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Is time simply the rate of change?

If this is the case and time was created during the big bang would it be the case that the closer you get to the start of the big bang the "slower" things change until you essentially approach a static, unchanging entity at the beginning of creation?

Also, to put this definition in relation to Einstein's conclusions that "observers in motion relative to one another will measure different elapsed times for the same event." : Wouldn't it be the case that saying the difference in elapsed time is the same as saying the difference in the rate of change.

With this definition there is no point in describing the "flow" of time or the "direction" of time because time doesn't move forward but rather things simply change according to the laws of physics.

Edit: Adding clarification based on @neil's comments:

The beginning of the big bang would be very busy, but if time was then created if you go back to the very beginning it seems there is no time and there is only a static environment.

So it seems to me that saying time has a direction makes no sense. There is no direction in which time flows. There is no time; unless time is defined as change.

So we have our three dimensional objects: and then we have those objects interact. The interaction is what we experience as time. Is this correct or is time more complicated than this?

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If you're concerned with the rate at which things change, shouldn't things go faster as you approach the Big Bang? The first hour of the universe was an extremely busy time. –  Niel de Beaudrap Oct 4 '11 at 15:36
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More generally and to the point: how do you determine "the rate of change" without a fixed standard for time, anyhow? Fast processes still happen now; just perhaps less frequently than before. That, and we're often more interested in glacially slow processes, such as human behaviour, and well, the movements of glaciers. It makes the most sense to establish a collection of commensurable standards of time reaching back to the Big Bang; but commensurability pretty much prevents any process of "time inflation" --- at least in how we measure time. –  Niel de Beaudrap Oct 4 '11 at 15:38
    
Things may happen "faster" compared to things happening on earth now but wouldn't you eventually reach the beginning where nothing is happening and you reach a static/stable environment –  coder Oct 4 '11 at 16:02
    
It depends on how you're trying to define a changing scale of time! If the "activity" (very vague) of the universe is getting slower with time in an exponential decay, then going backwards in time would look like watching a computer which performs one instruction in 1Gyr, a second instruction in .5Gyr, a third in .25Gyr, getting faster with time. If you "rescale time" so that each instruction takes one "operational time unit", what you find is not that things come to a rest but that you can squeeze in an infinite regress of activity immediately after the Big Bang. Very speculative of course! –  Niel de Beaudrap Oct 4 '11 at 16:10
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I admit how time apparently "flows" is a difficult problem and one of the most mysterious in physics. But reading one comment above I remember one of the famous quotes "Any intelligent fool can make things bigger and more complex... It takes a touch of genius - and a lot of courage to move in the opposite direction. " –  user1355 Oct 7 '11 at 17:05
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9 Answers

up vote 1 down vote accepted

Since for some reason this question has resurfaced, I would like to point to a similar one posed later than this.

Observation of change is important to defining a concept of time. If there are no changes, no time can be defined. But it is also true that if space were not changing, no contours, we would not have a concept of space either. A total three dimensional uniformity would not register.

Our scientific time definition uses the concept of entropy to codify change in space, and entropy tells us that there exists an arrow of time.

In special relativity and general relativity time is defined as a fourth coordinate on par with the three space directions, with an extension to imaginary numbers for the mathematical transformations involved. The successful description of nature, particularly by special relativity, confirms the use of time as a coordinate on par with the space coordinates.

It is the arrow of time that distinguishes it in behavior from the other coordinates as far as the theoretical description of nature goes.

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The concept of time is intimately related with the concept of causality. If we don't have the notion that something can cause some other thing then there is no objective meaning to the word "time". It's causality which enables us to decide and describe which event is past and which is present.

In relativity, as we know, space and time are intimately related to each other. What is just space to some observer may be a combination of space and time for another. It is therefore helpful to think of a $4$ dimensional space called spacetime whose points represent events. An event therefore needs $4$ independent numbers to be uniquely specified. Out of this $4$ numbers one is a little special. If you draw a light cone at any point in this space then all except one of the axes will be outside the light cone. This special axis is the direction of time and the numbers it represent is "time".

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Thanks for not commenting on the reason for the down vote. That's a huge relief ;) –  user1355 Oct 7 '11 at 17:08
    
+1 because this definitely doesn't deserve a -1 :-). You essentially rephrase my question in the first part. I could have rephrased as asking, "is it the case that time is simply causality?" If this is the case then it seems the notion of a "flow" of time only exists because we have a memory of the past events; when in fact there is no past, there is no future, there is only stuff which interacts. So the words "time", "causality" and "interaction" are interchangeable leaving us with only stuff that changes. –  coder Oct 7 '11 at 17:44
    
Not my downvote, but the concept of time does not require a concept of causality, which is notoriously hard to pin down in the microrealm and probably doesn't make any sense. –  Ron Maimon Oct 10 '11 at 5:30
    
I disagree with you Ron. First it is dangerous to say that causality doesn't make any sense in the micro realm. If it were so, then how can you ever trust QFT which is fully consistent with S.R. and which requires causality to hold strictly. Secondly, if two events are space like separated in the micro realm how do you decide which has taken place earlier? You can't, unless you seriously modify the existing theories or unless you are talking about some as yet unknown QG theory. –  user1355 Oct 11 '11 at 16:02
    
@RonMaimon: However, it is true that in the microscopic world there may be processes which may not have any intrinsic "arrow of time". But that's an altogether different issue, right? –  user1355 Oct 11 '11 at 16:09
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well the way time should be conceived is the same way you should look at motion or any type of energy kinetic or potential, ergo it should be treated as such. example, when a object falls from a table the time it takes to travel through the air co insists with the space around it ("space-time to be precise which the fine gent below me is proclaiming). So your question comes up which the answer would most likely be yes. but not to forget time is also a unit of measurement such as length width and depth and we use it as such. it simply being the rate of change is plausible under certain theoretical works in the past which many have been trying to prove fact in the present.

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This question ("Is time simply the rate of change?") is too ambiguous to have any meaningful answer. I can think of interpretations in which the question is vacuous (begging the question: "what is meant by 'rate of change'?"), tautological ("rate of change" == d/dt), or in which the answer is 'no' (GR).

You might find the answer you seek in this book:

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to rephrase: is time a thing in itself or is time simply things changing? This is probably a hard question to articulate. Add that to my lack of understanding of physics :-) –  coder Oct 10 '11 at 14:25
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@Jeremy: most questions that are hard to articulate in this way are not meaningful, they are only philosophical words that make the brain go in circles. The questions about time which are meaningful are those that can be answered by observations. –  Ron Maimon Dec 8 '11 at 5:47
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you seem to think time started with the big bang, how long was the matter there before the big bang? we are still only talking about half an equation. two points are still needed to justify either of our perspectives

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Time is what is measured by clocks.

But how is time modelled in physical theories ?

In the Schrödinger equation time enters as an external parameter. How does this parameter correspond to the time measured by clocks ?

The following reference might be a good introduction to this and related questions concerning time and quantum mechanics : http://www.physedu.in/uploads/publication/1/7/28-1-3-The-challenging-concept-of-time-in-quantum-mechanics1401.pdf

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There's is no such notion as "time" in isolation from space. Since time is a measure of entropy of space, then time wouldn't exist if the space is absolutely static.

Imagine that one will somehow manage to 'rollback' the matter & energy to a state in which it was yesterday. Would this be a time travel? I don't see reasons why it wouldn't.

There are things not affected by time - say, physical laws and regularities. Since we assume that they are the innate property of the universe, we also assume that they exist out of the scope of time and space. That is, time didn't exist before the BigBang, but the laws did.

Edit: it's rather difficult for me, though, to imagine a physical law existing in isolation from things that it governs.

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Physics Law is the description of the thing that it governs. –  Prathyush Oct 14 '12 at 14:45
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Certainly time is intriguing, but there are two different things going on here: (1) there is (classically) the manifold, (2) and the zeroth component of the momentum 4-vector.

To start, the temporal part of the gravitational potential does have some weird geometry that we aren't used to in everyday life and this certainly plays a role in some of the strangeness surrounding "time", but a decomposition of the EFE demonstrates that actually $g_{00}$ and $g_{0i}$ don't have time derivatives. The temporal parts of the space-time manifold, are static, only the spatial parts, $g_{ij}$ are dynamic. So where is this notion of "flow" coming from?

Instead, think of the manifold as a landscape, with something like a "temporal" direction. Our movement through that direction, is determined by the zeroth component of the momentum 4-vector, energy, temporal momentum. Why are almost all things in everyday life moving in the same "direction" of time? its not because we are all in the same river, its because we are all made of the same stuff. If you want to relate "time" with a rate of change, a place to start looking is at the momentum 4-vector, not the spacetime manifold.

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A clear understanding of time in my opinion Still eludes us.

Within scope of classical Concepts there is a Perfectly valid practical definition of time. Which essentially is the correlations between the periodic behaviour of systems. For instance the behaviour of a pendulum is correlated with the behaviour of the motion of the sun around the planet as N number of periods pendulum corresponds to 1 Period of earth orbit around the sun. The property of periodicity in classical systems is essential in the definition of a clock.

The Question about arrow of time in my opinion Boils down to our inability to prepare system in precise initial conditions, Which only allows the possibility of predicting its behaviour on in a statistical Sense. We are also limited to measure only certain properties of a system, and we cannot acquire complete information. This is a limitation we must accept on our ability to perform experiments. In this sense, if we use the clock we defined only using Classical Concepts, then this implies that flows have a preferred direction ie, a the direction of incerasing entropy.

Question of time In my opinion will completely resolve Itself if one understands what a memory impression is. Memory being impression being permanent contains a record of the passing of time. I think it is very closely connected to the foundational Issues that plague Quantum measurement.

Saying this coming to your question on Time running Slower closer to the big-bang, In one sense One can say that there is no structure to measure the movement of time. But really to answer this question we have to wait for the discovery of Quantum Gravity.

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