GR interpretation of a scenario

[PAllen]

No, you would have to make the somewhat tautological statement that a coordinate system based a a specified measurement procedure that shows distance change, will then show spatial coordinate change. There may be a different measurement procedure that shows no change.

I thought of a simple example of this in SR, no need for GR. Consider the front and back of uniformly accelerating rocket. In an inertial frame, there is relative motion between the front and back of the ship due to increasing length contraction. In the non inertial ship frame, there is no relative motion between front and back. Each is using a perfectly natural distance measurement for the given frame.

 

[PAllen]

I was assuming you were suggesting that different measurement procedures could give different distance readings, thus your statement: "But a specifically described measurement of something you want to call a distance, is physical and invariant. " (emphasis added).

If there was no spatial coordinate change, and the distance reading had changed, how were you thinking the specifically described measurement was invariant? Would it not be varying depending on some factor other than the difference between the spatial coordinates? Or were you considering the distance between two spatial coordinates to be something other than the difference in their values.

Yes, to your last question. Consider polar coordinates. Coordinate differences are generally not distances per normal measurement procedure. This would be capture in the metric for polar coordinates.

 

[name123]

Yes, to your last question. Consider polar coordinates. Coordinate differences are generally not distances per normal measurement procedure. This would be capture in the metric for polar coordinates.

That was related to the question prior to it. Were you suggesting using polar coordinates that the measurement of distance would be invariant while changing with no change in the spatial coordinates?

 

[PAllen]

That was related to the question prior to it. Were you suggesting using polar coordinates that the measurement of distance would be invariant while changing with no change in the spatial coordinates?

I was trying to answer your question. Polar coordinates are just a simple example of coordinates where coordinate differences cannot be related to distance without a metric function. They do actually provide an example of lines of constant coordinate position with changing distance. Consider two radial lines, each of constant angular coordinate. The coordinate difference between them as function of r is constant. Yet the distance between them changes as function of r. The Euclidean metric transformed to polar coordinates would allow computation of geodesic distance between points on the lines of given r.

Now just imagine spacetime analogs where r coordinate is replaced with a time coordinate.

At this point I am dropping out of this thread because it seems to me you want everyone to put great effort into explaining everything to you down to the last detail while you make no effort to learn anything systematically.

 

[Nugatory]

Out of curiosity how would you explain the scenario given in this thread using the concept of no absolute space, using an A centred coordinate system assuming A to be at rest?

You would introduce a fictitious force accelerating B, C, and F towards A. Of course this is a bizarre thing to do, but that just means that the "A at rest" coordinate system is an ugly choice for doing a classical analysis of this problem. There are many other problems in which using a coordinate system that requires a fictitious force is perfectly natural and leads to a simple intuitive picture of what's going on - anything involving centrifugal force is an example.

But that's the classical explanation that you asked for. One of the beautiful things about general relativity is that it handles these problems without the need to introduce fictitious forces, and puts all coordinate systems on an equal footing - the "A at rest" coordinate system is no longer a poor choice for analyzing your thought experiment.

 

[Nugatory]

Are you suggesting that with GR a meteor could pass the Earth and fly into a star in a distant solar system, and that neither the Earth orbiting the Sun, nor the meteor traveled any distance in space?

The meteor, the earth, and the sun are all traveling some distance along their worldlines through spacetime. How much of that you call "travelling through space" depends on the coordinate system you use, and you can always find a coordinate system in which the distance traveled in space for anyone of the three is zero.

The physical fact you get from GR is that the worldline of the meteor runs from a particular point on the worldline of the Earth to a particular point on the worldline of the distant planet.

 

[name123]

You would introduce a fictitious force accelerating B, C, and F towards A. Of course this is a bizarre thing to do, but that just means that the "A at rest" coordinate system is an ugly choice for doing a classical analysis of this problem. There are many other problems in which using a coordinate system that requires a fictitious force is perfectly natural and leads to a simple intuitive picture of what's going on - anything involving centrifugal force is an example.

But that's the classical explanation that you asked for. One of the beautiful things about general relativity is that it handles these problems without the need to introduce fictitious forces, and puts all coordinate systems on an equal footing - the "A at rest" coordinate system is no longer a poor choice for analyzing your thought experiment.

Well from the context of the conversation the question was about how the scenario could be explained without absolute space using Newtonian physics. With absolute space Newtonian physics can explain it easily. Assuming your answer was correct (you would need to introduce fictitious forces to Newtonian physics), it seems strange that apparently at schools now they are teaching Newtonian physics without absolute space, even though once it was removed, it could no longer explain the scenario I outlined. Newtonian physics doesn't include the fictitious forces. Though I should point out that earlier PAllen stated in #30 that he/she knew how to explain it using Newtonian physics with no absolute space, but mentioned in post #27 that he/she had no interest in explaining it. Perhaps (if you thought it was of interest) you could pm them and they could tell you (probably easier than trying to explain it to me as I don't know nearly as much physics as you, and so can be slow to understand which can be frustrating for the person trying to explain), just to let any readers of this thread know if there is an alternative to fictitious forces which might explain school's choosing to teach Newtonian physics without absolute space.

 

[name123]

The meteor, the earth, and the sun are all traveling some distance along their worldlines through spacetime. How much of that you call "travelling through space" depends on the coordinate system you use, and you can always find a coordinate system in which the distance traveled in space for anyone of the three is zero.

The physical fact you get from GR is that the worldline of the meteor runs from a particular point on the worldline of the Earth to a particular point on the worldline of the distant planet.

But can you get a coordinate system where the distance traveled through space for all three is zero?
Would a physicalist consider that the measurements imply that some relative physical distance has been traveled through space by at least one (or perhaps two) of the three, or would the theory applied to the measurements not imply any distance was traveled through space by any of the three, but instead just regard the concept (of traveling through space) as a mathematical artifact based on an arbitrary choice of coordinates, and not consider it to reflect any physical spatial movement?

I admit that I find the idea of "some relative physical distance" slightly confusing even though I typed those words, because as you mentioned, depending on frame of reference, the theory seems to suggest that some distance could have been travelled, or it could not have been travelled, such that the statement "some distance has been travelled" and the statement "no distance has been travelled" could both be true, even though they seem like contradictory statements, distinct from "maybe a distance has been traveled maybe it hasn't we cannot tell".

 

[Nugatory]

Assuming your answer was correct (you would need to introduce fictitious forces to Newtonian physics), it seems strange that apparently at schools now they are teaching Newtonian physics without absolute space, even though once it was removed, it could no longer explain the scenario I outlined.

Absolute space is a complete red herring here - the Newtonian explanation is the same with or without absolute space. (The easiest way to see this might be to consider your thought experiment under three different conditions: no absolute space; absolute space in which A and B are at initially at rest; absolute space in which A and B are initially moving at a constant absolute speed).

The reason is that I cannot yet see how distance can be traveled in space, and yet there be no motion.

Go back a few posts to where we explained what motion is...

To highlight the point slightly further, imagine that a meteor is in freefall following its geodesic passing and scrapping a slower moving spaceship. The spaceship then accelerates and catches it up and as it does so, it collides with it again. Has the spaceship not moved through space during its journey to catch the meteor up, and if it has, has not the meteor?

There are coordinate systems in which the meteor does all the moving (that is, the meteor's position coordinate is changing with time and the ship's is not), coordinate systems in which the ship does all the moving (the ship's position coordinate is changing in time and the meteor's is not), and coordinate systems in which both are moving. However, the physical fact is that the ship's worldline passes through one set of points in spacetime and the meteor's worldline passes through another. The coordinates are just labels that we attach to these points, and we can choose to label all the points on either worldline with an unchanging position coordinate if we wish. (We cannot do this to both worldlines at once in this particular case).

 

[Nugatory]

But can you get a coordinate system where the distance traveled through space for all three is zero?

Not in this situation, because the worldlines intersect. If they didn't intersect it would be possible (although whether we'd want to use such coordinates is a different matter).. However, this is also a red herring because the physics is in the paths taken through spacetime not the labels that we attach to points along those paths. The physics isn't different just because some labeling scheme doesn't work. In fact, it's the other way around - the physics determines which labeling schemes will work.

I admit that I find the idea of "some relative physical distance" slightly confusing even though I typed those words, because as you mentioned, depending on frame of reference, the theory seems to suggest that some distance could have been travelled, or it could not have been travelled, such that the statement "some distance has been travelled" and the statement "no distance has been travelled" could both be true, even though they seem like contradictory statements, distinct from "maybe a distance has been traveled maybe it hasn't we cannot tell".

OK, let's try an analogy from space, as opposed to spacetime. I am standing at the Earth's equator. You are standing one meter to my left. We both start walking due north; as we move farther north we draw closer to one another until we collide at the north pole. Now consider this situation from the point of view of someone at the pole watching us through binoculars. If he keeps his binoculars pointed directly at me, he will find that I am moving straight towards him without an iota of east/west deviation; you however are moving slowly to the east so that the initial one meter separation between us shrinks to zero as we meet at the pole. However, if he points his binoculars directly at you, I'll be the one that is moving west to gradually close up the distance between us. So we're both walking due north, and the statement "I am moving west" or "you are moving east" has no physical significance at all; it's just an artifact of the direction the watcher pointed his binoculars, which is to say his choice of coordinates.

That's what happens with paths through curved space, such as on the surface of the earth. It gets trickier when we're working with curved spacetime. To see why, think about how I was able to talk about the shrinking distance between us as we walked from the equator to the pole. To find the distance between you and me at any given moment, I have to identify the point on the Earth's surface where I am standing at that moment; then identify the point on the Earth's surface where you are standing AT THE SAME TIME; and then I can measure the distance between those points. But "at the same time" in four-dimensional space-time just means "has the same time coordinate", so the points I'm measuring between will depend on my choice of coordinate systems. That's why there's no general coordinate-independent definition of the distance between two objects in GR; if you think you've found "the" definition, you are overlooking an arbitrary assumption about how time coordinates are assigned.

 

[name123]

Absolute space is a complete red herring here - the Newtonian explanation is the same with or without absolute space. (The easiest way to see this might be to consider your thought experiment under three different conditions: no absolute space; absolute space in which A and B are at initially at rest; absolute space in which A and B are initially moving at a constant absolute speed).

1) With no absolute space I am not sure how to do it, adding fictitious forces changes the physics.

2) With absolute space in which A and B are initially at rest, then the coordinate system is just a mathematical device and although A and F gravitating towards each other could be described in an A based coordinate system, what caused A to change its motion is that gravity from F exerts a force on A pulling it towards it, while gravity from A exerts a force on F pulling it towards it. The amount each object's velocity is affected by the other depends on the mass of of the other. There would be no way to tell A or B's motion relative to absolute space, but you could tell during any point of A's gravitation towards F the change in A's velocity vector relative to absolute space due to the gravitation (the change will be in the direction of F).

3) With absolute space in which A and B are initially moving at a constant speed, then the coordinate system is just a mathematical device and although A moving to F could be described in an A based coordinate system, what caused A to change its motion is that gravity from F exerts a force on A pulling it towards it, while gravity from A exerts a force on F pulling it towards it. The amount each object's velocity is affected by the other depends on the mass of of the other. There would be no way to tell A or B's motion relative to absolute space, but you could tell during any point of A's gravitation towards F the change in A's velocity vector relative to absolute space due to the gravitation (the change will be in the direction of F).

 

[name123]

Not in this situation, because the worldlines intersect. If they didn't intersect it would be possible (although whether we'd want to use such coordinates is a different matter).. However, this is also a red herring because the physics is in the paths taken through spacetime not the labels that we attach to points along those paths. The physics isn't different just because some labeling scheme doesn't work. In fact, it's the other way around - the physics determines which labeling schemes will work.

Well when the meteor passes the Earth imagine that it does so at a 10km distance, so that the worldlines to not intersect, and while it goes of to fly into a distant star, ignore the star. Just consider the meteor passing the Earth while the Earth orbits the Sun. Since just considering these three there there is no contact I presume the worldlines do not intersect. So is it possible in GR to take a measurement of all three and conclude that none of them had traveled in space?

The reason I am bringing it up, is that while I understood your explanation of motion as an artifact of whatever arbitrary coordinate system was chosen, I was having a problem understanding it without also understanding that GR denied that any object ever actually physically traveled in space and instead such measurements are artifacts of whatever arbitrary coordinate system was chosen. Because if GR considered it to be a physical reality that objects did travel in space then that would be motion, and while in the scenario I described I could understand that measurements could disagree about which objects were moving in space I did not realize that it could be concluded that none of them were.

The other scenario with the meteor and the spaceship was just to consider whether the spaceship would be considered to travel in space given the acceleration that it experienced which I understood would show up on certain measurements. You mentioned in post #44 (will this number change if people delete posts in between?) that

"There are coordinate systems in which the meteor does all the moving (that is, the meteor's position coordinate is changing with time and the ship's is not), coordinate systems in which the ship does all the moving (the ship's position coordinate is changing in time and the meteor's is not), and coordinate systems in which both are moving."

I did not understand what type of coordinate system allowed the acceleration to be measured on the ship, but deny it had traveled any distance (are accelerating coordinate systems used, and if so are they not considered to be coordinate systems that travel distances (ignoring ones just spinning)).

 

[Vitro]

... physically traveled in space ...

How do you propose measuring travel through space (in the absolute sense, not relative to some other object or coordinate system), be able to say that a spaceship is moving with speed X through space and give a value for X? Try as hard as you like, you'll find out that you can't, and any speed you may determine will always be relative to something else (that's not "absolute space").

In physics "physically" means measurable, either directly or inferred from other things that are measurable. If such travel through space is not measurable then it's definitely not physical as far as physics is concerned. That's true for any physical theory, GR and Newtonian alike.

 

[name123]

How do you propose measuring travel through space (in the absolute sense, not relative to some other object or coordinate system), be able to say that a spaceship is moving with speed X through space and give a value for X? Try as hard as you like, you'll find out that you can't, and any speed you may determine will always be relative to something else (that's not "absolute space").

In physics "physically" means measurable, either directly or inferred from other things that are measurable. If such travel through space is not measurable then it's definitely not physical as far as physics is concerned. That's true for any physical theory, GR and Newtonian alike.

You ignored where I wrote:

Because if GR considered it to be a physical reality that objects did travel in space then that would be motion, and while in the scenario I described I could understand that measurements could disagree about which objects were moving in space I did not realize that it could be concluded that none of them were.​

I was no way suggesting that you could measure travel through space in an absolute sense in GR or Newtonian physics for that matter. As I understand it the idea that in physics "physically" means measurably is a 20th century concept. Newton for example did not share it (he understood that he could not measure absolute space, but still considered it to exist in his model of physics). Plus it could be argued that travel through space could be inferred if there was no measurement of the scenario given in which travel through space did not occur for example.

 

[PeterDonis]

1) With no absolute space I am not sure how to do it, adding fictitious forces changes the physics.

2) With absolute space in which A and B are initially at rest, then the coordinate system is just a mathematical device and although A and F gravitating towards each other could be described in an A based coordinate system, what caused A to change its motion is that gravity from F exerts a force on A pulling it towards it, while gravity from A exerts a force on F pulling it towards it. The amount each object's velocity is affected by the other depends on the mass of of the other. There would be no way to tell A or B's motion relative to absolute space, but you could tell during any point of A's gravitation towards F the change in A's velocity vector relative to absolute space due to the gravitation (the change will be in the direction of F).

3) With absolute space in which A and B are initially moving at a constant speed, then the coordinate system is just a mathematical device and although A moving to F could be described in an A based coordinate system, what caused A to change its motion is that gravity from F exerts a force on A pulling it towards it, while gravity from A exerts a force on F pulling it towards it. The amount each object's velocity is affected by the other depends on the mass of of the other. There would be no way to tell A or B's motion relative to absolute space, but you could tell during any point of A's gravitation towards F the change in A's velocity vector relative to absolute space due to the gravitation (the change will be in the direction of F).

Why would the answer you gave to #2 and #3 not also work for #1? What role does "absolute space" play in the reasoning in #2 and #3? Particularly since being at rest vs. moving at a constant speed makes no difference whatever to your explanation?

 

[PeterDonis]

You would introduce a fictitious force accelerating B, C, and F towards A.

Note that this is true regardless of whether you think there is "absolute space" or not. The key point is that you are using coordinates in which A is at rest.

 

[name123]

Why would the answer you gave to #2 and #3 not also work for #1? What role does "absolute space" play in the reasoning in #2 and #3? Particularly since being at rest vs. moving at a constant speed makes no difference whatever to your explanation?

Because in #1 how F, B and C moved to A should in the theory be equally as explainable as how A moved to F. And I do not know how to explain how F and B and C would significantly move to A in Newtonian physics. Nugartory considered that you could add fictitious forces to do it, and while that would work, it would no longer be Newtonian physics (as Newtonian physics doesn't include those added forces). Absolute space in Newtonian physics removes the need to explain how F, B and C moved to A because Newtonian physics would deny that they did (significantly). The main change would be a change in A's velocity vector relative to absolute space due to the gravitation, the change being in the direction of F.

How were you thinking you could get rid of absolute space and explain a change in F's velocity vector in the direction of A, and the same velocity vector change to the velocity vectors of B and C? What in Newonian physics would be responsible for such changes?

 

[PeterDonis]

Because in #1 how F, B and C moved to A should in the theory be equally as explainable as how A moved to F.

Motion is relative, so these are the same thing. That's just as true in Newtonian physics as in relativity. "Absolute space" in Newtonian physics does not mean motion is not relative. It just means Galilean invariance instead of Lorentz invariance.

Absolute space in Newtonian physics removes the need to explain how F, B and C moved to A because Newtonian physics would deny that they did (significantly).

This is not correct. See above.

The main change would be a change in A's velocity vector relative to absolute space due to the gravitation

This is true, but it doesn't mean what you think it means. See above.

I think you need to get clear about exactly what "absolute space" means in Newtonian physics; once you get clear about that the apparent problems you think you see should go away.

 

[name123]

Motion is relative, so these are the same thing. That's just as true in Newtonian physics as in relativity. "Absolute space" in Newtonian physics does not mean motion is not relative. It just means Galilean invariance instead of Lorentz invariance.

In Newtonian physics all motion is relative to absolute space, and when I am discussing motion with regards to Newtonian physics, I am discussing it relative to absolute space. From https://en.wikipedia.org/wiki/Galilean_invariance:

Among the axioms from Newton's theory are:

1. There exists an absolute space, in which Newton's laws are true. An inertial frame is a reference frame in relative uniform motion to absolute space.
2. All inertial frames share a universal time.

It seems to me that Newtonian physics predicts and explains that in such a scenario the magnitude of change in A's velocity vector (relative to absolute space) in the direction of F > than the magnitude of change in F's velocity vector (relative to absolute space) in the direction of A.

I do not see how it predicts or explains that in the scenario, relative to absolute space, A's velocity vector would undergo no change, and that it could explain F, B and C undergoing a change in their velocity vectors relative to absolute space instead. Why would A's position remain constant relative to absolute space, but not F, B, and Cs'?

 

[PeterDonis]

It means that motion is relative to absolute space

That's not what Newtonian physics says. Wikipedia is not a good source (and the galilean invariance page in particular seems to me to invite a number of serious misunderstandings). You need to actually look at a textbook on classical mechanics.

The "B" level answer to the general question you are asking is that there are only two really significant differences between Newtonian mechanics and relativity:

(1) Newtonian mechanics obeys Galilean invariance, and relativity obeys Lorentz invariance. Everything else about motion flows from that, and if you understand the implications of that, you can forget all about "absolute space" and the other things that are confusing you.

(2) In Newtonian mechanics, gravity is a force; in relativity, it isn't. That makes relativity simpler because it doesn't have to try to deal with the question of why objects don't feel gravity as a force, i.e., why objects moving solely under gravity are in free fall, weightless. In Newtonian mechanics this has to be dealt with by a special ad hoc assumption that gravity works different in this respect from all other forces. In relativity, the question doesn't even arise.

In particular, as far as choosing coordinates, inertial vs. non-inertial frames, etc., there is really no difference between Newtonian mechanics and relativity, other than the invariance difference above. In both cases, you can choose coordinates in which any object you like is at rest, but those coordinates might not be inertial; and if they are not inertial, additional coordinate artifacts will appear that do not have a straightforward interpretation as being caused by a "source" (these are called "fictitious forces" in Newtonian mechanics, but similar effects appear in non-inertial frames in GR).

 

[name123]

That's not what Newtonian physics says. Wikipedia is not a good source (and the galilean invariance page in particular seems to me to invite a number of serious misunderstandings). You need to actually look at a textbook on classical mechanics.

The "B" level answer to the general question you are asking is that there are only two really significant differences between Newtonian mechanics and relativity:

(1) Newtonian mechanics obeys Galilean invariance, and relativity obeys Lorentz invariance. Everything else about motion flows from that, and if you understand the implications of that, you can forget all about "absolute space" and the other things that are confusing you.

(2) In Newtonian mechanics, gravity is a force; in relativity, it isn't. That makes relativity simpler because it doesn't have to try to deal with the question of why objects don't feel gravity as a force, i.e., why objects moving solely under gravity are in free fall, weightless. In Newtonian mechanics this has to be dealt with by a special ad hoc assumption that gravity works different in this respect from all other forces. In relativity, the question doesn't even arise.

In particular, as far as choosing coordinates, inertial vs. non-inertial frames, etc., there is really no difference between Newtonian mechanics and relativity, other than the invariance difference above. In both cases, you can choose coordinates in which any object you like is at rest, but those coordinates might not be inertial; and if they are not inertial, additional coordinate artifacts will appear that do not have a straightforward interpretation as being caused by a "source" (these are called "fictitious forces" in Newtonian mechanics, but similar effects appear in non-inertial frames in GR).

Although you think wiki isn't a good source, if you look at the page https://en.wikipedia.org/wiki/Absolute_time_and_space you will see a quote from Isaac Newton from (I assume) Philosophiæ Naturalis Principia Mathematica.

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space ... Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another ...

— Isaac Newton​

Lower down you will notice in the section titled Differing Views how Newtonian physics has been modified, that:

Even within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. Instead, the notion of inertial frame of reference has taken precedence, that is, a preferred set of frames of reference that move uniformly with respect to one another.​

My point that you snipped was that relative to absolute space, certain results could be explained, but not others. A further point is that I am not clear how by removing absolute space those results unexplainable by Newtonian physics (which has absolute space) are by the removal of absolute space are suddenly explainable by modified Newtonian physics.

 

[PeterDonis]

relative to absolute space, certain results could be explained, but not others

Only if you insist on using your incorrect concept of what "absolute space" means and what role it plays in Newtonian mechanics. Stop reading Wikipedia and look at a textbook.

Thread closed.