The case for True Length = Rest Length

[Matterwave]

Yes, in the end this is undeniable of course. However, would you also argue that the foreshortened width of the Rubik's Cube a few posts back is just as "true" a width as if we were to measure the width squarely?

I would hope that you would read more of my post than just the last statement.

Since option 1 and 2 that you posted, are not possible, and 3 is just manipulating some formulas, then I would say that there is no better reason to call the distance I measure to be "true" than to call, say, the rest-energy of a particle as it's "true" energy.

 

[rjbeery]

The measurement of length is a projection of a 4D object onto a 3D space called a hyperplane of simultaneity. In that sense, it is in fact a "shadow".

I see, so you're saying that the foreshortened width of the Rubik's Cube as it's projected from 3D onto our 2D perspective devoid of depth IS ACTUALLY the width? You've defined length in these terms, I'm just applying your definition.

your opinion is not relevant and does not change the facts.

I'm sorry you feel this way; I feel my logic is sound, but if you think my opinion is irrelevant why are we having this discussion? For the sake of others?

 

[Dale]

I'm sorry you feel this way

It is not a feeling. The process I described has been the accepted definition of "length" since Einstein's 1905 OEMB paper.

 

[rjbeery]

Since option 1 and 2 that you posted, are not possible, and 3 is just manipulating some formulas, then I would say that there is no better reason to call the distance I measure to be "true" than to call, say, the rest-energy of a particle as it's "true" energy

Yes, I read the entire post. I'm not saying that length contraction has no consequences. That being said, I think there's a very valid reason to consider the rest-energy of a particle as its "true" energy...and that is because it's the only energy that is intrinsic to it. "Where" exactly does the additional energy of an object with relativistic velocity reside? Certainly not in the object itself!

 

[rjbeery]

The process I described has been the accepted definition of "length" since Einstein's 1905 OEMB paper.

...and I'm pointing out the following shortcoming with that definition which you did not address.

I see, so you're saying that the foreshortened width of the Rubik's Cube as it's projected from 3D onto our 2D perspective devoid of depth IS ACTUALLY the width? You've defined length in these terms, I'm just applying your definition.

 

[JesseM]

Anyway, I'm asserting a correspondence between Lorentz transforms and foreshortening.

But it's purely a mathematical analogy involving abstract vectors in abstract an abstract space of speed vs. time dilation (or length contraction). Would you agree that in the actual 3 dimensions of space plus one of time, there is no sense in which length contraction follows from foreshortening, i.e. the angle between lines-of-sight to either end shrinking because we are viewing the object at an angle?

Consider the analogy I earlier mentioned as being more similar to length contraction, the one of considering the "width of a horizontal 2D cross-section" of a 3D object like a cylinder, which of course depends on the amount that the 2D plane you're defining as "horizontal" is inclined relative to a plane orthogonal to the central axis of the cylinder (call that the "orthogonal plane"). Now suppose we instead consider the inverse, or "1/width of a horizontal 2D cross-section". If theta is the angle between the plane we define as horizontal and the "orthogonal plane", then it works out that "1/width of a horizontal 2D cross-section" = cos(theta)*"1/width of a 2D cross-section taken in the orthogonal plane". So we could draw a speedomenter diagram where the x-axis represented "1/width of a horizontal 2D cross-section", and the angle that the speedometer needle makes with the x-axis is the same as the angle between the plane you define as "horizontal" and the orthogonal plane. In that case, if the needle has a constant length "1/width of a 2D cross-section taken in the orthogonal plane", then as it rotates through different angles, the length of its "shadow" on the x-axis (or the foreshortened visual length seen by someone at a great distance along the y-axis) would correctly represent "1/width of a horizontal 2D cross-section" for the "horizontal" plane at that angle relative to the orthogonal plane. Do you think this representation of "1/width of a horizontal 2D cross-section" as the shadow of a needle in an abstract space somehow proves that the "true" value of "1/width of a horizontal 2D cross-section" is the value it takes when we define the "horizontal" plane to be the same as the orthogonal plane, the plane at a right angle to the central axis of the cylinder? So somehow we are "wrong" if we define "horizontal" in a way where the central axis of the cylinder is not "vertical"?

(if you have trouble following this, it may help to replace the cylinder with a 2D strip and the 2D planes with 1D lines)

Also, consider Wiki's explanation of the bar-and-ring paradox:

In mathematical terms, a Lorentz transformation can be separated into the product of a spatial rotation and a "proper" Lorentz transformation which involves no spatial rotation. The mathematical resolution of the bar and ring paradox is based on the fact that the product of two proper Lorentz transformations may produce a Lorentz transformation which is not proper, but rather includes a spatial rotation component.

In other words, the bar and ring problem is resolved by one party disagreeing with the other on the amount of relative rotation between the two objects! If a simple rotation can explain how we fit a 2 meter pole through a 1 meter ring in that scenario, doesn't it support the analogy between Lorentz length contraction and a physical rotation?

No, because in this case we are dealing with a "real" rotation in ordinary 3D space, not in some abstract phase space we've cooked up.

 

[Dale]

I see, so you're saying that the foreshortened width of the Rubik's Cube as it's projected from 3D onto our 2D perspective devoid of depth IS ACTUALLY the width? You've defined length in these terms, I'm just applying your definition.

No you are not applying the definition. You are simply deliberately confusing an analogy with a definition.

I would say: "the foreshortened width of the Rubik's Cube as it's projected from 3D onto our 2D perspective devoid of depth IS ANALOGOUS to the width"

 

[Dale]

The measurement of length is a projection of a 4D object onto a 3D space called a hyperplane of simultaneity.

I have to correct myself. The measurement of length is an intersection of a 4D object with a 3D space called a hyperplane of simultaneity. Intersection and projection are related, but not the same.

In any case, length is a well-defined term, and it has the property that it is frame variant. End of story.

 

[Matterwave]

Yes, I read the entire post. I'm not saying that length contraction has no consequences. That being said, I think there's a very valid reason to consider the rest-energy of a particle as its "true" energy...and that is because it's the only energy that is intrinsic to it. "Where" exactly does the additional energy of an object with relativistic velocity reside? Certainly not in the object itself!

This is not a problem with relativity, even under Galilean transforms, the energy is frame-dependent. So, are you really saying that the "true kinetic energy" of a particle is always 0?

 

[rjbeery]

In any case, length is a well-defined term, and it has the property that it is frame variant. End of story.

Very intellectually brave of you. Anyway, I've never technically mentioned redefining "length", I've just been laying out out the reasons I personally consider an object's proper length to be its "true length". In almost all human experience the colloquial "length" and what I'm calling the "true length" are going to be the same thing. In any event, why do you continue to try persuading me? I thought my opinion was irrelevant?

 

[Dale]

In almost all human experience the colloquial "length" and what I'm calling the "true length" are going to be the same thing.

So what? Relativity is designed to also work in situations outside of that small realm of experience.

I've just been laying out out the reasons I personally consider an object's proper length to be its "true length".

Out of curiosity, why do you feel the need to change the term from "rest length" to "true length"? After all, your "true length" is exactly the same as the standard "rest length", so why do you feel the need to invent a new term when a standard one already exists.

 

[rjbeery]

So, are you really saying that the "true kinetic energy" of a particle is always 0?

Yes. A particle cannot have "true kinetic energy". Kinetic energy exists in the INFORMATION between two objects as a POTENTIAL to do work, not in either one of them individually. If you don't believe me, throw a baseball and calculate what its apparent kinetic energy is from various moving points around the Universe.

 

[JesseM]

Kinetic energy exists in the INFORMATION between two objects as a POTENTIAL to do work, not in either one of them individually.

Do you think there is a "true" kinetic energy "between two objects" then? The total kinetic energy of the pair depends what frame you use too...

 

[Matterwave]

Yes. A particle cannot have "true kinetic energy". Kinetic energy exists in the INFORMATION between two objects as a POTENTIAL to do work, not in either one of them individually. If you don't believe me, throw a baseball and calculate what its apparent kinetic energy is from various moving points around the Universe.

Uh...even without a potential, objects can have kinetic energy, and the difference in kinetic energy is especially meaningful (even if the absolute value is not).

For example, a particle moving at .5c in one reference frame really should be assigned a higher kinetic energy as a particle moving at .1c in that same reference frame...a lot of physics would be thrown out the window if you just assigned them both 0 kinetic energy.

 

[PAllen]

The 'rest momentum' of all particles is zero. So all momentum is an illusion.







I hope ;) is obvious.

 

[bobc2]

So, to be clear, you would call the following a mis-calibrated mearurement:

A rocket with rest length of 100 meters is moving by at relativistic speed. I have a pair of super fast barriers I can raise and lower simultaneously (as I see it). I can momentarily contain the rest length 100 meter rocket between my barriers set 10 meters apart. My conclusion that the length is less than 10 meters is mis-calibrated, and inferior in some way to the rocket's own perception that what happened is that a barrier went up and down in front of the rocket, then both barriers moved, then the other barrier went up and down behind the rocket.

PAllen,

I really love the way you described the old "pole in the barn" example.

 

[rjbeery]

Do you think there is a "true" kinetic energy "between two objects" then? The total kinetic energy of the pair depends what frame you use too...

Well frankly I think anyone here would have a hard time strictly defining energy of any sort without a bit of hand-waving. "The ability to do work" is very common but...you seem to be suggesting that the ability of two objects to do work depends upon who is observing them. This doesn't seem right to me; does it to you?

If kinetic energy "actually existed" then I could create something approaching an infinite amount of energy by simply jumping in the air...just THINK of all that energy created between me and the infinitude of masses moving at varying relative velocities all over the Universe!

 

[Matterwave]

So, your argument is starting to sound more and more like you're Zeno (a stoic who believe motion was illusion)! According to the same reasoning as your argument then, "true velocity" is 0 always!

 

[ghwellsjr]

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 ?

Where did I ever say or imply that I think one object can have more than one length?

Greg and rjbeery are the ones, and now maybe you too, that believe that one object can have more than one length. I have said that you need to pick one inertial reference frame and then define, observe, analyze or do whatever you want for everything (all objects and all observers) according to that one frame. The lengths of all objects will have unique values assigned to them according to your arbitrarily selected reference frame.

Greg and rjbeery, and now maybe you too, want to use two different frames at the same time, one for each observer/object. They want to call the length of the first object the true length in one frame while the length of the second object is illusory and at the same time they want to call the length of the second object the true length in a second frame while the length of the first object is illusory. So they, and now maybe you too, want to have multiple lengths for each object, one they call true and the other one they call illusory.

This is not the way Special Relativity works.

 

[JesseM]

Well frankly I think anyone here would have a hard time strictly defining energy of any sort without a bit of hand-waving.

It's simply defined by the equations which define it. These definitions are useful because as you compute the value for kinetic energy + potential energy + rest mass energy at different times, you find it stays constant over time (assuming you are sticking to a single coordinate system).

"The ability to do work" is very common

No, word-definitions aren't how concepts like "energy" are understood in physics.

but...you seem to be suggesting that the ability of two objects to do work depends upon who is observing them. This doesn't seem right to me; does it to you?

"Work" is simply defined as the displacement multiplied by the component of force parallel to the displacement, integrated over the path if the force is changing or it's not a straight line. Since displacement is frame-dependent (you can always pick an inertial frame where the endpoints have the same position coordinate so displacement is zero), work is too.

Are you bothered by the fact that the velocity of an object depends on who's observing it? If not, why should you be any more bothered by the fact that work (or energy in general) is frame-dependent?

If kinetic energy "actually existed" then I could create something approaching an infinite amount of energy by simply jumping in the air...

The usual Newtonian definition of kinetic energy only applies in an inertial frame, if you jump into the air you move non-inertially. It's true that in your temporary inertial rest frame mid-jump the kinetic energy of the Earth is much larger than the kinetic energy of the Earth in your inertial rest frame while standing, but in each frame the total energy is constant with time, you aren't "creating" energy in any inertial frame.

 

[rjbeery]

Greg and rjbeery, and now maybe you too, want to use two different frames at the same time, one for each observer/object. They want to call the length of the first object the true length in one frame while the length of the second object is illusory and at the same time they want to call the length of the second object the true length in a second frame while the length of the first object is illusory. So they, and now maybe you too, want to have multiple lengths for each object, one they call true and the other one they call illusory.

This is not the way Special Relativity works.

Hey man, either you appreciate my analogy or you don't. Does a cube face have a true width, or does it vary depending on the angle from which we observe it? It ALL boils down to semantics, really, and this entire discussion is little more than navel-gazing, but I feel that the analogy is strong particularly due to the fact that the math is equivalent.

 

[bobc2]

Yes, I read the entire post. I'm not saying that length contraction has no consequences. That being said, I think there's a very valid reason to consider the rest-energy of a particle as its "true" energy...and that is because it's the only energy that is intrinsic to it. "Where" exactly does the additional energy of an object with relativistic velocity reside? Certainly not in the object itself!

rjbeery,

I think to be more consistent with your expressed views, you should have been talking about four-momentum rather than energy.

 

[rjbeery]

I think to be more consistent with your expressed views, you should have been talking about four-momentum rather than energy.

That's an interesting proposition bobc2. Let me think about it...

 

[Dale]

Does a cube face have a true width

What is this fixation on the word "true". Again: why do you feel the need to change the term from "rest length" to "true length"? After all, your "true length" is exactly the same as the standard "rest length", so why do you feel the need to invent a new term when a standard one already exists.

 

[ghwellsjr]

Greg and rjbeery, and now maybe you too, want to use two different frames at the same time, one for each observer/object. They want to call the length of the first object the true length in one frame while the length of the second object is illusory and at the same time they want to call the length of the second object the true length in a second frame while the length of the first object is illusory. So they, and now maybe you too, want to have multiple lengths for each object, one they call true and the other one they call illusory.

This is not the way Special Relativity works.

Hey man, either you appreciate my analogy or you don't. Does a cube face have a true width, or does it vary depending on the angle from which we observe it? It ALL boils down to semantics, really, and this entire discussion is little more than navel-gazing, but I feel that the analogy is strong particularly due to the fact that the math is equivalent.

No, I do not appreciate your analogy. This is not semantics. It is not navel-gazing. The fact that your analogy has math that is equivalent to whatever does not make it strong if your conclusion is wrong. If that were the criterion for making a good analogy, you could prove anything.

You started your thread with this sentence:

I wanted to discuss Lorentzian length contraction (and time dilation, for that matter).

How about we talk about time dilation now since you said you wanted to. Do you have the same attitude about the rate at which clocks at rest tick versus moving clocks? Do you make the claim that the tick rate of a moving clock is an illusion and that the true tick rate is that of the rest tick rate?

 

[ghwellsjr]

For the purposes of this discussion, all I ask is this:

If an object is transported from one laboratory to another that is moving relative to the first laboratory, then if its length is measured in that lab, the outcome will be the same as the identical procedure that was carried out earlier in the first lab. So there is some property of the object that was unaffected by being moved between the labs. Sort of like "the laws of physics are the same in all inertial frames".

Allowed this premise, I assert that relativistic effects cause miscalibrated measurements to give wrong answers. However if the instruments are made so they can take into account these effects, then all inertial observers will actually be measuring the length, and agreeing. Using miscalibrated measurement procedures, one is not measuring anything.

A question for you, if there is no objective reality, what exactly is the nature of thing you call length, and is there any point in measuring it ?

I have to leave now, but I'll check in again in about eight hours.

Aren't you aware that if the rod while in the second laboratory is measured by someone in the first laboratory, the length will be measured as contracted? And aren't you aware that if someone in the second laboratory measured the rod while it was still in the first laboratory using an identical procedure, the exact same contrated length will be measured? So couldn't we then say, as you did before, "So there is some property of the object that was unaffected by being moved between the labs. Sort of like 'the laws of physics are the same in all inertial frames'"?

Bear in mind, this doesn't have anything to do with frames, it's just the facts of nature. If you do analyze either of these two measurements using any inertial frame of reference, you will get the same results, because all measurements are frame invariant. How could they not be? When I observe you making a measurement and I see 39.37 inches show up on your measuring device, how can it matter how fast I am going relative to you? (I'm talking about me observing you making a measurement, not me making the same measurement.)

And aren't you aware that when a rod is accelerated from the first laboratory to the second laboratory it experiences an objective, real, actual, and true change in length? Did I leave out any words?

 

[Mentz114]

Aren't you aware that if the rod while in the second laboratory is measured by someone in the first laboratory, the length will be measured as contracted? And aren't you aware that if someone in the second laboratory measured the rod while it was still in the first laboratory using an identical procedure, the exact same contrated length will be measured? So couldn't we then say, as you did before, "So there is some property of the object that was unaffected by being moved between the labs. Sort of like 'the laws of physics are the same in all inertial frames'"?

Bear in mind, this doesn't have anything to do with frames, it's just the facts of nature. If you do analyze either of these two measurements using any inertial frame of reference, you will get the same results, because all measurements are frame invariant. How could they not be? When I observe you making a measurement and I see 39.37 inches show up on your measuring device, how can it matter how fast I am going relative to you? (I'm talking about me observing you making a measurement, not me making the same measurement.)

No but I don't have a clue what you're trying to say, and you clearly don't understand what I'm saying.

I stand by my assertion that an object only has one length.

You quoted the barn-pole 'paradox' in an earlier post. Is the resolution of the 'paradox' not made by correcting for the relatvistic effects that caused the confusion in the first place ?

And aren't you aware that when a rod is accelerated from the first laboratory to the second laboratory it experiences an objective, real, actual, and true change in length?

So you keep saying, but I don't know what it means.

 

[Mentz114]

What do you mean by 'objective reality' ?

'Objective' is a kind of antonym of 'subjective'. What it means in this context is that there are certain things which when measured in identical circumstances but at different times and places, will give the same answer. This is the nearest we can get to a test of 'reality' - that the outcome does not depend on the state of mind of the observer or idiosyncrasies of the measuring process.

It's the basis of physics. An objective property is not coordinate dependent, but measurements of it may be. But in the inertial frames of SR, all the local frames are the same so that is not the case here.

 

[JesseM]

I stand by my assertion that an object only has one length.

Well, only if you wish to define "length" differently from how physicists normally define it, i.e. coordinate distance between the ends of an object at a single moment in coordinate time. You can make up any definitions you want and I guess it's OK if you're consistent about it, but why would you want to create confusion by ignoring mainstream terminology?

You quoted the barn-pole 'paradox' in an earlier post. Is the resolution of the 'paradox' not made by correcting for the relatvistic effects that caused the confusion in the first place ?

No, there is no "correcting", you simply show that each frame has their own view of things and that these different views translate correctly to one another by the Lorentz transformation, and lead to no contradictions in their predictions about localized events.

It's the basis of physics. An objective property is not coordinate dependent, but measurements of it may be.

That distinction doesn't seem to make any sense. How could a property not be coordinate dependent if "measurements of it" were coordinate dependent? Our way of defining the values of any "properties" in physics is via measurements, no?

 

[Mentz114]

That distinction doesn't seem to make any sense. How could a property not be coordinate dependent if "measurements of it" were coordinate dependent? Our way of defining the values of any "properties" in physics is via measurements, no?

Yes, I didn't express that very well. I'll rephrase it to : perceptions of the property will depend on the method used to measure it.

Regarding the barn-pole scenario. In the pole frame the barn is (incorrectly) measured to be shorter than the pole. If the pole guy corrects this to give the length of the barn, there's no suggestion of a paradox. As you say, the correction factors are given by the LT.
(Don't you ever sleep ? . I'm working today so I'll have to let it stand there.)

 

[JesseM]

That distinction doesn't seem to make any sense. How could a property not be coordinate dependent if "measurements of it" were coordinate dependent? Our way of defining the values of any "properties" in physics is via measurements, no?

Yes, I didn't express that very well. I'll rephrase it to : perceptions of the property will depend on the method used to measure it.

That was me, not DaleSpam...and no, I don't sleep ;) But what are "perceptions of the property" as distinct from measurements of the property?

 

[Mentz114]

That was me, not DaleSpam...and no, I don't sleep ;)

Sorry, Jesse, I've amended it and added a bit it an earlier edit.

But what are "perceptions of the property" as distinct from measurements of the property?

Of course measurements are a type of perception so the words could be interchanged in what I said.

(You should try sleep, sometime. It's great. I really do have to go ...)

 

[JesseM]

Regarding the barn-pole scenario. In the pole frame the barn is (incorrectly) measured to be shorter than the pole.

Why "incorrectly"? At any given moment in this frame, the coordinate distance between ends of the barn really is shorter than the coordinate distance between ends of the pole, and this frame makes no errors in its predictions of frame-invariant facts. Again, you are free to use your own definition of "length" in which the word only refers to rest length, but hopefully you acknowledge that this is nonstandard terminology, and that if you use the standard meaning of "length" it is totally correct that the barn is shorter than the pole in the pole frame.

If the pole guy corrects this to give the length of the barn, there's no suggestion of a paradox.

Huh? I have no idea what you're referring to here, an analysis in the pole frame doesn't involve any "corrections" of the length of the barn. The usual resolution of the paradox is just to note that the two frames differ about simultaneity, which means they won't have any conflicts in their predictions about local events (like if the doors briefly close simultaneously in the barn frame when the pole is fully inside, in the pole frame neither door hits the pole because they close non-simultaneously) Perhaps tomorrow you could give a numerical example showing what this "correction" you're referring to would look like.

Of course measurements are a type of perception so the words could be interchanged in what I said.

OK, but I'm still not clear on whether you are trying to make a distinction between "the property" and "perceptions of the property" in your statement "perceptions of the property will depend on the method used to measure it". If perception is just a synonym for measurement, then the value of a property is whatever value is measured, no? If different frames get different values for some property, that means that particular property is inherently frame-dependent.

 

[ghwellsjr]

Aren't you aware that if the rod while in the second laboratory is measured by someone in the first laboratory, the length will be measured as contracted? And aren't you aware that if someone in the second laboratory measured the rod while it was still in the first laboratory using an identical procedure, the exact same contrated length will be measured? So couldn't we then say, as you did before, "So there is some property of the object that was unaffected by being moved between the labs. Sort of like 'the laws of physics are the same in all inertial frames'"?

Bear in mind, this doesn't have anything to do with frames, it's just the facts of nature. If you do analyze either of these two measurements using any inertial frame of reference, you will get the same results, because all measurements are frame invariant. How could they not be? When I observe you making a measurement and I see 39.37 inches show up on your measuring device, how can it matter how fast I am going relative to you? (I'm talking about me observing you making a measurement, not me making the same measurement.)

No but I don't have a clue what you're trying to say, and you clearly don't understand what I'm saying.

I stand by my assertion that an object only has one length.

You quoted the barn-pole 'paradox' in an earlier post. Is the resolution of the 'paradox' not made by correcting for the relatvistic effects that caused the confusion in the first place ?

And aren't you aware that when a rod is accelerated from the first laboratory to the second laboratory it experiences an objective, real, actual, and true change in length? Did I leave out any words?

So you keep saying, but I don't know what it means.

First off, I never quoted or made any mention of the barn-pole 'paradox'. You are referring to PAllen's post #39 where he described a similar 'paradox' that was later called the old "pole in the barn" example by bobc2 in post #66. JesseM answered your question to me already in post #79 so I won't comment further on it.

Now you think I don't understand what you are saying. I think you are saying that because of special relativity, observers can make incorrect measurements about the lengths of moving objects but they can always correct for these errors and if they did, the length of any object would always be the same as its rest length. Is this an adequate summary of your position?

 

[Dale]

'Objective' is a kind of antonym of 'subjective'. What it means in this context is that there are certain things which when measured in identical circumstances but at different times and places, will give the same answer.

If I am understanding you correctly then by "objective reality" you simply mean that the laws of nature exhibit time and space translation symmetry. If so I agree with that, but then "objective reality" does not contradict length contraction nor is it incompatible with other frame-variant or relative quantities.

 

[rjbeery]

OK, but I'm still not clear on whether you are trying to make a distinction between "the property" and "perceptions of the property" in your statement "perceptions of the property will depend on the method used to measure it". If perception is just a synonym for measurement, then the value of a property is whatever value is measured, no?

Jesse, this goes back to my rotated cube. "The property" is the width of the cube face; "perceptions of the property" is the apparent, foreshortened width due to a partial rotation. Are you suggesting that if a cube is rotated a full 90 degrees then its face width is actually zero?

 

[Mentz114]

At any given moment in this frame, the coordinate distance between ends of the barn really is shorter than the coordinate distance between ends of the pole,

But the barn is not in at rest in this frame which is why comparing the coordinates of the pole with the coordinates of the barn lead to the apparent paradox. If the measurements are adjusted for the relative velocity this erroneous conclusion is avoided.

Perhaps tomorrow you could give a numerical example showing what this "correction" you're referring to would look like.

That's disingenuous - of course I mean the LT to change coordinates so you get a comparison 'as if' both objects are at rest in the same frame.

I think further discussion about 'objective reality' belongs elsewhere and I believe I have given a definition adequate for this discussion.

I'm not sure what you mean by 'compatible with frame-variant or relative quantities.' They certainly exist as uncorrected data, but they don't measure anything, really.

Now you think I don't understand what you are saying. I think you are saying that because of special relativity, observers can make incorrect measurements about the lengths of moving objects but they can always correct for these errors and if they did, the length of any object would always be the same as its rest length. Is this an adequate summary of your position?

I apologise if I misattributed something to you. Your summary is close. SR allows us to change coordinates between frames so every inertial observer can measure the length that is found by using the same procedure in the objects rest frame.


I see no point in defining multiple lengths for the same physical manifestation because it leads to confusion ( viz. this and the other similar thread).

 

[Dale]

But the barn is not in at rest in this frame

Being at rest is not required in the definition of length.

comparing the coordinates of the pole with the coordinates of the barn lead to the apparent paradox. If the measurements are adjusted for the relative velocity this erroneous conclusion is avoided.

No, doing that only reinforces the paradox since the rest length of the pole is longer than the rest length of the barn.

 

[Mentz114]

Being at rest is not required in the definition of length.

By your ( standard ?) definition, yes.

No, doing that only reinforces the paradox since the rest length of the pole is longer than the rest length of the barn.

We're looking at different paradoxes. In the one I'm talking about, the pole is shorter than the barn when they are compared at rest, but not so from the moving pole frame.

However, I'm doing some calculations and I might find that the one-length interpretation won't fly.

 

[rjbeery]

Mentz114 and others: I was given the following link from the author on another forum. His Java applet appears to be quite powerful and capable of helping in analyzing SR length contraction and time dilation scenarios.

http://mysite.verizon.net/mikelizzi/Tutorials/TutorialMeterstickAndHole.html"

 

[PAllen]

By your ( standard ?) definition, yes.


We're looking at different paradoxes. In the one I'm talking about, the pole is shorter than the barn when they are compared at rest, but not so from the moving pole frame.

However, I'm doing some calculations and I might find that the one-length interpretation won't fly.

I think the 'standard' pole in the barn 'paradox' is the analogous to the alternate formulation I gave in my post #39. That is a rod with a rest length of 100 meters is hurtling towards a barn whose width is 10 meters. Assuming very rapid doors, you can open one door, let the rod in, close that door. Then open the other door to let the rod out. So briefly your 'true length' 100 meter rod has been enclosed in a 10 meter barn.

As I explained in my post #39, this would, in principle be possible. In the rod's frame, it would all look different: a barn door opens, then another opens; the really squashed barn than traverses the rod; then the door that opened first, closes. So the ordering of opening and closing has changed due to simultaneity differeences. However, the containment of the 100 meter rod in the 10 meter barn is awfully 'real' to the barn observer.

 

[JesseM]

Jesse, this goes back to my rotated cube. "The property" is the width of the cube face; "perceptions of the property" is the apparent, foreshortened width due to a partial rotation. Are you suggesting that if a cube is rotated a full 90 degrees then its face width is actually zero?

In my way of speaking, looking at how wide the face appears visually is not a valid method of measuring the property of "face width", though it is a valid way to measure separate properties like "apparent angular width" or "width of projection of face onto your visual plane". I would say that each property is defined in terms of how it is measured, if you use the wrong type of measurement for a given property you've just mixed up the definitions, you're not measuring your "perception" of the value of the property.

 

[JesseM]

At any given moment in this frame, the coordinate distance between ends of the barn really is shorter than the coordinate distance between ends of the pole,

But the barn is not in at rest in this frame which is why comparing the coordinates of the pole with the coordinates of the barn lead to the apparent paradox. If the measurements are adjusted for the relative velocity this erroneous conclusion is avoided.

Once again you have me confused with DaleSpam ;) Anyway, of course I understand the barn is not at rest in this frame, but why should that lead to any "apparent paradox"? In this frame the pole really doesn't fit entirely into the barn at any moment in time, as I said the seeming "contradiction" between what happens in the pole frame and what happens in the barn frame is resolved by realizing this is really just an issue of the relativity of simultaneity, that the order of the events "back end of pole enters rear of barn" and "front end of pole exits front of barn" is different in the two frames, thus there is no frame-independent truth about whether the pole was "really" ever entirely inside the barn. Perhaps you could be more specific about what you think the "apparent paradox" is here, and why you think the solution has anything whatsoever to do with "adjusting for the relative velocity"?

Perhaps tomorrow you could give a numerical example showing what this "correction" you're referring to would look like.

That's disingenuous - of course I mean the LT to change coordinates so you get a comparison 'as if' both objects are at rest in the same frame.

"Disingenuous" is a pretty strong word, are you suggesting I being intentionally deceptive and pretending not to know what you're talking about when I really do? I assure you that's not the case, I really have no idea what you mean by "correction" in this context, and your new clarification is equally confusing, I have no idea what it would mean mathematically to do "a comparison 'as if' both objects are at rest in the same frame". Again, if you can give me a numerical example perhaps I would understand what you're trying to say, but your verbal explanations don't correspond to any use of the Lorentz transform I can imagine.

I think further discussion about 'objective reality' belongs elsewhere and I believe I have given a definition adequate for this discussion.

I haven't been following every post on this thread, mostly just looking at the ones that were responses to my own comments, so can you tell me in which post you gave a definition of what you mean by "objective reality"?

 

[Mentz114]

I think the 'standard' pole in the barn 'paradox' is the analogous to the alternate formulation I gave in my post #39. That is a rod with a rest length of 100 meters is hurtling towards a barn whose width is 10 meters. Assuming very rapid doors, you can open one door, let the rod in, close that door. Then open the other door to let the rod out. So briefly your 'true length' 100 meter rod has been enclosed in a 10 meter barn.

As I explained in my post #39, this would, in principle be possible. In the rod's frame, it would all look different: a barn door opens, then another opens; the really squashed barn than traverses the rod; then the door that opened first, closes. So the ordering of opening and closing has changed due to simultaneity differences. However, the containment of the 100 meter rod in the 10 meter barn is awfully 'real' to the barn observer.

I've been analysing diagrams of the pole-barn type scenarios, especially the ordering of events in the frames. Then I started adding light rays to work out what the obervers see and I was struck by how quickly the information reaching the observers gets out of date ( at relativistic speeds ). So, while I'm not so adamant about the 'one-length interpretation' it's not quite dead yet. I'm going to work on the diagrams and analysis rather than post here for now and maybe have something worth reporting later.

Thanks for your inputs.

 

[Mentz114]

Once again you have me confused with DaleSpam ;) Anyway, of course I understand the barn is not at rest in this frame, but why should that lead to any "apparent paradox"? In this frame the pole really doesn't fit entirely into the barn at any moment in time, as I said the seeming "contradiction" between what happens in the pole frame and what happens in the barn frame is resolved by realizing this is really just an issue of the relativity of simultaneity, that the order of the events "back end of pole enters rear of barn" and "front end of pole exits front of barn" is different in the two frames, thus there is no frame-independent truth about whether the pole was "really" ever entirely inside the barn. Perhaps you could be more specific about what you think the "apparent paradox" is here, and why you think the solution has anything whatsoever to do with "adjusting for the relative velocity"?

Once again, I apologise. Your remarks are apposite and for now I'll give the same response I give to PAllen in my previous post.

(the post you're looking for is #78, I think)

This "thus there is no frame-independent truth about whether the pole was "really" ever entirely inside the barn. " is pretty much what I was beginning to think, but I'm not sure yet. I'll have to draw some more light beams.

Rather than repeating my arguments I'd like to work on it. I'll get back to you, thanks for your inputs.

Also thanks to other respondees and the OP, I don't have the time to reply to all of them, unfortunately.

 

[PAllen]

I've been analysing diagrams of the pole-barn type scenarios, especially the ordering of events in the frames. Then I started adding light rays to work out what the obervers see and I was struck by how quickly the information reaching the observers gets out of date ( at relativistic speeds ). So, while I'm not so adamant about the 'one-length interpretation' it's not quite dead yet. I'm going to work on the diagrams and analysis rather than post here for now and maybe have something worth reporting later.

Thanks for your inputs.

That would be great! I've made some attempts at this without ever carrying it through to a conclusion; but enough to see that what a movie shows would be quite different from the same data interpreted by removing light delays with standard conventions. Also, note that you can remove issues of interpreting light signals (at least in thought experiments) by such direct means as a hypothetical sheet of detecting tissue across each door opening (separate from the doors), attached to recording clock 'right there' so no time delay. Then, irrespective of what an observer would 'see' from any single vantage point, they could put all their data together and find it hard to avoid concluding they had momentarily trapped the 100 meter rocket in the 10 meter barn.

However, be all this as it may, I actually favor the idea of rest length being special for a sufficiently rigid body, and that it is reasonable to treat it as a property of the object. For larger and larger bodies, sufficient rigidity breaks down both in the real world and in theory (1 light year born rigid rulers, anyone?). What I also think is that other lengths observed for the object are also real in the only way that matters to me: what you would measure and reasonably conclude from your measurements.

My analogy is to a cylinder with arbitrary cross section. If someone says, without qualification, 'what is the cross section of that cylinder?' , we all assume an orthogonal slice and discuss the resulting shape and area. We do this even though if we actually cut the cylinder at an angle, we don't pretend that the result we got is an illusion and not real. Furthering this analogy, the more irregular the shape (rather than a cylinder), the more it breaks down to talk about any standard cross section. The analogy to space time seems very direct to me. A rigid body is the analog of the cylinder (cylindrical world tube), while not rigid bodies are like messy objects.

 

[ghwellsjr]

You started your thread with this sentence:

I wanted to discuss Lorentzian length contraction (and time dilation, for that matter).

How about we talk about time dilation now since you said you wanted to. Do you have the same attitude about the rate at which clocks at rest tick versus moving clocks? Do you make the claim that the tick rate of a moving clock is an illusion and that the true tick rate is that of the rest tick rate?

Rjberry, I'm still waiting for a response from you to my questions posed in post #75.

 

[PAllen]

I've been analysing diagrams of the pole-barn type scenarios, especially the ordering of events in the frames. Then I started adding light rays to work out what the obervers see and I was struck by how quickly the information reaching the observers gets out of date ( at relativistic speeds ). So, while I'm not so adamant about the 'one-length interpretation' it's not quite dead yet. I'm going to work on the diagrams and analysis rather than post here for now and maybe have something worth reporting later.

Thanks for your inputs.

I have a suggestion that might be of interest. Instead of pole/ barn, consider the following based on my equivalent variant in post #39; this provides several different types of measurements at once:

100 meter rest length rocket going near c left to right (close enough to c that its contracted length is less than 10 meters). Assume the rocket has fins signficant wider than the body of the rocket.

Imagine tissue like detecting membrane and associated clocks. These can directly measure the passage of nose and fins of the rocket. These are placed 10 meters apart.

Also imagine barriers shooting up and down as in post #39 adjacent to the tissue detectors, but with cameras on them positioned to take head on / tail on pictures of the rocket when the barriers are fully up.

So now we have the sense of containment from barriers, direct measurement of rocket nose tail passing, plus a very interesting pair of images.

I think these end on cameras or more relevant than side cameras, though that would be interesting too.

(The right image would show the rocket from well before it reached the left barrier. The left image would, all the same, show a distorted picture of the tail).

 

[rjbeery]

How about we talk about time dilation now since you said you wanted to. Do you have the same attitude about the rate at which clocks at rest tick versus moving clocks? Do you make the claim that the tick rate of a moving clock is an illusion and that the true tick rate is that of the rest tick rate?

Depends what you mean by "illusion". You might take it to mean that the measurement itself is false, rather than simply differing from the true value of the property being measured, but that isn't right (or rather, that's not what I mean). When I say illusion I mean that the property of an object being measured isn't its "true" value, but that doesn't mean that the "illusion" has no physical consequences. As an example, I had to fit an ottoman through a door the other day which would not fit because the ottoman was wider than the doorway. I rotated the ottoman, such that its foreshortened length was able to fit. Did I actually change the length of the ottoman, or was its foreshortening "illusory"? The illusory effect of foreshortening has physical consequences.

Another example: analyze the color of a binary star and you'll find that it alternates between being redshifted and blueshifted as it orbits its partner. Is it "actually changing color", or is it "an illusion"? The answer that most people would give is that the apparent color change is an illusion...yet the blueshifted color has more energy than the redshifted color nonetheless. Therefore the illusory effect of wavelength shifting has physical consequences. Ask yourself why we feel it's proper to correct for Doppler induced red- and blue-shifting caused by relative motion but NOT to correct for SR-related length contraction caused by relative motion...

When we make measurements we must consider perspective before assigning "true" values to the object under consideration. The whole point of this thread for me is to point out that "perspective" includes relative speed, and that leads me to conclude that "true" length is that which is measured locally and inertially to an object. In the end it's nothing more than a (possibly unnecessary) semantic convention but I find the logic to be sound.

 

[ghwellsjr]

Depends what you mean by "illusion".

I meant whatever you meant at the end of your first post:

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.

Would you also make this claim:
Considering SR in this light, one could make the case that clocks DO have an absolute time, that being their minimally-measured proper time, and that any Lorentzian dilation is in fact an illusion.

You are using the words "true" and "false" and "illusion" and "actually" and "apparent" and "absolute" when applied to lengths of moving objects. I'm asking you to use whatever you mean by those words (and I don't care what you mean) and tell me if you believe those same words apply to times on moving clocks.