When Does an Observer Become an Inertial Observer?

Again, it's similar to saying "rate of speed". Speed is a rate, but that doesn't mean "rate of speed" is a correct use of the terms.

Well, you could concede the point. That would end the discussion pretty quick.

 

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All I can concede at this point is how easy it is to confuse people who have small brains.

 

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And yet, physicists and mathematicians do use the term "instantaneous rate of change". So what does "rate of change" otherwise mean in physics?

 

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A short argument:
https://en.wikipedia.org/wiki/Length_contraction

Excerpt:
"Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame."

Note that there is no mention of your requirement of "uniform linear motion" in that sentence. It only has to be a "moving object." So your source or argument for your claim that uniform linear motion is required is.........???


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Another longer argument:

You state (correctly) that that an object in uniform linear motion with respect to some inertial frame (let's call it frame K) will be measured by that frame to be length contracted along the direction of motion. That is equivalent to saying that frame K would have measured that same object when it was at rest, i.e. before it was accelerated up to speed, as being longer in length. So we know that, according to frame K, the object went from its longer length (prior to acceleration) to its contracted length (after the acceleration was over).

Now, if uniform motion is required for length contraction, as you claim, then frame K could not have measured the object as length-contracted during any of the time it was accelerating. It would have to have remained its proper length that whole time, until finally the acceleration period was over, and then the object would have to instantly become length-contracted once it reached a constant velocity, which is absurd.

On the other hand, if relative motion is all that is required for length contraction to apply, then the object would have been measured as becoming gradually shorter and shorter during the time it was accelerating to greater and greater speeds.

Okay, so are you actually saying that, in my example above, the object would have been measured as becoming gradually shorter and shorter during the time it was accelerating to greater and greater speeds? And are you actually saying the only reason is because you chose to break that whole duration of time up into instantaneous moments of time where the object had only one instantaneous velocity? If so then your claim is indistinguishable from mine, and Occam's razor applies.

 

Neddy, you claim to be a whizz when it comes to the Special Theory. Then obviously you will have no problem with the following re-formulation.......

For any object whatever, there exists coordinate systems relative to which it can be considered to be in (almost) any state of linear motion whatever, including rest. Of course, the "almost" here excludes light speed; this is a postulate of the Special Theory.

 

I never claimed to be a whizz, but otherwise, yes, agreed. Assuming you mean for a sufficiently short period of time.

However, I had established an inertial frame I called "frame K" and made my measurements from there. So, does that frame measure the moving object I described as length-contracted during the time it is accelerating up to speed? Of course it must become gradually more length contracted as its speed increases, relative to frame K.

So what other frame are you invoking here?

 

Here try this test. Choose which of the following equivalent statements is simpler, and apply Occam's razor:

1. Length contraction is the phenomenon that the length of an object which is moving is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame.

2. Length contraction is the phenomenon that the length of an object which is moving with uniform linear velocity is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame, and this also applies to objects which are moving with non-uniform linear velocity, because (insert your reason here).

Hint: The second statement is identical to the first, with the exception of the added words shown in red.

 

As it happens, I agree with neither statement (as written), so I refuse your "test"

I also apologize for claiming you are a "whizz" at SR. Clearly you do not understand any form of relativity.

P.S. Do NOT attempt to learn any form of science from Wikipedia - you may get lucky or you may not. Thinking or even calculating is a better option

 

All you have to do is show us your source for claiming that Lorentz contraction only applies to objects with uniform linear velocity.

 

Once again, you demonstrate your lack of understanding - the above phrase "uniform linear velocity" is missing a crucial qualifier. Here's my test - what is it?

 

I don't know, I got that phrase from your post #34:

You say this right after quoting Einstein applying Lorentz contraction to a rotating system, which is clearly not linear. Of course all instantaneous velocities are just vectors, and so the descriptors "uniform" and "non-uniform" do not apply to them. So please explain, or give a reference, or something.

 

anyone interested;

The truth of a statement is in the statement, not who says it. It's not true because Euclid says so. Not faulting anyone, but challenging some statements.

Note: In reading publications from the 1900's, by Einstein, Born, etc., the term 'velocity' was synonymous with 'speed', and direction was in addition to speed.
Current definition of 'velocity': a vector composed of magnitude and direction.
The thing measured is the instantaneous value. A derivative is a method of finding that value.

Example of a derivative (see graphic):
A straight line from p intersects a curve at q.
As q approaches p the line p-q rotates clockwise until p and q are coincident.
The line v is now tangent to the curve at p, with a slope of y/x.
This provides the direction for a vector v, but not the speed. The speed and direction of a vector are not necessarily related. The speed could be constant or variable. and requires additional information.

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The 'still shot' of a moving object, is another 'ideal' case, using universal time and instantaneous light speed. For the image from different locations on the object (which has extent in space) to arrive simultaneously at the camera, the light from the far surface must leave before the light from the near surface. The image is a composite for a brief period of time. Eg. if the object is a rod approx. 1 foot long moving toward you, along its length, at common speeds, the image will be approx. 1 nanosec duration. Obviously not perceptible to human vision, but challenging the idea of a zero time snapshot. Zeno was arguing that the concept of continuous space and time led to illogical results. He was way ahead of his time!

length contraction:
In SR, it's measurable for objects moving at constant relative speed with no acceleration. The dimensional change occurred during prior acceleration.
In GR, the gravitational gradient causes length expansion and radial contraction for a rod (moving or not) aligned vertically toward the center of mass. This distortion seems different from that of SR.

 

Some comments:

Newton's first law, sometimes called the "law of inertia" says that a free particle has a constant velocity; it's free if no external forces act on it.
But that's an ideal, in practice no particle is free of interaction with other particles. However for sufficiently small amounts of time, a frame of reference which is non-inertial can be considered inertial--we do this all the time with the surface of the earth, upon which "inertial" experiments can be conducted.

For example, magnetic pucks on an air table are inertial--frictional forces are minimal and the surface of the earth won't rotate by much in the handful of seconds it might take for a puck to move with constant (more or less) momentum. The sun can be considered inertial compared to the earth, over small enough amounts of time.

So an observer is inertial if they can choose an inertial frame of reference, and be comoving with it. Choice of inertial frames seems to be quite arbitrary, then.

 

Not always. Here is a scenario where it is not true:

In special relativity, an observer (he) who is accelerating in a direction TOWARD another person (she) who is a sufficiently long distance away from him, will conclude that she is ageing much FASTER than he is. Any inertial observer would consider her to be ageing more SLOWLY than themselves. So that accelerating observer can by no means be considered to be even approximately inertial.

 

I'm not sure how that refutes what arfa is saying.

Since his qualifier is "for sufficiently small amounts of time" it becomes meaningless to talk about who is aging at all, let alone faster or slower.

 

No, that's not meaningless at all. He was still referring to a sufficiently small INTERVAL of time ... i.e., not a single instant of time, but a small but non-zero continuous RANGE of times. During that interval of time, ageing occurs for EACH of the two people. ... the smaller the interval, the smaller the ageing, but the ageing is non-zero. When comparing two INERTIAL frames that are moving at a constant non-zero relative velocity , each observer will ALWAYS conclude that the distant person is ageing more slowly. But in my example with an accelerating observer, the accelerating observer (he) will conclude that the other person (she) is ageing FASTER. So the two outcomes (inertial observer versus accelerating observer) are opposite ... not similar at all. Accelerating observers are NOT approximately inertial, no matter how small the interval is.

 

If it's large enough to determine that they're aging, then it isn't sufficiently small.

Newtonian calculus would disagree.

 

Hang on Dave, Newtonian calculus would agree with Mike. This is what I, Neddy and others have been maintaining throughout.

The value of acceleration remains finite at each point, i.e. as the interval tends to zero, i.e. a ~ δv/δt -> a= dv/dt.

 

. . .

 

Suppose there is a particle with a high velocity, but high relative to what? And if this particle has 'inert mass' it can only be acted on by an external force (Newton), or equivalently it can only follow the local curvature (Einstein). . .

Relativistic mechanics says the force and acceleration vectors (for massive particles) don't stay parallel at high velocities.

And just might mention that in an expanding universe, particles slow down.