Is Time Necessary?

[swansont]

To Swanshot; is that strictly true what you said? I mean, even on [math]\mathbb{R}^{2}[/math] thought of as a (trivial) fibre bundle, that is one copy for time and one for space there exists diffeomorphisms that are not bundle automorphisms and hence destroy the distinction between space and time.

 

I wouldn't be surprised if you can find examples where you can do this (my very sparse recall of Lie algebra/symmetry groups isn't helping me here) but I think the salient point is that it's not generally true. (In fact, I've seen some recent discussion of GR elsewhere that have included the concept of non-orthogonal time). But being possible and being universal aren't the same thing; e.g. you can use non-orthgonal coordinates, but it's usually useful not to.

 

Happy to be shown wrong, though, if someone can do it rigorously

[swansont]

no two objects can exist simultaneously in the same space. if we take away time then we have no two objects can exist at the same coordinates.

 

For Fermions, of course. Photons, for example, are Bosons and are quite capable of doing so.

[insane_alien]

For Fermions, of course. Photons, for example, are Bosons and are quite capable of doing so.

 

yes well, i was reffering to macroscopic things like us. we're made of fermions so we can exist in the same place as someone else. i was trying to keep it simple by not going into the intricases of QM

[abskebabs]

I'm sorry if this sounds clumsy, but I think a lot of JohnF's difficulties can be overcome if this is thought about carefully with a useful analogous relation to ordinary euclidian geometry.

 

The importan lesson of relativity is that inspite of the time and space between events is relative to a frame in which they are measured, BUT; The spacetime interval between 2 events remains invariant regardless of the frame. The notion that time is a dimension is a useful one, but needs careful geometric definition I feel.

 

For example the invariant we commonly see in Euclidian geometry between our 3 dimensions is: l^2=(dx)^2+(dy)^2+(dz)^2

Here are our invariant interval is l^2 or l, as it doesnt matter what orientation our x,y and z coordiantes are, our interval remains constant. For example imagine I rotated the axes, the distance between 2 points remains constant.

 

If we extend this notion of invariance to what can be called "spacetime geometry" we end up with a different equation(I have included just one length dimension for simplicity, but extension is easy) and invariance:

s^2=(c^2)(dt^2)-(dx)^2

Similiarly here, what I referred to as "rotating my axes", in Euclidian geometry, would be changing the frame of reference with which I viewed events, and hence their velocity relative to me.

 

By applying a similiar notion of invariance, we can see here that time plays a role of a "dimension" within this geometry. It is important to recognise however that this is not a direct analogy from what we normally think of as dimensions, aka, the ones from Euclidian geometry. I think this is an important mathematical subtlety that often is omitted in discussions about the "dimensionality" of time.

 

I hope that helps, and I am sorry to any experts if I have stumbled ad made errors in my attempt at an explanation.

[fredrik]

is it really a dimension or has the dimension of time been invented?

 

What's the difference? Suppose "it's invented", does that mean it's not "real"?

 

Perhaps it's an effect. I don't really like the idea that it is something we travel in or through. It's more like something that we witness

 

If that makes you more satisfied, why not? The question is still, what difference do you think it makes?

 

They way I think about it, time is a parametrisation of progress into the future. Wether we "travel into an uknown but pre-existing future" or if the future are created/revealed on the fly as progress is made - what is the difference? To me it's the same thing still unless someone can think of an experiment to distinguish they two options.

 

Considering that physics tries to "explain" the universe from scratch, I'd say we have to invent all of it. Time, space and matter. We just need to find that minimalistic starting point, that most people accept that at least for the next few hundred years need to further explanation.

 

In despite of my comments I think the original question was a good one.

 

/Fredrik

[fredrik]

Another personal reflection in line with my thinking is

 

> Is Time Necessary?

 

If changes would be completely chaotic time would not be necessary, or rather time itself (as read from a clock device) would also be chaotic and we would not be able to distinguish it from the noise. At this point, space probably wouldn't be distinguishable either. I somehow picture time beeing the last thing to go away.

 

The fact that we can successfully define a clock device and get a useful parametrization of history that allows us to learn something, proves that changes are not comptely chaotic. So in that sense, to ask is time necessary, is to ask, is it necessary to learn, or make progress?

 

/Fredrik

[JohnF]

Does anyone know of a way of measuring time without counting events?

 

It just seems that time is nothing more than events being counted. Is this enough for it to be considered a dimension. If some sort of external force was applied to the planet that slowed all events down then although we would be unaware of a change an external observer would. Would that external observer think time has slowed down or just everything on the planet has slowed down?

[insane_alien]

is there a way of measuring distance with out using regular events like the mile wheels the romans used that clicked every mile they travelled? its a conveinient way of measuring it.

 

a force like gravity perhaps? yeah the external observer would(and does) observe a time difference. this has to be factored into the programming of GPS sattelites for them to work properly.

[JohnF]

is there a way of measuring distance with out using regular events like the mile wheels the romans used that clicked every mile they travelled? its a conveinient way of measuring it.

 

Triangulation is a good way to measure distance without events. The unit you use to seperate the two observing positions can just be a big stick. You could then work out how many 'big sticks' away the distance was.

[insane_alien]

yeah, but we cant get a big stick that can be jammed between two points in time since we have no real control over our velocity and position in it. so we measure regular events. you can take the event as sticks. we count how many sticks are between two events.

 

distance uses a stick, time uses the emmision of radiation. dimensions aren't defined by how they are measured.

[JohnF]

you can take the event as sticks. we count how many sticks are between two events.

 

I'm afraid I can't agree with that.

 

But where time is slowed down, when travelling at high velocity for example, does the stick get shorter, longer or stay the same size?

 

And this should be from the point of view of the observer who is experiencing time running slower.

[insane_alien]

if its from the point of view of an observer in the same frame as the event that gets slowed down then the event would appear to be happening at the same rate. she/he/it wouldn't notice any difference. an outside observer would.

 

an example of this is ground level muons. by classical theory they shouldn't get down this far without decaying. if you include the relativistic effect of time dilation acting on the particles due to their high velocity compared to our frame then its perfectly reasonable for them to get down this far. time for them is running slower compared to us from our reference frame.

[JohnF]

if its from the point of view of an observer in the same frame as the event that gets slowed down then the event would appear to be happening at the same rate. she/he/it wouldn't notice any difference. an outside observer would.

 

So you're saying that an outside observer would see the stick get shorter?

Would that would mean the inside observer would see the outside get bigger?

[fredrik]

This has turned out somewhat elaborate and philosophical already so here are some more along those lines.

 

It just seems that time is nothing more than events being counted. Is this enough for it to be considered a dimension. If some sort of external force was applied to the planet that slowed all events down then although we would be unaware of a change an external observer would. Would that external observer think time has slowed down or just everything on the planet has slowed down?

 

In your terminology I'd say it's a relative count, and specifically *your* counting. Somebody elses counts gives their time, not yours.

 

I think I know what you are after, and if you think what I think you do, "slowing all events uniformly" does not affect the pereception of local time. The pace of a clock has it's meaning only in the context where the clock "lives", a *relative pace in it's environment*, since a clock isn't something unreal god like device, a clock is just a part of reality, that we use for internal reference. And a clock device is bound to obey the same rules and limitations as does everything else.

 

Here are some related speculative ideas taken out of my current thinking that I'm working on...

 

And these relative or internal paces, can be given probabilistic interpretations so that time can be thought of as a parametrisation of change. If you (not litteraly) consider the future as a vector, you do not know in which direction the future points, but you may see that some changes are far more likely than others, based on the present. So you can picture the differential future vector mapping out a surface of a possible future, and you can normalize this surface so that each point on the surface represents in an infinitesimal sense the nearest future and each point on the surface is equally probable.

 

One point on this abstract surface represents the scenario that the ONLY change you see is a clock tick. The vector from the present configuration to this point can be called the "clock vector".

 

By probabilistic reasons "the most probable future" (which would be THE future in the classical case), is the shortest path into the future. Shortest path here meaning, that only a small disturbance is required for the transition. "Now measure" this disturbance relative to the disturbance that the clock device would require for the same probability. This ration is always smaller than 1 as per construction, irrespective of choice of clock! (Note that this can be taken as a seed to the lorentz invariance, though much more fundamental) That is, you are technically free to choose *any device* as "your clock". They all measure the same flow, just of course the units are different and the referenc is more or less weird, but that's your choice.

 

This is fuzzy, but I'm struggling with giving this a definite and proper mathematical description. The "measure" I refer to, will be related to information content and entropy, and the nice part is that it will not depend on absolute entroyp, only the relative entropy, and if I am correct any strictly increasing bijective function of entropy will do. Which I think will solve the critics that there are different kinds of entropy. So only the relative entropy is interesting, and I think the variations will leave the system invariant.

 

I also great hope that these ideas will from first principles generate symmetries similar to SR and probably also GR. The SR and GR transformations will hopefully be replaced with a uniform reference transformations, that transform information between observers. My expectations is also that things like the lorentz invaraiance will be broken in chaotic domains (where the "future surface") is more symmetric. And these symmetries would be recovered as the chaos is reduced.

 

This is not intented to remain talking though, all the details will achieve mathematical suites, and I'm still working on it + trying to scan what the existing work in this aread has accomplished so far. There are several working along these lines but so far the progress seems modest. But from my impression the number of people working along these lines are very small as compared to the other things like strings.

 

/Fredrik

[insane_alien]

So you're saying that an outside observer would see the stick get shorter?

Would that would mean the inside observer would see the outside get bigger?

 

well, there is no stick. its the time between two events in relation to the observer. the outside observer would observe the pace slowing down. but the inside observer would witness the same happen to a clock outside. it would appear to slow down as well.

 

this is where it gets confusing and in my current state of mind(hungover) i don't think that i'll be able to think about it without forcing my brain out through my ears.

[JohnF]

well, there is no stick. its the time between two events in relation to the observer. the outside observer would observe the pace slowing down. but the inside observer would witness the same happen to a clock outside. it would appear to slow down as well.

 

this is where it gets confusing and in my current state of mind(hungover) i don't think that i'll be able to think about it without forcing my brain out through my ears.

 

It's the stick I was particularly interested in as I'm thinking along the lines that three dimensional space, the stick, is a constant; but time is a variable.

 

But considering your 'current state' perhaps you should have some of the pills I've just taken after reading the post by fredrik.

 

Fredrik: I really wish I understood what you are saying. I'm a software engineer not a mathematician though. It probably goes against me too, because I prefer to view the world in 'black and white' if you know what I mean. I've read it a couple of times and I'll try again later but I'm not too hopeful.

[insane_alien]

well, you see. if you looked at the sticks then both would be getting shorter.

 

this is time and space rotating into each other. this part of the effect is called length contraction.

[fredrik]

Does anyone know of a way of measuring time without counting events?

 

An even can mean simply "change", change of state, or an additional bit of information reaching your brain. That's an event. As soon as you register any change whatsoever, there is an event.

 

So sticks or not, you still need to be able to have your brain register whatever you measure. So it can still be thought of as events?

 

It just seems that time is nothing more than events being counted. Is this enough for it to be considered a dimension.

 

Interesting that you see this as a problem. I see it as a feature Isn't what we all think an explanation of things to the point where we can all say that this complicated thing is in fact, just x. And we all know x. We only need to reveal some entanglement to see it. That kind of thing?

 

To explain something complex in terms of something that is even more complex that the original raw data, is not progress. The simpler the better.

 

/Fredrik

[JohnF]

An even can mean simply "change", change of state, or an additional bit of information reaching your brain. That's an event. As soon as you register any change whatsoever, there is an event.

 

So sticks or not, you still need to be able to have your brain register whatever you measure. So it can still be thought of as events?

 

But does a stick not occupy multiple places in space simultaneously? To be aware of the stick I may need events but the stick doesn't need events to exist. Therefore the stick is not an event unless you are saying the stick does not exist until it is witnessed.

 

 

 

Interesting that you see this as a problem. I see it as a feature Isn't what we all think an explanation of things to the point where we can all say that this complicated thing is in fact, just x. And we all know x. We only need to reveal some entanglement to see it. That kind of thing?

 

To explain something complex in terms of something that is even more complex that the original raw data, is not progress. The simpler the better.

 

I agree that the least complex answer is better. So I see it as less complex to say that processes, events, etc. slow down with speed rather than saying time slows down. There seems to be an implication that if time can be varied then time can be controlled. But if it's just events that can be varied then time could be a constant and beyond control.

[swansont]

I agree that the least complex answer is better. So I see it as less complex to say that processes, events, etc. slow down with speed rather than saying time slows down. There seems to be an implication that if time can be varied then time can be controlled. But if it's just events that can be varied then time could be a constant and beyond control.

 

But saying that time slowed is actually simpler. If you say that all processes slowed you need to come up with a mechanism by which various processes would all be affected in the same fashion, e.g. a nuclear decay and an atomic transition, both seeing the same effect on their rate from a given force or motion, even though the characteristic interaction strength is different.

[fredrik]

But does a stick not occupy multiple places in space simultaneously?

 

Yes, but when I picture the clock vector above as my "stick", it is in the differential sense. It defines dt, not a finite time t2-t1, which i think requires integrating along the evolution which is not elementary. The existence and uniqeness of such finite time parametrization is not obvious, because of the toplogy of the system. But I do not see that as a major problem, except from a technical point of view of solving equations.

 

The minimum differential needed to establish an event may be discussed and is one of the issues I work on. I count on that it is solvable. One may also wonder if events are really discrete or continous. But I think there is a way to unite it.

 

To be aware of the stick I may need events but the stick doesn't need events to exist. Therefore the stick is not an event unless you are saying the stick does not exist until it is witnessed.

 

A stick or clock may seem trivial as compared to a human, but from a first principle view, a stick also makes it's "observations" on you. The stick interacts with the environment just like humans do, although in a much more trivial, and less intelligent way. Technically the situation is symmetric, it's just that you are more intelligent and have more information storage. I expect a good theory to explain this symmetry.

 

So a stick needs to interact to exist. If the stick doesn't interact with anything you would not be able to see it, nor use it. This may in fact happen if the conditions are strongly chaotic. You have easily loose track of your stick in the noise. But then you can also argue that a stick that you are not able to track in the ambient noise is a useless reference anyway. That's how you can "loose dimensions".

 

/Fredrik

[JohnF]

But saying that time slowed is actually simpler. If you say that all processes slowed you need to come up with a mechanism by which various processes would all be affected in the same fashion, e.g. a nuclear decay and an atomic transition, both seeing the same effect on their rate from a given force or motion, even though the characteristic interaction strength is different.

 

Would nuclear decay occur at the same rate when tavelling fast from the point of view of someone travelling with the material? If the answer is yes then either time has slowed and the nuclear decay has slowed with time so that it appears to decay at the normal rate. Or, the nuclear decay has slowed together with any event counter that is used to measure the rate of decay. How could you possibly know which of the two was true?

 

Just because I don't know of a mecanism that slows down nuclear decay in relation to speed doesn't mean there isn't one.

[swansont]

Would nuclear decay occur at the same rate when tavelling fast from the point of view of someone travelling with the material? If the answer is yes then either time has slowed and the nuclear decay has slowed with time so that it appears to decay at the normal rate. Or, the nuclear decay has slowed together with any event counter that is used to measure the rate of decay. How could you possibly know which of the two was true?

 

Yes, it has been observed in muon decay, which is a standard relativity example. That's mediated by the weak force. But the same effect happens in atomic clocks, which are mediated by the electromagnetic force. (And with different atoms, with different transition frequencies). The scaling is all wrong for it to be a physical effect.

 

Just because I don't know of a mecanism that slows down nuclear decay in relation to speed doesn't mean there isn't one.

 

Bzzzzt. Sorry, that's shifting the burden of proof/appeal to ignorance.

[fredrik]

If the answer is yes then either time has slowed and the nuclear decay has slowed with time so that it appears to decay at the normal rate. Or, the nuclear decay has slowed together with any event counter that is used to measure the rate of decay. How could you possibly know which of the two was true?

 

If you mean what I think you do, I would say you can't know, implying that and that there is no difference and it's the same thing, you just try to illustrate the same thing in different ways.

 

The "rates" of these "event counters" would not be independently observable themselves in an objective manner, because you always need a reference. It's only the relative drift of different "counters" that is observable, and it's this drift that defines the evolution. The ticks of each counter alone are just changes - no "rate" implied. The concept of rate is born when you start to compare *different* changes.

 

Thus to tweak the local perception of time, you need something that tweaks the relative drifts of different events.

 

/Fredrik

[JohnF]

I seem to have contradicting answers now from swansont and fredrik

 

But with regards to

The scaling is all wrong for it to be a physical effect.

this can only be the scaling of the parts that are known about. What about the god particle for example; does it not yet have to be discovered?

 

All I'm suggesting is that apparent changes in time might be changes in all structure at some level that has been miss-interpreted as a change in time.

 

Assume for a moment that I'm correct. Would it mean that time has lost it's value or is it just as good as it's always been to help us understand how things work. If time keeps its value anyway then it doesn't matter whether time really slows down or not; does it?