# Time and space

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Time and space are what make a universe but are they both fundamental things?

What I am asking is one the source and the other emergent i.e. does time emerge from space or does space emerge from time? These two things are so closely related and interchangeable that I am asking if it is far more likely they are one in the same thing, for example if you are a certain distance from me you are also a proportional amount of time from me, to be here is to be now so are we really talking about two separate things or just one thing and that which emerges from it?

There may be some speculative way to look at time and space that explains their compatibility while maintaining they are two completely different things but I doubt their relationship is just coincidental and it seems quite unscientific and arbitrary to be basing our entire understanding of the universe on there being two fundamentals instead of just one.

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Time and space are not fundamental at all. They are abstractions.

Time is the most general abstraction of change, and space is the most general abstraction of distance. It makes no sense to speak of time or space when nothing changes and there are no objects at all.

It is one of the reasons that Einstein, in explaining his special theory of relativity (from which the idea of spacetime was born), falls back to operative definitions of time and space: e.g. the ticks of a clock (=(regular) change), or the length of a rod (= distance between one end of the rod to the other).

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18 minutes ago, Eise said:

Time is the most general abstraction of change, and space is the most general abstraction of distance. It makes no sense to speak of time or space when nothing changes and there are no objects at all.

I am not sure I would agree with this. First of all, distance does not require any “objects”, I do not see any issue defining separations between points in a completely empty space. You may not be able to physically measure those without introducing objects, but that’s a different issue.

As for time, consider an elementary particle with a finite lifetime - while it is in existence, there is no notion of “change”, since it is elementary without any internal structure or mechanisms. Yet there clearly is some notion of time here, because otherwise it would not end up eventually decaying.

On the other hand though, the notion of “change” does not actually imply the existence of time at all. Consider two physical quantities A and B; usually when we say that these quantities “change”, we assume that they are functions of some other quantity “t”, so we write them as functions A(t) and B(t), and say they change with respect to that third quantity. This is one possible notion of change - introduce an external reference point. However, we have to remember that this is a purely arbitrary convention. The quantity “t” is not a physical observable, it’s simply an abstract concept; it would be just as possible to describe the situation as A and B changing with respect to each other, rather than some external notion of time. Like so:

$\displaystyle{\frac{\partial A}{\partial B};\; \frac{\partial B}{\partial A}}$

This is also “change” - but no time is involved. Our two quantities are now simply interdependent functions of each other: A(B) and B(A).

This is not just philosophical nitpicking, but has deep physical significance - for example, it is ultimately the reason why no “time” appears in the Wheeler-deWitt equation for quantum gravity. On a fundamental level, time does not appear to exist at all, there is just a vast network of interdependent physical entities changing with respect to each other. The nature of these “entities” depends on the specific model you use, but the overarching principle remains the same.

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Posted (edited)
51 minutes ago, Markus Hanke said:

I am not sure I would agree with this. First of all, distance does not require any “objects”, I do not see any issue defining separations between points in a completely empty space. You may not be able to physically measure those without introducing objects, but that’s a different issue.

There's no such thing as completely empty space, so that's moot. Volume is a function of 'things', even if it's just an ensemble of virtual particles. You might as well say 'nothing' exists.

Edited by StringJunky

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Posted (edited)
1 hour ago, Markus Hanke said:

First of all, distance does not require any “objects”, I do not see any issue defining separations between points in a completely empty space.

What you describe is an abstraction, just as @Eise said in his/her comment. Just like any mathematical abstract solution - your calculations may be self-consistent, but you can't apply those to the real physical world without introducing objects.

1 hour ago, Markus Hanke said:

As for time, consider an elementary particle with a finite lifetime - while it is in existence, there is no notion of “change”, since it is elementary without any internal structure or mechanisms. Yet there clearly is some notion of time here, because otherwise it would not end up eventually decaying.

Well, the 'change' for this particle would be becoming a completely different particle via decay. If said particle is not the only one in the universe, 'change' would involve interactions with other particles.

On the other hand, your comment brought me onto something: imagine a universe with same physics laws as ours but populated by only one photon. Photons don't experience time and there will be no interactions with anything else. Would such a universe have a notion of time, or space for that matter too?

Edited by pavelcherepan

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Posted (edited)
1 hour ago, Markus Hanke said:

The quantity “t” is not a physical observable, it’s simply an abstract concept; it would be just as possible to describe the situation as A and B changing with respect to each other, rather than some external notion of time.

Exactly. But would the same not apply to space? One can define the length of a rod in terms of the length of another one. One does not need the abstract notion of 'distance', and therefore not the just as abstract notion of space.

And can you really define 2 points in empty space? Don't you need at least a coordinate system with an origin? I know that this is easy stuff in mathematics (e.g. just pick one based on independent vectors), but what would be the physical meaning of that?

To paraphrase your argument against my idea: I can define 2 events on a timeline without reference to any change. But when the 'timeline' is empty this is pretty difficult, just as with space.

1 hour ago, Markus Hanke said:

As for time, consider an elementary particle with a finite lifetime - while it is in existence, there is no notion of “change”, since it is elementary without any internal structure or mechanisms. Yet there clearly is some notion of time here, because otherwise it would not end up eventually decaying.

Well, I think you here are confronted with the probability character of QM. A clock based on the decay of one single unstable particle would not be a very precise clock, is it? But of course you could do it with many particles of the same sort, say 6x1023 muons, and e.g. you define the 2.16 microseconds as the time that half of the muons have decayed. But still I do not see how I could define this 'lifetime' without reference to other changes, e.g. compare with 6x1023 uranium-238 nuclei. You just must wait a little longer before half of them has decayed...  Or you use some regular events like a clock, might be easier.

1 hour ago, Markus Hanke said:

You may not be able to physically measure those without introducing objects, but that’s a different issue.

Forgot this one: Weren't we talking physics here?

Edited by Eise

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Posted (edited)
8 hours ago, argo said:

Time and space are what make a universe but are they both fundamental things?

First of all neither time nor space are things so their fundamentality is moot.

4 hours ago, Eise said:

Time and space are not fundamental at all. They are abstractions.

Time is the most general abstraction of change,

Yes indeed they are abstractions, but distance is not the same as space (or a generalisation of it) any more than an interval is the same or a generalisation of time.

An no, time is most definitely not the most general abstraction of change, if it is an abstraction of change at all.

Change is (a process of) comparison which may or may not involve time as Marcus pointed out, but they are separate abstractions.

For instance I can measure/observe the value of pretty well any point variable at two or more points and compare the change from one point to another.

Which brings me to my thoughts that both sides of this dicussion have made valid and questionable points but have not articulated either particularly well (don't claim any better I just hope that another worm's eye view might help)

I can sympathise there since it is very difficult to get one's head around these ideas.

Personally I think of the abstractions (both time and space) as chosing and naming variables as suitable for the purpose of working (mathematically) with what we observe about the world around us.

I often find this approach to entropy switches on the light bulb for people who find that idea difficult.

2 hours ago, StringJunky said:

There's no such thing as completely empty space, so that's moot. Volume is a function of 'things', even if it's just an ensemble of virtual particles. You might as well say 'nothing' exists.

I do indeed (often) say that nothing exists - and offer demonstrations / rationalisations.

But I also say that Nature is more perverse and diverse than Man's best endeavours and has more tricks up her sleeve.

So space is a set of some or all points.

The points are members of the set.

But Nature offers us sets whose members are conspicuous by their absence.

For example a shadow is a set of points there there is an absence of light.

Edited by studiot

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3 hours ago, Markus Hanke said:

On the other hand though, the notion of “change” does not actually imply the existence of time at all. Consider two physical quantities A and B; usually when we say that these quantities “change”, we assume that they are functions of some other quantity “t”, so we write them as functions A(t) and B(t), and say they change with respect to that third quantity. This is one possible notion of change - introduce an external reference point. However, we have to remember that this is a purely arbitrary convention. The quantity “t” is not a physical observable, it’s simply an abstract concept; it would be just as possible to describe the situation as A and B changing with respect to each other, rather than some external notion of time. Like so:

AB;BA

This is also “change” - but no time is involved. Our two quantities are now simply interdependent functions of each other: A(B) and B(A).

Any specific examples? A is a function of B. What might that function  look like? Would B be the inverse function of A?

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1 hour ago, studiot said:

First of all neither time nor space are things so their fundamentality is moot.

Yes indeed they are abstractions, but distance is not the same as space (or a generalisation of it) any more than an interval is the same or a generalisation of time.

An no, time is most definitely not the most general abstraction of change, if it is an abstraction of change at all.

Change is (a process of) comparison which may or may not involve time as Marcus pointed out, but they are separate abstractions.

For instance I can measure/observe the value of pretty well any point variable at two or more points and compare the change from one point to another.

Which brings me to my thoughts that both sides of this dicussion have made valid and questionable points but have not articulated either particularly well (don't claim any better I just hope that another worm's eye view might help)

I can sympathise there since it is very difficult to get one's head around these ideas.

Personally I think of the abstractions (both time and space) as chosing and naming variables as suitable for the purpose of working (mathematically) with what we observe about the world around us.

I often find this approach to entropy switches on the light bulb for people who find that idea difficult.

I do indeed (often) say that nothing exists - and offer demonstrations / rationalisations.

But I also say that Nature is more perverse and diverse than Man's best endeavours and has more tricks up her sleeve.

So space is a set of some or all points.

The points are members of the set.

But Nature offers us sets whose members are conspicuous by their absence.

For example a shadow is a set of points there there is an absence of light.

'Nothing' is an accounting word; not a thing unto itself.

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54 minutes ago, geordief said:

Any specific examples? A is a function of B. What might that function  look like? Would B be the inverse function of A?

Think about two processes: let's take a stone falling, and water running out of a can with a small hole in the bottom. Both are functions of time: the stone falls faster and faster (as usual in such examples we neglect air friction...); but the water output becomes less and less during time (because the water pressure becomes less and less, because water is running out of the can). Now if your experiment is very precise, you will get the same relation again and again: when the stone has fallen 10 meters, there will be still 2 liter water in the can, and this for every point (20 meter fallen 1.5 liter water, 30 meters fallen 1.2 liter water etc etc.)

This means you have a function between the two processes: if you have 1.5 liter water, you know that the stone has fallen 20 meters, or the other way round, if the stone has fallen 30 meters, you know there is still 1.2 liter water in the can. So to every value of one process, belongs exactly one value of the other process, and the other way round. Mathematically this means that one value can be expressed as a function of the other, in this case in both directions.

With that, you can leave out the time as 'independent factor'. You can express the change in one process in terms of the other, and yes, therefore one function is the inverse of the other. You do not need time as intermediate factor if you are only interested in the relationship between the distance the stone has fallen, and the amount of water left in the can. And, as Markus points out, you can also express the 'measure of change' of one process in terms of the 'measure of change' of the other. That is what his mathematical formula is saying.

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29 minutes ago, Eise said:

Think about two processes: let's take a stone falling, and water running out of a can with a small hole in the bottom. Both are functions of time: the stone falls faster and faster (as usual in such examples we neglect air friction...); but the water output becomes less and less during time (because the water pressure becomes less and less, because water is running out of the can). Now if your experiment is very precise, you will get the same relation again and again: when the stone has fallen 10 meters, there will be still 2 liter water in the can, and this for every point (20 meter fallen 1.5 liter water, 30 meters fallen 1.2 liter water etc etc.)

This means you have a function between the two processes: if you have 1.5 liter water, you know that the stone has fallen 20 meters, or the other way round, if the stone has fallen 30 meters, you know there is still 1.2 liter water in the can. So to every value of one process, belongs exactly one value of the other process, and the other way round. Mathematically this means that one value can be expressed as a function of the other, in this case in both directions.

With that, you can leave out the time as 'independent factor'. You can express the change in one process in terms of the other, and yes, therefore one function is the inverse of the other. You do not need time as intermediate factor if you are only interested in the relationship between the distance the stone has fallen, and the amount of water left in the can. And, as Markus points out, you can also express the 'measure of change' of one process in terms of the 'measure of change' of the other. That is what his mathematical formula is saying.

Does that still allow one to make predictions? (I am guessing no )

If not is this method of measuring change only trivially  rigorous?

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42 minutes ago, StringJunky said:

'Nothing' is an accounting word; not a thing unto itself.

Perhaps I should offer the use of my famous toilet seat that does not have nothing in the middle.

41 minutes ago, Eise said:

Think about two processes: let's take a stone falling, and water running out of a can with a small hole in the bottom. Both are functions of time: the stone falls faster and faster (as usual in such examples we neglect air friction...); but the water output becomes less and less during time (because the water pressure becomes less and less, because water is running out of the can). Now if your experiment is very precise, you will get the same relation again and again: when the stone has fallen 10 meters, there will be still 2 liter water in the can, and this for every point (20 meter fallen 1.5 liter water, 30 meters fallen 1.2 liter water etc etc.)

This means you have a function between the two processes: if you have 1.5 liter water, you know that the stone has fallen 20 meters, or the other way round, if the stone has fallen 30 meters, you know there is still 1.2 liter water in the can. So to every value of one process, belongs exactly one value of the other process, and the other way round. Mathematically this means that one value can be expressed as a function of the other, in this case in both directions.

With that, you can leave out the time as 'independent factor'. You can express the change in one process in terms of the other, and yes, therefore one function is the inverse of the other. You do not need time as intermediate factor if you are only interested in the relationship between the distance the stone has fallen, and the amount of water left in the can. And, as Markus points out, you can also express the 'measure of change' of one process in terms of the 'measure of change' of the other. That is what his mathematical formula is saying.

Good explanation. +1

In this case time is mathematically called a parameter. This means that both processes are functions of the same variable.
This has implications in the study of dimensions.

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25 minutes ago, geordief said:

Does that still allow one to make predictions? (I am guessing no )

I would say that your guess is wrong. Say, you want to make a picture of the stone after 20 meters of falling. Now you can look at your can of water, and at the moment it has 1.5 liter water left in it, you make the picture.

Think about what a prediction is, e.g the totality of the sun eclipse starts at 11:03h. It means that when a certain event occurs (your clock shows 11:03h), then another event happens, in this case the sun is totally covered by the moon. So a prediction is nothing else than saying two events will happen together. Obviously that makes most sense when one of the events is of a series of standard events we all know, i.e. the turning of the days on a calendar, and the running of a clock.

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Posted (edited)

In the two examples given by Eise, both processes are essentially clocks.
One translates time into distance fallen and the other, time into volume remaining.
It is then trivial to make the 'changes' of one clock a function of the 'changes' of the other.
But the relation is not fundamental.

The Wheeler-DeWitt equation, on the other hand, is fundamental.
And has no dependence on time.

Edit : ( then again, one could argue that the Wheeler-DeWitt equation is an abstraction )

Edited by MigL

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21 minutes ago, studiot said:

In this case time is mathematically called a parameter. This means that both processes are functions of the same variable.

But the essence of  Markus' argument is that you can leave time out. You can express the change of one process in term of the change of another process, without referring to time. And it is my viewpoint that this is exactly what one is doing when one uses time: describe the change of one process with an other, standard process: the ticking of a clock.

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31 minutes ago, Eise said:

I would say that your guess is wrong. Say, you want to make a picture of the stone after 20 meters of falling. Now you can look at your can of water, and at the moment it has 1.5 liter water left in it, you make the picture.

Think about what a prediction is, e.g the totality of the sun eclipse starts at 11:03h. It means that when a certain event occurs (your clock shows 11:03h), then another event happens, in this case the sun is totally covered by the moon. So a prediction is nothing else than saying two events will happen together. Obviously that makes most sense when one of the events is of a series of standard events we all know, i.e. the turning of the days on a calendar, and the running of a clock.

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Posted (edited)
22 minutes ago, Eise said:

But the essence of  Markus' argument is that you can leave time out. You can express the change of one process in term of the change of another process, without referring to time. And it is my viewpoint that this is exactly what one is doing when one uses time: describe the change of one process with an other, standard process: the ticking of a clock.

Yes, but that is not the essence of my comment.

Mathematically the variable that forms the parameter in Mathematics is a dummy variable and can be replaced with another so long as the mathematical form is maintained.

However my comment was about comparison of something, say the value of g or perhaps the water level at inlet and outlet, at one location with the value of that same something at another location, irrespective of time.

This process allows us to establish a change, irrespective of time.

Edited by studiot

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Posted (edited)
1 hour ago, MigL said:

In the two examples given by Eise, both processes are essentially clocks.

Not really. I intentionally chose 2 processes that are not regular: one is accelerating, the other is slowing down. But I would say that every regular process can be used as a clock. If you take my process as clocks, then every process is a clock. (which maybe theoretically right, but not very practical).

I just took the argument Markus made, that every change in a process can, so to speak, plotted against the change of another. You can leave time out, if you do not need it.

54 minutes ago, geordief said:

I do not understand what you are asking. Can you elaborate?

Edited by Eise

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6 minutes ago, Eise said:

Not really. I intentionally chose 2 processes that are not regular: one is accelerating, the other is slowing down. But I would say that every regular process can be used as a clock. If you take my process as clocks, then every process is a clock. (which maybe theoretically right, but not very practical).

I just took the argument Markus made, that every change in a process can, so to speak, plotted against the change of another. You can leave time out, if you do not need it.

I would use predictable. It sounds like that's what you were meaning.

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4 minutes ago, swansont said:

I would use predictable. It sounds like that's what you were meaning.

Ehhm... Use 'predictable'? Instead of what? You mean my 'plotting'? I just pictured a graph of the amount of water at the x-axis and the distance the stone has fallen at the y-axis. Of course you can predict then one value out of the other (and because it is a bijection, it goes in both ways). Is that what you mean?

At least it fits to what I am arguing for.

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15 minutes ago, Eise said:

I don not understand what you are asking. Can you elaborate?

Well what I am getting at is that your examples seem a bit like the clock that is right twice a day.

I f you attempt to use the correlation between the two  processes to estimate what the correlation would be a second time around ,then errors would enter the scenario as the   setup could not be repeated exactly.

To address Markus' point a little more directly (well tangentially) if anyone were to  show how time based processes emerged fro timeless processes this would be an amazing achievement but I  haven't heard that this has been done (or even attempted?)

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2 hours ago, Eise said:

Ehhm... Use 'predictable'? Instead of what? You mean my 'plotting'?

Instead of regular. I'm not sure what you mean by that.

Quote

I just pictured a graph of the amount of water at the x-axis and the distance the stone has fallen at the y-axis. Of course you can predict then one value out of the other (and because it is a bijection, it goes in both ways). Is that what you mean?

At least it fits to what I am arguing for.

That a future value can be predicted.

2 hours ago, geordief said:

Well what I am getting at is that your examples seem a bit like the clock that is right twice a day.

I f you attempt to use the correlation between the two  processes to estimate what the correlation would be a second time around ,then errors would enter the scenario as the   setup could not be repeated exactly.

Thought experiments typically exclude annoyances like measurement errors and noise.

All you are saying is that the "clocks" will have some level of disagreement. That's true of all real clocks.

Quote

To address Markus' point a little more directly (well tangentially) if anyone were to  show how time based processes emerged fro timeless processes this would be an amazing achievement but I  haven't heard that this has been done (or even attempted?)

Parameterizing equations to eliminate a variable is nothing new.

The position of an object can be a function of time, s(t)

But so is the position (angle) of the hand on a traditional clock display. A(t)

It's not hard to rewrite the position of the object as a function of the angle, to get s(A). Time will not appear in that equation.

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Posted (edited)
2 hours ago, geordief said:

To address Markus' point a little more directly (well tangentially) if anyone were to  show how time based processes emerged fro timeless processes this would be an amazing achievement but I  haven't heard that this has been done (or even attempted?)

Carlo Rovelli (a contemporary theoretical phycisist working in the area of quantum gravity) has written extensively about this, and makes a specific proposal how time naturally emerges from the statistical behaviour of small-scale systems that are themselves “timeless”. It ultimately comes down to thermodynamics and entropy. Rovelli works specifically on Loop Quantum Gravity, in which neither space nor time are fundamental to the world - they arise only from the macroscopic statistics of microscopic background-independent systems. The Wilson loops which give LQG its name can be taken as solutions to the Wheeler-deWitt equation for specific forms of the Hamiltonian constraint, so LQG is more than just an ad-hoc invention. Many of Rovelli’s publications are aimed at the general public, and are easy to understand for anyone with elementary physics knowledge. I highly recommend his books on the subject - if nothing else, they are fascinating and thought provoking. Whether or not his ideas have any physical value still remains to be seen.

Just to clarify this here, it is not my attention to make any claims with regards to this. I do not know the ultimate nature of time and space - no one does. There is a variety of interesting, yet very disparate, models out there on this subject, but no consensus on which - if any - of them might describe our world. I have my own thoughts on which direction I think might be most promising, but I am keeping an open mind, and do not outright subscribe to any specific model just yet. It is safe to say however, that many of these models will require us to fundamentally change the way we think about space and time - quantum gravity will be an even bigger paradigm shift than relativity was.

I am merely attempting to point out that the notion of “change” is not enough to give rise to a flow of time as we experience it, and as it is used in most models of physics. Quantities can change with respect to other quantities, without the need for time. Clearly, time as we experience it requires more than just “change”. But this does not mean that time plays no role in the macroscopic world - it is, for example, an integral part of how gravity works, so we can’t just do away with it, at least not on large scales. I think it is more a matter of recognising that our notion of time might be scale-dependent, and might not be part of physics at the Planck scale. But then again, it may - there are still many unresolved problems around all this.

Edited by Markus Hanke

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Perhaps space can be considered as the distance between three dimensional objective positions when the universe splits
Perhaps time can be considered as the distance between two dimensional  virtual positions as the universe splits

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You don't even need to go to Planck scales for time to assume a 'statistical' behaviour.
It is already demonstrated at the quantum level.

A single particle can decay immediately today, yet repeat the same experiment tomorrow and it can take ten years for a like particle to decay.
And since it can be different every time, a single particle's behaviour is not time dependent.

It is only when you repeat the experiment with a billion, billion, billion like particles that you can say half will decay after 5.75 years.
And since that is  repeatable, the statistical behaviour of particles is time dependant