[namaan (OP)]

This question follows from conjectures that time is just a tool we invented to divide up our day into manageable parts (granted I've only heard of this in popsci). But it also follows from my earlier post on whether time dilation can be looked as simply being a case of a longer-than perceived route that particles have to take at a quantum/planck scale.

So to approach the question from a more fundamental level, I wondered about particle systems. Can we describe the transitioning of states of a well-defined particle system without referencing time? I ask this because knowing all the variables of a system allows us to know exactly what the next state of the system will be without a need to reference time.

This is not the case, however, when considering a singular exception (as far as I can gather): that of a collision. While we can know in advance the path of any particle given any systemic state, we seem to inherently need to speak of a very specific moment in time in order to describe a collision event. So I guess the question becomes, can we describe collisions without referencing time?

[CliffordK]

You could certainly describe the particle collision, and the components created, or energy released without time, although, at least energy is defined with time.

However, you may just start redefining different measurements of time. 

Say you have 10 particles on a collision course.
3 have collided, 7 haven't
So, now, 30% out of 100% of the particles have collided. 
At another snapshot, 80% would have collided. 

So, in sense you have time.

Also, if you take sequential snapshots, you must have time to have sequential snapshots.

Concepts of "Before" and "After" need some kind of progression of time.

[MikeS]

Nothing happens, that does not happen within time.

Even a photo of a collision which is both stationary in action and a snapshot in time  has a built in (or at least can be inferred) arrow of time within a dynamic event.

[yor_on]

Let's put it like this. At the beginning of the Big Bang there is a moment before 'the energy' becomes radiation. If we now use radiation as a 'clock' then there was no arrow existent before that 'time' radiation exist.

So does that mean that 'time' didn't exist?

Can't be true, not if we by that mean interactions as in a ordered form. What, and how, it expressed itself before that we can't say really, not as I think anyway. It might be that what ordered a 'SpaceTime' was more of a synergetic effect, not linear at all. It might be that the ground is a little like when water becomes ice, a 'instant' expression of several probabilities 'coagulating'.

[JP]

You need time.  The idea of a transition implies that there is a before and an after state, which requires time.

[Soul Surfer]

Yes they can be described without any reference to time.  Consider the particle interaction as a box.  Two particles go in with known momenta and two (or possibly more) particles come out with known momenta.  This is an interaction. However it is quite possible to reverse the arrows and the interaction will be completely legitimate.  However there may be multiple possibilities and different probabilities for all possible interactions in either direction.  Time just does not enter into the equation.

[Bill S]

Yes they can be described without any reference to time.  Consider the particle interaction as a box.  Two particles go in with known momenta and two (or possibly more) particles come out with known momenta.

Surely, if no time were involved, the particleswould not be able to enter or leave the box; they would just remain in their original position.

Similarly, had there been no time before the Big Bang, it would not have been able to happen.

[namaan (OP)]

I'd respond to each post individually, but time flies (lame puns are fun Well, I'll try a bit.

Soul Surfer:

I'm not so sure. I don't think we can speak about particle systems so generally. The collision dynamics of any particle system has to take into account the exact shape of the particles (i.e. two spheres colliding head on will produce a far different result then if two spheres just clipped each others' sides). In any simulated particle system on a computer, the calculations are divided into "frames" that make up a continuous "video". Each frame can be represented by a single system state.

Having built 2D particle systems myself, time has been an unnecessary consideration for me when we're simply shifting states from one to the next. In this way, you could say from the perspective of the "universe" that is the particle system program, it is just a bunch of static states the transitioning of which happens to obey the law of cause and effect. You could further say that the program universe appears to us to simulate a particle system moving through time because it is "borrowing" the time from our universe (through the oscillations of quartz crystals).

Anyway, at least the way I've built particle systems, I've found time to be ultimately inescapable because it becomes important in between each frame or system state: that is when the collision generally takes place. No matter how you setup your system or even if you use quantized variables, you will still need to invoke time so long as one particle can move faster than another particle.

I'm not sure whether the above implies anything for or against the idea of time as being necessary, still just contemplating on it (and perhaps getting a little too philosophical).

[namaan (OP)]

CliffordK, MikeS and JP:

You're implying that to speak of state transitions is really a semantics game that ultimately doesn't affect a technical description of time? If so, I get where you're coming from but in an attempt at thoroughness, I'd like to point out something.

It's a bit technical in that it involves some programming concepts, but let's say you define a 2D particle system with five circular particles, each with position, velocity, radius and mass. Now, let's say you quantize the variables in that they can only increment or decrement in integer steps and preset the range of values that they can take on (i.e. x position can take values from -10000 to 10000 units only, and mass can be from 0 to 500 only).

With this sort of setup, there's a way to abstract a single integer that represents the exact state of the entire particle system. If you find the highest such integer N, you can go from 0 to N and cycle through every possible state in the system. And if you apply the set of rules that govern how these particles interact amongst each other to each state in a manner that respects cause and effect, you will get a list that tells you N_cause -> N_effect. Just these two integers per state [transition] (which are beyond astronomically large even for relatively simple systems) describe the system for all time. In other words, information about the system with time defined to infinity would exist all at once.

I'm still just contemplating on this, and would be interested to hear all your thoughts on this.

yor_on: I'll have to do some more thinking about your post before I can respond

[namaan (OP)]

In other words, information about the system with time defined to infinity would exist all at once.

I realized (on my drive home while not being a nuisance to the public at large) that this is wrong since it assumes that if you left a system to run on forever, it will necessarily cycle across all possible states over time. But if entropy has its way, which it will, a particle system that starts out in an ordered state will never again go back to that state no matter how long in time you let the system run. And if the system doesn't cycle across all its states, you can't contain all state transitions across time in a nice little (well, astronomically large) list.

I'm not sure where that leaves me...

[JP]

Well, you can describe certain processes without reference to time.  Time stationary random processes are one example (those whose statistics don't change over time).  Time stationary processes are another (trivial) example, which by definition don't change over time. 

But you asked specifically about collisions, which account for the transfer of energy and momentum between objects over time.  Classical collisions, and your example above, also specify velocity, which is the derivative of position with respect to time, so again you need time. 

[MikeS]

'Time' is what allows things to happen but stops them from happening all at once.

It does that because, like a river, it has a certain flow.  Why does it have a certain flow?  A rivers flow is driven by gravity and slowed by friction.  Surely the passage of time must be caused by something?  Personally I believe its  a relationship between gravity on the one hand and energy on the other.  Gravity we know slows the passage of time and I believe an increase in energy speeds the flow. 

We know that everywhere in the universe has its own particular time dilation.  I see no reason why all of these local 'times' can not be averaged to obtain a universal rate of time dilation.  That seems perfectly reasonable to me but I appreciate not everyone agrees with that.  If there is a universal rate of time dilation then it is reasonable to imagine that whatever is causing it, if it can vary, can effect the rate of universal time dilation. In other words, universal time, may not be constant.  For example it could have passed slower in the past and be speeding up.  Personally I believe 'Time' itself is an outcome of functions of the universe.  Therefore, prior to the universe there was no time.  The transition period between no universe (no energy) and universe (energy) saw the creation of time.

Shortly after the 'big bang' as it started to cool, the first simple atoms formed (hydrogen and helium).  This is the fuel that the universe continues to burn throughout its life.  Mass is being continually converted into energy.  So the universe is going from matter dominated to energy dominated.  Useful energy that was 'tied up' in matter is liberated and subject to entropy.  If the relationship that creates time is between energy and gravity then it seems reasonable to believe that the passage of time is increasing. 

The point being, nothing happens outside of time.  Time defines an event.

You need time.  The idea of a transition implies that there is a before and an after state, which requires time.

I don't think this is true.  It is more a problem of the inadequacies of language.

Another way of looking at it.
Before the 'big bang' there was no mass and therefore no gravity.  No gravity, no defined arrow of time. Time in a sense may have existed but flowed equally in both directions at the same time.   No causality.

The transition may have been between times arrow having no direction and having a direction.  In which case, the transition, in some sense, took place within time.

[yor_on]

How about this?

Let's split time in 'two'. One is the arrow we percieve around us, the other is time as a description of 'change'.
We live under a 'linear' arrow, it is what makes it possible for us to correlate events. But, it is also a conceptual description of what we observe as our 'linear' causality chains.

And then we have 'change' itself. As JP points out any change presumes a 'before and a 'after' You can't discuss a change without that inside SpaceTime, not as I see it. But maybe that is the 'arrow' expressing itself? Not 'time' itself. As if 'time' is what allows the stream(s) we find to be the arrow to exist?

[Soul Surfer]

Bill s Namaan and possibly other you are probably misreading what I have said.  The box is the volume defined by quantum uncertainty in this case  I also specified the particles momentum (mass times velocity) in all cases.  Assuming that there are no other interactions outside the box nothing else happens to the only time is the instant the interaction happens.

[namaan (OP)]

Well, you can describe certain processes without reference to time.  Time stationary random processes are one example (those whose statistics don't change over time).  Time stationary processes are another (trivial) example, which by definition don't change over time.

Searching for Time stationary processes among other things throughout the day has made me realize how much I've come to rely on wikipedia for getting a quick overview of different terms (what with the whole SOPA blackout [which worked apparently]). Anyway, as you allude to later, I'm not approaching it from a probabilistic POV.

I'm trying my level best to steer clear of empty logic, but reflecting on MikeS's post, I approach it like this. It is fairly reasonable, I think, for one to expect a unified theory of physics to explain all phenomena that take place in the universe, depending perhaps on your definition of phenomena. I guess thinking down this road led me to see time as a bit more mysterious than it first appears, especially when considering computer program analogies.

So, yor_on, JP, I understand that it is very reasonable to conclude that change implies a before and after, and in turn, time. But I guess for some reason, that explanation doesn't seem adequate with respect to a thorough description of the universe's underlying structure. Especially so if we mix up the mathematical description of time with a perceptual description. For example, do our pets perceive time like we do? Or how about this: http://newsfeed.time.com/2011/05/26/amazonian-tribe-lacks-abstract-concept-of-time/? Is there anything meaningful to ponder on here?

It does that because, like a river, it has a certain flow.  Why does it have a certain flow?  A rivers flow is driven by gravity and slowed by friction.  Surely the passage of time must be caused by something?  Personally I believe its  a relationship between gravity on the one hand and energy on the other.  Gravity we know slows the passage of time and I believe an increase in energy speeds the flow.

This, for example, seems to exemplify the issue quite nicely: we can perhaps come up with a qualitative description about time's "structure", and this implies that we might find a discreet quantitative description upon further investigation?

Or maybe I'm just letting my thoughts get tied up in knots -_-

SS: I think I get what you're saying; similar to what JP mentioned about "Time stationary random processes"? But I think that probabilistic description rests more on the scale of the system instead of the individual particles.

[MikeS]

Light travels instantaneously (from its reference point) but has a finite speed in the real world.
Why is that?

Mass without energy slows time to a standstill. (The event horizon of a black hole.)
It therefore seems to me that the concept of 'time' is the relationship of energy (photons) (that wants to travel at infinite speed [it  {c}can travel an infinite distance in one second if a second is infinitely long]) and gravity (which wants time to stop) slowing it down.  The finite speed of c that is arrived at is where the clock 'stops'.  To go any faster than c would imply the clock going backwards in time.

To sum up
Light travels in its own reference frame instantaneous.
It is only when observed from any other reference frame that light light has a finite speed. 
That finite speed is always the same in all reference frames because it is infinite  (in its own reference frame) but it does not appear to be infinite (in any other reference frame) as time has dilated to compensate.

(This is a very simple concept but very difficult to explain using language, which is grossly inadequate.  Well, at least, mine is)

[yor_on]

Maybe you can think of 'times arrow' as somewhat of a fountain. It springs out everywhere, in every 'point' of SpaceTime. Always, locally, of the same pace, relative the local 'change', having a 'same' direction into SpaceTime too. You can describe it locally as 'changes', which in a way connect to the idea of entropy, but as it is at a locally same pace it's to me related to the way 'c' behaves, always locally of the same 'beat'. So maybe you could see it as a 'constant' too, equivalent to 'c' in all practical respects.

If that is true, then we have 'geometrical 4-dimensional displacements' as time dilations and Lorentz contractions all around us, as well as in us. And then the really interesting question becomes what makes us macroscopically possible at all? How do SpaceTime 'join up' particles into what we are, and observe, macroscopically?

Answer that one if you can

[LetoII]

time is not a tool we invented.
It can't be, if you ask me humans are incapable of coming up with new idea's, we work on copying stuff and putting it in different oders to come up with new idea's. It will always be an invluence from outside that will inspire humans to come up with truely new concepts.
it's the same with time, time is a thing too hard for us to understand completely just yet. however, it's a phenomenon that can be partially observed by us and we have done so and learned from it.

for now time is simply a point in time to which you reference, like the beginning of the universe. however before the big bang occured there were forces in effect too if you ask me. We simply dont understand that part of time since it's so different from what we can see now.

taking this to your collision's it means you will always need to reference to time if you want us to know exactly what you mean, because to do so we need to know the "when" factor.

[imatfaal]

time is not a tool we invented.
It can't be, if you ask me humans are incapable of coming up with new idea's, we work on copying stuff and putting it in different oders to come up with new idea's. It will always be an invluence from outside that will inspire humans to come up with truely new concepts.

If not humans who else?

it's the same with time, time is a thing too hard for us to understand completely just yet. however, it's a phenomenon that can be partially observed by us and we have done so and learned from it.

for now time is simply a point in time to which you reference, like the beginning of the universe. however before the big bang occured there were forces in effect too if you ask me. We simply dont understand that part of time since it's so different from what we can see now.

  Before the big bang doesn't really have a great deal of meaning if you use accepted definitions

taking this to your collision's it means you will always need to reference to time if you want us to know exactly what you mean, because to do so we need to know the "when" factor.

  2+2=4

[MikeS]

Going back to the original question;-

Can Collisions be Described Without Referencing Time?

The answer is No for this simple reason.
When two objects collide the combined mass causes time to dilate (locally) thereby reducing the useful energy level (increase in entropy) and increasing the stability of the system.

The important thing, as regards the question, is they cannot collide (combine) without time dilating.  It is built into the system.

The collision also converts gravitational potential energy into kinetic energy and ultimately heat.  Again, increasing entropy (which is time dependant) and the stability of the system.