For those who dabble in theoretical physics, can you help answer questions on the bulleted items listed under “Mathematical Construction” at this link:
a) What is the difference between a point on the future light cone and a point inside the future light cone? Wouldn’t they behave the same? Or, would a point on the cone never catch up to influence some future event? (Analogous to a permanent dusk seen on the arctic circle at the first day of winter?)
b) Why is do past events form a past light cone? I find this hard to fathom. The article says imagine the time clock running backwards. From that perspective, I get it. i just struggle with the concept of both past and future being cone-shaped at the same time. (I’m not sure what shape I see the collection of past events being if time runs forward, but a cone doesn’t seem logical. In other words, with time running forward, am I to picture that past events would “funnel” into and converge upon event, “E”???)
c) Last, why do all events appear the same regardless of your frame of reference? Does it have something to do with the fact that you cannot accelerate light?
On the cone means that only something as fast as the speed of light (e.g., a photon in a vacuum) can possible receive or transmit data with the Event in the center. In the cone is for everything else moving slower than C.
If an event 10 light-years from you took place 5 years ago, it is outside your past cone. It is impossible for you to know that event took place or for it to have some sort of causal effect on your present Event. So, like the future cone but in reverse: Instead of the future cone indicating the range of space-time you can send a message to or have a causal effect upon; the past cone indicates all those events in the past that can get a message to you or causally effect you.
Sort of. No matter what your frame of reference, you and all other observers will measure the same beam of light as going at exactly light-speed. Your own relative movement ‘distorts’ space itself making everyone come to the same conclusion over how fast that that beam of light traveled. And since the ‘cones’ are determined by the speed of light, everyone measures out the same cone for a specific Event.
Wow, Moriah! Thanks for the responses! I find this stuff fascinating, but hard to wrap my brain around until I read it several times and let it simmer in my brain for several days. Eventually, the light dawns and I have a better understanding of these abstract concepts.
You can be sure I will be reading and re-reading your reply until it “clicks”!
Thanks again!
Just to add a bit here, keep in mind, the further you are separated in space, the further you are separated in time because the fastest light and information can proliferate through space is c.
The future cone (to you) shows whatever event you’ve done (let’s say, turned on a disco ball) can only be detected from the point you turned the disco ball on (the point of the cone), and as its dazzling light shoots across space at c, it maps out a conical shape as it graphs this proliferation across time and space.
The past cone simply shows whatever events that led up to you turning on the disco ball that could’ve affected you doing so (barring time travel). If I learned the dance started exactly at 9:00 pm, your time, and I was a light-hour away, but it was already 8:01 pm your time, I would be outside your past cone, and could do absolutely nothing to stop it.
In more pragmatic terms, astronomers, cosmologists and physicists can determine what events could’ve or couldn’t have had an affect on other objects separated across spacetime.
Also, in reality, it’s not a cone, but a 4-dimensional sphere (3+1) that spreads throughout spacetime at the speed of light, like a bubble.
If someone was a light minute away, they couldn’t dance until your disco ball cone (or bubble, really) grew to 1 light-minute in radius.
Not a four-dimensional sphere: in 1+1 dimensions, you have the two points (a zero-dimensional sphere) tracing out the light rays, forming the ‘cone’, in 2+1 dimensions, you have a circle, a one dimensional sphere, which traces out a proper 2-dimensional double cone, and in 3+1 dimensions, you have the heavenly sphere of light rays incident on (past lightcone) or emitted from (future lightcone) a certain event. This traces out a ‘3-cone’, the three-dimensional analog to the 2-dimensional double cone in 2+1 dimensions.
I didn’t want to muddy the waters yet yet with hyperdimensional analogies. But yes, since we’re talking about spacetime, you’d have your typical sphere, expanding at c, and if you graphed that sphere in 2 dimensions (isometrically) along the 1 dimension of time, you’d get the graph as drawn on the Wiki page provided from the OP.
It’s somewhat harder to imagine using all the dimensions (3 spatial + 1 temporal), but it’d be a sphere starting from a point, and would smear out a mirrored, conical volume along the time axis as it expands at c in all directions. Any timelines you’d care to draw would trace out a line within that volume, so if you we’re dancing to the music and light of the disco ball, your body would trace out a far, far tinier worm-like filament in the future cone (emerging from the origin) as you were Stayin’ Alive.