What is the true nature of time?

[ghwellsjr]

"Time is what happens when nothing else is happening"

Surely if NOTHING else is happening, time stands still. If nothing is happening, everything is frozen, nothing moves and that includes clocks. If clocks do not move there is no time. ie. NOTHING moving equals no time passing.

"...tantamount to a derailment of the thread"

Point was, with regard to recent discussion over time being another dimension, if its' existence is dependent on relative movement/change then surely it is not a dimension in its' own right.

The point is, everyone knows what time is and like the original poster, you also are wondering about how it can be a dimension. I really don't know what most of the posters on this thread are concerned about because they won't be specific about their concerns. I explained what I believe the issue with time being involved as a "dimension" here:

But, just in case you are talking about "spacetime interval", let me explain what it is and then you can tell me if it helps.

First you have to understand what an event is. It is nothing more than a specified location (in three dimensions) at a specified time as defined by a specified coordinate system. It does not necessarily have anything to do with observers or paths or any actual event, although it may. You can then transform the event (location plus time) to any other coordinate system and the numbers you get to describe the four components of the event could be totally different.

In Galilean spacetime, if you have two events, the spatial distance between any two events can be calculated by taking the square root of the sum of the squares of the differences in the three dimensions and the time difference is merely the difference in the two times. Then if you transform the two events into a different coordinate system, even though all the numbers are different to describe the locations and times of the two events, if you perform the same computation, you will get the same answers for the spatial distance and time difference between the same two events defined by the second coordinate system, even if this second coordinate system is in motion with respect to the first one.

By Galilean spacetime, we mean that the relative speed between the two coordinate sytems, otherwise known as frames of reference, is much less than the speed of light.

But if the two coordinate systems (frames of reference) have a high speed between them, then the calculations that we did under the Galilean spacetime do not give the same spatial distance and time difference in the two frames of reference. However, we can define a new "distance" or "difference" between the two events which is called the "spacetime interval" that will be the same no matter what frame of reference we do the computation in, but instead of getting two numbers, a spatial distance and time difference, we get just one, the spacetime interval, based on a calculation of the two previous values.

The computation is very similar to the spatial distance, in fact we start with that prior to taking the square root but instead we subtract the square of the time difference multiplied by the square of the speed of light.

It should be no surprise that this computaton yields a frame invariant quantity, since we use the Lorentz Transform to produce the numbers for the second frame of reference, and the transform guarantees that the spacetime interval is frame invariant.

And you will note that it isn't time that is the fourth dimension, it is time multiplied by the speed of light, which is the distance that light travels for the time in question. So I don't know what the big concern is.

 

[cshum00]

The point is, everyone knows what time is and like the original poster, you also are wondering about how it can be a dimension. I really don't know what most of the posters on this thread are concerned about because they won't be specific about their concerns. I explained what I believe the issue with time being involved as a "dimension" here:

I think neophysicist2's question is more like this:
-Let's assume that it is possible for the entire world to be in a motionless state.
-Proper time is dependent to the spatial dimensions x, y, z or also defined as:
<br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br />
-Meaning that proper time in the world of motionless state will yield to the line integral path of 0 (zero).
-Then does it mean that time has come to a complete stop for the world that is at the motionless state?

 

[matheinste]

I think neophysicist2's question is more like this:
-Let's assume that it is possible for the entire world to be in a motionless state.
-Proper time is dependent to the spatial dimensions x, y, z or also defined as:
<br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br />
-Meaning that proper time in the world of motionless state will yield to the line integral path of 0 (zero).
-Then does it mean that time has come to a complete stop for the world that is at the motionless state?

With regard to the universe being in a motionless state I assume this means that all entities within it are at spatially at rest with respect to each other. Now is it implicit in the statement that time has somehow ceased to move onwards. If it does not then entities still have a path through spacetime. Anyway given that the question does not assume the answer we sort of come to a deeply philosphical question, does time exist if there are no means of measuring it. Clocks require some sort of repetitive cycle, impossible if you remove all happenings right down to a subatomics level and lower. It is a question I have not given much thought to but my intitial reaction is that time becomes irrelevant and meaningless.

Another interesting thought. I believe, that classically, that is ignoring quantum effects, once all things have ceased to move, if that is ever possible, they can never start to do so again.

Matheinste.

 

[Dale]

<br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br />
-Meaning that proper time in the world of motionless state will yield to the line integral path of 0 (zero).

Look carefully at the equation. If dx=dy=dz=0 then the proper time is not zero, it is in fact maximized.

 

[FlexGunship]

Look carefully at the equation. If dx=dy=dz=0 then the proper time is not zero, it is in fact maximized.

i.e. no movement through z, y, x implies maximum movement through t.

 

[Dale]

My problem, what confuses me, is when a word's meaning in one context is applied in another different context. Don't u see how this can be an issue?

Obviously, that is why I have posted my many comments in this thread clarifying the most relevant meanings of the word time.

 

[Dale]

that's not my definition. I suggest we stick to my actually definition of dimension: a concept used to specify the structure/orientation or shape/geometry of a physical object.

Can you cite any mainstream reference for this definition?

These are qualitative attributes. Duration is a quantitative attribute.

Your first statement is simply false. Distance and duration are both quantitative. A brick is e.g. 7 cm in height by 10 cm in width by 20 cm in length by 100 years in duration. All quantitative.

I point to an object and ask u what shape is it. If it has a defined shape u name it (square, octogon, tetrahedron, etc). If it doesn't u qualify it with it's dimensions.

Exactly the same with time, except that we have fewer words for 4D shapes so we make up new ones like "light cone" and "helical worldline", etc.

I might ask you how long, wide or high is it. You go measure it with a calibrated device. I point to the same object again and i ask u, what time is it. Please tell me how u go about answering this.

With a clock. Btw, your phrasing is wrong here. You are confusing e.g. length with position.

 

[DaveC426913]

I point to an object and ask u what shape is it. If it has a defined shape u name it (square, octogon, tetrahedron, etc). If it doesn't u qualify it with it's dimensions. I might ask you how long, wide or high is it. You go measure it with a calibrated device. I point to the same object again and i ask u, what time is it. Please tell me how u go about answering this. Thanks.

Shape is a qualititative measurement, yes. No one is talking about shape except you.

Asking 'what is the time of a brick' is like asking 'what is the x of a brick?' Poorly worded, but we can deduce what you meant.

Length, width and height are quantitative. I can specify the brick's x, y and z extent as arbitrarily precisely as I want. I can also specify its extent in time. It came into existence on Aug 23, 2003, and ceased to exist *WHAM* now.



Point of order: correct spelling is actually a PF rule.

https://www.physicsforums.com/showthread.php?t=414380
"...posts are required to show reasonable attention to written English communication standards. This includes the use of proper grammatical structure, punctuation, capitalization, and spelling. SMS messaging shorthand, such as using "u" for "you", is not acceptable."

 

[Passionflower]

I can also specify its extent in time. It came into existence on Aug 23, 2003, and ceased to exist *WHAM* now.

Different clocks do not necessarily agree on the age of an object.

 

[cshum00]

Look carefully at the equation. If dx=dy=dz=0 then the proper time is not zero, it is in fact maximized.

i.e. no movement through z, y, x implies maximum movement through t.

Then that is the answer. I just don't see the mathematics of it, can you guys help me?

Let's say that x, y, z are functions of a dummy parametric variable. Then parametric equations of the curve is:
x(s)=k_1; y(s)=k_2; z(s)=k_3
dx(s)=0; dy(s)=0; dz(s)=0
dt = 0ds
\int_D = \int_0^0

Then:
<br /> t_p = \int_0^0 0 \sqrt {1 - \frac{(0)^2 + (0)^2 + (0)^2}{c^2}} ds<br />
I must be doing something wrong since i get zeros everywhere. I get that the parametric curve is zero. The limits of integration is zero.

Edit: Ok, i see where i started wrong. The general line integral is:
\int_D f(x,y,z) ds
And the parametric form of the line integral is:
\int_a^b f(x(t),y(t),z(t)) \sqrt {(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 + (\frac{dz}{dt})^2}dt

This means that the proper time equation: <br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br /> is already in its parametric form where t (time) is the parametric variable. It doesn't change the fact that:
x(s)=k_1; y(s)=k_2; z(s)=k_3
dx(s)=0; dy(s)=0; dz(s)=0

But i still don't get the following:
-\int_D implies the integral around the curve D but the limits of the parametric form of the line integral are plain limits a and b.
-Even assuming that they are just limits a and b, what are a and b since my parametric variable is time but time is what i want to calculate too?

 

[DaveC426913]

Different clocks do not necessarily agree on the age of an object.

Likewise different rulers do not necessarily agree on its length.

Point made in favour of time being a dimension like space.

 

[Ich]

-Even assuming that they are just limits a and b, what are a and b since my parametric variable is time but time is what i want to calculate too?

Don't use the same word for different things. Suppressing two dimensions, you have
ds²=-dt²+dx², IOW
dtau² = dt²-dx²,
where tau is proper time, and t is coordinate time. Two different things.
Now obviously you integrate t, so your bounds a,b are different coordinate times.
Likewise, x is not a function of tau, but a function of t.
Integrating the formula from t1 to t2 gives Delta tau, the elapsed proper time.

 

[Passionflower]

Point made in favour of time being a dimension like space.

So because different clocks record different ages of an object in sapcetime is a point in favor of time being a dimension of spacetime?

 

[cshum00]

Don't use the same word for different things. Suppressing two dimensions, you have
ds²=-dt²+dx², IOW
dtau² = dt²-dx²,
where tau is proper time, and t is coordinate time. Two different things.
Now obviously you integrate t, so your bounds a,b are different coordinate times.
Likewise, x is not a function of tau, but a function of t.
Integrating the formula from t1 to t2 gives Delta tau, the elapsed proper time.

Sorry for mixing up proper time and coordinate time.

I know i might be wrong but i am just trying to piece the information you gave me with what i have.
x(t)=k_1; y(t)=k_2; z(t)=k_3
dx(t)=0; dy(t)=0; dz(t)=0
\int_D = \int_{t_1}^{t_2}
t_p = \tau = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt
\tau = \int_{t_1}^{t_2} \sqrt {1 - \frac{(0)^2 + (0)^2 + (0)^2}{c^2}} dt
\tau = \int_{t_1}^{t_2} \sqrt {1} dt = \int_{t_1}^{t_2} 1 dt
\tau = t |_{t_1}^{t_2} = t_2 - t_1 = \Delta t

-How do i know what are the coordinate time values t_1 and t_2?
-If i did something wrong please point it out again. Also, please show me the entire calculation please so that i can see the entire picture faster.

 

[DaveC426913]

So because different clocks record different ages of an object in sapcetime is a point in favor of time being a dimension of spacetime?

In that, using your example, you have shown another way they are similar, yes.

Note what it requires for the clocks to show different ages; it requires a difference in frames of reference. Same with spatial dimensions. Objects observed at relativistic velocities will be measured as shorter in a spatial dimension just as they are measured longer in the time dimension.

 

[nismaratwork]

In that, using your example, you have shown another way they are similar, yes.

Note what it requires for the clocks to show different ages; it requires a difference in frames of reference. Same with spatial dimensions. Objects observed at relativistic velocities will be measured as shorter in a spatial dimension just as they are measured longer in the time dimension.

To me, this seems intuitive once you accept Relativity.

To neophysicist... sorry about the late reply, but my internet died a terrible death for a bit there. You could imagine a universe without any discernable motion and time could still be a dimension there. Perhaps you have a classical universe at absolute rest, but it is still capable of being perturbed. Even in thought experiments or pondering your view of time as a measure of change is just that: a measurement problem. Time can be a dimension even when it's not measurable, and that in my view is another point in favor of time as just another dimension like any other.

If it isn't, 4-Momentum/Velocity, etc... makes no sense... yet it works.

 

[Passionflower]

Note what it requires for the clocks to show different ages; it requires a difference in frames of reference. Same with spatial dimensions.

Hold on so the dimensions of spacetime are frame dependent? Frame dependent dimensions? What are frame dependent dimensions?

Let me ask you this: do you think spacetime has a notion of absolute space and time? Are the, what you call time ans space dimensions, of spacetime absolute?

 

[DaveC426913]

Hold on so the dimensions of spacetime are frame dependent?

I did not say this. How do you get that from what I said?

 

[Passionflower]

I did not say this. How do you get that from what I said?

Ok, so then do you say they are fame independent?

 

[DaveC426913]

Ok, so then do you say they are fame independent?

Dimensions are, our measurements of things in them is not.

 

[Dale]

Are the, what you call time ans space dimensions, of spacetime absolute?

The dimensionality of a manifold and the signature of the metric are both invariants.

 

[Passionflower]

Dimensions are, our measurements of things in them is not.

I see, let me get this straight so you are calling the dimensions of spacetime space and time but we cannot measure them?

 

[Passionflower]

The dimensionality of a manifold and the signature of the metric are both invariants.

I agree with that, that is exactly the reason why the dimensions of spacetime cannot be called pure space and time because space and time separately are not invariants for observers only in combination they are.

This, what you call, timelike dimension of spacetime do you think that is a measure of some kind of absolute time and for space dimension absolute space? A sort of LET kind of interpretation?

 

[DaveC426913]

I see, let me get this straight so you are calling the dimensions of spacetime space and time but we cannot measure them?

What do you mean measure "them"? Measure a dimension? One does not measure a dimenson; it is a continuum. You measure something in a dimension.

If I measure the width of a brick, that is utterly independent of its length or height. It must have a width and height, but measuring its width tells me nothing about its length or width (because they are orthagonal).

Likewise, if I measure the duration of the brick, it is also independent of its length and width and height. All 4 are orthagonal.

 

[DaveC426913]

Hold on so the dimensions of spacetime are frame dependent? Frame dependent dimensions? What are frame dependent dimensions?
Are the, what you call time ans space dimensions, of spacetime absolute?

I see, let me get this straight so you are calling...

...A sort of LET kind of interpretation?

Passionflower, there's got to be a better way of discussing this than trying to put words in other peoples' mouths.

 

[Dale]

I agree with that, that is exactly the reason why the dimensions of spacetime cannot be called pure space and time because space and time separately are not invariants for observers only in combination they are.

I don't think anyone has called them "pure space and time", whatever that means.

I don't know where you pulled the LET from. This is basic GR. Spacetime is a 4D pseudo-Riemannian manifold with three dimensions of space and one dimension of time. Do you understand what that means?

 

[Passionflower]

What do you mean measure "them"? Measure a dimension? One does not measure a dimenson; it is a continuum. You measure something in a dimension.

Ok fair enough, if I the measure time between two events in spacetime, do you think all observers agree on how much time is between them? You call time a dimension of spacetime right?

Likewise, if I measure the duration of the brick, it is also independent of its length and width and height. All 4 are orthagonal.

Let me ask you this do you understand the difference between a Galilean spacetime and a Minkowski spacetime? Do you understand that time and space are not independent in spacetime?

 

[Dale]

Do you understand that time and space are not independent in spacetime?

Do you understand that x, y, and z are not "independent" in space? If you do then it should be clear that being "independent" is not a requirement for a dimension. In fact, if it were "independent" in this sense then it wouldn't be a dimension in the same mathematical space.

 

[Passionflower]

I don't think anyone has called them "pure space and time", whatever that means.

Ok, fair enough then what kind of time is it? Coordinate time perhaps? You call a coordinate dependent entity a dimension of spacetime the spacetime we live in?

This is basic GR. Spacetime is a 4D pseudo-Riemannian manifold with three dimensions of space and one dimension of time. Do you understand what that means?

Spacetime is certainly a 4D pseudo-Riemannnian manifold I completely agree with that. No single dimension of this manifold can be attributed to time and space for all observers, in fact in non-stationary spacetimes no single observer will measure the, what you call, timelike dimension as time and no single observer will measure the spacelike dimensions as space as GR is basically a background independent theory.

Unlike in the case of Galilean spacetime time for any observer is the path length between two events not the amount traveled in the timelike dimension.

 

[Dale]

Spacetime is certainly a 4D pseudo-Riemannnian manifold I completely agree with that.

OK. So, in your understanding, what distinguishes a 4D pseudo-Riemannian manifold from a 4D Riemannian manifold?