? I understand the "future" light cone (I think). However, what of the "past" light cone? Is that what is observed when detecting redshifts?

Thank you for your answers/comments. They have helped my understanding of the light cone concept.

Answer 1

Think of dropping a pebble into a pond, and the circular pattern the resulting wave makes. Now take a photo every second, and stack these one on top of another, and you have a "cone" of sounds waves. The oldest image of the wave is also the biggest, and furthest back in time.

Answer 2

Regarding the recent edit:

A light cone is not a physical object, nor is it made of light. Wikipedia calls it

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.

More accurately, it is the path that a massless particle traveling at the speed of light would take.

So to clear up your confusion: It's just the imaginary boundary causally separating two regions of space. Nothing more.

Answer 3

You are on the surface of the Earth now (I assume), as are almost all other humans. The surface of the Earth can be thought of as a two dimensional plane.

OK, let's say you do something amazing and you want to tell everyone on Earth about it, so you set up a means of broadcasting your news, at the speed of light, across the surface of the Earth. The speed of light is quick, but it still takes nearly two tenths of a second for your signal to make it round the world.

Before that signal gets to them, nobody knows your news. You can imagine a circle, defined by the speed of light times the travel time, spreading outward from your location, containing those regions that have heard the news.

Now what you do is imagine those circles stacked on top of each other, each drawn after a small increment in time, with a larger radius, and separated vertically by an amount that represents that increment in time. The circles begin at your position, when you start to broadcast. This stack of circles of increasing radius forms a light cone. Inside the cone are regions of space and time that it is possible for you to communicate your news to. Outside the cone are regions (of space and time) that can never hear the news because no signal can get there faster than the speed of light.

A concrete example. It is about 5000 km between London and New York. If the stock market crashes at 17:00 (UT) in New York, it is impossible for traders in London to hear about it for at least 0.016 seconds. For that period, they lie outside the light cone of a signal produced at 17:00 in New York. More distant cities take even longer to intercept the light cone.

The light cone idea also works in reverse. You can invert the cone to mark regions of space and time from which you could have heard some news. In the example above, the inverted light cone of the London traders does not contain New York until 0.016 seconds after 17:00.

A point of confusion is the idea of a cone, which is really only appropriate if space is defined as two dimensional - e.g. points on the surface of the Earth. Conceptually it is harder to work with in 3D (though mathematically equivalent). In 1D (points along a line), the light cone approximates to a light triangle.

Answer 4

However, I still have questions: is a cone emitted overtime there is a disturbance i the electromagnetic spectrum?

In relativity, a light cone is not actually conceptually dependent on light or electromagnetism, though those things are related. It's a bit more abstract that that, and it exists regardless of whether or not anything is actually going on.

Once you get a bit used to thinking about spacetime as one thing, and the sequence-of-snapshots is a reasonable analogy, you can ask: given an event (a location and a time), what events could it be affected by, and what events could it affect? Thus, we can define an $O$'s causal future as all events that a signal originating from $O$ could reach, and its causal past as all events that could from which a signal that reaches $O$ could originate.

Because in there is a maximum speed any signal could propagate, the boundary of the causal future of any event looks like a cone in spacetime. That speed is indeed the speed of light (as well as that of any massless particle), which is why it's called a (future) light cone, and similarly for the past light cone. But that's incidental--relativity would work even if light was massive. In that case, we'd just have to call the invariant speed $c$ something else.

Note that this means that light cone is defined in terms of all possible signals that could be sent, not just those that are actually sent. Therefore, no, it's not something that's 'emitted' by disturbances in the electromagnetic field or anything else. Some disturbances might travel along the light cone, but that's not what the light cone is about, and it exists regardless of whether there are such disturbances.