The Illusion of Time

[michel123456]

 

Of course it's "true."

 

 

 

It's unclear what you mean by "true." All you did was change variables. It still physically represents the same thing. As long as your functions are analytic (which they usually are), you're free to make any variable complex. Both equations are "true." Let's define T=it. Then the metric (in 1+1 dimensions) is:

 

[math]ds^2= -dt^2+dx^2= dT^2+dx^2[/math]

 

We're now completely free to define the variable T as "time." In other words, the numbers we read on clocks are no longer called "time." Instead, we read a number off a clock and we multiply that number by i to get time. If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions. Plus, we get the added bonus that a lot of physics becomes much simpler.

 

Which variable is more fundamental: t or T? Your instinct might be to say, "well obviously t is more fundamental." But why? If we interpret the numbers on clocks as "distances measured in an imaginary dimension," then T is a real number and t is imaginary.

 

 

 

I don't know what you mean by this. Why would our ability to change variables depend on how long after the big bang we waited?

 

it is not independent of t, so it's not an additional dimension. If we know t then we know it.

You said it.

 

Through c (SOL), one space dimension (be it X, y or Z) is also directly dependent of t.

[elfmotat]

You said it.

 

Through c (SOL), one space dimension (be it X, y or Z) is also directly dependent of t.

 

What? x, y, and z aren't dependent on the value of t. For example, let's say I want to hang a painting on the wall. I tell you exactly when (t) I'm going to be hanging the painting. Based on this information, can you tell me where (x,y,z) on my wall I'm going to hang it? Of course not, because they are completely independent variables.

[JonG]

By elfmotat:

 

[latex] ds^2= -dt^2+dx^2= dT^2+dx^2 [/latex]

 

We're now completely free to define the variable T as "time." In other words, the numbers we read on clocks are no longer called "time." Instead, we read a number off a clock and we multiply that number by i to get time. If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions. Plus, we get the added bonus that a lot of physics becomes much simpler.

 

The majority of people would consider time to be a real number. Defining it in such a way that it becomes imaginary doesn't help. It wouldn't just make time imaginary, but also velocities and many other things which depend on time.

 

As for, If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions., it must surely be obvious that if you define time in that way it is clearly very different to spatial dimensions - time would be imaginary and spatial dimensions would be real!

[elfmotat]

By elfmotat:

 

[latex] ds^2= -dt^2+dx^2= dT^2+dx^2 [/latex]

 

We're now completely free to define the variable T as "time." In other words, the numbers we read on clocks are no longer called "time." Instead, we read a number off a clock and we multiply that number by i to get time. If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions. Plus, we get the added bonus that a lot of physics becomes much simpler.

 

The majority of people would consider time to be a real number. Defining it in such a way that it becomes imaginary doesn't help. It wouldn't just make time imaginary, but also velocities and many other things which depend on time.

 

It doesn't matter what the majority of people believe. What does that have to do with my point? The fact that we're free to redefine time this way is all that matters. Defining it this way sometimes does help, and I've already given you some examples where it does.

 

 

 

 

As for, If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions., it must surely be obvious that if you define time in that way it is clearly very different to spatial dimensions - time would be imaginary and spatial dimensions would be real!

 

No different in the sense that the signature is + for all dimensions instead of -+++, which is what your original post was all about.

[MigL]

Oh wow.

Now we're arguing about the choice of variables.

What's next, why x, y and z and not k, l and m ?

[michel123456]

What? x, y, and z aren't dependent on the value of t. For example, let's say I want to hang a painting on the wall. I tell you exactly when (t) I'm going to be hanging the painting. Based on this information, can you tell me where (x,y,z) on my wall I'm going to hang it? Of course not, because they are completely independent variables.

Yes of course. That is why I added "through c (SOL)".

 

If you tell me the time you will need to hang your painting (the duration), the only thing I can tell you is the maximum distance you may have reached in order to hang your painting. In no case it would be all x,y,z. But the duration can become a maximum distance (because nothing can go faster than c).

 

If you were a photon, then duration would give me exactly the distance. I could then align one axis on your trajectory, and t (duration) would give me x (the distance on the X axis). In this particular case there would be no difference between the information t and the information x.

Edited October 5, 2014 by michel123456

[JonG]

In this particular case there would be no difference between the information t and the information x.

There is a difference between the time axis and spatial axes (provided we accept the Minkowski metric and regard time and spatial coordinates as real numbers). The time axis is always within the light cone of an observer, whereas the spatial axes are outside. Assuming the observer to be at the origin, points along the time axis can be causally connected, but points along a spatial axis (x,y or z) can't be causally connected. This amounts to ds² having one sign in one case and the opposite sign in the other case.

[michel123456]

There is a difference between the time axis and spatial axes (provided we accept the Minkowski metric and regard time and spatial coordinates as real numbers). The time axis is always within the light cone of an observer, whereas the spatial axes are outside. Assuming the observer to be at the origin, points along the time axis can be causally connected, but points along a spatial axis (x,y or z) can't be causally connected. This amounts to ds² having one sign in one case and the opposite sign in the other case.

Right.

 

Do you agree about the concept of "motion" through time? Similar to motion through space.

The concept by which there is only one "yourself" changing coordinates in time ?

A concept by which when you change coordinate in time, you leave your ancient coordinate "empty", exactly like motion through space?

Because when an object moves, it changes coordinates, IOW the same object does not occupy 2 sets of xyz coordinates. An object changes from one set of coordinates to another.

I believe the same happens with time.

Does that seem sensible?

Edited October 5, 2014 by michel123456

[studiot]

 

Do you agree about the concept of "motion" through time? Similar to motion through space.

The concept by which there is only one "yourself" changing coordinates in time ?

A concept by which when you change coordinate in time, you leave your ancient coordinate "empty", exactly like motion through space?

Because when an object moves, it changes coordinates, IOW the same object does not occupy 2 sets of xyz coordinates. An object changes from one set of coordinates to another.

I believe the same happens with time.

Does that seem sensible?

 

 

But objects in space, including that famous picture on the wall and yourself, do not just exist at spatial coordinates (x,y,z), which is a mathematical 'point'.

Objects occupy a region of space, containing many such points.

 

If you say that time is similar what region is occupied in the time axis?

[JonG]

 

Do you agree about the concept of "motion" through time? Similar to motion through space.

The concept by which there is only one "yourself" changing coordinates in time ?

A concept by which when you change coordinate in time, you leave your ancient coordinate "empty", exactly like motion through space?

Because when an object moves, it changes coordinates, IOW the same object does not occupy 2 sets of xyz coordinates. An object changes from one set of coordinates to another.

I believe the same happens with time.

Does that seem sensible?

 

What I believe is summarised in the idea of a "world line". If someone, or an object, is at a point (x₁, y₁, z₁) at time t₁ and at a point (x₂, y₂, z₂) at a later time, t₂, then the existence of these two events is a matter of fact, and the point (x₁, y₁, z₁, t₁) has not been "emptied" at the later time t₂. Note that you cannot verify that "ancient" coordinates have or have not been emptied because you can't go back in time to check.

 

But there is no evidence, as far as I know, to support these beliefs. The reason for believing them is simply that the alternative - what you describe as "emptying" , or having events wiped out in some way as they slip into the past - would require a mechanism to explain how they are wiped out, and there isn't one that I am aware of.

[elfmotat]

Right.

 

Do you agree about the concept of "motion" through time? Similar to motion through space.

The concept by which there is only one "yourself" changing coordinates in time ?

A concept by which when you change coordinate in time, you leave your ancient coordinate "empty", exactly like motion through space?

Because when an object moves, it changes coordinates, IOW the same object does not occupy 2 sets of xyz coordinates. An object changes from one set of coordinates to another.

I believe the same happens with time.

Does that seem sensible?

 

This seems more like philosophy than physics. Can you describe your idea more concretely?

Yes of course. That is why I added "through c (SOL)".

 

If you tell me the time you will need to hang your painting (the duration), the only thing I can tell you is the maximum distance you may have reached in order to hang your painting. In no case it would be all x,y,z. But the duration can become a maximum distance (because nothing can go faster than c).

 

If you were a photon, then duration would give me exactly the distance. I could then align one axis on your trajectory, and t (duration) would give me x (the distance on the X axis). In this particular case there would be no difference between the information t and the information x.

 

You're right, of course, that x, y, and z are linearly related to t when you're describing light spreading out over time. But that isn't what I was talking about. My point was that T=it for all t, so if you know t then you know T regardless of what physical situation you're trying to describe. That's why it isn't an additional dimension - because it contains no new information. x, y, and z are only linearly related to t in very specific circumstances.

[MigL]

But that's not what theory or interpretation says, Michel123456.

 

If we consider space as 2dimensional, then we would have a sheet with a spot on it denoting your current position. The time dimension adds a multitude of additional sheets, or foliations, with your position at various times, past and future, forming your world-line. None of the previous time co-ordinates are vacated, nor are future co-ordinates empty. Your world-line is fully populated for all times.

 

This is what makes it difficult to consider the passing of time as motion through the time dimension.

Remember also that GR is fully classical and does not take into consideration Quantum indeterminacy and this would, at very least, affect the 'fuzzyness' of the world-line.

 

That may be one of the reasons that it is easier to think of the foliation representing the 'present' ( a hypothetical construct ), moving foreward through the time dimension at a rate dependant on the local curvature ofspace-time, i.e. normally in locally flat areas, slower in strong gravity fields, and not at all at a BH's event horizon

[michel123456]

 

What I believe is summarised in the idea of a "world line". If someone, or an object, is at a point (x₁, y₁, z₁) at time t₁ and at a point (x₂, y₂, z₂) at a later time, t₂, then the existence of these two events is a matter of fact, and the point (x₁, y₁, z₁, t₁) has not been "emptied" at the later time t₂. Note that you cannot verify that "ancient" coordinates have or have not been emptied because you can't go back in time to check.

 

But there is no evidence, as far as I know, to support these beliefs. The reason for believing them is simply that the alternative - what you describe as "emptying" , or having events wiped out in some way as they slip into the past - would require a mechanism to explain how they are wiped out, and there isn't one that I am aware of.

Very interesting post.

 

Note that you cannot verify that "ancient" coordinates have or have not been emptied because you can't go back in time to check.

 

Indeed!

 

This seems more like philosophy than physics. Can you describe your idea more concretely?

The idea is that "motion through time" acts EXACTLY the same way as motion through space.

 

If you are here, you are not there. Motion through space indicates that multiple positions are muyually exclusive.

 

IOW when you move from x1,y,z to x2,y,z, you hace changed coordinates. There is no a first "you" at x1 and a second "you" at x2. There is a single 'you" that has changed position. That's what motion is about.

 

I believe the same happens with time.

Positions in time are mutually exclusive. If I am today here, I cannot be "yesterday" here. i have translated from "yesterday" to 'today". IOW there is no other "me" frozen in time "yesterday". I have not duplicated myself through the passage of time. I have only changed coordinates.

And if I am right, that I have changed coordinates, it means that my ancient set of coordinates is empty.

And as JonG noted, we cannot directly check that.

Edited October 5, 2014 by michel123456

[elfmotat]

The idea is that "motion through time" acts EXACTLY the same way as motion through space.

 

If you are here, you are not there. Motion through space indicates that multiple positions are muyually exclusive.

 

IOW when you move from x1,y,z to x2,y,z, you hace changed coordinates. There is no a first "you" at x1 and a second "you" at x2. There is a single 'you" that has changed position. That's what motion is about.

 

I believe the same happens with time.

Positions in time are mutually exclusive. If I am today here, I cannot be "yesterday" here. i have translated from "yesterday" to 'today". IOW there is no other "me" frozen in time "yesterday". I have not duplicated myself through the passage of time. I have only changed coordinates.

And if I am right, that I have changed coordinates, it means that my ancient set of coordinates is empty.

And as JonG noted, we cannot directly check that.

 

This still seems like philosophy. What do "empty coordinates" mean, numerically?

[swansont]

 

And as JonG noted, we cannot directly check that.

 

Depends on what is meant by "directly". Can you "directly" check whether someone in view is also someplace else not within your line of sight? Because if "direct" checking is not required (i.e. instrumentation is allowed) then you can indeed record and check the status of past states. Time-tagged photos, for instance.

[JonG]

This is just a note regarding "motion through time*" and motion through space. It is impossible to move through space without also "moving through time". This is simply a consequence of there being a maximum speed at which things can move. However, it is possible to "move through time", i.e. to occupy successive points along the time axis, without moving through space - all you have to do is stand still.

 

These conclusions are another consequence of the time axis being within the light cone and the spatial axes being outside it as I noted in an earlier post.

 

 

(*The idea of motion through time is hard to define, which is why I prefer to refer to it as "to occupy successive points along the time axis".)

Edited October 6, 2014 by JonG

[michel123456]

This is just a note regarding "motion through time*" and motion through space. It is impossible to move through space without also "moving through time". This is simply a consequence of there being a maximum speed at which things can move. However, it is possible to "move through time", i.e. to occupy successive points along the time axis, without moving through space - all you have to do is stand still.

 

These conclusions are another consequence of the time axis being within the light cone and the spatial axes being outside it as I noted in an earlier post.

 

 

(*The idea of motion through time is hard to define, which is why I prefer to refer to it as "to occupy successive points along the time axis".)

I am happy you have understood my point.

 

"to occupy successive points along the time axis"

 

The question is: if you occupy coordinate T2, do you occupy coordinate T1?

 

My answer is No. For me the 2 coordinates are mutually exclusive.

That is because you have translated from T1 to T2. You simply don't continue to "exist" somewhere in the past. And similarly, you don't already "exist" in the future.

Upon your time line you occupy only one coordinate. There is only one single JonG translating in time. Your time coordinate is continuously changing, making you feel as if it were a "flow of time".

 

 

Depends on what is meant by "directly". Can you "directly" check whether someone in view is also someplace else not within your line of sight? Because if "direct" checking is not required (i.e. instrumentation is allowed) then you can indeed record and check the status of past states. Time-tagged photos, for instance.

There is a flaw.

A time-tagged photo is an object that travels in time like all other objects around us. There is no object that you can retrieve from the past without having traveled in time with us.

Edited October 6, 2014 by michel123456

[studiot]

 

The question is: if you occupy coordinate T2, do you occupy coordinate T1?

 

My answer is No. For me the 2 coordinates are mutually exclusive.

That is because you have translated from T1 to T2. You simply don't continue to "exist" somewhere in the past. And similarly, you don't already "exist" in the future.

Upon your time line you occupy only one coordinate. There is only one single JonG translating in time. Your time coordinate is continuously changing, making you feel as if it were a "flow of time"

 

I note that no Time Lord here has attempted to answer my post#59

 

Ask The Doctor.

[swansont]

 

There is a flaw.

A time-tagged photo is an object that travels in time like all other objects around us. There is no object that you can retrieve from the past without having traveled in time with us.

 

That's a problem if you are asserting that the picture (which is data) changes. But that would be a problem for all of science, since we couldn't trust the outcome of an experiment that occurred in the past (and I'm sure there are other scenarios where this is problematic).

 

Try that in court and see how well it works.

[JonG]

 

I note that no Time Lord here has attempted to answer my post#59

 

Ask The Doctor.

I'm not a Lord, but here goes anyway. I wasn't sure what point you were making in post 59 and what I write might be irrelevant, but it did bring to mind the idea of the "specious present", according to which the present isn't an instant in time but an interval of time of finite duration (It seems like an instant to me but some claim it can last several seconds!).

 

See here for more:

 

https://en.wikipedia.org/wiki/Specious_present

[studiot]

Thank you, Jon, I had not heard of the specious present, but it is not what I meant.

 

There has been some discussion of 'objects' moving (or being moved) in space by changing their x (and y and z) coordinates.

There is no physical object that I know of that can be attributed to a single x or y or z coordinate ie no physical object has zero length, but occupies a connected segment of space.

 

For instance when I move my 18" screen across the desk I move one side and the other and everything in between.

 

I was seeking a corresponding statement in time for "movement" in time.

Edited October 6, 2014 by studiot

[JonG]

By michel123456;

 

The question is: if you occupy coordinate T2, do you occupy coordinate T1?

 

My answer is No. For me the 2 coordinates are mutually exclusive.

That is because you have translated from T1 to T2. You simply don't continue to "exist" somewhere in the past. And similarly, you don't already "exist" in the future.

Upon your time line you occupy only one coordinate. There is only one single JonG translating in time. Your time coordinate is continuously changing, making you feel as if it were a "flow of time".

 

You can't occupy T1 and T2 at the same time. That much I accept. There is a quote from Einstein relevant to this. A lifetime friend of Einstein named Michele Besso died shortly before Einstein died. Einstein is alleged to have said to Besso's widow, "There is a sense, understood by physicists, in which people never die". In relation to your question, I think that implies that existence can extend over T1 and T2. I am inclined to go along with that, but I can't think of any way of proving it other than to note that if people, or things, are assumed to cease to exist as they slip into the past (our idea of past is subjective) then there is no known mechanism which would eliminate their existence.

 

(If Einstein had ever expressed his views on a forum such as this he would probably have been reprimanded for being too philosophical - he was very interested in Philosophy: "Einstein had a lifelong interest in Philosophy. As a schoolboy, he has read Kant" - from "Subtle is the Lord - The Science and the life of Albert Einstein," by Abraham Pais, page 318.)

Edited October 6, 2014 by JonG

[elfmotat]

Studiot and michel: snap your fingers at the same time. For a moving observer, your snaps are not simultaneous. Instead there is a finite period of time between them. You may feel like you're only occupying one time coordinate, but that's only because you're trapped in your own rest frame!

 

Edit: to expand on this to make it easier to visualize, pretend for a moment that you're a (1+1)-dimensional creature. You have some finite length. In your rest frame, if you were to plot your location as a function of time, it would appear as a series of straight lines with each line occupying exactly one time coordinate:

 

 

 

But if a moving observer were to plot your position over time, they would plot something like this:

 

 

Notice how you occupy a finite interval of time. Your body is "smeared out" over time for a moving observer due to relativity of simultaneity.

Edited October 6, 2014 by elfmotat

[studiot]

 

Studiot and michel: snap your fingers at the same time

 

 

So how does that affect my comment?

[elfmotat]

 

 

So how does that affect my comment?

 

Maybe you were saying something different than what I interpreted, but what I read was that you wanted to know if we occupied multiple time coordinates. And we do. If that wasn't your point, then I'm not exactly sure what you're trying to say/ask.