Naked Science Forum
On the Lighter Side => New Theories => Topic started by: butchmurray on 13/09/2011 20:02:50

Within frame K’ and always with the same relative velocity as frame K’ is a round disk. At the center of the disk is a light source that radiates light with a 600nanometer wavelength outward in all directions. There is a line (X’) that extends from the center of the disk to the edge. Perpendicular to X’ there is another line (Y’) that extends from the center of the disk to the edge. At relative rest the wavelength of the light along lines X’ and Y’ is 600nm. Alternatively that light wave can be described as having the cycle time of 2.0E15 seconds. The values are directly proportional and interchangeable.
Relative rest:
X’=X wavelength: 600nm or cycle time: 2.0E15 seconds
Y’=Y wavelength: 600nm or cycle time: 2.0E15 seconds
The following are for lengths as judged from within the moving frame.
The traditional formulas for time dilation and length contraction for X’ and Y’:
Equation for length contraction of length in the direction of motion:
L’=L*(sqrt (1 v2/c2))  For these purposes L’=X’ and L=X therefore X’=X*(sqrt (1 v2/c2))
Equation for time dilation in the moving frame:
t’=t*1/(sqrt (1 v2/c2))  The waveform can be expressed in terms of cycle time. Here the cycle time is used for the calculation; t’ (the cycle time of X’) =t (the cycle time of X) *1/(sqrt (1 v2/c2)) or X’=X*1/(sqrt (1 v2/c2))
Equation for length perpendicular the direction of motion:
Y’=Y
With K’ in motion at the relative velocity of .866 times the speed of light: (sqrt (1 v2/c2))=.5
Equation for time dilation in the moving frame:
Time dilation: t’=t*1/(sqrt (1 v2/c2))=t*1/.5=2
(Use the cycle time of the waveform) X’=2.0E15 seconds*2=4.0E15 seconds or wavelength 1200 nm
Equation for length contraction of length in the direction of motion:
Length contraction: X’=X*(sqrt (1 v2/c2))=X*.5
(Use time dilation calculation result) wavelength 1200 nm*.5= wavelength 600 nm or 2.0E15 seconds
Result for length in the direction of motion: X’=X = wavelength 600nm or cycle time 2.0E15 seconds
Equation for length perpendicular the direction of motion:
Y’=Y
Result for length in the direction of motion: Y’= Y = wavelength 600nm or cycle time 2.0E15 seconds
The traditional result:
X’=Y’
The following proves the traditional method of calculation incorrect. Specifically, time dilation occurs for the frame and not for particular lengths. This fact nullifies the conventional wisdom that length perpendicular to the direction of motion is not affected by time dilation.
With K’ in motion at the relative velocity of .866 times the speed of light: (sqrt (1 v2/c2))=.5
The result for length in the direction of motion is the same: X’=X = wavelength 600nm or cycle time 2.0E15 seconds
It was demonstrated with the traditional method that the “at rest” cycle time value of the waveform in the direction of motion (X) was multiplied by the time dilation factor for the frame. Here the proper rebuts the traditional method of calculation. Absent bona fide justification for the contrary, the “at rest” cycle time value for the waveform perpendicular to the direction of motion (Y) must also be multiplied by the time dilation factor. Hence:
Equation for time dilation in the moving frame:
Time dilation: t’=t*1/(sqrt (1 v2/c2))=t*1/.5=2
(Use the cycle time of the waveform) Y’=2.0E15 seconds*2=4.0E15 seconds or wavelength 1200 nm
The proper result:
X’=X = cycle time 2.0E15 seconds or wavelength 600nm
Y’= cycle time 4.0E15 seconds or wavelength 1200 nm
X'≠ Y'
Butch Murray  Houston

So, what's your question Butch?

Hi Geezer,
At issue is that as judged from within a frame in relative motion, traditionally Y’=Y and Z’=Z. There, not taken into consideration is the fact that a component of length is time. The 17th General Conference on Weights and Measures in 1983 defined a meter as “the length of the path traveled by light in a vacuum during a time interval of 1/299792458 of a second”. Therefore, if relative to a rest frame, time within a frame in motion is dilated by the factor 1/(sqrt (1 v2/c2)), time defining length in that frame is dilated by that factor, thereby, dilating length (to include length perpendicular to the direction of motion) by that factor relative to a rest frame.
Therefore, there exists a direct conflict with the tenets of Special Relativity that Y’=Y and Z’=Z and the fact that Y’=Y*1/(sqrt (1 v2/c2)) and Z’=Z*1/(sqrt (1 v2/c2)). More directly: Y’≠Y and Z’≠Z unless velocity v is zero.
The real bottom line is that time dilation is not traditionally applied to length perpendicular to the direction of motion although it should be (at great consequence).
Thank you,
Butch

Butch  I find it very hard to follow your arguments. First off
The following are for lengths as judged from within the moving frame.
The traditional formulas for time dilation and length contraction for X’ and Y’:
Equation for length contraction of length in the direction of motion:
L’=L*(sqrt (1 v2/c2))  For these purposes L’=X’ and L=X therefore X’=X*(sqrt (1 v2/c2))
There are no changes to "lengths as judged from within the moving frame"  nothing changes when you move with the frame, it is relative velocities that matter.
From frame K then
L(x) = L_{0}(x).γ^{1}
L(y) = L_{0}(y)
Δt = Δt_{0}.γ
so X' dne Y' if gamma is nonzero when viewed from o/s K'  I cannot see why you would bother using any other formulae. the claim that traditional thinking is wrong is based on a misunderstanding of traditional thinking
edit
sorry the gammas are not obvious  these are the equations
From frame K then
L(x) = L_{0}(x).gamma^{1}
L(y) = L_{0}(y)
Δt = Δt_{0}.gamma

You might also find it instructive to read up on the relativistic doppler effect. I see no reason to go through this in your experiment as X' dne Y' when viewed from the unprimed reference frame  but if you want to then the formula for frequencies (which are much more commonly dealt with than time length of cycles  it makes things easier for reader if you don't make them take reciprocals in their heads).
fsource sqrt (1 + v/c)
 = ()
fobserved (1  v/c)
(why oh why cant we have latex)
this equation changes at point of closest approach so should only be used when distance is changing not at the instant of closest approach

OK this time in Latex cos my asciart version failed
[ Invalid Attachment ]

imatfaal
Thank you!
I'll reply as soon as I can.
Butch

Imatfaal:
Judged from the unprimed frame:
L’(x)=L(x)*gamma
L’(y)=L(y)
Judged from frame K which is at relative rest, L’(x) in the frame in relative motion, is contracted by the factor gamma and L’(y)=L(y).
Judged from frame K’ which is in relative motion, L’(x) is not observed to be contracted because time in the frame is dilated by 1/gamma, the reciprocal of the contraction factor.
I am attempting to communicate that as judged in K’ that L’(x)=L(x) because in K’:
L’(x)= L(x)*gamma*1/gamma=L(x).
In other words the null result of Michelson Morley was attributed to the affects of length contraction in the direction of motion and time dilation in the frame effectively canceling each other to yield a net result of no change of length in the direction of motion.
My point is that if time dilation in a frame affects length in the direction of motion it must also affect length perpendicular to the direction of motion in the same manner unless there is a good reason that it doesn't.
Thank you, Butch

The transverse relativistic Doppler shift suggests that you may be right Butch.
http://en.wikipedia.org/wiki/Relativistic_Doppler_effect
I once read an article about the LHC stating that protons appear to be smaller at a relative velocity near C. The probability of collision is smaller with increasing speed but they did not give any specification. The problem is that even the length contraction in the direction of propagation will affect the probability due to a non zero angle between the 2 protons at collision.
If anyone has the answer, please...

Judged from frame K’ which is in relative motion, L’(x) is not observed to be contracted because time in the frame is dilated by 1/gamma, the reciprocal of the contraction factor.
No  this is incorrect. Within the frame there is no contraction and no dilation  you cannot tell that you are in relative motion to something by measurement of either time or distance within your own frame.

Imatfaal,
You are absolutely correct when you say that you cannot tell that you are in relative motion to something by measurement in your own frame. However, Einstein and Lorentz were in agreement that in the Michelson Morley experiment length in the direction of motion relative to the sun was contracted by the factor gamma. But time dilation within the inertial frame of the experiment was responsible for the “null” result.
Or in mathematical terms as judged in the moving frame: L’(x)= L(x)*gamma*1/gamma=L(x) where gamma is the length contraction factor and 1/gamma is the time dilation factor and being reciprocal to each other they cancel to exhibit zero net change.
Butch

Imatfaal,
You are absolutely correct when you say that you cannot tell that you are in relative motion to something by measurement in your own frame. However, Einstein and Lorentz were in agreement that in the Michelson Morley experiment length in the direction of motion relative to the sun was contracted by the factor gamma. But time dilation within the inertial frame of the experiment was responsible for the “null” result.
Or in mathematical terms as judged in the moving frame: L’(x)= L(x)*gamma*1/gamma=L(x) where gamma is the length contraction factor and 1/gamma is the time dilation factor and being reciprocal to each other they cancel to exhibit zero net change.
Butch
Sorry Butch but it is just plain wrong  there is no contraction nor dilation within the frame that measurement takes place in. you never measure your own time to be slow nor your own metre stick to be short. And L'(x) dne L(x) if they are in relative motion  as soon as you bring in the unprimed frame then you have contraction  you seem to be treating the unprimed frame as some form of absolute; this is entirely incorrect, there is no correct length and no universal time. And you are misintepreting MM  SR is not incorrect and it tallies perfectly with MM.

Imatfaal,
You are, of course, correct. There is no physical contraction in frame K’ and there is no preferred state of rest.
Relative to the rest frame K, length in the direction of motion L’(x) in the moving frame K’ is contracted by the factor gamma.
And relative to the rest frame K, time in the moving frame is dilated by the factor 1/gamma.
So, even though there is no “cause and effect” the fact remains that per Special Relativity the relationship of L’(x) and L(x) can be defined as:
L’(x)= L(x)*gamma*1/gamma= L(x)
Substitution of actual values for their variables bares this out and serves as proof of validity.
With that, L’(x) and L’(y) are lengths with no particular attributes specific to either within the frame that is in relative motion because “there is no contraction nor dilation within the frame that measurement takes place in”.
Previously stated: relative to the rest frame K, time in the moving frame is dilated by the factor 1/gamma. But relative to the rest frame K, length perpendicular the direction of motion L’(y) in the moving frame K’ is NOT contracted by the factor gamma. Then following the same logic used for L’(x) it follows that:
L’(y)= L(y)*1/gamma= L(y)
That, however, only holds true if v equals zero in which case gamma=1. That is the only case that L’(y)= L(y) as prescribed by Special Relativity.
Thank you,
Butch
By the way, you have probably heard that neutrinos at CERN have very likely exceeded the speed of light. That is consistent to the prediction I made in my post The Special Relativity Discovery MMXI.0 on the BAUTforum and directly relates to this thread.

So, even though there is no “cause and effect” the fact remains that per Special Relativity the relationship of L’(x) and L(x) can be defined as:
L’(x)= L(x)*gamma*1/gamma= L(x)
Substitution of actual values for their variables bares this out and serves as proof of validity.
But no  you are multiplying a length by the time dilation. Just because the metre is now defined in relation the speed of light, doesn't mean you can ignore dimensional analysis. L' will be contracted when K' is in relative motion to K  this is by a faction of gamma. To bring in another factor of 1 over gamma is meaningless.
Within a single frame there is no contraction or dilation. The whole point of relativity is that it doesnt matter if it is K moving or K'  ie you can set the frame you are measuring within to rest or motion. Within your own frame light travels a metre in just under 1/3*10^8 s it does not travel less than a metre nor more than a metre in this time
With that, L’(x) and L’(y) are lengths with no particular attributes specific to either within the frame that is in relative motion because “there is no contraction nor dilation within the frame that measurement takes place in”.
Previously stated: relative to the rest frame K, time in the moving frame is dilated by the factor 1/gamma. But relative to the rest frame K, length perpendicular the direction of motion L’(y) in the moving frame K’ is NOT contracted by the factor gamma. Then following the same logic used for L’(x) it follows that:
L’(y)= L(y)*1/gamma= L(y)
That, however, only holds true if v equals zero in which case gamma=1. That is the only case that L’(y)= L(y) as prescribed by Special Relativity.
Thank you,
Butch
By the way, you have probably heard that neutrinos at CERN have very likely exceeded the speed of light. That is consistent to the prediction I made in my post The Special Relativity Discovery MMXI.0 on the BAUTforum and directly relates to this thread.
Unfo  I think that discovery will go the same way as your breach of SR  it will be explained away. One experiment stretching the bounds of error and without being repeated is a long way from being proved.

Imatfaal is right, L is a function of (x,y,z,t). In spacetime, L and T are already related.

Imatfaal,
I must say I really appreciate your patience and I thank you for making it necessary for me to carefully examine every aspect of what I want to relate.
I will be able to reply yo your last post later today.
Also thanks to all who have shown an interest.
Again
Thank you,
Butch

Imatfaal,
Sorry for the delay.
I, of course, agree with you and understand that nothing in frame K’ is changed due to its relative constant velocity. I used “relative to” but I will use the phrase “judged from” to prevent confusion.
“L’ will be contracted when K’ is in motion relative to K”
I concur that L’(x) is contracted judged from K when K’ is in motion relative to K.
“This is by a fraction of gamma”
I’m took this to mean by the factor gamma.
“To bring in another fraction 1/gamma is meaningless”
I respectfully disagree because 1/gamma is the time dilation factor as in t’=t*1/(sqrt (1 v2/c2))
The process by which I derived L’(x)=L(x)*gamma*1/gamma=L(x) is:
L’=L*(sqrt (1 v2/c2)) – Lorentz contraction
Substitute L’(x) for L’
Substitute L(x) for L
Substitute gamma for (sqrt (1 v2/c2))
L’(x)=L(x)*gamma
Solve for L(x)  multiply both sides by 1/gamma
L’(x)*1/gamma=L(x)*gamma*1/gamma
gamma*1/gamma=1
L’(x)*1/gamma=L(x) or
L(x)=L’(x)*1/gamma
Substitute L(x)*gamma for L’(x)
L(x)= L(x)*gamma*1/gamma
L’(x) not only equals L(x), it is L(x) judged in frame K’ at any relative velocity and judged from K when K’ is at relative rest. So L’(x)= L(x) judged from any frame. Therefore:
L’(x)=L(x)= L(x)*gamma*1/gamma or L’(x)=L(x)*gamma*1/gamma=L(x)
That is a physical reality and must remain true judged from K even though L(x) is contracted by the factor gamma, and is thus L’(x), judged from rest frame K. But, judged from rest frame K; L’(x)=L(x)*gamma. Conflict of the facts L’(x)=L(x) judged in K’ and L’(x)=L(x)*gamma, judged from rest frame K is reconciled by: L’(x)=L(x)*gamma*1/gamma=L(x) in which gamma is the length contraction factor and 1/gamma is the time dilation factor.
Then: L’(x)=L(x) judged in K’
And L’(x)=L(x) judged from rest frame K
Is this incorrect or is there different resolution?
There is absolutely no doubt that experiments must be repeatable. Do you think the results of the 1971 Hafele and Keating single Ce clock experiment should be held as conclusive proof of SR?
Thank you,
Butch

butch _ I will try and get around to reading your latest, but tied up at present

No problem!
Thanks,
Butch

Imatfaal,
Glad you haven’t replied yet.
You have made it clear that I didn’t convey my point understandably. That is what I needed to know and I thank you for your input.
I am working on an approach from an alternate perspective with emphasis on making it bulletproof. I will be able to post it in this thread in the next day or two.
Thanks,
Butch

OK  will wait for bulletproof theory

Imatfaal,
This has become far more complicated than it needs to be.
Please close this thread. I have posted my last word on the subject as “The BOTE of Special Relativity”.
Thank you,
Butch

Hello Butch
We might as well leave the thread open  it is out there already; but given your message above no one will expect you to defend the theory now.
iMatfaal

In other words the null result of Michelson Morley was attributed to the affects of length contraction in the direction of motion and time dilation in the frame effectively canceling each other to yield a net result of no change of length in the direction of motion.
My point is that if time dilation in a frame affects length in the direction of motion it must also affect length perpendicular to the direction of motion in the same manner unless there is a good reason that it doesn't.
Thank you, Butch
Butch, that is a very valid question. I'm not entirely sure of that one either. The main reason, as I understand it, to why it is not expected has to do with 'frames of reference' and the expectations of them making sense when compared against each other. I have a good link to it somewhere.
Yep Q: Why does Lorentz contraction only act in the direction of motion? (http://www.askamathematician.com/2011/01/qwhydoeslorentzcontractiononlyactinthedirectionofmotion/)

Sorry for the delay.
Yor_on,
I readily accept that only length in the direction of motion is contracted judged from the rest frame.
The point that I am making is time in the moving frame is slower relative to time in the rest frame. Length perpendicular to the direction of motion is in the same moving frame as length in the direction of motion. Therefore, the “slower time” has the exact same influence on both lengths. SR dictates that only length in the direction of motion is influenced by the slower/dilated time in the frame where both lengths exist.
Butch

Dr. M
Your message was garbled. Is this the one you referred to?
Thank you,
Butch