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

[GregAshmore]

In an earlier thread, I asserted that a rod has one true length, its rest length. If so, then the shorter coordinate length which is measured in some other frame must be somehow untrue. In this thread I argue that the coordinate length is a distorted view of the true length.

In the graphic below (fig. 1), there are two rods, each with a rest length of four units. The horizontal rod is at rest in frame S; the other rod is at rest in frame M. Frame M is moving at 0.6c relative to frame S. In this discussion, the focus will be on the rod in frame M [red], and its coordinate length in frame S [purple].

http://www.how-do-i-know-its-true.net/media/wpmu/uploads/blogs.dir/1/files/2011/02/RodMovementNumbered.png

[1] The rod which is at rest in frame M will always be parallel to the XM axis, no matter at what time the rod is drawn. Thus each instance of the rod in the graphic is parallel to the XM axis.

[2] The view of the rod from frame S (its coordinate length) is horizontal. Therefore, the view is not one view, but a composite of many views. The coordinate length is composed of many snapshots, each snapshot showing a specific point on the rod at a specific time in frame M. In the graphic, four instances of the rod are marked as they cross time TS = 6.68. The four marked points of the rod are at times TM = 5.35, 6.01, 6.67, and 7.33, respectively. The fifth mark, at TM = 7.75, is where the trailing end of the rod crosses TS = 6.68; no instance of the rod is drawn at that point.

[3] As one moves along the view of the rod in frame S, from leading end to trailing end, the time in frame M increases. This means that, in the view as seen from frame S, the trailing end of the rod has traveled farther than the leading end of the rod. This explains, qualitatively, the contracted coordinate length in frame S.

[4] When the velocity is reversed, the effect is the same, as shown in this graphic (fig. 2):

http://www.how-do-i-know-its-true.net/media/wpmu/uploads/blogs.dir/1/files/2011/02/RodMovementReverse.png

[5] The time differential from the leading end to the trailing end is equal to the relative velocity of the two frames multiplied by the rest length of the rod. In this example, (7.75 - 5.35) = 2.4 = 0.6 * 4, where T = ct and V = v/c. This can be better seen in figure 3:

http://www.how-do-i-know-its-true.net/media/wpmu/uploads/blogs.dir/1/files/2011/02/LengthContraction.png

Thus, the apparent contraction of the rod is directly related to the relative velocity of the frames. Taylor and Wheeler show that the contracted length can be developed by integrating from relative velocity 0 to V. (See exercise L-14 in Spacetime Physics.) Their interpretation is that the trailing end of the rod, as seen in frame S, begins to move before the leading end, thus contracting the rod in frame S. (The same is true for each differential segment of the rod. The differential time at each segment is smaller than at the trailing end, thus leading to a contraction proportional to the length.)

The interpretation proposed here is that the integration describes the compressive shifting of the individual snapshots in frame S. The coordinate length of the rod in frame S is thus a distorted view of the rod, while the rod itself is completely unaffected. The rest length of the rod is therefore its one true length.

Of course, the measured coordinate length is the same regardless of the interpretation of the result.

 

[John232]

In relativity the length of an object doesn't change due to an outside observer traveling at relativistic speeds as it is anyways. For example, a ship traveling 0.6c relative to Earth couldn't make us earthlings observe ourselves to be distorted in the ships direction of motion. I don't think it actually proves that there is no length contraction, but the contraction is only observed differently by different observers.

I think it is key to remember that the length contraction is used to only maintain the constant speed of light. In time dialation, the amount of time you observe another object to expereince has to be a value that makes you see them measure the speed of light to be the same as you do. If they expereince the dilation themselves this wouldn't happen because they measure light to still travel the same 300,000 km/s or so faster than them. So then two observers couldn't see themselves as their measuring rods as being a different length because the measured speed of light is always the same speed faster for both of the two, otherwise the theory would be useless because they would measure different speeds of light with their distorted measureing rods.

 

[bcrowell]

In an earlier thread, I asserted that a rod has one true length, its rest length.

Please define "true."

 

[GrayGhost]

GregAshmore,

You are thorough, I'll give you that.

There is the "proper length" of a body, observable by only those who reside at rest in the proper frame of said body.

There is the "contracted length", observable by only those in luminal motion wrt (the proper frame of) the body.

Relative motion allows us to witness the body as it exists "not in its own instant of time", but rather as it exists "across a duration of its own time". Technically, as it exists "over a length of its own worldline" thru spacetime. Temporally, and wrt its own sense of time, FWD points of the moving body lag AFTward points.

That said, its not about "true or real" vs "untrue or apparent". It's about "proper vs non-proper". There is a "proper view" of the body, which can only be obtained while at rest with the body. There also exists a "non-proper (rotated) view" of the body, when seen in motion. Both views are verifiable via measurement (in theory) by the observer. Neither is less real, or less true, than the other. It's all about POV.

There is one point worth mentioning IMO. None of us ever experience ourselves except in the moment. If we do exist in the continuum as luminally moving others record of us, we are unware of this in our own experience. Yet, this alone does not require that the rotated view does not exist, or that it is any less true or real. The mathematics of the theory require it.

Good work though ! Believe me, everyone who understands relativity theory eventually came across your discovery here at one time or another, and questioned it at length. So, you are in good company.

GrayGhost

 

[ghwellsjr]

Greg, when you think about two rods with a relative motion between them, do you think that the true speed of both of them is zero? Or do you think that the true speed of both of them is whatever their relative speed is? Or do you think that the true speed of both of them is some smaller identical value but in opposite directions?

I doubt it. I'm going to guess that you have no problem with the concept of relative speed and you realize that even though each one views the other one as traveling in the opposite direction at the same speed, you understand that you cannot then say that the true difference in speed is double their relative speed.

It is a fact that when two rods are in relative motion, you cannot say that both are stationary at the same time and for the same reason, you cannot say that both their true lengths are their rest lengths at the same time. Special Relativity is all about picking a single frame of reference from which to assign locations, dimensions, and times to everything. It is not possible to pick a frame of reference in which both rods will be their rest length.

If we could say that the length of one rod was its true length, then we would also be saying that we have identified the absolute ether rest frame and the true length of the second moving rod would be a contracted length. When you rotate the first rod, since it is stationary in the ether, its true length will remain the same but when you rotate the second moving rod, its true length would be changing, even though its speed is not changing.

So the bottom line is that your effort to attribute "trueness" to a rod's length is no different than an effort to promote an absolute ether rest frame. Is that really what you want to do?

 

[Dale]

Hi GregAshmore, none of what you presented here is new, surprising, or unusual. It does not change the way that the term "length" is defined nor does it make anything about that definition invalid.

You are certainly free to adopt the arbitrary personal definition that the term "true length" means the same as the common term "proper length". In fact, you don't need any of the above justification to do so, you can simply assert "I am defining the term 'true length' to mean the proper length". However, since a common term already exists for the concept why not use it? All you are going to accomplish with this approach is to make communication barriers and encourage confusion.

 

[ghwellsjr]

In an earlier thread, I asserted that a rod has one true length, its rest length. If so, then the shorter coordinate length which is measured in some other frame must be somehow untrue. In this thread I argue that the coordinate length is a distorted view of the true length.

...

The coordinate length of the rod in frame S is thus a distorted view of the rod, while the rod itself is completely unaffected. The rest length of the rod is therefore its one true length.

Of course, the measured coordinate length is the same regardless of the interpretation of the result.

But, DaleSpam, would you also say that Greg is free to call a contracted "measured coordinate length" the "untrue length" or "a distorted view of the true length" and that rods are "completely unaffected" by their accelerations?

I'm saying that when two rods are in relative motion, Greg needs to understand that they cannot both be at rest at the same time, and so it is not a true statement that their "true lengths" are the same as their "rest lengths".

 

[PAllen]

Hi GregAshmore, none of what you presented here is new, surprising, or unusual. It does not change the way that the term "length" is defined nor does it make anything about that definition invalid.

You are certainly free to adopt the arbitrary personal definition that the term "true length" means the same as the common term "proper length". In fact, you don't need any of the above justification to do so, you can simply assert "I am defining the term 'true length' to mean the proper length". However, since a common term already exists for the concept why not use it? All you are going to accomplish with this approach is to make communication barriers and encourage confusion.

Dalespam,

I have only seen proper length described as length measured between two spacetime points in an inertial frame in which they are simultaneous (SR; more complex in GR). It is invariant given the points (and the implied geodesic between them). Thus one can talk about the proper length of a moving ruler, whose end events will not be simultaneous in the frame of the ruler, but are simultaneous in the frame of the observer seeing the moving ruler.

OP is defining proper length in the frame in which the ruler is at rest, sort of analgous to rest mass. I haven't seen such a definition in any of my books (or in Wikipedia def. of proper length). Seems a somewhat interesting idea.

Can you clarify this terminology?

 

[Meir Achuz]

Hi Greg,
I agree with your assertion that "a rod has one true length, its rest length.",
but I find your pictures confusing.
You might want to look at <http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v3.pdf>.

 

[GregAshmore]

But, DaleSpam, would you also say that Greg is free to call a contracted "measured coordinate length" the "untrue length" or "a distorted view of the true length" and that rods are "completely unaffected" by their accelerations?

In relativity--both special and general--every observer is always at rest. As a given observer sees it, all other objects are moving; he himself is stationary. What, then, is the meaning of "their accelerations"? And, how can a rod be affected by acceleration if it never accelerates?

I'm saying that when two rods are in relative motion, Greg needs to understand that they cannot both be at rest at the same time, and so it is not a true statement that their "true lengths" are the same as their "rest lengths".

Each rod is at rest, so far as its resident observer is concerned. Each observer says that it is the other rod which is in motion. No one can prove either one of them wrong.

 

[GregAshmore]

Hi GregAshmore, none of what you presented here is new, surprising, or unusual. It does not change the way that the term "length" is defined nor does it make anything about that definition invalid.

I didn't expect that I would be the first to interpret length contraction this way. However, I have not seen this interpretation in the books I have read.

The choice to accept or reject the coordinate length as a valid length of the object will be driven by one's philosophy of reality. There is no disagreement as to the result of the measurement.

You are certainly free to adopt the arbitrary personal definition that the term "true length" means the same as the common term "proper length". In fact, you don't need any of the above justification to do so, you can simply assert "I am defining the term 'true length' to mean the proper length".

For me, the issue is the meaning of the measurements. Such questions cannot be resolved by the adoption of a definition.

However, since a common term already exists for the concept why not use it? All you are going to accomplish with this approach is to make communication barriers and encourage confusion.

I'm not trying to change the world. I have no problem with using the accepted terms in all discussions of practical matters.

 

[GregAshmore]

Hi Greg,
I agree with your assertion that "a rod has one true length, its rest length.",
but I find your pictures confusing.
You might want to look at <http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v3.pdf>.[/QUOTE]
Thanks for the link. I've started reading the paper; I'll finish it this evening.

I found the opening paragraph very interesting. I'll bet it gives DaleSpam fits. (I appreciate your point of view, DaleSpam. There is little practical value in a philosophical discussion of "reality". That's why such discussions must be limited to the appropriate times and places.)

We have put the term ‘Lorentz contraction’ in quotes, because, as we will ex-
plain, Lorentz contraction is not what actually occurs for a moving object in
special relativity (SR). This is well known to most physicists, but too often
‘Lorentz contraction’ is given a spurious physical reality.

 

[Dale]

I have only seen proper length described as length measured between two spacetime points in an inertial frame in which they are simultaneous (SR; more complex in GR). It is invariant given the points (and the implied geodesic between them). Thus one can talk about the proper length of a moving ruler, whose end events will not be simultaneous in the frame of the ruler, but are simultaneous in the frame of the observer seeing the moving ruler.

OP is defining proper length in the frame in which the ruler is at rest, sort of analgous to rest mass. I haven't seen such a definition in any of my books (or in Wikipedia def. of proper length). Seems a somewhat interesting idea.

Can you clarify this terminology?

You are correct. According to my understanding the term "proper length" (or better "proper distance") refers to the invariant interval between two spacelike separated events. Whereas the term "rest length" refers to the length of an object in the reference frame where it is at rest. For massive inertial objects they are equivalent so the distinction is somewhat hazy at times. This is similar to "invariant mass" vs "rest mass".

 

[Dale]

The choice to accept or reject the coordinate length as a valid length of the object will be driven by one's philosophy of reality.

One's philosophy of reality is not relevant here. The coordinate length is the length of the object in the given reference frame by definition. There is no question of validity, it is defined as such.

Although you are free to introduce new terms and their definitions you are not free to un-define already defined terms.

For me, the issue is the meaning of the measurements. Such questions cannot be resolved by the adoption of a definition.

Then I don't know what you hope to accomplish by defining your new term "true length".

IMO, the entire discussion is purely semantic and will remain purely semantic while you focus on introducing new words for already defined concepts. You would be better off to simply adopt the existing terminology "coordinate length" and "proper length" and discuss the physics.

 

[Dale]

In relativity--both special and general--every observer is always at rest.

I wouldn't say it this way. I would say that for every observer there exists a valid frame where that observer is at rest. However, the observer is no more constrained to use that frame than any other frame.

What, then, is the meaning of "their accelerations"? And, how can a rod be affected by acceleration if it never accelerates.

Acceleration is not relative, particularly not proper acceleration.

 

[bcrowell]

GregAshmore, please listen to what DaleSpam is trying to tell you. You're not accomplishing anything meaningful here.

 

[PAllen]

You are correct. According to my understanding the term "proper length" (or better "proper distance") refers to the invariant interval between two spacelike separated events. Whereas the term "rest length" refers to the length of an object in the reference frame where it is at rest. For massive inertial objects they are equivalent so the distinction is somewhat hazy at times. This is similar to "invariant mass" vs "rest mass".

Actually, the part I don't quite agree with is that proper length of a massive body is equivalent to rest length as you've (and Greg and the paper linked by Clem) have defined it. Proper length is defined for the object in motion, and is then less than rest length. That is, an observer seeing the massive object in motion perceives a different slice of its world tube as simultaneous than the object's rest frame, and proper length along a cut of this slice will be shorter than proper length along a cut of the simultaneity slice of the object's rest frame. So proper length of a massive object is observer dependent (even though it is invariant *given* a particular simultaneity slice), while rest length is defined as observer independent by the specification that is always computed in the object's rest frame.

 

[ghwellsjr]

Greg, what do you say about two clocks in relative motion? Do you agree with these comments:

I assert that a clock keeps one true time, its rest time. If so, then the dilated coordinate time which is measured in some other frame must be somehow untrue. I argue that the coordinate time is a distorted view of the true time.

A clock is completely unaffected by acceleration. It is always at rest and keeping its one true time.

 

[Dale]

Actually, the part I don't quite agree with is that proper length of a massive body is equivalent to rest length as you've (and Greg and the paper linked by Clem) have defined it. Proper length is defined for the object in motion, and is then less than rest length. That is, an observer seeing the massive object in motion perceives a different slice of its world tube as simultaneous than the object's rest frame, and proper length along a cut of this slice will be shorter than proper length along a cut of the simultaneity slice of the object's rest frame. So proper length of a massive object is observer dependent (even though it is invariant *given* a particular simultaneity slice), while rest length is defined as observer independent by the specification that is always computed in the object's rest frame.

When you say "proper length between events A and B" it is simply the (spacelike) spacteime interval. When you say "proper length of object A" you are not specifying the events explicitly. The events are then implicitly chosen to be the end points of the object which are simultaneous in the object's frame. At least that is my understanding.

 

[PAllen]

When you say "proper length between events A and B" it is simply the (spacelike) spacteime interval. When you say "proper length of object A" you are not specifying the events explicitly. The events are then implicitly chosen to be the end points of the object which are simultaneous in the object's frame. At least that is my understanding.

Ok, fine, with that definition. I guess the confusion there is why the paper linked by Clem proposed the term rest length to be unambiguous.

 

[GrayGhost]

I've always seen it used in this way, and I've always used it this way ...

The proper length of a body "is its rest length". It's the largest recordable length for a body. The most important thing ... just as in the case of the spacetime interval (where the observer is present at both events), the proper length is an invariant ... all agree. IOWs, the moving contracted length is not a proper length.

The word PROPER, as I've ever seen it used, relates to the POV of that which is being measured. IOWs, it's the measurement result if relativistic effects are non-existent.

GrayGhost

 

[GregAshmore]

I wouldn't say it this way. I would say that for every observer there exists a valid frame where that observer is at rest. However, the observer is no more constrained to use that frame than any other frame.

True, an observer is not constrained to use his rest frame only. In the context of ghwellsjr's post, the important thing is that every observer is at rest, if he chooses to be.

Acceleration is not relative, particularly not proper acceleration.

If I understand Born and Einstein correctly, the achievement of general relativity was the "relativization" of acceleration through the equivalence of inertial and gravitational mass.

I have a suspicion that the effort was not entirely successful. The resolution of the twin paradox is based on the fact that one of the two twins is not in an inertial frame--accelerating. Therefore, there is a kind of absolute reality to acceleration, even though Born says that GR does away with it. However, I limit myself to "suspicion" until I learn the math of GR--my next project.

Regardless, my point was that an object at rest does not accelerate. If it is true that every observer may always consider himself to be at rest, then he never accelerates. In that case, I don't know what ghwellsjr means by the effect on an object of the object's acceleration.

 

[PAllen]

True, an observer is not constrained to use his rest frame only. In the context of ghwellsjr's post, the important thing is that every observer is at rest, if he chooses to be.


If I understand Born and Einstein correctly, the achievement of general relativity was the "relativization" of acceleration through the equivalence of inertial and gravitational mass.

I have a suspicion that the effort was not entirely successful. The resolution of the twin paradox is based on the fact that one of the two twins is not in an inertial frame--accelerating. Therefore, there is a kind of absolute reality to acceleration, even though Born says that GR does away with it. However, I limit myself to "suspicion" until I learn the math of GR--my next project.

Regardless, my point was that an object at rest does not accelerate. If it is true that every observer may always consider himself to be at rest, then he never accelerates. In that case, I don't know what ghwellsjr means by the effect on an object of the object's acceleration.

You may say GR has a lot less 'relativity' in it than SR. It only accomplished that an accelerated object may consider itself at rest in a gravititational field. Similarly, an object at rest in a gravitational field is actually a non-inertial observer, with a real acceleration (relative to any adjacent inertial object; an inertial object would be in free fall).

An object at 'rest' in an accelerating rocket can in no way consider their frame equivalent to an inertial frame. It can be considered equivalent to an observer standing on planet of appropriate gravity.

Note that for measurements over significant distances, even this equivalence breaks down. Accleration and gravity are absolutely distinguishable by the absence of tidal forces in the former case.

 

[GregAshmore]

Greg, what do you say about two clocks in relative motion? Do you agree with these comments:

I assert that a clock keeps one true time, its rest time. If so, then the dilated coordinate time which is measured in some other frame must be somehow untrue. I argue that the coordinate time is a distorted view of the true time.

A clock is completely unaffected by acceleration. It is always at rest and keeping its one true time.

I'm not sure what I think about it. My initial reaction is that distance and time are not interchangeable, so the parallelism which you have drawn between true length and true time will perhaps not hold up under scrutiny. For example, what precisely do you mean by "view of time"?

 

[GregAshmore]

GregAshmore, please listen to what DaleSpam is trying to tell you. You're not accomplishing anything meaningful here.

I am listening, respectfully.

 

[JesseM]

The choice to accept or reject the coordinate length as a valid length of the object will be driven by one's philosophy of reality. There is no disagreement as to the result of the measurement.

What does it mean for a length to be "valid"? How is this any different from calling it "true"? You're using language in a way that seems to make sense to you but you can never actually explain to anyone else in a non-circular way, which is a hint that maybe your ideas don't make as much sense as you think they do.

For me, the issue is the meaning of the measurements. Such questions cannot be resolved by the adoption of a definition.

How can a measurement have "meaning", aside from purely practical questions like what physical procedure you must adopt to make a given type of measurement, or what the result of that measurement implies for your predictions about other empirical results? You really need to provide some explicit explanation of how notions like "true", "valid", "meaning" etc. are supposed to apply to physical measurements, perhaps explain in detail the "philosophy of reality" you refer to in an offhand way above.

 

[JesseM]

[2] The view of the rod from frame S (its coordinate length) is horizontal. Therefore, the view is not one view, but a composite of many views.

Do you think somehow this is not true in the rest frame? The rest frame's view of the rod at a single instant is actually composed of a bunch of different events on worldlines of different parts of the rod, events which occur at different times in some other frame such as S. Unless you think the rod rest frame's definition of simultaneity is more "true" than any other's, the situation seems to be totally symmetric here, each frame's view of "the rod at a single moment" is composed of a set of events which occur at different moments in the other frame.

 

[Dale]

there is a kind of absolute reality to acceleration, even though Born says that GR does away with it.

Coordinate acceleration is relative, proper acceleration is absolute.

Regardless, my point was that an object at rest does not accelerate. If it is true that every observer may always consider himself to be at rest, then he never accelerates. In that case, I don't know what ghwellsjr means by the effect on an object of the object's acceleration.

An object at coordinate rest may still undergo proper acceleration. Since proper acceleration is absolute all observers will agree if something is (proper) accelerating, including the observer himself.

I am not sure what this has to do with the OP.

 

[bobc2]

Do you think somehow this is not true in the rest frame? The rest frame's view of the rod at a single instant is actually composed of a bunch of different events on worldlines of different parts of the rod, events which occur at different times in some other frame such as S. Unless you think the rod rest frame's definition of simultaneity is more "true" than any other's, the situation seems to be totally symmetric here, each frame's view of "the rod at a single moment" is composed of a set of events which occur at different moments in the other frame.

GregAshmore, I really think JesseM is right about this. Look at a symmetric spacetime diagram of your rod. Except, this time I've imagined a red rod and a blue rod were prepared at rest in the same system, then each rod is made to move at the same speed in opposite directions relative to the rest black coordinate system in the sketch. I've made the sketch symmetric so that the red and blue sketched line lengths correspond to the same distance, and the time coordinates are scaled the same as well.

You could have put in some hyperbolic calibration curves (for both distance and time) with your sketch. Then proper distances and proper times would have been obvious.

Now, who's 3-D cross-section of the universe has cut out the 3-D rod with the "True" length?" Which 3-D rod has the Proper length?

 

[GrayGhost]

Regardless, my point was that an object at rest does not accelerate. If it is true that every observer may always consider himself to be at rest, then he never accelerates. In that case, I don't know what ghwellsjr means by the effect on an object of the object's acceleration.

I'd state it this way ...

Although an object at rest does not undergo any proper acceleration, any POV may consider itself the stationary and all others in motion. However if an observer undergoing proper acceleration assumes the stationary, he'll realize that energy considerations are not satisfactory even though the LTs continue to make accurate kinematic predictions.

GrayGhost

 

[ghwellsjr]

Greg, what do you say about two clocks in relative motion? Do you agree with these comments:

I assert that a clock keeps one true time, its rest time. If so, then the dilated coordinate time which is measured in some other frame must be somehow untrue. I argue that the coordinate time is a distorted view of the true time.

A clock is completely unaffected by acceleration. It is always at rest and keeping its one true time.

I'm not sure what I think about it. My initial reaction is that distance and time are not interchangeable, so the parallelism which you have drawn between true length and true time will perhaps not hold up under scrutiny. For example, what precisely do you mean by "view of time"?

I mean exactly what you mean when you use the expression "view of length".

In case you haven't noticed, I took some of your sentences and changed "rod" to "clock", "length" to "time", and "shorter" to "dilated". (I hope no one thought I was agreeing with the comments I asked you about.)

I'm not suggesting that distance and time are interchangeable. When an observer views a moving rod and a moving clock, he sees the rod as a shorter length (along the axis of relative motion) but the clock as taking a longer (dilated) time.

I'm just wondering since you have a problem with the observer's view of the rod's shorter length if you also have a similar problem with the observer's view of the clock's longer time?

 

[GrayGhost]

... In case you haven't noticed, I took some of your sentences and changed "rod" to "clock", "length" to "time", and "shorter" to "dilated". (I hope no one thought I was agreeing with the comments I asked you about.)

Yes, I was wondering about that before :) Good to hear you did not agree. I figured you didn't.

GregAshmore,

Another caveate ... the stationary observer inquires via the LTs as to how the moving clock must presently exist. The hands of the clock, if the clock's motion is luminal enough, will be bent. That is, in the stationary observer's moment, the moving clock will denote the entire proper duration over which its contracted self exists, per the stationary POV. Best part, it's all real. It's difficult to swallow this at first, however you'll likely warm up to it in due time, like it or not. While the moving clock is not perceived in its proper state, it's just as real. IOWs, per the theory, its just another POV of that which exists.

GrayGhost

 

[Dale]

But, DaleSpam, would you also say that Greg is free to call a contracted "measured coordinate length" the "untrue length" or "a distorted view of the true length" and that rods are "completely unaffected" by their accelerations?

I'm saying that when two rods are in relative motion, Greg needs to understand that they cannot both be at rest at the same time, and so it is not a true statement that their "true lengths" are the same as their "rest lengths".

Sorry about my delay in responding to this direct question. I had to think about this for a bit.

You are correct that if the proper lenth is defined as the "true length" then any coordinate length would by implication be an "untrue length". While anyone is free to define any new term that they choose to, it seems that using words like "true" and "untrue" adds a certain level of emotional connotation which is not appropriate. It is also not appropriate to assign personal labels to concepts which are not new but already clearly defined and labeled.

There is precedence, for example, the third generation of quarks were originally called "truth" and "beauty" by the discoverers as was their perogative. However, the community as a whole objected to the connotation and changed the names to "top" and "bottom". Now, even the discoverers should use the accepted terminology for the sake of communication and consistency.

Similarly here, the community has already adopted a name for the concept that the OP would like to label "true length". That name is "rest length", and the OP should use that terminology. If the OP comes up with a new concept then it would be acceptable for him to coin a name for the concept, but even then he should probably avoid terms like "true length" with an unwarranted emotional connotation.

 

[Meir Achuz]

There is precedence, for example, the third generation of quarks were originally called "truth" and "beauty" by the discoverers as was their perogative. However, the community as a whole objected to the connotation and changed the names to "top" and "bottom"

I think the reason for the change was the considerable delay in finding the t quark. During that period people did not want to say that the standard model had beauty but no truth

 

[Dale]

I think the reason for the change was the considerable delay in finding the t quark. During that period people did not want to say that the standard model had beauty but no truth

I don't know if that is correct or not, but I do like that explanation very much!

 

[GregAshmore]

Do you think somehow this is not true in the rest frame? The rest frame's view of the rod at a single instant is actually composed of a bunch of different events on worldlines of different parts of the rod, events which occur at different times in some other frame such as S. Unless you think the rod rest frame's definition of simultaneity is more "true" than any other's, the situation seems to be totally symmetric here, each frame's view of "the rod at a single moment" is composed of a set of events which occur at different moments in the other frame.

I do not accept as fact the sentence in bold. That is, I do not accept that a material object is a composite of an infinite number of separate events, events which just happen to be at the same time in the object's rest frame. I don't know how the assertion could be tested. It fact, I'm completely in the dark as to what kind of events you have in mind.

Someone--DaleSpam or GrayGhost, I think--said that my assertion of true length is a matter of semantics, and can never be more than that. I agree, because (as DaleSpam pointed out months ago) there is no way to experimentally test it. For the same reason, your assertion that the rod is a collection of events is also a matter of semantics.

I'm pretty sure that's why bcrowell believes that I am not accomplishing anything meaningful in this thread. If so, I respectfully disagree. I am not of the opinion that the numbers collected in an experiment are an end in themselves. I want to know what the numbers mean; I want to understand the reality of the world I live in. As GrayGhost has mentioned, many others have felt the same way. In every book on relativity and quantum physics that I have read--perhaps ten in all--the author has spent some time on the subject of reality.

I've concluded that there are (for the moment at least) limits to our ability to understand physical reality. From my perspective, it is meaningful to have a sense of what those limits are.

I appreciate the input from all of you. I do try and learn from it.

I'll be back when I get stumped in GR math.

 

[JesseM]

I do not accept as fact the sentence in bold. That is, I do not accept that a material object is a composite of an infinite number of separate events, events which just happen to be at the same time in the object's rest frame. I don't know how the assertion could be tested. It fact, I'm completely in the dark as to what kind of events you have in mind.

Someone--DaleSpam or GrayGhost, I think--said that my assertion of true length is a matter of semantics, and can never be more than that. I agree, because (as DaleSpam pointed out months ago) there is no way to experimentally test it. For the same reason, your assertion that the rod is a collection of events is also a matter of semantics.

I said "The rest frame's view of the rod at a single instant is actually composed of a bunch of different events", I didn't say that "the rod is a collection of events", I don't even know what that would mean. By the frame's "view" of the rod I just meant the set of points in spacetime (each point is identified by a unique set of space and time coordinates, and is termed an 'event' regardless of whether anything physically interesting is happening at those coordinates) that are occupied by the rod at a single moment in that frame. And in any case, I was just responding to your analogous statement:

[2] The view of the rod from frame S (its coordinate length) is horizontal. Therefore, the view is not one view, but a composite of many views.

If you don't agree that "view of the rod from frame S" just means the set of points in spacetime occupied by the rod at a single moment in S, then you need to define what this phrase means in order for your statement [2] not to be hopelessly vague. I can't really imagine a coherent definition of "view of the rod from frame S" where "the view is not one view, but a composite of many views" would not be just as true in the rest frame as it is in any other frame, unless you just make it true-by-definition by defining "one view" to mean the view of the rod's rest frame so that other frames by definition do not have one view.

 

[John232]

Every book I have read that touched on this topic all explained that the observer using the measuring rod would always measure his rod to stay the same length because the measuring rod itself had contracted.

Say your length is contracted, you measure your ship, it is the same length because your rod is also shorter.

The only problem I see with this is that multiple frames of references would require different amounts of length contraction. But, I have came to terms with the fact that no matter what relativistic observers there are you will always measure your rod at rest with you to be the proper length. So then the different observers at different constant speeds would need to measure different amounts of length contraction since the velocity they are traveling is all different. A third party would see it as one ship as being contracted using his proper length to measure less contraction of another ship.

I think that acceleration could be different. You can prove that a body is accelerating. It can't assume that it is at rest. Light will bend due to its motion. If Einstein was traped in an elevator he could prove that it was accelerating by measuring the curvature of a beam of light, similair to what happens in the presence of gravity.

His light clock in the elevator would become distorted by this curvature and then it would seem that he would also be able to measure the decrease in the clocks speed since he is able to detect the longer path the photon takes in the clock when at the same amount of acceleration. In effect, allowing him to measure the difference of how his light clock measures time. But, at constant speeds this would be impossible.

 

[Dale]

I've concluded that there are (for the moment at least) limits to our ability to understand physical reality.

I would go even further. There are limits to our ability to even define "physical reality", let alone understand it.

 

[GregAshmore]

I said "The rest frame's view of the rod at a single instant is actually composed of a bunch of different events", I didn't say that "the rod is a collection of events", I don't even know what that would mean. By the frame's "view" of the rod I just meant the set of points in spacetime (each point is identified by a unique set of space and time coordinates, and is termed an 'event' regardless of whether anything physically interesting is happening at those coordinates) that are occupied by the rod at a single moment in that frame. And in any case, I was just responding to your analogous statement:

If you don't agree that "view of the rod from frame S" just means the set of points in spacetime occupied by the rod at a single moment in S, then you need to define what this phrase means in order for your statement [2] not to be hopelessly vague. I can't really imagine a coherent definition of "view of the rod from frame S" where "the view is not one view, but a composite of many views" would not be just as true in the rest frame as it is in any other frame, unless you just make it true-by-definition by defining "one view" to mean the view of the rod's rest frame so that other frames by definition do not have one view.

As I understand your position, no observer ever sees the rod itself--all observers see a view of the rod. This is where we disagree. I believe that an observer at rest with the rod sees the rod itself. All other observers see a view of the rod.

The problem with your interpretation is that the definition of "the rod" is hopelessly vague, because no one ever sees the rod. The problem with my interpretation is that the definition of "the view of the rod" is hopelessly vague, because no one can tell the difference between a view of the rod and the rod itself.

I am more comfortable with my interpretation because I can identify the rod itself at all times in the spacetime diagram--it is a line parallel to the X axis of the rod's rest frame. So on paper I am able to distinguish between the one rod and the many views of the rod. In practice--in the lab with measuring instruments--that distinction is not verifiable.

Which leads to DaleSpam's contention that we are unable even to properly define physical reality, let alone understand it.

 

[JesseM]

As I understand your position, no observer ever sees the rod itself--all observers see a view of the rod.

I have no idea what "the rod itself" means, and in fact I have repeatedly objected whenever you use this language--"the rod itself" sounds like some sort of metaphysical absolute, like "the soul" or "God". All that science can deal with are measurable properties of things, which I guess is what you mean by "view", although you ignored my request to define this word. Among these measurable properties are the coordinates of the points in spacetime occupied by the rod at some moment in time, and my argument was just that no matter what frame you use, this set of points will be a set of points at different moments in time in some other frame. So again, I don't see why the rest frame has "one view" while other frames do not, this claim seems totally arbitrary as long as you aren't willing to define "one view". As long as you continue to ignore all requests to define your terminology, I don't think this conversation can really go anywhere. Refusing to define is equivalent to refusing to question or think carefully about one's initial vague intuitions, in my opinion.

 

[pervect]

I don't really have time to read this thread, but I thought I'd say a few things about the philosophy of relativity, in the hopes that they might help.

Pre-relativity, length was taken to be a property of an object that was independent of the observer.

Post-relativity, it was realized that length was not independent of the observer. The usual way of describing this is to say that the length depends on the object and the frame of reference.

The proper length of an object is a property of the object itself and independent of the observer - though it can also be viewed as picking out one particular observer, this isn't really the most powerful view of proper length. If one focuses on things that are independent of the observer in relativity, one comes to the conclusion that the Lorentz Interval between points is independent of the observer. Furthermore, though I don't want to get into a detailed discussion, there is a sense in which the proper length of an object is an example of a Lorentz interval.

While there are many ways to interpret relativity philosophically, one of the easiest ways is to focus on observer-independent quantites, in particular the Lorentz Interval (which includes proper length and proper time as specific examples), just because the Lorentz interval IS observer-independent. Because these quantities are observer-independent, we can say they are going to be the fundamental elements of our philosophical system, or in some sense "real". We will calculate observer-dependent quantites when necessary if we have the necessary information (which observer) to do so.

Just because it's easy, "natural", and in general makes things a lot simpler doesn't mean that everyone does this, however. :-).

The general idea is that specifying the Lorentz interval between all possible pairs of points determines the geometry of space-time. The old-style observer-dependent notions of distance and time between points can be recovered from this information about the observer independent Lorentz intervals always when space-time if flat, and with a few ambiguities when space-time is not flat.

 

[GrayGhost]

As I understand your (JesseM's) position, no observer ever sees the rod itself--all observers see a view of the rod. This is where we disagree. I believe that an observer at rest with the rod sees the rod itself. All other observers see a view of the rod.

Greg,

There are basically 4 situ ...

(1) the rod as it presently exists per the observer
(2) the image of the rod per receipt of light signals per the observer
(3) the rod as it presenty exists per itself
(4) the image of the rod per receipt of light signals per itself

You speak of the rest (proper) length as though it is the only true length. However, that is to say ... the LTs predict spacetime solns that are not real, when relative motion is involved. Clearly, this is not the case, given the theory has stood for >100 yr now under intense scrutiny by the finest minds, every inch the way. Therefore, one should always evaluate, and re-evaluate, their disagreements with the theory before assuming the contrary.

Light signals alone cannot be used to determine how a body presently exists within the spacetime. The reason is that the image of the body, moving or not, takes time to reach your eyes (or equipment). Let's consider the body at rest with yourself. Since different points of the body reside at different distances from your eye, the collective image received by your eye at any instant is composed of a collection of photons which have traveled different distances from reflection-points of the body. Since some of these rays travel longer, the image conveyed by said photon must exist from an earlier point in time. Therefore, and generally speaking, no image you ever see is an image as the body existed in either it's own present moment, or your own. You might imagine a rod 1 lt-sec long at rest with yourself, lined with attached-atomic-clocks all in sync per the rod's own frame of reference. The image you receive at your eye at any moment (if magic eyes) would not see rod-clocks all in sync.

That said, to know how a body "presently exists", this must be predicted. It's a prediction of how the body exists NOW from some specific POV. It has nothing to do with light transit time conveying the image. If you and I move relatively, my NOW and your NOW are not the same per SR. In fact, they are angularly rotated wrt one another in spacetime in a non-classical way, just as your illustration has shown. So how is this prediction made? Well, it's made in the way JesseM has explained, because that's how the LTs actually do achieve it. Your euclidean stationary system is a collection of all spacetime points as they presently exist per you. The body (moving or not) has its own coordinate system, a collection of all spacetime points as they presently exist per it. The LTs map every point of one system into the other, which is why JesseM's stated process is accurate. If every point of the moving system is indeed mapped 1:1 into your own stationary system, then it is true (as JesseM says) that every point "of the moving body istelf" is mapped into your own stationary system's POV. IOWs, one really must consider the mapping of each point of the other body (moving or not) into your own POV, to know how it presently exists per oneself. Inherent in that process and its outcome is the meaning of the Special Relativity.

Which leads to DaleSpam's contention that we are unable even to properly define physical reality, let alone understand it.

Well we may never understand everything, and hence the argument that we can never truly define reality. On the other hand, we understand a lot more these days than in the dark ages. I prefer it in this way .. we have an incomplete understanding of reality, but an understanding nonetheless. It improves as we learn more. Yet, we do not even know why time passes, and so the relativity is built upon some things we do not yet fully grasp, so.

GrayGhost

 

[GregAshmore]

I have no idea what "the rod itself" means, and in fact I have repeatedly objected whenever you use this language--"the rod itself" sounds like some sort of metaphysical absolute, like "the soul" or "God". All that science can deal with are measurable properties of things, which I guess is what you mean by "view", although you ignored my request to define this word. Among these measurable properties are the coordinates of the points in spacetime occupied by the rod at some moment in time, and my argument was just that no matter what frame you use, this set of points will be a set of points at different moments in time in some other frame. So again, I don't see why the rest frame has "one view" while other frames do not, this claim seems totally arbitrary as long as you aren't willing to define "one view". As long as you continue to ignore all requests to define your terminology, I don't think this conversation can really go anywhere. Refusing to define is equivalent to refusing to question or think carefully about one's initial vague intuitions, in my opinion.

I believe that I clearly defined the distinction between the true view and the distorted view in the original post. The true view sees the entire rod all at once, at one instant of the rod's proper time. The distorted view sees a collection of individual points on the rod at different instants of the rod's proper time. I maintain that the distortion is the result of the movement of the rod over the time difference, where the time difference = V * L.

I understand that you may not wish to accept that the view in the rest frame is "true", and the view in other frames is "distorted". But I think the distinction between the view in the rest frame and the view from other frames is clear enough.

 

[JesseM]

I believe that I clearly defined the distinction between the true view and the distorted view in the original post. The true view sees the entire rod all at once, at one instant of the rod's proper time.

Only point particles have "proper time". We can talk about the proper time on any given point on the rod like the left end, but there's nothing inherent in the definition of proper time that would tell you which event on the left end occurs at the same proper time as an event on the right end, that's purely a matter of your simultaneity convention. So to use correct terminology, you should say "at one instant in the inertial frame where the rod is at rest". But stated this way, it seems that the "true view" involves that definition of simultaneity only because you have chosen to define it that way, I could just as easily pick a different definition that says "the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is aligned parallel to the x-axis and moving in the +x direction at 0.99c". If you think there is something inherent in your notion of the meaning of the word "true" that would make this definition incorrect (as opposed to just different from your own preferred definition of 'true view', a merely aesthetic matter) then please explain it, otherwise I don't see how you are doing anything other than playing games with semantics.

I understand that you may not wish to accept that the view in the rest frame is "true"

I don't know what you mean by "true", unless "true view" is just an arbitrary term that you are defining in the quote above without claiming it has any connection with the ordinary English associations of the word (in much the same way that words like 'energy' and 'action' had preexisting meanings in English before being used as technical terms in physics, and when physicists use them they don't intend the words to have the same meaning as their colloquial English meanings). If that's the case you could have easily chosen some other arbitrary word, like "I define the 'maroon-colored view' to be the view sees the entire rod all at once, at one instant in the inertial rest frame of the rod", and it would make no difference to your argument.

 

[GregAshmore]

Greg,

There are basically 4 situ ...

(1) the rod as it presently exists per the observer
(2) the image of the rod per receipt of light signals per the observer
(3) the rod as it presenty exists per itself
(4) the image of the rod per receipt of light signals per itself

You speak of the rest (proper) length as though it is the only true length. However, that is to say ... the LTs predict spacetime solns that are not real, when relative motion is involved. Clearly, this is not the case, given the theory has stood for >100 yr now under intense scrutiny by the finest minds, every inch the way. Therefore, one should always evaluate, and re-evaluate, their disagreements with the theory before assuming the contrary.

I'm not challenging the conformation of the measured results with the predictions of the Lorentz transform. I'm trying to understand what the numbers mean. The equations meant one thing to Lorentz, and quite another thing to Einstein.

Light signals alone cannot be used to determine how a body presently exists within the spacetime. The reason is that the image of the body, moving or not, takes time to reach your eyes (or equipment). Let's consider the body at rest with yourself. Since different points of the body reside at different distances from your eye, the collective image received by your eye at any instant is composed of a collection of photons which have traveled different distances from reflection-points of the body. Since some of these rays travel longer, the image conveyed by said photon must exist from an earlier point in time. Therefore, and generally speaking, no image you ever see is an image as the body existed in either it's own present moment, or your own. You might imagine a rod 1 lt-sec long at rest with yourself, lined with attached-atomic-clocks all in sync per the rod's own frame of reference. The image you receive at your eye at any moment (if magic eyes) would not see rod-clocks all in sync.

That said, to know how a body "presently exists", this must be predicted.

If I set up an array of cameras with synchronized clocks, I can collect an image of the resting rod as it is at a given instant. I can then examine at my leisure the rod as it existed at that moment.

It's a prediction of how the body exists NOW from some specific POV. It has nothing to do with light transit time conveying the image. If you and I move relatively, my NOW and your NOW are not the same per SR. In fact, they are angularly rotated wrt one another in spacetime in a non-classical way, just as your illustration has shown. So how is this prediction made? Well, it's made in the way JesseM has explained, because that's how the LTs actually do achieve it.

But no transformation is needed to see the rod "as it was" if one collects the data in the rest frame as described above.

 

[Dale]

I'm not challenging the conformation of the measured results with the predictions of the Lorentz transform. I'm trying to understand what the numbers mean. The equations meant one thing to Lorentz, and quite another thing to Einstein.

The two interpretations are completely equivalent experimentally. In other words, you are free to choose either interpretation and you will not be proven wrong by current evidence. You are even free to switch interpretations on an arbitrary whim, either works fine. I tend to use Lorentz's interpretation only when thinking about the Doppler effect and Einstein's interpretation for everything else.

Personally, I don't think that the interpretations that we use are particularly important for anything other than helping us remember how to correctly apply the formulas for a given situation. So as long as you are consistently able to use the equations to get the right predictions then you are OK, IMO.

 

[GregAshmore]

Only point particles have "proper time". We can talk about the proper time on any given point on the rod like the left end, but there's nothing inherent in the definition of proper time that would tell you which event on the left end occurs at the same proper time as an event on the right end, that's purely a matter of your simultaneity convention. So to use correct terminology, you should say "at one instant in the inertial frame where the rod is at rest".

I did say that. It is the frame M in the diagram.

But stated this way, it seems that the "true view" involves that definition of simultaneity only because you have chosen to define it that way, I could just as easily pick a different definition that says "the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is aligned parallel to the x-axis and moving in the +x direction at 0.99c". If you think there is something inherent in your notion of the meaning of the word "true" that would make this definition incorrect (as opposed to just different from your own preferred definition of 'true view', a merely aesthetic matter) then please explain it, otherwise I don't see how you are doing anything other than playing games with semantics.

I don't see it as a matter of aesthetics. As a practical matter, the closer one gets to light speed, the greater the error in the measurement. Even given perfect instruments, it seems to me that there is a difference in principle between a measurement taken in the rod's rest frame and one taken from a frame moving relative to the rod. That difference is hinted at in the way velocities add in SR, and confirmed by the lifting of the speed limit 'c' in GR. (I understand [or think I do] that one can never actually measure a speed greater than c in GR, because our measurements are taken in a projection of the GR spacetime onto a locally flat spacetime where the Lorentz transformations apply. But this supports my argument that measurements taken at speed are distorted--or perhaps better said, less informative--than measurements taken at rest.)

 

[GregAshmore]

The two interpretations are completely equivalent experimentally. In other words, you are free to choose either interpretation and you will not be proven wrong by current evidence. You are even free to switch interpretations on an arbitrary whim, either works fine. I tend to use Lorentz's interpretation only when thinking about the Doppler effect and Einstein's interpretation for everything else.

Personally, I don't think that the interpretations that we use are particularly important for anything other than helping us remember how to correctly apply the formulas for a given situation. So as long as you are consistently able to use the equations to get the right predictions then you are OK, IMO.

For all practical purposes, I agree.

 

[GrayGhost]

I'm not challenging the conformation of the measured results with the predictions of the Lorentz transform. I'm trying to understand what the numbers mean. The equations meant one thing to Lorentz, and quite another thing to Einstein.

Well, to best understand their meaning wrt Einstein, I'd recommend you forget about Lorentz for the moment. Assume that any absolute reference for motion or simultaniety never existed. Then, consider your illustrations at face value.

If I set up an array of cameras with synchronized clocks, I can collect an image of the resting rod as it is at a given instant. I can then examine at my leisure the rod as it existed at that moment. ... no transformation is needed to see the rod "as it was" if one collects the data in the rest frame

By attaching the cameras and clocks to the rest-rod, and photographing the rod they are attached to, one verifies only one thing ... that SR reduces to classical mechanics at non-luminal motion. Well the theory already predicts that, so that won't help you much.

Your test cannot prove whether the rod exists in only its rest state, or not. It only verifies how the rod exists from its own POV. Your cameras must be in luminal relative motion wrt the rod to find the truth to the matter. The photos will either be consistent with your illustrations, or not. Countless tests to date support that they would be consistent. Keep in mind that the desynchronisation of luminally-moving-synchronised-clocks (as your illustration suggests) is neither an optical or illusionary effect per the theory.

GrayGhost