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 speed of length contraction - explanation/contradiction 
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Post Re: speed of length contraction - explanation/contradiction
adam0702 wrote:
Earlier you suggested accelerating all parts of the rod simultaneously. After the rod has achieved the new velocity along its entire length, then it will be contracted by the factor (1 - (v/c)^2)^.5.


This is basically correct, but it has an semantic ambiguity. The word 'simultaneous' has an objective meaning only for events that occur at the same point of space. The word simultaneous is subjective for all events occurring in different spatial locations. If two events are simultaneous to all observers, then they have to occur at the same point in space. If events occur very far apart in space, then the events occur at the same time in only one inertial frame. For the infinite number of other inertial frames, the two events occur at different times.

This is a very, very long rod made up an an infinite number of infinitesimal segments. Suppose we have two segments that are very far apart. There is only one inertial frame where the two segments start accelerating at the same time. The two segments start accelerating at different times in every other inertial frames. This is why simultaneous has a subjective meaning in this case.

A segment starts to accelerate when a mechanical force starts to act on that segment. If the instruments of one inertial frame applies force at the same time, then all segments can start accelerating at the same time according to that inertial frame. However, the forces are independent by definition. There is no causal connection between the start of acceleration. In order to synchronize the motion of segments, a force has to propagate from one segment to the other. The mechanical forces in this case are determined by the elasticity and density of the segments. The propagation of the mechanical force in this case is the speed of sound.

However, this probably isn't what the OP had in mind. Let us consider a case more similar to what the OP has in mind.

Consider a long rod in free fall in outer space. Choose an inertial frame where the observer is at the center of mass of the rod. Let us say that every non-overlapping segment of the rod has a node of the inertial frame nearby. Each node of the inertial frame has an identical laser, very small, that pushes the rod segment with light pressure. The lasers independently start pushing the segments at the same time as observed in this one inertial frame.

Note that in this case there doesn't have to be a sound wave carrying mechanical force from one segments to another. The lasers turn on 'at the same time' by an amazing coincidence. It is an amazing coincidnece only in the inertial frame where the center of mass of the rod is at rest. There is no causal connection between the mechanical forces that start pushing each segment.

Now, I add some instruments that measure mechanical stress in the rod. I hypothesize that the rod is made of transparent material that is isotropic. There is no optical birefringence in the rod unless there is stress. Stress induces optical birefringence in the rod segment. Stress induced birefringence is known in every transparent material on earth.

If a rod segment is in equilibrium, then it has no birefringence.

The segments of the rod show birefringence when stressed. I assume that each segment of rod is sandwiched by infinitesimal crossed polarizers. An LED and photodiode near each segment measrues the birefringence of each segmetn. So now the observer in the reference frame can reconstruct a stress profile for the rod. Two cases

1) Administrator case where external force is applied to one end of the rod.

Consider what happens when one laser beam is applied to one end of the rod. The entire rod doesn't accelerate at the same time. A sound wave has to pass through the rod to make the whole rod accelerate. So the birefringence in the rod is no longer uniform. It shows sinusoidal banding because of the sound wave.

If a sound wave passed down the rod, then the shape of the sound wave could be determined from the stress profile as a function of time. Thus, the start of acceleration of each rod segment would be indicated by the start of stress as measured by laser transmission. The wave front would be seen to move down the rod at the speed of sound. To measure the new length of the rod, one would have to wait until the energy of the sound wave dissipated. The rod would have to lose heat energy to reach the same temperature as before a force was applied.

2) OP case where each segment of the rod is accelerated at the same time as seen in one reference frame.

Let us look at one inertial frame where all segments of the rod are accelerated at the same time. This is the a causal case, since there is no one force that actually moves the rod.

The rod is one length while it is stationary. It has a certain geometric length before the lasers turn on. The geometric length is its equilibrium length before the lasers turn on. Furthermore, its geometric length remains the same while the lasers alone are doing the acceleration. However, the geometric length is no longer the equilibrium length. The rod segmetns show birefringence. So the geometric length is longer than the equilibrium length.

The rod is accelerated to the same velocity as in case (1). Unlike in case (1), the rod now shows a uniform birefringence. There is extra elastic energy in the rod because of the stress.

Now, turn off the lasers off. The rod is now allowed to shrink or expand, as determined by elasticity. It vibrates for a while. The birefringence shows the vibration. However, the vibrations eventually have to damp. Energy is radiated into space. Eventually, the rod is in equilibrium at the same temperature as before. The state of equilibrium is indicated by the absence of stress.

The geometric length of the rod is once again the same as the equilibrium length of the rod. The equilibrium length of the rod after acceleration is shorter than the equilibrium length of the rod before acceleration. The rod has shrunk as determined by the Lorentz length contraction formula.

What I always emphasize is that in dynamics, geometry is never independent of the forces that hold bodies together. So to precisely model the dynamics behavior of the rod, one needs to monitor the forces that hold the body together. This is as true in Newtonian mechanics as it is in relativity. Someone who has never analyzed stress in Newtonian physics is likely to be surprised when it reappears in relativistic physics.

Mechanical forces appear in the last quarter of Einstein's 1905 article on relativity. The first half of the paper discusses 'geometry' alone. It is tempting to drop the last half of the paper, looking only at the first half. However, it was not placed near the end because it is unimportant. The laws of mechanical force close the equations of motion. If a reader ignores mechanical force entirely, then the first half of the article is under determined. If you take into account both parts of the paper, relativity becomes exactly determined. The paradoxes of relativity arise because the geometry of relativity is under-determined.

Einstein never said that the length of a body is determined by only time and space. The shape of a body is determined by the directions of the internal forces that hold it together. The direction of the internal forces are determined by time and space. Space and time tell you how, not why. So when looking for 'why' the shape of a body happens, one has to look at the mechanical forces.

I am sure that you understand :?:


Thu Oct 27, 2016 6:32 pm
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Post Re: speed of length contraction - explanation/contradiction
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Fri Apr 21, 2017 3:36 am
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Post Re: speed of length contraction - explanation/contradiction
adam0702 wrote:
Hi David,

Still trying to find ahole in SR, I see.
*********************

dseppala: In explaining relativity extremely high velocities are typically used so that relativistic effects occur with time and distance parameters we use in our everyday thinking. These same relativistic effects can be seen with common, everyday velocities if the distance between events becomes extremely large. Here is a simple problem. I don't understand how it is explained using the concepts of relativitity.
Let's say we have a very long rod of length L along the x-axis in a rest frame. At one end of the rod, we have an object A, one meter in length, sharing the same end point coordinate as one end of the rod. At the other end of the rod, we have an object B, one meter in length, sharing the same end point coordinate with the other end of rod. At time t0, as measured in the rest frame, we simultaneously accelerate all points of the rod, and all points of objects A and B along the x-axis. Let's say after the acceleration changes the velocity of the rod and objects A and B from zero meters / second to 1 meter / second and takes only a second or two. Let's make the length of the rod, L, a very long length such that we expect a length contraction of a few meters.
As measured in the rest frame, the distance between objects A and B hardly changes during this acceleration. Since both objects accelerated at the same time and in an identical manner, the only change in distance is related to how much a one meter object changes in length when its velocity changes from zero to one meter a second (which is generally negligible). But somewhere in this process, the rest frame must measure that the rod has changed its length by a few meters (because of its extremely long length). So we have object A and one end of the rod accelerate in an identical fashion, and at the other end of the rod we have object B accelerate in an identical fashion as that end of the rod. The distance between A and B after the acceleration is virtually identical to the distance between A and B before the acceleration. However the rest frame observers must measure a length contraction in the rod (per Einstein), so some time during or after the acceleration object A and object B can no longer be at the end points of the rod. But when did the length contraction occur?
Since the amount of length contraction depends on the length L of the rod, some sort of effect must have been transmitted along the rod. If the length contraction occurred instantly, then we can send information faster than c. For rods around a light-year in length, if info cannot be transmitted faster than c, then it would take at least a year to reach the contracted length. That would mean that moving frame observers (with V = one meter/second relative to the rest frame) would have to wait around a year before they notice any change in length of the rod. But the moving frame observers, per Einstein, notice a change in length of the rod immediately since one end of the rod starts accelerating before the other end starts (acceleration start was not simultaneous in the moving frame). They also notice that the distance between object A and object B changes immediately. Since the rest frame doesn't measure any significant change in the distance between A and B, and it might take a year or more for the change of a few meters in length of the rod to show up in the rest frame, how is possible to reconcile both views?
Isn't this contradictory, or how is this explained?

cinci: I'm not sure what teh 1 meter rods at the end of the long rod do so I won't comment on them.

Transmitting a force along he rod is probably limited to the speed of sound in the material so there's plenty of time for this change to occur. Earlier you suggested accelerating all parts of the rod simultaneously. After the rod has achieved the new velocity along its entire length, then it will be contracted by the factor (1 - (v/c)^2)^.5.

For your velocity of 1 m/s, this factor is 1. followed by at least 30 zeroes. So you're talking about a very long rod, impractically so.

Your problem is similar to one posed by JS Bell where he proposes tying a string between two rockets some distance apart and then accelerating them identically along the directin of the string. In this case, the string must break because identical acceleration of the rockets relative to the stationary frame will maintain their separation; but, the string will be accelerating relative to the stationary frame and, because of it's velocity, it will contract and break.


Yeah, but this works only for small velocities at which the relativity factor is very close to 1, right?

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Wed Nov 15, 2017 4:39 am
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Post Re: speed of length contraction - explanation/contradiction
Greetings, Didents.

Luckily there is no problem...
Didents wrote:
adam0702 wrote:
Hi David,

Still trying to find ahole in SR, I see.
*********************

dseppala: In explaining relativity extremely high velocities are typically used so that relativistic effects occur with time and distance parameters we use in our everyday thinking. These same relativistic effects can be seen with common, everyday velocities if the distance between events becomes extremely large. Here is a simple problem. I don't understand how it is explained using the concepts of relativitity.
Let's say we have a very long rod of length L along the x-axis in a rest frame. At one end of the rod, we have an object A, one meter in length, sharing the same end point coordinate as one end of the rod. At the other end of the rod, we have an object B, one meter in length, sharing the same end point coordinate with the other end of rod. At time t0, as measured in the rest frame, we simultaneously accelerate all points of the rod, and all points of objects A and B along the x-axis. Let's say after the acceleration changes the velocity of the rod and objects A and B from zero meters / second to 1 meter / second and takes only a second or two. Let's make the length of the rod, L, a very long length such that we expect a length contraction of a few meters.
As measured in the rest frame, the distance between objects A and B hardly changes during this acceleration. Since both objects accelerated at the same time and in an identical manner, the only change in distance is related to how much a one meter object changes in length when its velocity changes from zero to one meter a second (which is generally negligible). But somewhere in this process, the rest frame must measure that the rod has changed its length by a few meters (because of its extremely long length). So we have object A and one end of the rod accelerate in an identical fashion, and at the other end of the rod we have object B accelerate in an identical fashion as that end of the rod. The distance between A and B after the acceleration is virtually identical to the distance between A and B before the acceleration. However the rest frame observers must measure a length contraction in the rod (per Einstein), so some time during or after the acceleration object A and object B can no longer be at the end points of the rod. But when did the length contraction occur?
Since the amount of length contraction depends on the length L of the rod, some sort of effect must have been transmitted along the rod. If the length contraction occurred instantly, then we can send information faster than c. For rods around a light-year in length, if info cannot be transmitted faster than c, then it would take at least a year to reach the contracted length. That would mean that moving frame observers (with V = one meter/second relative to the rest frame) would have to wait around a year before they notice any change in length of the rod. But the moving frame observers, per Einstein, notice a change in length of the rod immediately since one end of the rod starts accelerating before the other end starts (acceleration start was not simultaneous in the moving frame). They also notice that the distance between object A and object B changes immediately. Since the rest frame doesn't measure any significant change in the distance between A and B, and it might take a year or more for the change of a few meters in length of the rod to show up in the rest frame, how is possible to reconcile both views?
Isn't this contradictory, or how is this explained?

cinci: I'm not sure what the 1 meter rods at the end of the long rod do so I won't comment on them.

Transmitting a force along he rod is probably limited to the speed of sound in the material so there's plenty of time for this change to occur. Earlier you suggested accelerating all parts of the rod simultaneously. After the rod has achieved the new velocity along its entire length, then it will be contracted by the factor (1 - (v/c)^2)^.5.

For your velocity of 1 m/s, this factor is 1. followed by at least 30 zeroes. So you're talking about a very long rod, impractically so.

Your problem is similar to one posed by JS Bell where he proposes tying a string between two rockets some distance apart and then accelerating them identically along the directin of the string. In this case, the string must break because identical acceleration of the rockets relative to the stationary frame will maintain their separation; but, the string will be accelerating relative to the stationary frame and, because of it's velocity, it will contract and break.


Yeah, but this works only for small velocities at which the relativity factor is very close to 1, right?
...since TD&LC (time dilation and length contraction) are pseudophenomena depending on believing in a stagnant aether or absolute reference frame (ARF), neither of which have been proven to exist. If we stick with Galilean relativity we are led to construct a new theory of light. :)

Yours faithfully
OZLOFT

PS: Cincirob******** died heroically, like Samson - i.e. the Fizzout Forum (the Physics Forum) fell down upon him when they removed his postings on the Rolling Wheel about which I was commenting about on the Miscellaneous Forum here. See:

viewtopic.php?f=1&t=6933

He had exposed their claims as utter nonsense so they had to remove the material as cinci forced them to reveal that it was logically paradoxical i.e. covertly invoking parallel universes and revealing SR for the BS it is - even though cinci himself tried to claim otherwise! :o


Wed Nov 15, 2017 6:05 am
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Post Re: speed of length contraction - explanation/contradiction
As measured in the rest outline, the separation between objects An and B barely changes amid this increasing speed. Since the two articles quickened in the meantime and in an indistinguishable way, the main change in remove is identified with how much a one-meter protest changes long when its speed changes from zero to one meter a moment (which is by and large insignificant).

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