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Length Contraction and Time Dilation Contradict the Constancy of Light Speed
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Length Contraction and Time Dilation Contradict the Constancy of Light Speed
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butchmurray
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Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
on:
06/06/2013 05:05:00 »
LENGTH CONTRACTION AND TIME DILATION CONTRADICT THE CONSTANCY OF THE SPEED OF LIGHT - MMXIII
By
Thorntone E. ‘Butch’ Murray
Houston, Texas, USA
June 4, 2013
CONTENTION:
This contention is in strict adherence to and based exclusively on principles presented in the 1905 Theory of Special Relativity (SR) by Albert Einstein. The following mathematical analysis of an ordinary, unremarkable circumstance proves that time dilation and length contraction as presented in SR contradict a fundamental assumption of SR that the speed of light is constant and the same for all observers.
FOR THESE PURPOSES:
There are two identical circular clocks each with a pointer and there are three identical light clocks each with a light pulse. A light clock is a particular type of light path. The length of a measuring rod, the length of a light clock and the length of a light path are analogous. When light clocks are judged to have the same length, the light pulses in those light clocks are judged to have the same round trip distance. When the length of a light clock is judged contracted by a factor, the round trip distance for the light pulse in that light clock is judged contracted by that same factor. The amount of time for the pointer in a circular clock to complete one revolution is the amount of time for light pulses in light clocks in the same frame to complete one round trip. Frame K and frame K’ are inertial frames. Frame K’ is in motion relative to frame K.
IN ACCORDANCE WITH LENGTH CONTRACTION
AS PRESENTED IN SR:
The proper length of a measuring rod and so the proper length of a light clock is its length judged from within the frame it occupies. The three light clocks are the same proper length. The round trip distance for a light pulse in a light clock of proper length is d. Judged from frame K the length of a measuring rod and so the length of a light clock oriented perpendicular to the direction of motion in frame K’ is its proper length. Then, judged from frame K the round trip distance for a light pulse in a light clock in frame K and the round trip distance for a light pulse in a light clock oriented perpendicular to the direction of motion in frame K’ are both d. Judged from frame K the length of a measuring rod and so the length of a light clock oriented in the direction of motion in frame K’ is its proper length contracted by the length contraction factor sqrt(1-(v*v/c*c)). The round trip distance for a light pulse in a light clock judged as its proper length contracted by the length contraction factor sqrt(1-(v*v/c*c)) is d*sqrt(1-(v*v/c*c)). Then, judged from frame K the round trip distance for a light pulse in a light clock oriented in the direction of motion in frame K’ is d*sqrt(1-(v*v/c*c)).
IN ACCORDANCE WITH TIME DILATION
AS PRESENTED IN SR:
Judged from frame K when K’ is in motion relative to frame K time in K’ advances at a slower rate than time in frame K. Judged from frame K time in frame K advances at a faster rate than time in K’. Judged from frame K time in frame K advances at a faster rate than time in K’ by the factor 1/sqrt(1-(v*v/c*c)). Then judged from frame K the pointer in the circular clock in K advances at a faster rate than the pointer in the identical circular clock in frame K’ by the factor 1/sqrt(1-(v*v/c*c)). Judged from K the amount of time for the pointer in the circular clock in K’ to complete one revolution is the amount of time for the pointer in the identical circular clock in frame K to complete 1/sqrt(1-(v*v/c*c)) revolutions. Judged from frame K t is the amount of time for the pointer in the circular clock in frame K to complete one revolution. Then judged from K the amount of time for the pointer in the circular clock in frame K’ to complete one revolution is t/sqrt(1-(v*v/c*c)).
THE LIGHT CLOCK IN FRAME K:
One of the previously described circular clocks and one of the light clocks are in frame K. Judged from K that light clock is its proper length. Then, judged from frame K the round trip distance for the light pulse in that light clock in frame K is d. Judged from K the pointer in the circular clock in frame K completes one revolution in amount of time t. The amount of time for the pointer in a circular clock to complete one revolution is the amount of time for a light pulse to complete one round trip in light clocks in the same frame. Then, judged from K the light pulse in the light clock in frame K completes one round trip in that light clock in amount of time t.
For these purposes, v is the speed of the light pulse, the speed of light c. The amount of time for the light pulse to complete the round trip is t. The round trip distance for the light pulse is d. All is judged from frame K.
The speed formula
v=d/t
Substitute c for v
c=d/t
For these purposes, judged from frame K the expression (d/t) represents the speed of the light pulse thus the speed of light in the light clock in frame K.
BOTH LIGHT CLOCKS IN K’:
The remaining circular clock and two light clocks are in frame K’. The amount of time for a light pulse to complete one round trip in the light clocks in frame K’ is the amount of time for the pointer in the circular clock in frame K’ to complete one revolution. Judged from K the amount of time for the pointer in the circular clock in frame K’ to complete one revolution is the amount of time for the pointer in the circular clock in K to complete 1/sqrt(1-(v*v/c*c)) revolutions. Judged from K the amount of time for a light pulse to complete one round trip in the light clocks in frame K’ is the amount of time for the pointer in the circular clock in K to complete 1/sqrt(1-(v*v/c*c)) revolutions. Judged from K the amount of time for the pointer in the circular clock in K to complete 1/sqrt(1-(v*v/c*c)) revolutions is t/sqrt(1-(v*v/c*c)). Therefore, judged from K the amount of time for a light pulse to complete one round trip in the light clocks in frame K’ is t/sqrt(1-(v*v/c*c)).
THE LIGHT CLOCK PERPENDICULAR TO
THE DIRECTION OF MOTION IN K’:
One of the light clocks in frame K’ is oriented perpendicular to the direction of motion. Judged from frame K the length of the light clock that is perpendicular to the direction of motion in frame K’ is its proper length. Then, judged from frame K the round trip distance for the light pulse in that light clock is d. Judged from frame K the amount of time for the light pulse in each light clock in K’ complete one round trip is t/sqrt(1-(v*v/c*c)). Judged from K the round trip distance for the light pulse in the light clock in frame K’ that is oriented perpendicular to the direction of motion is d.
For these purposes, v is the speed of the light pulse, the speed of light c. The amount of time for the light pulse to complete the round trip is t/sqrt(1-(v*v/c*c)). The round trip distance for the light pulse is d. All is judged from frame K.
The speed formula
v=d/t
Substitute c for v
c=d/t
Substitute t/sqrt(1-(v*v/c*c)) for t
c=d/t/sqrt(1-(v*v/c*c))
Simplify
c=(d/t)*sqrt(1-(v*v/c*c))
For these purposes, judged from frame K the expression (d/t)*sqrt(1-(v*v/c*c)) represents the speed of the light pulse thus the speed of light in the light clock that is perpendicular to the direction of motion in frame K’.
BOTH LIGHT CLOCKS IN K’: (Intentionally repeated)
Previously established under this heading, judged from frame K the amount of time for a light pulse to complete one round trip in the light clocks in frame K’ is t/sqrt(1-(v*v/c*c)).
THE LIGHT CLOCK IN
THE DIRECTION OF MOTION IN K’:
The remaining light clock in frame K’ is oriented in the direction of motion. Judged from frame K the length of the light clock that is in the direction of motion in frame K’ is its proper length contracted by the length contraction factor sqrt(1-(v*v/c*c)). Then, judged from frame K the round trip distance for the light pulse in that light clock is d*sqrt(1-(v*v/c*c)). Judged from frame K the amount of time for the light pulse in each light clock in K’ to complete one round trip is t/sqrt(1-(v*v/c*c)). Judged from K the round trip distance for the light pulse in the light clock in frame K’ that is oriented in the direction of motion is d*sqrt(1-(v*v/c*c)).
For these purposes, v is the speed of the light pulse, the speed of light c. The amount of time for the light pulse to complete the round trip is t/sqrt(1-(v*v/c*c)). The round trip distance for the light pulse is d*sqrt(1-(v*v/c*c)). All is judged from frame K.
The speed formula
v=d/t
Substitute c for v
c= d/t
Substitute t/sqrt(1-(v*v/c*c)) for t
c=d/t/sqrt(1-(v*v/c*c))
Simplify
c=(d/t)*sqrt(1-(v*v/c*c))
Substitute d*sqrt(1-(v*v/c*c)) for d
c=(d*sqrt(1-(v*v/c*c))/t)*sqrt(1-(v*v/c*c))
Simplify
c=(d/t)*sqrt(1-(v*v/c*c))*sqrt(1-(v*v/c*c))
Simplify further
c=(d/t)*(1-(v*v/c*c))
For these purposes, judged from frame K the expression (d/t)*(1-(v*v/c*c)) represents the speed of the light pulse thus the speed of light in the light clock that is in the direction of motion in frame K’.
SUMMARY:
Judged by an observer in frame K with frame K’ in motion relative to frame K at a relative speed greater than zero and less than c the speed of light in each of the three light clocks is unique.
Judged by the observer in frame K the speed of light in the light clock in inertial frame K:
c= d/t
Judged by the observer in frame K the speed of light in the light clock perpendicular to the direction of motion in inertial frame K’:
c=(d/t)*sqrt(1-(v*v/c*c))
Judged by the observer in frame K the speed of light in the light clock in the direction of motion in inertial frame K’:
c=(d/t)*(1-(v*v/c*c))
The speed of light in the three light clocks is not constant and the same judged by an observer in frame K.
CONCLUSION:
This mathematical analysis of an ordinary, unremarkable circumstance proves that time dilation and length contraction as presented in SR contradict a fundamental assumption of SR that the speed of light is constant and the same for all observers.
Butchmurray
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Last Edit: 06/06/2013 05:13:19 by butchmurray
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
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Reply #1 on:
06/06/2013 18:51:51 »
I don't think anyone's going to be able to find the time to try to understand all that. Perhaps some diagrams would help make it more intelligible. There's a tool for drawing them here which can be accessed by clicking on "Create a new diagram", just under the box where you type your message in (assuming you aren't using the "Quick reply" one).
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butchmurray
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #2 on:
08/06/2013 00:58:52 »
Hi David.
Your response to my message was quicker than I anticipated.
You make a good point. I’ll post a synopsis in the next few days.
Thanks for the insight.
Butch
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #3 on:
09/07/2013 08:25:33 »
I apologize for my prolonged absence.
Butch
This explanation by example should make the concept easier to understand. The math is basic.
The contention uses only the principles as set forth in The Theory of Special Relativity (SR) and the speed formula, v=d/t. It proves mathematically that length contraction and time dilation as set forth by SR contradict the fundamental assumption of SR that the speed of light is constant and the same for all observers. Judged from within the frame of the observer the speed of light is 300,000 km/s. The same observer judges the speed of light perpendicular to the direction of motion to be 150,000 km/s and the speed of light in the direction of motion to be 75,000 km/s in an inertial frame in relative motion at the at the speed .866c.
FOR THESE PURPOSES:
A light clock is an imaginary construction that consists of two reflectors with a light pulse continuously reflected from one reflector to the other.
Judged from within the inertial frame it occupies the length of a light clock is its proper length.
For a light clock judged as its proper length, the round trip distance for the light pulse in that light clock is 300,000 km.
For a light clock judged as its proper length contracted by the length contraction factor, the round trip distance for the light pulse in that light clock is judged as 300,000 km contracted by that same factor.
There are 2 identical circular clocks and 3 identical light clocks.
The light pulse in each light clock completes 1 round trip in the time it takes for the pointer in the circular clock in that same frame to complete 1 revolution.
Judged from within the inertial frame it occupies the pointer in a circular clock completes 1 revolution in 1 second.
1 circular clock and 1 light clock are in frame K with the observer.
1 circular clock and 2 light clocks are in frame K’.
Inertial frame K’ is in motion relative to inertial frame K at the speed .866c.
THE LIGHT CLOCK IN FRAME K:
Judged by the observer in frame K the length of the light clock is its proper length. Then judged by the observer in frame K the round trip distance for the light pulse in that light clock is 300,000 km. Judged by the observer in frame K the amount of time for that light pulse to complete 1 round trip and the time for the pointer in the circular clock to complete 1 revolution is identical, 1 second.
The speed formula
v=d/t
Judged by the observer in frame K
d= 300,000 km - the round trip distance for the light pulse
t= s - 1 second
v= c the speed of the light pulse
Substitute 300,000 km for d, s for t, c for v
c=300,000 km/s
Judged by the observer in frame K the speed of light in the light clock in frame K is 300,000 km/s.
Inertial frame K is at relative rest, inertial frame K’ is in relative motion at .866c.
Per SR relative to time in frame K time in frame K’ is dilated/slower.
Per SR for the relative speed .866c the time dilation factor is 2.
Per SR judged by the observer in frame K length perpendicular to the direction of motion in frame K’ is the proper length.
Per SR judged by the observer in frame K length in the direction of motion in frame K’ is the proper length factored by the length contraction factor.
Per SR for the relative speed .866c the length contraction factor is .5.
FOR BOTH LIGHT CLOCKS IN K’:
The light pulse in each of the light clocks in K’ complete 1 round trip and the pointer in the circular clock in K’ completes 1 revolution in the same amount of time. As the time dilation factor is 2, judged by the observer in frame K the pointer in the circular clock in K’ completes 1 revolution and the pointer in the circular clock in frame K completes 2 revolutions in the same amount of time. Then judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip and the pointer in the circular clock in frame K completes 2 revolutions in the same amount of time. Judged by the observer in frame K the pointer in the circular clock in frame K completes 1 revolution in 1 second. Then judged by the observer in frame K the pointer in the circular clock in frame K completes 2 revolutions in 2 seconds. Then judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip in 2 seconds.
THE LIGHT CLOCK PERPENDICULAR TO THE DIRECTION OF MOTION IN FRAME K’:
Judged by the observer in frame K the length of the light clock that is perpendicular to the direction of motion in frame K’ is the proper length. Then judged by the observer in frame K the round trip distance for the light pulse in that light clock is 300,000 km. Stated in “FOR BOTH LIGHT CLOCKS IN K’ ”, judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip in 2 seconds.
The speed formula
v=d/t
Judged by the observer in frame K
d= 300,000 km - the round trip distance for the light pulse
t= 2s - two seconds
v= c the speed of the light pulse
Substitute 300,000 km for d, 2s for t, c for v
c=300,000 km/2s
Simplify
c=150,000 km/s
Judged by the observer in frame K the speed of light in the light clock perpendicular to the direction of motion in frame K’ is 150,000 km/s.
THE LIGHT CLOCK IN THE DIRECTION OF MOTION IN FRAME K’:
Judged by the observer in frame K the length of the light clock that is in the direction of motion in frame K’ is the proper length factored by the length contraction factor .5. Then judged by the observer in frame K the round trip distance for the light pulse in that light clock is 300,000 km factored by .5. Stated in “FOR BOTH LIGHT CLOCKS IN K’ ”, judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip in 2 seconds.
The speed formula
v=d/t
Judged by the observer in frame K
d= .5*300,000 km the round trip distance for the light pulse factored by .5
t= 2s - two seconds
v= c the speed of the light pulse
Substitute .5*300,000 km for d, 2s for t, c for v
c=.5*300,000 km/2s
Simplify
c=150,000 km/2s
Simplify further
c=75,000 km/s
Judged by the observer in frame K the speed of light in the light clock in the direction of motion in frame K’ is 75,000 km/s.
Butch
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #4 on:
09/07/2013 18:41:04 »
I'm sorry, but I've cracked. I just can't load all that stuff into my head any more. Maybe someone else can have a go.
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butchmurray
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #5 on:
14/07/2013 02:31:08 »
David,
Please don’t crack now!
Is this better?
Judged by one observer a light pulse, therefore, light has 3 distinct speeds.
Everything here is judged by one observer in the inertial frame that is at relative rest.
WITHIN THE FRAME OF THE OBSERVER:
Orientation of light path – does not apply
Length – proper length
Time – proper time
Length of the light path – the proper length, 299,792,548 meters (300,000 km)
Time for the light pulse to traverse the light path – 1 second proper time
Speed of the light pulse in the light path – 300,000 km/1 second
300,000 km/s – the proper speed of light judged by the observer
Speed of relatively moving frame - .866c
Time dilation factor for .866c – 2
Length contraction factor for .866c - .5
THE RELATIVELY MOVING FRAME:
LIGHT PATH PERPENDICULAR TO THE DIRECTION OF MOTION:
Length – proper length
Length of the light path – the proper length 300,000 km
Time for moving frame – proper time is factored by 2, the time dilation factor
Time dilation factor 2 * 1 second proper time = 2 seconds dilated time
Time for the light pulse to traverse the light path – 2 seconds dilated time
Speed of the light pulse in the light path – 300,000 km/2 seconds
150,000 km/s – Speed of light judged by the observer (at relative rest)
LIGHT PATH IN THE DIRECTION OF MOTION:
Length – proper length is factored by .5, the length contraction factor
Length contraction factor .5 * the proper length 300,000 km = 150,000 km
Length of the light path – the contracted length 150,000 km
Time for moving frame – proper time is factored by 2, the time dilation factor
Time dilation factor 2 * 1 second proper time = 2 seconds dilated time
Time for the light pulse to traverse the light path – 2 seconds dilated time
Speed of the light pulse in the light path – 150,000 km/2 seconds
75,000 km/s – Speed of light judged by the observer (at relative rest)
JUDGED BY THE OBSERVER AT RELATIVE REST:
300,000 km/s is the proper speed of light in the frame of the observer
150,000 km/s is the speed of light in a light path perpendicular to the direction of motion in a frame in relative motion at .866c
75,000 km/s is the speed of light in a light path in the direction of motion in a frame in relative motion at .866c
Butch
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #6 on:
14/07/2013 21:46:11 »
Sorry, but I just can't do it any more. It's still all presented in a form that I simply can't get my mind to work with. I'm sure your argument could be presented in a form where the central part of it comes up front and where it's described clearly to avoid unnecessary confusion, but as it stands it's asking the reader to do ten times as much work as should be necessary. Experience also tells me that what you have above is likely to be nothing more than a more convoluted version of your earlier attempts to prove something where it didn't appear to work and you didn't appear to be able to see that it didn't work (or maybe where it did work and I just couldn't see it, in which case I'm not up to the task anyway), so I simply can't motivate myself to work with the new version unless it's presented enormously better than any of the past versions (which were always far too hard to follow comfortably). It's just got to the point where I can't get my mind to work on it any more, and it's beginning to turn into a mental block now which means that even if you do manage to present it properly I'm going to have a hard time getting up the energy to attempt to work with it, but it would at least make it more likely that someone else would give it a go. [I still think diagrams would help.]
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butchmurray
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #7 on:
20/07/2013 04:53:46 »
SYNOPSIS:
Speed = distance divided by time, d/t e.g. 300,000 kilometers/1 second or simply 300,000 km/s
IN ACCORDANCE WITH THE THEORY OF SPECIAL RELATIVITY (SR):
Judged by an observer at relative rest the speed of a light pulse (the speed of light) in a light path in the OBSERVER’S FRAME is defined as the proper length of the light path (its length in the observer’s frame) divided by the proper time (time in the observer’s frame):
- proper length/proper time
Judged by that same observer at relative rest, when a light path in a FRAME IN MOTION relative to that observer is PERPENDICULAR TO THE DIRECTION OF MOTION the speed of the light pulse is defined as the proper length of the light path divided by the product of the proper time multiplied by the time dilation factor:
- proper length/proper time * time dilation factor
Again, judged by that same observer at relative rest, when that light path in that same FRAME IN MOTION is IN THE DIRECTION OF MOTION, the speed of the light pulse is defined as the proper length of the light path multiplied by the length contraction factor divided by the product of the proper time multiplied by the time dilation factor:
- proper length * length contraction factor/proper time * time dilation factor
Then in accordance with SR, for that one observer light has 3 distinct speeds.
- proper length/proper time
- proper length/proper time * time dilation factor
- proper length * length contraction factor/proper time * time dilation factor
HOWEVER, according to SR the speed of light is constant and the same for all observers.
Butch
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #8 on:
09/08/2013 09:10:15 »
Frames K and K' have their origins O and O' coincident at time t=t'=0. Let x be the direction of motion of K' with respect to K the speed being v. A ray of light leaves the origin and propagates in the vertical direction y with speed C, as seen by an observer at rest in the K' frame. We have C = d'/t', where d' is the distance traveled in the time t'. The distance d' could be represented by a vertical rod of length d' = O'A'.
Another ray of light leaves the origin and propagates in the vertical direction y with speed C, as seen by an observer at rest in the K frame. We have C = d/t, where d is the distance traveled in the time t. The distance d could be represented by a vertical rod of length d = OA.
The vertical distances traveled, d and d', are equal in both K and K'. Since C = d'/t' then t’=d’/C. Since C = d/t then t=d/C. Since d=d’ then t’=d/C and t=d/C therefore, t’=t.
Since t’=t, then time is equal in both frame K and frame K’.
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #9 on:
11/08/2013 00:41:16 »
This is an unpolished version of the quantitative mathematical description of the contention. A significant modification was made.
Frames K and K' have their origins O and O' coincident at time t=t'=0. Let x be the direction of motion of K' with respect to K the speed being v. A ray of light leaves the origin and propagates in the vertical direction y with speed C, as seen by an observer at rest in the K frame. We have C = d/t, where d is the distance traveled in the time t. The distance d could be represented by a vertical rod of length d = OA. Then, as seen by an observer at rest in the K frame C = d/t=C
Another ray of light leaves the origin and propagates in the vertical direction y with speed C, as seen by an observer at rest in the K' frame. We have C = d'/t', where d' is the distance traveled in the time t'. The distance d' could be represented by a vertical rod of length d' = O'A'. When d’ is in the vertical direction y, d’=d. (Per SR, time in K’ is dilated relative to time in K.) So, t’=(t)(square root[1-(v²/C²)]). Then, as seen by an observer at rest in the K frame C = d'/t' = d/(t)(square root[1-(v²/C²)]) =C
An additional ray of light leaves the origin and propagates in the horizontal direction x with speed C, as seen by an observer at rest in the K' frame. We have C = d'/t', where d' is the distance traveled in the time t'. The distance d' could be represented by a horizontal rod of length d'. When d’ is in the horizontal direction x, d’=(d)(square root[1-(v²/C²)]). Time, t’=(t)(square root[1-(v²/C²)]). Then, as seen by an observer at rest in the K frame C = d'/t' = (d)(square root[1-(v²/C²)])/(t)(square root[1-(v²/C²)]) = d/t=C
As seen by an observer at rest in the K frame the speed of light is not constant:
C = d/t within frame K
C = d/(t)(square root[1-(v²/C²)]) in the vertical direction y in frame K’
C = d/t in the horizontal direction x in frame K’
Butch
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
«
Reply #10 on:
12/08/2013 20:33:50 »
Dear Dr.
Is the proof of the inconsistency of the speed of light within SR clarified for you?
Here is something completely different:
The equation t’=(t)square root(1-v²/C²) is obtained from the equation (vt)² + (Ct’)² = (Ct)². The time dilation factor is 1/square root(1-v²/C²).
The equation L’=(L)square root(1-v²/C²) is sited as the equation from which the length contraction factor was obtained. The length contraction factor is: square root(1-v²/C²). The length contraction factor does not apply to length perpendicular to the direction of motion.
How is L’=(L)square root(1-v²/C²) mathematically obtained? How is its directionality mathematically justified? If either of these questions has no mathematically valid answer the length contraction factor, and therefore, length contraction are not scientifically valid. The most ardent supporters of SR would be forced to abandon it in that case.
Thank you,
Butch
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Re: Length Contraction and Time Dilation Contradict the Constancy of Light Speed
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Reply #11 on:
18/09/2013 09:57:38 »
Pursuant to SR, for measuring rods of identical proper length that are perpendicular to the direction of motion, length is the same in all frames and the same for all observers. Pursuant to SR, the speed of light is equal in all frames and the same for all observers. Then, pursuant to the laws of physics, the time for light to propagate the length of measuring rods of identical proper length that are perpendicular to the direction of motion is the same in all frames and the same for all observers. Therefore, in accordance with the laws of physics, time is the same in all frames and the same for all observers.
Inertial frame K’ is in motion relative to frame K at a speed >0<C. Within frame K’ as seen by the observer in K’ light propagates length perpendicular to the direction of motion, d’, at speed C in the time t’. Within frame K as seen by the observer in K light propagates length perpendicular to the direction of motion, d, at speed C in the time t. Per SR, d’=d.
d=Ct
Solved for t --------------- t=d/C
d’=d
d’=Ct’
Substitute d for d’
d=Ct’
Solved for t’ -------------- t’=d/C
Then, ---------------------- t’=t
The time dilation factor and the length contraction factor are derived from the equation (vt)² + (Ct’)² = (Ct)² solved for t’.
(vt)² + (Ct’)² = (Ct)² --------------- Solve for t’
(Ct’)² = (Ct)² - (vt)²
C²t’² = t² (C² - v²)
t’² = t² (1- v²/ C²)
t’ = (t)square root(1- v²/ C²)------- Solved for t’
t’=t Proved previously
Substitute t for t’
t = (t)square root(1- v²/ C²)---Obviously, the formula is invalid.
The formula t’ = (t)square root(1- v²/ C²) and everything derived from it are invalid. The formula is dependent on t’<t. It is now proved t’=t. Therefore:
t=t’/square root(1-v²/C²)--- Time Dilation – is invalid
L’(x)=L(x)square root(1-v²/C²)---Length Contraction – is invalid
1/square root(1-v²/C²)--- gamma – is invalid
September 18, 2013
Thorntone Errick ‘Butch’ Murray
butchmurray
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Last Edit: 18/09/2013 11:16:04 by butchmurray
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