Two faces of time?

[michel123456]

These are some thoughts about Time.

 

The usual way of describing the space-time continuum is the following:

we have 3 dimensions related to space, and one related to time.

The 3 spatial dimensions are given by spatial coordinates (x,y,z) & the temporal one is added to form a four coordinates system (x,y,z,t).

So far, so good.

But we know from our observations that time can be used as a representation of distance. It is a consequence of the observed Speed Of Light. We can replace a distance-unit of 300.000 km with a time-unit of 1 sec. It doesn't change a thing.

So that we can build another spatial coordinate system (3D spatial) made of 2 orthogonal angles and a distance (α, β, d). α is an angle in the XY plane, β is an angle in XZ plane, d is the distance to origin.

It is 3D coordinate system that is enough for determining the placement of a point in space. In this coordinate system, we can replace d=distance by t=time.

We have described a spatial coordinate system with the help of 2 spatial (geometric) instances (angles) plus time. 3D space has been relaced by 2D+T.

Just like time was "inside" the notion of space. As a natural consequence of the replacement of distance by time.

I suppose this is not something new, nor something weird.

The fact that Time is intimately related with space is well-known. It is the common face of time.

But is that enough for the description of Time?

Isn't it another face of time, related to chronologic order, or the fact that one event happen before another?

An event far away can happen before an event close to the observator. A star can explode one day, and the other day a ring can bell. The 2 events are completely unrelated, except the fact that one happened before the other. There is no distance, there is no causality. Only Time.

That is the 2nd face of time.

Any comments?

[Klaynos]

I don't think it is fair or correct to say that you can replace space with time... A distance of 1 second makes little sense in space, a distance of 1 lightsecond does make sense... But that is a different unit.

 

As for changing into angles + distance I'm guessing you're familiar with spherical polar coordinates?

[Mr Skeptic]

You are trying to replace 4 dimensions with 3... it won't work.

[michel123456]

I don't think it is fair or correct to say that you can replace space with time... A distance of 1 second makes little sense in space, a distance of 1 lightsecond does make sense... But that is a different unit.

 

As for changing into angles + distance I'm guessing you're familiar with spherical polar coordinates?

 

In the army i was in the artillery:-) (artillery calculations are based on polar coordinates). and from my work i know what polar coordinates mean.

 

In my description, space is not replaced by time: distance is. Can't we do that? a distance of 1 sec. is equal to 300.000km. Not very useful in everyday life but I suppose is correct from a physical point of vue.

[swansont]

Isn't it another face of time, related to chronologic order, or the fact that one event happen before another?

 

This can depend on your frame of reference.

[Klaynos]

Again replacing distance (space, there is no real difference) with time is not quite right, you need to replace it by (this is just a standard, any speed will dimensionally work) time * speed of light... hence, lightsecond not just second.

[Moontanman]

I can see the first dimension being time instead of looking at it from the idea of the last. As in One dimension is a time two is a line, three is a plane, and four a cube type thinking. take away 4, 3, and 2 and you still have time left. Time would be the fundamental dimension.

[Sisyphus]

I can see the first dimension being time instead of looking at it from the idea of the last. As in One dimension is a time two is a line, three is a plane, and four a cube type thinking. take away 4, 3, and 2 and you still have time left. Time would be the fundamental dimension.

 

Why would there be a first or last dimension?

[Moontanman]

Why would there be a first or last dimension?

 

I see what you mean but when most people think of time they add it to the other three, like an after thought, My idea is that time be thought of as the basis for the other three not an add on after the fact. With out time you cannot have the other three. Most ideas seem to put it the other way around and say time only applies after you have the three space dimensions. What I was suggesting it that time is the background all the other dimensions apply to. Of course it's just an idea, that makes better sense to me when i imagine things like space time. Not a assertion of reality.

[Mr Skeptic]

You can have any combination of spacelike and timelike dimensions, and the order you add them doesn't matter.

[michel123456]

I see what you mean but when most people think of time they add it to the other three, like an after thought, My idea is that time be thought of as the basis for the other three not an add on after the fact. With out time you cannot have the other three. Most ideas seem to put it the other way around and say time only applies after you have the three space dimensions. What I was suggesting it that time is the background all the other dimensions apply to. Of course it's just an idea, that makes better sense to me when i imagine things like space time. Not a assertion of reality.

 

I agree.

 

Take a point. Zero dimension.

Zero "spatial" dimension.

But you have time already.

Otherwise, you can't have a point.

[Sisyphus]

With out time you cannot have the other three.

 

Why not?

[toastywombel]

I agree.

 

Take a point. Zero dimension.

Zero "spatial" dimension.

But you have time already.

Otherwise, you can't have a point.

 

I don't think time already exists just because you have determined a point. If there was a zero "spatial dimension" point, how would time be determined at that point? Time is determined by the movement of matter and energy relative to an observer. How could you determine time if where you are trying to determine it (the point) has no space?

 

I think it would be possible to determine time with two points, but just one point no.

[Tau Meson]

I don't think time already exists just because you have determined a point. If there was a zero "spatial dimension" point, how would time be determined at that point? Time is determined by the movement of matter and energy relative to an observer. How could you determine time if where you are trying to determine it (the point) has no space?

 

Can't time be defined at a point if it is parameterized though?

[toastywombel]

I got this from here:

 

"The passage of time is measured in three principle ways: rotational time, dynamic time, and atomic time."

 

Rotational time, which could be described for example a point (our earth) moving around another point (our sun).

 

Dynamic time, which can be described as the position of the moon relative to the backdrop of stars and our earth, which requires a point for our moon, a point for our earth and many points for the positions of the stars.

 

Atomic time, is kept by the fluctuations of caesium-133 through different energy levels (could be plotted as a wave). So by measuring from one point (observation device) you can track the vibration of the caesium-133 and determine the time.

 

You can see from the above that time can only be measured if there is more than one point. It would not be possible to determine time with one "zero spatial" point by itself.

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Can't time be defined at a point if it is parameterized though?

 

Yes you can. But the point would no longer be alone, through the parametrization you are placing the point in a system of other points that make up a model or a geometric shape.

[michel123456]

I think it would be possible to determine time with two points, but just one point no.

 

You can see from the above that time can only be measured if there is more than one point. It would not be possible to determine time with one "zero spatial" point by itself.

 

Yes you can. But the point would no longer be alone,

 

Toasty, we agree completely.

 

A point considered as a zero-dimension spatial entity is in fact a section of a simplified Minkowski diagram.

A spatial point is a section of the Time Line.

If you want to reduce the time line to a point, you surely can. But you won't have space any more.

[toastywombel]

Toasty, we agree completely.

 

A point considered as a zero-dimension spatial entity is in fact a section of a simplified Minkowski diagram.

A spatial point is a section of the Time Line.

If you want to reduce the time line to a point, you surely can. But you won't have space any more.

 

I apologise for misinterpreting. Thanks for the clarification.

[Sisyphus]

Toasty, we agree completely.

 

A point considered as a zero-dimension spatial entity is in fact a section of a simplified Minkowski diagram.

A spatial point is a section of the Time Line.

If you want to reduce the time line to a point, you surely can. But you won't have space any more.

 

"Space" implies three dimensions.

[michel123456]

There are many interesting points. I will focus on only one.

Someone wrote (Klaynos was)

Again replacing distance (space, there is no real difference) with time is not quite right, you need to replace it by (this is just a standard, any speed will dimensionally work) time * speed of light... hence, lightsecond not just second.

 

That's the question.

Klaynos is right. From the regular point of vue. But not considering myself as a regular thinker, I had some thoughts about it.

Take Space, represented through cartesian coordinates x,y,z.

Take a point of random coordinates: 6, 56, 83. These coordinates describe exactly and uniquely the position of this point in space.

Is there another way to describe exactly & uniquely the position of this point in space, using time?

The answer is yes (IMHO)

 

Let's say our units are Light Years (LY), instead of Meters. This point has a distance to origins which is blahblah (a number=distance, say D=100.1449=~100).

If I transform this distance D=100LY by a certain amount of time T=100Y, I can write down with certainty that this point is 100 years away from me. But there is an infinity of such points around me, describing the surface of a sphere 100 years of radius around me. In order to describe uniquely this point , you can use a set of 2 angles, getting the description of my first post.

 

But I can do better:

I can replace the x coordinate, which is a distance, by time. And then I can replace the y coordinate too, and finally the z coordinate. And I will get the spatial coordinates of this point using only time.

Which is pretty amazing.

The only thing that you have to accept is a consequence of Relativity: you can transform units of time into units of space and vice-versa. Because a point positioned in space is also positioned in time, because movement need time, because distance=elapsed time, no matter the value of the transformation coefficient, namely C)

 

So, because it is too amazing, I will get some refuses saying that no, I cannot replace distance by time.

Think about it.

 

What is terribly amazing, is that the notion of Speed (meter/sec) which is distance related to time, becomes a simple coefficient of time/time. In this case C=1, without unit.

 

And what is finally amazing, is that what we use to consider 3D space can be considered as 3d time as well. That's the reason why space & time are so intricated. They are the one and same thing.

[Sisyphus]

It's not replacing distance with time, it's just describing distance in terms of how long it takes something to travel with a fixed speed. You're not measuring in t, you're measuring in t*(d/t), i.e. distance.

 

You could do that with literally any type of unit. Start with a fixed time: 1 year. Then you can measure distance in terms of how fast you need to go to get there in exactly one year. Or, under what constant acceleration starting from zero. Three acceleration dimensions! (Except not, because you're still just measuring distance in a convoluted way.)

[michel123456]

It's not replacing distance with time, it's just describing distance in terms of how long it takes something to travel with a fixed speed. You're not measuring in t, you're measuring in t*(d/t), i.e. distance.

 

You could do that with literally any type of unit. Start with a fixed time: 1 year. Then you can measure distance in terms of how fast you need to go to get there in exactly one year. Or, under what constant acceleration starting from zero. Three acceleration dimensions! (Except not, because you're still just measuring distance in a convoluted way.)

 

Quite right.

But you cannot travel a distance by zero time.

"how long it takes something to travel with a fixed speed" is another definition of distance, as you said. And I must agree on this.

To get time of travel=zero, you should need infinite speed. The "fixed speed" you mentioned cannot be infinite (that is told by physical reality, not by pure geometry).

It means that to describe physical distance is such a manner, you always need time. Time is inscribed into distance, you cannot get rid of it.

For example:

for D=zero, T=zero.

For D=infinite, T=infinite.

For D=anything (unit Meter), Time = anything (unit seconds)

Or, in other words, you can always describe distance in unit of time.

IMO it means that distance = time.

 

The difficult point on this is not to transform distance in time. It is well known that everything we observe is in the past. The more far away = the more in the past. So that distance somehow contains the idea of time by definition.

 

The difficult point is about the other concepts of Time: the Past, the Future, the arrow of time. All these do not arise immediately from the distance-time equality.

And that is the reason why you may refuse the notion of distance=time.

 

And that was in fact the meaning of this post.

All the precedent discussion about time in reality is not about time, it is about space: how to describe 3D space in units of time.

Still 3D space.

There is something missing.

Time is missing.

Time as we understand it through the notion of sequence & causality: an event happening before another, and the impossibility of going back in time. That description is the 2nd face of Time and it is missing.

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I know how difficult it is to swallow that distance=time.

I had to swallow it by myself. I haven't digest completely yet.

 

Maybe the most important point is that when we include the statement of the speed of light as a constant ©, we step directly out of pure geometry and enter the physical world.

With all consequences.

[Mr Skeptic]

The thing is, Sisyphus, that the speed of light is a constant, and not a variable. Or at least we seem pretty sure about that. If it is constant as everyone is saying, then we can convert between meters and seconds just like we can convert between meters and nanometers. Likewise, that would mean we can convert between matter and energy. The latter seems much easier to swallow.

[michel123456]

Correct.

The equality distance=time is the result of the introduction of C.

 

If you look very (very) deeply, as I am trying to do with much difficulty, you may see, and especially as a physicist you will see it clearly than I do, that the reason of introducing C, is mass.

[Sisyphus]

The thing is, Sisyphus, that the speed of light is a constant, and not a variable. Or at least we seem pretty sure about that. If it is constant as everyone is saying, then we can convert between meters and seconds just like we can convert between meters and nanometers. Likewise, that would mean we can convert between matter and energy. The latter seems much easier to swallow.

 

That makes them related. It doesn't make them the same thing. You can't reduce distance to duration or vice versa with dimensional analysis. So no, you can't convert between meters and seconds. You can convert between meters and light-seconds.

[michel123456]

Pause.

.............

Accept the statement distance=duration (just to negate it better).

Inverse it.

duration=distance.

That should mean that everything is moving.

Is that the case?