# Naked Science Forum

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

Title: Time dilation vs. perpendicular length
Post 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 600-nanometer 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 2.0E-15 seconds. The values are directly proportional and interchangeable.

Relative rest:
X’=X wavelength: 600nm or cycle time: 2.0E-15 seconds
Y’=Y wavelength: 600nm or cycle time: 2.0E-15 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’=2.0-E15 seconds*2=4.0E-15 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 2.0E-15 seconds
Result for length in the direction of motion: X’=X = wavelength 600nm or cycle time 2.0E-15 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 2.0E-15 seconds
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 2.0E-15 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’=2.0-E15 seconds*2=4.0E-15 seconds or wavelength 1200 nm
The proper result:
X’=X = cycle time 2.0E-15 seconds or wavelength 600nm
Y’= cycle time 4.0E-15 seconds or wavelength 1200 nm
X'≠ Y'

Butch Murray - Houston
Title: Time dilation vs. perpendicular length
Post by: Geezer on 14/09/2011 08:26:24
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 14/09/2011 22:26:03
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
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 20/09/2011 17:28:12
Butch - I find it very hard to follow your arguments.  First off

Quote
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) = L0(x).γ-1
L(y) = L0(y)
Δt = Δt0

so X' dne Y' if gamma is non-zero 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) = L0(x).gamma-1
L(y) = L0(y)
Δt = Δt0.gamma
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 20/09/2011 17:50:01
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
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 20/09/2011 17:55:12
OK this time in Latex cos my asci-art version failed

[ Invalid Attachment ]

Title: Time dilation vs. perpendicular length
Post by: butchmurray on 20/09/2011 21:39:40
imatfaal

Thank you!

I'll reply as soon as I can.

Butch
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 21/09/2011 00:11:45
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
Title: Time dilation vs. perpendicular length
Post by: CPT ArkAngel on 21/09/2011 01:15:38
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.

Title: Time dilation vs. perpendicular length
Post by: imatfaal on 21/09/2011 11:18:08

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.
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 21/09/2011 20:08:01
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
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 22/09/2011 10:32:30
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.
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 23/09/2011 10:21:52
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.
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 23/09/2011 14:05:07
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

Quote

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.
Title: Time dilation vs. perpendicular length
Post by: CPT ArkAngel on 23/09/2011 17:23:07
Imatfaal is right, L is a function of (x,y,z,t). In spacetime, L and T are already related.
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 24/09/2011 12:22:00
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
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 25/09/2011 22:43:11
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
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 26/09/2011 18:14:21
butch _ I will try and get around to reading your latest, but tied up at present
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 26/09/2011 18:39:15
No problem!

Thanks,
Butch
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 28/09/2011 19:08:55
Imatfaal,

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
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 29/09/2011 15:52:04
OK - will wait for bullet-proof theory
Title: Time dilation vs. perpendicular length
Post by: butchmurray on 04/10/2011 10:47:43
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
Title: Time dilation vs. perpendicular length
Post by: imatfaal on 04/10/2011 16:56:25
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
Title: Time dilation vs. perpendicular length
Post by: yor_on on 13/12/2011 00:25:50

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/q-why-does-lorentz-contraction-only-act-in-the-direction-of-motion/)
Title: Re: Time dilation vs. perpendicular length
Post by: butchmurray on 19/12/2011 03:24:52
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
Title: Re: Time dilation vs. perpendicular length
Post by: butchmurray on 02/02/2012 07:10:59
Dr. M

Your message was garbled. Is this the one you referred to?

Thank you,
Butch