Can We "See" Effect Before Its Cause?

[silverrahul]

TL;DR Summary

I know effect cannot occur before cause. But is it possible to "see" effect before cause ?I

If there are 2 events E1 and E2 which have a causal relationship, E1 is the cause and E2 is the effect. We know that there is no frame of reference in which E2 occurs before E1

Now, if there are 2 more events
E1x = light from E1 reaching observer X
E2x = light from E2 reaching obseever X

Now ,is it possible that there is some observer X in whose frame of reference, E2x occurs before E1x i.e. he "sees" E2 happening before E1 ?

 

[phinds]

You'll want to study the relativity of simultaneity and timelike and spacelike separations

 

[PeterDonis]

is it possible that there is some observer X in whose frame of reference, E2x occurs before E1x i.e. he "sees" E2 happening before E1 ?

No. This follows from the fact that E1 must be in the past light cone of E2 (since that is required for E1 to be a cause of E2) and that both E1 and E2 must be in the past light cone of the observer who sees them (since that is required for the events to be seen). The details are left as an exercise for the reader.

 

[PeroK]

Now ,is it possible that there is some observer X in whose frame of reference, E2x occurs before E1x i.e. he "sees" E2 happening before E1 ?

The light from event 1 could take a longer path to your eyes than the light from event 2. E.g. if the light from the event 1 has to bounce off a mirror to reach your eyes.

Or, in gravitational lensing, light from the same distant event may reach you from two different paths that take different times to reach your eyes. So, you may see the same event twice at different times with the light arriving dfrom different directions.

 

[PeterDonis]

The light from event 1 could take a longer path to your eyes than the light from event 2. E.g. if the light from the event 1 has to bounce off a mirror to reach your eyes.

This could be the case if there were an artificial obstruction that prevented light from traveling straight to your eyes from event 1. But there will always be a direct lightlike path through spacetime from event 1 that reaches the observer before the most direct lightlike path through spacetime from event 2. Whether some obstruction prevents light rays from traveling on such a direct lightlike path is not really relevant to the question the OP appears to be asking.

 

[silverrahul]

The light from event 1 could take a longer path to your eyes than the light from event 2. E.g. if the light from the event 1 has to bounce off a mirror to reach your eyes.

Or, in gravitational lensing, light from the same distant event may reach you from two different paths that take different times to reach your eyes. So, you may see the same event twice at different times with the light arriving from different directions.

I guess, I was not talking about artificial constraints like light having to bounce off mirrors and travel a roundabout path etc. In that case, of course, the light from a "cause" event could take a circuitous path and reach the observer's eyes MUCH later than the light from the "effect" event.

My response to your reply echo what PeterDonis says "Whether some obstruction prevents light rays from traveling on such a direct lightlike path is not really relevant to the question the OP appears to be asking."

 

[PeroK]

I was just asking about the case of flat space time, no gravitational effects etc. and no artificial constraints making the light from one event take a circuitous path

I guess the answer is that in an inertial reference frame in flat spacetime, space is Euclidean and the triangle inequality applies. Let's say event 1 takes place at location $X_1$, event 2 at location $X_2$ and the observer is at location $O$. In some inertial reference frame where $O$ is at rest.

The triangle inequality says that $|X_1O| \le |X_1X_2| + |X_2O|$, with equality only when the three locations are colinear. The constancy and maximality of the speed of light does the rest.

 

[Dale]

In order to see the effect an observer must be in the future light cone of the effect. The future light cone of the effect lies entirely within the future light cone of the cause. So if an observer is within the future light cone of the effect then they are also within the future light cone of the cause.

 

[Mister T]

I guess, I was not talking about artificial constraints like light having to bounce off mirrors and travel a roundabout path etc. In that case, of course, the light from a "cause" event could take a circuitous path and reach the observer's eyes MUCH later than the light from the "effect" event.

My response to your reply echo what PeterDonis says "Whether some obstruction prevents light rays from traveling on such a direct lightlike path is not really relevant to the question the OP appears to be asking."

Then let's take a closer look at the last statement you made in your OP:

Now ,is it possible that there is some observer X in whose frame of reference, E2x occurs before E1x i.e. he "sees" E2 happening before E1 ?

He may see E2 before he sees E1, but he will always conclude that E2 occurs after E1. He may have to account for the light travel time due to reflections from distant mirrors or the like, but after doing so he will conclude that E1 occurred before E2.

 

[PeterDonis]

He may see E2 before he sees E1

Only if some artificial obstruction prevents light from taking the direct path from E1 to him. If light from both E1 and E2 follows the direct path to the observer, the observer will always see E1 before he sees E2, not just calculate that E1 occurs first. (There is actually one edge case where the observer sees both events at the same instant: if E1 is directly behind E2 from the observer's viewpoint.)

 

[silverrahul]

Then let's take a closer look at the last statement you made in your OP:
He may see E2 before he sees E1, but he will always conclude that E2 occurs after E1. He may have to account for the light travel time due to reflections from distant mirrors or the like, but after doing so he will conclude that E1 occurred before E2.

The intent of my question was that there is no such reflections from mirrors or anything like that.

 

[Office_Shredder]

The intent of my question was that there is no such reflections from mirrors or anything like that.

Then E1 occurs. Light travels along a straight line to an observer. Also something travels no faster than light to where E2 occurs, after which light travels to the observer. So the second thing is no faster than the first thing, and doesn't travel in the straight line. Hence it gets there later.