View Full Version : Velocity Addition Formula (VAF)


MacM
07-22-05, 12:57 AM
In addition to the reciprocity and simultaneity failures of Special Relativity I thought I would add a bit in
food for thought regarding the Velocity Addition Formula.

Given the case: Rest distance = 200 units.


1 - A<-----------(100 units) ---------------------->B = 0.866c

The relavistic affects are based on a gamma = 2.000. Meaning that time
(clocks) tick at half the rate they did at rest and distance is cut in half.


2 - A<-----~82 units-------------C------~82 units--------->B ; where AC
= -0.577c and BC = +0.577c; and = 164 units

AB according to the VAF = 0.866c and equals 100 units.


3 - The problem is that relativists like you to see only one aspect of their theory at a time.

(1 above) A<--------------------------------------->B = 100 units @ 0.866c.
(2 above)..................A<-------------->B = 164 units @ 0.866c.

Both of course are 0.866c. Further in case 2 the actual situation is not so simple. You cannot disregard that
A still sees C as moving at 0.577c which means that A only sees B moving
away from C at 0.289c.

Distance from AC is therefore 0.8167 the rest distance (or time) and the affects at 0.289c is 0.9573.

A<---------~82 units--------------C---------~96 units------------->B
= 178 units.

But the distance AB is less than A sees for A to C + C to B.

A<---------------100 units---------------->B

Now if I must travel less distance (0.5) and my clock ticks slower (0.5),
then that would mean during the trip my clock would accumulate 0.25 as
much time.

Data would suggest that the reality is that clocks tick slower due to actual
velocity in a universal view and not a relavistic view but that spatial dimension does not contract.

Hmmmm.

UnderWhelmed
07-22-05, 06:00 AM
I assume that someone is going to ask what frame these measurements are in...so you might as well answer that.

*patiently awaits James R*

Rosnet
07-22-05, 08:32 AM
You're trying to show or at least entertain the possibilty that there is an absolute frame, since we can see that the time measurements done by an observer in only one frame come out as the right onee ultimately. But this is because you have already given a quality of absolutism to one frame, by the action of making the other two frames stop with respect to this particular frame. I agree that from the POV of the other frames, the frame which stops is the first one, but this is an invalid argument, because at no point in time does the first frame accelerate.
<Br>
Perhaps you should read up a bit on Proper Time, and try to understand this concept.

MacM
07-22-05, 09:41 PM
You're trying to show or at least entertain the possibilty that there is an absolute frame, since we can see that the time measurements done by an observer in only one frame come out as the right onee ultimately. But this is because you have already given a quality of absolutism to one frame, by the action of making the other two frames stop with respect to this particular frame. I agree that from the POV of the other frames, the frame which stops is the first one, but this is an invalid argument, because at no point in time does the first frame accelerate.
<Br>
Perhaps you should read up a bit on Proper Time, and try to understand this concept.

1 - I have not addressed anything about acceleration. In case you are unaware it is not included in SRT. I have only addressed SR which is based on inertial velocity.

2 - I am most certainly familiar with proper time.

3 - I don't see your post as addressing any of the issue.

MacM
07-22-05, 09:42 PM
I assume that someone is going to ask what frame these measurements are in...so you might as well answer that.

*patiently awaits James R*

Strange since each statement states according "to".

James R
07-23-05, 01:36 AM
The first post is misleading, either deliberately or through ignorance.


1 - A<-----------(100 units) ---------------------->B = 0.866c

Which frame is the 100 units in? Which has B going at 0.866c?
Are these two frames the same or different? Answer: different frames.

So, this diagram incorrectly mixes two frames.


2 - A<-----~82 units-------------C------~82 units--------->B ; where AC
= -0.577c and BC = +0.577c; and = 164 units

Which frame has A and B moving? Which frame measures 82 units? The same frame, or two different frames?

I leave it to readers to answer this question, and refer you to the first diagram for a hint.

The rest of the mistakes in the first post result from these basic errors.

Rosnet
07-23-05, 03:29 AM
I've addressed the length contraction issue in the anti-Relativity thread. The 'apparent' discrepancy is due to the fact that <I>time</I> intervals can be accumulated, and hence, compared after everyone comes to rest in one frame. On the other hand, you can't really have an accumulated <I>space</I> interval (that is length). Length contraction occurs only during motion, as time dilation does, too, but you can't add it up and store it for comparison afterwards. However, you can make measurements of length indirectly and compare them. This is what I've done in the other post. If time dilation is a fact, then you can't avoid length conraction.

MacM
07-23-05, 11:57 AM
The first post is misleading, either deliberately or through ignorance.

Only if you are bent on knit picking. The 100 units is the same in either frame. Perhaps you don't understand so well.


Which frame is the 100 units in? Which has B going at 0.866c?
Are these two frames the same or different? Answer: different frames.

So what. Perhaps you forget that SRT says either or both are at rest and also have all motion. Is it impossible for you to have a conversation or do you deliberately attempt to demean others posts rather than address the issues?


So, this diagram incorrectly mixes two frames.

False. You incorrectly attempt to seperate predictions of SRT from reality. The reality is that given a relative velocity of 0.866c either may view the other as having the motion and themselves at rest. Funny how you like to twist basic facts in effort to create a platform from which to attack.

It isn't working BTW:


Which frame has A and B moving? Which frame measures 82 units? The same frame, or two different frames?

I leave it to readers to answer this question, and refer you to the first diagram for a hint.

And I leave my responses above to apply to this as well. I could have specificed each frame and repeated the case by reversing the results but I think most here understand that issue. Perhaps you don't.


The rest of the mistakes in the first post result from these basic errors.

There are NO mistakes other than your ill thought out attack.

geistkiesel
07-23-05, 05:50 PM
You're trying to show or at least entertain the possibilty that there is an absolute frame, since we can see that the time measurements done by an observer in only one frame come out as the right onee ultimately. But this is because you have already given a quality of absolutism to one frame, by the action of making the other two frames stop with respect to this particular frame. I agree that from the POV of the other frames, the frame which stops is the first one, but this is an invalid argument, because at no point in time does the first frame accelerate.
<Br>
Perhaps you should read up a bit on Proper Time, and try to understand this concept.

Take another look. I didn't say that it was a non-inertial frame. I've specifically mentioned that this frame is purely circumstantial, and that it doesn't possess any special properties. This is <I>not </I> ruled out by special relativity. I've said that it is not possible to detect it, unless you bring every particle in the universe to a state of relative rest. That is what special relativity says too (its first postulate).

Rosnet,
Now you see the problem with SRT.

Your postulates leave much to be desired and are very arbitrary. For instance, when two photons are emitted from a common point simultaneously that point of emission locates an invariant point in space as defined by the motion of the photons emitted. This then is a zero velocity point in space. The stellar objects moving hither and yon wrt this point do not disturb the invarinace of the point.

But that is another problem for another day. What we have here is anethema to SRT in that a single inertial frame moving in deep space is able to determine its intrinsic speed Here "Intrinsic Speed" is taken in the sense that the frame under scrutiny was launched from Ve assumed at rest, earth's surface, and shortly thereafter began moving uniformly throughout this exercise. Of course, the A inertial frame observer was asleep when the A frame was launched and began moving uniformly.

http://www.msnusers.com/Savadance4me/Documents/aatri.GIF.

When Vcb = 0 then Vc = Vb in the Vcb system. At this instance Vac = the total change of velocity of C wrt A assumed at rest. The Vac = Vc as A is at rest, hence Vc is the difference in speed of the B frame wrt the A frame. As we have the relative motion Va + Vb = j, and now we have the difference in speeds of B wrt A, or Vb = Va + k, where k is the measured Vc, we conclude that Va + Va + k = j or Va = (j - k)/2, which then results in Vb = (j - k)/2 + k = (j + K )/2. Hence Va and Vb, the intrinsic speeds of the A and B frames are measured. This will work on only one unique set of intrinsics speeds, to wit, the measured set. Check it out. Notice, there was no mention of the a------e v------y words!

Geistkiesel :cool:

superluminal
07-23-05, 08:48 PM
Off topic:

MacM,

Have you found a Phd sponsor yet who could help you write a paper and get it submitted to Phys. Review D?

I thought you mentioned some time ago that you were working with someone.

MacM
07-23-05, 10:39 PM
Off topic:

MacM,

Have you found a Phd sponsor yet who could help you write a paper and get it submitted to Phys. Review D?

I thought you mentioned some time ago that you were working with someone.

I am and he wanted only credit for his work but I am unhappy with the pace of progress. I am thinking of actually hiring some assistance.

superluminal
07-23-05, 11:58 PM
Sounds good. Just curious. Thanks.

James R
07-24-05, 12:21 AM
MacM:

I tell you you are incorrectly mixing frames, and what is your response? This:


So what.

So, you made a mistake. A reasonable person at this point would try to correct their error, but you simply pretend it hasn't been pointed out. Your self-delusion is incredible.

Paul T
07-24-05, 08:16 AM
In addition to the reciprocity and simultaneity failures of Special Relativity I thought I would add a bit in
food for thought regarding the Velocity Addition Formula.

Given the case: Rest distance = 200 units.


1 - A<-----------(100 units) ---------------------->B = 0.866c

The relavistic affects are based on a gamma = 2.000. Meaning that time
(clocks) tick at half the rate they did at rest and distance is cut in half.


2 - A<-----~82 units-------------C------~82 units--------->B ; where AC
= -0.577c and BC = +0.577c; and = 164 units

AB according to the VAF = 0.866c and equals 100 units.


3 - The problem is that relativists like you to see only one aspect of their theory at a time.

(1 above) A<--------------------------------------->B = 100 units @ 0.866c.
(2 above)..................A<-------------->B = 164 units @ 0.866c.

Both of course are 0.866c. Further in case 2 the actual situation is not so simple. You cannot disregard that
A still sees C as moving at 0.577c which means that A only sees B moving
away from C at 0.289c.

Distance from AC is therefore 0.8167 the rest distance (or time) and the affects at 0.289c is 0.9573.

A<---------~82 units--------------C---------~96 units------------->B
= 178 units.

But the distance AB is less than A sees for A to C + C to B.

A<---------------100 units---------------->B

Now if I must travel less distance (0.5) and my clock ticks slower (0.5),
then that would mean during the trip my clock would accumulate 0.25 as
much time.

Data would suggest that the reality is that clocks tick slower due to actual
velocity in a universal view and not a relavistic view but that spatial dimension does not contract.

Hmmmm.

Damn...what a mess! Typical MacM's style. :D

MacM
07-24-05, 10:17 AM
MacM:

I tell you you are incorrectly mixing frames, and what is your response? This:



So, you made a mistake. A reasonable person at this point would try to correct their error, but you simply pretend it hasn't been pointed out. Your self-delusion is incredible.

The "So what" response is very valid for the discussion at hand. I was only showing the recipocal relationship predicted by SRT. In such case it is not necessary to be redundanat and spell out the view from each frame, that is for most people.

MacM
07-24-05, 10:18 AM
Damn...what a mess! Typical MacM's style. :D


What a waste. Typical of Paul T's responses.

Paul T
07-24-05, 01:03 PM
What a waste. Typical of Paul T's responses.

Yes, it was a waste from your side. Fortunately I did not make any attempt to response to your post, which I (and most others here as well, I believe) did not understand. Do not waste more of your time to rewrite your message, since crap will remain as crap no matter how you wrap it.... :D

Pete
07-24-05, 06:29 PM
I was only showing the recipocal relationship predicted by SRT
You comprehensively showed that you don't know how to show what SR predicts.

You mixed frames in a way inconsistent with SR theory. So what? So, the "reciprocal relationship" you showed is not a prediction of SR.

I might or not might not embrace a worldview consistent with SR, but I think that I do know how to apply the theory... do you? Do you think that you could work out a "correct" textbook answer to all (most? any?) exercises in a first-year relativity text?

Aer
07-24-05, 08:47 PM
In addition to the reciprocity and simultaneity failures of Special Relativity I thought I would add a bit in
food for thought regarding the Velocity Addition Formula.

Given the case: Rest distance = 200 units.


1 - A<-----------(100 units) ---------------------->B = 0.866c

The relavistic affects are based on a gamma = 2.000. Meaning that time
(clocks) tick at half the rate they did at rest and distance is cut in half.


2 - A<-----~82 units-------------C------~82 units--------->B ; where AC
= -0.577c and BC = +0.577c; and = 164 units

AB according to the VAF = 0.866c and equals 100 units.


3 - The problem is that relativists like you to see only one aspect of their theory at a time.

(1 above) A<--------------------------------------->B = 100 units @ 0.866c.
(2 above)..................A<-------------->B = 164 units @ 0.866c.

Both of course are 0.866c. Further in case 2 the actual situation is not so simple. You cannot disregard that
A still sees C as moving at 0.577c which means that A only sees B moving
away from C at 0.289c.

Distance from AC is therefore 0.8167 the rest distance (or time) and the affects at 0.289c is 0.9573.

A<---------~82 units--------------C---------~96 units------------->B
= 178 units.

But the distance AB is less than A sees for A to C + C to B.

A<---------------100 units---------------->B

Now if I must travel less distance (0.5) and my clock ticks slower (0.5),
then that would mean during the trip my clock would accumulate 0.25 as
much time.

Data would suggest that the reality is that clocks tick slower due to actual
velocity in a universal view and not a relavistic view but that spatial dimension does not contract.

Hmmmm. MacM, I've told you this before - Your version of "special relativity" does not adhere to the postulates of Einstein's special relativity. Length contraction, time dilation, reciprocity, et al are all results of the postulates of special relativity. You only want to consider the aspects of special relativity that have been experimentally proven and throw out the other stuff. You just cannot do this (well, technically you can). But you need to come up with new postulates that allow for time dilation but do not allow for length contraction and recirpocity as it appears to me you are doing.

James R
07-24-05, 10:54 PM
Well, MacM, this thread didn't get very far, did it? I guess we're done, unless you have something new to add. Or would you prefer to exchange insults for a while?

MacM
07-25-05, 03:55 AM
Yes, it was a waste from your side. Fortunately I did not make any attempt to response to your post, which I (and most others here as well, I believe) did not understand. Do not waste more of your time to rewrite your message, since crap will remain as crap no matter how you wrap it.... :D

We've noted that from your posts. :D

MacM
07-25-05, 03:58 AM
I've addressed the length contraction issue in the anti-Relativity thread. The 'apparent' discrepancy is due to the fact that <I>time</I> intervals can be accumulated, and hence, compared after everyone comes to rest in one frame. On the other hand, you can't really have an accumulated <I>space</I> interval (that is length). Length contraction occurs only during motion, as time dilation does, too, but you can't add it up and store it for comparison afterwards. However, you can make measurements of length indirectly and compare them. This is what I've done in the other post. If time dilation is a fact, then you can't avoid length conraction.


To the contrary. If you retain the emperically observed and recorded fact of time dilation with motion then you cannot declare spatial length contraction.

Where tr = tick rate

t * tr = d / v accounts for all relavistic trips regardless of velocity and with no change in distance.

MacM
07-25-05, 04:01 AM
You comprehensively showed that you don't know how to show what SR predicts.

You mixed frames in a way inconsistent with SR theory. So what? So, the "reciprocal relationship" you showed is not a prediction of SR.

It sure as hell is. If you understood that then perhaps you would convert. :D

************************************************** ************************************************** ****
http://www.mathpages.com/home/kmath307/kmath307.htm

Given this definition of inertial reference frames, the principle of relativity asserts that for any material particle in any state of motion there exists an inertial reference frame - called the rest frame of the particle - with respect to which the particle is instantaneously at rest (i.e., the change of the spatial coordinates with respect to the time coordinate is zero). This principle is usually extended to include reciprocity, meaning that for any two systems S1 and S2 of inertial coordinates, if the spatial origin of S1 has velocity v with respect to S2, then the spatial origin of S2 has velocity -v with respect to S1. The existence of this class of reference frames, and the viability of the principles of relativity and reciprocity, are inferred from experience. Once these principles have been established, the relationship between relatively moving inertial coordinate systems can then be considered.

************************************************** *************************


I might or not might not embrace a worldview consistent with SR, but I think that I do know how to apply the theory... do you? Do you think that you could work out a "correct" textbook answer to all (most? any?) exercises in a first-year relativity text?

I would imagine so certainly.

MacM
07-25-05, 04:09 AM
MacM, I've told you this before - Your version of "special relativity" does not adhere to the postulates of Einstein's special relativity.

I cite SRT correctly. I point out the falicy of its claims. If those claims are inherent from the postulates then the postulates are false and are based on mis-interpretatons of data. It really is that simple.

It is not imperative that I supply new postulates nor re-interprete data. It is only necessary to show the falicy. I have done so.


Length contraction, time dilation, reciprocity, et al are all results of the postulates of special relativity. You only want to consider the aspects of special relativity that have been experimentally proven and throw out the other stuff. You just cannot do this (well, technically you can). But you need to come up with new postulates that allow for time dilation but do not allow for length contraction and recirpocity as it appears to me you are doing.

Now this is disappointing. What I have claimed is in fact a proper interpretation which retains the gamma function, eliminates reciprocity and spatial length contraction. Relativity survives in my view but not as presented by Einstein.

Nothing in my view is in conflict with any observation or recorded experimental data.

The fact is that given tr = tick rate:

t * tr = d / v says it more clear than 20 pages of debate. If you retain the emperically supported view of time dilation of a moving clock then you cannot also claim physical contraction of spatial distance.

Length contraction only occurs when you disregard the physical disparity between clock tick rates.

MacM
07-25-05, 04:12 AM
Well, MacM, this thread didn't get very far, did it? I guess we're done, unless you have something new to add. Or would you prefer to exchange insults for a while?

Only when there are those that choose to remain ignorant. Don't take that as exchanging an insult. An insult would be false. :D

Aer
07-25-05, 11:28 AM
I cite SRT correctly. You are never going to convince me that you understand fully special relativity until you can take a special relativity problem and achieve the correct answers according to special relativity whether or not you agree with said answers. As such, the rest of your post isn't neccessary.

Pete
07-25-05, 05:48 PM
I would imagine so certainly.
OK Then! "Exercises in Special Relativity" thread coming right up.

MacM
07-25-05, 05:51 PM
You are never going to convince me that you understand fully special relativity until you can take a special relativity problem and achieve the correct answers according to special relativity whether or not you agree with said answers. As such, the rest of your post isn't neccessary.

Well, I have posted several gamma calculations and velocity addition calculations. Perhaps you might start by showing one error in such calculated results.

Aer
07-25-05, 06:45 PM
Well, I have posted several gamma calculations and velocity addition calculations. Perhaps you might start by showing one error in such calculated results. I will never be impressed by the ability to plug numbers into an equation (i.e. gamma calculations, etc). I'd like to see you take a story problem and achieve the answers that special relativity and only special relativity predicts.

MacM
07-25-05, 06:48 PM
I will never be impressed by the ability to plug numbers into an equation (i.e. gamma calculations, etc). I'd like to see you take a story problem and achieve the answers that special relativity and only special relativity predicts.

THese calculations are based on such gendankin stories. How else do you believe they are derived.

If you don't like my story give me one of your. Just don't turn it into an overly complex scenario unneccessarily, I like to get to the point and issue.

Aer
07-25-05, 06:51 PM
THese calculations are based on such gendankin stories. How else do you believe they are derived.

If you don't like my story give me one of your. Just don't turn it into an overly complex scenario unneccessarily, I like to get to the point and issue. The point and issue is not your interpretation of the story problem, it is the interpretation of special relativity to the story problem.

MacM
07-25-05, 08:07 PM
The point and issue is not your interpretation of the story problem, it is the interpretation of special relativity to the story problem.

Well, I anxiously await your demonstration of this statement by pointing out one specific falicy in my general position. I am not saying I have not posted errors I have, some however, do not represent what my view is and I have made corrections. So I await your specific allegations.

Aer
07-25-05, 08:11 PM
Well, I anxiously await your demonstration of this statement by pointing out one specific falicy in my general position. I am not saying I have not posted errors I have, some however, do not represent what my view is and I have made corrections. So I await your specific allegations.
Give a go at Pete's story problem here (http://www.sciforums.com/showthread.php?t=47571) and I'll allege away!

MacM
07-25-05, 09:05 PM
Give a go at Pete's story problem here (http://www.sciforums.com/showthread.php?t=47571) and I'll allege away!

I'll note that you have failed to point out any specific errors in my posts and you hope to make a challenge showing I do not understand relativity.

Whew :o what a relief that would be for you huh? You wouldn't be cornered by my presentation you could claim it is all my mis-understanding

Well here is Pete's problem:

************************************************** ********
Test your understanding of Special Relativity.
This thread isn't about whether you agree with the theory, it's about whether you understand it well enough to get "correct" answers to textbook problems.

Shall we begin with an easy one?

13. Equal speeds
A and B travel at 4c/5 and 3c/5, respectively, as shown in Fig. 10.36.
How fast should C travel between them, so that he sees A and B approaching him at the same speed?
What is this speed?

Code:
Figure 10.36
4c/5 ? 3c/5
* ---> * ---> * --->
A C B
************************************************** ********
Well perhaps you think I don't know about Velocity Addition. Strange since I have opened a thread on that subject and peformed VAF calculations. But to appease your curiosity I'll work it out and be back to you tonight.

Put in more simple terms:


* -------> 0.8c.........*-------->?.......*--------->0.6c
A............................C.................... ..B


I must note however that Pete fails to identify what such velocities must be in relation to. As written it must be some absolute system. :D

But I know what he wants and won't balk on that point.

REPLY:

I believe the correct answer would be 0.72c.