A Challenge to Special Relativity?

[Curious6]

Please consider this simple, but very interesting interpretation of the nature of space in special relativity.

Space is both relative AND absolute. Why? Let's take a very simple example.

The Eiffel Tower is 10,000 miles East from City X and 2,000 miles East from City Y. Michael is in City X, Tim is in City Y. If we were to plot everything that exists for Michael and for Tim on an imaginary map, Michael would disagree with Tim on where the Eiffel Tower is; for Michael it would be 10,000 miles East, for Tim it would be 2,000 miles East. Space in this case is relative; Michael and Tim disagree on what they find at 10,000 miles East and they disagree on what they find at 2,000 miles East. However, when Michael takes into account that Tim is where he is (i.e., 8,000 miles away from him) he now understands how Tim sees the Eiffel Tower as being only 2,000 miles East. Space here is absolute; they now both agree on where the Eiffel Tower is.

Is this distinction made at all in special relativity? I think it is a very important one. Basically, space is relative until we take into account the position of others, then space ceases to be relative. The same could be said for time (possibly challenging the notion of the relative simultaneity of events). Any insights would be much, much appreciated!

 

[atyy]

Yes, spacetime is absolute, and the events in spacetime are absolute. The relative thing is that different reference frames assign different numbers to the same event. Relativity tells us how the numbers of different reference frames are related.

 

[Curious6]

atty, thanks for your answer. I do know that special relativity says spacetime is absolute, but I haven't brought time into the picture in my example above, which shows a case where space is relative and space is absolute. I am not saying I am right or anything; on the contrary, I am hoping someone can point out the flaw in the reasoning above that leads to the seemingly paradoxical result.

 

[atyy]

atty, thanks for your answer. I do know that special relativity says spacetime is absolute, but I haven't brought time into the picture in my example above, which shows a case where space is relative and space is absolute. I am not saying I am right or anything; on the contrary, I am hoping someone can point out the flaw in the reasoning above that leads to the seemingly paradoxical result.

I didn't know what you said is wrong, I read it quickly and it made sense to me. I'll read it more carefully now.

 

[Curious6]

A further point. If, as in my example, space can be conceived of as relative and absolute, then a further step shows that 'absolute' space is the 'correct' way to conceive of existing things. Why? Well, if Michael says the Eiffel Tower is 10,000 miles East, and Tim says it is 2,000 miles East, and Marie says it is 5,000 miles North of her, then the Eiffel Tower is in effect existing in all these places. But we know there is only ONE Eiffel Tower. Therefore, once Michael, Tim, and Marie take into account their relative perspectives, they all agree there is only one place the Eiffel Tower exists in (thereby conceiving of space as being absolute).

Again, I am not saying I am right, I am just trying to share this thought with you all so that I have a better chance at seeing where the possible mistake lies.

 

[atyy]

atty, thanks for your answer. I do know that special relativity says spacetime is absolute, but I haven't brought time into the picture in my example above, which shows a case where space is relative and space is absolute. I am not saying I am right or anything; on the contrary, I am hoping someone can point out the flaw in the reasoning above that leads to the seemingly paradoxical result.

OK, I'm confused. What is paradoxical about what you said? There are relative and absolute descriptions of events in spacetime. The only thing that seems unconventional to me is that you say space is relative, whereas most people would say reference frames are relative, but that seems to be just terminology.

 

[matheinste]

Hello Curious6.

But how do you tell anyone where the Eiffel Tower is without refrerring to some other point and so on?

Matheinste.

 

[Curious6]

Hi, matheinste. Well, I don't think it's necessary to refer to another point to say where the Eiffel Tower is. You can just say: 'it's 200 miles due South of where I am' or 'it's 10,293 miles NE of where I am'.

 

[Doc Al]

If we were to plot everything that exists for Michael and for Tim on an imaginary map, Michael would disagree with Tim on where the Eiffel Tower is; for Michael it would be 10,000 miles East, for Tim it would be 2,000 miles East.

Without a common reference point, of course they would "disagree". But such a "disagreement" is trivially handled: Both agree that the Eiffel Tower is 10,000 miles east of Micheal and 2,000 miles east of Tim.

I don't see what this has to do with Special Relativity.

 

[Doc Al]

Hi, matheinste. Well, I don't think it's necessary to refer to another point to say where the Eiffel Tower is. You can just say: 'it's 200 miles due South of where I am' or 'it's 10,293 miles NE of where I am'.

That's good enough. Both will agree on this. Disagreement has magically vanished.

(I seriously hope you aren't troubled by the fact that Michael refers to himself as "I" while Tim refers to himself as "I".)

 

[Curious6]

Doc Al, they would disagree because from their perspectives on space differ, that is, their perspectives on space are relative to where they are. Nevertheless, they can find common ground and agree on where a specific object is (i.e., the location of the Eiffel Tower). The Eiffel Tower's position is therefore defined in absolute terms. There seems to be a contradiction. I posted this in the special relativity forum because it is chiefly concerned with our perception of space as being relative.

 

[Curious6]

That's good enough. Both will agree on this. Disagreement has magically vanished.

(I seriously hope you aren't troubled by the fact that Michael refers to himself as "I" while Tim refers to himself as "I".)

After posting it I realized that adding the 'where I am' bit might cause some controversy. Nevertheless, I don't see how that affects my main point.

 

[Doc Al]

Doc Al, they would disagree because from their perspectives on space differ, that is, their perspectives on space are relative to where they are. Nevertheless, they can find common ground and agree on where a specific object is (i.e., the location of the Eiffel Tower). The Eiffel Tower's position is therefore defined in absolute terms. There seems to be a contradiction.

What contradiction? The same object can certainly be a different distance and direction from different reference points. So what? How does that "contradict" anything?

 

[Curious6]

The same object can certainly be a different distance and direction from different reference points.

That is exactly the point. The same object appears to be at different distances and directions from different reference points, which suggests it has different locations in space (locations dependent on one's reference point), but in actuality it only has one location in space.

 

[JesseM]

That is exactly the point. The same object appears to be at different distances and directions from different reference points, which suggests it has different locations in space (locations dependent on one's reference point), but in actuality it only has one location in space.

What is "location in space"? Is it separate from its distance from other objects, or from position relative to a certain coordinate grid? If so, how do you measure it?

 

[Curious6]

What is "location in space"? Is it separate from its distance from other objects, or from position relative to a certain coordinate grid? If so, how do you measure it?

JesseM, I think your question is another way of asking what I am trying to get at. What I proposed is that there are two ways to think of 'location in space': one relative, one absolute, as explained briefly below.

'Location in space' is an imaginary grid where you can place where objects are with respect to you. In the example that started this thread, each person has an imaginary grid where they position their objects. For instance, Michal's grid positioned the Eiffel Tower 10,000 miles East from him whereas Tim positioned it only 2,000 miles East from him. Therefore, what Tim would find 10,000 miles East from him on his grid is different than what Michael finds 10,000 miles East from him on his grid (Michael finds the Eiffel Tower). In this sense then, 'location in space' is relative; Michael and Tim have different perceptions of objects' locations in space.

'Location in space' however also refers to an object's actual position on a universal grid. What I mean by this is a grid like for instance the geographic coordinates used to give positions of objects on Earth. By this definition of 'location of space' the Eiffel Tower has just one location, whereas we just saw above that it has various locations. Who's grid are we to trust therefore? Clearly, it does not appear to be any individual's grid (an object could be located at potentially an infinite number of places). There seems to be a universal grid on which objects can placed. That is what I mean and what I'd like further insights on.

 

[matheinste]

Hello Curiou6.

One point in empty space is indistinguishable from any other point and has no "position" and nothing to define it without reference to some object, such as yourself or the Eiffel Tower. I suppose using your own position as a reference point is a natural thing to do and is as valid as any other way.

Matheinste

 

[ZapperZ]

There seems to be a universal grid on which objects can placed. That is what I mean and what I'd like further insights on.

Then you are assuming that there is an 'absolute space' and an absolute reference point. Care to tell me what evidence that you have to know that such a thing exist?

Zz.

 

[Curious6]

Hello Curiou6.

I suppose using your own position as a reference point is a natural thing to do and is as valid as any other way.

I agree with that and so does special relativity, but there does appear to be a sense in which an object occupies a certain position within absolute space, i.e., there are certain coordinates in the entirety of space occupied by certain objects; this is the opposite case to our relative perception of space.

 

[Curious6]

Then you are assuming that there is an 'absolute space' and an absolute reference point. Care to tell me what evidence that you have to know that such a thing exist?

Zz.

I have no evidence for that besides my thought experiment outlined above. I am actually not assuming there is an absolute space; my example derives absolute and relative space as notions. Clearly, from the thought experiment there seem to be relative and absolute reference points.

 

[ZapperZ]

I have no evidence for that besides my thought experiment outlined above. I am actually not assuming there is an absolute space; my example derives absolute and relative space as notions. Clearly, from the thought experiment there seem to be relative and absolute reference points.

How is that? All you have shown in your example is the ability to transform from one reference point to another. Translational symmetry. This is your "evidence" for the existence of "absolute space"? Why haven't all the most brilliant physicists stumbled upon that?

Zz.

 

[matheinste]

Quote:-
----I agree with that and so does special relativity, but there does appear to be a sense in which an object occupies a certain position within absolute space, i.e., there are certain coordinates in the entirety of space occupied by certain objects; this is the opposite case to our relative perception of space.-----

Of course an object occupies a certain unique position in space but there is nothing about about that point that tells us where it is. I think it was Eddington who said that the only way to tell someone which location in space you wish to indicate without reference to another location was to actually point to it.

Matheinste.

 

[JesseM]

I agree with that and so does special relativity, but there does appear to be a sense in which an object occupies a certain position within absolute space, i.e., there are certain coordinates in the entirety of space occupied by certain objects; this is the opposite case to our relative perception of space.

Keep in mind that when people talk about things being relative to one's choice of reference frame, they are usually talking about different coordinate grids in motion relative to one another, not just coordinate grids with their origins at different locations. For example, if I am on a spaceship moving at constant speed relative to a space station, there could be one coordinate grid centered on the ship, and naturally in this grid the ship is at rest while the space station is moving. So, from one time to another the ship occupies the same space coordinate, while the space station's space coordinate is constantly changing. On the other hand, there could be another coordinate grid centered on the space station, and in this system the reverse would be true. Do you believe there must be a real truth about whether the ship or the station (or neither) is remaining at a fixed point in space while the other is moving? Even if there was a "real truth" about this in some metaphysical sense, relativity says it would be impossible to determine experimentally which was at rest in absolute space and which wasn't, because all the laws of physics work the same way in both coordinate systems, which negates the idea that there is an experiment either the ship or the station could do to determine their velocity relative to absolute space (since if they both perform the same experiment, they must get the same results if all the laws of physics are the same in both coordinate systems).

 

[atyy]

The Eiffel Tower's position is therefore defined in absolute terms.

Of course an object occupies a certain unique position in space

Both statements seem right and equivalent to me. Am I misunderstanding something?

In Newtonian physics, the position in space of the Eiffel tower is absolute. In special relativity, it would be the worldline in spacetime of the Eiffel tower which is absolute. (I suppose there's the detail about isometry.)

 

[atyy]

Is the discussion related to eg. Giulini's "the points that constitute M, which for the time being we think of as recognizable entities, as mathematicians do. (For physicists these points are mere ‘potential events’ and do not have an obvious individuality beyond an actual, yet unknown, event that realizes this potentiality.)" http://arxiv.org/abs/gr-qc/0603087

 

[atyy]

The preamble here may also be relevant: "Do we think of spacetime points as “determined well-distinguished objects of our intuition or of our thinking”?"

The Rich Structure of Minkowski Space
Domenico Giulini
http://arxiv.org/abs/0802.4345

 

[Dale]

There is nothing even remotely parodoxical in this. All you have said is:

1) Different coordinate systems assign different values for the coordinates of a given object

2) There exists some transformation between coordinate systems

 

[matheinste]

Hello atyy

Saying that a point occupies a unique position in space is really just saying that it exists as one object at one location but says nothing about its location.

Matheinste.

 

[atyy]

Saying that a point occupies a unique position in space is really just saying that it exists as one object at one location but says nothing about its location.

Doesn't it say that it's location is where it is? The fact that there is something there (say the Eiffel tower) distinguishes that location.

Or is that what you mean, ie. if there were nothing there, then empty space is all the same, we cannot give directions to a point in totally empty space.

Or do you mean that even with the Eiffel tower at some place and me at another place, we still have to lay out a grid between the the tower and me, so we can give it and the intervening points some addresses before I can get directions on how to get there?

What I'm trying to figure out is whether you are saying something different from Curious6, and if so, what is the difference? Or do you agree with him, and are just rephrasing what he's saying for clarity? I'm thinking Curious6 is right that absolute location exists (in Newtonian physics), otherwise how can we even say that I am here and the Eiffel tower is there in a coordinate independent sense? In special relativity, it would have to be the location of events in spacetime that is absolute, because simultaneity is conventional. The part I disagree with Curious6 about is not that absolute location exists, but that there's any paradox in having many different coordinate systems being able to describe the same absolute things.

 

[matheinste]

Hello atyy

The point I am making is that if you have an object then it occupies a location in space. If there was nothing else in space to refer it to, you cannot describe to me where it is, without my being able to see it or detect it some other way. That means the description of a space location is relative.

Matheinste.