Why does the universe move towards an observer at rest?

[Jeronimus]

In relativity, we do not talk about just space anymore, but space-time, with time being just another dimension.

An observer A at rest in an IRF who considers himself at rest at t=0 x=0, has a far away clock at t=100 for example moving towards him, i would like to say at 1second per second, but i guess that wouldn't make sense. It is however moving towards him at SOME pace.

Someone moving at vrel relative to observer A, sees him moving towards the clock along the x and t axis.

There has to be a reason for that, because otherwise it seems logical to assume that we would just stand at a fixed(static) coordinate without moving towards either the x or t axis.

 

[Nugatory]

An observer A at rest in an IRF who considers himself at rest at t=0 x=0

Wait a moment... He can't be at rest at t=0, x=0 because he's moving in the +t direction so his t coordinate is continually increasing. In fact, if he's carrying a stopwatch that he started at t=0,x=0 his t coordinate will always be the time that the stopwatch reads: x=0,t=1 when the stopwatch reads 1 second, x=0,t=2 when the stopwatch reads 2 seconds, and so forth.

has a far away clock at t=100 for example moving towards him

That doesn't make any sense either. t=100 is 100 seconds into the future, when his stopwatch would read 100. I don't see how a clock, or anything else for that matter, could start there and move towards our observer at t=0 (and moving in the direction of increasing t) unless the clock or whatever were traveling back in time. And I kinda doubt that's what you meant... so what did you mean?

There has to be a reason for that, because otherwise it seems logical to assume that we would just stand at a fixed(static) coordinate without moving towards either the x or t axis.

We're never standing at fixed static coordinates. We're always moving forward in the t direction (and after a half-century or so of moving in that direction, we start to get old and wish that we weren't moving quite so quickly in the direction of increasing t).

So it's not that the universe is "moving towards an observer". Everything, absolutely everything, is moving in spacetime. There are inertial reference frames in which the x coordinate of an object's is constant (it's at rest in that frame) and there are inertial reference frames in which the x coordinate is changes with time and is equal to vt (the object is moving at a speed of v in that frame, or equivalently the origin of the frame is moving at a speed of -v relative to the object), but there are no frames in which the t coordinate is not increasing.

 

[Jeronimus]

Wait a moment... He can't be at rest at t=0, x=0 because he's moving in the +t direction so his t coordinate is continually increasing. In fact, if he's carrying a stopwatch that he started at t=0,x=0 his t coordinate will always be the time that the stopwatch reads: x=0,t=1 when the stopwatch reads 1 second, x=0,t=2 when the stopwatch reads 2 seconds, and so forth.That doesn't make any sense either. t=100 is 100 seconds into the future, when his stopwatch would read 100. I don't see how a clock, or anything else for that matter, could start there and move towards our observer at t=0 (and moving in the direction of increasing t) unless the clock or whatever were traveling back in time. And I kinda doubt that's what you meant... so what did you mean?
We're never standing at fixed static coordinates. We're always moving forward in the t direction (and after a half-century or so of moving in that direction, we start to get old and wish that we weren't moving quite so quickly in the direction of increasing t).

So it's not that the universe is "moving towards an observer". Everything, absolutely everything, is moving in spacetime. There are inertial reference frames in which the x coordinate of an object's is constant (it's at rest in that frame) and there are inertial reference frames in which the x coordinate is changes with time and is equal to vt (the object is moving at a speed of v in that frame, or equivalently the origin of the frame is moving at a speed of -v relative to the object), but there are no frames in which the t coordinate is not increasing.

why do you think the t axis is special compared to the x axis? Why when an object on the x-axis is moving towards us, an observer considers himself at rest, while when an object at a distance on the t axis moving towards us you consider the object at rest?

Even if we were to take your point of view. Why do we move at all towards an object in the future? Shouldn't we remain static at one point unless there is a reason for that motion?

 

[Nugatory]

why do you think the t axis is special compared to the x axis? Why when an object on the x-axis is moving towards us, an observer considers himself at rest, while when an object at a distance on the t axis moving towards us you consider the object at rest?

I'm sorry, but I still don't understand what you mean by "an object at a distance on the t axis moving towards us". Can you construct a thought experiment in which such motion could be considered to be happening?

Even if we were to take your point of view. Why do we move at all towards an object in the future? Shouldn't we remain static at one point unless there is a reason for that motion?

I don't know of any good answer to that "Why?" question. But no matter why it happens, it appears to be a fact that all objects are always moving in the time direction of space-time. I can always find a frame in which I am at rest in space (my x, y, and z coordinates are constant) but I cannot find a frame in which I stop aging, the t coordinate is constant, and time is not passing.

It's tempting to explain this by saying that the 4-velocity of an object is never zero. But that's not really an explanation, it's just a mathematical restatement of what we're trying to explain.

 

[Chestermiller]

I have written up a set of notes on SR that specifically addresses the questions you are asking. The write up is in the form of a Word document which I can attach to an email. If you would like a copy of the write up, send me an email message at chestermiller@mindspring.com. The write up focuses on "what is it about the fundamental geometric structure and kinematics of 4D spacetime that can give rise to the peculiar effects that we observe?"

chet

 

[PAllen]

In relativity, we do not talk about just space anymore, but space-time, with time being just another dimension.

An observer A at rest in an IRF who considers himself at rest at t=0 x=0, has a far away clock at t=100 for example moving towards him, i would like to say at 1second per second, but i guess that wouldn't make sense. It is however moving towards him at SOME pace.

Someone moving at vrel relative to observer A, sees him moving towards the clock along the x and t axis.

There has to be a reason for that, because otherwise it seems logical to assume that we would just stand at a fixed(static) coordinate without moving towards either the x or t axis.

If you want to take the view of time as established dimension as much like spatial dimensions as possible (you can't make it exactly the same - the metric distinguishes timelike and spacelike), then the most natural picture is the block universe. This is the image I get from your description.

Then, you cannot talk about the point (t,x)=(0,0) moving at all, it just is. Meanwhile, if you speak of the world line of a particle, e.g. the line (t,x)=(t,0), the line just is. When you see a curve drawn on a piece of paper, you don't insist there is an 'existence point' moving along it.

The line (t,x)=(t,vt) also just is, in this picture. Within this particular frame, we can say the first line represents a stationary particle because dx/dt=0; and the second represents particle moving at v in this frame.

It seems your difficulty is trying to mix an 'evolving time' picture with a block universe picture. Both are workable, but the mixture is leading to confusion.

 

[Chestermiller]

It is not the universe that is moving toward us. 4D spacetime is stationary, and it is we who are doing the moving. Within or rest frame of reference, we are unaware of our motion because, as 3D beings with our inherent physical limitations, we cannot see into our own time direction. But we are moving into our own time direction at the speed of light.

Each inertial frame of reference has its own time direction, and the time direction for one frame is not the same as the time direction for any other frame. All objects and observers that are at rest within a given 3D frame of reference, as well as the frame of reference itself, are moving in the time direction for that frame at the speed of light. Because the time directions of objects in different frames of reference are different, so also are their velocity vectors through 4D spacetime. The differences between these 4D velocity vectors represents their relative velocities, and because the magnitude of the 4D velocities of all objects is the speed of light, even very tiny differences in their time directions corresponds to significant relative velocities. Of course, we can only observe the spatial components of these relative velocities, since, as 3D beings, we cannot see the component in the time direction.

Since 4D spacetime is stationary and it is we who are doing the moving through spacetime at the speed of light, even when we are at rest within our own inertial frame of reference, we can still accurately determine how far we are traveling through spacetime. This is because our clocks can be regarded not only as timepieces but also as odometers. For every tick of our clock, we travel 1 light-second along our own world line.

 

[PAllen]

It is not the universe that is moving toward us. 4D spacetime is stationary, and it is we who are doing the moving. Within or rest frame of reference, we are unaware of our motion because, as 3D beings with our inherent physical limitations, we cannot see into our own time direction. But we are moving into our own time direction at the speed of light.

I know there are a number of writers who say this, but quite a number of us here at PF (and before we ever discovered PF) find this idea of moving at the speed of light through time to be bogus. For example, you will not find it in any of Einstein's writing or any historic books on SR. It comes, basically, from giving meaning to d(c $\tau$)/dt as speed through time along a world line. More traditionally, this (without the c) is simply called the coordinate time dilation factor. Further, since t is an arbitrary coordinate quantity, it is quite arbitrary. Unlike 4 velocity (D/D $\tau$), it does not generalize meaningfully to GR, where it is often useful to have unusual coordinates (4 space like, none time like; or 2 light like, two space like). Even in SR, both Bondi and Dirac were fond of coordinates where two were light like, two spacelike, none timelike. 4-velocity works equally well in all of these, but this 'speed through time' becomes undefinable.

I think it also fosters over-interpreting time dilation (versus observables: differential aging comparing two paths between evetns; Doppler rate comparing exchanged signals). Dirac coordinates show the arbitrary character of time dilation per se - it doesn't exist at all in these coordinates (there is no t coordinate), while all observables are still well defined and easily computed.

 

[Chestermiller]

I know there are a number of writers who say this, but quite a number of us here at PF (and before we ever discovered PF) find this idea of moving at the speed of light through time to be bogus. For example, you will not find it in any of Einstein's writing or any historic books on SR. It comes, basically, from giving meaning to d(c $\tau$)/dt as speed through time along a world line. More traditionally, this (without the c) is simply called the coordinate time dilation factor. Further, since t is an arbitrary coordinate quantity, it is quite arbitrary. Unlike 4 velocity (D/D $\tau$), it does not generalize meaningfully to GR, where it is often useful to have unusual coordinates (4 space like, none time like; or 2 light like, two space like). Even in SR, both Bondi and Dirac were fond of coordinates where two were light like, two spacelike, none timelike. 4-velocity works equally well in all of these, but this 'speed through time' becomes undefinable.

I think it also fosters over-interpreting time dilation (versus observables: differential aging comparing two paths between evetns; Doppler rate comparing exchanged signals). Dirac coordinates show the arbitrary character of time dilation per se - it doesn't exist at all in these coordinates (there is no t coordinate), while all observables are still well defined and easily computed.

It was not my intention to give the impression that apparently came through to you. I was referring to an object or observer in its rest frame moving through spacetime at the speed of light. In the rest frame, the clock time is equal to the proper time, such that you would have d(cτ)/dτ = c, without a time dilation factor.

I was also thinking about 4 velocity when I was talking about relative velocities of objects (i.e., in a 4D sense), although I neglected to mention that in order to keep things simple for the OP. When considering relative velocities in 4D, the relative velocity is just the difference of the 4 velocities. In this case, the spatial components contain the relativity factor, and the time component of relative velocity is (γ - 1)c.

The viewpoint of 4 velocity being equal in magnitude to c carries directly over into GR.

 

[PAllen]

It was not my intention to give the impression that apparently came through to you. I was referring to an object or observer in its rest frame moving through spacetime at the speed of light. In the rest frame, the clock time is equal to the proper time, such that you would have d(cτ)/dτ = c, without a time dilation factor.

I was also thinking about 4 velocity when I was talking about relative velocities of objects (i.e., in a 4D sense), although I neglected to mention that in order to keep things simple for the OP. When considering relative velocities in 4D, the relative velocity is just the difference of the 4 velocities. In this case, the spatial components contain the relativity factor, and the time component of relative velocity is (γ - 1)c.

The viewpoint of 4 velocity being equal in magnitude to c carries directly over into GR.

I actually use the metric convention where 4-velocity norm is 1 (even when not setting c=1). Has this changed physics any?

I never picture particle moving through spacetime. In the spacetime picture, a world line exists, there is no motion.

I think of the 'angle' between 4 vectors as their relative velocity, as either would measure the other in their basis.

I am not saying there is anything inherently wrong with speed through space time. Just pointing out, FYI, that it is not part of the history of SR in either Einstein's initial point of view or in the spacetime picture developed from Minkowski to Synge (who is actually the person responsible for wide acceptance of space time diagrams), and isn't necessary to understand any part of SR or GR. It is a fairly recent conceptual innovation I don't see as as adding any value. A number of us here have spent time dealing with confusion it seems to instill in some people.

So definitely go ahead and use this idea if you find it helpful. Just be aware if its (lack of) history and that a number of people here (besides myself) find it adds confusion with no value.

 

[Chestermiller]

I actually use the metric convention where 4-velocity norm is 1 (even when not setting c=1). Has this changed physics any?

I never picture particle moving through spacetime. In the spacetime picture, a world line exists, there is no motion.

I think of the 'angle' between 4 vectors as their relative velocity, as either would measure the other in their basis.

I am not saying there is anything inherently wrong with speed through space time. Just pointing out, FYI, that it is not part of the history of SR in either Einstein's initial point of view or in the spacetime picture developed from Minkowski to Synge (who is actually the person responsible for wide acceptance of space time diagrams), and isn't necessary to understand any part of SR or GR. It is a fairly recent conceptual innovation I don't see as as adding any value. A number of us here have spent time dealing with confusion it seems to instill in some people.

So definitely go ahead and use this idea if you find it helpful. Just be aware if its (lack of) history and that a number of people here (besides myself) find it adds confusion with no value.

Thanks for the history lesson, but I'm not impressed.

Since you brought up the subject of confusion, let's talk about confusion. As a person with an engineering background coming at SR for the first time, I was quite confused by all the standard texts I read. Moreover, day after day, I see postings by new initiates to SR suffering the same confusion that I did trying to learn SR using the conceptualization that you so strongly advocate. They all ask the same questions over and over again. If this isn't confusion, I don't know what is.

In the end, I gave up on these texts, and decided to work things out on my own, starting from the Lorentz Transformation. This led to the much simpler conceptual picture that developed, and clarified for me what is really going on in terms of the fundamental geometry and kinematics of 4D spacetime. I'm sure I'm not the first one to do this. But, for me, it has simplified things tremendously, and removed all the confusion. Moreover, it has never failed me in enabling me to solve problems in SR with virtually no trouble. As I mentioned in a previous posting, I am prepared to make my notes available to whomever is interested. In addition, PAllen, I welcome any critique you might have on these notes. Just because SR has historically been conceptualized in a certain way doesn't necessarily mean that it is the best way. I might also mention that other people who have read my notes have provided very favorable feedback on its ability to reduce their confusion.

One final point: As an engineer, I am comfortable with expressing the 4 velocity in either dimensional form (with a norm of c), or, as we engineers would call it, dimensionless form, with a norm of 1. Either way is fine with me. However, working with the parameters in dimensional form makes it easier to make the connection with conventional Newtonian mechanics, in which velocity and acceleration are usually expressed dimensionally.