Naked Science Forum
On the Lighter Side => New Theories => Topic started by: butchmurray on 04/10/2011 10:45:22
-
The BOTE of Special Relativity
T. E. Butch Murray
Houston - USA
Frame K’ is in uniform motion. Frame K is at relative rest.
IN FRAME K’:
(A1) Judged in K’ t is a single interval of time in frame K’
(A2) Judged in K’ L is the length of a measuring rod in frame K’
(A3) Judged in K’ light traverses the length of the measuring rod in frame K’ in
time interval t
(A4) Judged in K’ the length of the measuring rod can be expressed as c*t ---per (A1) (A3)
(A5) With the measuring rod oriented in the direction of motion its length is
referred to as L(x) ---per (A2)
(A6) L(x)=c*t --- per (A2) (A4) (A5)
(A7) With the measuring rod oriented perpendicular to the direction of motion its
length is referred to as L(y) ---per (A2)
(A8) L(y)=c*t --- per (A2) (A4) (A7)
Judged in K’ the length of the measuring rod is c*t ---per (A3)
L(x) JUDGED FROM FRAME K:
(B2) While the measuring rod is oriented in the direction of motion, judged from K its length is L’(x) ---per (A5)
(B3) L’=L*gamma --- per Special Relativity
(B4) Judged from K, L’(x), the length of the measuring rod while oriented in the
direction of motion is contracted by the factor gamma relative to its length
L(x) judged in K’ --- per Special Relativity (B2) (B3)
(B5) Time t in frame K’ is t’ judged from K
(B6) t’=t*1/gamma ---per Special Relativity
(B7) Judged from K, time t in frame K’ is dilated by factor 1/gamma relative to
time in frame K ---per Special Relativity (B5) (B6)
Judged from frame K the length of the measuring rod is L’(x) ---per (B2)
L’(x)=L(x)*gamma --- per (B3) (B4)
Substitute c*t for L(x) --- per (A6)
L’(x)= c*t*gamma (provisional)
Substitute t’ for t --- per (B5)
L’(x)= c*t’*gamma
Substitute t*1/gamma for t’ --- per (B5) (B6) (B7)
L’(x)= c* t*1/gamma*gamma
Simplify
L’(x)= c* t
Judged from frame K, the length of the measuring rod in K’ while oriented in the direction of motion is c*t
L(y) JUDGED FROM FRAME K:
(C2) While the measuring rod is oriented perpendicular to the direction of motion,
judged from K its length is L’(y) ---per (A7)
(C3) Judged from K, the length of the measuring rod while oriented perpendicular
to the direction of motion is not contracted relative to its length L(y)
judged in K’ --- per Special Relativity (C2) (C3)
(C4) L’(y) is not contracted relative to L(y) --- per Special Relativity - y’=y
z’=z
(C5) Time t in frame K’ is t’ judged from K
(C6) t’=t*1/gamma ---per Special Relativity
(C7) Judged from K, time t in frame K’ is dilated by factor 1/gamma relative to
time in frame K ---per Special Relativity (C5) (C6)
Judged from frame K the length of the measuring rod is L’(y) ---per (C2)
L’(y)=L(y) --- per (C4)
Substitute c*t for L(y) --- per (A8)
L’(y)= c*t (provisional)
Substitute t’ for t --- per (C5)
L’(y)= c*t’
Substitute t*1/gamma for t’ --- per (C5) (C6) (C7)
L’(y)= c*(t*1/gamma)
Judged from frame K, the length of the measuring rod in K’ while oriented perpendicular to the direction of motion is c*(t*1/gamma)
Judged in K’ the length of the measuring rod is c*t
Judged from frame K, the length of the measuring rod in K’ while oriented in the direction of motion is c*t
Judged from frame K, the length of the measuring rod in K’ while oriented perpendicular to the direction of motion is c*(t*1/gamma)
CONCLUSION:
Per Special Relativity y’=y; length perpendicular to the direction of motion is identical judged from either frame. Yet, observed in K’ while the measuring rod is perpendicular to the direction of motion light traverses the length of the measuring rod in the time interval t. Judged in K’ the length of the measuring rod is c*t. But, Judged from K light traverses the length of the perpendicular measuring rod in the time interval t*1/gamma. Judged from K the length of the measuring rod is c*(t*1/gamma). According to Special Relativity the speed of light is constant and the same for all observers. According to Special Relativity light must traverse the length of the measuring rod at any orientation in K’ in the same interval of time every time judged from K and K’. The combination of length contraction and time dilation does not produce that result.
CONSEQUENCES:
The combination of time dilation and length contraction violates constancy of the speed of light. The combination of time dilation and length contraction is, therefore invalid. Further, the codependence of time dilation and length contraction renders each individually invalid. Even further, the y=y and z=z equations of the Lorentz transformation are now proven invalid. Therefore, the Lorentz transformation is invalid in its entirety. The validity of Special Relativity itself is now questionable.
-
Beginning of the end...? Brave words - when I can, I will have a look through .
iMatfaal
-
initially
1. You really need to stick to standard and accepted usage - makes life a lot easier for those you are trying to convince
2. Unless there is something weird going on (and there might be, see point one above) you have your gammas wrong. T=T_0.gamma and L=L_0/gamma, where T_0 and L_0 are measurements from the objects own frame.
3. The artifice and reason the idea fails is the l=ct. distance = speed * time is fine - but it is an equation of motion and your thought experiment fails to treat it like that. you are taking a truism and forming an instantaneous measurement from it. do the thought experiment and send a pulse of light from one end of L to the other - and view it from both the local frame and the moving frame.
-
Imatfaal,
1. You’re right.
2. That is exactly what I have.
(B3) L’=L*gamma --- per Special Relativity
(B4) Judged from K, L’(x), the length of the measuring rod while oriented in the direction of motion is
contracted by the factor gamma relative to its length L(x) judged in K’ --- per Special Relativity (B2)
(B3)
L’(x)=L(x)*gamma --- per (B3) (B4)
(B5) Time t in frame K’ is t’ judged from K
(B6) t’=t*1/gamma ---per Special Relativity
(B7) Judged from K, time t in frame K’ is dilated by factor 1/gamma relative to time in frame K ---per Special
Relativity (B5) (B6)
3. I’m looking at it as an equation of length. The measuring rod can be 1 light second long, the distance or length light traverses in one second. The measuring rod can be 1 light nano-second long, the distance or length light traverses in one nano-second. That’s just the length expressed in terms of light speed. There are no instantaneous measurements happening.
Beginning of the end??? Where did that come from?
Thanks,
Butch
[;)]
-
2. - No you have it wrong way around
(A2) Judged in K’ L is the length of a measuring rod in frame K’
this means that the proper length - ie the length in the local frame is L (normally called L_0). Therefore the length in the frame in relative motion is the proper length divided by gamma ie L'=L_0/gamma.
3. If it is just a length then you do not need to do time dilation on it. If it is length then call it a Butch or a Charlie, or even a metre - lengths do not have units of time, they have units of length. It does not matter if you use a number of wavelengths, the distance light travels in a second, or the length of a man's arm - length is the distance along the x-axis; it is not a rate of progress multiplied by a distance along the time axis - even though that might be equivalent.
Formally, the time dilation equations are as follows
ΔT'=ΔT0γ
So what is your time interval (cos that's the meaning of Delta)? If you do the measurement to get a time interval then the path is weird - and will work out correct by SR.
Thinking in terms of dimensional analysis what are the units? time * speed of light -> m/s * s = m . That's just metres - there is no time dimension for your dilation to act upon.
-
Butch
Beginning of the end??? Where did that come from?
Thanks,
Butch
[;)]
BOTE - I assumed that meant Beginning of the End. But I suppose it could be Back of the Envelope as well.
-
Judged from a rest frame a measuring rod oriented in the direction of motion in a frame in relative motion will be contracted. Judged from inside the frame in motion the length of the rod never changes due to relative velocity.
Special Relativity dictates that the speed of light is constant and the same for all observers. Light must traverse the exact length of that measuring rod in the same amount of time judged by any observer no matter how much it is contracted from the observer’s point of view.
Without time dilation but the speed of light being constant, light could not traverse various contracted lengths in one certain amount of time. It would take a lesser amount of time to traverse the measuring rod when is highly contracted and a greater amount of time to traverse the length of the measuring rod when it is just barely contracted.
Time dilation takes care of that. Time in the moving frame is dilated or slower compared to time in the rest frame. The greater the relative velocity of the moving frame the slower time is relative to the rest frame and the more contracted is the measuring rod in the direction of motion judged from the rest frame. Light can traverse the exact length of the measuring rod at any contracted length in exactly the same amount of time.
The “at rest” length of the measuring rod oriented in the direction of motion multiplied by the length contraction factor yields the contracted length. The contracted length multiplied by the time dilation factor yields the “at rest” length. Since the “at rest’ length and contracted and time dilated lengths are the same, light will traverse both lengths in the same amount of time.
For example, the “at rest” length of the measuring rod is one light second. For the relative velocity of the frame the length contraction factor is .4. The “at rest” length of 1 light second is multiplied by the length contraction factor .4. The contracted length is then .4 light seconds judged from the rest frame. The time dilation factor is the reciprocal of the contraction factor, so in this scenario, the time dilation factor is 2.5. That means time in the frame in motion is 2.5 times slower than time in the “at rest” frame. The contracted length of .4 light seconds is multiplied by the time dilation factor 2.5. The length .4 light seconds is the distance or length that light traverses in .4 seconds. The time of .4 seconds is multiplied by the time dilation factor of 2.5 to yield 1 second, the time calculated for light to traverse the length of the rod of 1 light second in length at the constant speed of light. Thus light traverses the contracted length and the “at rest” length in one second and the speed of light is constant and the same for both observers.
With the same measuring rod perpendicular to the direction of motion its length is not contracted and is 1 light second in length judged from the rest frame. Time is dilated for the moving frame the measuring rod is in. One second in the moving frame is 2.5 seconds judged from the rest frame. The length, 1 light second, is the distance or length that light traverses in 1 second. The time of 1 second is multiplied by the time dilation factor of 2.5 to yield 2.5 seconds. That is the time calculated for light to traverse the length of the rod that is 1 light second in length. Thus light traverses the unchanged length of 1 light second in 2.5 seconds judged from the “at rest” frame.
That is my point! Judged from within the frame in motion light takes one second to traverse the measuring rod that is 1 light second in length. Judged from the “at rest” frame light takes 2.5 seconds to traverse the same measuring rod. With the moving frame at relative rest it takes light 1 second for light to traverse the measuring rod that is 1 light second in length. Constancy of the speed of light is violated.
-
imatfaal,
or
Basics of the Equations
Butch
-
Light must traverse the exact length of that measuring rod in the same amount of time judged by any observer no matter how much it is contracted from the observer’s point of view.
So in your thought experiment at which points does light travel the exact length of that rod?
Go back to your equations - get the the primes and gammas at the right places - and demonstrate at which point light will travel at wrong speed.
Either light seconds is a distance, in which case we care not about time dilation; or it is the result of timing a pulse of light, where we need to consider its route. Both cases work out fine. It is a fallacious to state that as points A and B are a light second apart at time T=0 then then light mush be able to cross the distance between them in a second IF points A and are in motion and that at time T=x A_0 DNE A_x and B_0 DNE B_x
-
Imatfaal,
Thank you so much for your time.
Respectfully, the point is not that light literally travels the exact length of the rod. It is how long would light take to traverse the exact length. That may sound nit picky but I don’t want us to get on the wrong track. No light pulses are being used at all.
The statements “the speed of light is constant” and “the speed of light is the same for all observers” don’t mandate that a light pulse is generated and timed as it traverses the rod. More exactly, the statements taken together mean that if a light pulse went from one end of the measuring rod to the other end it would take the same amount of the time in the observers frame whether the observer is in the moving frame and, in essence, observing the rest length or in the rest frame observing the rod at any contracted length.
In other words if it would take time x for a light to traverse the exact length of the rod judged from inside the moving frame, it would take a light pulse the same amount of time, x, for light to traverse the exact length of the rod at any magnitude of contraction judged from the rest frame.
To determine what time x is for the measuring rod’s rest length, calculate the amount of time it would take for light to traverse the length of the measuring. If the length is already stated in terms of light speed i.e. light seconds, light microseconds etc. no calculation is necessary. The increment of time is the numeric value and the unit of time. The word “light” indicates at the speed of light. For example, the length of that measuring rod is 360 light nanoseconds. 360 is the number of the nanosecond time units that light would take to traverse a rod. If the length is not expressed in terms of light speed e.g. meters, yards, furlongs etc. it must be so converted.
To determine what time x is for the measuring rod’s contracted length, that length should be expressed in terms of light speed. Time in the moving frame that contains the rod is dilated relative to the rest frame. Therefore, the number of increments of time is multiplied by the time dilation factor for the moving frame. For example, for the relative velocity of the moving frame that results in the contraction factor of .5, the time dilation factor is 2, the reciprocal of the contraction factor. The measuring rod above has the contracted length of 180 light nanoseconds (360*.5). The increment of time of the contracted length (180) is multiplied by the time dilation factor for the frame, 180*2=360 increments of the unit of time. The number of increments of time is 360, the unit of time is nanoseconds. So, it would take 360 nanoseconds for light to traverse the contracted length. It would take 360 nanoseconds in the moving frame for light to traverse the non-contracted length. Light takes the same amount of time to traverse the contracted and non-contracted length.
This calculation is rarely done. The result is always the same. Light would always, by definition, take the same amount time as judged by all observers to traverse a particular length in the direction of motion.
As demonstrated above, any length can be expressed in terms of length or terms of light speed. Both are equally valid.
However, length perpendicular to the direction of motion can clearly be expressed in terms of the speed of light just as length in the direction of motion. Both lengths consist of increments of time. In the circumstance that both lengths are in a frame in motion relative to a rest frame, judged from the rest frame the time in the moving frame that contains both lengths is dilated relative to the rest frame. Repeat time in the FRAME that contains BOTH lengths is relatively dilated. The increments of time for both lengths MUST be multiplied by the time dilation factor for that frame. If anyone knows a legitimate explanation to the contrary, PLEASE enlighten me. I have no explanation.
Thank you,
Butch
-
I'm no expert, but I think this has something to do with it.
http://en.wikipedia.org/wiki/Length_contraction
-
Geezer,
Thank you.
I checked it out. Realized I had been there a few times before.
But, like everywhere else, it does not offer justification for why length perpendicular to the direction of motion is exempted from the affect of time dilation. Even in the translation of “Relativity The Special and General Theory” by Einstein himself, he explains nearly every idea in detail, but not that. There is no explanation there or anyplace else for y’=y and z’=z in the Lorentz transformation. It is as though everyone is just supposed to accept that proposition on faith. That is not good enough, especially since it is so easy to disprove. The problem seems to be that since it hasn’t been questioned in 100 years it never should be. One can be soundly criticized for questioning dogma that has no foundation in fact.
Go figure.
Too cynical?
I know someone out there at least has some ideas. Let's hear some.
This is the link to the translation of “Relativity The Special and General Theory” by Einstein
http://www.bartleby.com/173/
Thanks,
Butch
-
But, like everywhere else, it does not offer justification for why length perpendicular to the direction of motion is exempted from the affect of time dilation.
Because length isn't time?
-
JP
You are right. Length is not time but time is a component of length.
I hope you agree that length and distance are just 2 different words for the same thing.
What is 60 inches?
One answer is: that is the distance covered in 2 hours at 30 inches per hour
Change the 2 to a 3. Instead of 60 inches you have 90 inches.
The time –hours- is crucial for distance and/or length. If you discard the time there is no distance.
Length or distance can be defined as how far something will go at a certain speed for a certain 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”.
But in this case time is not really the problem.
Take a simple 12-inch ruler for instance.
Put it in a frame that is time dilated relative to a rest frame.
With the ruler in the direction of motion in a frame in motion, the dilated time of the moving frame affects how long the ruler is judged from the rest frame.
With that same ruler just turned perpendicular to the direction of motion instead in the same frame in motion, the same dilated time of the same moving frame does not affect how long it is judged from the rest frame.
The real kicker is that judged inside the moving frame where the ruler is, the length of the ruler never changes.
I omitted a detail or two, but they are not germane to the basic problem and I don’t want to bog you down in details.
Thanks,
Butch
You or anyone else have more ideas??
-
Butch - it is very simple. Lengths are not time dilated. It does not matter how you measure or what units you use the length it is not time dilated. The lightsecond is a measurement of distance or length - when viewing a time dilated frame the lightsecond does not change - if it did Gravitational time dilation would affect length and it does not.
The time –hours- is crucial for distance and/or length. If you discard the time there is no distance.
This is just plain wrong.
-
Imatfaal,
Again you are correct. Lengths are not time dilated. Lengths are contracted and time is dilated such that the speed of light is constant and the same for all observers.
Whether the observer is in the moving frame with the measuring rod and judges the length to be non-contracted or if the observer is in the rest frame and judges the measuring rod in the moving frame to be contracted, light will always be judged take the same amount of the observer’s time to traverse a measuring rod.
With this caveat:
That doesn’t work if the same measuring rod is perpendicular to the direction of motion!
Thanks,
Butch
-
Imatfaal
I missed the last part of your reply.
What is 60 inches?
One answer is: that is the distance covered in 2 hours at 30 inches per hour
Change the 2 to a 3. Instead of 60 inches you have 90 inches.
The time –hours- is crucial for distance and/or length. If you discard the time there is no distance.
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”.
Respectfully, if you discard the time, what is the distance?
Thanks,
Butch.
-
Whether the observer is in the moving frame with the measuring rod and judges the length to be non-contracted or if the observer is in the rest frame and judges the measuring rod in the moving frame to be contracted, light will always be judged take the same amount of the observer’s time to traverse a measuring rod.
Not true. The observer moving along with the rod will see the light traverse a distance equal to the entire length of the rod. The observer standing still and watching the rod move by will see the light travel a distance slightly less than the length of the rod (since the back end of the rod has moved forward a bit by the time the light reaches it.) Since the speed of light is constant, the observer moving with the rod will measure that it took longer for the light to traverse the rod.
-
Butch - this is just wrong. mathematically and physically length is not time! they are different dimensions that can be viewed as orthogonal to each other. The definition of a metre does not make it a time dependant measure - for instance the second is defined by oscillation between two states of a caesium ion - these are all just convenient ways of defining a number of units along an axis. The time axis and the length axes are orthogonal - not matter how far or how fast you move along one you do not necessarily move along another.
before 1983 the metre was defined as a fraction of the circumference of the earth - did this mean that SR worked then? your argument is frankly based on a foolish artifice that states that because one can in certain circumstances measure a distance by timing how long something moving at a speed takes to get from A to B, that one CAN ALWAYS state this. if A and/or B are moving this is clearly not the case.
take a ruler - hold it horizontally, what path would a bullet take fired from 0cm to 30cm take. Drop the ruler - what path would the bullet need to take now to pass both 0cm and 30cm whilst in flight? they are not identical.
the mistake is so simple you are not seeing it!
60 inches is 5 foot - and other things - tying it to a speed is artificial and unnecessary and has led to your misunderstanding. please just do a dimensional analysis (ie use proper SI units and cancel where necessary) there is no way you will have a seconds terms in your length - if there isnt then there is no time interval for time dilation to act upon. Please just try this because the dogged repeating of 'time is crucial for length' is wasting my time and yours
#
edited to save my blushes over error
-
I sincerely apologize for wasting your time.
Butch
-
Butch - not a problem at all I enjoyed it. But I do worry that you are obviously very keen on this subject and anxious to make progress - but that you seem to have got yourself stuck in a dead end. I cannot explain your error any better than I have already - but I promise you it is an error. If you still cannot get your head round why you are misthinking drop me another line
-
imatfaal,
Thank you.
Butch