Education and Crank Claims: Special Relativity

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I, too am incrediblized by your "crank" intellect!

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First, I agree with the mathematics. Good job.

Second, to keep from parrotting Special Relativity (SR), I know that the y-direction and the z-direction in (SR) are considered fixed or rigid; while only the x-direction is elastic or contracts; your mathematics above also agree with this.

1) However, why are the y-direction and the z-direction assumed to be fixed or rigid, while only the x-direction is allowed be elastic?

2) Can you prove using postulates, and mathematics why we can't assume that the y-direction and the z-direction can also be considered elastic.

For example why not?

Further if we are talking about the world-line of a particle, we can write \(\Delta x = x(\Delta t)\) (and similarly for y and z). And if we are talking about inertial motion, we are talking about constant velocity and \(\Delta x = u_x \Delta t + \Delta x_0\) (and similarly for y and z). So we may compute:
\(\begin{pmatrix}\Delta x' \\ \Delta y' \\ \Delta z' \\ \Delta t' \end{pmatrix} = \begin{pmatrix}1 & 0 & 0 & -v \\ 0 & 1 & -v & 0 \\ 0 & -v & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} u_x \Delta t \\ u_y \Delta t \\ u_z \Delta t \\ \Delta t \end{pmatrix} = \begin{pmatrix} ( u_x - v_x ) \Delta t \\ (u_y - v_y) \Delta t \\ (u_z - v_z) \Delta t \\ \Delta t \end{pmatrix} = \begin{pmatrix} ( u_x - v_x ) \Delta t' \\ (u_y - v_y) \Delta t' \\ (u_z - v_z) \Delta t' \\ \Delta t' \end{pmatrix}\).

Why not?

So \(u'_x = u_x - v_x\), and \(u'_y = u_y - v_y\), and \(u'_z = u_z - v_z\) is how inertial world lines transform under the Galilean transform.

Or why not?

\(\begin{pmatrix}\Delta x' \\ \Delta y' \\ \Delta z' \\ \Delta t' \end{pmatrix} = \begin{pmatrix} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} & 0 & 0 & \frac{-v}{\sqrt{1 - \frac{v^2}{c^2}}} \\ 0 & 1 & \frac{-v}{\sqrt{1 - \frac{v^2}{c^2}}} & 0 \\ 0 & \frac{-v}{\sqrt{1 - \frac{v^2}{c^2}}} & 1 & 0 \\ \frac{-v}{c^2 \sqrt{1 - \frac{v^2}{c^2}}} & 0 & 0 & \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \end{pmatrix} \begin{pmatrix} u_x \Delta t \\ u_y \Delta t \\ u_z \Delta t \\ \Delta t \end{pmatrix} = \begin{pmatrix} \frac{u_x - v_x}{\sqrt{1 - \frac{v^2_x}{c^2}}} \Delta t \\ \frac{u_y - v_y}{\sqrt{1 - \frac{v^2_y}{c^2}}} \Delta t \\ \frac{u_z - v_z}{\sqrt{1 - \frac{v^2_z}{c^2}}} \Delta t \\ \frac{1 - \frac{u_x v}{c^2}}{\sqrt{1 - \frac{v^2}{c^2}}} \Delta t \end{pmatrix} = \begin{pmatrix} \frac{u_x - v_x}{1 - \frac{u_x v_x}{c^2}} \Delta t' \\ \frac{u_y - v_y}{1 - \frac{u_y v_y}{c^2}} \Delta t' \\ \frac{u_z - v_z}{1 - \frac{u_z v_z}{c^2}} \Delta t' \\ \Delta t' \end{pmatrix}\)

3) Why is the y-axis and the z-axis treated differently than the x-axis? Can you prove it using mathematics and postulates or is this just parroting?

I also want AlphaNumeric to answer this question.:shrug:

 

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Sorry, it is the case under the standard configuration that z and y do not experience deformation.

 

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Did you not understand the question?? I know what Special Relativity assumes. Why doesn't the y-axis and the z-axis experience deformation? Why is it assumed that this is so?

And you have absolutely no authority to state what is standard and what is not standard based on your previous posts.

 

I am not concerned that your evolution standard is such that your eat insects for sustenance. Hey, many are on your evolutionary station.

But, the topic you attacked under SR is the y and z axis is the standard configuration. There is no math that refutes this logic.

If you think you have said logic, present it so I can correct you.

 

I did here: Previous Post

Oh, and your insects also eat for sustenance!

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OMG.

Prove y and z are deformed under the standard configuration.

I feel like am dealing with alpha.

Make your case or retract.

 

No. This is the question that I am asking the original poster.

I want you (Chinglu, RPenner, & AlphaNumeric) to prove that the y-axis and the z-axis are not deformed without assuming from initial conditions that they are fixed or rigid!

You assumed that the x-axis is elastic or deformable, and that the y-axis and z-axis are not elastic or deformable; why??

Why does Special Relativity (SR) assume that only the x-direction is deformable but the other two y-axis and z-axis dimension directions are rigid?

If you don't know, just say so; and admit defeat!

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This is I believe is an easy one....

SR deals with inertial frames of reference. Which means frames of reference in uniform motion relative to one another.

The y and z directions are fixed to make understanding the relationship between the relative motion(s) easier. As long as the relative motion of any two or more frames of reference is inertial (not accelerating) the motions can be a complex combination of dynamic change in all three directions. This would of course make it more difficult for most of us to understand the interaction.

So SR does not care if the motion involves change in all three directions simultaneously, x, y and z. It does not change any result or conclusion. It is just easier to express if all of the motion occurs along one axis. The x, y and z coordinate system is a convention we use to understand space, the relationship of objects in space and any change in the position of those objects in space over time, i.e. motion.

Easy peasy.., SR doesn't care but I do!

 

First off, you language is hilarious, showing ignorance on the subject. Second off, your claim is incorrect as it can be seen from the formulation of the general boost Lorentz transform.

 

I think that your post actually reveals your ignorance for reading comphrension.

What claim did I make?

I made no claim, I asked a question concerning the initial "Assumption" conditions of RPenners description and general eductational concepts and mathematics of "Relativity."

 

What is wrong with having uniform motion relative to one another in x, y and z directions like how nature behaves.

This is your final answer!! To make understanding the relationship between the relative motion(s) easier.??

This is true it does not change the conceptual results, but it does affect experimental results. For example if you are doing an experiment and you are expecting a certain amount of amplitude in y-axis or the z-axis and there is more or less amplitude than what you were expecting then your math is not correct!

Why assume a specific amount of elastic deformation in one direction but exclude elastic deformation in the other directions? This is what the mathematics of RPenner predicts.

 

This idiotic claim:

And this idiotic claim:

 

What I wonder is, did rpenner do this on purpose?

 

First, there is no elastic deformation in any direction. The x, y and z coordinate system is a construct of "ours". And it does not stretch or twist or turn, at least not within the context of SR.

Second, how an x, y and coordinate system is laid out is at least initially arbitrary.

Two inertia frames of reference could orient their independent coordinate systems any way they wish. If they do not agree, then comparing relative motions becomes far more difficult. We choose to agree that all three axis are in agreement as to spacial orientation with only the zero point being different from one to another. That just makes sense when trying to compare two inertial frames of reference, a common understanding.

Motion as I said in my precious post can occur in any direction or combination of the three agreed upon x, y and z directions. In fact when plotting real trajectories all three coordinates are used.

When explaining the relationship between inertial drams of reference assigning the motion to a single axis makes the comparison far less complex and thus easier to communicate.

At least that is the intent.

By convention the x axis is usually the axis assigned to the involved motion. It is just to make communication easier. It could be in any direction. SPECIAL RELATIVITY does not care. It works equally well in all directions between inertial frames of reference.

One more time, coordinate systems are things we use to describe the world around us. And in order to communicate what we experience we must agree on language, mathematics and yes there ya go the coordinate system we will use to describe the world.....

 

I been thinking maybe so. I know he can when he wants to explain the math better than he has here. It is almost as if he started at an interested lay level and progressed to a point where he assumes a working knowledge of the math.

 

If the discussion were to be kept at the layman level, I think you'd want to stay away from the Lorentz transforms altogether. It really is laughable that so many people think this theory is easy to debunk, before they've even mastered the basic details.

 

They do - depending on the orientation of the two observers. The axis (or axes) that represent the direction of travel experience deformation. The transformation matrix posted above describes that transformation. If you choose the relative direction to be the X axis, then only the X axis shrinks.

It's like asking "why does only the Z axis seem to disappear into the distance from my perspective?" That happens only when you choose the Z axis to be the one that parallels your line of sight. You can choose the X axis to the the one parallel to your line of sight, in which case _it_ will seem to disappear into the distance.

 

I didn't mean to be suggesting that it could be kept completely at a lay level. I also know the rpenner can when he wishes explain the mathematics a bit better.

Face it the thread begins by essentially inviting in, those who don't really understand SR or have questions about it. If you invite the interested lay person in you need to try and talk to them not completely beyond them.

Conceptually, while it may be hard to explain, a great deal of SR is applicable to everyday life. People make frame of reference conversions in real time all day long, without knowing any math. We even do that between inertial and accelerating frames of reference, in real time all day long. That is one place I believe that Einstein did a pretty good job, attaching thought experiments that most anyone could relate to, to the math.

 

Most "real" objects in motion travel in three dimesions of space relative to any external inertial frame of reference. Should'nt a more general theory of "Special Relativity" be able to take into account this three (3) dimensional relative motion? Or are we limited to only an single one (1) dimensional relative motion?

This is a good one!

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However, in this example above the vanishing perspectives are linked and built into an equation which is a three dimensional angle that includes line of site, azimuth, and elevation angles. And therefore the correct mathematics includes this relation or proportionality between the distances and the angles.

But in the mathematics of the Original Post (OP) by RPenner demonstrating Special Relativity (SR), as presented in most text books; howeveer, they have removed the relation or proportionality between the distances, velocities, or relative motion that would allow the vanishing perspectives that you are modeling.