Can causality exist without time?

[sol invictus]

Make the following analogy: event a causally influenced event b is like a<b. That's rather close to real causality, actually - more than close enough for our purposes, and if your argument were valid (which it isn't) it would apply to this. OK?

Then, take the "universe" to be the open set of real numbers t such that t>0.

If there were no t < 0, then there can be no cause for events at t = 0 and later.

Every number t>0 has a number less than it (t/2, for example). t=0 is not in the set and so is irrelevant.

My understanding is that current models say nothing about t = 0; they do not claim there was no t = 0.

True, but nevertheless this is an explicit counterexample to your argument. There is no logical problem with a universe that contains all times t>0 - for example, every time has an infinite chain of causes before it.

 

[arthwollipot]

Interesting discussion. Thanks everyone.

I think so far the conclusion is that causality does require time. But strange things happen as T->0.

 

[theneedtoknow]

Well I could never understand "time" myself...isn't "time" just relative changes in positions between two previously selected entities? Just a little thought experiment - if we centre the point of the birth of the universe at the origin of a coordinate system, and at the time the universe comes into existence, a photon starts travelling along the x-axis of this coordinate system, wouldn't we be able to decribe everything else in the universe by relating it to this one photon? If we measure the x-coordinte of the position of this photon a number of times, and the only property of photons we knew is that they travel in straight lines, wouldn't we be able to replace "before" with "lower value of x-coordinate" and after with "higher value of x-coordinate" when we compare two events, and then describe events in the universe with the coordinates (x, y, z, x-position of the primordial photon)?

 

[The Man]

Given the invariant nature of the speed of light, time and distance are related by that proportion. So when we speak of a length of time T we are also speaking of a distance T*c. Likewise we can also refer to spatial distance as a measure of time D*c^-1 or light travel time. So even if one were to consider no change in relative position over a period of time there is still a change in position with regard to time as T*c. It might be easier to just think of time as that constantly changing position relative to T=0. Basically it is what you are essentially saying.

 

[martu]

Given the invariant nature of the speed of light, time and distance are related by that proportion. So when we speak of a length of time T we are also speaking of a distance T*c. Likewise we can also refer to spatial distance as a measure of time D*c^-1 or light travel time. So even if one were to consider no change in relative position over a period of time there is still a change in position with regard to time as T*c. It might be easier to just think of time as that constantly changing position relative to T=0. Basically it is what you are essentially saying.

This change in position with regard to time is what we consider as things getting older am I right? What are the consequences for light that moves at c, does it mean it doesn't get older?

 

[The Man]

This change in position with regard to time is what we consider as things getting older am I right? What are the consequences for light that moves at c, does it mean it doesn't get older?

In the proper parlance it is said that a photon experiences no passage of Proper Time. However as a photon is never stationary it is always changing spatial position which can also be represented in units of time or Coordinate Time. Since time is not absolute, ones reference to how “old” something is would depend on the relative time applied in that consideration. Although proper time is defined as basically a clock that a reference frame caries with itself, so in that respect a photon does not get “older”.

 

[martu]

In the proper parlance it is said that a photon experiences no passage of Proper Time. However as a photon is never stationary it is always changing spatial position which can also be represented in units of time or Coordinate Time. Since time is not absolute, ones reference to how “old” something is would depend on the relative time applied in that consideration. Although proper time is defined as basically a clock that a reference frame caries with itself, so in that respect a photon does not get “older”.

Thanks, very interesting.

So if I have this right if you go faster than light you go backwards in time and time itself must be expressed as some sort of spatial dimension in our universe.

My post about time being defined by the expansion of the universe seems quite sensible now.

 

[Perpetual Student]

Make the following analogy: event a causally influenced event b is like a<b. That's rather close to real causality, actually - more than close enough for our purposes, and if your argument were valid (which it isn't) it would apply to this. OK?

*************

Then, take the "universe" to be the open set of real numbers t such that t>0.

**************

Every number t>0 has a number less than it (t/2, for example). t=0 is not in the set and so is irrelevant.

**************
True, but nevertheless this is an explicit counterexample to your argument. There is no logical problem with a universe that contains all times t>0 - for example, every time has an infinite chain of causes before it.

I see no validity to these mathematical analogies. They simply do not apply. Numbers do not cause each other.
If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical. If there was once "no time," and no causality, then there would still be "no time." and no causality.

 

[Belz...]

A question for those who know a lot more about physics, cosmology and philosophy than I do.

I'm engaged in a discussion on another forum, and the topic has drifted to the idea of causality. My erstwhile opponent (who is a religious moderate with fundamental leanings, if that makes any sense - he is also not stupid and a very good debating partner, so please don't underestimate him) is suggesting that causality can exist without time. Otherwise, how could the universe have begun? Since time began at the instant of the universe's creation, then the creation's cause must have existed outside of time. Of course, this "cause" is God.

My contention is that causality cannot exist without time, because any sequence of events requires the existence of time. Otherwise, how can any one event even be said to occur "after" another, let alone be caused by it. My contention is also that there can be uncaused events (qv. the Kalam Cosmological Argument).

Is he right? Can one event cause another in the absence of time?

Assuming causality could exist without time, there'd be no way to tell since all events happen simultaneously.

 

[martu]

I see no validity to these mathematical analogies. They simply do not apply. Numbers do not cause each other.
If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical. If there was once "no time," and no causality, then there would still be "no time." and no causality.

Not if time is created by the universe and is a property of that universe only, time is relative after all. Time can't exist without matter and movement and it easy to imagine a universe without movement isn't it?

 

[Perpetual Student]

Assuming causality could exist without time, there'd be no way to tell since all events happen simultaneously.

Or:

There would be no "events."

 

[martu]

Or:

There would be no "events."

Or there could some events that happened all at once and some that didn't.

I just had a thought - if light speed was unbounded wouldn't that result in a universe without causality?

 

[sol invictus]

I see no validity to these mathematical analogies. They simply do not apply. Numbers do not cause each other.
If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical. If there was once "no time," and no causality, then there would still be "no time." and no causality.

What you said above makes no sense - "the universe" is not an event. If you mean to say "the creation of the universe at t=0", that fails as well, since as I keep trying to explain to you, one can simply remove the point t=0. Then every time has an infinite sequence of times preceding it.

Your claim was that a universe which has existed since t=0 is impossible because there would be an event with no cause. That claim is false.

The whole point of logic is that it's formal - that is, it doesn't matter what the specific objects in question are, only the formal rules they obey. If there's some formal rule you think applies to cause that does not apply to >, or vice versa, what is it?

 

[Richard Masters]

The concept of "without time" is meaningless in our universe. "Cause" is a time-based concept. To "happen" requires a before and after. Even "exist" suggests that there is a "now".

And just try conjugating verbs without a reference to time.

You can do this in some languages.

 

[Perpetual Student]

What you said above makes no sense - "the universe" is not an event. If you mean to say "the creation of the universe at t=0", that fails as well, since as I keep trying to explain to you, one can simply remove the point t=0. Then every time has an infinite sequence of times preceding it.

Your claim was that a universe which has existed since t=0 is impossible because there would be an event with no cause. That claim is false.

The whole point of logic is that it's formal - that is, it doesn't matter what the specific objects in question are, only the formal rules they obey. If there's some formal rule you think applies to cause that does not apply to >, or vice versa, what is it?

Formal rules will apply to two systems in the same way if there is an underlying identity of the two systems. You cannot demonstrate the identity of the real numbers and rules of causality and time. The real numbers form a field with all the defined rules of that structure. As I'm sure you know, there are other fields: The rationals, the complex numbers, etc. To be sure, a definition within the real numbers like "all real numbers" > 0 has a counterpart in time -- all t > 0. However there is a well defined 0 within the real numbers; there is no t = 0 in your models. The analogy fails!
Again: If there once was no time and no causality, then there would still be no time and no causality.

 

[sol invictus]

You didn't answer the question. What feature of causality does > not have which is necessary for your argument? If there isn't one, the argument is invalid.

However there is a well defined 0 within the real numbers; there is no t = 0 in your models. The analogy fails!

Apparently you didn't read what I wrote. Please re-read my posts (or Vorpal's) more carefully.

 

[The Man]

Thanks, very interesting.

So if I have this right if you go faster than light you go backwards in time and time itself must be expressed as some sort of spatial dimension in our universe.

My post about time being defined by the expansion of the universe seems quite sensible now.

Well that was just one, the relativistic, consideration and we know that relativity alone can not completely describe a photon. There are quantum mechanical considerations as well. Where relativity is continuous and specifically maintains causality (at least as we currently understand it) quantum mechanics is discrete and our current understanding of causality becomes tenuous at best. Currently we have no quantum theory of relativity so this is the conundrum of modern physics. In a quantum mechanical sense it is basically meaningless to consider time scales below the Plank Time about 5.39 x 10^-44 Seconds. So in that sense we can place that as a quantum limit on the proper time a photon might experience. Experimental limits on the proper time for a photon are currently orders of magnitude above that quantum limit. When considering the Planck limits, space time has been proposed to be a sheathing froth of virtual particles, cause and effect become interchangeable and our current understanding of casualty breaks down at those scales. To further exemplify this point, under the considerations of the Path Integral a traveling electron can interact with a virtual positron, resulting in annihilation and a virtual photon of gamma radiation. That photon can then become a virtual positron electron pair with the electron of that pair being the real electron that we might eventually detect. The virtual positron (basically being an electron traveling backwards in time) can be the positron that resulted in the initial annihilation event. Although these events have a strict temporal sequence with annihilation event preceding pair production event, a strict interpretation of causality is more of a problem. As the cause of the annihilation event is the virtual positron and the cause of the virtual positron is the virtual gamma photon resulting from the annihilation event caused by the virtual positron. These are more then just theoretical musing as we must consider such events if we want to accurately calculate the probability of detecting that electron at some point in the future. In fact it is only the consideration of such virtual events that permit us to calculate the anomalous magnetic moment of the electron, a calculation that agrees with experimental results to perhaps the highest degree of accuracy of any physical consideration. So although we can fundamentally assert that without time there is no causality we can not assert that without causality there is no time, at least not within our current understanding.

 

[Perpetual Student]

You didn't answer the question. What feature of causality does > not have which is necessary for your argument? If there isn't one, the argument is invalid.



Apparently you didn't read what I wrote. Please re-read my posts (or Vorpal's) more carefully.

OK, I re-read your and Vorpal’s posts and I understood the continue to understand the points made, specifically one can have an infinite chain of moments of time as one approaches t = 0. The analogy with the positive real numbers is quite clear. However, if t and x can approach 0 as close as we want, it does not follow "causes" can do the same. "Causes" cause things; numbers and moments in time do not. All the numbers x and moments t are independent mathematical entities (independently existing members of a set); "causes" are not independent, they cause one another.

OK, here’s another issue. As the above poster reminds us, the plank time is 5.39x10^-44 seconds, so that we cannot have an infinite chain of moments in time. That destroys the analogy between time and the real numbers. There is no equivalence of the real numbers and time, as defined in the “quantum world.”

Finally, you have not addressed my point that: If there were no t < 0 and no causality, then there would still be no t and no causality.

 

[Vorpal]

However, if t and x can approach 0 as close as we want, it does not follow "causes" can do the same.

Why not?

"Causes" cause things; numbers and moments in time do not.

The point is simply this: what is to prevent an infinite chain of causes located at some chain of events with time coordinates all monotonically decreasing to zero, but staying positive? Hence my first post--you seem to have some particular notion of causality in mind, but I've no idea what it is. What I can say is that in GTR there is a mathematically rigorous definition for what it means for a spacetime to have a causal structure, and that the family of solutions commonly used to model the Big Bang do not violate it.

OK, here’s another issue. As the above poster reminds us, the plank time is 5.39x10^-44 seconds, so that we cannot have an infinite chain of moments in time.

I'm not sure how that follows. If you want to talk about quantum mechanics, since quantum states evolve deterministically in time, it makes sense to say that a past state "causes" a future state. In the more esoteric areas like string theory, time is still continuous, and even loop quantum gravity does not quantize time per se (as far as I'm aware of--they may have fuzzyness at the hypervolume level).

Again, if you've some other notion of what a "cause" is, this discussion won't progress if you keep it private.

That destroys the analogy between time and the real numbers. There is no equivalence of the real numbers and time, as defined in the “quantum world.”

Cf. Schrödinger's equation.

 

[sol invictus]

"Causes" cause things; numbers and moments in time do not. All the numbers x and moments t are independent mathematical entities (independently existing members of a set); "causes" are not independent, they cause one another.

I gave a precise mathematical definition of causality earlier in the thread. For these purposes, it's not much different than >. Do you have a different definition in mind?

OK, here’s another issue. As the above poster reminds us, the plank time is 5.39x10^-44 seconds, so that we cannot have an infinite chain of moments in time.

Why not? All the Planck time tells us is that if physics extrapolates unchanged to the Planck energy, quantum effects on gravity become large. So?

Finally, you have not addressed my point that: If there were no t < 0 and no causality, then there would still be no t and no causality.

Take an eternal universe that lasts from t=-infinity to t=+infinity. Now change coordinates to T=e^t. The description in the new coordinates is just as valid as the original. Nothing happens to causality - this is just a change in how you choose to label events. But T>0.