Rest Length, Coordinate Length, and an argument for True Length

[PAllen]

Sure, but if you are measuring the extent of an object it takes 4 numbers: length, height, width, and duration.

Temperature certainly can be a dimension in some space, e.g. in state space, but it does not measure the extent of an object. Additionaly, from a mathematical perspective, temperature is not a dimension in the same mathematical space as space and time. Similar arguments cannot be made for excluding duration.

Just to play a little devil's advocate here, I think an objective difference for duration can be made (not questioning SR/GR conceptual model of 4-d spacetime with 'all history' materialized). That is, you can define a variety of measurement methods for spatial dimensions as measured by a specified observer. I can think of no way to measure the duration of an object, in the real world (short of particles whose complete history is limited).

 

[Dale]

I can think of no way to measure the duration of an object, in the real world.

Really? You should think a little longer, there are a couple of obvious ways to do it, which correspond geometrically to a couple of obvious ways of measuring the length of the object.

 

[Samshorn]

Yes indeed: according to the PoR, an observer cannot claim to observe the "True Length" in the same way that an observer cannot claim "Absolute Left".

I think you're mixing up concepts. There's a difference between "true" and "absolute" (and between "absolutely true" and "truly absolute"), so you shouldn't conflate them.

Alice is TRULY to Bob's left, not just apparently. And Bob is TRULY to Alice's left, not just apparently. These statements are true, regardless of observations, i.e., they are not artifacts of observation, and they are not just apparent facts, they are absolutely true facts. Now, it so happens that the quality of Leftness is, by it's definition, contingent on some specified system of reference. So it isn't meaningful to assert the something is leftward of something else without specifying a system of reference.

This is intended to show that your earlier comment was wrong, when you said the issue is not A>B per A and B>A per B, but rather A>B and B>A. The point is that these latter inequalities, with no "per", are meaningless. And a meaningful statement, such as "A>B per A", can be absolutely true, and such a statement does not conflict with "B>A per B", which is also absolutely true. These are not just apparent facts, they are absolutely true statements.

The spatial length of a stable material configuration is only definable in terms of a specified system of reference, but it IS definable within such a system, and so it is a matter of fact. Of course, matters of fact also APPEAR as matters of fact (with suitable interpretation of data), so when we say, casually, that something appears to have a certain length with reference to a certain frame, this does not signify that it is ONLY apparent. It is both apparent and true. (Naturally the concept of "appear" has multiple meanings, but it's taken for granted that readers won't be confused, since the intended meaning is obvious in context.)

Thus, for example, it would be wrong to claim that the speed of light is only "apparently" isotropic in terms of every system of inertial coordinates. The isotropy of light speed in terms of every system of inertial coordinates is perfectly true, not merely apparent. We can define other systems of coordinates in which light speed is not isotropic, but that doesn't render the former statements untrue, nor even "merely apparent".

 

[PAllen]

Really? You should think a little longer, there are a couple of obvious ways to do it, which correspond geometrically to a couple of obvious ways of measuring the length of the object.

Not coming up with anything. Maybe we are talking about different things? If I have a rock, there is no direct way to determine when it formed and when it will cease to exist. There are indirect ways, subject to many assumptions.

 

[Dale]

Not coming up with anything. Maybe we are talking about different things? If I have a rock, there is no direct way to determine when it formed and when it will cease to exist.

Sure there is. Attach a clock to the rock when it was formed and look at the reading of the clock when the rock crumbles apart. This is geometrically equivalent to measuring the length of an object by laying a tape measure along the object. Alternatively you could use a standard reference frame and measure the coordinate time from the rock's beginning and end. This is geometrically equivalent to measuring the length in the same reference frame.

Perhaps you are thinking that if your measuring device does not cover the duration of the rock then you cannot measure it, but the same is true of length.

 

[PAllen]

Sure there are. Attach a clock to the rock when it was formed and look at the reading of the clock when the rock crumbles apart. This is geometrically equivalent to measuring the length of an object by laying a tape measure along the object. Alternatively you could use a standard reference frame and measure the coordinate time from the rock's beginning and end. This is geometrically equivalent to measuring the length in the same reference frame.

I agree these are mathematically equivalent, I thought of these and various other geometric measurement definitions as well. I was pointing out the the real world accessibility of time is different from space. If I give you a rock, you can give me its spatial measurements. You can't go back and attach a clock to it when it was formed. But maybe the more realisitic comparison is that you can trivially measure the duration of your awareness of the rock (period during which its world tube was accessible to you). Correspondingly, you can't measure its spatial dimentions in the past, when it was less weathered than now. And if the rock is moving relative to you, the spatial dimensions and duration of mutual accessibility (of rock and you), will be differently measured by devices on the rock, and direct measurements by you. Ok, so my distinction is artificial. It is equivalent to complaining about something being too big to measure directly, corresponding to too long lived to measure directly.

 

[bobc2]

Sure there is. Attach a clock to the rock when it was formed and look at the reading of the clock when the rock crumbles apart. This is geometrically equivalent to measuring the length of an object by laying a tape measure along the object. Alternatively you could use a standard reference frame and measure the coordinate time from the rock's beginning and end. This is geometrically equivalent to measuring the length in the same reference frame.

Perhaps you are thinking that if your measuring device does not cover the duration of the rock then you cannot measure it, but the same is true of length.

Excellent analysis, DaleSpam. It got me thinking that you might prepare a 4-dimensional measurement rod marked off for distance measurements along the 4th dimension.

 

[GrayGhost]

I say exactly the contrary: there is no question about the reality that different views exist and I explained how that works with the train example. We fully agree on that. I disagree with calling measured contractions "real", as it suggests "true contraction", corresponding to "True Length" (there can be no doubt that a real measurement was done; thus the precision "real" cannot refer to the reality of doing measurements!).

IMO, "real" is what must exist per the math, assuming the math is consistently supported by measurement. My position is this ... to say "the contraction is real", is not to say that any other measured contraction is less real, or that the proper length is less real. They are all real. I'd say the proper POV is nothing but "special".

Again: the topic of this thread is the claim that one observer has the right to say to be observing the "True Length". That is incompatible with the PoR, as I tried to explain, and now Samshorn added a nice illustration about "True Left".

Well, I would agree that to assume a contracted length is anything-less-than-real would reduce the theory to rediculous, and violate the conservation of energy and momentum. I think everyone here agrees on the LTs solns, and also that the proper POV is "special". I mean, we never witness ourselves to ever live desynchronised or contracted in everyday experience. So when folks say "the proper length is the true length, or the real length", they really mean nothing more than "the proper length is special". Because they declare it as "the true or the real" length, they then run into a problem when explaining what a contracted moving length is. IOWs, it's real "but not as real", so it's an untrue or apparent length. But then what does this mean? What is the implication of the theory under such an interpetation? Is momentum really conserved if real is one sided? I figure it best to say "proper and contracted" vs "real/true and apparent", with the proper POV being "special".

GrayGhost

 

[harrylin]

IMO, "real" is what must exist per the math, assuming the math is consistently supported by measurement. My position is this ... to say "the contraction is real", is not to say that any other measured contraction is less real, or that the proper length is less real. They are all real. I'd say the proper POV is nothing but "special". [..]
when folks say "the proper length is the true length, or the real length", they really mean nothing more than "the proper length is special". Because they declare it as "the true or the real" length, they then run into a problem when explaining what a contracted moving length is. IOWs, it's real "but not as real", so it's an untrue or apparent length. But then what does this mean? What is the implication of the theory under such an interpetation? Is momentum really conserved if real is one sided? I figure it best to say "proper and contracted" vs "real/true and apparent", with the proper POV being "special".

GrayGhost

Obviously we equally disagree with the OP's idea that a proper measurement provides the "True Length".

Apart of that, it appears that you mean with the word "real" what Einstein (as well as I) call "apparent", and I tried to explain why the use of "real" for "apparent" leads to misunderstandings. But I'm not going to waste time on a discussion about words!


Harald

 

[harrylin]

[..] Alice is TRULY to Bob's left, not just apparently. And Bob is TRULY to Alice's left, not just apparently. These statements are true, regardless of observations, i.e., they are not artifacts of observation, and they are not just apparent facts, they are absolutely true facts.

To the left and to the right are only "absolutely true facts" regardless of observations if one relates those statements to a reference system (or group of systems) with respect to which they are observed as that.

Now, it so happens that the quality of Leftness is, by it's definition, contingent on some specified system of reference. So it isn't meaningful to assert the something is leftward of something else without specifying a system of reference.

This is intended to show that your earlier comment was wrong, when you said the issue is not A>B per A and B>A per B, but rather A>B and B>A. The point is that these latter inequalities, with no "per", are meaningless. [..]

A>B (as I said, with the qualifier "True Length") is the topic of this thread.
There is no question or discussion about "measured length per coordinate system" but about "True Length". In the context of relativity of motion, "true" and "absolute" have been synonyms since the time of Newton and in line with that idea, the OP claimed that coordinate length is a distorted view of the rest length which would be the True Length.

My point was that such a "True length" is not compatible with the PoR, as according to the PoR nobody can claim that his measurements are more "true" than those of a system in relative inertial motion (or, if you like: such a "true length" is "meaningless" in view of the PoR).

Cheers,
Harald

 

[Samshorn]

To the left and to the right are only "absolutely true facts" regardless of observations if one relates those statements to a reference system (or group of systems) with respect to which they are observed as that.

You shouldn't include the word "observed". The fact that Alice is to Bob's left is not a matter of observation, per se. "Bob's left" is a perfectly well defined quality, and Alice possesses it absolutely, regardless of whether she or Bob or anyone else 'observes' it. So rather than saying "with respect to which they are observed as that", you should simply say "with respect to which they are true". Alice is truly to Bob's left, not just apparently to Bob's left.

There is no question or discussion about "measured length per coordinate system" but about "True Length".

Again, use of the word "measured" is misguided. Instead of saying "measured length per coordinate system", you should simply say "true length per coordinate system". This is a well-defined quantity, regardless of whether it is measured. The concept of spatial length of an object has no meaning without specifying some coordinate system, but once a coordinate system is specified, the length of an object in terms of that coordinate system is a matter of absolute fact, regardless of whether it is measured or observed.

In the context of relativity of motion, "true" and "absolute" have been synonyms since the time of Newton...

I think you mean "in the context of absolute motion", which was the context in which Newton used the word "true" as a synonym for "absolute". Obviously in the context of relativity of motion the expression "absolute motion" is meaningless, so it can't be a synonym for anything meaningful.

...in line with that idea, the OP claimed that coordinate length is a distorted view of the rest length which would be the True Length.

The rest length of an object is the true length relative to the object's rest frame, although the word "true" is sort of redundant.

My point was that such a "True length" is not compatible with the PoR, as according to the PoR nobody can claim that his measurements are more "true" than those of a system in relative inertial motion (or, if you like: such a "true length" is "meaningless" in view of the PoR).

You're still confusing true with absolute (see above). The expression "absolute left" is meaningless, but the expression "true left" is not meaningless (although somewhat redundant, since left and true left mean the same thing). Alice is truly (not just apparently) to Bob's left.

 

[GrayGhost]

Obviously we equally disagree with the OP's idea that a proper measurement provides the "True Length".

Yes, but I'd have ended your sentence this way ...

... "the True Length".​

Apart of that, it appears that you mean with the word "real" what Einstein (as well as I) call "apparent", and I tried to explain why the use of "real" for "apparent" leads to misunderstandings.

Einstein used the words "appears shortened", as opposed to "is apparently shorter" in his 1905 OEMB, at least thru section 3. To say "appears shortened" means either "is measured shortened" or "exists as shortened and supported by measurement". The problem is that when some folks say "is apparently shorter", they mean "it seems to be shortened but really is not" ... and therein lies the problem. If moving contracted lengths and proper lengths are anything less than real, then nothing in physics is real, IMO.

But I'm not going to waste time on a discussion about words!

"True" is a word, and that's the topic of the thread :)

GrayGhost

 

[harrylin]

Yes, but I'd have ended your sentence this way ...

... "the True Length".​

Yes, exactly! ("The Truth").

Einstein used the words "appears shortened", as opposed to "is apparently shorter" in his 1905 OEMB, at least thru section 3.
To say "appears shortened" means either "is measured shortened" or "exists as shortened and supported by measurement". The problem is that when some folks say "is apparently shorter", they mean "it seems to be shortened but really is not" ... and therein lies the problem.

I would say, "appears shortened" simply means "is measured shortened" (without existential claim). The dictionary is quite clear about that, it is simply what is perceived.
And "appears shortened" and "is apparently shorter" have the same meaning for me. For the meaning of "really is not", the usual expression is "only apparently" (which Einstein also uses in that text).

If moving contracted lengths and proper lengths are anything less than real, then nothing in physics is real, IMO.

It is popular to say that we can only make models of reality and never know reality itself. But I think that that is a bit too pessimistic, with increasing knowledge we can get improved understanding of reality.

"True" is a word, and that's the topic of the thread :)
GrayGhost

Sure - but such words are in the realm of metaphysics, or philosophy - and that's a never-ending story.

 

[harrylin]

You shouldn't include the word "observed". The fact that Alice is to Bob's left is not a matter of observation, per se. "Bob's left" is a perfectly well defined quality, and Alice possesses it absolutely, regardless of whether she or Bob or anyone else 'observes' it. So rather than saying "with respect to which they are observed as that", you should simply say "with respect to which they are true". Alice is truly to Bob's left, not just apparently to Bob's left. [..]

Yes, Alice is truly to Bob's left. Evidently you missed the point of this thread, as you also say that "true" is redundant. However, I expressed my agreement with your illustration that "The concepts of leftness and rightness have no meaning without specifying the reference system".

The idea that Bob's measurements correspond to "The True Length" so that Alice's measurements would be distorted is just as incompatible with modern physics as "True Leftness" in the case of Bob's opinion with Alice and Bob next to each other, facing in different directions. To make the comparison applicable, Bob says that Alice "Is Truly Left" of him, and that her view is distorted. In both cases, Alice would have equal right of claiming the contrary; neither can claim to have The True View.

I hope that it is clear now; but if not, please reply to the original post!

 

[GrayGhost]

For the meaning of "really is not", the usual expression is "only apparently" (which Einstein also uses in that text).

Harrylin,

Yes, but I do not see where Einstein used "only apparently" in OEMB, as you said he did. Maybe you can point that statement out for me. I do see "appears" and "appears shortened", but not "only apparently".

It seems that Einstein made the assumption in his 1905 OEMB that "observations" would match "what must presently exist per the math". IOWs, the effects of light transit time were not accounted for "far as the observed image goes". Terrell and Penrose considered those effects much later.

GrayGhost

 

[bobc2]

One measures the dimensions of objects with rulers... Length, width and height. Thus 3D, obviously!

BobC2 said: "If you are talking about observers making measurements on a 3-D rod, then you must recognize that the two observers are not even looking at the same rod. So it would not be correct to say that a given 3-D rod has two different measurements that are unequal."

You lost me there. Do you disagree with special relativity? By definition it is the same object:

A rigid body which, measured in a state of rest, has the form of a sphere, has in a state of motion (viewed from the stationary system) the form of an ellipsoid.
- http://www.fourmilab.ch/etexts/einstein/specrel/www/

If you accept the 4-D objects, it would be easy to reconcile the two different views for observers A and B below. In your view (we only have 3-D objects) one might say that A and B are viewing two different objects (this is the sense which I was referring to the other day).

The two observers are asked to record the object present in their 3-D space when each reaches the same proper time along their respective fourth dimension. Later they get back together to compare notes. Observer A reports the object is a space shuttle orbiter. Observer B reports the object is a car.

Did they both have the same 3-D object in their respective 3-D worlds?

 

[harrylin]

Harrylin,

Yes, but I do not see where Einstein used "only apparently" in OEMB, as you said he did. Maybe you can point that statement out for me. I do see "appears" and "appears shortened", but not "only apparently".

It seems that Einstein made the assumption in his 1905 OEMB that "observations" would match "what must presently exist per the math". IOWs, the effects of light transit time were not accounted for "far as the observed image goes". Terrell and Penrose considered those effects much later.

GrayGhost

Do you use another translation perhaps? With word search you find "only apparently" in the very first section:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

And yes, "observations" do not relate to telescope images but to determinations by means of measurements.


Harald

 

[harrylin]

[..]If you accept the 4-D objects, it would be easy to reconcile the two different views for observers A and B below. In your view (we only have 3-D objects) one might say that A and B are viewing two different objects (this is the sense which I was referring to the other day).

It was my point that the view that what I call two perceptions of the same object are "two different objects" is incompatible with Einstein's SRT (as well as with mine). If you disagree, please explain the passage that I already cited - here it is again:

"A rigid body which, measured in a state of rest, has the form of a sphere, has in a state of motion (viewed from the stationary system) the form of an ellipsoid."

Of course, it is a matter of definitions, what is meant with "an object" or "a body"...

The two observers are asked to record the object present in their 3-D space when each reaches the same proper time along their respective fourth dimension. Later they get back together to compare notes. Observer A reports the object is a space shuttle orbiter. Observer B reports the object is a car.

Did they both have the same 3-D object in their respective 3-D worlds?

[space-time diagram of transforming transformer]

That's a nice illustration! Still, it doesn't cut wood I'm afraid; it will still be a transformer, and if it is a permanent change one normally says that the observers perceive the time of transformation differently.
In normal language use, A typical 3D object like a rocket that is accelerated to speed and that next returns to Earth is still considered the same rocket (even if it lost a few boosters!). And during that set of events, the different perceptions of time rate and length occurred.

Perhaps you know the illustration of the elephant as "seen" by two blind people. They feel the elephant partly at different locations and give differing descriptions of the elephant. Do they describe two different elephants, or do they give two different descriptions of the same elephant?

 

[bobc2]

boosters!). Perhaps you know the illustration of the elephant as "seen" by two blind people. They feel the elephant partly at different locations and give differing descriptions of the elephant. Do they describe two different elephants, or do they give two different descriptions of the same elephant?

Yes, I'm very familiar with the elephant example. And you just made my point perfectly. Once you know the complete picture there is no paradox whatever. Since we understand the total object, its extent in all dimensions, etc., there is no puzzle. Once you acknowledge objects as four dimensional, then all of the SR paradoxes are resolved--the phenomena are explained. See, you could have tried to account for the different perceptions of the elephant by saying, "For observers standing in different positions the measurements are just different--that's just the way nature works." Better to understand an explanation for the phenomena by explaining that it is a big elephant and observers are just experiencing different views of the same elephant.

I was just trying to illustrate the advantage of understanding SR phenomena in the context of four dimensions and 4-D objects, rather than being satisfied by just saying, "...three dimensional objects just appear to be different for observers moving at various relativistic speeds--that's just the way nature works." For me such statements do not explain anything--they just itemize the observations.

 

[GrayGhost]

Do you use another translation perhaps? With word search you find "only apparently" in the very first section:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

And yes, "observations" do not relate to telescope images but to determinations by means of measurements.


Harald

In OEMB section I ...

We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity'') to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.​

However, the highlight here has nothing to do with "proper versus contracted length", so it doesn't apply to our discussion. Here, Einstein is discussing the compatibility of the principle of relativity with the speed of light. Nowehere does Einstein say the moving contracted length is "only apparent".

Also, whether APPEARS = ONLY APPARENTLY depends IMO on how it is used in context.

GrayGhost

 

[PAllen]

I would like to motivate the point of view (I forget whether it was raised by bobc2 or greyghost) that it is very reasonable to view the differfent lengths measured in different frames of reference as being measurements of different 3-d object.

Start with the observation that the spacetime description of the object is a 4-d world tube. Each observer's measurement of a 3-d object involves slicing it differently - using different 3-d hypersurfaces, incorporating in the slices completely different sets of events. Clearly, these are all derived from the same 4-d world tube. How should we view the different slices?

Well, going to 3-d geometry, consider conic sections. We have 3-d solid cone. We slice it different ways getting circular discs, elliptical discs, hyperbolic sections. Even thougth all the slices come from the same 3-d object, would we normally consider the different slices as representing the same 2-d object? I would, instead, think of each slice as different 2-d object derived from the same 3-d object.

Similarly, it seems perfectly valid to treat the differently measured 3-d objects as different 3-d objects derived from the same 4-d object. Which 3-d object you derive from your 'natural' foliation of spacetime determines what you will measure.

 

[bobc2]

I would like to motivate the point of view (I forget whether it was raised by bobc2 or greyghost) that it is very reasonable to view the differfent lengths measured in different frames of reference as being measurements of different 3-d object.

Start with the observation that the spacetime description of the object is a 4-d world tube. Each observer's measurement of a 3-d object involves slicing it differently - using different 3-d hypersurfaces, incorporating in the slices completely different sets of events. Clearly, these are all derived from the same 4-d world tube. How should we view the different slices?

Well, going to 3-d geometry, consider conic sections. We have 3-d solid cone. We slice it different ways getting circular discs, elliptical discs, hyperbolic sections. Even thougth all the slices come from the same 3-d object, would we normally consider the different slices as representing the same 2-d object? I would, instead, think of each slice as different 2-d object derived from the same 3-d object.

Similarly, it seems perfectly valid to treat the differently measured 3-d objects as different 3-d objects derived from the same 4-d object. Which 3-d object you derive from your 'natural' foliation of spacetime determines what you will measure.

Seems like a reasonable line of thought, PAllen. You get your 3-D objects without giving up the 4-D object.

 

[Dale]

We slice it different ways getting circular discs, elliptical discs, hyperbolic sections. Even thougth all the slices come from the same 3-d object, would we normally consider the different slices as representing the same 2-d object? I would, instead, think of each slice as different 2-d object derived from the same 3-d object.

That does sound reasonable. Would you EVER consider calling a parabola or some other section "the true slice" or "the true 2D object"?

 

[PAllen]

That does sound reasonable. Would you EVER consider calling a parabola or some other section "the true slice" or "the true 2D object"?

Not generally. One might invent technical terms for certain slices e.g. if the body has an axis of symmetry, you might want to distinguish 'orthogonal' slices as those orthogonal to an axis of symmetry. Or, for a more complex tube, if there exist slices orthogonal to the entire boundary surface, you might call those orthogonal slices as well. Then, if you refer to a cross section without any further qualification, it may be 'understood' to refer to some such special slice, and be meaningless if there is no such special slice. These technical terms match with use of a term like 'rest frame length' when it is well defined (e.g. for s sufficiently rigid body), for a slice 4-orthgonal to all world lines in a world tube.

The idea here is more of a 'standard' description rather than a 'true' description.

 

[Dale]

The idea here is more of a 'standard' description rather than a 'true' description.

Good. I am a fan of standards and conventions. They make communication easier and don't pretend to be anything they are not.

 

[GrayGhost]

... it seems perfectly valid to treat the differently measured 3-d objects as different 3-d objects derived from the same 4-d object. Which 3-d object you derive from your 'natural' foliation of spacetime determines what you will measure.

Well, I'll have to think on that more. There is a difference between 2 different atoms considered at the same time, versus 1 atom considered at 2 different times.

GrayGhost

 

[John232]

Well, I'll have to think on that more. There is a difference between 2 different atoms considered at the same time, versus 1 atom considered at 2 different times.

GrayGhost

LOL, sounds like you would be in favor of Star Trek teleportation. I don't really see the difference in the same atom being used to replicate an object as opposed to another identical atom being used to produce carbon. The only difference would be the quantum uncertainty of the position of its electrons, and if that is uncertain then there would be no way to reproduce an identical atom as the exact speed and postinon of its electrons would be unceartain.

 

[GrayGhost]

LOL ...

Well, this thread is about whether a length should be considered "the true length", thereby reducing other measured lengths of the same body to something less-than-real. The context is special relativity, not teleportation. So, I'm not quite sure how your comment applies here?

GrayGhost

 

[harrylin]

In OEMB section I ...

We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity'') to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.​

However, the highlight here has nothing to do with "proper versus contracted length", so it doesn't apply to our discussion. Here, Einstein is discussing the compatibility of the principle of relativity with the speed of light. Nowehere does Einstein say the moving contracted length is "only apparent".

Also, whether APPEARS = ONLY APPARENTLY depends IMO on how it is used in context.

GrayGhost

I can see nothing difficult here...

- Appears = apparently. By definition, appearance may be true or deceptive.
- only apparently = not really.

Where in his paper did you think to see a different use of language?

Cheers,
Harald

 

[harrylin]

[..]
I was just trying to illustrate the advantage of understanding SR phenomena in the context of four dimensions and 4-D objects, rather than being satisfied by just saying, "...three dimensional objects just appear to be different for observers moving at various relativistic speeds--that's just the way nature works." For me such statements do not explain anything--they just itemize the observations.

I fully agree with your criticism of "that's just the way nature works".

For me Lorentz contraction and clock retardation explain it all (together with the speed of light as a constant of nature). Those effects can be found as consequences of the conservation laws - but that's another topic.