B Do all events in my past lightcone have fewer past events in theirs?

[ESponge2000]

TL;DR Summary

And do all events in my future lightcone have fewer future events in theirs?

But all events in my past cone have
more future events in their cone even after they subtract off the ones in my past light cone? … than the number of events in my future light cone ?

And all events in my future cone have more past events in their cone even after they subtract off “their” past events that are also the ones in my future light cone?

Correction though: events in my past lightcone mean events that are by the laws of physics eligible for me to be able to observe, where what
( i actually can observe is limited by other restrictions of course such as brightness or frequency ot light and obstacles and mediums blocking transparency and choices of what to observe etc )

I just want to make sure I have this right.

Maybe this preaching to the choir obvious and is the definition of the preservation of cause-effect, but I want to confirm this.

My Past lightcone at present won’t be my past lightcone when my clock advances by one second.

At a snapshot my past lightcone represents all events that “could have been eligible to cause effects on my immediately present”

At a snapshot , my future lightcone represents all events that “could be eligible to have effects based on actions I take in the immediate present”.

Event - a point in spacetime, a snapshot at a single location point on a single point in clocktime at that location

And then the deeper points would be :
Events I can be eligible to on potentially observe at present are events that have the ability to “cause” effects outside my future lightcone and also outside my past lightcone too , correct ? Because if I’m looking a laser light beam of an object far away and that object far away had another laser lightbeam pointed in a different direction even farther from me , Then there is no way that some events in that future lightcone can be affected by my reaction to that same event.

 

[Ibix]

do all events in my future lightcone have fewer future events in theirs?

Both have an infinite number of events, so you can't really talk about it in those terms.

The future lightcone of any event in your future lightcone is a subset of the events in your future lightcone would be the correct way to say it. And that would be true.

The syntax of your other questions seems rather tortured and I'm not sure quite what you are asking. A Minkowski diagram would help - and probably answer the question for you.

 

[ESponge2000]

And one piece that is a bit confusing , cosmic inflation … some events in the universe will never ever ever be in our future lightcone, eternally but does that mean that all events that will be in our future light cone will also not have light cones containing the events that never will be in our future cone? I guess this is confusing because “locations” of objects in the universe are not fixed in space to our X coordinate. But when we say the light is moving away too fast to travel towards us a very confusing question i have is what about the light of an object at a distance that is viewable from a point and time that is in our past lightcone? Sorry for the confusion.

For us to never be able to see an object eternally , because it’s moving away too fast , does that also imply that all objects we can see that aren’t drifting away too fast also can’t see that same other object ever ever ? Because if the answer here is no it’s a puzzle for my head

 

[ESponge2000]

Both have an infinite number of events, so you can't really talk about it in those terms.

The future lightcone of any event in your future lightcone is a subset of the events in your future lightcone would be the correct way to say it. And that would be true.

The syntax of your other questions seems rather tortured and I'm not sure quite what you are asking. A Minkowski diagram would help - and probably answer the question for you.

This is simply a big X through an X-Y cartesian graph where X coordinate is a dimension of space and Y coordinate is Time
where the middle of the X is the origin of our present space time and the V-shapes at top and bottom of the giant X means our lightcone, right ? The v shapes to the left and right are what we are not allowed to be able to have any causal relationship with or else we would be eligible to have paradoxes.
Although I can see common-cause …. Like if I rapidly rotate a laser beam over a faraway star I can easily affect locations with my laser light at a faster interval than any light from one part of that star can travel to another part of that star, which shows as my top of my X v-shape overlaps part of the right or left v-shapes of a separate X originating inside the top of my V

And then since all line travels at exactly 45-degree angles and even when the reference frames are altered the , all X drawings From all points inside the top and bottom V of our X should have parallel diagonals to our X meaning future and future are subjects , and to the bottom , past and past are subsets,

But how do we show the cosmic inflation effects on Minkowski ?

 

[Ibix]

And then since all line travels at exactly 45-degree angles and even when the reference frames are altered the , all X drawings From all points inside the top and bottom V of our X should have parallel diagonals to our X meaning future and future are subjects , and to the bottom , past and past are subsets,

You seem to have it.

But how do we show the cosmic inflation effects on Minkowski ?

You don't - Minkowski spacetime is not expanding (Milne coordinates aside, before somebody picks me up on that). You can, however, draw diagrams of cosmological spacetimes in which light travels on 45° lines and obviously draw the same conclusions. Davis and Lineweaver shows some examples.

 

[Dale]

Both have an infinite number of events, so you can't really talk about it in those terms.

It seems fine to me. One is a proper subset of the other, so it isn’t about the number of elements but which set is the subset and which is the superset.

 

[Ibix]

It seems fine to me. One is a proper subset of the other, so it isn’t about the number of elements but which set is the subset and which is the superset.

I thought that was what I wrote? I had a problem with "has fewer events" applied to comparing two infinite sets, not the notion of one set being a subset of the other.

 

[Dale]

I thought that was what I wrote? I had a problem with "has fewer events" applied to comparing two infinite sets, not the notion of one set being a subset of the other.

You are not wrong. The word “fewer” refers to the number of entities. But “less events” just sounds awkward for some reason. I think we can let the English slide a bit

 

[pbuk]

You are not wrong. The word “fewer” refers to the number of entities. But “less events” just sounds awkward for some reason. I think we can let the English slide a bit

I think you are missing @Ibix's point: it doesn't matter whether you use "fewer", "less" or even "smaller", all of these words imply that the cardinality of two sets is unequal whereas that is clearly not the case here.

 

[Dale]

I think you are missing @Ibix's point: it doesn't matter whether you use "fewer", "less" or even "smaller", all of these words imply that the cardinality of two sets is unequal whereas that is clearly not the case here.

No. Fewer refers to cardinality, less refers to amount e.g. of a continuous thing. So, "distance A is less than distance B" doesn't mean that the cardinalities are different.

 

[pbuk]

But the OP did not say "distance A is less than distance B", they said "events in my past cone have more future events ... than the number of events in my future light cone".

How is this not cardinality?

 

[Dale]

But the OP did not say "distance A is less than distance B", they said "events in my past cone have more future events ... than the number of events in my future light cone".

How is this not cardinality?

”More water”
could refer to water as a continuum or as a countable number of water molecules. Personally, I usually measure water in liters rather than moles. But neither is wrong

The English is ambiguous. I never realized that the opposite of both “less” and “fewer” is “more”

 

[pbuk]

”More water”
could refer to water as a continuum or as a countable number of water molecules.

No, you are still missing the point. The OP is comparing two future light cones, each of which is by definition infinite, and it is therefore wrong to say that one has more of anything than the other.

 

[Dale]

No, you are still missing the point. The OP is comparing two future light cones, each of which is by definition infinite, and it is therefore wrong to say that one has more of anything than the other.

It isn’t wrong. It is just non-technical.

One light cone is a proper subset of the other. All of the events in the subset cone are in the superset cone. Some of the events in the superset cone are not in the subset. What other non-technical word captures this relationship better than “more”?

 

[Dale]

@ESponge2000

You can look up the terms proper subset and proper superset.

Let $A$, $B$, and $C$, be events with past light cones $P_i$ and future light cones $F_i$. Further, assume $A$ is in $P_B$ and $C$ is in $F_B$. Then $F_A$ is a proper superset of $F_B$ which is a proper superset of $F_C$. And $P_A$ is a proper subset of $P_B$ which is a proper subset of $P_C$.