Exploring the TL Interval Square Measurement

[LCSphysicist]

I was reading about the general theory of relativity, and came to a chapter that the author start to talk about an invariant measurement by [TL] named interval square. It's the first time that i read about it, and i don't get it yet.

An event, what he is calling, is anything? If I am thinking about this.

Is like, i am with my hands raised, so then i drop my hands to my side, this action will, even if small, modify the space and the information of my "lowering hands" will propagate with the speed of c??

Like, if the sun fades away, and we just find out 8min 20 seconds later??

Sorry if i am completely wrong, i really in doubt,

 

[Orodruin]

An event is a point in spacetime. In other words, it is a specified place at a specified time.

 

[jedishrfu]

Light travels at a defined speed in all inertial frames of reference.

If you are holding your hands up and someone is watching you from afar, then when you drop your hands they won't know it until the light from your hands has reached their eyes which depends on the distance between the two of you.

A simpler classical example of delayed signal is when you see lightning strike a tree some distance away and then a few seconds later you hear the thunderclap because sound travels so much slower than light.

 

[Nick-stg]

In other words, it is a specified place at a specified time.

But is it? It is a specific place and time to the observer but both the place and time can differ for another observer in a different inertial frame of reference, yet the event itself remains the event eg: you hands with up.

I'm not expert and if I'm understanding this wrong then please let me know, but this is my understanding.

 

[PeterDonis]

if the sun fades away

The sun can't fade away; that would violate conservation of energy. However, it is true that, if the sun were to, say, explode, we would not know about it for 8 minutes and 20 seconds, since that's how long light signals showing the explosion would take to reach Earth.

 

[Ibix]

An event, what he is calling, is anything?

Remember that relativity talks about spacetime, a 4d thing. A point in space is a line in spacetime because that point exists at all times. If that doesn't make sense, draw a pair of axes on a piece of paper amd label the horizontal one $x$ and the vertical one $t$. This is a sketch (called a Minkowski diagram or spacetime diagram) of a 2d slice through spacetime. Now draw $x=3$ (a specified point in space) - which should be a vertical line three units from the $t$ axis. If I want you to mark a dot on a spacetime diagram I need to specify a place and a time (e.g. $x=3,t=7$). That's called an event.

Nothing has to happen at an event. It's just a location in spacetime - a point at a given time, as Orodruin says. "Interval" is the "distance" between events. But spacetime is non-Euclidean and that "distance" is calculated using $\Delta s^2=c^2\Delta t^2-\Delta x^2-\Delta y^2-\Delta z^2$ instead of the familiar Pythagoras' Theorem.

 

[Ibix]

But is it? It is a specific place and time to the observer but both the place and time can differ for another observer in a different inertial frame of reference, yet the event itself remains the event eg: you hands with up.

Yes. A point in space at a specified time is a point in space at a specified time, whatever coordinate system is in use. Sure, two frames of reference might use "five metres to my left six seconds from now" to refer to different events, but that's what the Lorentz transforms are for - so frame S can determine in its coordinates what event frame S' is talking about when an event is specified in its coordinates.

You can, of course, often specify an event in coordinate free terms, such as "the event where particle A and particle B collide". That's a time and a place. If you want that in coordinates, it's up to you to calculate the particle paths and determine the intersection time in your coordinates.

 

[LCSphysicist]

The sun can't fade away; that would violate conservation of energy. However, it is true that, if the sun were to, say, explode, we would not know about it for 8 minutes and 20 seconds, since that's how long light signals showing the explosion would take to reach Earth.

Continiuing with this absurde, the sun just disappeared, the Earth will just feel this eight minutes after, but... Well this seems to run away from assumption, but yet is a doubt about relativity and the postulates. That's is strange, but let's imagine [using the logic, if A is false, A -> B is true anyway], the light will take time to came, but will the Earth remains in your trajectory or will go by tangent? I am sorry i am a fool in relativity, i just begin to study like today this [i stop when i came in this events to understand better], so what i know and a fish now about this theory is the same.

 

[Orodruin]

Continiuing with this absurde, the sun just disappeared, the Earth will just feel this eight minutes after

Again, the Sun cannot "just disappear". That would violate local energy-momentum conservation.

 

[LCSphysicist]

Yeh, just to summarize so, a event is like a point (x,y,z,t) in space time, suject or not a some phenomenon?

 

[PeterDonis]

Continiuing with this absurde

That's not what PF is for.

a event is like a point (x,y,z,t) in space time

Yes, as you've already been told.

Thread closed.

 

[jedishrfu]

As a final post here: to further your understanding of Relativity there are a couple of books that might interest you:

For Special Relativity:

http://lightandmatter.com/sr/

and General Relativity for the upper-level undergraduate:

http://lightandmatter.com/genrel/