Are the transformations just observed ones or real ones?

[Noyhcat]

What does any of that have to do with my post?

The rethinking bit.

 

[Windows]

First, I didn't define time at all. I answered your question about why time was related to velocity. That question already presupposes that time is well defined elsewhere.

Second, it is not obviously wrong, especially not for the reason you gave. Currently, the best definition of a unit of time, the SI second, is based on atomic transitions (hyperfine splitting of cesium). That is fundamentally an EM process, so it is reasonable to say that time is defined in terms of light, from an experimental standpoint, and the definition is far from obviously wrong. In the case of the second, the motion of the light is not important, just it's frequency.

You didn't get it. You define time as what you see, i.e, as the information you get from photons. Time is related to motion, photons do travel, so without time photons would not even travel. And the EM process is just photons, you again define time as the motion of photons which is incorrect.

 

[Dale]

You didn't get it. You define time as what you see, i.e, as the information you get from photons. Time is related to motion, photons do travel, so without time photons would not even travel. And the EM process is just photons, you again define time as the motion of photons which is incorrect.

Again, I didn't define time in this thread, and please don't presume to put words in my mouth, particularly not words that are so completely unrelated to anything I have ever or would ever say. If I were to define time I certainly wouldn't define it as "what I see" nor as "information I get from photons".

The definition I like is "time is the quantity referred to by the variable 't' in the standard physics formulas." This can be practically restated as "time is what a clock measures".

I wouldn't define time as "the motion of photons" because time is part of the strong and weak nuclear forces as well as gravity. Time is not exclusive to the EM force, and time passes even when there are no photons.

 

[Sugdub]

Right and if you check out the common thought experiment whereby a flashlight is pointed up toward the ceiling of a moving train, you will see why time is affected by velocity.

Because light travels at the same speed for all observers, and because the light coming from a flashlight that is sitting on the floor of and that is pointed at the ceiling of a moving train has to travel a farther distance when viewed by someone who is not on the train, AND because the universe behaves the same no matter what you're doing... time must dilate.

It takes just as long for light to hit the ceiling when viewed by observer A in the train as it does when viewed by observer B outside the train.

I took this from the internet via http://www.copyright.gov/fls/fl102.html special powers: ...

Observing and measuring imply dealing with events which affect the observer and his/her measurement devices. Such events are co-located with the observer or with his/her devices. Hence a signal must bring some information there and the physical characteristics of its propagation must be taken into account. There is no such thing in your input, therefore I believe you are not actually dealing with observations and neither with measurements. This thought experiment will become clear once all references to “observers” or “someone” or “view” has been removed.
You are dealing with two theoretical representations of a thought experiment: one description (A) hooked on an inertial reference frame which is at rest in respect to the train; a second description (B) hooked on another inertial reference frame which is in relative motion in respect to the train. You are representing the same three events (emission, reflection and detection of a single light ray) by assigning to each event different coordinates in both reference frames. These are precisely the conditions under which the Lorentz transformation has been formally derived under the SR theory: it enables swapping from the coordinates of an event represented in frame A to the coordinates of the same event represented in frame B. SR deals with providing a continuous range of Lorentz-equivalent representations of the world (or the relevant subset of it) lying in the background of one single experiment. In any of these “representations of the world” time is dilated and lengths are contracted as compared to the “world” attached to frame A.
But these values should not be confused with the outcome of observations or measurements: the propagation of different signals towards an observer at rest in frame A and towards an observer at rest in frame B, respectively, must be applied to the aforementioned values in order to compute their respective “observed” or “measured” values.

I hope you could rework the text below the diagram you presented in this post since it is fully relevant to clarifying what is "real".

 

[harrylin]

You didn't get it. You define time as what you see, i.e, as the information you get from photons. Time is related to motion, photons do travel, so without time photons would not even travel. And the EM process is just photons, you again define time as the motion of photons which is incorrect.

Again, that's putting things upside down. Our time concept is based on motion and measured with clocks - even light clocks are possible. Clock frequency is a result of motion. No motion => no clocks and no concept of time possible.

 

[harrylin]

So my comment was correct? [..].

No. I explained that already in great detail in post #74 - but post #95 is pertinent for understanding that clock readings can depend on motion. And the lightclock illustration in post #79 is most useful to explain the concept.

 

[Noyhcat]

I hope you could rework the text below the diagram you presented in this post since it is fully relevant to clarifying what is "real".

If I get you correctly, I need to work on my terminology, and I don't disagree. I am consciously working to better this as I move forward.

You didn't get it. You define time as what you see, i.e, as the information you get from photons. Time is related to motion, photons do travel, so without time photons would not even travel. And the EM process is just photons, you again define time as the motion of photons which is incorrect.

I wonder if maybe a more real-world example would help...

I think of a GPS satellite, up in space. The engineers building it on Earth must purposely configure it's clock to move faster that what we normally see a clock running at. In other words, in the lab, before it's launched into space the satellite's clock is ticking at a faster rate than the clock on the wall in the same lab. This is by design.

Now they send the satellite up into space, and the clock, relative to us, slows down, as predicted by SR. If the engineers did their calculations right, the clock on the satellite now in orbit ticks at the same rate as the clock on the wall in the lab, relative to lab. In order for us on the ground to directly interact with the satellite now in orbit sensibly, we have to account for the actual time dilation that is going on.

Relative to the satellite, the clock on the wall in the lab is now ticking faster, but sure enough, it's ticking at the same rate as the satellite's clock. This is how we actually build satellites.

Time is not absolute. It is perceived differently by people moving relative to each other, but it behaves the same everywhere. Time does not appear to pass slower on the satellite to people on Earth because the light coming from it hits our eyes slower or later. Time appears to pass slower because it is passing slower, relative to us.

 

[harrylin]

A few little corrections:

[..]
I wonder if maybe a more real-world example would help...

I think of a GPS satellite, up in space. The engineers building it on Earth must purposely configure it's clock to move faster that what we normally see a clock running at. In other words, in the lab, before it's launched into space the satellite's clock is ticking at a faster rate than the clock on the wall in the same lab. This is by design.

Now they send the satellite up into space, and the clock, relative to us, slows down, as predicted by SR.

The clock must be made to tick at a slower rate to compensate for the combined effects of speed and gravitation as predicited by GR. See: https://en.wikipedia.org/wiki/Error...sitioning_System#Calculation_of_time_dilation

If the engineers did their calculations right, the clock on the satellite now in orbit ticks at the same rate as the clock on the wall in the lab, relative to lab. In order for us on the ground to directly interact with the satellite now in orbit sensibly, we have to account for the actual time dilation that is going on.

Relative to the satellite, the clock on the wall in the lab is now ticking faster, but sure enough, it's ticking at the same rate as the satellite's clock. This is how we actually build satellites.

Time is not absolute. It is perceived differently by people moving relative to each other, but it behaves the same everywhere. Time does not appear to pass slower on the satellite to people on Earth because the light coming from it hits our eyes slower or later. [..].

"Relative to the satellite" doesn't mean much: the satellite isn't even nearly in rest in any inertial frame (and I did not copy your last sentence which I could not parse).
[addendum: and the clock on the wall uses the ECI frame]

 

[yuiop]

... "Relative to the satellite" doesn't mean much: the satellite isn't even nearly in rest in any inertial frame ...

I think you are being a little bit picky here. The satellite is moving inertially, in so much as it does not experience proper acceleration and it is moving along a geodesic. The spacetime local to the satellite is almost Minskowkian. However I would agree that the clock on the Earth's surface that it being compared with, is not at rest in a inertial reference frame as it experiences proper acceleration. The difference in altitude between the two clocks in a gravitational field, excludes it from being a purely SR situation.

I think the spirit of the OP is about the physical significance of measurements made between two purely inertial reference frames, where the measurements are exactly symmetrical, so I agree that the satellite example does not fit in very well with that premise.

 

[harrylin]

I think you are being a little bit picky here. The satellite is moving inertially, in so much as it does not experience proper acceleration and it is moving along a geodesic. The spacetime local to the satellite is almost Minskowkian. [..]
I think the spirit of the OP is about the physical significance of measurements made between two purely inertial reference frames, where the measurements are exactly symmetrical, so I agree that the satellite example does not fit in very well with that premise.

My reason for being a bit picky about that is that the comparison is non-local and includes "absolute" SR time dilation per each rotation (just like Einstein's SR clock scenario). With all mentioned caveats and the level of discussion it's perhaps better not to bring GPS in it, or otherwise to leave out all the details and just point out the main result: the clocks are offset before launch in order to tick approximately in synch in the ECI frame after launch; and the total effect can be calculated with the transformation equations (SR+GR).

 

[Sugdub]

If I get you correctly, I need to work on my terminology, and I don't disagree. I am consciously working to better this as I move forward.

Don't take me wrong. I "hope" you will clarify whether the thought experiment you presented actually deals with observers attached to different observation frames or with the representation of three events related to one light ray in two reference frames irrespective of any "observation" or "measurement" being performed.
Also, and if you are dealing with observations, there is no point in mentionning someone outside the train as opposed to on-board since the relevant criterion for SR is the relative motion of the observer in respect to the train (along the x axis), irrespective of the location.

 

[kaplan]

Sorry for my long absence but here is what I mean: I was just asking if I was moving at a great velocity, if someone sees me holding a clock, he will see it go slowly, but from my reference frame, the clocks is not slowed down and that is just a consequence of the electrodynamics of moving objects taking in consideration the constant speed of light.
So time has nothing to do with velocity just as length, they are just 'measured' transforms because the speed of light is constant, i.e, that my time is the same as yours even if my v=0.999c but you just observe me having a slower time because of the constant speed of light.

Take a meter stick, and hold it so you're viewing it like this --. It's got a length of one meter (this way --), a height of maybe one cm (this way |), and a width of a few cm (into the page). Now rotate it 90 degrees so you're viewing it like this |. Now it's got a length of 1 cm, a height of one meter, and a width (into the page) of a few cm.

Did the meter stick "really" change? I'd say no, you're just describing it with respect to a new set of orientations. That's almost exactly analogous to time dilation and length contraction - they tell you how time and length transform when you use coordinates that are moving with respect to the original ones.

Of course these transformations have real consequences when two things interact - getting hit by a meter stick will hurt more or less depending on its orientation relative to you, and the traveling twin comes back younger.

 

[WannabeNewton]

The spacetime local to the satellite is almost Minskowkian.

Just for clarification, this has nothing to do with the satellite being locally inertial.

 

[yuiop]

Just for clarification, this has nothing to do with the satellite being locally inertial.

I guess so, because the spacetime is locally Minkowskian even for non inertial objects. Thanks for the pointer. For further clarification, would you agree that the satellite is locally inertial and the clock on the ground is not?

 

[WannabeNewton]

Certainly yes I would agree with that.

 

[Noyhcat]

A few little corrections:

The clock must be made to tick at a slower rate to compensate for the combined effects of speed and gravitation as predicited by GR. See: https://en.wikipedia.org/wiki/Error...sitioning_System#Calculation_of_time_dilation

Right! Thanks for the great link. Net GAIN of 38640ns. I was trying to give a real world example of how time dilation is "real" vs "observed" per OP's original question, but I may just have confused matters by including another layer of complication by bringing GR into it.

"Relative to the satellite" doesn't mean much: the satellite isn't even nearly in rest in any inertial frame (and I did not copy your last sentence which I could not parse).
[addendum: and the clock on the wall uses the ECI frame]

I've only started to get into GR (evinced by my complete omition of its existence in my post), and I get the idea that there is nothing inertial about an object that is actively being accelerated on. I concede your Yuiop's points and will be doing some more reading.

Though, does every reference frame need to be inertial? If the clock on the lab wall and the satellite are moving relative to the ECI frame, allbeit at different speeds, I get that, but can we not speak of things from the satellite's reference frame as well? Shouldn't a person who is "standing" at the center of the Earth be able to state the laws of physics just as a person who is on board the satellite should?

If your point is "stop mixing IRF's with non inertial ones" I get that too. :)

 

[yuiop]

Though, does every reference frame need to be inertial?

No, they do not need to be inertial, as for example in the Rindler metric which considers the reference frame of an accelerating observer. I suspect (although it is hard to be sure) that the OP is interested in the tangible physical differences between measurements made between two purely inertial observers where all the measurements are symmetrical. It is easy to show that there are tangible physical differences when non inertial reference frames are considered because the measurements are not symmetrical.

If the clock on the lab wall and the satellite are moving relative to the ECI frame, allbeit at different speeds, I get that, but can we not speak of things from the satellite's reference frame as well? Shouldn't a person who is "standing" at the center of the Earth be able to state the laws of physics just as a person who is on board the satellite should?

I think we can, by stating the laws of physics in an invariant way that all observers can agree on. When we consider the results purely due to a Lorentz boost with no proper acceleration involved, there are no physical quantities that vary in a invariant way. This I think is the crux of the matter that the OP is asking about. (I hope I stated that correctly as I am not very good with the formal language of relativity.)

We can rule out GR (but not non inertial motion) by modifying your example and placing the reference clock on an absurdly high tower that has the same altitude as the satellite. Now the orbiting clock will show less elapsed time than the reference clock on the tower, each time it passes. I think someone also gave the more practical example (that also excludes GR) of how the half life of particles is considerably extended when they are circulating at high speed in a cyclotron, but again that is a non inertial example.

 

[harrylin]

In addition:

[..] Shouldn't a person who is "standing" at the center of the Earth be able to state the laws of physics just as a person who is on board the satellite should? [..]

If you want to keep things conceptually simple and straightforward as in classical physics and SR, then you (and those persons) should stick to using Newtonian ("Galilean") reference systems. The ECI frame is approximately such a system (only approximately due its orbit around the Sun).

 

[Noyhcat]

I think I'm going to stick to trains for a bit longer. :)

 

[harrylin]

I think I'm going to stick to trains for a bit longer. :)

The trains (as long as they go at constant speed in a straight line) are great.

 

[phyti]

You didn't get it. You define time as what you see, i.e, as the information you get from photons. Time is related to motion, photons do travel, so without time photons would not even travel. And the EM process is just photons, you again define time as the motion of photons which is incorrect.

'Time' does not cause anything. Photon motion can define a unit of 'time'.
Refer to drawing.
Light is emitted from a source in a direction p, perpendicular to x, the direction of motion, and reflects from a mirror a distance d=1, to a detector/counter. For the clock to function, the photon path must have an x and p component. The x component compensates for the motion of the clock at speed v. The p component becomes the active part of the clock. Since the photon speed is constant, its path in any direction generates a circular arc for the 90º between the p axis and x axis. This means the relative photon speed along p = c*sqrt(1-(v/c)^2) = c/γ, i.e. the clock ticks slower, the faster it moves past an observer.
The clock moves in a 1-dimensional space, while/(simultaneously) the photon moves in a 2-dimensional space. The clock is counting spatial increments of (2γd) which are labeled in the traditional manner as ‘time’.

With vt the x component and pt the p component, the relation can be rephrased as
1. (vt)^2 + (pt)^2 = (ct)^2, or
2. (object motion)^2 + (light motion)^2 = (light motion)^2, or
3. (object motion)^2 + (object time)^2 = (light motion)^2
Line 3 is the misconception, equating ‘object time’ to ‘object motion’, that leads to the idea of ‘moving thru time’.

‘Time’ is a relation between events, a scalar or number (thus no direction) that is always cumulative. A clock never runs backward reducing ‘time’. It can be likened to a ships log, or a diary, or any method of historical record keeping.

 

[Dale]

The term "length contraction" has two different meanings; one meaning relates to a reduction in a moving object's or system's equilibrium length according to a system in which that object or system was in rest before. This was also how Einstein used it in 1905: "let a constant velocity v be imparted in the direction of the increasing x of the other stationary system".

You are taking the Einstein quote out of context. The full quote, in context, is:

... a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod. We now inquire as to the length of the moving rod, and imagine its length to be ascertained by the following two operations:—

(a)The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest.
(b)By means of stationary clocks set up in the stationary system and synchronizing in accordance with § 1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated “the length of the rod.”

So in Einstein's 1905 the imparting of velocity v is merely setting up the initial conditions that the rod is moving in the "stationary" system. The actual length contraction comparison (a vs b) is clearly between frames, not before and after acceleration in a single frame.

 

[harrylin]

You are taking the Einstein quote out of context. The full quote, in context, is: [..]
So in Einstein's 1905 the imparting of velocity v is merely setting up the initial conditions that the rod is moving in the "stationary" system. The actual length contraction comparison (a vs b) is clearly between frames, not before and after acceleration in a single frame.

You took my side remark ("This was also how") to be an issue. As a reminder, this concerns your insistence that:

It is not a change in an observed phenomenon [..] Again, length contraction isn't about changes in length, it is about disagreement between frames.

I referred to a century old paper to illustrate that we are telling you nothing new - I could also have cited from Bell and others incl. a paper by myself not so long ago. However, as your reading of Einstein appears to be different from mine and this may also be instructive for more people, I now spent some time to clarify Einstein's development with a fuller context in italics and with some added precisions by me in non-italics. Einstein's symbol l may be confusing, so I replaced it by L₀.

Let there be given a stationary rigid rod; and let its length be L₀ as measured by a measuring-rod which is also stationary.
[ Definition: L₀ = length as measured in rest in "stationary system" S. ]
We now imagine the axis of the rod lying along the axis of x of the stationary system of co-ordinates, and that a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod. We now inquire as to the length of the moving rod [..]
In accordance with the principle of relativity [..]"the length of the rod in the moving system"- [let's label that L'₀] must be equal to the length L₀ of the stationary rod.
[According to POR: L'₀ = L₀]
[..] "the length of the (moving) rod in the stationary system" [let's label that L_t] [..] we shall find that it differs from L₀.
Current kinematics tacitly assumes [..] that a moving rigid body at the epoch t may in geometrical respects be perfectly represented by the same body at rest in a definite position.

He finds thus that in S, L_t ≠ L₀.
And a note about "kinematics": classical mechanics makes its assumption for the equilibrium length of the object under the condition of negligible plastic deformation; and the same specifications apply to the ruler for the measurement in motion. SR doesn't change those specifications.

Einstein elaborated next (emphasis mine):

Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks

[..] The equation of the surface of this sphere moving relatively to the system K with velocity v [..]
Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body of no matter what form) do not appear modified by the motion, the X dimension appears shortened in the ratio 1/sqrt{1-v^2/c^2}, i.e. the greater the value of v, the greater the shortening. [..]
Equation of shape in S: Δx = Δx₀/γ
A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion -viewed from the stationary system- the form of an ellipsoid'

Once more, I illustrated that with my calculation example and yuiop illustrated it as follows (emphasis mine):

[..] Ehrenfest paradox [..] the length contraction of the outside edges of a rotating object causes real stresses that would eventually tear the the object apart if the radius was not permitted to alter as the rotational speed varied. The next best demonstration is Bell's rockets paradox, where a string of fixed length (in one reference frame) breaks due to length contraction[..].

BTW, I thought that it was understood -notwithstanding Einstein's limited scope in 1905- that Ehrenfest's disc can't be rigid and that Bell's string isn't supposed to be rigid - but see next!

Stevendaryl added as further clarification (emphasis mine):

Yeah, there are two "length contraction" effects, one having to do with the changes in the measured equilibrium length of an object that is set in motion, and the second having to do with a comparison of distances in two different inertial coordinate systems.

There are similarly two "time dilation" effects: the changes in the measured rate of a clock that is set in motion, and the second having to do with a comparison of elapsed times in two different inertial coordinate systems.

Of course, these pairs of effects are closely related:

• From the assumption that clocks and rods undergo time dilation and length contraction when set into motion, one can show that a coordinate system based on those moving clocks and rods will be related to the original coordinate system through the Lorentz transformations.
• From the assumption that the forces governing rates of clocks and lengths of objects are Lorentz-invariant, one can derive that they must undergo time dilation and length contraction.

But then the following amazing remarks appeared in a parallel thread despite all the preceding:

[..] There is no such thing as length contraction in one frame.

In reaction I suggested to digest the information by myself, yuiop and Stevendaryl in this thread, but apparently that did not happen:

Fixed it for you [AT added rigid]. This the key element that people often forget, when assuming "length contraction" in that historical sense. And it is a good reason to avoid that historical usage [..] This leads to confusion [..] generally in Bell-Spacehip-Paradox threads.

[my correction deleted by Dalespam]

[..] I don't want any historical apologists cluttering up the thread.

[my correction deleted by Dalespam]

The above is self-explaining, so I will leave it at that.

 

[Dale]

I referred to a century old paper

Your reference was out of context. Now, your explanation here is also very selectively edited to keep it out of context.

Your first [..] hides his comment

and imagine its length to be ascertained by the following two operations:—

(a)The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest.
(b)By means of stationary clocks set up in the stationary system and synchronizing in accordance with § 1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated “the length of the rod.”

Which clearly identifies the comparison being done between frames.

Your second [..] hides the comment

the length to be discovered by the operation (a)—we will call it

Your third [..] hides his statement

The length to be discovered by the operation (b) we will call

And your fifth [..] hides

that the lengths determined by these two operations are precisely equal

All of which completely cement the fact that all of Einstein's previous comments are concerning the comparison between two frames, the operations a and b he defined.

Your selective reading of Einstein's paper is truly amazing. It makes me no longer certain that there even is a historical case to be made for the pre- vs. post-acceleration interpretation of length contraction. Certainly, it isn't to be found in Einstein's 1905 paper, and if your reading of his paper led you to that conclusion then I suspect that your reading of other sources also led you to a similar erroneous conclusion.

Furthermore, English is always ambiguous, and more so German translated into English. So the best place to look for an unambiguous definition is in the mathematical derivation. All the mathematical derivations of length contraction which I have seen (including Einstein's 1905 derivation in section 3) are a comparison of the length in two frames, not a comparison of the length before and after acceleration in a single frame. That further casts doubt on the idea that length contraction has multiple historical definitions.

Can you find even a single example where length contraction is mathematically derived using pre- and post-acceleration lengths in a single frame rather than deriving length contraction as a comparison between two frames?

 

[kaplan]

Can you find even a single example where length contraction is mathematically derived using pre- and post-acceleration lengths in a single frame rather than deriving length contraction as a comparison between two frames?

The length of an object is an experimentally measurable quantity, and it depends only of the object's current state and how you do the measurement, not the object's past history.

In other words it doesn't make the slightest bit of difference whether an object got to its current state of motion "after acceleration in a single frame" (whatever that even means) versus always being in that state of motion, or something else.

Einstein might never have said that explicitly, but if so it's because he considered it obvious. If you want a related example that Einstein did discuss, take the twin paradox.

 

[universal_101]

The length of an object is an experimentally measurable quantity, and it depends only of the object's current state and how you do the measurement, not the object's past history.

In other words it doesn't make the slightest bit of difference whether an object got to its current state of motion "after acceleration in a single frame" (whatever that even means) versus always being in that state of motion, or something else.

Einstein might never have said that explicitly, but if so it's because he considered it obvious. If you want a related example that Einstein did discuss, take the twin paradox.

Exactly, Twin Paradox is all about the comparison of state of NO motion and after some acceleration the state of Relative Motion. In daily scientific practice, accelerators are also very good example and they are almost always accelerating the particles, but we do apply all the relativistic corrections nonetheless. And these corrections are applied because there is a relative motion between lab frame particles and tunneled ones, neglecting the acceleration needed to achieve the state of relative motion. So, if the two states are not related (i.e. no motion and relative motion), why do we compare them for the time dilation!

 

[Dale]

The length of an object is an experimentally measurable quantity, and it depends only of the object's current state and how you do the measurement, not the object's past history.

Correct. That is another reason why length contraction is correctly understood as a disagreement between frames, not a change over time.

 

[Dale]

And these corrections are applied because there is a relative motion between lab frame particles and tunneled ones, neglecting the acceleration needed to achieve the state of relative motion.

Here you seem to understand. I am not sure where you are missing the connection in the case of current.

 

[stevendaryl]

Correct. That is another reason why length contraction is correctly understood as a disagreement between frames, not a change over time.

I just don't understand why you say that. It's BOTH a disagreement between frames AND a change over time. If you take a stiff rod of length L, initially at rest in some frame F, and give it a really hard shove on one end so that it is moving at speed v relative to F, the rod will contract. A compression wave will propagate through the rod, and when it reaches the far end, that end will start moving forward. Between the times that you push one end and the time the compression wave reaches the other end, the rod is shrinking. That's because the rear end is moving forward, but the front end is not. After the whole rod is moving, it's length will fluctuate. After compressing to a minimum length of L (1-\frac{v}{c}), it will then expand and contract, until it reaches an equilibrium length of L \sqrt{1-\frac{v^2}{c^2}}. That is all from the point of view of a single reference frame. If instead, you had pulled the front end, then initially the rod would stretch to a maximum length of L (1+\frac{v}{c}), and then it would contract, and expand, etc., until eventually it settled down to the same final length of L \sqrt{1-\frac{v^2}{c^2}}.

Now, I certainly agree with you that there is no easy way to prove what the final length would be without using multiple frames, but the facts as outlined above are all about what happens according to a single frame.

 

[kaplan]

Correct. That is another reason why length contraction is correctly understood as a disagreement between frames, not a change over time.

If an object undergoes linear acceleration, its length - as measured in a fixed inertial frame - will change over time. That follows immediately from the Lorentz transformations.