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Author Topic: The Murray Contention MMXI 1.0 vs. Special Relativity  (Read 4414 times)

Offline butchmurray

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The Murray Contention MMXI 1.0
Thorntone E. Murray
(google+ butchmurray houston)
November 30, 2011

Abstract:

The arm in the direction of motion and the arm perpendicular to the direction of motion of the interferometer for the famous Michelson Morley Experiment were obviously in the same moving frame. The apparently disregarded, yet indisputable fact is that slower time in the moving frame, compared to time in the rest frame has the identical influence on both arms. That is the basis of the contention presented here.

Experiment:

An interferometer similar to the instrument of the famous Michelson Morley experiment has two arms of equal length. One arm is oriented in the direction of motion. The other arm is perpendicular to the direction of motion. The instrument is within a frame that is in motion characterized as non-rotating uniform lateral translation, compared to a frame that is at relative rest. From within the moving frame the observed length of each arm is exactly 10 light-nanoseconds, approximately 2.988 meters. Relative to the rest frame the velocity of the moving frame is .866 times the speed of light.

According to the Theory of Special Relativity, judged from the rest frame the length of the arm that is oriented in the direction of motion is sqrt(1-v*v/c*c) times the length of the arm as observed from within the frame in motion. Sqrt(1-v*v/c*c) is the length contraction factor. In this case, the length contraction factor is .5, so the length of the arm as judged from the rest frame is 5 light-nanoseconds. According to Special Relativity, the length of the arm that is oriented perpendicular to the direction of motion is the same length as judged from the rest frame and as observed from within the frame in motion. In this case, the length is 10 light-nanoseconds.

According to the Theory of Special Relativity compared to time in the rest frame, time in the moving frame is slower by the factor 1/sqrt(1-v*v/c*c), the time dilation factor. In this case, relative to time in the rest frame time in the moving frame is 2 times slower. For each nanosecond that occurs in the rest frame, 2 nanoseconds occur in the moving frame. For each 5 nanoseconds that occur in the rest frame, 10 nanoseconds occur in the moving frame. The arm in the direction of motion that is judged from the rest frame to be 5 light-nanoseconds in length computes to be 10 light-nanoseconds in length as judged from within the frame in motion. That agrees with the length of the arm as observed from within the frame in motion.

Here, the stated facts that both of the arms of the interferometer are in the same moving frame and that the relatively slower time in the moving frame has exactly the same influence on both arms is taken into account. Again, for each nanosecond that occurs in the rest frame, 2 nanoseconds occur in the moving frame. The length of the arm that is perpendicular to the direction of motion is 10 light-nanoseconds as judged from the rest frame. The arm perpendicular to the direction of motion computes to be 20 light-nanoseconds in length as judged from within the frame in motion. Observed from within the frame in motion the length of that arm is 10 light-nanoseconds. The theoretical result does not match the observation. The theory is therefore, by definition, incorrect.

Definitions:

For these purposes:
The word “relative” is implicit in reference to “moving frame” and “rest frame”
Ordinary units of length are meter(s), mile(s), feet and the like.
Time based units of length are light-years, light-seconds, light-nanoseconds and the like.
L(x) is the length of the arm that is oriented in the direction of motion as observed from within the frame in motion expressed in ordinary units of length.
L(y) is the length of the arm that is oriented perpendicular to the direction of motion as observed from within the frame in motion expressed in ordinary units of length.
L(x)’ is the length of the arm that is oriented in the direction of motion as judged from the rest frame expressed in ordinary units of length.
L(y)’ is the length of the arm that is oriented perpendicular to the direction of motion as judged from the rest frame expressed in ordinary units of length.
c*t is length expressed in time based units of length such as light-years, light-seconds, light-nanoseconds and the like.

Detailed Description:

Those with a working knowledge of Special Relativity understand that the length of the arm of the interferometer that is oriented in the direction of motion in a moving frame is shorter as judged from the rest frame by the factor sqrt(1-v*v/c*c), the length contraction factor, relative to the length of that arm of the interferometer as judged from within the moving frame. The length contraction factor does not apply to the length of the arm that is perpendicular to the direction of motion. For circumstances in which the length of the arm that is oriented in the direction of motion as observed from within the moving frame is known and the value of the length contraction factor is known, multiplication of that observed length by the length contraction factor provides the length of that arm as judged from the frame that is at rest.

       L(x)’=L(x)*sqrt(1-v*v/c*c)

Time in the moving frame is slower by the factor 1/sqrt(1-v*v/c*c), the  time dilation factor, relative to time in the rest frame. For circumstances in which the length of the arm that is oriented in the direction of motion as judged from the rest frame is known and the factor by which time in the moving frame is slower compared to time in the rest frame is known, seemingly, multiplication of this known length by the time dilation factor results in the length of that arm as observed from within the moving frame. Following is this simplified calculation to obtain L(x), the length of that arm as observed from within the frame in motion.

       L(x)’*1/sqrt(1-v*v/c*c)=L(x)
       L(x)=L(x)     the calculated length equals the actual length

However, the properly executed calculation is slightly more complex than that shown in the simplified equations above. The length of the arm as judged from the rest frame, L(x)’, is expressed in ordinary units of length. The time dilation factor, 1/sqrt(1-v*v/c*c), is the factor by which time in the moving frame is relatively slower than time in the rest frame. Multiplication of those two quantities has no meaning. Only time is multipliable by the time dilation factor.

To perform the properly executed calculation convert ordinary units of length to time based units in the equivalent of L(x)’.

       L(x)’=L(x)*sqrt(1-v*v/c*c)     L(x)’ and its equivalent
       L(x)’=c*t*sqrt(1-v*v/c*c)       ordinary units converted to time based units of length

Multiply the converted equivalent of L(x)’ by the time dilation factor, the factor by which time in the frame in motion is relatively slower compared to time in the rest frame to obtain L(x), the length of that arm as observed from within the frame in motion.

       c*t*sqrt(1-v*v/c*c)*1/sqrt(1-v*v/c*c)=L(x)       

Rearrange to emphasize the time/time dilation factor relationship.

       c*t*1/sqrt(1-v*v/c*c)*sqrt(1-v*v/c*c)=L(x)       

Carry out the calculation. 1/sqrt(1-v*v/c*c)*sqrt(1-v*v/c*c) cancel. c*t remains from that calculation.  L(x) is the length of the arm as observed from within the frame in motion.

       c*t=L(x)

Convert the time based units of length to ordinary units of length for the calculated length of the arm.

       L(x)=L(x)     the calculated length of the arm and the observed length of the arm are the same

The length calculated for the arm of the interferometer that is oriented in the direction of motion and the length of that arm observed from within the frame in motion are the same. The theoretical result matches the observation.


Perform the identical calculation for the length of the arm that is oriented perpendicular to the direction of motion. The length contraction factor does not apply to lengths perpendicular to the direction of motion per Special Relativity.

       L(y)=L(y)’             analog for the y’=y (and z’=z) equation(s) from Special Relativity

To perform the properly executed calculation convert ordinary units of length to time based units of length in the equivalent of L(y)’.

       L(y)’=L(y)     L(y)’ and its equivalent
       L(y)’=c*t      ordinary units converted to time based units of length

Multiply the converted equivalent of L(y)’ by the time dilation factor, the factor by which time in the frame in motion is relatively slower compared to time in the rest frame to obtain L(y), the length of the arm as observed from within the frame in motion.

       c*t*1/sqrt(1-v*v/c*c)=L(y)       

Convert the time based units to ordinary units of length for the calculated length of the arm.

       L(y)*1/sqrt(1-v*v/c*c)=L(y)     the calculated length of the arm and the observed length of the arm

The length calculated for the arm of the interferometer that is oriented perpendicular to the direction of motion and the length of that arm observed from within the frame in motion are not the same. The theoretical result does not match the observation.

Conclusion:

The length of the arm of the interferometer that is perpendicular to the direction of motion as judged from within the moving frame obtained with known facts and applicable principles set forth in the Theory of Special Relativity do not coincide with the length of that arm as observed from within the moving frame. Therefore, by definition, the Theory is incorrect.


 

Offline imatfaal

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #1 on: 01/12/2011 17:46:38 »
Butch - I will not rehearse the arguments again.  But I can confirm again that SR has been shown to be completely mathematically internally consistent - that means within the limits of application it is impossible for a thought experiment within SR to show that SR is incorrect.  SR can only be shown to be incorrect through observation (which the folks in OPERA/Gran Sasso are doing their damnedest to do).

 

Offline butchmurray

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #2 on: 02/12/2011 01:33:28 »
Imatfaal,

I understand your frustration and skepticism, probably more than you can imagine. I truly appreciate and thank you for the input you gave me. I, however, must respectfully disagree with your assertion that Special Relativity can only be proven incorrect by corporeal observation.

You helped me realize the importance of something I have the tendency to forget. It does not matter how momentous an idea may be. If it is not communicated such that it can be properly understood, the idea has no real value. With that in mind I wrote the contention.

Thank you,
Butch

By the by, I’m sure you know that the ICARUS team at Gran Sasso rejected the initial finding of FTL neutrinos. In their paper, the ICARUS team states that their findings “refute a superluminal interpretation of the OPERA result."

 

Offline imatfaal

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #3 on: 02/12/2011 11:27:16 »
Away from the particulars.  mathematics and science works in such a way that something just do mesh and others that cannot.

First.  mathematics allows us in certain circumstances to prove things and make exact statements. In sufficiently simple systems (ie sub godel complexity) and with the acceptance of mathematical axiomata we can create mathematical systems that are internally completely consistent.  SR uses flat euclidean space, very simple maths and just two postulates (no effect of translation from frames in uniform relative motion) and the absolute speed of light without regard to the speed of source or observer.  Now your last work used all these concepts.  Within these concepts and using the mechanics of special relativity it is impossible to generate an internal contradiction.   If you vary the concepts then you can generate a contradiction - but the very point is that you varied the concepts and thus it cannot be used to criticise the theory. 

Second.  SR can be shown to be dodgy using experimental results - as it is (very slightly possible) that OPERA/Gran Sasso are doing so.  What is frustrating is that some physicists are so wedded to SR that they are using the theoretical consequences of SR to try and refute an experimental result.  And that is equally as bad - it is a fine day when a nobel laureate like Glashow (who was the first to go down this avenue) gets criticised, but there is some philosophically/logically poor thinking going on.  The OPERA/Gran Sasso results will almost certainly be shown to be a result of experimental/systematic/calculational error and they will be discredited.  BUT no amount of theory can refute an experimental result.  If Neutrinos are clocked as massive particles travelling faster than light then SR needs to be revised and its limits examined and narrowed. 
 

Offline butchmurray

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #4 on: 05/12/2011 17:05:51 »
Very eloquently stated!

Butch
 

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #5 on: 05/12/2011 17:38:22 »
Very eloquently stated!

Butch

From someone who puts as much time and effort into his posts as it is clear you do that comment is much appreciated - thanks
 

Offline dareo

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #6 on: 11/12/2011 15:38:21 »
Hello butch, sir.. in plain words, what are you conveying?
 

Offline yor_on

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The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #7 on: 13/12/2011 03:07:20 »
I think Butch is questioning why we say that a object only 'shrink', as in Lorentz contract, in the direction of its motion. And assuming that this is wrong he then defines it as Special Relativity is wrong. What he really expect here is a classical universe as I think of it. One where it stops with Newton.

We've gone a far bit away from that in physics, but one thing we still have in common with the old notions is that we still expect 'events to fit' inside our universe, able to agree on for all, as a explosion for example. No matter where you observed it take place, in time and position, all should agree to that there was a explosion. 'Symmetries' as time dilations versus Lorentz contractions, has to make sense for all observers watching the event. That's also why we don't expect a Lorentz/Fitzgerald contraction to 'shrink' at all points of the object. If it did it would lead to conflicting statements of reality, in where our 'common SpaceTime' would be split by different observations defining different events taking place. If you like you can place that one beside the conservation laws, it's a little like axioms that we assume, which we also experimentally find to make sense. Why does Lorentz contraction only act in the direction of motion?

Special Relativity doesn't build on Lorentz contractions, instead they becomes the mirror needed to explain why light always have one constant speed, no matter where you are or how fast you go. In the Michelson Morley Experiment If I remember correctly Lorentz suggested a contraction as to explain why the light never changed its 'speed' relative the aether. But there is a subtlety to it, you have the contraction as described by the object itself, as well as the contraction the object perceives relative all other frames of reference, in Lorentz original it was a effect solely defined as the object being squashed, compressed.

Also the MM experiment used interference, not trying to define a 'speed' but to find if there was an aether 'slowing' light down. But to their surprise finding that light was a constant instead? Forcing (possibly:) Lorentz to later introduce a 'contraction' to resurrect the idea of our earth moving through a aether. The Michelson-Morley Experiment. And for those interested in the math A Deeper Understanding of the Mathematics of the Michelson-Morley Experiment. 

It's not the same as the modern (Einstein) definition in where it has to do with what different 'frames of reference' observe as their 'reality', defined through Special relativity and 'c'. In that definition you have both 'space' contracting when compared between 'frames of reference' as well as the 'objects' themselves, depending on observer. Length Contraction. Try to see the difference there, because it is important.

And it makes sense in a slightly weird way, imagine a photon speed two ways, using a mirror to reflect it back. The mirror contraption made and anchored on (as being 'at rest' with) Earth. One of the photon legs moving in the same direction as Earth move relative (choose your preferred 'frame of reference' to compare Earths 'motion' relative), well, some other galaxy for example, or maybe using the cosmic background radiation as your preferred 'frame of reference'. With its other 'photon leg' reflected back in the opposite direction. Now going against Earths 'relative motion', versus that galaxy or sun or ??. Then the question becomes how it always, invariantly, in a two way experiment, can come out as 'c' in your measurement.

Or better expressed, it's not the 'speed' that is important for creating time dilations and Lorentz contractions. The important part is the idea of light being a constant, invariantly and constantly the same 'value' no matter where and how fast you go as you measure it. And that the MM experiment showed very clearly, that no matter how you tested light always gave them the same (c)onstant value. That the speed of light is a 'constant' is what Special relativity is all about, Time dilations and Lorentz contractions becoming the outcome of that (c)onstant relative different 'frames of reference', as different gravity/accelerations and different 'relative motions'.

So 'c', as in a universal constant, is special relativity. Also being one of the most experimentally proved statements there is, not theoretically, but through real experiments. To disprove a Lorentz Fitzgerald contraction won't make 'c' go away, it will just create the need for another definition of how light behave as it does. And General relativity, which is the larger framework incorporating gravity, flows from that concept of 'c' too. Also proven experimentally in a lot of experiments. None the least here on Earth, as tested by NIST. That using very precise atomic clocks, found time dilations existing when comparing two atomic clocks, originally synchronized, but starting to differ as soon as the clocks were slightly displaced relative each other, even at distances as short as centimeters. What defines a gravitational 'time dilation' on earth is only dependent on how good/exact we make those clocks, as I see it, down to Plank length.

So 'time dilations' definitely exist, and if they do then Lorentz contractions is needed too. You can also question yourself if you notice those time dilations on Earth as you traverse those centimeters? Well, your impression of 'time' won't change, as far as I know. And going very fast (relative Earth) the difference between what you find to be your time relative your own local clock, versus what Earth finds it to be relative theirs will increasingly grow, to finally become as if you were just 'hanging there', stopped in time according to Earth.

Do you think you will be stopped in time, hanging there, same as Earth sees it? And going so fast, what do you expect to happen with those 'distances'? It has a lot to do with all motion being 'relative' something else too naturally, but the real thing defining it is the universal constant 'c', lights speed in a vacuum. But a contraction is a simple way of explaining it, making sense. That is, if we assume that there are more objects and people than me, existing in this universe.
=

This could be a lot clearer, I need to rewrite it later. And it was originally the aether that made Lorentz think of a contraction, not earths motion, although that too plays a role for explaining why a contraction is needed to explain the experiment, as I think of it. But it's a little better now, maybe :)

« Last Edit: 13/12/2011 11:28:07 by yor_on »
 

Offline butchmurray

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #8 on: 19/12/2011 03:38:38 »

Yor_on and dareo,

This is the same as my reply in "Time dilation vs. perpendicular length" thread. How about letting that thread die and we can use this one to discuss both?

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
 

Offline yor_on

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #9 on: 19/12/2011 05:21:35 »
Butch all of those definitions comes from one experimental fact.
'c'

From that you will need 'time dilations' as well as 'Lorentz/Fitzgerald contractions', but made Einsteins way.
And 'time dilations' is a fact, proved on Earth relative 'gravity', that according to Einsteins principle of equivalence can be defined as a constant uniform acceleration.

So to break relativity you will need to find a reason, and experiment, disproving 'c' as a constant.
 

Offline butchmurray

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #10 on: 19/12/2011 09:27:48 »
Yor_on,

It looks like the basis of my contention is not understood. I would like to present it to you a step at a time, if I may, and get your comments for each step, please. This will make it possible for me to elaborate as necessary before moving on to the next step. This could help me as much as anyone.

Given:
The speed of light is constant.
Judged from rest, the length of a body in motion in the direction of motion is contracted by the factor sqrt(1-v*v/c*c) relative to that length of the body as measured from within the moving frame.

L(x) is the length of the body in the direction of motion as measured from within the moving frame.
L(y) and L(z) are the lengths of the body perpendicular to the direction of motion as measured from within the moving frame.
L’(x) is the length of the body in the direction of motion as judged from the rest frame.
L’(y) and L’(z) are the lengths of the body perpendicular to the direction of motion as judged from the rest frame.

L’(x)=L(x)*sqrt(1-v*v/c*c)
L’(y)=L(y)
L’(z)=L(z)

Does this need clarification? Please don’t hesitate to let me know if it does.

Thank you,
Butch
 

Offline yor_on

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #11 on: 22/12/2011 09:11:38 »
Okay, so you accept the definition of Length contraction we use, only contracting in the direction of motion, not perpendicularly to it? If so, I still don't get your purpose Butch. Either you are questioning 'c' as a 'speed', and then the MM experiment isn't your best choice, or you're questioning if light was a constant? In which case the interference clearly stated light to be so.

Now, if you want to present a new way of interpreting how light came to to be a constant in the MMX , that's cool. But if you want to question what the experiment told us, that light is a constant, then you better look up the two way definition of lights speed too, because those experiments tell us the exact same, the added thing being that they also give us a 'speed'.

As for light being slower in the rest frame? I don't get that at all. Light is a constant 'c'. It only have one speed, you want it to have different speeds depending on some mysterious fudge factor of 'densities'? Relativity is built on this concept, you want it differently, then you need to first answer the two way experiments we have of a speed, then the one way experiments of it being a constant.
 

Offline yor_on

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #12 on: 22/12/2011 09:26:47 »
To see the point of view, you can think of 'frames of reference' relative you observing. Each one of them is a 'whole frame' in Einsteins definition, meaning that it is in four dimensions, seamlessly together. No matter what 'frame of reference' you compare yourself too, the two way definition will be true for a 'speed' and a constant. Using the one way definition you will need to consider 'gravity' rewriting lights path in SpaceTime, as SpaceTime is one thing, always including 'gravity' in all 'frames of reference' you measure lights speed relative.

There is both a time dilation and a Lorentz contraction relative each 'frame of reference', as I see it. And they are 'real',  but always as a aspect of your relation observing other frames. Your own 'arrow of time',, as you measure your lifespan won't change, no matter what new 'frame of reference' you move too. So the idea of SpaceTime being some sort of different 'time densities' is, although understandable, wrong. The arrow only have one 'beat' for you, the same everywhere.

And that's also a 'constant', which is why 'c' and the arrow fits so well together.
 

Offline PhysBang

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #13 on: 22/12/2011 14:49:33 »
It might be helpful to use the correct time transformation that SR uses rather than simply, "time in the moving frame is slower by the factor 1/sqrt(1-v*v/c*c)." Often mistaken critiques of SR fail to incorporate the relativity of simultaneity, thus assigning coordinates incorrectly when plotting the effects of SR.
 

Offline yor_on

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #14 on: 23/12/2011 11:38:04 »
Rereading you Butch :)

"Length perpendicular to the direction of motion is in the same moving frame as length in the direction of motion."

I'm confused here. What exactly are we talking about, is it the MMX? Or SR, measuring lengths of a rod, as observed from/in different 'frames of reference'? Light is neither shrinking nor elongating, it may become blue or red shifted relative the observer, but that's about it as far as I know?

If it is rods I have a very nice link. In it he also discuss rods perpendicular to each other.

Special Theory of Relativity: The Basics

But read it from the beginning as he builds it up.
 

Offline butchmurray

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #15 on: 24/12/2011 07:15:00 »
Okay, so you accept the definition of Length contraction we use, only contracting in the direction of motion, not perpendicularly to it? If so, I still don't get your purpose Butch. Either you are questioning 'c' as a 'speed', and then the MM experiment isn't your best choice, or you're questioning if light was a constant? In which case the interference clearly stated light to be so.

Now, if you want to present a new way of interpreting how light came to to be a constant in the MMX , that's cool. But if you want to question what the experiment told us, that light is a constant, then you better look up the two way definition of lights speed too, because those experiments tell us the exact same, the added thing being that they also give us a 'speed'.

As for light being slower in the rest frame? I don't get that at all. Light is a constant 'c'. It only have one speed, you want it to have different speeds depending on some mysterious fudge factor of 'densities'? Relativity is built on this concept, you want it differently, then you need to first answer the two way experiments we have of a speed, then the one way experiments of it being a constant.

My last reply is the first step in the explanation of my contention. It is strictly an affirmation that:
1. Length in the direction of motion is contracted/shortened by the factor sqrt(1-v*v/c*c) as judged from the rest frame compared to that length as measured in the moving frame.
2. Lengths perpendicular to the direction of motion are not contracted/shortened as judged from the rest frame compared to those lengths as measured in the moving frame.
3. The speed of light is constant and the same for all observers in all frames.

Absolutely nothing else is inferred or implied.
If I can get an agreement to that it will help alleviate unnecessary complications and make it easier to understand the next step which is the basis of the contention.

Thank you,
Butch

 

Offline butchmurray

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #16 on: 04/01/2012 05:36:40 »
The next step will not be necessary. My next post is unassailable proof of my contention.

Butch
 

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #17 on: 04/01/2012 05:58:51 »
IRREFUTABLE PROOF OF DIAMETRICALLY OPPOSED STIPULATIONS WITHIN SPECIAL RELATIVITY FOR LENGTHS PERPENDICULAR TO THE DIRECTION OF MOTION
For Dr. A

Thorntone E. Murray
(butchmurray)
January 3, 2012

(Reference will be made to this video: http://www.learner.org/vod/vod_window.html?pid=611  (time 11:50), the Cal Tech/Annenberg production of ‘The Mechanical Universe and Beyond’ program number 42 “The Lorentz Transformation’ by Dr. David L. Goldstein. It was broadcast on PBS in the late 80’s or early 90’s. This information source is unimpeachable. Starting at time 11:50 the term ct’ is established as the height of the light clock in the moving frame.) You may have to set your browser to allow popups.

The mathematical foundation of Special Relativity is the expression sqrt(1-v*v/c*c). Its formulation is based on the Pythagorean theorem applied to a right triangle for which the vertical leg is the height of a light clock within a moving frame. The light clock is perpendicular to the direction of motion. Hence, the height of the light is analogous to length perpendicular to the direction of motion within a moving frame and for these purposes has the value ct’. Time in the moving frame is represented by t’. Time in the rest frame is represented by t. The speed of light which is constant and the same for all observers is represented by c.

The equation formulated by Lorentz with the Pythagorean theorem is c*c*t*t=v*v*t*t+c*c*t’*t’. Solved for t’ the result is t’=t*sqrt(1-v*v/c*c). The value of t’ relative to t is variable and dependent upon the value of v, the velocity of the moving frame relative to the rest frame.

Per the referenced Cal Tech video, as measured from within the moving frame the height of the light clock, thus the length perpendicular to the direction of motion is ct’. Per Special Relativity that length remains constant as measured from within the moving frame at any relative velocity =>0<c. Per the equation t’=t*sqrt(1-v*v/c*c) from Special Relativity for the relative velocity zero (0), sqrt(1-v*v/c*c)=1 so t’=t. As c is constant, the height of the light clock as measured from within the moving frame, ct’, and that height judged from the rest frame, ct, are equal for the relative velocity zero (0). However at any relative velocity >0<c the value of sqrt(1-v*v/c*c)<1 and as such per the equation t’=t*sqrt(1-v*v/c*c), t’>t. Therefore, as judged from the rest frame ct’>ct.

The use of principles exclusively from Special Relativity produce the result in which length perpendicular to the direction of motion as judged from the rest frame is greater than that length as measured from within the frame in motion (ct’>ct). This is in direct contradiction to the tenet, long-established in yet uncorroborated by Special Relativity, that length perpendicular to the direction of motion is equal judged from either frame (ct’=ct). 


« Last Edit: 04/01/2012 07:50:54 by butchmurray »
 

Offline butchmurray

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Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #18 on: 13/01/2012 11:36:13 »
Dr. M

Thank you for your time.

Per your instruction here are the equations with values:

For all examples: c=1,  t=1,  t’=t*1/sqrt(v*v/c*c)

v=.866c------- sqrt(v*v/c*c)=.5--------t’=1/.5=2--------------ct=1, ct’=2
v=0------------- sqrt(v*v/c*c)=1----------t’=1---------------------ct=1, ct’=1
v=.1c---------- sqrt(v*v/c*c)=.944-----t’=1/.994=1.006----ct=1, ct’=1.006

The methods to determine what the actual length of a light clock in a moving frame:
A. Measure it from within the moving frame.
B. With the moving frame at relative velocity=0, judge it from the rest frame. t’=t therefore ct=ct’
C. With the moving frame at relative velocity >0<c  convert t’ to t.
D. Special Relativity stipulation: Length perpendicular to the direction of motion is the same judged from the rest frame and as measured from within the moving frame, ct’=ct

The point is that according to Special Relativity a length perpendicular to the direction of motion in a frame in motion is the same length for all circumstances. Shown above, that clearly is not the case.

This has become more than a theoretical issue as of late because of the preliminary faster than light neutrino results from Cern.

Please fell free to call me at any time.

Thank you,
Butch

 

The Naked Scientists Forum

Re: The Murray Contention MMXI 1.0 vs. Special Relativity
« Reply #18 on: 13/01/2012 11:36:13 »

 

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