That said, I can certainly write a computer program in which there’s a tier of objects affecting each other, and a second tier—a lower tier—of epiphenomenal objects which are affected by them, but don’t affect them.
I would like to point out that any space-like surface (technically 3-fold) divides our universe into two such tiers.
Okay, I can see that I need to spell out in more detail one of the ideas here—namely that you’re trying to generalize over a repeating type of causal link and that reference is pinned down by such generalization. The Sun repeatedly sends out light in individual Sun-events, electrons repeatedly go on traveling through space instead of vanishing; in a universe like ours, rather than the F(i) being whole new transition tables randomly generated each time, you see the same F(physics) over and over. This is what you can pin down and refer to. Any causal graph is acyclic and can be divided as you say; the surprising thing is that there are no F-types, no causal-link-types, which (over repeating time) descend from one kind of variable to another, without (over time) there being arrows also going back from that kind to the other. Yes, we’re generalizing and inducting over time, otherwise it would make no sense to speak of thingies that “affect each other”. No two individual events ever affect each other!
I will probably reskim the post, but in general it’s not clear to me that editing content into a preexisting posts is better than incorporating then into the next post where it would be appropriate. The former provides the content to all people yet to read it and all people who will reread it while the latter provides the content to all people who yet to read it. So you are trading the time value of getting updated content to the people who will reread this post faster at the expense of not getting updated content to those who will read the next post but not reread the present post.
I don’t have readership and rereadership stats, but this seems like an answerable question.
Okay, I can see that I need to spell out in more detail one of the ideas here—namely that you’re trying to generalize over a repeating type of causal link and that reference is pinned down by such generalization.
Somewhat tangentially, I’d like to point out that simply bringing up relative frequencies of different types of events in discussion doesn’t make one a crypto-frequentist—the Bayesian approach doesn’t bar relative frequencies from consideration. In contrast, frequentism does deprecate the use of mathematical probability as a model or representation of degrees of belief/plausibility.
Er, no, they’re called Dynamic Bayes Nets. And there are no known unique events relative to the fundamental laws of physics; those would be termed “miracles”. Physics repeats perfectly—there’s no question of frequentism because there’s no probabilities—and the higher-level complex events are one-time if you try to measure them precisely; Socrates died only once, etc.
So… the past can affect the future, but the future cannot affect the past (barring things like tachyons, which may or may not exist in any case). Taking this in context of the article could lead to an interesting discussion on the nature of time; does the past still exist once it is past? Does the future exist yet in any meaningful way?
Consider for a moment the concept of the lack of simultaneity in special relativity.
Consider, specifically, the train and platform experiment. A train passes a platform travelling at a significant fraction of the speed of light; some time before it does so, a light bulb in the precise centre of the train flashes, once.
The observer T on the train will find that the light reaches the front and back of the train simultaneously; the observer P on the platform finds that the light hits the back of the train before it hits the front of the train.
Consider now the instant in which the train observer T says that the light is currently hitting the front and the back of the train simultaneously. At that precise instant, he glances out of the window and sees that he is right next to the platform observer P. the event “P and T pass each other” occurs at that same instant. Thus, all three events—the light hitting the front of the train, the light hitting the rear of the train, and P and T passing, are simultaneous.
Now consider P. In P’s reference frame, these events are not simultaneous. The occur in the following order:
The light hits the rear of the train
T passes P
The light hits the front of the train
So. In the instant in which T and P pass each other, does the event “the light hits the rear of the train” exist? It is not in the past, or future, lightcone of the event “T and P pass each other”, and thus cannot be directly causally linked to that event (barring FTL travel, which causes all sorts of headaches for relativity in any case).
In the instant in which T and P pass each other, does the event “the light hits the rear of the train” exist?
The phrase “In the instant in which T and P pass each other” has a different meaning (namely, it refers to a different spacelike hypersurface) depending on what frame of reference the speaker is using. Some of those hypersurfaces include the event “the light hits the rear of the train” and others don’t.
That is true. Nonetheless, you have two observers, T and P, who disagree at a given moment on whether the event “the light hits the rear of the train” is currently happening, or whether it has already happened. (Another observer can be introduced for whom the event has not yet happened).
So. If the present exists—that is, if everything which is on the same spacelike hypersurface as me at this current moment exists—then every possible spacelike hypersurface including me must exist. Which means that, over in the Andromeda galaxy, there must be quite a large time interval that exists all at once (everything that’s not in my past/future light cone). Applying the same argument to a hypothetical observer in the Andromeda Galaxy implies that a large swath of time over here must all be in existance as well.
Now, it is possible that there is one particular spacelike hypersurface that can be considered to be the only spacelike hypersurface in existance at any given time; if this were the case, though, then I would expect that there would be some experiment that could demonstrate which spacelike hypersurface it is. That same experiment would disprove special relativity, and require an updating of that theory. On the other hand, if the past and future are in existance in some way, I would expect that there would be some way, as yet undiscovered, to affect them—some way, in short, to travel through time (or at least to send an SMS to the past). Either way, it leads to interesting possibilities for future physics.
First of all, natural language sucks at specifying whether a statement is indexical/deictic (its referent depends on who is speaking, and where and when they are speaking, etc.) or not. The compulsory tense marking on verbs is part of the problem (“there is” is usually but not always taken to mean “there is now” as “is” is in the present tense, and that’s indexical—“now” refers to a different time in this comment than in one written three years ago), though not the only one (“it’s not raining” is usually taken to mean “it’s not raining here”, not “it’s not raining anywhere”).
Now, it is possible that there is one particular spacelike hypersurface that can be considered to be the only spacelike hypersurface in existance at any given time
Yes, once you specify (explicitly or implicitly) what you mean by “at any given time” (i.e. what frame of reference you’re using). But there’s no God-given choice for that. (Well, there’s the frame of reference in which the dipole anisotropy of the cosmic microwave background vanishes, but you have to “look out” to know what that is; in a closed system you couldn’t tell.) IOW the phrase “at any given time” must also be taken as indexical; in everyday life that doesn’t matter much because the hypersurfaces you could plausibly be referring to are only separated by tiny fractions of a second in the regions you’d normally want to talk about.
On the other hand, if the past and future are in existance in some way,
Yes, if “are” is interpreted non-indexically (i.e. not as “are now”).
I would expect that there would be some way, as yet undiscovered, to affect them—some way, in short, to travel through time (or at least to send an SMS to the past).
Why? In special relativity, “X can affect Y” is equivalent to “Y is within or on the future light cone of X”, which is a partial order relation, and that’s completely self-consistent. (But in the real world, special relativity only applies locally, and even there we can’t be 100% sure it applies exactly and in all conditions.)
Yes, once you specify (explicitly or implicitly) what you mean by “at any given time” (i.e. what frame of reference you’re using).
This is where it all gets complicated. If I’m trying to talk about one instantaneous event maintaining an existence for longer than an instant—well, language just isn’t structured right for that. An event can partake of many frames of reference, many of which can include me at different times by my watch (particularly if the event in question takes place in the Andromeda Galaxy). So, if there is one reference frame where an Event occurs at the same time as my watch shows 20:00, and another reference frame shows the same (distant) event happening while my watch says 21:00, then does that Event remain in existence for an entire hour?
That’s basically the question I’m asking; while I suspect that the answer is ‘no’, I also don’t see what experiment can be used to prove either a positive or a negative answer to that question (and either way, the same experiment seems likely to also prove something else interesting).
Yes, if “are” is interpreted non-indexically (i.e. not as “are now”).
I meant it as “are now”.
I would expect that there would be some way, as yet undiscovered, to affect them—some way, in short, to travel through time (or at least to send an SMS to the past).
Why? In special relativity, “X can affect Y” is equivalent to “Y is within or on the future light cone of X”, which is a partial order relation, and that’s completely self-consistent.
Because if it is now in existence, then I imagine that there is now some way to affect it; which in this case would imply time travel (and therefore at least some form of FTL travel)
First of all, Thou Shalt Not use several frames of reference at once unless you know what you’re doing or you risk being badly confused. (Take a look at the Special Relativity section of the Usenet Physics FAQ, especially the discussion of the Twin Paradox.) Possibly, get familiar with spacetime diagrams (also explained in that FAQ).
According to special relativity, the duration of the set of instants B in your life such as there exists an inertial frame of reference such that B is simultaneous with a fixed event A happening in Andromeda is 2L/c, where L is the distance from you to Andromeda. (Now you do need experiments to tell whether special relativity applies to the real world, but any deviation from it—except due to gravitation—must be very small or only apply to certain circumstances, or we would have seen it by now.)
I meant it as “are now”.
I’d say that the concept of “now” needs a frame of reference to be specified (or implicit from the context) to make sense.
Because if it is now in existence, then I imagine that there is now some way to affect it; which in this case would imply time travel (and therefore at least some form of FTL travel)
I think you are trying to apply to Minkowski spacetime an intuition that only applies to Galilean spacetime (and even then, it’s not an intuition that everyone shares; IIRC, there have been people thinking that instant action at a distance is counterintuitive and a reason to suspect that Newtonian physics is not the whole story for centuries, even before Einstein came along).
First of all, Thou Shalt Not use several frames of reference at once unless you know what you’re doing or you risk being badly confused.
I think that this is important; I have come to suspect that I am somewhat confused.
I think you are trying to apply to Minkowski spacetime an intuition that only applies to Galilean spacetime
This is more than likely correct. I would also note that I have been applying, over very long (intergalactic) distances, the assumption that there is no expansion, which is clearly wrong. I suspect that I should probably look more into General Relativity before continuing along this train of thought.
I would also note that I have been applying, over very long (intergalactic) distances, the assumption that there is no expansion, which is clearly wrong.
Andromeda is nowhere near so far away that the expansion of the universe is important. (In fact, according to Wikipedia it’s being blueshifted, meaning that its gravitational attraction to us is winning over the expansion of space.)
I would like to point out that any space-like surface (technically 3-fold) divides our universe into two such tiers.
Okay, I can see that I need to spell out in more detail one of the ideas here—namely that you’re trying to generalize over a repeating type of causal link and that reference is pinned down by such generalization. The Sun repeatedly sends out light in individual Sun-events, electrons repeatedly go on traveling through space instead of vanishing; in a universe like ours, rather than the F(i) being whole new transition tables randomly generated each time, you see the same F(physics) over and over. This is what you can pin down and refer to. Any causal graph is acyclic and can be divided as you say; the surprising thing is that there are no F-types, no causal-link-types, which (over repeating time) descend from one kind of variable to another, without (over time) there being arrows also going back from that kind to the other. Yes, we’re generalizing and inducting over time, otherwise it would make no sense to speak of thingies that “affect each other”. No two individual events ever affect each other!
Maybe you should elaborate on this in a top-level post.
I edited the main post to put it in.
I will probably reskim the post, but in general it’s not clear to me that editing content into a preexisting posts is better than incorporating then into the next post where it would be appropriate. The former provides the content to all people yet to read it and all people who will reread it while the latter provides the content to all people who yet to read it. So you are trading the time value of getting updated content to the people who will reread this post faster at the expense of not getting updated content to those who will read the next post but not reread the present post.
I don’t have readership and rereadership stats, but this seems like an answerable question.
So in the end, we’re back a frequentism.
Also, what about unique events?
Somewhat tangentially, I’d like to point out that simply bringing up relative frequencies of different types of events in discussion doesn’t make one a crypto-frequentist—the Bayesian approach doesn’t bar relative frequencies from consideration. In contrast, frequentism does deprecate the use of mathematical probability as a model or representation of degrees of belief/plausibility.
Er, no, they’re called Dynamic Bayes Nets. And there are no known unique events relative to the fundamental laws of physics; those would be termed “miracles”. Physics repeats perfectly—there’s no question of frequentism because there’s no probabilities—and the higher-level complex events are one-time if you try to measure them precisely; Socrates died only once, etc.
What about some of the things going on at the LHC?
So… the past can affect the future, but the future cannot affect the past (barring things like tachyons, which may or may not exist in any case). Taking this in context of the article could lead to an interesting discussion on the nature of time; does the past still exist once it is past? Does the future exist yet in any meaningful way?
I’d say “No, unless you’re using the words still and yet in a weird way.”
Consider for a moment the concept of the lack of simultaneity in special relativity.
Consider, specifically, the train and platform experiment. A train passes a platform travelling at a significant fraction of the speed of light; some time before it does so, a light bulb in the precise centre of the train flashes, once.
The observer T on the train will find that the light reaches the front and back of the train simultaneously; the observer P on the platform finds that the light hits the back of the train before it hits the front of the train.
Consider now the instant in which the train observer T says that the light is currently hitting the front and the back of the train simultaneously. At that precise instant, he glances out of the window and sees that he is right next to the platform observer P. the event “P and T pass each other” occurs at that same instant. Thus, all three events—the light hitting the front of the train, the light hitting the rear of the train, and P and T passing, are simultaneous.
Now consider P. In P’s reference frame, these events are not simultaneous. The occur in the following order:
The light hits the rear of the train
T passes P
The light hits the front of the train
So. In the instant in which T and P pass each other, does the event “the light hits the rear of the train” exist? It is not in the past, or future, lightcone of the event “T and P pass each other”, and thus cannot be directly causally linked to that event (barring FTL travel, which causes all sorts of headaches for relativity in any case).
The phrase “In the instant in which T and P pass each other” has a different meaning (namely, it refers to a different spacelike hypersurface) depending on what frame of reference the speaker is using. Some of those hypersurfaces include the event “the light hits the rear of the train” and others don’t.
That is true. Nonetheless, you have two observers, T and P, who disagree at a given moment on whether the event “the light hits the rear of the train” is currently happening, or whether it has already happened. (Another observer can be introduced for whom the event has not yet happened).
So. If the present exists—that is, if everything which is on the same spacelike hypersurface as me at this current moment exists—then every possible spacelike hypersurface including me must exist. Which means that, over in the Andromeda galaxy, there must be quite a large time interval that exists all at once (everything that’s not in my past/future light cone). Applying the same argument to a hypothetical observer in the Andromeda Galaxy implies that a large swath of time over here must all be in existance as well.
Now, it is possible that there is one particular spacelike hypersurface that can be considered to be the only spacelike hypersurface in existance at any given time; if this were the case, though, then I would expect that there would be some experiment that could demonstrate which spacelike hypersurface it is. That same experiment would disprove special relativity, and require an updating of that theory. On the other hand, if the past and future are in existance in some way, I would expect that there would be some way, as yet undiscovered, to affect them—some way, in short, to travel through time (or at least to send an SMS to the past). Either way, it leads to interesting possibilities for future physics.
First of all, natural language sucks at specifying whether a statement is indexical/deictic (its referent depends on who is speaking, and where and when they are speaking, etc.) or not. The compulsory tense marking on verbs is part of the problem (“there is” is usually but not always taken to mean “there is now” as “is” is in the present tense, and that’s indexical—“now” refers to a different time in this comment than in one written three years ago), though not the only one (“it’s not raining” is usually taken to mean “it’s not raining here”, not “it’s not raining anywhere”).
Yes, once you specify (explicitly or implicitly) what you mean by “at any given time” (i.e. what frame of reference you’re using). But there’s no God-given choice for that. (Well, there’s the frame of reference in which the dipole anisotropy of the cosmic microwave background vanishes, but you have to “look out” to know what that is; in a closed system you couldn’t tell.) IOW the phrase “at any given time” must also be taken as indexical; in everyday life that doesn’t matter much because the hypersurfaces you could plausibly be referring to are only separated by tiny fractions of a second in the regions you’d normally want to talk about.
Yes, if “are” is interpreted non-indexically (i.e. not as “are now”).
Why? In special relativity, “X can affect Y” is equivalent to “Y is within or on the future light cone of X”, which is a partial order relation, and that’s completely self-consistent. (But in the real world, special relativity only applies locally, and even there we can’t be 100% sure it applies exactly and in all conditions.)
This is where it all gets complicated. If I’m trying to talk about one instantaneous event maintaining an existence for longer than an instant—well, language just isn’t structured right for that. An event can partake of many frames of reference, many of which can include me at different times by my watch (particularly if the event in question takes place in the Andromeda Galaxy). So, if there is one reference frame where an Event occurs at the same time as my watch shows 20:00, and another reference frame shows the same (distant) event happening while my watch says 21:00, then does that Event remain in existence for an entire hour?
That’s basically the question I’m asking; while I suspect that the answer is ‘no’, I also don’t see what experiment can be used to prove either a positive or a negative answer to that question (and either way, the same experiment seems likely to also prove something else interesting).
I meant it as “are now”.
Because if it is now in existence, then I imagine that there is now some way to affect it; which in this case would imply time travel (and therefore at least some form of FTL travel)
First of all, Thou Shalt Not use several frames of reference at once unless you know what you’re doing or you risk being badly confused. (Take a look at the Special Relativity section of the Usenet Physics FAQ, especially the discussion of the Twin Paradox.) Possibly, get familiar with spacetime diagrams (also explained in that FAQ).
According to special relativity, the duration of the set of instants B in your life such as there exists an inertial frame of reference such that B is simultaneous with a fixed event A happening in Andromeda is 2L/c, where L is the distance from you to Andromeda. (Now you do need experiments to tell whether special relativity applies to the real world, but any deviation from it—except due to gravitation—must be very small or only apply to certain circumstances, or we would have seen it by now.)
I’d say that the concept of “now” needs a frame of reference to be specified (or implicit from the context) to make sense.
I think you are trying to apply to Minkowski spacetime an intuition that only applies to Galilean spacetime (and even then, it’s not an intuition that everyone shares; IIRC, there have been people thinking that instant action at a distance is counterintuitive and a reason to suspect that Newtonian physics is not the whole story for centuries, even before Einstein came along).
I think that this is important; I have come to suspect that I am somewhat confused.
This is more than likely correct. I would also note that I have been applying, over very long (intergalactic) distances, the assumption that there is no expansion, which is clearly wrong. I suspect that I should probably look more into General Relativity before continuing along this train of thought.
Andromeda is nowhere near so far away that the expansion of the universe is important. (In fact, according to Wikipedia it’s being blueshifted, meaning that its gravitational attraction to us is winning over the expansion of space.)