A Challenge to Special Relativity?

[Saw]

This is like knowing that Tolstoy is a great author but the English translations are lacking. The solution is not to do yet another English translation which cannot express all the artistry of the original, but the solution is simply to learn Russian.

DaleSpam, you adhere to Galileo's view, when he suggested something like "the universe is written in mathematical language". Another view: the universe is what is and the human intellect may "represent" or "reproduce" it in any language, whether mathematical, geometrical (a different language, after all, even if akin to the mathematical formulation), conventional (English just being one of this subset...) or even emotional! I agree that mathematical and geometrical rules are far more effective..., when it comes to drawing consequences from axioms. But if you doubt about the axioms, you may need some pre-mathematical discussion... in plain English or Russian words... or in the mathematical language of a superior culture who has pushed mathematical terminology farther than your own! For instance: in ancient mathematics, when they did not handle the concept of "convergence of infinite series", how did mathematicians discuss over the proposal to include such new concept in the list of approved terms? By exchanging formulas with mysterious symbols of unknown meaning or in some conventional language?

Anyhow, this is a side-matter and the crucial aspect of my proposal was: can you do step 3, in any language you prefer, mathematical if you prefer? But, sorry, because I start writing and cannot stop. Maybe this is the subject for another thread. Please forget this parenthesis and continue your discussion.

 

[atyy]

3) in particular, always within the boundaries of this elementary example, explain the transition from a Galilean viewpoint to the Einsteinian one (this may sound strange, since here there is no motion, but it may be possible, if you hit on the right analogy…)

Maybe with Escher's famous picture:
http://www.geom.uiuc.edu/graphics/images/medium/Special_Topics/Hyperbolic_Geometry/escher.gif

And mathematically by the new metric given by Eq 1 here:
http://mathworld.wolfram.com/PoincareHyperbolicDisk.html

?

 

[Curious6]

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.

No, translational symmetry is not what I am referring to. Translational symmetry refers to the mapping of one's coordinates upon the others, so that they both agree. This refers to one's coordinates taking into account the other's coordinates to understand why they have different coordinate systems and come to the realization there is actually only one real coordinate system (objects can be found in one place).

 

[Dale]

DaleSpam, you adhere to Galileo's view, when he suggested something like "the universe is written in mathematical language".

Yes, and you are kidding yourself if you believe that you can understand it without putting in the effort required to learn the math. I have had this discussion before, and frankly the anti-math position always seems lazy to me.

Another view: the universe is what is and the human intellect may "represent" or "reproduce" it in any language

The difference is that math is the only language where illogical statements are gramatically incorrect.

 

[Curious6]

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.

I agree that there is nothing about a point that tells us where it is. We need to look at it with respect to other points in order to know where it is. Take point X. Point X's position cannot be known by just looking at point X. However, if you now take another point, point Y for instance, then you can say point X is 5 metres South of point Y. Point X is also 5 metres East of point Z. Point X is at different points on point Y's and point Z's respective coordinate systems; space is relative. Nevertheless, in reality point X is just at one single point; a position both point Y and point Z will agree upon (that's why we agree upon where objects are located; e.g., we agree the Eiffel Tower is in Paris); space is in this sense absolute.

 

[Curious6]

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).

Good insight. I agree with that. What I would like to suggest though, and this differs from special relativity and is therefore controversial, is that one object IS actually moving whereas the other one is remaining stationary. Please take one minute to read the reasoning behind this statement, and then point out where it's wrong because it clearly differs from what SR says and I'd therefore appreciate it if someone could point out any flaw which I have overlooked. Take any empty field. You have two people, Mike and Jane, at rest with respect to each other, and Tim, who is about 100 meters away riding on his bicycle. Now Tim rides past Mike on his bicycle. Mike records him as being in motion. Tim records Mike as being in motion. Each other's positions change on their relative coordinate systems; each observer's reference point is equally valid - this is SR. However, Jane also notes Tim's position as changing on her coordinate system; she doesn't see Mike's position changing on her coordinate system. Not only for Mike, but for Jane, Tim has moved as well. Now you may argue that both Mike and Jane are in the same frame of reference so that doesn't matter. However, you could say that for every other object in the field, the only position that has changed is that of Tim; the relative positions between the other points in the field have remained the same. Taking it one step further, all the remaining positions of points in the Universe with respect to other points have staid the same; only Tim's relation to other points in the Universe has changed. It can therefore be said Tim is in motion.

Any comments on the above?

 

[Curious6]

The approach proposed by Curious6 is, in my view, very interesting. It does not “challenge” SR, but it may serve at least to clarify its concepts.

SR is right, but it plays with some obscure concepts, at least at the level of pure English. Its mathematics and its geometry may be undisputable, but it is my impression that when you try to put it in plain words, problems arise. (Hence the “paradoxes”.)

To try to solve this, I would propose this challenge, not for SR but for our discussion skills:

1) start with this rudimentary example, which only deals with objects stationary wrt each other and hence excludes time;

2) give a sound account of what it conceptually means for you, handling the concepts of what “space” is, what is “absolute” and “relative”, what a “measurement” means and so on;

3) in particular, always within the boundaries of this elementary example, explain the transition from a Galilean viewpoint to the Einsteinian one (this may sound strange, since here there is no motion, but it may be possible, if you hit on the right analogy…) and

4) only then introduce the complication of motion and apply your concepts to this new context, “mutatis mutandi” (changing what needs to be changed and leaving unaltered what does not need to be changed).

In this exercise, it’d be fundamental not to skip step 3: you would have to fully explain SR within the constraints of the situation described by Curious6 (a pure example of distances), so that, when you shift into the domain of motion, the meaning of SR shines up effortlessly, causing an Aha! of instantaneous comprehension in all your listeners…

Would anyone take the challenge? I would, but I can’t (I am still looking for the right analogy...)

Very interesting proposal. I'd like to take it up but given that I have raised objections to SR which I'd like to see debunked I'd like someone else to try it.

 

[JesseM]

Good insight. I agree with that. What I would like to suggest though, and this differs from special relativity and is therefore controversial, is that one object IS actually moving whereas the other one is remaining stationary. Please take one minute to read the reasoning behind this statement, and then point out where it's wrong because it clearly differs from what SR says and I'd therefore appreciate it if someone could point out any flaw which I have overlooked. Take any empty field. You have two people, Mike and Jane, at rest with respect to each other, and Tim, who is about 100 meters away riding on his bicycle. Now Tim rides past Mike on his bicycle. Mike records him as being in motion. Tim records Mike as being in motion. Each other's positions change on their relative coordinate systems; each observer's reference point is equally valid - this is SR. However, Jane also notes Tim's position as changing on her coordinate system; she doesn't see Mike's position changing on her coordinate system. Not only for Mike, but for Jane, Tim has moved as well. Now you may argue that both Mike and Jane are in the same frame of reference so that doesn't matter. However, you could say that for every other object in the field, the only position that has changed is that of Tim; the relative positions between the other points in the field have remained the same.

But you've stacked the deck by including a bunch of objects at rest relative to one another and only one object in motion relative to these other objects. And all the objects at rest relative to one another are just at rest relative to the surface of the Earth which carries them--unless you are a geocentrist, why would you think the Earth is "really" at rest in an absolute sense? The point is that although some frames may seem more "natural" to use as rest frames than others because their happen to be more objects at rest in that frame in your local neighborhood, that doesn't justify the idea that these frames represent a state of absolute rest, since after all the laws of physics say that even if there was an absolute rest frame in a metaphysical sense, this frame would not be privileged as far as the laws of physics are concerned so a group of observers would make exactly the same observations regardless as to whether they were at rest in absolute space or moving at 99% the speed of light in absolute space.

Taking it one step further, all the remaining positions of points in the Universe with respect to other points have staid the same; only Tim's relation to other points in the Universe has changed. It can therefore be said Tim is in motion.

What are "positions in the universe"? Are they measurable things, so that you have an experimental way to decide whether something is at a fixed position in the universe or has a changing position in the universe? If not, then once again, you are talking about a metaphysical idea which may or may not be true, but even if it is true it would have no relevance to physics if it made no difference to the outcomes of any experiments/observations.

 

[Curious6]

But you've stacked the deck by including a bunch of objects at rest relative to one another and only one object in motion relative to these other objects. And all the objects at rest relative to one another are just at rest relative to the surface of the Earth which carries them--unless you are a geocentrist, why would you think the Earth is "really" at rest in an absolute sense? The point is that although some frames may seem more "natural" to use as rest frames than others because their happen to be more objects at rest in that frame in your local neighborhood, that doesn't justify the idea that these frames represent a state of absolute rest, since after all the laws of physics say that even if there was an absolute rest frame in a metaphysical sense, this frame would not be privileged as far as the laws of physics are concerned so a group of observers would make exactly the same observations regardless as to whether they were at rest in absolute space or moving at 99% the speed of light in absolute space.

OK, I see what you mean; you're right - the laws of physics don't differentiate between frames of reference. Nevertheless, it seems to me that if we were to imagine a still Universe then if something within that Universe would move it would only be partially right to say both the person is moving as well as the Universe is moving. This is only true if you consider the reference frame of the person moving. From all other objects or points in the Universe, it is the person who is moving though, whereas the other objects are at rest to each other. The laws of physics don't differentiate, but our common sense and intuition does. Perhaps it is a metaphysical question, but as one bearing on the nature of our reality, an important one nevertheless.

What are "positions in the universe"? Are they measurable things, so that you have an experimental way to decide whether something is at a fixed position in the universe or has a changing position in the universe? If not, then once again, you are talking about a metaphysical idea which may or may not be true, but even if it is true it would have no relevance to physics if it made no difference to the outcomes of any experiments/observations.

Positions in the Universe are basically fixed points in the fabric of space (i.e., the coordinates we can agree upon to specifically state where an object is) which are not dependent upon your point of observation. Again, perhaps a metaphysical point as you rightly pointed out. I do think though that here it comes down to your perspective on science: if physics can only tell us so much about the nature of reality, should we use our reasoning to probe deeper or should we content ourselves with what physics tells us we can know?

 

[matheinste]

Hello Curious6.

For clarification, what is your definition of absolute space?

Matheinste.

 

[Mentz114]

Curoius6 is coming at this from the wrong direction. Space is only defined by the objects in it ( in physics anyway). There's no 'absolute space' and no such thing as 'position' except as perceived by observers. I wish absolutists would stay away from this relativity forum, especially those who think they have found something that contradicts SR. What a chimera.

Who said 'everything got to be somewhere' ? ( Popeye ? )

 

[JesseM]

Positions in the Universe are basically fixed points in the fabric of space (i.e., the coordinates we can agree upon to specifically state where an object is) which are not dependent upon your point of observation. Again, perhaps a metaphysical point as you rightly pointed out. I do think though that here it comes down to your perspective on science: if physics can only tell us so much about the nature of reality, should we use our reasoning to probe deeper or should we content ourselves with what physics tells us we can know?

Perhaps this thread should be moved to the philosophy section then? As I said, relativity doesn't rule out the idea of an "absolute space" with absolutely no empirical consequences, but just from a philosophical point of view, I don't see what "reasoning" compels us to believe in such a thing, or to think of space as a "fabric" with identifiable points which persist over time. Do you also believe in an absolute coordinate grid, so that there is an absolute truth about what an object's "real" x-coordinate is at a given moment? If not, what makes the idea of an absolute truth about whether an object is moving or at rest any more compelling?

 

[atyy]

Point X is at different points on point Y's and point Z's respective coordinate systems; space is relative. Nevertheless, in reality point X is just at one single point; a position both point Y and point Z will agree upon (that's why we agree upon where objects are located; e.g., we agree the Eiffel Tower is in Paris); space is in this sense absolute.

Yes. Let's stick to Newtonian physics. The location of an object is absolute. The description of where the object is relative.

Let's have 2 objects for convenience. The vector pointing from one object to the other is absolute. But you can represent that vector in many ways. If you fix one set of axes, that vector will be some set of 3 numbers {rx,ry,rz}. If you use a set of axes rotated, the same vector will be described by a different set of 3 numbers {sx,sy,sz}. In Newtonian physics, there is an absolute number called the distance d between the two objects that can be obtained from either one of the relative descriptions:

d=sqrt(rx²+ry²+rz²)=sqrt(sx²+sy²+sz²)

 

[Curious6]

Hello Curious6.

For clarification, what is your definition of absolute space?

Matheinste.

Hi, my definition of absolute space is simply based on the observation that we can all agree on where specific objects are, that is, they occupy only point in space. Even though an object can appear at different points on different coordinate grids, taking into account one another's position yields agreement on where the object is in an absolute sense. I think the numerical example I gave about point X, point Y, and point Z clarifies the above sentence.

 

[Doc Al]

Perhaps this thread should be moved to the philosophy section then?

Sounds more appropriate to me.

 

[Curious6]

Perhaps this thread should be moved to the philosophy section then?

Our discussion has effectively led us to consider the issue from a metaphysical perspective, given that the example I put forth at the very beginning does not contradict SR, is in partial agreement with it, but also proposes a further point (i.e., that besides relative space there is also absolute space), a point which the SR framework cannot test, as you have aptly pointed out.

but just from a philosophical point of view, I don't see what "reasoning" compels us to believe in such a thing, or to think of space as a "fabric" with identifiable points which persist over time. Do you also believe in an absolute coordinate grid, so that there is an absolute truth about what an object's "real" x-coordinate is at a given moment? If not, what makes the idea of an absolute truth about whether an object is moving or at rest any more compelling?

For the while being, given that I am not convinced by any of the proposed counter-arguments, my reasoning does lead me to believe in an object having a 'real' x-, y-, and z-coordinate. This all follows from the simple observation that we agree on where objects are once we take into account our specific reference frames. I am in no sense an absolutist or have any preference for an absolute space, I am just saying that even taking into account SR we can be led to conclude through the reasoning expounded through my first example that there are absolute space coordinates.

 

[Mentz114]

Yes. Let's stick to Newtonian physics. The location of an object is absolute. The description of where the object is relative.

Let's have 2 objects for convenience. The vector pointing from one object to the other is absolute. But you can represent that vector in many ways. If you fix one set of axes, that vector will be some set of 3 numbers {rx,ry,rz}. If you use a set of axes rotated, the same vector will be described by a different set of 3 numbers {sx,sy,sz}. In Newtonian physics, there is an absolute number called the distance d between the two objects that can be obtained from either one of the relative descriptions:

d=sqrt(rx²+ry²+rz²)=sqrt(sx²+sy²+sz²)

I have to disagree with this. What you have shown is that position is meaningless but length or distance is not. Position can only be described by using a frame of reference, so absolute position implies an absolute frame. But we know that any frame can be chosen to be the absolute frame without changing any physical laws. So why bother ?

Curious6:

I am in no sense an absolutist or have any preference for an absolute space, I am just saying that even taking into account SR we can be led to conclude through the reasoning expounded through my first example that there are absolute space coordinates.

I don't follow your reasoning. "Basically, space is relative until we take into account the position of others, then space ceases to be relative."
What do you mean by 'space' ? Distance ? Or position ? You can't define distance without something to have distance between, and position is just something that some observer marks on a map.

 

[matheinste]

Hello Curious6

Quote:-
---For the while being, given that I am not convinced by any of the proposed counter-arguments, my reasoning does lead me to believe in an object having a 'real' x-, y-, and z-coordinate.------

If you have coordinates they are referred to an origin. So an object in space can be located with reference to this origin. But how do you specify the location of this origin. If you specify its coordinates these must be referred to something else and so on and son on. And of course you cannot specify the first origin as being at coordinates 0,0,0.

Matheinste.

 

[JesseM]

For the while being, given that I am not convinced by any of the proposed counter-arguments, my reasoning does lead me to believe in an object having a 'real' x-, y-, and z-coordinate.

I think you may have misunderstood what I meant--do you really believe that there are three objective universal coordinate axes with objective positions in space, regardless of how humans choose to define their own coordinate systems? And that there is a single unique position in space that is "really" the origin where these three ghostly axes meet?

 

[atyy]

Position can only be described by using a frame of reference, so absolute position implies an absolute frame.

I'm thinking that one could do something like this, where there are absolute objects, and no coordinates (frame): http://www.math.umbc.edu/~campbell/Math306Spr02/Axioms/Hilbert.html

 

[Mentz114]

I'm thinking that one could do something like this, where there are absolute objects, and no coordinates (frame): http://www.math.umbc.edu/~campbell/Math306Spr02/Axioms/Hilbert.html

Atyy,
in Hilbert space only direction of the vectors is significant. So defining a 'position' is tricky if not impossible.