Relative motion in Minkowski spacetime

roosh

This has been the subject of discussion elsewhere, but I would be interested in hearing the thoughts of those who are more "scientifically minded".

Essentially the question is, how is it possible for relative motion to occur in Minkowski spacetime; if objects exist as worldlines, or worldtubes, extended in 4 space how, can they possible move relative to each other, when those worldlines are fixed in spacetime.

If we think of the worldlines of two relatively moving bodies, two planets say; it might be helpful to think of those worldlines crosssing; to use an analogy, we could represent the two worldlines in spacetime as two chopsticks suspended in jelly (or whatever material is more helpful), at angles to each other, crossing at some point. Now, if we imagine such a physical structure, it isn't immediately clear how relative motion would occur between the planets. We could obtain a mathematical figure for "relative motion" by working with the relevant co-ordinates, but that number would be distinct from the "phsysical" (as opposed to mathematical) relative motion that occurs between planets.


I'm just wondering how relative motion would occur in such a universe?

dlouth15

Its not like rods suspended in jelly or another solid substance though.

Imagine there being only one dimension of time and one of space and imagine various objects moving in relative motion to one another. Imagine further that Each of these objects considers itself at rest at the centre of its own spacial coordinate system. So Object 1 draws its own worldline along its own t-axis with no x-component. Other worldlines are seen as tilted either towards or away from the Object 1's worldline.

Each of the other objects describes its own worldline in the same way as along the t-axis with x=0.

The Lorentz transformation then predicts, if we have described the system from the perspective of one worldline, how it will be seen from the perspective of another.

Note that this doesn't correspond exactly to how we might view rods suspended in a solid. Yes, there are lines that cross but the way that the system changes according to different frames of reference is different to that of solids in a Cartesian system.

Is this merely messing about with coordinates? According to Special Relativity, objects in relative motion to one another really do experience time and space differently. You could regard Minkowski spacetime a way of representing this in graphical form. You have one spacetime but you don't have one single coordinate system; you have many and in each of them there is a worldline representing that of the observer that is only in the time dimension and other tilted worldlines representing motion relative to it. At the same time, no one coordinate system is privileged which means that relative motion is fully expressible in the system.

roosh

dlouth15 wrote: »

Its not like rods suspended in jelly or another solid substance though.

Imagine there being only one dimension of time and one of space and imagine various objects moving in relative motion to one another. Imagine further that Each of these objects considers itself at rest at the centre of its own spacial coordinate system. So Object 1 draws its own worldline along its own t-axis with no x-component. Other worldlines are seen as tilted either towards or away from the Object 1's worldline.

Each of the other objects describes its own worldline in the same way as along the t-axis with x=0.

The Lorentz transformation then predicts, if we have described the system from the perspective of one worldline, how it will be seen from the perspective of another.

Note that this doesn't correspond exactly to how we might view rods suspended in a solid. Yes, there are lines that cross but the way that the system changes according to different frames of reference is different to that of solids in a Cartesian system.

Is this merely messing about with coordinates? According to Special Relativity, objects in relative motion to one another really do experience time and space differently. You could regard Minkowski spacetime a way of representing this in graphical form. You have one spacetime but you don't have one single coordinate system; you have many and in each of them there is a worldline representing that of the observer that is only in the time dimension and other tilted worldlines representing motion relative to it. At the same time, no one coordinate system is privileged which means that relative motion is fully expressible in the system.

It is, I feel, worth making the distinction between the physical motion of planets relative to each other and the mathematical representation of that relative motion, the latter being represented by the spatial co-ordinate systems.

With regard to what we observe, we don't actually observe objects or systems extended in the temporal dimension, we only ever observe systems in a single instant, or a single instant of "time", if you like; we observe them extended in 3 spatial dimensions but not in the temporal dimension. The Einsteinian interpretation of relativity requires that objects be fully extended through spacetime from the beginning to the end of their lifetime; logic would seem to necessitate that each instant in the life of an object be connected to the instant immediately preceding it and following it, such that the object exists as a quasi-tube, or worldtube, extended through spacetime. This is where the chopsticks analogy comes in - the continuity of a worldtube isn't necessary for the question in hand, but it might be helpful to picture it as continuous. Regardless of whether it is exactly like chopsticks suspended in a solid or not, we still have worldtubes extended in 4D spacetime, at angles to each other, where there is no relative motion between the worldtubes themselves; this is where the question arises from, how is it possible to have relative motion in such a universe?

Spacetime Diagram
Below is a spacetime diagram, posted by a user on another forum,

I've only just started to learn how to interpret spacetime diagrams, but I think it might be helpful for illustrating the point. The diagram depicts two observers, red and green, moving relative to each other, as well as the worldlines of both a tree and a house, as represented in the rest frame of the red observer - which I'm sure you could gather.

At event E1, the green observer fires a bullet towards the house; the path of the bullet will take it across the red observer and the tree. At event E9, red and green cross paths; at this instant, the red observer says that the bullet is passing the tree, while the green observer says that it is passing the house.

Location, Location, Vacation
Relativity requires that the bullet occupy, and continue to occupy, all of the locations in the 3D world, along the bullets path; that is, it must occupy, and continue to occupy, the location, in the 3D world, it had as it was passing the tree and also when it was passing the house. If it were to vacate any of the locations along it's path, let's say it's location as it passed the house, then the red observer would never observe the bullet passing the house.

To look at it another way; if we imagine the scene at a later point, any arbitrary moment after the two observers cross paths; for the green observer, he would observe the bullet at a location beyond the house, or having passed the house, but he would have to agree that the bullet still occupies a location to the left of the house, as this is what the red observer sees.

If the bullet never vacates any of it's locations in the 3D world, how can there be relative motion in the 3D world?

dlouth15

roosh wrote: »

It is, I feel, worth making the distinction between the physical motion of planets relative to each other and the mathematical representation of that relative motion, the latter being represented by the spatial co-ordinate systems.

With regard to what we observe, we don't actually observe objects or systems extended in the temporal dimension, we only ever observe systems in a single instant, or a single instant of "time", if you like; we observe them extended in 3 spatial dimensions but not in the temporal dimension. The Einsteinian interpretation of relativity requires that objects be fully extended through spacetime from the beginning to the end of their lifetime; logic would seem to necessitate that each instant in the life of an object be connected to the instant immediately preceding it and following it, such that the object exists as a quasi-tube, or worldtube, extended through spacetime. This is where the chopsticks analogy comes in - the continuity of a worldtube isn't necessary for the question in hand, but it might be helpful to picture it as continuous. Regardless of whether it is exactly like chopsticks suspended in a solid or not, we still have worldtubes extended in 4D spacetime, at angles to each other, where there is no relative motion between the worldtubes themselves; this is where the question arises from, how is it possible to have relative motion in such a universe?

But unlike say chopsticks through 3-d solids, the angles aren't fixed. They can vary by applying the Lorentz transformation. We can consider any of these worldlines to be "at rest" by applying a Lorentz transformation such that it's worldline is pointed only in the t direction. All other worldlines are adjusted accordingly. No worldline is privileged. That's relative motion. If we found that we had to privilege certain worldlines then you would be right.

Spacetime Diagram
Below is a spacetime diagram, posted by a user on another forum,

I've only just started to learn how to interpret spacetime diagrams, but I think it might be helpful for illustrating the point. The diagram depicts two observers, red and green, moving relative to each other, as well as the worldlines of both a tree and a house, as represented in the rest frame of the red observer - which I'm sure you could gather.

At event E1, the green observer fires a bullet towards the house; the path of the bullet will take it across the red observer and the tree. At event E9, red and green cross paths; at this instant, the red observer says that the bullet is passing the tree, while the green observer says that it is passing the house.

Location, Location, Vacation
Relativity requires that the bullet occupy, and continue to occupy, all of the locations in the 3D world, along the bullets path; that is, it must occupy, and continue to occupy, the location, in the 3D world, it had as it was passing the tree and also when it was passing the house. If it were to vacate any of the locations along it's path, let's say it's location as it passed the house, then the red observer would never observe the bullet passing the house.

I don't think that's an interpretation people conversant with relativity would hold. Yes, the bullet occupies every position in spacetime, but in 3-d space it only occupies one position at any given time. Of course, how each of the observers, slices up spacetime will vary according to their motion. So the red observer sees the bullet hitting the tree as simultaneous with the meeting of the observers whereas the green observe sees the bullet hitting the tree as happening earlier.

But that diagram is a good example of how relative motion is possible. There's no privileged frame involved. The same scenario could have been drawn with the green observer being "at rest" and the red observer, the house and the tree moving towards the green observer. All the same results would have been obtained with the two observers disagreeing about the timing of events in the same way.

To look at it another way; if we imagine the scene at a later point, any arbitrary moment after the two observers cross paths; for the green observer, he would observe the bullet at a location beyond the house, or having passed the house, but he would have to agree that the bullet still occupies a location to the left of the house, as this is what the red observer sees.

No, they don't have to agree on that. The only thing they have to agree on is two events happening at the the same time and at the same place. For example if the lights went out at the house at the exact moment the bullet hit, the two observers would have to agree on that.

If the bullet never vacates any of it's locations in the 3D world, how can there be relative motion in the 3D world?

Essentially if for a given frame we have a worldline that is not purely in the t direction but has a spacial component then it is in relative motion with respect to that frame. From the perspective of that frame, the bullet is continually vacating space as it moves. Of course, there is another frame where the bullet is not moving but everything else is, but that is the nature of relative motion.

roosh

dlouth15 wrote: »

But unlike say chopsticks through 3-d solids, the angles aren't fixed. They can vary by applying the Lorentz transformation. We can consider any of these worldlines to be "at rest" by applying a Lorentz transformation such that it's worldline is pointed only in the t direction. All other worldlines are adjusted accordingly. No worldline is privileged. That's relative motion. If we found that we had to privilege certain worldlines then you would be right.

Again, it is probably worth making the distinction between the relative motion of 2 planets in the 3D world and the mathematical description of relative motion. To say that we can represent the worldlines of an object as being "at rest" by applying the Lorentz transform doesn't explain how relative motion manifests, in the 3D world, from worldlines in spacetime. Similarly, saying that the angles can vary when the Lorentz transforms are applied doesn't explain it either. They just explain how we represent relative motion mathematically.

If we take a spacetime diagram though, from the perspective of any given observer, the worldlines are extended in spacetime and the analogy of the chopsticks can be applied; if we look at things from the perspective of a different observer, and the angles change, then we can represent this using a similar analogy, just with the chopsticks at different angles. When we do this, it would seem to suggest that relative motion should not occur in such a universe.

dlouth15 wrote: »

I don't think that's an interpretation people conversant with relativity would hold. Yes, the bullet occupies every position in spacetime, but in 3-d space it only occupies one position at any given time. Of course, how each of the observers, slices up spacetime will vary according to their motion. So the red observer sees the bullet hitting the tree as simultaneous with the meeting of the observers whereas the green observe sees the bullet hitting the tree as happening earlier.

But that diagram is a good example of how relative motion is possible. There's no privileged frame involved. The same scenario could have been drawn with the green observer being "at rest" and the red observer, the house and the tree moving towards the green observer. All the same results would have been obtained with the two observers disagreeing about the timing of events in the same way.

The issue with saying that the slicing up of spacetime depends on an observers motion is that it assumes the motion of the observer; the same issue applies to the observer as it does the bullet; an observer must occupy all his locations in the 3D world also.

When we say that the bullet occupies every position (on its worldline) in spacetime this is translatable into the 3D world; in terms of the 3D world, it means that the bullet occupies all of the locations along it's path, in the 3D world.

If we look at the spacetime diagram we can see that the green observer sees the bullet at the tree before he crosses paths with the red observer, but the red observer sees the bullet at the tree as they cross paths

Put another way, after the green observer sees the bullet pass the tree, the red observer sees it at the tree; this means that the bullet cannot have left its position in 3D space at the tree, even though the green observer saw it move past the tree.

dlouth15 wrote: »

No, they don't have to agree on that. The only thing they have to agree on is two events happening at the the same time and at the same place. For example if the lights went out at the house at the exact moment the bullet hit, the two observers would have to agree on that.

According to the spacetime diagram, the green observer would have to agree that, after he has seen the bullet pass the tree - which happens before he crosses paths with the red observer - that the red observer sees the bullet at the tree, as they cross paths.

So, the bullet cannot have vacated the position at the tree after the green observer saw it at the tree, because after the green observer has seen it there, the red observer sees it there.

dlouth15 wrote: »

Essentially if for a given frame we have a worldline that is not purely in the t direction but has a spacial component then it is in relative motion with respect to that frame. From the perspective of that frame, the bullet is continually vacating space as it moves. Of course, there is another frame where the bullet is not moving but everything else is, but that is the nature of relative motion.

Again, this is a mathematical representation of relative motion; that a mathematical value for relative motion can be derived from the mathematics of relativity, however, isn't in question; the question is, how can worldlines in spacetime which do not move relative to each other give rise to the relative motion of, say, planets, in the 3D world?

Morbert

Relative motion is a frame-dependent quantity. The green man will measure the speed of the bullet to be v. The red man will measure the speed of the bullet to be v'. That there is relativity of simultaneity doesn't change this.

dlouth15

Roosh,

Physics is about representing the world mathematically so we're always dealing with representations of one sort or another.

When we're dealing with representations (the spacetime diagram being one), all we can do is explain the meaning of a particular component (e.g. worldlines) in the context of that representation.

If we have, say, a graph of temperature against time and the line has a positive slope then we can say that the graph represents a rising temperature. We don't expect the line itself to move in order to represent a rising temperature. We know that the temperature rises because we know how to interpret graphs.

In a similar way if we have two worldlines and they cross then that represents relative motion of particles towards each other. The worldlines themselves don't have to move in order to represent particles in relative motion.

If you think that because the worldlines don't move they can't represent relative motion then you are incorrectly interpreting the diagram.

roosh

Morbert wrote: »

Relative motion is a frame-dependent quantity. The green man will measure the speed of the bullet to be v. The red man will measure the speed of the bullet to be v'. That there is relativity of simultaneity doesn't change this.

Relative motion isn't necessarily a frame dependent property though, is it? When you say it is a frame dependent quantity, I think you're talking about relative velocity, aren't you; because, if two objects are in relative motion, this will be reflected in every reference frame, won't it?

That a quantity for relative velocity can be derived from the mathematics of relativity isn't in question, the question is how relative motion can arise from the physical structure that relativity (and RoS) necessitate?

roosh

dlouth15 wrote: »

Roosh,

Physics is about representing the world mathematically so we're always dealing with representations of one sort or another.

When we're dealing with representations (the spacetime diagram being one), all we can do is explain the meaning of a particular component (e.g. worldlines) in the context of that representation.

If we have, say, a graph of temperature against time and the line has a positive slope then we can say that the graph represents a rising temperature. We don't expect the line itself to move in order to represent a rising temperature. We know that the temperature rises because we know how to interpret graphs.

In a similar way if we have two worldlines and they cross then that represents relative motion of particles towards each other. The worldlines themselves don't have to move in order to represent particles in relative motion.

If you think that because the worldlines don't move they can't represent relative motion then you are incorrectly interpreting the diagram.

Worldlines in spacetime
Spacetime diagrams represent more than just the relative motion of two objects/particles*; it also represents the worldlines of the objects in spacetime, as represented by a given reference frame.

The worldlines of objects are fixed in spacetime, they don't move. This is somewhat different from the idea of graphing the motion of an object over "time", where only one point on the worldline of an object is ever "physically real" - as opposed to all the points on the wordline being "physically real". This is where we can use the chopstick analogy, because the chopsticks represent the worldlines of objects in spacetime, as represented by a given reference frame. The question is, how can relative motion arise out of such a structure?


Location vacation
You mentioned above, that the bullet occupies every position in spcacetime, but that it only occupies one position, in 3D space, at any given time. This just means that there is an associated clock reading for every location of the bullet in the 3D world, but that doesn't demonstrate how relative motion occurs from the strucuture of worldlines in spacetime.


As was mentioned above, the green observer says that the bullet is at the tree; then he crosses paths with the red observer and says that the bullet is at the house; but, as he crosses paths with the red observer, he must agree that the bullet is at the tree for the red observer. So, he must agree that the red observer sees the bullet at the tree after he has seen it there, so the bullet cannot have left that location, in the 3D world.

If the bullet doesn't leave any of it's locations in the 3D world, how can it move relative to anything?

dlouth15

roosh wrote: »

Worldlines in spacetime
Spacetime diagrams represent more than just the relative motion of two objects/particles*; it also represents the worldlines of the objects in spacetime, as represented by a given reference frame.

The worldlines of objects are fixed in spacetime, they don't move. This is somewhat different from the idea of graphing the motion of an object over "time", where only one point on the worldline of an object is ever "physically real" - as opposed to all the points on the wordline being "physically real". This is where we can use the chopstick analogy, because the chopsticks represent the worldlines of objects in spacetime, as represented by a given reference frame. The question is, how can relative motion arise out of such a structure?

The core issue seems to be that although you regard space as physically real you don't regard time as physically real. Therefore spacetime can't be physically real.

Location vacation
You mentioned above, that the bullet occupies every position in spcacetime, but that it only occupies one position, in 3D space, at any given time. This just means that there is an associated clock reading for every location of the bullet in the 3D world, but that doesn't demonstrate how relative motion occurs from the strucuture of worldlines in spacetime.

As was mentioned above, the green observer says that the bullet is at the tree; then he crosses paths with the red observer and says that the bullet is at the house; but, as he crosses paths with the red observer, he must agree that the bullet is at the tree for the red observer. So, he must agree that the red observer sees the bullet at the tree after he has seen it there, so the bullet cannot have left that location, in the 3D world.

If the bullet doesn't leave any of it's locations in the 3D world, how can it move relative to anything?

I should have said that although the bullet only occupies one point in space for any given time, this is from the point of view of a given frame of reference. From a different frame of reference the bullet will occupy a different space at a different time, but always only one point in space for any given time.

citrus burst

roosh wrote: »

Relative motion isn't necessarily a frame dependent property though, is it? When you say it is a frame dependent quantity, I think you're talking about relative velocity, aren't you; because, if two objects are in relative motion, this will be reflected in every reference frame, won't it?

That a quantity for relative velocity can be derived from the mathematics of relativity isn't in question, the question is how relative motion can arise from the physical structure that relativity (and RoS) necessitate?

I think the first sentence of this would dispute what you are saying.
Motion

roosh

dlouth15 wrote: »

The core issue seems to be that although you regard space as physically real you don't regard time as physically real. Therefore spacetime can't be physically real.

I think we can infer the spatial dimensions of objects, whereas we cannot infer a temporal dimension.

dlouth15 wrote: »

I should have said that although the bullet only occupies one point in space for any given time, this is from the point of view of a given frame of reference. From a different frame of reference the bullet will occupy a different space at a different time, but always only one point in space for any given time.

I don't think this explains how relative motion in the 3D world arises from static worldlines in 4D spacetime, though.

roosh

citrus burst wrote: »

I think the first sentence of this would dispute what you are saying.
Motion

If something is true for all reference frames is it not said to be frame independent?

citrus burst

roosh wrote: »

If something is true for all reference frames is it not said to be frame independent?

Well that depends on what you mean. Motion is true for all reference frames, but not all references will say that there is motion. Subtle difference.

In physics, motion is a general term encompassing velocity, acceleration, displacement etc. These are all frame dependent quantities.

I think you are hung up on the semantics of what is going on, rather then focusing on the physics at play. All reference frames can experience motion, this does not mean motion is frame independent since, not all reference frames will agree there is motion.

roosh

citrus burst wrote: »

Well that depends on what you mean. Motion is true for all reference frames, but not all references will say that there is motion. Subtle difference.

In physics, motion is a general term encompassing velocity, acceleration, displacement etc. These are all frame dependent quantities.

I think you are hung up on the semantics of what is going on, rather then focusing on the physics at play. All reference frames can experience motion, this does not mean motion is frame independent since, not all reference frames will agree there is motion.

It was relative motion we were talking about though.

roosh wrote: »

Relative motion isn't necessarily a frame dependent property though, is it?

citrus burst

roosh wrote: »

It was relative motion we were talking about though.

Whats the difference between relative motion and motion? The silent relative?

roosh

citrus burst wrote: »

Whats the difference between relative motion and motion? The silent relative?

Relative motion is frame independent while motion, apparently, isn't?

citrus burst

roosh wrote: »

Relative motion is frame independent while motion, apparently, isn't?

Source?

As far as I am aware the two are the same thing.

roosh

citrus burst wrote: »

Source?

As far as I am aware the two are the same thing.

Is relative motion frame dependent; that is, will frames disagree as to whether relative motion occurs between two objects?

citrus burst

roosh wrote: »

Is relative motion frame dependent; that is, will frames disagree as to whether relative motion occurs between two objects?

Yes

roosh

citrus burst wrote: »

Yes

So, if two bodies are moving relative to each other according to one reference frame, there will be another reference frame which says those bodies are at rest, relative to each other??

Morbert

roosh wrote: »

So, if two bodies are moving relative to each other according to one reference frame, there will be another reference frame which says those bodies are at rest, relative to each other??

If we restrict ourselves to special relativity, the answer is no. However, general relativity can be used to describe the increasing distance between two bodies as a coordinate transformation. I.e. The two bodies are at rest relative to each other, but the length scale used to measure the distance between them is is transformed, such that we measure the distance as increasing. The passage of time becomes a coordinate transformation, and coordinate transformations are unphysical. This is the seed within modern ideas which posit time as unphysical.

roosh

Morbert wrote: »

If we restrict ourselves to special relativity, the answer is no. However, general relativity can be used to describe the increasing distance between two bodies as a coordinate transformation. I.e. The two bodies are at rest relative to each other, but the length scale used to measure the distance between them is is transformed, such that we measure the distance as increasing. The passage of time becomes a coordinate transformation, and coordinate transformations are unphysical. This is the seed within modern ideas which posit time as unphysical.

How does this translate into the physical world?

Let's say we are watching a car drive by and the distance appears to increase; we're not necessarily performing a mathematical transformation but the distance appears to increase.

Morbert

roosh wrote: »

How does this translate into the physical world?

Let's say we are watching a car drive by and the distance appears to increase; we're not necessarily performing a mathematical transformation but the distance appears to increase.

The increase in distance would be due to our frame of reference. And yes, since it would ultimately amount to a transformation, and since quantum physics says such transformations are not observables, modern physicists attempt to formulate a timeless theory.

roosh

Morbert wrote: »

The increase in distance would be due to our frame of reference. And yes, since it would ultimately amount to a transformation, and since quantum physics says such transformations are not observables, modern physicists attempt to formulate a timeless theory.

How do you mean it would be due to my reference frame; are you using the term reference frame here in the sense of mathematical co-ordinates?

Morbert

roosh wrote: »

How do you mean it would be due to my reference frame; are you using the term reference frame here in the sense of mathematical co-ordinates?

Mathematical coordinates are what codifies your frame of reference. I.e. " Your frame of reference" means "what you will observe"

roosh

Morbert wrote: »

Mathematical coordinates are what codifies your frame of reference. I.e. " Your frame of reference" means "what you will observe"

Apologies, I don't think I fully follow.

You mentioned that under GR two relatively moving bodies would be at rest relative to each other, but the increasing distance between them would be due to a co-ordinate transformation; but when we observe relatively moving bodies in the physical world, we're not performing mathematical transformations.

In the physical world, we see distances between relatively moving bodies increasing, which you mentioned was due to our frame of reference, but you mentioned that a frame of reference is just "what you will observe".


So, we have the observation (or what we will observe) of relatively moving bodies and the distance between them increasing. GR says this is due to a co-ordinate transformation but we don't perform such transformations when we are observing relatively moving bodies in the world around us.

Morbert

roosh wrote: »

Apologies, I don't think I fully follow.

You mentioned that under GR two relatively moving bodies would be at rest relative to each other, but the increasing distance between them would be due to a co-ordinate transformation; but when we observe relatively moving bodies in the physical world, we're not performing mathematical transformations.

In the physical world, we see distances between relatively moving bodies increasing, which you mentioned was due to our frame of reference, but you mentioned that a frame of reference is just "what you will observe".


So, we have the observation (or what we will observe) of relatively moving bodies and the distance between them increasing. GR says this is due to a co-ordinate transformation but we don't perform such transformations when we are observing relatively moving bodies in the world around us.

You would be performing a coordinate transformation insofar as you would be changing what you define as distance. I.e. You say they are 2 feet apart, then you say they are 4 feet apart. Time becomes unphysical. It is these types of transformations that have made it so hard for quantum theory to extend to gravity.

[edit]- Let me put it this way: Say you and I observe a car move away from us. You say "The car is moving relative to us because I measure the coordinate distance between us and the car as increasing", to which I reply "the car isn't moving relative to us, because I am using a coordinate system such that the distance between us and the car is always the same." Special relativity would say I am wrong, but General relativity says my coordinates are no more or less valid than yours.

A real life example of this is the movement of galaxies away from us. You will often hear this described as "the expansion of space" or "the expansion of the distance between us and the galaxies"

http://en.wikipedia.org/wiki/Space_expansion

roosh

Morbert wrote: »

You would be performing a coordinate transformation insofar as you would be changing what you define as distance. I.e. You say they are 2 feet apart, then you say they are 4 feet apart. Time becomes unphysical. It is these types of transformations that have made it so hard for quantum theory to extend to gravity.

[edit]- Let me put it this way: Say you and I observe a car move away from us. You say "The car is moving relative to us because I measure the coordinate distance between us and the car as increasing", to which I reply "the car isn't moving relative to us, because I am using a coordinate system such that the distance between us and the car is always the same." Special relativity would say I am wrong, but General relativity says my coordinates are no more or less valid than yours.

A real life example of this is the movement of galaxies away from us. You will often hear this described as "the expansion of space" or "the expansion of the distance between us and the galaxies"

http://en.wikipedia.org/wiki/Space_expansion

Ah, is this where the idea of the "expansion of space" comes from?

What I'm trying to get at, with regard to not doing a co-ordinate transformation, is that we don't necessarily have to measure the increasing distance between us and the car; that is, we see the car moving relative to us and to other objects, such that the car moves towards another object which we can see in the distance, which isn't moving relative to us. We don't necessarily express it in units of measurement, and we don't necessarily know what the actual measurement is.


I know it would probably require too much time and board space, to understand, but is there a short hand answer to get an idea of how you could use a co-ordinate system which says that the distance is between us and the car is always the same? It seems [almost] indisputable that the distance is increasing.

Morbert

roosh wrote: »

Ah, is this where the idea of the "expansion of space" comes from?

What I'm trying to get at, with regard to not doing a co-ordinate transformation, is that we don't necessarily have to measure the increasing distance between us and the car; that is, we see the car moving relative to us and to other objects, such that the car moves towards another object which we can see in the distance, which isn't moving relative to us. We don't necessarily express it in units of measurement, and we don't necessarily know what the actual measurement is.


I know it would probably require too much time and board space, to understand, but is there a short hand answer to get an idea of how you could use a co-ordinate system which says that the distance is between us and the car is always the same? It seems [almost] indisputable that the distance is increasing.

We have to be careful about terminology here. I will be clearer/more technical about what I mean.

Let's abstract some things. Let's arbitrarily slice the history of the car "moving" away from us into a series of moments. A consequence of general covariance is there is no unique way to connect the locations of one moment to the locations of another. I.e. If you have a can of coke on your desk, you cannot strictly say it is in the "same" location from one moment to the next. So what scientists sometimes do is connect nearby moments with a coordinate transformation. I.e. They take the "locations" of one moment and the locations of the next, and connect them via a coordinate transformation. So they could say the "location" of the car is the same in each moment, but the distance between your location and the car's location is scaled differently. You could say the distance scale is transformed from moment to moment.

Though it's important to keep in mind that general relativity does not say this is the "true" description of things. Instead, it says you can describe things this way, and it will be no more or less physically valid than other consistent coordinate descriptions.