B-theory: Specifying the temporal ordering of all events in space-time exhausts all the objective temporal facts about those events.
A-theory: Specifying the temporal ordering of all events in space-time does not exhaust all the objective temporal facts about them. There is a further temporal fact about a given event: whether it is in the past, in the present or in the future. These are objective facts that are not fixed by merely specifying which events happen earlier or later.
There is a further temporal fact about a given event: whether it is in the past, in the present or in the future.
In the past, present or future of what?
Of me, who is saying it? But that is merely a temporal fact of the first kind: the given event is in the past/future of the event of my saying whether it is in my past/future.
The point of A-theory is that past, present and future are non-relational. There is an objective fact of the matter about which slice of the space-time manifold is the present, although this fact keeps changing, of course. So yeah, one way to think of the difference between A-theory and B-theory is that the B-theorist thinks of past, present and future as relational terms. Just saying “past” isn’t enough, you need to specify what it is in the past of. But the A-theorist thinks it makes sense to talk of past, present and future simpliciter.
An event (a point in spacetime) is really objective wrt time: that is, it is outside of time. The ordering of two events is also objective.
The matter of where we are in time—and therefore, whether an event is in our past or in our future—is constantly changing as time flows. It is not a time-objective fact about an event that it is in our future, for tomorrow it will be a fact about the same event that it is in our past. So these facts about an event are subjective: they depend on when in time you are when you are making the judgement.
Disagreeing with this seems like saying the word “objective” should mean two different things in the two above paragraphs. Which is apparently what almost all big philosophical arguments reduce to. Sigh.
So these facts about an event are subjective: they depend on when in time you are when you are making the judgement.
You’re describing a B-theoretical perspective. An A-theorist will disagree with this characterization. Many A-theorists believe that the only objects that exist are present objects. So time isn’t like space, where “here” is “here” rather than “there” simply because you happen to be “here” and not “there”. You could have been “there”, in which case “there” would have been “here” for you. Time, A-theorists claim, is different, because you couldn’t be located anywhere (anywhen) else except in the present. It’s not that the present is the present for you because you happen to be there; it’s that the only time at which objects exist (and, by extension, you could exist) is the present. So it’s not like there are other people who exist at other times, for whom the present is different.
Don’t ask me to defend this view, though, because I think it’s nuts. A-theory vs. B-theory is one of those philosophical debates which should be declared closed. B-theory has clearly won.
I don’t think anyone’s made A-theory consistent with special relativity. But you can bodge general relativity/cosmological models a bit to get something that looks a bit like A-theory by insisting on a preferred foliation (e.g. look at spacelike surfaces with constant proper time since the Big Bang, and count everything on one such surface as the “real now”)
Bourne, from what I recall, makes A-theory consistent with special relativity by positing that there is an (undetectable) privileged reference frame. Is this correct? If it is, I wouldn’t really call that “consistent with special relativity”, more like “flying in the face of the central lesson of special relativity”.
Yeah, that’s basically right but I’m not sure that you’re being entirely fair to Bourne.
First, I think under standard definitions of consistent, he does show that an A-theory is consistent with SR (ie. they can both be true at once).
Second, I’m not sure it’s fair to say that he is “flying in the face of the central lesson of SR”—he may be flying in the face of the standard way of interpreting this lesson but his claim is precisely that this way of intrepreting the lesson isn’t the only way. The lesson can also be interpretted as “no privileged reference frame can be detected.”
I agree with the basic anti-Bourne sentiment but wonder whether the wording of your response undermines his claims more than they deserve—I don’t think they are inconsistent nor that they fly in the face of the central lesson. I guess I more just think that postulating undetectable physical features of the world in order to make a metaphysical thesis - that is based on intuition (the “present” intuition) that can be explained away—come out to be true is undesirable.
Though it should be noted that Bourne’s conclusion is mostly that presentism is the only sensible A-theory but that it’s not possible to decide between presentism and a B-theory (that is, he doesn’t argue that presentism must be true).
So this is just like the “bodge” I described for general relativity/cosmology, but with even less justification? The preferred foliation has no physical motivation at all, and is plucked entirely out of the aether (so to speak).
I’m not sure I’d count that as consistent with special relativity. Though in principle it would give the same predictions as special relativity.
A theory: The English sentence “Today is a Thursday” has the same meaning on all days when it is spoken, but its truth-value varies depending on when it is spoken. (The sentence always corresponds to the same proposition, but that proposition has variable truth value).
B theory: The English sentence “Today is a Thursday” means something different when it is spoken on different occasions. Each specific utterance has a truth value which never changes. (Again, each utterance corresponds to a different proposition, but any one such proposition always has the same truth value.)
If you can live with propositions whose truth value changes with time, then you’re probably an A-theorist. If something smells fishy about that, and you think that in any given possible world, a proposition is either true or false and never changes its truth value, you’re probably a B-theorist.
If put this way, definitely B. “Now” is a deictic, meaning ‘at the time when I’m speaking’, much like ‘here’ is a deictic meaning ‘in the place where I’m speaking’.
What happens when you throw relativity into the mix? How do you specify the order of events in space-time when it varies based on the location of the observer?
In relativity you still have temporal ordering of events, but it is not a total order. In a Newtonian world, every event is either earlier than, later than or simultaneous with every other event. In relativity, some events can still be unambiguously described as earlier than or later than others. Event A is earlier than event B if it is in B’s past light cone. There is no longer a relationship of simultaneity, however, and some pairs of events are not related by the earlier than/later than relation. The temporal order is a partial order.
That makes sense. Although it looks like you either have all information regarding where/when all events occurred relative to each other (which would necessarily give information about where/when all events happened in relation to an observer) or you have a partial ordering, which means you don’t have all the information.
The more I think about this, the more confused I get. How exactly does A differ from the information of what is in the observer’s past light cone and what isn’t? Or is this based on the idea of there being a single, consistent “present time” throughout the universe?
Although it looks like you either have all information regarding where/when all events occurred relative to each other (which would necessarily give information about where/when all events happened in relation to an observer) or you have a partial ordering, which means you don’t have all the information.
The partial ordering actually encodes a surprising amount of information about space-time. Specifying the temporal ordering relationship between space-time points also fixes the topological structure of space-time, its differential structure, and the metric up to a conformal factor. It doesn’t let you reconstruct the full metric, and maybe you think that certain metrical facts count as “temporal facts” (which seems right), in which case the definition of B-theory I gave above should be modified to include the claim that those metrical facts are provided as well. I don’t want to make the definitions too technical though, and I think the current version gets the essential idea across, so I’m going to leave it as is.
Also, who the hell has invented the names for that?
I hate names likes that (incl. System 1 vs. System 2 thinking, Type I vs Type II errors, etc.). I can never remember which name stands for which thing.
Wikipedia appears to confirm my memory of it (“McTaggart argued that the A series was a necessary component of any full theory of time, but that it was also self-contradictory and that our perception of time was, therefore, ultimately an incoherent illusion.”)
It seems like the sentence I quoted indicates that he didn’t consider it a “full theory of time”. I don’t feel like rereading the actual paper, though.
From memory, McTaggart argues that change is a necessary part of our concept of time. That B-theories can’t account for change and that A-theories are incoherent. Consequently, time does not exist (but presumably something with some similarities to time does)
Sort of lean toward B-theory, but I suspect other temporal facts may exist. However, they are not of the form “X is in the present/future/past.” Also, the nature of time may make these the wrong questions to ask as noted below.
Other: Events might not be ordered, yet time exists. This would be the case with the Timeless Barbourian Physics Yudkowsky discusses in the sequences.
Also could be the case if some variety of many worlds of quantum style, or all possible worlds of Lewis style is the case.
The Anthopic folk, like me, Katja, Bostrom and several others, might also amuse themselves by inquiring: Could in one of the many infinite universe (or Big universe) theories be the case that all time-like facts are some form of indexical fact?
Other. I think the most fundamental aspect of time is local quantum instability, rather than relationships such as “earlier than/later than” or “past-present-future” between events.
Poll: Should these polls have an “I don’t know” / neutral option?
[pollid:95]
Note: I haven’t included “I don’t know” on this poll because its purpose is to get the balance of opinion for/against. The other polls in the comments on this article are intended to get an overall picture of the local population, so it would be interesting if a question had a high percentage of “I don’t know” responses.
I’m amazed that these philosophy types get paid to to write about and teach what is essentially a trivial point in math, affine spaces (removing absolute point of origin), no pun intended.. How annoying.
I’m pretty sure that you don’t understand the problem being discussed, but that’s an uncharitable impression. Could you indulge me in some further explanation of what you mean by, say, the reference to affine spaces?
I’m pretty sure that you don’t understand the problem being discussed
That’s quite possible, though, having studied some General Relativity, I probably understand a bit more about time than an average philosopher.
Could you indulge me in some further explanation of what you mean by, say, the reference to affine spaces?
Indulging, quoting some Wikipedia:
A-series (non-affine) “is past”, “is present” and “is future.” Here there is a fixed (for a given time) origin.
B-series (affine): “comes before” (or precedes) and “comes after” (or follows). Here there is no fixed origin (no “fundamental difference between past and future”, whatever the vague term “fundamental” might mean).
That’s quite possible, though, having studied some General Relativity, I probably understand a bit more about time than an average philosopher.
I’d love to ask you some questions about that, average philosopher to physicist.
Indulging, quoting some Wikipedia:
Okay, so given the distinction between affine and non-affine spaces, the question which (I think) remains is whether or not time is an affine space or a non-affine space. How is that to be resolved?
Right, A-theory’s origin has to be ‘the present moment’. I think A theory probably even excludes the possibility of a beginning of time (Hawking once wrote an article in which he had to coin the phrase ‘imaginary time’ to discuss the question of how long ago the big bang was). I’m sure that’s not an uncontroversial claim though.
This may seem like a kind of fringe metaphysical concern (and it’s certainly a metaphysical concern), but I think the question of the reality of change is probably the original philosophical problem.
Ahh, that. What would be an empirical difference between the two? If none, then there is nothing to resolve.
But that’s the whole question: is it affine or non-affine?
As to what empirical difference it makes (and whether or not ‘none’ means that the question is meaningless) is I suppose a matter for another survey question.
But, if you think Julian Barbour or EY are generally on the right track about the implications of quantum physics, then you’re a B-theorist. Fundamentally, the rejection of A-theory is the rejection of the reality of change. If you’re a B-theorist, change is on the map, but not anywhere in the territory.
Ah, again. See, it matters to me not in the least whether it’s A or B or something else, if they predict all the same things. (As far as I can tell, they predict nothing of consequence, so they are not interesting at all.) As for Barbour, his models have nothing testable in them, as far I know (replace time with “change”? so?), which is a big negative against them. Whether the “block universe” notion is a good one still remains to be seen, so far it is not instrumentally useful. I do not understand EY’s fascination with Barbour. At least MWI, when taken literally, has a chance of being falsifiable.
Because it is not relevant. B-theory time and A-theory time are not related like an affine space is related to a vector space. You can’t get from B-theory time to A-theory time by picking an origin and calling it “the present”. The whole point of the A-theory is that the present is not a static point in time. It moves. The particular mathematical representation you suggest doesn’t capture this.
A-series (non-affine) “is past”, “is present” and “is future.” Here there is a fixed (for a given time) origin.
Indeed the transformation does not capture this apparently moving origin. What does “moving” mean in this context? How would you describe it mathematically? In the block universe model, this is ought to be pretty easy by introducing a shifting origin, but it is probably harder in the growing block universe model. I need to think about it some more, feel free to point me to any mathematical references if you know of any. Though I do not think I will continue in this thread, due to the distracting karma burn it seems to extract, reminding me that, on average, people don’t want me to.
This paper gives a reasonably rigorous mathematical treatment of the growing block model in the Newtonian, relativistic and causal set contexts. Also see this paper for a discussion of whether quantum gravity offers brighter prospects for A-theory than classical relativity. Let me know if you’d like ungated versions of either of these.
Time: B-theory or A-theory?
[pollid:79]
B-theory: Specifying the temporal ordering of all events in space-time exhausts all the objective temporal facts about those events.
A-theory: Specifying the temporal ordering of all events in space-time does not exhaust all the objective temporal facts about them. There is a further temporal fact about a given event: whether it is in the past, in the present or in the future. These are objective facts that are not fixed by merely specifying which events happen earlier or later.
In the past, present or future of what?
Of me, who is saying it? But that is merely a temporal fact of the first kind: the given event is in the past/future of the event of my saying whether it is in my past/future.
The point of A-theory is that past, present and future are non-relational. There is an objective fact of the matter about which slice of the space-time manifold is the present, although this fact keeps changing, of course. So yeah, one way to think of the difference between A-theory and B-theory is that the B-theorist thinks of past, present and future as relational terms. Just saying “past” isn’t enough, you need to specify what it is in the past of. But the A-theorist thinks it makes sense to talk of past, present and future simpliciter.
An event (a point in spacetime) is really objective wrt time: that is, it is outside of time. The ordering of two events is also objective.
The matter of where we are in time—and therefore, whether an event is in our past or in our future—is constantly changing as time flows. It is not a time-objective fact about an event that it is in our future, for tomorrow it will be a fact about the same event that it is in our past. So these facts about an event are subjective: they depend on when in time you are when you are making the judgement.
Disagreeing with this seems like saying the word “objective” should mean two different things in the two above paragraphs. Which is apparently what almost all big philosophical arguments reduce to. Sigh.
You’re describing a B-theoretical perspective. An A-theorist will disagree with this characterization. Many A-theorists believe that the only objects that exist are present objects. So time isn’t like space, where “here” is “here” rather than “there” simply because you happen to be “here” and not “there”. You could have been “there”, in which case “there” would have been “here” for you. Time, A-theorists claim, is different, because you couldn’t be located anywhere (anywhen) else except in the present. It’s not that the present is the present for you because you happen to be there; it’s that the only time at which objects exist (and, by extension, you could exist) is the present. So it’s not like there are other people who exist at other times, for whom the present is different.
Don’t ask me to defend this view, though, because I think it’s nuts. A-theory vs. B-theory is one of those philosophical debates which should be declared closed. B-theory has clearly won.
I don’t think anyone’s made A-theory consistent with special relativity. But you can bodge general relativity/cosmological models a bit to get something that looks a bit like A-theory by insisting on a preferred foliation (e.g. look at spacelike surfaces with constant proper time since the Big Bang, and count everything on one such surface as the “real now”)
See Craig Borne “A Future for Presentism” for someone who claims to have made an A-theory consistent with special relativity.
Bourne, from what I recall, makes A-theory consistent with special relativity by positing that there is an (undetectable) privileged reference frame. Is this correct? If it is, I wouldn’t really call that “consistent with special relativity”, more like “flying in the face of the central lesson of special relativity”.
Yeah, that’s basically right but I’m not sure that you’re being entirely fair to Bourne.
First, I think under standard definitions of consistent, he does show that an A-theory is consistent with SR (ie. they can both be true at once).
Second, I’m not sure it’s fair to say that he is “flying in the face of the central lesson of SR”—he may be flying in the face of the standard way of interpreting this lesson but his claim is precisely that this way of intrepreting the lesson isn’t the only way. The lesson can also be interpretted as “no privileged reference frame can be detected.”
I agree with the basic anti-Bourne sentiment but wonder whether the wording of your response undermines his claims more than they deserve—I don’t think they are inconsistent nor that they fly in the face of the central lesson. I guess I more just think that postulating undetectable physical features of the world in order to make a metaphysical thesis - that is based on intuition (the “present” intuition) that can be explained away—come out to be true is undesirable.
Though it should be noted that Bourne’s conclusion is mostly that presentism is the only sensible A-theory but that it’s not possible to decide between presentism and a B-theory (that is, he doesn’t argue that presentism must be true).
So this is just like the “bodge” I described for general relativity/cosmology, but with even less justification? The preferred foliation has no physical motivation at all, and is plucked entirely out of the aether (so to speak).
I’m not sure I’d count that as consistent with special relativity. Though in principle it would give the same predictions as special relativity.
Here’s maybe another way of thinking about it …
A theory: The English sentence “Today is a Thursday” has the same meaning on all days when it is spoken, but its truth-value varies depending on when it is spoken. (The sentence always corresponds to the same proposition, but that proposition has variable truth value).
B theory: The English sentence “Today is a Thursday” means something different when it is spoken on different occasions. Each specific utterance has a truth value which never changes. (Again, each utterance corresponds to a different proposition, but any one such proposition always has the same truth value.)
If you can live with propositions whose truth value changes with time, then you’re probably an A-theorist. If something smells fishy about that, and you think that in any given possible world, a proposition is either true or false and never changes its truth value, you’re probably a B-theorist.
If put this way, definitely B. “Now” is a deictic, meaning ‘at the time when I’m speaking’, much like ‘here’ is a deictic meaning ‘in the place where I’m speaking’.
What happens when you throw relativity into the mix? How do you specify the order of events in space-time when it varies based on the location of the observer?
In relativity you still have temporal ordering of events, but it is not a total order. In a Newtonian world, every event is either earlier than, later than or simultaneous with every other event. In relativity, some events can still be unambiguously described as earlier than or later than others. Event A is earlier than event B if it is in B’s past light cone. There is no longer a relationship of simultaneity, however, and some pairs of events are not related by the earlier than/later than relation. The temporal order is a partial order.
That makes sense. Although it looks like you either have all information regarding where/when all events occurred relative to each other (which would necessarily give information about where/when all events happened in relation to an observer) or you have a partial ordering, which means you don’t have all the information.
The more I think about this, the more confused I get. How exactly does A differ from the information of what is in the observer’s past light cone and what isn’t? Or is this based on the idea of there being a single, consistent “present time” throughout the universe?
The partial ordering actually encodes a surprising amount of information about space-time. Specifying the temporal ordering relationship between space-time points also fixes the topological structure of space-time, its differential structure, and the metric up to a conformal factor. It doesn’t let you reconstruct the full metric, and maybe you think that certain metrical facts count as “temporal facts” (which seems right), in which case the definition of B-theory I gave above should be modified to include the claim that those metrical facts are provided as well. I don’t want to make the definitions too technical though, and I think the current version gets the essential idea across, so I’m going to leave it as is.
Partial ordering.
What? since when can you specify a global order of events?
See here. Of course, we have to assume that our space-time meets certain causal conditions (it doesn’t have closed timelike curves, for instance).
Lean toward B-theory if pushed to answer, but I wonder what cognitive algorithm even generated this as a possibly interesting question.
Also, who the hell has invented the names for that?
I hate names likes that (incl. System 1 vs. System 2 thinking, Type I vs Type II errors, etc.). I can never remember which name stands for which thing.
J. M. E. McTaggart.
And he didn’t mean to name competing theories about time; he was trying to dismiss the both of them.
I think he was just a B-theorist (though he thought the self-contradictory A-theory was an ineliminable part of our thoughts about time).
Wikipedia appears to confirm my memory of it (“McTaggart argued that the A series was a necessary component of any full theory of time, but that it was also self-contradictory and that our perception of time was, therefore, ultimately an incoherent illusion.”)
Does it say he rejected the B-Theory?
It seems like the sentence I quoted indicates that he didn’t consider it a “full theory of time”. I don’t feel like rereading the actual paper, though.
Looking at the paper, I find that you’re right.
From memory, McTaggart argues that change is a necessary part of our concept of time. That B-theories can’t account for change and that A-theories are incoherent. Consequently, time does not exist (but presumably something with some similarities to time does)
Philosophy trivia: “J.M.E. McTaggart” stands for “John McTaggart Ellis McTaggart”.
“Other”: The nature of physics has a strong possibility of being such that the question makes no sense.
Same other, but with the nuance that there is probably a refinement of the question that does make sense.
A rough, likely wrong attempt at a refinement:
B’-time: as before, but with a partial order of events;
A’-time: as before, but with the extra data coming from any observer who can specify those events that conclusively are in their past or future.
Sort of lean toward B-theory, but I suspect other temporal facts may exist. However, they are not of the form “X is in the present/future/past.” Also, the nature of time may make these the wrong questions to ask as noted below.
Other: Events might not be ordered, yet time exists. This would be the case with the Timeless Barbourian Physics Yudkowsky discusses in the sequences.
Also could be the case if some variety of many worlds of quantum style, or all possible worlds of Lewis style is the case.
The Anthopic folk, like me, Katja, Bostrom and several others, might also amuse themselves by inquiring: Could in one of the many infinite universe (or Big universe) theories be the case that all time-like facts are some form of indexical fact?
Other. I think the most fundamental aspect of time is local quantum instability, rather than relationships such as “earlier than/later than” or “past-present-future” between events.
Other: I don’t know.
Poll: Should these polls have an “I don’t know” / neutral option? [pollid:95]
Note: I haven’t included “I don’t know” on this poll because its purpose is to get the balance of opinion for/against. The other polls in the comments on this article are intended to get an overall picture of the local population, so it would be interesting if a question had a high percentage of “I don’t know” responses.
I’m amazed that these philosophy types get paid to to write about and teach what is essentially a trivial point in math, affine spaces (removing absolute point of origin), no pun intended.. How annoying.
I’m pretty sure that you don’t understand the problem being discussed, but that’s an uncharitable impression. Could you indulge me in some further explanation of what you mean by, say, the reference to affine spaces?
That’s quite possible, though, having studied some General Relativity, I probably understand a bit more about time than an average philosopher.
Indulging, quoting some Wikipedia:
A-series (non-affine) “is past”, “is present” and “is future.” Here there is a fixed (for a given time) origin.
B-series (affine): “comes before” (or precedes) and “comes after” (or follows). Here there is no fixed origin (no “fundamental difference between past and future”, whatever the vague term “fundamental” might mean).
I’d love to ask you some questions about that, average philosopher to physicist.
Okay, so given the distinction between affine and non-affine spaces, the question which (I think) remains is whether or not time is an affine space or a non-affine space. How is that to be resolved?
It does have an origin (the Big Bang) if you will, but that’s not the kind of origin you’d need for A-theory to make sense.
Right, A-theory’s origin has to be ‘the present moment’. I think A theory probably even excludes the possibility of a beginning of time (Hawking once wrote an article in which he had to coin the phrase ‘imaginary time’ to discuss the question of how long ago the big bang was). I’m sure that’s not an uncontroversial claim though.
This may seem like a kind of fringe metaphysical concern (and it’s certainly a metaphysical concern), but I think the question of the reality of change is probably the original philosophical problem.
First, I would not want to give a wrong impression. While I do have a PhD, physics is not my day job.
Ahh, that. What would be an empirical difference between the two? If none, then there is nothing to resolve.
But that’s the whole question: is it affine or non-affine?
As to what empirical difference it makes (and whether or not ‘none’ means that the question is meaningless) is I suppose a matter for another survey question.
But, if you think Julian Barbour or EY are generally on the right track about the implications of quantum physics, then you’re a B-theorist. Fundamentally, the rejection of A-theory is the rejection of the reality of change. If you’re a B-theorist, change is on the map, but not anywhere in the territory.
Ah, again. See, it matters to me not in the least whether it’s A or B or something else, if they predict all the same things. (As far as I can tell, they predict nothing of consequence, so they are not interesting at all.) As for Barbour, his models have nothing testable in them, as far I know (replace time with “change”? so?), which is a big negative against them. Whether the “block universe” notion is a good one still remains to be seen, so far it is not instrumentally useful. I do not understand EY’s fascination with Barbour. At least MWI, when taken literally, has a chance of being falsifiable.
I think that’s a pretty good ‘other’ answer to the question. Thanks for taking the time.
A lot of philosophy is like this.
However, it takes a while to get to this point. The math in question dates essentially from the 19th century, while questions about time are ancient.
One would think that in over 100 years the philosophers would have caught on, if only they bothered to try.
Believe me, plenty of philosophers understand what an affine space is. Not enough, unfortunately, but still plenty.
Why then does SEP not mention it in the discussion of this A and B stuff? Certainly detracts from its credibility.
Because it is not relevant. B-theory time and A-theory time are not related like an affine space is related to a vector space. You can’t get from B-theory time to A-theory time by picking an origin and calling it “the present”. The whole point of the A-theory is that the present is not a static point in time. It moves. The particular mathematical representation you suggest doesn’t capture this.
Right, I was pondering that, too:
Indeed the transformation does not capture this apparently moving origin. What does “moving” mean in this context? How would you describe it mathematically? In the block universe model, this is ought to be pretty easy by introducing a shifting origin, but it is probably harder in the growing block universe model. I need to think about it some more, feel free to point me to any mathematical references if you know of any. Though I do not think I will continue in this thread, due to the distracting karma burn it seems to extract, reminding me that, on average, people don’t want me to.
This paper gives a reasonably rigorous mathematical treatment of the growing block model in the Newtonian, relativistic and causal set contexts. Also see this paper for a discussion of whether quantum gravity offers brighter prospects for A-theory than classical relativity. Let me know if you’d like ungated versions of either of these.