SR composition of velocities question

[vuquta]

Can anyone tell me the direction of the resiltant velocity vector for the composition of velocities equations of SR?

 

Thanks

[swansont]

It's given by the sign of the answer.

[vuquta]

It's given by the sign of the answer.

 

No, it is not that simple. Normally, it would be atan2(y/x).

 

I do not have the correct y and x. They are not simply wt and vt.

 

A veclocity magnitude as produced by the equations can be satisfied by an infinite number of directions.

[swansont]

http://en.wikipedia.org/wiki/Velocity-addition_formula#General_case

 

You should be able to tell which quadrant the resultant vector is in. v+u is given by the sign, and the perpendicular component can't change that.

[vuquta]

http://en.wikipedia.org/wiki/Velocity-addition_formula#General_case

 

You should be able to tell which quadrant the resultant vector is in. v+u is given by the sign, and the perpendicular component can't change that.

 

No, I think I need to use the x and y in the equations for the composition.

 

He has a w_ξ and a w_η in chapter 5.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

I guess this is the x component speed and the y component speed of the second moving object in the moving frame coords where the moving frame has v along the positive x-axis of the stationary frame.

 

This is what I am not sure about but I cannot ses it any other way.

[swansont]

No, I think I need to use the x and y in the equations for the composition.

 

He has a w_ξ and a w_η in chapter 5.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

I guess this is the x component speed and the y component speed of the second moving object in the moving frame coords where the moving frame has v along the positive x-axis of the stationary frame.

 

This is what I am not sure about but I cannot ses it any other way.

 

Yes, he defines that in the first equation of that section.

[ambros]

Hello, I've seen some of Vuquta's previous threads and I believe this is his website:http://www.proofofabsolutemotion.com/intro.html -- I have to say I agree with the point Vuquta is making. In my view, there is no real disagreement in what most of you and he was saying, it's just that he talks about something else too that no one else is really addressing and I believe to have a solution to his "paradox", so both he and SR can be right in the same time. I think his point is most obvious from those animation and java applets on that web page above, but let me try to rephrase and illustrate in my way how I see this problem and what I still do not understand.

 

X________________                              
       moving   |
      observer  |
                | ---> v (moving speed train)
 photon         | 
^________________|


               X________________
               ^       moving   |
           ^   ^      observer  |
    d1 ^       ^                | ---> v
   ^           ^d2              | 
^               ^________________|


---------------standing observers see d1, passengers see d2

...however, if photons are to retain their speed of light for all frames, if that speed is to be independent of the movement of object that emitted it which means NO HORIZONTAL MOMENTUM for this photon, then it must miss the target. If it was a bullet then it would have this horizontal momentum and it will hit the target, but photon actually has to miss it, right? How can it "know" it has to move horizontally (as well) if it can not be impacted with this sideways momentum like a bullet would? Solution, then...

X________________                             
       moving   |
      observer  |
                | ---> v
photon          | 
^________________|


                 X________________
^                          moving  | 
^                         observes |
^d1                                | ---> v
^                    d1=d2         | 
^                 . _______________|

---------------standing observers see d1, passengers see d1

...and so the speed of light is constant and same in all frames. What I do not understand in this whole story is what is the SR's prediction or measurement for this case scenario really supposed to be? I always thought SR is actually saying something like this anyway.

[Amr Morsi]

The resultant velocity vector has three components; x,y,z. Suppose that the relative motion of the frames is in the x-direction. Then; the x-component will be got from the transformation relations, and the y,z-components are same as in the original frame multiplied by a simple factor due to time dilation effects.

[vuquta]

Hello, I've seen some of Vuquta's previous threads and I believe this is his website:http://www.proofofabsolutemotion.com/intro.html -- I have to say I agree with the point Vuquta is making. In my view, there is no real disagreement in what most of you and he was saying, it's just that he talks about something else too that no one else is really addressing and I believe to have a solution to his "paradox", so both he and SR can be right in the same time. I think his point is most obvious from those animation and java applets on that web page above, but let me try to rephrase and illustrate in my way how I see this problem and what I still do not understand.

 

X________________                              
       moving   |
      observer  |
                | ---> v (moving speed train)
 photon         | 
^________________|


               X________________
               ^       moving   |
           ^   ^      observer  |
    d1 ^       ^                | ---> v
   ^           ^d2              | 
^               ^________________|


---------------standing observers see d1, passengers see d2

...however, if photons are to retain their speed of light for all frames, if that speed is to be independent of the movement of object that emitted it which means NO HORIZONTAL MOMENTUM for this photon, then it must miss the target. If it was a bullet then it would have this horizontal momentum and it will hit the target, but photon actually has to miss it, right? How can it "know" it has to move horizontally (as well) if it can not be impacted with this sideways momentum like a bullet would? Solution, then...

X________________                             
       moving   |
      observer  |
                | ---> v
photon          | 
^________________|


                 X________________
^                          moving  | 
^                         observes |
^d1                                | ---> v
^                    d1=d2         | 
^                 . _______________|

---------------standing observers see d1, passengers see d1

...and so the speed of light is constant and same in all frames. What I do not understand in this whole story is what is the SR's prediction or measurement for this case scenario really supposed to be? I always thought SR is actually saying something like this anyway.

 

They are not compatible and here is why.

 

I will disprove SR.

 

Einstein argued the following.

 

We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity.

 

At the time t = τ = 0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then

x² +y² +z² =c² t² .

 

Transforming this equation with the aid of our equations of transformation we obtain after a simple calculation

ξ² + η² + ς² = c² τ²

 

The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

He claimed the above is the proof of logical consistency. He stated the requirement for the logical consistency of the light postulate and the relativity postulate is the spherical light wave in the stationary frame must be spherical when translated by LT in the moving frame. He made the statement, "The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system."

 

Here is what he did.

 

He started with a point (x, y, z) that was struck by the spherical light in stationary K.

 

He performed LT on that point.

 

He then claimed in moving k, ξ² + η² + ς² = c² τ² . This is in fact true for any arbitrary light beam.Thus, he claimed he proved the spherical wave in K is also spherical in moving k, based on the equation above.

 

But, for the spherical light wave in K to be spherical in k, c² τ² would need to be constant for all (x, y, z ) attained by the stationary light sphere after translation by LT.*This is easily proven false by considering (r,0,0,r/c) and (-r,0,0,r/c) in the stationary frame and translating them using LT.

 

Hence, he committed the logical fallacy, dicto simpliciter.

 

Therefore, the light sphere in K is not spherical in k when translated by LT

 

Hence, the light postulate and the relativity postulate are logically inconsistent.

[ambros]

They are not compatible and here is why.

 

I will disprove SR.

 

Einstein argued the following.

 

Hmmm, these are the questions:

 

Q1: What do you believe is correct diagram, 1st or 2nd one?

 

Q2: What do you believe Einstein believed is correct diagram, 1st or 2nd?

[swansont]

Einstein argued the following.

 

 

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

He claimed the above is the proof of logical consistency. He stated the requirement for the logical consistency of the light postulate and the relativity postulate is the spherical light wave in the stationary frame must be spherical when translated by LT in the moving frame. He made the statement, "The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system."

 

Here is what he did.

 

He started with a point (x, y, z) that was struck by the spherical light in stationary K.

 

He performed LT on that point.

 

He then claimed in moving k, ξ² + η² + ς² = c² τ² . This is in fact true for any arbitrary light beam.Thus, he claimed he proved the spherical wave in K is also spherical in moving k, based on the equation above.

 

But, for the spherical light wave in K to be spherical in k, c² τ² would need to be constant for all (x, y, z ) attained by the stationary light sphere after translation by LT.*This is easily proven false by considering (r,0,0,r/c) and (-r,0,0,r/c) in the stationary frame and translating them using LT.

 

Hence, he committed the logical fallacy, dicto simpliciter.

 

Therefore, the light sphere in K is not spherical in k when translated by LT

 

Hence, the light postulate and the relativity postulate are logically inconsistent.

 

The topic of this thread is the composition of velocities in SR. It is not for ideas on disproving relativity, since those discussions belong in speculations. You are also precluded from reintroducing topics that were closed.

[vuquta]

Hmmm, these are the questions:

 

Q1: What do you believe is correct diagram, 1st or 2nd one?

 

Q2: What do you believe Einstein believed is correct diagram, 1st or 2nd?

 

Please open your own thread on this and I will discuss it with you.

 

In this thread, I just wanted to make sure my views on SR's velocity composition equations were correct. I am satisified with that.

[ambros]

Please open your own thread on this and I will discuss it with you.

 

In this thread, I just wanted to make sure my views on SR's velocity composition equations were correct. I am satisified with that.

 

I do not understand. The example I gave is classic scenario to employ whatever equations you have for velocity vector composition. -- You wanna see if your equations are correct, me too, so can those equations answer my questions? I'm asking my questions to make sure I understand how you equations work, and I do not see why would you hesitate to USE them.