The case for True Length = Rest Length

[rjbeery]

I wanted to discuss Lorentzian length contraction (and time dilation, for that matter). Books on the subject do a fine job describing it but I've generally found that they lack an adequate explanation of it. What follows is my personal explanation.

Special Relativity, in my opinion, is best explained in the following way: there is but one speed in the universe, c, at which all objects travel for a given (inertial) observer. In SR, though, "travel" occurs through spacetime, rather than space only, and one must consider the space- and time-vector component of such travel when making measurements.

Time Dilation. In the picture below, the car is sitting in your driveway. It's spatial travel component, relative to you, is null; in other words, it's "travelling" through time along with you at a speed of c and there is no time dilation.

Now your wife takes the car out to go shopping, and tears off down the road at a speed of .5c. Since we postulate that her "spacetime" speed is constant at c, and we know her "space-component" speed is .5c, we calculate that her "time-component" speed to be .86c because
(.5c)^2+(.86c)^2=c^2

...and indeed, SR calculates that your wife's watch would be ticking at 86% of yours as she speeds away.

Length Contraction. In this description we're only concerned with treating dimensions as temporal or spatial but Lorentzian length contraction has a purely spatial analogy: Hold a the blue face of a Rubik's Cube squarely in front of your face and measure it with the ruler also squarely facing you. Now, turn the Rubik's Cube face partially away from you without moving the ruler and...it's length will APPEAR to contract.

Turn it such that the blue face is completely to the side and its width appears to be zero. In fact, if we consider in this analogy the blue face to be the c invariant, the width dimension to be temporal, and the depth dimension to be spatial, SR makes the same predictions as shown below...

Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.

Thanks for your time and feedback. *8^)

 

[JesseM]

Your diagrams are confused because they have the car's spatial length be parallel to the time axis--i.e. the front of the car seems to be at a later time than the back! If you're going to have a diagram with 1 space and 1 time dimension, better to imagine a 1-dimensional car parallel to the horizontal axis whose "back" is at the left and whose "front" is at the right. Alternately you could have a 3D diagram with two space dimensions, but either way you need a diagram showing the "world-tube" (analogue of a world-line for an object that's extended in space) of the car where a horizontal cross-section (space at a particular moment in time) shows the complete spatial extent of the car at that moment in time, both front and back. It would then be more obvious that disagreements about length have to do with the relativity of simultaneity and the fact that different frames slice spacetime into spatial cross-sections at different angles, which means they disagree about what a single cross-section of the car's world-tube looks like. And hopefully you agree that there is no absolute truth about simultaneity (and likewise no absolute truth about velocity, so there can be no objective fact about their "time-component speed" and whether it's zero or nonzero)

 

[rjbeery]

It would then be more obvious that disagreements about length have to do with the relativity of simultaneity and the fact that different frames slice spacetime into spatial cross-sections at different angles, which means they disagree about what a single cross-section of the car's world-tube looks like. And hopefully you agree that there is no absolute truth about simultaneity (and likewise no absolute truth about velocity, so there can be no objective fact about their "time-component speed" and whether it's zero or nonzero)

Yes, the graphs require some imagination. The spatial dimension isn't there to "show length" but rather "describe the constant-velocity components". They are also performing the double-duty of giving a visual aid which would have been more appropriately done in another graph.

I tried to show that considering a Lorentz-contracted length to be valid is equivalent to considering the length-contracted width of a Rubik's Cube face turned at an angle. If this analogy is valid, it is always your prerogative to consider ALL Rubik's Cube apparent face widths to be on equal footing but I don't believe that would be popular sentiment.

 

[JesseM]

I tried to show that considering a Lorentz-contracted length to be valid is equivalent to considering the length-contracted width of a Rubik's Cube face turned at an angle. If this analogy is valid, it is always your prerogative to consider ALL Rubik's Cube apparent face widths to be on equal footing but I don't believe that would be popular sentiment.

But the analogy isn't valid as it depends entirely on the fact that you have misrepresented what "a car" looks like on a spacetime diagram, drawing it exactly the same as you would in an ordinary spatial diagram, and misrepresented its "length" as just somehow viewing a single ordinary car from an angle in space. If you had more accurate graphs, a better analogy would be if we had some solid 3D objects like cylinders, and different observers were disagreeing about the "width of a 2-dimensional horizontal cross-section" of the cylinders, but the reason they disagree is that they use different coordinate systems that define "horizontal" differently. Arguing for a true "width of a 2-dimensional horizontal cross-section" would require believing in a "true" definition of "horizontal", just like arguing for a "true" length in relativity would require believing in a true definition of simultaneity, a fact which is covered up by your distorted diagram.

 

[rjbeery]

JesseM, the car's length in the diagram is primarily representative of it's velocity "direction", where direction in this case is broken up into either spatial or temporal components. I was exploiting the fact, perhaps our of laziness, that the actual MEASURED length of the vehicle contracts at the same proportionality as it's temporal velocity component does.

But the analogy isn't valid as it depends entirely on the fact that you have misrepresented what "a car" looks like on a spacetime diagram

The validity of the analogy should stand independent from my sloppy use of graphs, unless you're telling me that you're actually unable to understand what I meant by them. Is that the case?

 

[JesseM]

The validity of the analogy should stand independent from my sloppy use of graphs, unless you're telling me that you're actually unable to understand what I meant by them. Is that the case?

Yes, I have no idea what you meant since the whole concept of "viewing something at an angle" and seeing it foreshortened visually, which is the basis for both your graphs and the Rubik's Cube analogy, seems to have no real connection to length contraction.

 

[Dale]

rjbeery, I am curious, why did you put "True Length = Rest Length" in your title when you have no discussion of "True Length" at all. It seems like a very mis-named thread.

In any case, we have a very long thread already currently running on this topic. I would recommend you go through it and see if you think you have anything that has not already been discussed in excruciating detail.

https://www.physicsforums.com/showthread.php?t=469311

 

[rjbeery]

Yes, I have no idea what you meant

No problem. I'll see if I can come up with a "better" graph. In the meantime, if you happen to have an epiphany of imagination and see what exactly it is I'm trying to communicate I'd love to continue the conversation.

rjbeery, I am curious, why did you put "True Length = Rest Length" in your title when you have no discussion of "True Length" at all. It seems like a very mis-named thread.

If you read the thread all the way through, my closing statement references objects' "true length".

Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.

Also, I've never seen anyone make the case above for Lorentzian length contraction as being an illusion (specifically for the reasons mentioned), including in the other thread that you linked to. If you don't mind, I felt my points are connected to the other thread in only a single way, which is that we both mention rest length, and that it would be a disservice to myself and the other author to conflate our competing ideas into a single conversation.

 

[Dale]

If you read the thread all the way through, my closing statement references objects' "true length".

No it doesn't.

Also, I've never seen anyone make the case above for Lorentzian length contraction as being an illusion (specifically for the reasons mentioned), including in the other thread that you linked to.

Specifically which argument do you believe is novel? I bet I can find it in that other thread.

 

[rjbeery]

DaleSpam, with respect, are you a moderator? I had assumed so but you seem a bit argumentative for a Mod. When I say

Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.

...I am equating "absolute length" with "true length". This should be clear when I refer to other measured lengths as "an illusion". I have to feel that you're being a bit disingenuous if you're protesting that I didn't LITERALLY use the phrase "true length" when it should be apparent that I referred to it nonetheless.

Specifically which argument do you believe is novel? I bet I can find it in that other thread.

Here are my two points, summarized. If you can find both of these in the other thread I will remove this one.

1) There is a direct connection between the time-component of the constant spacetime velocity of an object and its time dilation and length contraction factors.
2) As a measured length, such as that of the face of a Rubik's Cube, is gradually twisted away from the width dimension in which we are measuring it, it's apparent width is altered in the same proportion as the car's apparent length is altered as it's constant spacetime velocity is "twisted" from being purely temporal to having a spatial component.

 

[Matterwave]

Can you explain what it means to have a "time component" speed of something something c?

What does it mean to travel through time at some "speed" (which is measured in meters/second)?

 

[JesseM]

No problem. I'll see if I can come up with a "better" graph. In the meantime, if you happen to have an epiphany of imagination and see what exactly it is I'm trying to communicate I'd love to continue the conversation.

If you can represent what you mean on a normal spacetime diagram drawn accurately, please do so. But if you can't, then consider the possibility that there isn't any well-defined idea that you are "trying to communicate", that in fact you just have a vague analogy that you have convinced yourself is meaningful even though maybe it isn't.

 

[rjbeery]

Can you explain what it means to have a "time component" speed of something something c?

What does it mean to travel through time at some "speed" (which is measured in meters/second)?

Can I explain it? Yes and no. It's a good question. The problem is that we're blending SR's concept of spacetime with traditional definitions based on a strict separation of space and time. Velocity is defined in terms of distance (or space) / time, as you said. In my explanations above, you must simply consider the "constant spacetime velocity" to be the physical manifestation of the Lorentzian invariant quantity under SR, while what you would traditionally consider "velocity" now becomes the "spatial component" of that constant spacetime velocity.

 

[rjbeery]

If you can represent what you mean on a normal spacetime diagram drawn accurately, please do so. But if you can't, then consider the possibility that there isn't any well-defined idea that you are "trying to communicate", that in fact you just have a vague analogy that you have convinced yourself is meaningful even though maybe it isn't.

The auto graphs are clearly imperfect; I was trying to do this over lunch today. But I think you're confused...normal spacetime diagrams represent world-lines, etc. Here, the graphs are doing double-duty: 1) The car length is a representation of the direction of an object's constant spacetime velocity as it relates to it's temporal and spatial components. It says nothing of time lines, proper times, etc. 2) It also serves as a visual aid to show the connection between the time-component of the constant spacetime velocity and its time dilation and length contraction factors. On the graphs with 2 automobiles, the 2nd auto doesn't really apply to the graph itself, it's rather an attempt to "show" this connection visually.

 

[ghwellsjr]

I have a comment to make but I have already made it in post #5 in the thread the DaleSpam linked to in post #7 of this thread:

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?

And I have the same questions for you that I presented to Greg in that post.

 

[bobc2]

Here are my two points, summarized. If you can find both of these in the other thread I will remove this one.

1) There is a direct connection between the time-component of the constant spacetime velocity of an object and its time dilation and length contraction factors.
2) As a measured length, such as that of the face of a Rubik's Cube, is gradually twisted away from the width dimension in which we are measuring it, it's apparent width is altered in the same proportion as the car's apparent length is altered as it's constant spacetime velocity is "twisted" from being purely temporal to having a spatial component.

rjbeery, here is a quick copy of one of the posts. Does this represent the idea you are offering here? Was Greg (with his discussion below) trying to make the same point you are?

 

[Dale]

...I am equating "absolute length" with "true length". This should be clear when I refer to other measured lengths as "an illusion". I have to feel that you're being a bit disingenuous if you're protesting that I didn't LITERALLY use the phrase "true length" when it should be apparent that I referred to it nonetheless.

The term "absolute" is well defined. It means that the quantity in question is frame invariant. Everyone agrees that the rest length is absolute.

EDIT: this may not be correct, see below

The term "true" on the other hand is not well defined. While you are certainly free to arbitrarily define "true" to mean "absolute" the choice is completely arbitrariy and not without controversy. That is the whole point of the other thread and by making this personal definition you are simply doing the same thing that has been discussed at length in the other thread.

2) As a measured length, such as that of the face of a Rubik's Cube, is gradually twisted away from the width dimension in which we are measuring it, it's apparent width is altered in the same proportion as the car's apparent length is altered as it's constant spacetime velocity is "twisted" from being purely temporal to having a spatial component.

This point was made multiple times by multiple different people in the other thread. It appears that I am not the only one who thinks this thread is redundant with the other one.

 

[JesseM]

The auto graphs are clearly imperfect; I was trying to do this over lunch today. But I think you're confused...normal spacetime diagrams represent world-lines, etc. Here, the graphs are doing double-duty: 1) The car length is a representation of the direction of an object's constant spacetime velocity as it relates to it's temporal and spatial components.

Are you defining "spacetime velocity" the same as Greene does on p. 392 of The Elegant Universe?

For the mathematically inclined reader, we note that from the spacetime position 4-vector $$x = (ct, x_1, x_2, x_3) = (ct, \vec{x})$$ we can produce the velocity 4-vector $$u$$, $$dx/d\tau$$, where $$\tau$$ is the proper time defined by $$d\tau^2 = dt^2 - c^{-2}(dx_1^2 + dx_2^2 + dx_3^2)$$. Then, the "speed through spacetime" is the magnitude of the 4-vector $$u$$, $$\sqrt{((c^2dt^2 - d\vec{x}^2)/(dt^2 - c^{-2}d\vec{x}^2))}$$, which is identically the speed of light, $$c$$. Now, we can rearrange the equation $$c^2(dt/d\tau)^2 - (d\vec{x}/d\tau)^2 = c^2$$, to be $$c^2(d\tau/dt)^2 + (d\vec{x}/dt)^2 = c^2$$. This shows that an increase in the object's speed through space, $$\sqrt{(d\vec{x}/dt)^2}$$, must be accompanied by a decrease in $$d\tau/dt$$, the latter being the object's speed through time (the rate at which time elapses on its own clock, $$d/tau$$, as compared with that on our stationary clock, $$dt$$).

If so can you explain what you mean by "direction of an object's constant spacetime velocity as it relates to it's temporal and spatial components" in mathematical terms like this? Are you imagining a sort of graph where we plot $$\sqrt{(d\vec{x}/dt)^2}$$ (which is just the magnitude of the velocity vector, i.e. speed) on one axis and $$d\tau/dt$$ on the other, such that the length of the vector for any object always adds up to 1? And is the "direction" you're talking about in this abstract space of speed vs. time dilation, rather than direction in ordinary spacetime? If so how does this have anything to do with length contraction?

It says nothing of time lines, proper times, etc. 2) It also serves as a visual aid to show the connection between the time-component of the constant spacetime velocity and its time dilation and length contraction factors.

What "connection" would that be? Just that they both happen to involve a gamma-factor when you relate their value to the object's speed? I don't see how that would imply we should view the rest length as "true" or how this helps make sense of an analogy involving visual foreshortening.

 

[bobc2]

Are you defining "spacetime velocity" the same as Greene does on p. 392 of The Elegant Universe?

That's exactly the same impression I had.

rjbeery, the repeat visitors to this forum understand spacetime diagrams quite well. You really can't convey the story you have in mind if your spacetime diagram is not at least qualitatively correct. It really doesn't work to provide an incorrect sketch and assume people will know what you meant (that is, if you did mean for it to be different than what you sketched).

Please don't think I intend anything critical here. Spactime diagrams can be tough to interpret for some of the newer visitors sometimes, even when done correctly.

 

[rjbeery]

This point was made multiple times by multiple different people in the other thread.

Could you please give me some links in the other thread? While I was unable to find it myself, I would be curious to see how others are framing my argument.
JesseM and bobc2, yes Greene's description of a constant spacetime velocity is equivalent what I was attempting to outline. I had assumed that this description of SR was well-known and that a rigorous graphical and mathematic proof was not necessary. Also, there is nothing particularly ground-breaking in this way of looking at SR. My novelty lies in my Rubik's Cube analogy, so if you could please reread it and critique it such that I can make it clearer it would be most appreciated.

My ultimate point is that to the extent that my spatial-parallax analogy (i.e. width-to-depth dimensional perspective) applies to to the constant spacetime velocity concept (i.e. temporal-to-spatial dimensional perspective) we are able to say that a rest length is just as valid as a squarely-measured length (i.e. they are both "true lengths"), and a Lorentz-contracted length is just as illusory as a parallax-affected one.

If you would like to argue that the analogy does not hold, that's OK, but the math is equivalent which I find to be compelling.

 

[JesseM]

JesseM and bobc2, yes Greene's description of a constant spacetime velocity is equivalent what I was attempting to outline. I had assumed that this description of SR was well-known and that a rigorous graphical and mathematic proof was not necessary.

It's not actually a very common way of explaining SR, I've never seen it in any textbook for example (nor any author besides Greene in fact). I think it's a poor explanation in terms of building intuitions because there if you imagining looking at things from a 4D perspective you won't see anything actually "moving", just a bunch of static worldlines. In any case, I figured this was what you meant, but you could you answer my followup questions?

If so can you explain what you mean by "direction of an object's constant spacetime velocity as it relates to it's temporal and spatial components" in mathematical terms like this? Are you imagining a sort of graph where we plot $$\sqrt{(d\vec{x}/dt)^2}$$ (which is just the magnitude of the velocity vector, i.e. speed) on one axis and $$d\tau/dt$$ on the other, such that the length of the vector for any object always adds up to 1? And is the "direction" you're talking about in this abstract space of speed vs. time dilation, rather than direction in ordinary spacetime? If so how does this have anything to do with length contraction?

Also, there is nothing particularly ground-breaking in this way of looking at SR. My novelty lies in my Rubik's Cube analogy, so if you could please reread it and critique it such that I can make it clearer it would be most appreciated.

My critique is that I see no connection whatsoever between visual foreshortening and length contraction, you need to actually explain what the details of the analogy are. Visual foreshortening has to do with rays going from the top and bottom of the cube and converging on your eye, if the cube is tilted the angle between these rays shrinks so the angular size of the cube appears to shrink. Your diagram of the car also seemed to show yellow "rays" but they made no sense taken literally because they would seem to be rays through spacetime which started from two points at different times (the top and bottom of the car drawn at different points on the time axis, which I critiqued earlier) converging on a single point in spacetime. I'm not aware of any derivation of length contraction that would look anything like this, so how is the analogy supposed to work?

If you would like to argue that the analogy does not hold, that's OK, but the math is equivalent which I find to be compelling.

What math is equivalent? Please give the math of visual foreshortening which you think is "equivalent" to the math deriving length contraction, you didn't provide anything like that in your original post, just confusing diagrams.

 

[ghwellsjr]

The term "absolute" is well defined. It means that the quantity in question is frame invariant. Everyone agrees that the rest length is absolute.

This is a new one on me. Wouldn't this also mean that since everyone agrees that proper time is frame invariant, it is also absolute time?

I thought "absolute" was in contrast to "relative". I did a search on relativity and "absolute length" and all I could find was that there is no such thing as absolute length, there is only relative length dependent upon a selected frame of reference, just like there is no absolute time, just a relative time dependent on a selected frame of reference.

Can you please provide some links that show that "the rest length is absolute" or that the term absolute "means that the quantity in question is frame invariant"?

 

[Dale]

This is a new one on me. Wouldn't this also mean that since everyone agrees that proper time is frame invariant, it is also absolute time?

I thought "absolute" was in contrast to "relative". I did a search on relativity and "absolute length" and all I could find was that there is no such thing as absolute length, there is only relative length dependent upon a selected frame of reference, just like there is no absolute time, just a relative time dependent on a selected frame of reference.

Can you please provide some links that show that "the rest length is absolute" or that the term absolute "means that the quantity in question is frame invariant"?

Interesting. Thanks for calling me out on this one, I may be incorrect. It seems that this idea is something that I picked up here, on PF where it has been mentioned several times. I even found some other science forums where the same idea is mentioned, but nothing peer reviewed.

I even found this philosophy paper that argues against equating invariant and absolute:
http://www.phil-inst.hu/~szekely/PIRT_BP_2/papers/CZERNIAWSKI_09_ft.pdf

I am no longer so certain that "absolute" is generally understood to mean "frame invariant" although that has been my understanding for quite some time. If anyone else has a good reference I would appreciate it. Until then I will have to refrain from making this assertion.

 

[bobc2]

This is a new one on me. Wouldn't this also mean that since everyone agrees that proper time is frame invariant, it is also absolute time?

Hi ghwellsjr, I was just curious. Would regard 4-vectors as absolute?

 

[bobc2]

What math is equivalent? Please give the math of visual foreshortening which you think is "equivalent" to the math deriving length contraction, you didn't provide anything like that in your original post, just confusing diagrams.

rjbeery, This is the part that I was really trying to understand as well--it would go a long way toward clarifying where you are coming from if you could answer JesseM's question (as well as his other points).

 

[Dale]

Could you please give me some links in the other thread? While I was unable to find it myself, I would be curious to see how others are framing my argument.

Sure, in https://www.physicsforums.com/showthread.php?t=469311 see posts 4, 17, 43, 107, 149, 154, 155, 165, 166, 172, 173, 195, and 231. Also bobc2 had several drawings that showed this idea graphically, but they are not showing up now. I don't know what is causing that but perhaps you can get an idea of his points from the text.

That discussion itself spawned from a previous discussion at https://www.physicsforums.com/showthread.php?t=464397 and in the previous discussion at post 5, 6, 7, 9, 10, 14, 20, 32, 43, 44, 48, 63, and 66.

Note that many posts speak of rotating and slicing rather than rotating and projecting which are related (almost "orthogonal") operations.

If you would like to argue that the analogy does not hold, that's OK, but the math is equivalent which I find to be compelling.

I don't argue that it doesn't hold, just that it is not new and has been discussed ad nauseum recently in other threads. The conclusion is quite clear: the statement "True Length = Rest Length" is at most an arbitrary personal definition.

 

[Mentz114]

Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.

An object has one length. If the length is measured from a moving frame, the observers (knowing the configuration and velocities involved) can calculate this length from their data. Arguing about 'true' or 'actual' etc is just complicating a simple fact.

I don't argue that it doesn't hold, just that it is not new and has been discussed ad nauseum recently in other threads. The conclusion is quite clear: the statement "True Length = Rest Length" is at most an arbitrary personal definition.

Right. Especially the ad nauseam.

 

[ghwellsjr]

The conclusion is quite clear: the statement "True Length = Rest Length" is at most an arbitrary personal definition.

I don't agree that it is an arbitrary personal definition. It is a wrong definition. We are not at liberty to redefine the word "true" just because we use it in a phrase like "true length". There is no truth to the claim that two rods in relative motion both can have their "true lengths" equal to their "rest length". That's like saying that the relative motion is the true motion for both of them at the same time. You can pick one of them and say that in its rest frame the length is its rest length but the other one cannot then also have its length be its rest length. Lengths are relative, just like time is relative.

Both rjbeery and GregAshmore are basing their arguments on the idea that the shortened length of a moving rod is an illusion but what they fail to realize is that the rest length is identically an illusion (if it is an illusion) because the ruler that is used to measure a rod at rest is also contracted to the same degree as the rod that is being measured.

 

[ghwellsjr]

Hi ghwellsjr, I was just curious. Would regard 4-vectors as absolute?

The spacetime interval (a 4-vector) between two events is frame invariant. Aside from that one example of a 4-vector (which I don't consider to be absolute), I'm not into 4-vectors.

In the context of Special Relativity, I reserve the word "absolute" to the speed of light. Times are relative. Lengths are relative. Speeds are relative. But anything that anybody measures is frame invariant. Anyone's measurements of times, lengths, speeds, etc. will be the same independent of the frame that may be used to describe the situation. They better be or they wouldn't comport with reality.

 

[Mentz114]

what they fail to realize is that the rest length is identically an illusion (if it is an illusion) because the ruler that is used to measure a rod at rest is also contracted to the same degree as the rod that is being measured.

That is sophistry and has no content.

Why do you think that one object ( something with a single manifestation) can have more than one length ?

 

[Dale]

Why do you think that one object ( something with a single manifestation) can have more than one length ?

Because length is relative to a given coordinate system and one object can be described in more than one coordinate system. You seem to think that length is solely a property of the object, it is not, no more than an object's energy is solely a property of the object.

 

[Dale]

I don't agree that it is an arbitrary personal definition. It is a wrong definition.

That is why I said "at most" above.

 

[Mentz114]

Because length is relative to a given coordinate system and one object can be described in more than one coordinate system. You seem to think that length is solely a property of the object, it is not, no more than an object's energy is solely a property of the object.

I disagree completely. It is a property of the object. In SR an object has one, and only one length, at the time it is measured. Inertial observers moving relative to the object will use their instruments and fit their data to the SR model and get the same length. It's common sense.

If you don't believe in an underlying objective reality, what's the point of physics ?

 

[Dale]

I disagree completely. It is a property of the object. In SR an object has one, and only one length

This is simply factually incorrect.

If you don't believe in an underlying objective reality, what's the point of physics ?

What does "objective reality" mean and what is it's relationship to the discussion? Is your idea of "objective reality" fundamentally incompatible with relative quantities? If not, then why do you object to the fact that length is one such relative quantity?

 

[Mentz114]

This is simply factually incorrect.
What does "objective reality" mean and what is it's relationship to the discussion?

Is your idea of "objective reality" fundamentally incompatible with relative quantities.

If not, then why do you object to the fact that length is one such relative quantity?

Underlying all these objections is a confusion between length, the property, and it's value.

The 'relative quantities' you speak of are the result of relative velocity on measuring instruments, and unless they are corrected for the effects of the velocity, they are not measurements of the length.

I'm disappointed by your reply, where you've thrown questions rather than reply to what I explained very simply.