The Nature of Time: Should It Be Considered a 4th Dimension?

[saderlius]

Given a 3D-Euclidean space, it does make sense to define a new, fourth dimension that can be defined as perpendicular to that space. That new dimension is associated with the "time" associated with that given 3D space. Mystical as this may sound at first, this construction is used in describing the evolution of 3D systems in Galilean physics... however, its interpretation as a spacetime geometry is not as familiar as Minkowski spacetime.

If a 4th dimension makes sense, why not "n" dimensions? In math, the 4th dimension, in which "exists" such entities as hyper-cubes, the dimension is treated like a euclidean dimension. It doesn't make sense in math to describe that dimension as time. If anything, the use of time as a "4th dimension" is confusing from a mathematical perspective, because i would expect to get some tesseracts out of it.

 

[saderlius]

I would be interested in hearing what you think the word "dimension" means.

Fair enough.
i define dimension as dichotomous direction.
However, i admit "dimension" has a much further range of uses than that. If you were to say time is a dimension of reality, in that it is a faculty of existence, i would agree in that use. What gets me is the treatment of time as if it were a spatial dimension. If you were to say time is a "dimension" but in a class of it's own, you would distinguish it from spatial dimension. However, as it is called a "4th dimension", it is ascribed the properties of the previous 3 euclidean dimensions. This i question.
cheers,
sad

 

[MeJennifer]

It's not clear to me what your position on this topic is. (I get hints of what is not your position... but it's murky to me what your position is.) For the benefit of the readers of this thread, in a short paragraph, can you precisely define "dimension"? "t"? "time"? "proper time"?

In relativity, time is simply that what a clock reads, which is also called proper time. In relativity there is no absolute time, each object in the universe could, in principle, have its own unique time. A dimension is simply a means to describe something. It turns out that in (the kinematics of) relativity we need four of them. The relationship between these four dimensions is such that the metric is not Euclidean but Lorentzian. One consequence of this is that hyper surfaces of proper time are hyperbolic rather than Euclidean.

Note that if you let c go to infinity, these hyperbolic hyper surfaces become Euclidean and actually do represent the t dimension.

So in other words, one could argue that the t dimension does not represent time in relativity because the speed of light is not infinite.

 

[yogi]

Garth - your post 28 - Thanks for the erudition. Shucks - I was only off by about 17 centuries.

Yogi

 

[saderlius]

I think that when most people wonder about a fourth dimension, they're thinking of a fourth spatial dimension. Time is of course a temporal dimension so naturally time as the fourth dimension comes as an unexpected answer. But what, really is the significance of this? No one is really claiming that time is a fourth spatial dimension. But it so happens that the math works out quite well if we treat it in a similar way to the spatial dimensions. I think the bottom line is that time is being treated as a fourth dimension only because of the similarity between separate relativistic transformations of space and time. So even though we treat time and space similarly in the mathematics, they are indeed inherently different quantities.

My gratitudes! Your answer is very reasonable, and of all the ones given, the easiest to understand from a lay perspective.

 

[masudr]

To me, this regards time relative to position, but it doesn't tell me why time is treated as synonymous with position. Also, depending on velocity, my values of time and distance can be very drastically different.

Well exactly: coordinate measurements of time and space vary according to choice of frame. And they do so in such a way that it makes sense to lump them together (albeit with some caveats that others have mentioned: e.g. the differing signature in the metric).

The only thing they seem to have in common is our ability to quantify them. However, i can also quantify mass, so why shouldn't i make it a 5th dimension and graph it perpendicular to the other 4?

Well you could do that, but it turns out that rest mass is proportional to the length of the energy-momentum 4-vector. It's determined by the dynamics, and not really a free coordinate in the sense time and space are.

 

[Tzemach]

The trouble with understanding time is that people can only see entropy. Entropy is the way that things move from order to disorder, they spread out, run down, wear out all these are symptoms of entropy. New things always become old, we cannot buy old goods and see them become new as we use them, scientists call this entropy this is known as the second law of thermodynamics. Physical reactions always only go one way. Which is why
Vesselin Petkov, wrote (Relativity and the Dimensionality of the World – 2004), “that Minkowski spacetime leads to a clear dilemma: Minkowski spacetime should be regarded either as nothing more than a mathematical space which represents an evolving in time 3D world (the present) or as a mathematical model of a timelessly existing 4D world with time entirely given as the fourth dimension. The implications of a 4D world for a number of fundamental issues such as temporal becoming, flow of time, determinism, and free will are profound - in such a world (often called block universe) the whole histories in time of all physical objects are given as completed 4D entities since all moments of time are not "getting actualized" one by one to become the moment "now", but form the fourth dimension of the world and therefore all are given at once. And if temporal becoming and flow of time are understood in the traditional way - as involving 3D objects and a 3D world that endure through time - there is no becoming, no flow of time, and no free will in a 4D world.”

This view indicates an inability to perceive a fourth or time dimension as a whole; it is extremely difficult for those who experience time as a progression to visualize it in entirety. A separate dimension of time does not rule out free will, it simply means that although we are not yet aware of future decisions we are actually making them now. The fourth dimension can contain all history from the earliest moments of creation until the ultimate end of the universe. However, the structure of the four-dimensional universe in which past, present and future all inhabit the same moment requires very specific quantum structure, which Planck demonstrated exists naturally. The common view of time is as an observed one-way flow providing, together with space, the matrix of events. It can be measured as an epoch, (the moment of an instantaneous event as marked by a clock) or as the interval of duration of a continuous event, and by reference to either moving bodies or electromagnetic phenomena (atomic time) its flow has been found, in contemporary physics, to be relative to the observer’s velocity and acceleration perspectives and gravity. The four dimensional Minkowski universe has all time permanently existing and our perception passes through it experiencing each moment consecutively. Four dimensions are easily depicted mathematically the difficulty comes when we try to perceive how such a universe could physically exist.

 

[masudr]

We don't have free will. However it appears as if we do, and that is good enough.

 

[rewebster]

We don't have free will. However it appears as if we do, and that is good enough.

hmmmm---

Are you saying that you had 'no' choice --(at all!)-- when you typed that response?

OK---then--who made you type it?

hmmmm?!

 

[Ballon]

hmmmm---

Are you saying that you had 'no' choice --(at all!)-- when you typed that response?

OK---then--who made you type it?

hmmmm?!

Humm, there is a flow, flow is movement, if no flow, then we are stuck.. at least we can say a flow to move to event in time A to event in time B , maybe all the events are "already" there, in the whole life of the universe and we are sliding on the time, like moving from a room to another room (so time is a door), in that case, "who made this person to write" are the past event already there drawing a line to that current event that is a middle point (present) to the futur ...anyway, that's a good question, are we in a movie playing foward frame by frame ? or are we actualy "acting"...:) (sorry for my bad english but this is not my mother language)

 

[masudr]

OK---then--who made you type it?

Easy -- a combination of factors:

i. my genetic makeup
ii. my collective past experiences
iii. external stimulus

(ii. and iii. can be lumped together if you wish: ii. is merely all the external stimuli I have ever experienced)

Since there is no plausible way to analyse all these/recreate the situation to perfection, I have the illusion of free will.

 

[rewebster]

...I have the illusion of free will.

Do you consider yourself as an 'illusion'?

 

[masudr]

Do you consider yourself as an 'illusion'?

We are no longer discussing physics, but for those interested:

The fact my senses receive the data that they do is the only thing I can be absolutely certain of.

Analysing my sensory data has helped me build up this picture of quantum mechanics, and Earth orbiting the sun, wind being air, sound being air, light being EM radiation etc.

If you call that an illusion (I don't know why you would) then yes; but in my interpretation of the word, I am most certainly not an illusion.

 

[rewebster]

well, if you are not an illusion--but the world around you is (I don't), then how does 'time' or 'the measurement of time' figure into the illusion?

are you suggesting 'the measurement of time' is 'unreal' in just about all aspects?

 

[masudr]

well, if you are not an illusion--but the world around you is (I don't), then how does 'time' or 'the measurement of time' figure into the illusion?

Emphasis mine. I don't remember implying that (no pun intended).

 

[rewebster]

The fact my senses receive the data that they do is the only thing I can be absolutely certain of.

Analysing my sensory data has helped me build up this picture of quantum mechanics, and Earth orbiting the sun, wind being air, sound being air, light being EM radiation etc.

What I was headed toward is if 'time' was received as data, was/is it quantum; or do you think it is/has references toward a quantum nature?

 

[masudr]

What I was headed toward is if 'time' was received as data, was/is it quantum; or do you think it is/has references toward a quantum nature?

Hang on: my tangent onto illusory free will was nothing to do with how we perceive time.

 

[rewebster]

Hang on: my tangent onto illusory free will was nothing to do with how we perceive time.

You didn't bite--darn!




To me that shows free will

 

[pmb_phy]

In Galilean space-time you could consider time the fourth dimension, but in relativity time is not the fourth dimension!

Ah my dear friend MJ. You've once more confused the hell out if me.

In relativity, the relative measure of time between any two observers is related to their relative orientations in space-time.

The only difference between an Euclidean 4-dimensional Galilean space-time and a Minkowski space-time is that the rotations work differently.

In both Lorentzian and Galilean space-time, time still is the 4rth dimension of the manifold of interest.

Both the Galilean E⁴ and the Lorentz O(1,3) make a 10-dimensional symmetry group.

But nothing you've said here would even hint at the notion that time is not the 4th component of an event/position 4-vector etc. Why would you say that the time component of X = (ct, x, y, z) does not have time as the 4th dimension?

Best wishes

Pete

 

[JesseM]

Perhaps it would help to distinguish between "time is equivalent to a fourth spatial dimension" (which no one would claim) and "time is a dimension" (which is true in physics, but on the other hand any continuous parameter can be treated as a dimension in physics, like in statistical mechanics where every particle's position and momentum are treated as separate dimensions in the phase space).

 

[MeJennifer]

Perhaps it would help to distinguish between "time is equivalent to a fourth spatial dimension" (which no one would claim) and "time is a dimension" (which is true in physics, but on the other hand any continuous parameter can be treated as a dimension in physics, like in statistical mechanics where every particle's position and momentum are treated as separate dimensions in the phase space).

In pre-relativistic kinematics and dynamics time is indeed a dimension but not in relativity.

Time in space-time is proper time which is not expressed as a dimension but is expressed by the metric of space-time, and this metric is composed of four separate dimensions.

As I wrote before, the hypersurfaces of constant proper time of space-time are hyperbolic. These hypersurfaces could only overlap the hypersurfaces of constant t (for the commonly called "time" dimension) in the case the speed of light would be infinite.

Actually, if you want to, in relativity, you can do away with time. The theory is diffeomorphism invariant and that means that each instance in time is simply the same thing just in another format. A bit like the same paper in word and pdf format.

 

[pmb_phy]

Time in space-time is proper time which is not expressed as a dimension but is expressed by the metric of space-time, and this metric is composed of four separate dimensions.

I disagree. The temporal dimension of a 4-vetor is coordinate time, not proper time. - Pete

 

[MeJennifer]

Originally Posted by MeJennifer
Time in space-time is proper time which is not expressed as a dimension but is expressed by the metric of space-time, and this metric is composed of four separate dimensions.

I disagree. The temporal dimension of a 4-vector is coordinate time, not proper time. - Pete

Pete, I am not sure what you are disagreeing with since I did not write that the t dimension of a vector is proper time.

 

[pmb_phy]

Pete, I am not sure what you are disagreeing with since I did not write that the t dimension of a vector is proper time.

Sorry my dear lady. Let me rephrase. What did you mean when you wrote

Time in space-time is proper time which is not expressed as a dimension but is expressed by the metric of space-time, and this metric is composed of four separate dimensions.

Pete

 

[MeJennifer]

Sorry my dear lady. Let me rephrase. What did you mean when you wrote

Time in space-time is proper time which is not expressed as a dimension but is expressed by the metric of space-time, and this metric is composed of four separate dimensions.

In mathematical terms:

$$\tau = \int \sqrt {dt^2 - dx^2/c^2 - dy^2/c^2 - dz^2/c^2}$$

If we let $c \rightarrow \infty$ we can see that $$\tau = t$$ as is the case in pre-relativistic kinematic and dynamic models.

As Minkowski said about 98 1/2 years ago:

"Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

The union is the metric.

 

[JesseM]

In pre-relativistic kinematics and dynamics time is indeed a dimension but not in relativity.

Once again it seems you are inventing your own language, rather than using the standard language of physicists. What are the precise criteria for something to be treated as "a dimension" in physics, according to you? Would you disagree that any variable one chooses--temperature, say--can be considered a dimension?

Time in space-time is proper time which is not expressed as a dimension

What does the phrase "not expressed as a dimension" mean you you, exactly?

but is expressed by the metric of space-time, and this metric is composed of four separate dimensions.

You could similarly say that space in ordinary 2D euclidean geometry is expressed by a metric with two dimensions--but this wouldn't justify the statement that an x-axis and a y-axis placed on this space cannot themselves be described as "spatial dimensions", it's standard terminology in mathematics to refer to them that way.

As I wrote before, the hypersurfaces of constant proper time of space-time are hyperbolic.

If you take a bunch of clocks radiating out from a single event at different velocities, with each reading t=0 where their worldlines intersect this event, and then draw a hypersurface based on the event of each clock reading the same proper time t=T, then sure, you get a hyperbola. But what does this have to do with whether time is "a dimension"?

These hypersurfaces could only overlap the hypersurfaces of constant t (for the commonly called "time" dimension) in the case the speed of light would be infinite.

I still don't get what point you think you're making here. If you like you are free to use a coordinate system where the t-coordinate is based on the proper time along worldlines radiating out from a single event (although the coordinate system can only cover the future and past light cone of that event), but you'll still need four coordinates to pinpoint any event in the region covered by the coordinate system, and there'll still be an unambiguous notion of whether the separation between two events is timelike, spacelike or lightlike (though I think in this coordinate system it'd be possible for two events to have the same t-coordinate but a timelike separation). And the conventional coordinate systems used in SR can also be understood in terms of the proper time on physical clocks, except that instead of using a collection of physical clocks radiating out from a single point in spacetime at different velocities, you have a collection of clocks at rest with respect to each other and synchronized according to the Einstein synchronization convention. In this case if you look at the hypersurface of constant proper time (the event on each clock's worldline where it has ticked some time T since t=0), then you have the standard surface of simultaneity of an inertial coordinate system in SR. Leaving aside the question of why you think your choice of coordinate system shows "time is not a dimension", do you think that your choice of coordinate system, based on the proper time of clocks radiating out from a single event and all set to read the same time where their worldlines intersect that event, is somehow more "physical" than this one, based on the proper time of clocks at rest with respect to each other and synchronized according to the Einstein clock synchronization convention?

Actually, if you want to, in relativity, you can do away with time. The theory is diffeomorphism invariant and that means that each instance in time is simply the same thing just in another format.

I don't understand what diffeomorphism invariance has to do with "doing away with time", or what you mean by "each instance in time"--each instance of what, exactly? Would you agree that the question of whether two events are timelike separated, spacelike separated, or lightlike separated is a physical issue which is not affected by your choice of coordinate system?

 

[MeJennifer]

Jesse, I am trying to explain why none of the four dimensions of space-time represent time, but that instead the metric of space-time represents time.

I am not arguing the philosophy of what a dimension is.
Let's keep these two things separate.

 

[pmb_phy]

In mathematical terms:

$$\tau = \int \sqrt {dt^2 - dx^2/c^2 - dy^2/c^2 - dz^2/c^2}$$

If we let $c \rightarrow \infty$ we can see that $$\tau = t$$ as is the case in pre-relativistic kinematic and dynamic models.

I don't see what that matters in this thread? Please clarify.

"Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

Ya got to love that Minkowski. Did you read that article? Minkowski went on to say in that same article

But I still respect the dogma that both space and time have independent significance.

The union is the metric.

That makes no sense to me.

Thanks

Pete

 

[MeJennifer]

Pete, perhaps it helps if you can explain your views on this, then we can perhaps understand why and how we differ.

Suppose we have a space-time of say 7 observers. Now do you think that the t-dimension of this space-time expresses time in relativity?

I can readily see it does so in pre-relativistic kinematics and dynamics, afteral those theories postulate a notion of absolute time, so the t-dimension is indeed time.

But in relativity, clearly there is no such thing as absolute time, each of the 7 observers of can measure time quite differently.

So how do you conclude that the t-dimension represents time?

 

[masudr]

I can only repeat what I have said previously, as I feel that this is the source of the problem:

It must be stressed here that time being the 4th dimension is coordinate time. This is very different from the time that clocks will measure (the so-called proper time): that is proportional to lengths of paths in spacetime and can involve as much space as they do time.

MeJennifer is simply saying that time is proper time; and I'm sure we all here recognise that the metric is needed to define proper time. I think that's what is meant by the metric unifying the two.

 

[robphy]

Maybe the unqualified term "time" should be replaced by:
"proper time" when associated with [the spacetime arclength of] an observer's worldline [and events on that worldline],
"coordinate time" (or "time-coordinate") when associated with an observer's coordinate system [which can be used to label events not on the observer's worldline],
"clock reading" when referring to particular event.

Note that the metric by itself doesn't give us the notion of proper time. It is the metric and the choice of particular timelike path that does.


What this discussion needs [as well as many discussions in this forum] are more precise-definitions (when needed) and less loose talk.

 

[MeJennifer]

Note that the metric by itself doesn't give us the notion of proper time. It is the metric and the choice of particular timelike path that does.

Since,

$$\tau = \int \sqrt {dt^2 - dx^2/c^2 - dy^2/c^2 - dz^2/c^2}$$

I do not see any reason why it would be wrong to say that the metric in relativity gives us the the notion of proper time in relativity. The value obviously depends on the path but the way it is summed is by the metric.

 

[robphy]

Since,

$$\tau = \int \sqrt {dt^2 - dx^2/c^2 - dy^2/c^2 - dz^2/c^2}$$

I do not see any reason why it would be wrong to say that the metric in relativity gives us the the notion of proper time in relativity.

By itself, the metric does not.
There is an integral over a path-to-be-specified to be done.

So, the metric is just one of the needed structures that "gives us the the notion of proper time in relativity".

 

[robphy]

The value obviously depends on the path but the way it is "summed over" is by the metric.

The sum is over infinitesimal neighboring segments [the integrand].
The metric came in when determining what each segment contributes.

 

[MeJennifer]

The sum is over infinitesimal neighboring segments.

That is exactly right!

The metric came in when determining what each segment contributes

The metric determines what each segment contributes!

Anyway we are arguing miniscule details.