False, I have never observed that objects don’t spontaneously vanish when they’re out of my range.
A convenient implication of the “things past the Cosmological Horizon don’t exist anymore” belief occurs to me. All it takes to utterly annihilate any enemy you have is a fast ship. Fly as fast as you can away from them and poof, you’ve caused them to cease to exist! The “Ignore Them And They Will Go Away For Real” doomsday device.
You’re trying to come up with examples of my belief that seem silly, instead of focusing on rational arguments. You’re so focused on this goal that you ignore that flying beyond the Cosmological Horizon solves your problem even under your interpretation. If your enemies can never get you ever again, then isn’t it safe to say you’ve ended the war? Why would you be upset that your enemies exist somewhere in some other impossibly far away region of the galaxy, how would this be any different than having destroyed them or banished them to a different dimension?
The desire for vengeance has always seemed like another broken intuition to me. It increases the probability that someone will act on sunk costs. If you meant to talk about punishment as deterrence aimed at stopping bad actions from occurring, then flying away arguably achieves this end by making their bad actions cease to exist from your reference point. According to other views, it doesn’t. That would bring us back to the initial conflict.
My larger point is that we shouldn’t try using thought experiments or examples on things like this because they sneak moral and metaphysical assumptions into the argument without justifying those assumptions, and they also increase the prevalence of emotional biases. Although his specific example fails to help his point, and although it fails to help mine, I think that using any examples at all on problems like this should be avoided as much as possible.
Lightcone only makes sense as a concept if FTL is impossible. If impossible, you can never get far enough away to get the enemy outside your lightcone (without cooperation from your enemy). If possible, the limit of what you could ever see / interact with is unconnected from speed of light.
If FTL is impossible, then so is your travel-to-get-enemy-out-of-lightcone scenario.
No. This is actually a curious feature of living on an expanding universe. If you travel far enough away from something the expansion will be sufficient for light to be unable to reach it. My future light cone as of {now} actually contains things that my future light cone as of {now} does not. The status of the matter that has been taken out of our reach like that is the focus of the discussion.
Ok, I’ve thought about it, and I’m still confused about the terminology.
Suppose Alice and Bob agree to try to escape each other’s lightcone—so they start traveling away from each other at .5c (relative to the resting frame they started in). I’m a lawyer and can’t do the transformations, but I know that the speed Alice perceives Bob traveling at is less than c—let’s call that speed X.
If Alice breaks the agreement, turns around, and starts traveling towards Bob at a speed greater than X (relative to the mutual starting frame), she’ll eventually catch up with Bob.
Given that, either (a) I’ve made a mistake about how relativity works, or (b) it seems impossible for Bob to get outside of Alice’s lightcone. Please help.
You forgot that space itself is expanding. In theory, it’s possible for Alice and Bob to travel far enough apart that the space between them expands faster than light, meaning the distance between them continues to increase even if they travel toward each other at the speed of light.
Isn’t that violating the lightspeed limit? As you describe it, there’s a frame of reference in which Alice and Bob are moving away from each other faster than the photons they are traveling near.
The lightspeed limit is a local notion. Something whizzing by you cannot be clocked to travel at or faster than light, but there is no clear definition of the relative velocity of two spatially separated objects in a curved spacetime.
Putting this here to help passers-by. My basic confusion appears to have been caused by not realizing that the universe is stretching. Thus, we aren’t in an inertial frame with respect to other galaxies.
Inertial frame is a local notion, as well, so “inertial frame with respect to other galaxies” is not a meaningful statement. In GR inertial frame is generalized to a geodesic. There is also the concept of comoving frame, that in which the expansion rate looks the same in all directions.
It’s not so much ‘violating’ the lightspeed limit as laughing in its face because it isn’t constrained by it. Stuff within space travels at or less than the speed of light, space itself can do as it pleases (as determined by weirder stuff than just special relativity).
As you describe it, there’s a frame of reference in which Alice and Bob are moving away from each other faster than the photons they are traveling near.
I’m not sure on the appropriate terminology here. Do they call it “moving away from” when neither thing has moved but have simply become further away from due to space changing?
I guess the second {now} was supposed to be {later} or something?
No, if spoken the temporally separated ’now’s would be spoken such that it was obvious to the speaker that it was referring to the time between the first mark and the second mark—about a second and a half I’d guess. Similar to the usage when syncronyzing watches with “12:30 as of… now”. I had expected the formatting to convey to most readers a similar message but for reading—so a bit under a second. But not all readers have the same intuitions regarding ad hoc markup.
A convenient implication of the “things past the Cosmological Horizon don’t exist anymore” belief occurs to me. All it takes to utterly annihilate any enemy you have is a fast ship. Fly as fast as you can away from them and poof, you’ve caused them to cease to exist! The “Ignore Them And They Will Go Away For Real” doomsday device.
You’re trying to come up with examples of my belief that seem silly, instead of focusing on rational arguments. You’re so focused on this goal that you ignore that flying beyond the Cosmological Horizon solves your problem even under your interpretation. If your enemies can never get you ever again, then isn’t it safe to say you’ve ended the war? Why would you be upset that your enemies exist somewhere in some other impossibly far away region of the galaxy, how would this be any different than having destroyed them or banished them to a different dimension?
Depends, are you trying to escape your enemies or to punish them?
The desire for vengeance has always seemed like another broken intuition to me. It increases the probability that someone will act on sunk costs. If you meant to talk about punishment as deterrence aimed at stopping bad actions from occurring, then flying away arguably achieves this end by making their bad actions cease to exist from your reference point. According to other views, it doesn’t. That would bring us back to the initial conflict.
My larger point is that we shouldn’t try using thought experiments or examples on things like this because they sneak moral and metaphysical assumptions into the argument without justifying those assumptions, and they also increase the prevalence of emotional biases. Although his specific example fails to help his point, and although it fails to help mine, I think that using any examples at all on problems like this should be avoided as much as possible.
Works for you. They really can’t come after you.
Lightcone only makes sense as a concept if FTL is impossible. If impossible, you can never get far enough away to get the enemy outside your lightcone (without cooperation from your enemy). If possible, the limit of what you could ever see / interact with is unconnected from speed of light.
Yes, which universe do you live in? FTL is impossible in this one!
If FTL is impossible, then so is your travel-to-get-enemy-out-of-lightcone scenario.
No. This is actually a curious feature of living on an expanding universe. If you travel far enough away from something the expansion will be sufficient for light to be unable to reach it. My future light cone as of {now} actually contains things that my future light cone as of {now} does not. The status of the matter that has been taken out of our reach like that is the focus of the discussion.
Ok, I’ve thought about it, and I’m still confused about the terminology.
Suppose Alice and Bob agree to try to escape each other’s lightcone—so they start traveling away from each other at .5c (relative to the resting frame they started in). I’m a lawyer and can’t do the transformations, but I know that the speed Alice perceives Bob traveling at is less than c—let’s call that speed X.
If Alice breaks the agreement, turns around, and starts traveling towards Bob at a speed greater than X (relative to the mutual starting frame), she’ll eventually catch up with Bob.
Given that, either (a) I’ve made a mistake about how relativity works, or (b) it seems impossible for Bob to get outside of Alice’s lightcone. Please help.
You forgot that space itself is expanding. In theory, it’s possible for Alice and Bob to travel far enough apart that the space between them expands faster than light, meaning the distance between them continues to increase even if they travel toward each other at the speed of light.
Isn’t that violating the lightspeed limit? As you describe it, there’s a frame of reference in which Alice and Bob are moving away from each other faster than the photons they are traveling near.
The lightspeed limit is a local notion. Something whizzing by you cannot be clocked to travel at or faster than light, but there is no clear definition of the relative velocity of two spatially separated objects in a curved spacetime.
I don’t suppose you have a link to a reasonably accessible explanation of this point?
Maybe this will help… It’s not overly accurate, but seems to be accessible enough.
Putting this here to help passers-by. My basic confusion appears to have been caused by not realizing that the universe is stretching. Thus, we aren’t in an inertial frame with respect to other galaxies.
Inertial frame is a local notion, as well, so “inertial frame with respect to other galaxies” is not a meaningful statement. In GR inertial frame is generalized to a geodesic. There is also the concept of comoving frame, that in which the expansion rate looks the same in all directions.
I’m afraid the links I’ve seen are all actually less accessible than shminux’s explanation.
It’s not so much ‘violating’ the lightspeed limit as laughing in its face because it isn’t constrained by it. Stuff within space travels at or less than the speed of light, space itself can do as it pleases (as determined by weirder stuff than just special relativity).
I’m not sure on the appropriate terminology here. Do they call it “moving away from” when neither thing has moved but have simply become further away from due to space changing?
I guess the second {now} was supposed to be {later} or something?
No, if spoken the temporally separated ’now’s would be spoken such that it was obvious to the speaker that it was referring to the time between the first mark and the second mark—about a second and a half I’d guess. Similar to the usage when syncronyzing watches with “12:30 as of… now”. I had expected the formatting to convey to most readers a similar message but for reading—so a bit under a second. But not all readers have the same intuitions regarding ad hoc markup.
Is one of those {now}s supposed to be a {then}?
Was going for instantiation while typing or reading.
Ah! Yeah, that works. It might be clearer to make that instantiation explicit by replacing the ‘now’ with ‘time of writing’ and ‘time of reading.’