Can causality exist without time?

[69dodge]

A: I've this model in which there's a cosmological time t takes only positive values.
B: Doesn't that contradict causality? I mean, every event should be preceded by a cause.
A: Well, the state of the universe at every t has a prior state that determines it, which is as strong a sense of "cause" as it gets.
B: But what about t≤0? What happens then?
A: That makes no sense in this model; the entire universe has t>0. That's all there is.
B: I still think there's a contradiction. I like the idea of t in (-inf,inf) better, since it avoids it. Your model has nothing before t = 0; this one does!
A: What are you talking about? The model satisfies causality as you defined it. If you've some version of causality in mind, what is it?

I suppose it could be formalized thus: Not only every individual event has a cause that precedes it, but also every set of events, provided they all lie within a finite time interval.

 

[Perpetual Student]

OK, we have an unmistakable dissonance here. Thanks everyone for your responses. I will very carefully reread and study all the comments about the subject of t <(=) 0 to see what I'm missing. Clearly, either I have not understood some of the comments made and/or I have not articulated my thoughts well.

 

[69dodge]

So, I am now asking the question, "what was the universe like 16 billion years ago?" (years are defined as we all know, ultimately using the cesium atom.)

Now, the answer to that question may be among the following:
[...]
4. There was no universe and no time.
[...]
#4. is absurd because there is no basis for such a statement and it leads to all the contradictions I have already amply described. If the universe were nothing with no time 16 billion years ago, then there would still be nothing.

Language is funny.

Is the king of France bald?

Neither "yes" nor "no" is a correct answer. France doesn't have a king, who could have, or fail to have, hair. The question appears to ask about a particular person, but it really doesn't. There is no such person to ask about. The only reasonable response is that the question is meaningless.

"There was no universe and no time" is not an answer to the question "what was the universe like 16 billion years ago?" It's an explanation of why the question is meaningless. There never was a time called "16 billion years ago", so one can't meaningfully ask what the universe was like then. There is no such 'then' to ask about.

 

[The Man]

If you're using it that way, then it's true but without content--every space is clopen in itself, no matter what topology or other structure is defined on it. It's also extremely confusing, since in the same breath we're discussing differences of [0,inf) and (0,inf), so if they're both clopen in themselves (and neither is in the reals), what's the point of introducing topological distinctions? The word you're looking for as it applies to intervals is "half-open" (or "half-closed").

Actually what I was looking for was to make a comparison between a discrete space at the Planck scales with one at ‘universals’ scales, where even though the space of our current universe might be continuous it would still be discrete from some possible universe before and perhaps another after. I guess the Clopen reference was just a hold over from that consideration where [0,∞) would be the entire space for any one of those discrete universes but (0,∞) would just be a proper subset. You are correct though, since I choose not to go that route, by including that “content”, and just decided to keep it simple instead, the clopen reference was completely out of place in what I did end up writing and that was entirely my fault. Sorry, everyone.

I've been consistently making the exact opposite of his argument in various forms throughout this thread, including in the part you've just quoted.

Correct again, which is why I tried to address how it might seem supportive of his assertions, how it was not actually and specifically that I did not think you were arguing for his assertions. Of course all of that was in the text and context that was originally around that one single statement you’ve just quoted.

Well, that explains why he's slowly driving Sol insane (j/k). I made no claims about what PS has or hasn't done in that post, but since doing so would be a direct way to meet Sol's objection to him, so it was relevant.

Also correct, you’re batting 1000. Although you were making no claims about what PS has or hasn't done in that post, I was specifically addressing PS and his claims in the post to which you were responding. The question I was asking was specifically directed at PS and his claims which had nothing to do with any objections that might have already been addressed about or where others where moving the question (apparently without PS as his claims basically have not moved). So relevant, certainly, just not that relevant to what I was specifically asking PS.


Again, I am sorry for any confusion I might have caused as that was not my intent.

 

[Vorpal]

I guess the Clopen reference was just a hold over from that consideration where [0,∞) would be the entire space for any one of those discrete universes but (0,∞) would just be a proper subset.

But (0,∞) is not clopen in [0,∞) either, so how would that work? If you mean 'discrete' in the sense of that there is always a well-defined 'next moment in time', then you would have the opposite problem of every subset of [0,∞) being clopen under the induced topology (which would be, appropriately enough, the discrete topology).

Of course all of that was in the text and context that was originally around that one single statement you’ve just quoted.

Well, I confess I didn't parse your next sentence back then because of insomnia, but looking back, the missing word and your intended meaning should have been dead obvious, and the next part even more so. My mistake; apologies.

 

[The Man]

But (0,∞) is not clopen in [0,∞) either, so how would that work? If you mean 'discrete' in the sense of that there is always a well-defined 'next moment in time', then you would have the opposite problem of every subset of [0,∞) being clopen under the induced topology (which would be, appropriately enough, the discrete topology).

If your remember (0,∞) was the open interval (as a proper subset of the ‘Clopen’ [0,∞)). The idea really was a discrete series of [0,∞) intervals each representing the whole space (or in this case proper time) for some given universe like ours. The problem was representing them as equivalent disjoint connected components. As intervals of the set of real numbers with say the next universe (after our current one) being Universe₁ as interval [2,3], the previous universe perhaps Universe_-1 as [-3,-2] and our current universe then being as Universe₀ being [-1,1]. Which would give the topological space U for those three universes as the union of [-3,-2], [-1,1] and [2,3]. Those sets would be Clopen in space U and would make that space discrete, if I was thinking right. Set theory and topology have never been my forte. I was going to do a similar thing for a discrete space in our current universe where instead of universes being considered it would be Planck units. So Universe₁ as interval [2,3] becomes Planck₁ as interval [2,3]. The real problem was at our current universe (or Planck value) at [-1,1] spanning two units and thus giving it a distinguishing feature. If I could have gotten it to make sense to me I might have actually put it in the post, but as it was just confusing me I figured it would most likely cause me to make it incomprehensible to others. So I opted for the “hey let’s try to make things actually understandable for most readers” approach, but still must have had the clopen aspect stuck in my head.

Well, I confess I didn't parse your next sentence back then because of insomnia, but looking back, the missing word and your intended meaning should have been dead obvious, and the next part even more so. My mistake; apologies.

No problems and thanks again for pointing out my oversights.

 

[Vorpal]

Well, you could just define the topology to have the basis of consisting of all the open real intervals (which by itself forms the standard Euclidean topology) together with the singleton sets {n} for nonzero integers n. Then the connectied components include {..., (-3,-2),(-2,-1),(-1,1),(1,2),...}, all of which would now be clopen. This is almost what you describe, just lacking the endpoints and not skipping intervals. It might represent something like the cyclic version of a closed universe with its "parts" completely separated from each other, since the [nonzero] integer singletons are now topologically isolated. But why have a special two-unit interval?

Which would give the topological space U for those three universes as the union of [-3,-2], [-1,1] and [2,3]. Those sets would be Clopen in space U and would make that space discrete, if I was thinking right.

They would be clopen in their union, yes, but not 'discrete' as the word is used in topology (having nontrivial clopen subsets just means the space is disconnected, not discrete). However, somehow I get the feeling you are doing something other than what you literally described here. If you define an equivalence relate identifying the points in each individual subintervals (but not across the subintervals), that would be a discrete space, but then it seems like an overly complicated way of just taking the induced topology of the nonzero integers from the reals. The end results are identical. If that's not what you're doing, then I don't understand your intended connection to Planck units.

 

[Perpetual Student]

Question:

Using current big bang models, is the universe's past considered to be a finite period of time or an infinite one?

 

[martu]

Question:

Using current big bang models, is the universe's past considered to be a finite period of time or an infinite one?

Finite.

 

[The Man]

Well, you could just define the topology to have the basis of consisting of all the open real intervals (which by itself forms the standard Euclidean topology) together with the singleton sets {n} for nonzero integers n. Then the connectied components include {..., (-3,-2),(-2,-1),(-1,1),(1,2),...}, all of which would now be clopen. This is almost what you describe, just lacking the endpoints and not skipping intervals. It might represent something like the cyclic version of a closed universe with its "parts" completely separated from each other, since the [nonzero] integer singletons are now topologically isolated. But why have a special two-unit interval?

The two unit interval was a problem not intent. Yeah, I did consider excluding the endpoints, I also considered just having the central intervals half open like {…, [-3,-2], [-1,0), (0,1], [2,3], …}but wasn’t quite sure if that would work also it made those intervals special (or inconsistent with the others) and both of those considerations had the problem of loosing 0 as a member meaning not having any definitive ordinate for “now”, although they do get rid of the two-unit interval.

They would be clopen in their union, yes, but not 'discrete' as the word is used in topology (having nontrivial clopen subsets just means the space is disconnected, not discrete). However, somehow I get the feeling you are doing something other than what you literally described here. If you define an equivalence relate identifying the points in each individual subintervals (but not across the subintervals), that would be a discrete space, but then it seems like an overly complicated way of just taking the induced topology of the nonzero integers from the reals. The end results are identical. If that's not what you're doing, then I don't understand your intended connection to Planck units.

Form my understanding a topological space “is discrete if and only if all of its subsets are clopen”. Again if I had felt it significant or could have gotten it to make sense to myself, I most likely would have actually posted it before. Without that understanding myself it is highly unlikely that I can effectively explain it to anyone else. Really it was just something that clicked in my head when thinking about an actual no time after T = 0 limit for this universe. Then [0,∞) becomes the whole space that any discrete or continuous topology could be applied (at least for time). The one fact that did stick with me that I did include in that post is that as the whole space (at least for time in this universe) it would be clopen. Although, as I said, including that was really pointless in what I did end up writing (especialy without explaing it). As usual with me I have got to mull things over until they make sense to me otherwise I just do not make sense myself when talking with others. Most times I’ve just got to leave it alone for a wile until something else clicks that brings it up again, sometimes it just gets tossed away when some better understanding comes along or it just remains as another dead end of my understanding. I certainly do appreciate your tying to help but I’ve just got to get it right in my head first before I can try to put it in someone else's head.

 

[arthwollipot]

Okay. Well, the discussion has definitely passed waaaaay over my head now and I no longer have any clue what you guys are talking about.

My opponent has indicated on the other board that he has registered here, and intends to come and post in this thread. Try to be nice to him, okay? He's really a good bloke.

 

[orange31]

Ultimately (no pun intended), Time is a dimension that is no more or less 'real' than the other 3, so perhaps this dimension simply didn't exist prior to the bang. That doesn't rule out 'something' existing prior to the bang.
We have difficulty conceptualizing a universe without time, but we also have difficulty conceptualizing things proven to exist like nonlocality in QM.

 

[ynot]

In my non-academic opinion - Time is a verb not a noun. Time is no more a thing than bounce is. Time describes the actions of things but time is not a thing. One event causing another event is what we generically describe as time. Time doesn’t become a thing just because a theory requires it to be so.

 

[arthwollipot]

In my non-academic opinion - Time is a verb not a noun. Time is no more a thing than bounce is. Time describes the actions of things but time is not a thing. One event causing another event is what we generically describe as time. Time doesn’t become a thing just because a theory requires it to be so.

Time can be a transitive verb - you can "time" how long someone takes to finish a race. But in general, time is not a verb. It is a noun - technically an abstract noun, since it refers to something that cannot in principle be placed in a box. Time in the sense of this thread is definitly not a verb.

Just because time is not reified doesn't mean that the word is not a noun. You can't put thought in a box either.

I agree that by some definitions, "time" is simply the word we use to label the fact that things don't all occur at once.

 

[RevDisturba]

Hi Mr Arthwollipot and hello to everyone. I will post a proper intro in the intro section. I am known as Rev Binary in the other forum where I and Arthwollipot have some spirited and productive debates. We don’t agree on a lot of topics I being a Open Christian Theist (think liberal Christian theist) and he a spirited and somewhat evangelical atheist. (I am not sure of his position about being a hard or soft atheist etc).

Thanks to everyone for attempting to define and encapsulate our question. Has anyone definitely answered the question yet? ie can causality operate independent of time (I think it can although its very counter intuitive). I apologize for not reading all the replies in their entirety.

We may need a professor of mathematics to give us a ‘slam dunk answer‘. I approached the professor of mathematics (a PhD) at the state university where I do some volunteer work at and asked him the question. He told me that quite frankly, physics wasn’t his specialty but he would research it and give me a definite answer as soon as time allowed.

I have a Masters in comparative theology which is not heavy on physics! I now wish I had took some electives in advanced math, and still may as I am taking some night classes.

Anyway my understanding is that time is a dimension in ‘space’. We can present time and space as definite equal, or equivalent members of space time. There is no preferred direction like up down back or forward (but there is, of course an ‘arrow of time’ .

I think what confuses us is that we think of cause and effect as related to time, when its really not! We are really trying to explain causality by the arrow of time rather than time itself. Time does not ‘care’ if events run forwards or backwards etc. Yes, time as one physicists said exists only to keep everything from happening at once.

However these individual things still exist but without time. Time is not a requirement for the 'existence' of events. Time is only a coordinate. Nevertheless, our intuition lies to us telling us that they need the effect of time to unfold! So I do not think that time is necessary for events to remain separate.

I need to get an answer from that professor fast!

Thanks for everyones replies.

: {>

 

[Modified]

However these individual things still exist but without time. Time is not a requirement for the 'existence' of events. Time is only a coordinate. Nevertheless, our intuition lies to us telling us that they need the effect of time to unfold! So I do not think that time is necessary for events to remain separate.

Even if you define things that way, separate events does not get you causation.

 

[RevDisturba]

Why? The events exist eh?

; {>

 

[sol invictus]

Anyway my understanding is that time is a dimension in ‘space’. We can present time and space as definite equal, or equivalent members of space time. There is no preferred direction like up down back or forward (but there is, of course an ‘arrow of time’ .

That's incorrect. Time is mathematically distinct and different from the spatial dimensions.

I think what confuses us is that we think of cause and effect as related to time, when its really not!

Again, incorrect. I don't know of any definition of causality that does not involve time - certainly the physics definitions do.

Time does not ‘care’ if events run forwards or backwards etc.

It's true that the laws of physics look essentially identical if you reverse the direction of time. But that has little to do with the technical definition of causality (which I gave early on).

In causal theories you can start from any point in time and go forward or backward. The fact that we perceive time as going forward is irrelevant.

 

[martu]

Hi Mr Arthwollipot and hello to everyone. I will post a proper intro in the intro section. I am known as Rev Binary in the other forum where I and Arthwollipot have some spirited and productive debates. We don’t agree on a lot of topics I being a Open Christian Theist (think liberal Christian theist) and he a spirited and somewhat evangelical atheist. (I am not sure of his position about being a hard or soft atheist etc).

Thanks to everyone for attempting to define and encapsulate our question. Has anyone definitely answered the question yet? ie can causality operate independent of time (I think it can although its very counter intuitive). I apologize for not reading all the replies in their entirety.

We may need a professor of mathematics to give us a ‘slam dunk answer‘. I approached the professor of mathematics (a PhD) at the state university where I do some volunteer work at and asked him the question. He told me that quite frankly, physics wasn’t his specialty but he would research it and give me a definite answer as soon as time allowed.

I have a Masters in comparative theology which is not heavy on physics! I now wish I had took some electives in advanced math, and still may as I am taking some night classes.

Anyway my understanding is that time is a dimension in ‘space’. We can present time and space as definite equal, or equivalent members of space time. There is no preferred direction like up down back or forward (but there is, of course an ‘arrow of time’ .

I think what confuses us is that we think of cause and effect as related to time, when its really not! We are really trying to explain causality by the arrow of time rather than time itself. Time does not ‘care’ if events run forwards or backwards etc. Yes, time as one physicists said exists only to keep everything from happening at once.

However these individual things still exist but without time. Time is not a requirement for the 'existence' of events. Time is only a coordinate. Nevertheless, our intuition lies to us telling us that they need the effect of time to unfold! So I do not think that time is necessary for events to remain separate.

I need to get an answer from that professor fast!

Thanks for everyones replies.

: {>

No. Time is required for events to happen, without time there are no events.

 

[Perpetual Student]

I have extracted and pasted together the following from Wikipedia:

"Extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This singularity signals the breakdown of general relativity. How closely we can extrapolate towards the singularity is debated—certainly not earlier than the Planck epoch.[The Planck epoch ... is the earliest period of time in the history of the universe, from zero to approximately 10⁻⁴³ seconds (one Planck time), during which quantum effects of gravity were significant.] The early hot, dense phase is itself referred to as "the Big Bang", and is considered the "birth" of our universe. Based on measurements of the expansion using Type Ia supernovae, measurements of temperature fluctuations in the cosmic microwave background, and measurements of the correlation function of galaxies, the universe has a calculated age of 13.73 ± 0.12 billion years. The agreement of these three independent measurements strongly supports the ΛCDM model that describes in detail the contents of the universe."



"Stephen Hawking in particular has addressed a connection between time and the Big Bang. ... Hawking says that even if time did not begin with the Big Bang and there were another time frame before the Big Bang, no information from events then would be accessible to us, and nothing that happened then would have any effect upon the present time-frame. Upon occasion, Hawking has stated that time actually began with the Big Bang, and that questions about what happened before the Big Bang are meaningless. This less-nuanced, but commonly repeated formulation has received criticisms from philosophers such as Aristotelian philosopher Mortimer J. Adler."

"Scientists have come to some agreement on descriptions of events that happened 10−35 seconds after the Big Bang, but generally agree that descriptions about what happened before one Planck time (5 × 10⁻⁴⁴ seconds) after the Big Bang will likely remain pure speculation."

After having re-read and re-thought my comments about time and causality if t > 0, I see several flaws in my comments. Nevertheless, a "beginning of time (as viewed by Hawking)" is not a satisfactory concept for me. "Time having a beginning" is profoundly counterintuitive. Proposals like the following (hopefully in time there will be more work done) are promising:

"__brane cosmology models in which inflation is due to the movement of branes in string theory; the pre-big bang model; the ekpyrotic model, in which the Big Bang is the result of a collision between branes; and the cyclic model, a variant of the ekpyrotic model in which collisions occur periodically.
__chaotic inflation, in which inflation events start here and there in a random quantum-gravity foam, each leading to a bubble universe expanding from its own big bang."*

*The above is also taken from a Wikipedia article.