Naked Science Forum
On the Lighter Side => New Theories => Topic started by: butchmurray on 01/07/2012 19:13:18
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Thorntone E. Murray
July 1, 2012
PROBLEM:
The 1887 Michelson Morley interferometer experiment was conducted throughout the year at all times of day and night. No fringe was observable for the experiment from within the moving frame. All lengths, including wave length, in the direction of motion in the moving frame are contracted judged from relative rest. Lengths perpendicular to the direction of motion are not contracted judged from relative rest. Then, significant fringe was observable for the experiment from relative rest. The problem: How can significant fringe exist and not exist for the same experiment?
HYPOTHESIS:
The 1887 Michelson Morley experiment consistently produced insignificant fringe, hereafter referred to as no fringe. That was proof by experiment the frequency of the light in the light path in the direction of motion and the frequency of the light in the light path perpendicular to the direction of motion were the same judged from within the moving frame. It is a rule of physics that the speed of light divided by the frequency of light is the wavelength of that light. The speed of light was the same for both light paths and the frequency of the light was the same for both light paths. Therefore, judged from within the moving frame the wavelength of the light in the perpendicular light paths was the same. (Data 1)
The magnitudes of distance, wavelength, the length of a light path and the length of a measuring rod can all be expressed with the same interchangeable units of linear measure. Mathematically there is no distinction. It is a rule of physics that distance divided by speed equals time. Then, distance, a single wavelength in this case divided by speed, the speed of light in this case equals time, the duration of a single wavelength of the monochromatic light in the interferometer experiment in the moving frame. The wave length and the speed of light were the same for both light paths. Therefore, the wave length duration was the same for the perpendicular light paths as judged from within the moving frame. (Data 2)
The lengths of the perpendicular light paths were made equal for the experiment. The wave count of the monochromatic light in the two light paths was, therefore, equal. The wave count multiplied by the wave length yields the length of each of the light paths judged from within the moving frame. The wave count multiplied by the wave length duration yields the time for light to traverse the length of each of the light paths. Then, the time was equal for both light paths judged from within the moving frame. (Data 3)
The equal length of the light paths and the equal duration of time for light to traverse each were constant judged from within the moving frame. A rule of physics is that time equals distance divided by speed. A rule of physics is that when time is constant distance and speed are directly proportional. A rule of physics is that when one of two directly proportional variables is made constant the remaining variable is made constant. There can be no doubt that when one of the variables made constant is the speed of light which is the same for all observers the remaining directly proportional variable made constant is the same for all observers. Distance and length are analogous. The length of the light paths and the time are constant judged from within the moving frame. The time for light to traverse each light path is equal to the length of the light path divided by the speed of light. Then, length and the speed of light are directly proportional. The speed of light is constant and the same for all observers. Then, the equal lengths of the perpendicular light paths of the experiment were constant and the same for all observers. Then, the length of the light paths as judged from within the moving frame and judged from relative rest were the same. Therefore, there was no length contraction judged from relative rest. (Data 4)
It is a rule of physics that speed equals distance divided by time. Then, the speed of light equals the length of the light paths divided by the duration of time for light to traverse either of the light paths. The length of the light paths and time are directly proportional. The length of each of the light paths is constant and the same for all observers. Then, time is also constant and the same for all observers. Then, the time for light to traverse either light path judged from within the moving frame and judged from relative rest were the same. Therefore, compared to time in the frame at relative rest, time in the moving frame was not dilated. Further, in accordance with the rule of physics that the rules of physics are the same for all observers, no fringe was observable for the experiment from relative rest. (Data 5)
DATA:
(Data 1)
No fringe – The 1887 Michelson Morley experiment.
Equal frequency – Law of physics: When combined light waves produce no fringe the light waves are synchronous. Law of physics: When light waves are synchronous the light waves are of the same frequency.
Equal wave length – Law of physics: The speed of light divided by the frequency of the light equals the wave length of the light; c/f=w (due to font restraints “w” is used in lieu of lambda for wave length)
(Data 2)
Distance/length equivalence – Example: The distance between two points is one meter. The length of a line between the two points is one meter.
Measuring rod/light path length equivalence – Example: The length of the measuring rod is one light second. The length of the light path delineated by the ends of the measuring rod is one light second. The length of the measuring and the length of the light path delineated by the ends of the measuring rod are always equal.
Distance divided by speed equals time – Rule of physics: d/v=t
Wave length (w) divided by the speed of light (c) equals wave length duration (T); for the equation d/v=t; substitute w for d; substitute T for t; w/c=T
(Data 3)
Wave count multiplied by the wave length (w) equals the light path length (L) – Rule of physics: Wave count multiplied by the wave length equals the light path length.
Wave count multiplied by the wave length duration (T) equals the time (t) for light to traverse the length of the light path – Rule of physics: Wave count multiplied by T=t
The light path lengths are equal judged from within the moving frame – Verified during experiment preparation; L(x) is the length of the light path in the direction of motion; L(y) is the length of the light path perpendicular to the direction of motion; L(x)= L(y)=L; Then, the time for light to traverse each of the light paths is also equal; t(x)= t(y)=t
(Data 4)
The equal lengths of the light paths are constant and the same for all observers – Judged from within the moving frame both lengths are constant and equal L(x)= L(y)=L; Then, judged from within the moving frame the time for light to traverse the length of each of the light paths is also constant and equal t(x)= t(y)=t; Rule of physics: d/v=t; substitute L for d; substitute c for v; Then, L/c=t; Rule of physics: L and c are directly proportional; Rule of physics: The speed of light (c) is constant and the same for all observers; Then, L is constant and the same for all observers; Rule of physics: When the value of L is changed for an observer the value of c is changed for that observer; As c is constant and the same for all observers, the value of L will not change for any observer; Previously demonstrated, L(x)= L(y)=L; Then, lengths L(x) and L(y) are constant and the same for all observers; Therefore, L(x) is not contracted judged from relative rest.
(Data 5)
Time is constant and the same for all observers – Previously demonstrated, L/c=t; solved for c, c=L/t; Previously demonstrated L is constant and the same for all observers; L and t are directly proportional; Then, t is constant and the same for all observers; Previously demonstrated t(x)= t(y)=t; Then, t(x) and t(y) are constant and the same for all observers; Therefore, t(x) and t(y) are not dilated judged by any observer.
No fringe was observable from relative rest for the experiment in the moving frame – All values for length and time are the same judged from within the moving frame and judged from relative rest; No fringe was observable for the experiment from within the moving frame. Therefore, no fringe was observable for the experiment from relative rest.
CONCLUSION:
No fringe was observable for the experiment from relative rest.
The length of a light path or a measuring rod is constant and the same for all observers.
The time for light to traverse the length of a light path or the time for light to traverse a measuring rod is constant and the same for all observers.
An inertial frame has no property, force or capability to interact with or influence any aspect of light in a vacuum under any circumstances. An inertial frame has no property, force or capability to interact with or influence any aspect of time under any circumstances. (Currently, only gravity is known to influence light in a vacuum. Currently, only gravity is known to influence time.)
PREDICTIONS:
Relative velocities greater than the speed of light will be discovered to be common place.
The inertial frame and gravitational frame relationship will be elucidated.
Alternative explanations for the results of the Ce clock and muon experiments will be found.
Thorntone Murray
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The illustration is a depiction of the Michelson Morley experiment.
The rows marked “A” are the experiment as judged from within the moving frame.
The rows marked “B” are the experiment as judged from relative rest.
The horizontal lines represent the light path that is in the direction of motion.
The vertical lines represent the light path that is perpendicular to the direction of motion.
The dots represent the split Nth light wave as it traversed the light paths.
Judged from both frames, at T1 (time 1) the light wave was being split.
Judged from both frames, at T5 the two portions of the split light wave reached the reflectors at the ends of the arms of the interferometer in the experiment.
Judged from both frames, at T9 both portions of the split Nth light wave reached the place in the interferometer where the were recombined.
Judged from relative rest (row B) the arm of the interferometer, thus, the length of the light path in the direction of motion was contracted. The arm perpendicular to the direction of motion was not contracted.
There can be no doubt that judged from relative rest (row B) the light pulse was split at T1 and recombined at T9.
Judged from relative rest the light paths were unequal, yet, light traversed both light paths in an equal amount of time.
The speed of light is constant and the same for all observers. Then, light will not traverse unequal lengths in an equal amount of time as necessitated by length contraction. Therefore, there was no length contraction judged from relative rest.
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huh ?
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Dario,
Here is a stand alone proof in normal English.
The Theory of Special Relativity reconciled the result of the 1887 Michelson Morley experiment and the constancy of the speed of light. The theory hypothesized that length in the direction of motion in a moving frame is contracted judged from relative rest and length perpendicular to the direction of motion is not.
In the experiment a special light beam was split and the two resultant beams were projected onto two light paths that were perpendicular to each other and equal in length. Each of the beams was projected to a reflector at the end of each of the two arms of the instrument which were carefully set to the identical length. The beams were reflected back to the point where they were split. There they were recombined. The two beams recombined perfectly. Each pair of waves that was split from a particular wave was reunited when the light beams were recombined. THIS IS CRUCIAL: Because the beams reunited perfectly “no fringe” happened. That was proof by observation that the amount of time for light to traverse the light paths was equal and the length of the light paths was equal. Again, no fringe happened. There can be no doubt that because no fringe happened at the site of the experiment for the experiment, no fringe happened for the experiment for any observer.
There was no fringe observed from within the moving frame. Then, no fringe is observable from relative rest. Because no fringe is observable from relative rest the pairs of light waves recombined perfectly judged from relative rest. Because the pairs of light waves recombined perfectly judged from relative rest the amount of time for light to traverse each of the light paths was equal judged from relative rest. Because the time was equal for both light paths judged from relative rest and the speed of light is equal for both light paths, both light paths and both arms of the instrument were of equal length judged from relative rest. Therefore, neither arm was contracted compared to the other judged from relative rest. Therefore, the concept of length contraction in the direction of motion and not perpendicular to the direction of motion in the moving frame judged from relative rest as hypothesized in the Theory of Special Relativity is invalid.
The preceding does not preclude the possibility that both lengths are contracted judged from relative rest. After rebuttals for this are addressed proof of no contraction whatsoever will be given in normal English.
Butchmurray
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This graphic illustrates just one of the ways the Michelson Morley experiment proves length contraction as hypothesized in the Theory of Special Relativity violates the constancy of light speed.
The rule of physics violated by the angle of the half silvered mirror judged from relative rest is covered separately.
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I wrote the following in a different order from the way you're about to read through it, so just absorb it as best you can.
The problem: How can significant fringe exist and not exist for the same experiment?
I was under the impression that the experiment has never shown up any difference - that no significant fringe ever showed up at all.
The length of a light path or a measuring rod is constant and the same for all observers.
If it's in the same frame as they are, it will be the same. If it's in some other frame, it will appear to be different (depending on its alignment).
The time for light to traverse the length of a light path or the time for light to traverse a measuring rod is constant and the same for all observers.
True in one sense, but false in another - if the measuring rod is moving relative to an observer, light may appear to get from one end of it to the other end faster in one direction than the opposite direction.
PREDICTIONS:
Relative velocities greater than the speed of light will be discovered to be common place.
They are observed all the time when looking at objects moving relative to the frame of the observor. It's only when you measure stationary things within your own frame that you measure the relative speed of light to those things as c.
The constancy of light speed can be tested by experiment - you measure the speed of light and it is always the same (even if it isn't). Someone else can be moving at enormous speed relative to you and yet when they measure the speed of light, they get the same value for c. When you look at the way light collides with them, you may calculate that the speed of light will be higher or lower than c for them, but when you take into account the slowing of their clocks and allow for that, you will calculate that they are measuring the speed of light to be c. You can of course determine that they will see the light as a different colour from the colour it appears to be to you, and that is the only way that the actual difference will show up.
Here's another point to consider. If you observe two objects moving towards each other at more than 50% the speed of light each, their relative velocities will appear to be greater than the speed of light. However, if you then sit on one of those two objects and travel with it, the other object will appear to pass you at less than the speed of light.
The point is this - when looking at other frames, the speed of light will appear to be faster than the speed of light when it collides with objects moving in the opposite direction. This is allowed, and it may look as if the light could be colliding with some objects at a fraction under 2c. The speed of light across moving objects will also appear to be different in different directions, and that is allowed too. If you are measuring the speed of light relative to you though (within your own frame), it will always be c, and it doesn't matter which frame you are in, that will still apply.
Because the pairs of light waves recombined perfectly judged from relative rest the amount of time for light to traverse each of the light paths was equal judged from relative rest. Because the time was equal for both light paths judged from relative rest and the speed of light is equal for both light paths, both light paths and both arms of the instrument were of equal length judged from relative rest.
The first sentence of that is correct, but the second is wrong. The light covered the same distance on both paths, but the arms of the instrument are not equal lengths. Consider a gun pointing sideways out through of the window of a car such that it is pointing at 90 degrees to the direction of travel. Now drive the car at 400mph - the same speed as the gun fires bullets. The gun is a metre long. The bullet will travel at 45 degrees to the direction the gun is pointing, so the distance it travels while it is inside the barrel of the gun will be 1.41 metres instead of the single metre lenght of the gun. The same kind of thing will happen with one of the arms of the MM experiment - the one that isn't contracted - so the distance the light travels is greater than twice the length of that arm. For the arm which is contracted, the light will spend more time travelling in one direction along that arm than it does when returning the other way, and it may travel many times the length of the arm for the first part of that journey (to the mirror at the leading end of the arm), and then it may travel only slightly more than half the length of the arm to get back to the semi-silvered mirror (which was moving towards it).
Therefore, neither arm was contracted compared to the other judged from relative rest. Therefore, the concept of length contraction in the direction of motion and not perpendicular to the direction of motion in the moving frame judged from relative rest as hypothesized in the Theory of Special Relativity is invalid.
Conclusion not valid - the arm has to contract in order to make the two light paths the same length as each other.
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This is a GREAT question!
I was under the impression that the experiment has never shown up any difference - that no significant fringe ever showed up at all
You are absolutely right and that is my point.. There was never any significant fringe observed from within the relatively moving frame of the experiment. However, fringe would have been observed from relative rest pursuant to The Theory of Special Relativity due to the following:
(for these purposes w is used for wave length in lieu of lambda due to font restraints)
1. Per SR the speed of light is constant and the same for all observers.
2. Per SR observed from relative rest length in the direction of motion, including wave length, is contracted judged from relative rest.
3. Per SR the rules of physics are the same for all observers.
4. Rule of physics: when light of an equal frequency is combined no fringe is produced. Conversely, when the frequencies are not equal fringe is produced.
5. Rule of physics: for light the frequency (f) multiplied by the wavelength (w) equals the speed of light (c). – fw=c – solved for f – c/w=f
For the Michelson Morley experiment judged from relative rest:
Per 1: wave length perpendicular to the direction of motion = w and wave length in the direction of motion = w*sqrt(1-v*v/c*c)
Per 1, 2, 3, and 5: For light perpendicular to the direction of motion – f=c/w . For light in the direction of motion – f=c/w*sqrt(1-v*v/c*c).
Per 4 and above: when v is greater than zero the frequency of light perpendicular to the direction of motion does not equal the frequency of light in the direction of motion and fringe is produced observed from relative rest.
(Personal note: Excuse 26s: When immersed in a problem and the AH HA comes and seems so obvious that it has to be obvious to everyone – Think again. Even to me it was as clear as mud for a while. THANK YOU! I will definitely have to make a major revision to the Problem.)
If it's in the same frame as they are, it will be the same. If it's in some other frame, it will appear to be different (depending on its alignment).
That conclusion is verified by the facts cited in the beginning of this thread. However, according to SR the length of a measuring rod oriented in the direction of motion is contracted judged from relative rest. In what sense of the word “alignment” do you mean?
True in one sense, but false in another - if the measuring rod is moving relative to an observer, light may appear to get from one end of it to the other end faster in one direction than the opposite direction.
Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.
http://www.bartleby.com/173/
VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity
Paragraph 1
“By means of similar considerations based on observations of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light. The assumption that this velocity of propagation is dependent on the direction “in space” is in itself improbable.”
They are observed all the time when looking at objects moving relative to the frame of the observer. It's only when you measure stationary things within your own frame that you measure the relative speed of light to those things as c.
Per SR “the speed of light is constant and the same for all observers”
The first sentence of that is correct, but the second is wrong. The light covered the same distance on both paths, but the arms of the instrument are not equal lengths. Consider a gun pointing sideways out through of the window of a car such that it is pointing at 90 degrees to the direction of travel. Now drive the car at 400mph - the same speed as the gun fires bullets.
Within the relatively moving frame, relative to the moving frame the instrument is at rest and the length of the arms of are equal. Also, the relatively moving frame is moving at different relative velocities compared to different rest frames. That is, it may have the relative velocity of .01c compared to one rest frame and .99c compared to another rest frame or any other relative velocity. So within the frame there is no sense of motion the motion is only observable from other frames and any consequences of that motion can only be observed from those frames per SR.
Conclusion not valid - the arm has to contract in order to make the two light paths the same length as each other.
Please clarify “one arm has to contract…”
If my answers are not specific enough, need elucidation, need references etc. please don’t hesitate to let me know. In the future I will indicate whether the answer is from the SR point of view to avoid confusion.
Thank you very much,
Butch
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I was under the impression that the experiment has never shown up any difference - that no significant fringe ever showed up at all
You are absolutely right and that is my point. There was never any significant fringe observed from within the relatively moving frame of the experiment. However, fringe would have been observed from relative rest pursuant to The Theory of Special Relativity due to the following:
Let's go through it point by point:-
1. Per SR the speed of light is constant and the same for all observers.
Correct.
2. Per SR observed from relative rest length in the direction of motion, including wave length, is contracted judged from relative rest.
I find that hard to follow, but the wave length is not contracted.
3. Per SR the rules of physics are the same for all observers.
Correct.
4. Rule of physics: when light of an equal frequency is combined no fringe is produced. Conversely, when the frequencies are not equal fringe is produced.
Correct.
5. Rule of physics: for light the frequency (f) multiplied by the wavelength (w) equals the speed of light (c). – fw=c – solved for f – c/w=f
Correct.
For the Michelson Morley experiment judged from relative rest:
Per 1: wave length perpendicular to the direction of motion = w and wave length in the direction of motion = w*sqrt(1-v*v/c*c)
Per 1, 2, 3, and 5: For light perpendicular to the direction of motion – f=c/w . For light in the direction of motion – f=c/w*sqrt(1-v*v/c*c).
Per 4 and above: when v is greater than zero the frequency of light perpendicular to the direction of motion does not equal the frequency of light in the direction of motion and fringe is produced observed from relative rest.
Wrong with all of those - the wavelength is the same in both directions as it is not contracted. Objects are contracted, but light is not affected.
If it's in the same frame as they are, it will be the same. If it's in some other frame, it will appear to be different (depending on its alignment).
That conclusion is verified by the facts cited in the beginning of this thread. However, according to SR the length of a measuring rod oriented in the direction of motion is contracted judged from relative rest. In what sense of the word “alignment” do you mean?
If a measuring rod is moving past you and aligned such that it is moving along its length (with the trailing end passing through the same point which the leading end went through a moment earlier), then it will be contracted from your point of view. If the measuring rod is moving past you and aligned such that it is moving along its width (i.e. sideways), then it's width will be contracted instead of its length. At other alignments, both its length and width will be contracted. We are only interested in the first case, and if you hold up a stationary measuring rod (which you know to be identical to the moving one) such that for a moment they are side by side as the moving one goes past, the moving one will be measured by the stationary one as shorter. The moving one will also measure the stationary one as shorter, but that's another issue.
True in one sense, but false in another - if the measuring rod is moving relative to an observer, light may appear to get from one end of it to the other end faster in one direction than the opposite direction.
Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.
http://www.bartleby.com/173/
VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity
Paragraph 1
“By means of similar considerations based on observations of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light. The assumption that this velocity of propagation is dependent on the direction “in space” is in itself improbable.”
Indeed - the light that comes off a moving torch will always be travelling at c from your point of view as the torch moves towards or away from you. My point was that when you take into account the movement of the torch, you can measure the relative speed of the torch and the light coming from it as being greater or less than c. If the relative speed of torch and light from your point of view was required to be c, the torch would be banned by the laws of physics from moving relative to you. It isn't though - light is allowed to move at speeds relative to the torch which are greater or less than c (from the point of view of an observer who is moving relative to the torch). When you measure the speed of the light, though, it will have to be exactly c (in a vacuum), and when you calculate the speed of the same light from the point of view of the torch by applying the Lorentz transformation, you will get exactly c as the result of your calculations (once you've taken into account the effect that has on length and time for the torch).
They are observed all the time when looking at objects moving relative to the frame of the observer. It's only when you measure stationary things within your own frame that you measure the relative speed of light to those things as c.
Per SR “the speed of light is constant and the same for all observers”
Same misunderstanding as above. The speed of light is constant for all observers - that doesn't ban you from measuring light as being faster or slower than c for objects which are moving relative to you.
The first sentence of that is correct, but the second is wrong. The light covered the same distance on both paths, but the arms of the instrument are not equal lengths. Consider a gun pointing sideways out through of the window of a car such that it is pointing at 90 degrees to the direction of travel. Now drive the car at 400mph - the same speed as the gun fires bullets.
Within the relatively moving frame, relative to the moving frame the instrument is at rest and the length of the arms of are equal. Also, the relatively moving frame is moving at different relative velocities compared to different rest frames. That is, it may have the relative velocity of .01c compared to one rest frame and .99c compared to another rest frame or any other relative velocity. So within the frame there is no sense of motion the motion is only observable from other frames and any consequences of that motion can only be observed from those frames per SR.
I'm having difficulty working out what's moving relatively to what - your descriptions are confusing and could be worded a lot more clearly. My point (the end of which is missing from that quote) is simply that if you're going to consider a moving frame (meaning that it's moving relative to you), you have to go the whole hog and analyse the whole situation on the basis that it is moving. If the gun is moving sideways at 400mph while a bullet travels through it lengthways at 400mph (we can completely ignore the acceleration of the bullet aspect to simplify things), the bullet will travel 1.41 times the length of the barrel while travelling through the barrel.
Conclusion not valid - the arm has to contract in order to make the two light paths the same length as each other.
Please clarify “one arm has to contract…”
The arm which is aligned with the direction of travel of the apparatus has to contract (or be treated as if it has contracted). [From Einstein's point of view there is no actual contraction - if you're looking at things from a different frame you're merely seeing things as contracted because they are not actually contracted when viewed from within their own frame.] In the case of the MM equipment moving at 0.866c in the direction of one of the arms, that arm can from a stationary frame be measured as having contracted to half its known length. The light moving along it is not contracted though.
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I find that hard to follow, but the wave length is not contracted.
The magnitudes of distance, wavelength, the length of a light path and the length of a measuring rod can all be expressed with the same interchangeable units of linear measure. Mathematically there is no distinction.
Wrong with all of those - the wavelength is the same in both directions as it is not contracted. Objects are contracted, but light is not affected.
Same as above. Whether it is the length of a measuring rod or the physical distance between the crests of light waves, length is length.
If a measuring rod is moving past you and aligned such that it is moving along its length (with the trailing end passing through the same point which the leading end went through a moment earlier), then it will be contracted from your point of view. If the measuring rod is moving past you and aligned such that it is moving along its width (i.e. sideways), then it's width will be contracted instead of its length. At other alignments, both its length and width will be contracted.
In this circumstance the length of the measuring rod as well as its angle relative to the direction of motion as judged from relative rest is calculated by constructing a rectangle for which that measuring rod is a diagonal. In the coordinate system of the moving frame the difference of the X coordinates for the ends of the angular rod is the length in the direction of motion (horizontal length of the rectangle) applicable to the rod. The difference of the Y coordinates for the ends of the angular rod is the length perpendicular to the direction of motion (vertical length of the rectangle) applicable to the rod. Contract the rectangle in the direction of motion (horizontal length) by the factor sqrt 1-v*v/c*c per SR to obtain the value of the horizontal length of the rectangle as judged from relative rest. Using that horizontal length of the rectangle, and the original vertical length (it is not contracted) the length and the angle of the diagonal measuring rod as judged from relative rest can be calculated mathematically.
Indeed - the light that comes off a moving torch will always be travelling at c from your point of view as the torch moves towards or away from you. My point was that when you take into account the movement of the torch, you can measure the relative speed of the torch and the light coming from it as being greater or less than c. If the relative speed of torch and light from your point of view was required to be c, the torch would be banned by the laws of physics from moving relative to you. It isn't though - light is allowed to move at speeds relative to the torch which are greater or less than c (from the point of view of an observer who is moving relative to the torch). When you measure the speed of the light, though, it will have to be exactly c (in a vacuum), and when you calculate the speed of the same light from the point of view of the torch by applying the Lorentz transformation, you will get exactly c as the result of your calculations (once you've taken into account the effect that has on length and time for the torch).
My original statement:
The time for light to traverse the length of a light path or the time for light to traverse a measuring rod is constant and the same for all observers.
Your original reply:
True in one sense, but false in another - if the measuring rod is moving relative to an observer, light may appear to get from one end of it to the other end faster in one direction than the opposite direction.
In the Michelson Morley experiment within the relatively moving frame, both arms were made to measure the same length. The arms of the interferometer, for all intents and purposes, were measuring rods. The time for light to traverse the equal length of the arms was equal.
For the Michelson Morley experiment:
1. The time (t) for light to traverse the light paths was constant judged from within the moving frame
2. The equal length (L’=d) of the light paths was constant judged from within the moving frame
3. The speed of light (c=v) is constant and the same for all observers
4. Speed equals distance divided by time v=d/t.
5. Substitute c for v, c=d/t. Substitute L’ for d, c=L’/t. Solved for time t=L’/c.
6. Time, t, was constant within the moving frame of the experiment.
7. Then, L’ and c are directly proportional. When the value of one is changed the value of the other is changed.
8. If length, L’, was changed for any observer including observers at relative rest c was changed proportionally.
9. But, c, the speed of light is constant and the same for all observers!
10. Then, length L’, did not change for any observer including observers at relative rest!
11. Therefore, length L’, was and is constant and the same for all observers.
Same misunderstanding as above. The speed of light is constant for all observers - that doesn't ban you from measuring light as being faster or slower than c for objects which are moving relative to you.
Per SR: If an object is moving relative to you, that object in a relatively moving frame and you are in a frame which is at relative rest and the rules of SR apply.
I'm having difficulty working out what's moving relatively to what - your descriptions are confusing and could be worded a lot more clearly.
The first sentence of that is correct, but the second is wrong. The light covered the same distance on both paths, but the arms of the instrument are not equal lengths. Consider a gun pointing sideways out through of the window of a car such that it is pointing at 90 degrees to the direction of travel. Now drive the car at 400mph - the same speed as the gun fires bullets…
My original statement:
There was no fringe observed from within the moving frame. Then, no fringe is observable from relative rest. Because no fringe is observable from relative rest the pairs of light waves recombined perfectly judged from relative rest. Because the pairs of light waves recombined perfectly judged from relative rest the amount of time for light to traverse each of the light paths was equal judged from relative rest…
Within the relatively moving frame of the experiment the arms were made equal by the experimenters. Light traversed both arms of the instrument in the same amount of time.
1. The time (t) for light to traverse the light paths was constant judged from within the moving frame
2. The equal length (L’=d) of the light paths was constant judged from within the moving frame
3. The speed of light (c=v) is constant and the same for all observers
4. Speed equals distance divided by time v=d/t.
5. Substitute c for v, c=d/t. Substitute L’ for d, c=L’/t. Solved for length L’=ct
“The light covered the same distance on both paths, but the arms of the instrument are not equal lengths.”
The speed of light (c) is the same for both paths. The time is the same for both (t). Then the length is the same for both. L’=ct
The arm which is aligned with the direction of travel of the apparatus has to contract (or be treated as if it has contracted). [From Einstein's point of view there is no actual contraction - if you're looking at things from a different frame you're merely seeing things as contracted because they are not actually contracted when viewed from within their own frame.] In the case of the MM equipment moving at 0.866c in the direction of one of the arms, that arm can from a stationary frame be measured as having contracted to half its known length. The light moving along it is not contracted though.
“In the case of the MM equipment moving at 0.866c in the direction of one of the arms, that arm can from a stationary frame be measured as having contracted to half its known length. The light moving along it is not contracted though.”
That is more or less my point. Light cannot contract. Therefore, its light path cannot contract.
LIGHT CANNOT CONTRACT!!!
Thank you David Cooper!!!
“Whew” (in a very good way),
Butch
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If your position has evolved as a result of our conversation, I think you need to try to construct a new statement setting out what your argument now is, starting a single new thread for it [and linking to the older two threads (this being one of them) to make it easy to track them down in the future if either of us needs to look them up].
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(Personal note: Excuse 26s: When immersed in a problem and the AH HA comes and seems so obvious that it has to be obvious to everyone – Think again. Even to me it was as clear as mud for a while. THANK YOU! I will definitely have to make a major revision to the Problem.)
The PROBLEM: stated in the original post of this thread is hereby replaced with the following:
PROBLEM:
In the 1887 Michelson Morley experiment the length of the arm of the interferometer oriented in the direction of motion determined the length of the light path in the direction of motion for the experiment. Judged from within the relatively moving frame of the experiment the length of that arm, thus, the length of that light path was constant. Time equals distance (in this case the length of the light path) divided by speed (in this case the speed of light). Judged from within the frame of the experiment the time for light to traverse the distance of the light path was constant. As such, distance (the length of the arm, thus, light path in the direction of motion) and speed (the speed of light) are directly proportional. When the value of one of directly proportional quantities is changed the value of the other is changed proportionally. In the environment of special relativity, the speed of light is constant and the same for all observers with no exceptions. The speed of light does not change for any observer. Therefore, for the Michelson Morley experiment the speed of light and the directly proportional length of the arm and light path in the direction of motion could not change judged by any observer to include an observer at relative rest.
The problem is the Theory of Special Relativity hypothesizes this length in the direction of motion is changed (contracted) judged by an observer at relative rest notwithstanding contradictory laws of physics.
Thorntone Murray
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When the value of one of directly proportional quantities is changed the value of the other is changed proportionally. In the environment of special relativity, the speed of light is constant and the same for all observers with no exceptions. The speed of light does not change for any observer. Therefore, for the Michelson Morley experiment the speed of light and the directly proportional length of the arm and light path in the direction of motion could not change judged by any observer to include an observer at relative rest.
The length of the arm does change for observers who aren't moving relative to the MM apparatus, and the time it takes for light to go through it also changes. When you watch the apparatus pass by you will see the arm shortened and the time taken to complete both trips along the arms and back being lengthened as well. The thing that doesn't change for different observers is the speed of light.
The problem is the Theory of Special Relativity hypothesizes this length in the direction of motion is changed (contracted) judged by an observer at relative rest notwithstanding contradictory laws of physics.
The theory of special relativity says that this length will appear to be shortened, and that fits in with what happens in the real universe. It also says that time for the apparatus will appear to be slowed down, if you're looking at a clock attached to the apparatus and displaying the time that's passing for it. When you do the maths to work out how it appears to a scientist travelling with the apparatus, you can then see that (s)he will not notice any slowing of time for it and will not notice any length contraction either, but from your vantage point that is not how it looks at all.
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The length of the arm does change for observers who aren't moving relative to the MM apparatus, and the time it takes for light to go through it also changes. When you watch the apparatus pass by you will see the arm shortened and the time taken to complete both trips along the arms and back being lengthened as well. The thing that doesn't change for different observers is the speed of light.
http://www.bartleby.com/173/16.html
Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.
XVI. Experience and the Special Theory of Relativity - Paragraph 7
“Here the contraction of moving bodies follows from the two fundamental principles of the theory without the introduction of particular hypotheses; and as the prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the earth the mirror system of Michelson and Morley is not shortened, but it IS shortened for a co-ordinate system which is at rest relatively to the sun.”
Here he states that the length is shortened, but shortened only judged from relative rest.
The theory of special relativity says that this length will appear to be shortened, and that fits in with what happens in the real universe. It also says that time for the apparatus will appear to be slowed down, if you're looking at a clock attached to the apparatus and displaying the time that's passing for it. When you do the maths to work out how it appears to a scientist travelling with the apparatus, you can then see that (s)he will not notice any slowing of time for it and will not notice any length contraction either, but from your vantage point that is not how it looks at all.
You are correct here with one caveat: It is hypothesized in the Theory of Special Relativity that the length IS shorter judged from relative rest and the clock IS slower relative to time in the frame that is at relative rest. The length does not “appear” to be shortened and the clock does not “appear” to be slower.
However, the laws of physics invalidate that hypothesis, to wit:
Within the inertial frame of the Michelson Morley experiment the lengths of the arms of the interferometer determine the lengths of the perpendicular light paths. Within that frame the length of the arm, thus, light path in the direction of motion was constant. Additionally, within that frame the speed of light as well as the time for light to traverse the length of that arm/light path was constant.
The equation for speed can be stated as t=d/v. In this case t is the time for light to traverse the arm/light path, v is the speed of light and d is the length of the arm/light path. Since t is constant within the frame d and v are directly proportional. Per the rule of proportions when the value of d, the length of the arm/light path is decreased (contracted) for an observer at relative rest the value of v is also decreased by the same factor for that observer. However, v is the speed of light which is constant and the same for all observers and does not change, then d, the length of the arm/light path cannot change for any observer.
Then, for the Michelson Morley experiment, d, the length of the arm/light path in the direction of motion does not change/contract judged by an observer at relative rest.
Therefore, length contraction as hypothesized in the Theory of Special Relativity is invalidated by the following laws of physics:
1. The rule of proportions
2. The constancy of the speed of light
3. The physics speed formula
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Per the rule of proportions when the value of d, the length of the arm/light path is decreased (contracted) for an observer at relative rest the value of v is also decreased by the same factor for that observer. However, v is the speed of light which is constant and the same for all observers and does not change, then d, the length of the arm/light path cannot change for any observer.
Then, for the Michelson Morley experiment, d, the length of the arm/light path in the direction of motion does not change/contract judged by an observer at relative rest.
When the value of d is decreased, the value of v will stay the same, so it has to be t that changes instead, but d will actually increase rather than decrease, and that means that t will increase with it. If the equipment is moving at 0.866c relative to you, you will give v its standard value of c, you will then measure the distance that light has to travel to cover what is a round trip within the moving apparatus (which means that d will double), and when you feed that into your formula you'll calculate a value for t which matches up with what you'll see (also doubling).
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When the value of d is decreased, the value of v will stay the same, so it has to be t that changes instead, but d will actually increase rather than decrease, and that means that t will increase with it.
The relative state of motion of an external observer has no bearing on the amount of time light takes to traverse the arms/light paths within the frame of the experiment. So even if time was different in the frame of an external observer, time within the frame of the experiment is not influenced. So time, t, within the frame of the experiment is constant and does not change due to any external cause. Here is the proof:
The Michelson Morley experiment from the perspective of the Theory of Special Relativity:
The speed formula: v=d/t speed equals distance divided by time
In this case:
v is the speed of light
d is the length of the arm/light path which is in the direction of motion
t is the time for light to traverse that light path
The speed of light equals the length of the arm/light path divided by the time for light to traverse that light path.
Judged from within the inertial frame of the experiment: v=d/t
Per the Theory of Special Relativity judged from relative rest length in the direction of motion is contracted by sqrt(1-v*v/c*c).
Judged from relative rest: v=d*sqrt(1-v*v/c*c)/t
v=d*sqrt(1-v*v/c*c)/t is only valid when the relative velocity is zero so that sqrt(1-v*v/c*c)=1 in which case the length is not contracted. d*1/t=d/t
Otherwise, length contraction as hypothesized is invalidated by two laws of physics:
The constancy of the speed of light – the speed of light is d/t NOT d*sqrt(1-v*v/c*c)/t
The rule of proportions – v, the speed of light, is constant so d and t are directly proportional. When d is changed t is changed by the same factor. Here it is NOT.
Thank you,
Butch Murray
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There are two lengths you need to treat as separate values. One is the length of the contracted arm and the other is the distance the light has to travel through space to get along the arm and back. At 0.866c the length of the arm is halved, but the distance the light has to travel to complete a trip from one end to the other and back is doubled. Until you take that into account, you will keep attacking a straw man. What you need to do is draw the MM apparatus in snapshots at intervals as it moves across a piece of paper - the paper represents the frame you're observing it from, and that's why the MM apparatus has to move across it. If you do this, you can chart the progress of the light through the apparatus AND across the sheet of paper as the apparatus moves. Move the apparatus at 0.866c and move the light across the paper at c (you can slow these down to make this physically possible - just keep the two speeds in proportion). Once you've done this you can measure the distance the light has travelled across the paper (and back a bit) and you can also measure the length of the contracted arm. They are not the same - one is halved while the other is doubled
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There are two lengths you need to treat as separate values. One is the length of the contracted arm and the other is the distance the light has to travel through space to get along the arm and back. At 0.866c the length of the arm is halved, but the distance the light has to travel to complete a trip from one end to the other and back is doubled.
This is what Einstein wrote:
http://www.bartleby.com/173/7.html
Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.
VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity
Paragraph 1
“By means of similar considerations based on observations of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light. The assumption that this velocity of propagation is dependent on the direction “in space” is in itself improbable.”
Butch
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Reading Einstein's actual words is like reading mud - it's always hard to tell what he's trying to say and easy to misunderstand everything. You'd be better off finding some other route into reading up on relativity where it's been written in clearer language.
The point I was making was that you are to take your own frame of reference as the one in which light travels at c and to make this frame the sheet of paper. The equipment is moving across the sheet of paper, as it must do if the arm is to be seen as shortened, and light will move through it at a speed controlled by the sheet of paper. Light cannot excede the speed of light across the sheet of paper without exceding the speed of light for you in your frame.
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The equipment is moving across the sheet of paper, as it must do if the arm is to be seen as shortened...
In accordance with the Theory of Special Relativity:
Observer “A” is standing in the lab with the interferometer. The velocity of the instrument relative to observer “A” is zero. Judged by observer “A”, the length of the arm/light path as well as the wavelength of the light in that light path are not contracted nor is the instrument in motion relative to the light in the light path.
The state of motion of observer “A”, the lab, and the instrument are unchanged. But, judged by observer “B” in a different frame, the frame of observer “A” and all else in that frame are in relative motion. Since the state of motion of the frame containing observer “A” and all else mentioned is unchanged, the relationship of the light and the instrument within that frame is also unchanged. However, the length of the arm/light path and the wavelength of the light in the light path in the direction of relative motion are contracted judged by observer “B” at relative rest.
Again, the state of motion of observer “A”, the lab and the instrument have not changed. As far as observer “A” can tell (s)he is at rest and the light within the frame is not “chasing” anything.
However, ONE of the problems is that the wavelength of light in the direction of motion is contracted judged from relative rest. Within the frame of observer “A” the wavelength of light multiplied by the frequency of light equals the speed of light. That is a rule of physics. But, for observer “B” at relative rest, that wavelength is contracted. That contracted wavelength multiplied by the unchanged frequency of the light equals speed less than the speed of light. That invalidates length contraction as hypothesized because it violates the rule of physics that stipulates the speed of light is constant and the same for all observers.
Thank you,
Butch
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However, the length of the arm/light path and the wavelength of the light in the light path in the direction of relative motion are contracted judged by observer “B” at relative rest.
In working out the wavelength of the light, you have to take into account the slowing of time for the moving apparatus - at 0.866c a clock will from the point of view of a stationary observer tick at half the normal rate, and light being produced by a source in the moving apparatus will also be affected in the same manner. If the light source was to send light out at 90 degrees to the direction of travel of the apparatus it would be easier for us to judge the frequency of the light as that removes any Doppler effect complications, so that would be half the frequency it would be if the apparatus was stationary, and that's automatically going to result in a doubled wavelength. This matches up exactly with the doubling in the path that light has to follow to get along either arm and back. One of the arms is contracted to half the length it would be if it was stationary, but the light travelling along it has its wavelength doubled and has to travel twice as far to complete the trip.
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I apologize for the delay. I will get back to you as soon as I can.
Thank you,
Butch
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I apologize for the delay. I will get back to you as soon as I can.
Thank you,
Butch
Don't worry - it isn't a race.
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Again, I apologize for the delay. Thank you for your patience. Butch
How does light in a relatively moving frame compare judged from within the moving frame and judged from relative rest? Here is the answer.
at 0.866c a clock will from the point of view of a stationary observer tick at half the normal rate, and light being produced by a source in the moving apparatus will also be affected in the same manner.
The operative formula is the wavelength formula for light, wf=c.
In which:
w= wavelength of light (w is used in lieu of lambda due to font restraints)
f= frequency of light
c= the speed of light
t= unit of time
d= distance or length or wavelength
Wavelength is the distance per individual light wave: d/light wave
Frequency is the number of light waves per unit of time: light wave/t
wf=c and d/light wave * light wave/t=c are interchangeable formulas
1. Example: The relative velocity of the moving frame is .866c, so, the length contraction factor is .5 and the time dilation factor is 2.
Judged from within the relatively moving frame:
wf=c or d/light wave * light wave/t=c the “light wave” term cancels
d/t=c
d/light wave * light wave/t=c or wf=c
Judged from relative rest for light in the direction of motion length is contracted by the factor .5 and time is slower in the moving frame by the factor of 2.
wf=c or .5d/light wave * light wave/2t=c the “light wave” term cancels
.5d/2t=c
.5d/2t * 2/.5= c * 2/.5 simplify
d/t=4c
d/light wave * light wave/t=4c or wf=4c
Judged from relative rest for light perpendicular to the direction of motion length is not contracted and time is slower in the moving frame by the factor of 2.
wf=c or d/light wave * light wave/2t=c the “light wave” term cancels
d/2t=c
d/2t * 2= c * 2 simplify
d/t=2c
d/light wave * light wave/t=2c or wf=2c
The example above proves that length contraction and time dilation as hypothesized in the Theory of Special Relativity results in 3 distinctive values for the constant speed of light!
2. Formulation: The length contraction factor is sqrt(1-v*v/c*c) and the time dilation factor is 1/sqrt(1-v*v/c*c)
Judged from within the relatively moving frame:
wf=c or d/light wave * light wave/t=c the “light wave” term cancels
d/t=c
d/light wave * light wave/t=c or wf=c
Judged from relative rest for light in the direction of motion length is contracted by the factor sqrt(1-v*v/c*c) and time is slower in the moving frame by the factor of (1/sqrt(1-v*v/c*c)).
wf=c or sqrt(1-v*v/c*c)d/light wave * light wave/(1/sqrt(1-v*v/c*c))t=c “light wave” cancels
sqrt(1-v*v/c*c)d/(1/sqrt(1-v*v/c*c))t=c
sqrt(1-v*v/c*c)d/(1/sqrt(1-v*v/c*c))t * (1/sqrt(1-v*v/c*c))/sqrt(1-v*v/c*c)= c * (1/sqrt(1-v*v/c*c))/sqrt(1-v*v/c*c) simplify
d/t=c*(1/sqrt(1-v*v/c*c))/sqrt(1-v*v/c*c) simplify
d/t=c*1/(1-v*v/c*c)
d/light wave * light wave/t=c*1/(1-v*v/c*c) or
wf=c*1/(1-v*v/c*c)
Judged from relative rest for light perpendicular to the direction of motion length is not contracted and time is slower in the moving frame by the factor of (1/sqrt(1-v*v/c*c)).
wf=c or d/light wave * light wave/2t=c the “light wave” term cancels
d/(1/sqrt(1-v*v/c*c))t=c
d/(1/sqrt(1-v*v/c*c))t * (1/sqrt(1-v*v/c*c))= c * (1/sqrt(1-v*v/c*c)) simplify
d/t=c*(1/sqrt(1-v*v/c*c))
d/light wave * light wave/t=c*(1/sqrt(1-v*v/c*c)) or
wf=c(1/sqrt(1-v*v/c*c))
The above formulation applies length contraction and time dilation as hypothesized in the Theory of Special Relativity. Only when v=0 does wf=c judged from relative rest. Otherwise, wf=c, the true speed of light, only exists judged from within the moving frame. Judged from relative rest the wavelength multiplied by the frequency of light has 2 different values, neither of which is the speed of light, which is constant, and the same for all observers.
it would be easier for us to judge the frequency of the light as that removes any Doppler effect complications,
http://galileo.phys.virginia.edu/classes/109N/lectures/michelson.html
Einstein’s Answer
The results of the various experiments discussed above seem to leave us really stuck. Apparently light is not like sound, with a definite speed relative to some underlying medium. However, it is also not like bullets, with a definite speed relative to the source of the light. Yet when we measure its speed we always get the same result. How can all these facts be interpreted in a simple consistent way?
http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html
It is found that, despite the expected boost from being emitted by a very fast source, the light from the little explosions is going forward at the usual speed of 186,300 miles per second. In the last century, the emitter theory was rejected because it was thought the appearance of certain astronomical phenomena, such as double stars, where two stars rotate around each other, would be affected. Those arguments have since been criticized, but the pion test is unambiguous. The definitive experiment was carried out by Alvager et al., Physics Letters12, 260 (1964).
Although this was designed to detect any boost in the speed of light, the addition of the speed of the source and the speed of light, it also indicates there is no lag. That is, the speed of light was not measured to be slower, which would be the case if emission source moved forward in relationship to the point in space it occupied when the light was emitted. I understand your logic, but this is the rule until proved otherwise.
Butch
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Case (1):-
The MM apparatus is stationary and we are stationary with it. The wavelength * the frequency = c. No problem there, as you know.
Case (2):-
The MM apparatus is moving at 0.866c and we are moving with it. The frequency is halved by the movement, so the wavelength is automatically doubled to match [it moves away from the source at the same speed as before so it's going to go twice as far before it's completed one wave, once you've removed any Doppler shift from it], and that means that we still have w * f = c. The light now has to go twice as far to complete a round trip along either arm and back because of the movement of the equipment. The light will be perceived by us as being the same frequency as it was in Case (1) because we are moving with it.
Case (3):-
The MM apparatus is moving at 0.866c and we are stationary, watching it fly past at a distance. At its closest approach, light emitted by laser which happens to be diverted in our direction (we can add a semi-silvered mirror to the experiment to do this) is seen by us to have half the wavelength which it would if the equipment was stationary with us or if we were moving with it. As in case (2), the wavelength is doubled as a direct result of the frequency being halved.
You're making exactly the same mistake as you did last time. You have to distinguish between length contraction of the arm and the extra length light has to travel in order to complete a round trip. You're getting 4c in one case because you're taking the distance to be halved when it's actually doubled: the arm is halved in length, but the distance along it and back is doubled due to its movement. In the other case you're getting 2c because you're failing to take into account that the light has to travel twice as far as the length of the perpendicular arm in order to get from one end of it to the other.
If the apparatus is contracted in its direction of travel, you're automatically working with a case where the behaviour of light has to conform to the rules of a frame in which there is no contraction. That means the distances the light travels will be drawn out in that stationary frame while the frame of the apparatus moves across it, and that's where the true distances the light is covering will appear and where they should be measured. You then have to consider the Doppler effect as the frequency will vary due to the movement of the light source, being higher in one direction along the contracted arm than the other.
Although this was designed to detect any boost in the speed of light, the addition of the speed of the source and the speed of light, it also indicates there is no lag. That is, the speed of light was not measured to be slower, which would be the case if emission source moved forward in relationship to the point in space it occupied when the light was emitted. I understand your logic, but this is the rule until proved otherwise.
You're attacking a position I have never held. The movement of the source has no impact on the speed of light whatsoever. It affects the frequency instead, so if the source is moving towards you it will result in blue shift, whereas if it is moving away it will result in red shift. The point I've been making concerns how you should handle the speed of light when you're working things out from within any particular frame of reference. The speed of light is fixed for that frame of reference just as it would be if that frame was a preferred frame of reference. The behaviour of all other frames is then governed by the preferred frame. If you want to set the speed of light by some other frame, then that frame has to be treated as if it is the preferred frame of reference instead, at which point anything which is stationary in that frame cannot have any length contraction applied to it. You can only have length contraction for objects stationary in a frame that isn't the one you're using as a preferred frame, and you can't then treat light as travelling at c in the frame of those objects at the same time as treating some other frame as a preferred frame for imposing contractions on objects in other frames.
This illustrates why an understanding of Lorentz's theory should be considered as essential before people try moving on into exploring SR. All of this should be worked out under a theory which has a preferred frame. Once you've understood all the details of how that works, then you'll understand straight away how the rules have to be applied in SR to make SR work properly.
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The scope of this discussion was always limited to the violation of the constancy of the speed of light vis a vis length contraction and time dilation as hypothesized in the Theory of Special Relativity applied instantaneously to the properties of light in light paths delimited by a rigid body of fixed position within a relatively moving inertial frame as judged by an observer in a frame which is at relative rest rather than the comparison of the coordinates on a space time diagram of active events within both frames and simultaneity calculations which, though a more cumbersome process, when properly carried out yield the same result.
As such, all formulations, examples etc. in this discussion are pursuant to:
1. An inertial frame, which in relative motion
2. An inertial frame, which is at relative rest
3. Light paths delimited by a rigid body of fixed position only within the relatively moving inertial frame
4. An observer of a fixed position within relatively moving inertial frame
5. An observer of a fixed position within the frame, which is at relative rest
6. It is understood that the arms of the Michelson Morley experiment are one half the length of each associated light path
7. All judgments, observations etc. are those of one of the two observers for phenomenon in the moving frame only
8. The distance between the observer at relative rest and the contents of the relatively moving frame is of no consequence and is not a consideration
9. All values, magnitudes etc. within the relatively moving frame are, and judged by the observer within the moving frame as, the “proper” values, which are constant within the frame and independent of the relative velocity of the moving frame.
The MM apparatus is moving at 0.866c and we are moving with it...
The velocity of the apparatus compared to the velocity of the observer is zero. The velocity of one relative to the other is zero. At the relative velocity of zero there is no relativistic effect and all else is moot.
The MM apparatus is moving at 0.866c and we are stationary,...
Here it appears that phenomena from one frame crossed into the other frame. Only that which is entirely within the relatively moving frame is a consideration.
You're making exactly the same mistake as you did last time...arm is halved in length,... the length of the perpendicular arm...
No mistake was made. There was no mention of arm length in my last reply.
However, the lengths of the arms are one half the length of the corresponding light path in all circumstances without exception. The calculation for light path lengths at the relative velocity .866c is at the end of this reply.
Please share the mathematical calculations you used for your comment.
If the apparatus is contracted in its direction of travel, you're automatically working with a case where the behaviour of light has to conform to the rules of a frame in which there is no contraction.
Please share the mathematical calculations for this as well.
You're attacking a position I have never held.
I never attack a person or an idea. An attack does not promote constructive discourse, is generally counter productive and can easily result in avoidable useless acrimony.
It affects the frequency instead, so if the source is moving towards you it will result in blue shift, whereas if it is moving away it will result in red shift. The point I've been making concerns how you should handle the speed of light when you're working things out from within any particular frame of reference....
This is a discussion of simultaneity.
This illustrates why an understanding of Lorentz's theory should be considered as essential before people try moving on into exploring SR. All of this should be worked out under a theory which has a preferred frame. Once you've understood all the details of how that works, then you'll understand straight away how the rules have to be applied in SR to make SR work properly.
Thank you for your input.
The operative formula is the speed formula, d/t=v.
In which:
t= unit of time (proper time)
d= distance or length of the light path (proper length)
c= the speed of light
v= speed
v= c
Judged from within the relatively moving frame: The length of the light path in the direction of motion and the length of the light path perpendicular to the direction of motion are equal at one unit of proper distance (d). It takes one unit of proper time (t) for light to traverse each. Then, light traverses the proper length of each light path, d, in one unit of proper time, t, at velocity c.
d/t=v v=c then;
d/t=c
Judged from relative the relative velocity of the moving frame is .866c, so, the length contraction factor is .5 and the time dilation factor is 2. The length of the light path is .5 times the proper length (.5d) and time is 2 times proper time (2t) judged from relative rest. Then:
.5d/2t=v
.5d/2t * 2/.5= v * 2/.5 simplify
d/t=4v v=c then;
d/t=4c
Judged from within the relatively moving frame light traversed the proper length of the light path, d, in one unit of proper time, t, at velocity c. However, judged from relative rest light traversed the proper length of the light path, d, in one unit of proper time, t, at velocity 4c.
Judged from relative rest for light perpendicular to the direction of motion length is not contracted and time is slower in the moving frame by the factor of 2. Time is 2 times proper time (2t) judged from relative rest. Then:
d/2t=v
d/2t * 2= v * 2 simplify
d/t=2v v=c then;
d/t=2c
Again, judged from within the relatively moving frame light traversed the proper length of the light path perpendicular to the direction of motion, d, in one unit of proper time, t, at velocity c. However, judged from relative rest light traversed the proper length of the light path perpendicular to the direction of motion, d, in one unit of proper time, t, at velocity 2c.
This is more mathematical proof that length contraction and time dilation as hypothesized in the Theory of Special Relativity results in 3 distinctive values for the constant speed of light. Further, the length of the light path in the direction of motion is contracted judged from relative rest. Therefore, the light in the light path in the direction of motion is contracted judged from relative rest. The problem is light does not contract nor can light be judged as contracted by any observer.
Thank you,
Butch
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The MM apparatus is moving at 0.866c and we are moving with it...
The velocity of the apparatus compared to the velocity of the observer is zero. The velocity of one relative to the other is zero. At the relative velocity of zero there is no relativistic effect and all else is moot.
It can still be treated as a moving system and is worth looking at to see why it doesn't affect the result of the experiment.
The MM apparatus is moving at 0.866c and we are stationary,...
Here it appears that phenomena from one frame crossed into the other frame. Only that which is entirely within the relatively moving frame is a consideration.
If you're only going go consider it from one frame, you're only going to be looking at cases where observers are moving with the equipment.
You're making exactly the same mistake as you did last time...arm is halved in length,... the length of the perpendicular arm...
No mistake was made. There was no mention of arm length in my last reply.
However, the lengths of the arms are one half the length of the corresponding light path in all circumstances without exception. The calculation for light path lengths at the relative velocity .866c is at the end of this reply.
Please share the mathematical calculations you used for your comment.
When you put the distance in as 0.5d, that's halving the length of the arm where you ought to be doubling it instead:-
Judged from relative rest for light in the direction of motion length is contracted by the factor .5 and time is slower in the moving frame by the factor of 2.
wf=c or .5d/light wave * light wave/2t=c the “light wave” term cancels
.5d/2t=c
.5d/2t * 2/.5= c * 2/.5 simplify
d/t=4c
d/light wave * light wave/t=4c or wf=4c
You've calculated the distance to be half the uncontracted length of the arm instead of twice the uncontracted length of the arm (which it needs to be if you're going to use the actual distance the light has to travel). And in this bit...
Judged from relative rest for light perpendicular to the direction of motion length is not contracted and time is slower in the moving frame by the factor of 2.
wf=c or d/light wave * light wave/2t=c the “light wave” term cancels
d/2t=c
d/2t * 2= c * 2 simplify
d/t=2c
d/light wave * light wave/t=2c or wf=2c
...you're using d instead of 2d, so you're taking the distance to be the length of the arm instead of the distance that the light actually has to travel to get from one end of the arm to the other.
If the apparatus is contracted in its direction of travel, you're automatically working with a case where the behaviour of light has to conform to the rules of a frame in which there is no contraction.
Please share the mathematical calculations for this as well.
You don't seem to have got the key point about how things work, so let me try to explain it more clearly. If you are looking at a system where there is no contraction, you must be stationary in the frame of reference in which the thing you're observing is also stationary. As soon as you're moving relative to the thing you're observing, you're going to see length contraction in the thing you're observing - you and the object are stationary in different frames, so you must treat the object as if it is moving through your frame and you must consider the light to be moving at c through your frame at all times. This means that when you observe the MM apparatus moving through your frame, you will work out that light will take much longer to travel along the contracted arm than it does when going back the other way and you will also work out that for light to get from one end of the uncontracted arm to the other it will have to cover twice the distance through your frame than the length of that arm because the arm is moving through your frame.
You're attacking a position I have never held.
I never attack a person or an idea. An attack does not promote constructive discourse, is generally counter productive and can easily result in avoidable useless acrimony.
It wasn't a criticism about attacking - there's nothing wrong with attacking something that you think is wrong.
Looking at your latest version...
The length of the light path is .5 times the proper length (.5d)
...you're still clearly taking the light path to be half the length of the arm instead of double. In the other case (where you're looking at the uncontracted arm) you're taking d as the length of the arm instead of doubling it. That's why you're getting wrong answers out.
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Please provide the math that illustrates the errors I made when you get a chance.
Quote
You're making exactly the same mistake as you did last time...arm is halved in length,... the length of the perpendicular arm...
No mistake was made. There was no mention of arm length in my last reply.
However, the lengths of the arms are one half the length of the corresponding light path in all circumstances without exception. The calculation for light path lengths at the relative velocity .866c is at the end of this reply.
Please share the mathematical calculations you used for your comment.
Quote
Quote
If the apparatus is contracted in its direction of travel, you're automatically working with a case where the behaviour of light has to conform to the rules of a frame in which there is no contraction.
Please share the mathematical calculations for this as well.
You don't seem to have got the key point about how things work, so let me try to explain it more clearly. If you are looking at a system where there is no contraction, you must be stationary in the frame of reference in which the thing you're observing is also stationary. As soon as you're moving relative to the thing you're observing, you're going to see length contraction in the thing you're observing - you and the object are stationary in different frames, so you must treat the object as if it is moving through your frame and you must consider the light to be moving at c through your frame at all times. This means that when you observe the MM apparatus moving through your frame, you will work out that light will take much longer to travel along the contracted arm than it does when going back the other way and you will also work out that for light to get from one end of the uncontracted arm to the other it will have to cover twice the distance through your frame than the length of that arm because the arm is moving through your frame.
Thank you,
Butch
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Is that a satisfied "thank you" or an unsatisfied one?
Either way, I'll be posting a link here soon that may help - it's to a page containing JavaScript programs that I've written to illustrate how the MM experiment works as viewed from different frames. There's still a little bit of code needing to be added so it may not be ready tomorrow, but I'm aiming for tomorrow.
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Actually, it could take weeks to finish the text (which you don't need to read), so I'll link to what's there now - the programs are now finished (I've just added the ability to hide the apparatus so that you can see clearly that the light really is moving at constant speed across the screen).
http://www.magicschoolbook.com/science/relativity.html (http://www.magicschoolbook.com/science/relativity.html)
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David,
VERY, VERY, VERY GOOD!!!
I am truly impressed!
You proved my point!!!
Light traverses the arm that is in the direction of motion at half the speed that light traverses the arm that is perpendicular to the direction of motion judged from relative rest.
THE PROBLEM IS:
The speed of light is constant and the same for all observers yet for this observer at relative rest LIGHT HAS TWO DIFFERENT SPEEDS and both of those speeds are different that the speed of light observed within the relatively moving frame THE THIRD SPEED OF LIGHT in this exercise!!!!
Coincidentally, this is post number 100 for me.
THANK YOU,
Butch
EVERYONE---YOU MUST WATCH HIS SECOND ANIMATION!!!!
http://www.magicschoolbook.com/science/relativity.html
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Good to know all that work was appreciated. Thanks.
You proved my point!!!
Light traverses the arm that is in the direction of motion at half the speed that light traverses the arm that is perpendicular to the direction of motion judged from relative rest.
In the case of the moving apparatus where the length contraction is shown (in the second of the JavaScript programs), light makes the journey along each arm and back in the same time on each arm. If you're only looking at the parts of the trip taking the light back in from the ends of the arms, then light takes nearly twice as long to travel along the contracted arm as it does to travel along the perpendicular arm, but it's only the time for the complete round trip that actually counts.
THE PROBLEM IS:
The speed of light is constant and the same for all observers yet for this observer at relative rest LIGHT HAS TWO DIFFERENT SPEEDS and both of those speeds are different that the speed of light observed within the relatively moving frame THE THIRD SPEED OF LIGHT in this exercise!!!!
When you watch the contracted apparatus moving across the screen, the speed of light running through it is constant across the screen at all times (until captured by the detector at the end) - the red blobs of light (which are actually large full stops [or periods if you're American]) are programmed to move across the screen at the speed of 1.
var a=0; b=0; c=0; d=0; f=0.8660254; e=-0.5; h=0.8660254; g=-0.5; y=0.8660254; z=0; zz=0; bc2=1;
mms=10; d1t=-6; d1l=-124; d2t=-6; d2l=-144; d3t=-6.5; d3l=-60; d4t=-6.5; d4l=-80;
function run()
{ z+=bc2; if(z<0){z=0; bxc2()} else{
mms+=y; mm.style.left=mms;
d1t+=a; d1l+=b; dot1.style.top=d1t; dot1.style.left=d1l;
d2t+=c; d2l+=d; dot2.style.top=d2t; dot2.style.left=d2l;
d3t+=e; d3l+=f; dot3.style.top=d3t; dot3.style.left=d3l;
d4t+=g; d4l+=h; dot4.style.top=d4t; dot4.style.left=d4l;
ttec2();
zz=z-79; time.innerHTML=zz}}
function ttec2()
{ if(z==39 && bc2==1){a=-1; c=-1}
if(z==39 && bc2==-1){a=0; c=0}
if(z==79 && bc2==1){a=0; b=-1; e=0; f=-1}
if(z==79 && bc2==-1){a=1; b=0; e=0.5; f=-0.8660254}
if(z==112){f=1}
if(z==204){b=1; c=1}
if(z==329 && bc2==1){c=0; d=1; g=0.5}
if(z==329 && bc2==-1){c=-1; d=0; g=0.5}
if(z==349 && bc2==1){b=0; d=0}
if(z==349 && bc2==-1){b=-1; d=-1}
if(z==578 && bc2==1){g=0; h=1}
if(z==578 && bc2==-1){g=-0.5; h=-0.8660254}
if(z==654 && bc2==1){f=y, h=y}
if(z==654 && bc2==-1){f=-1, h=f}}
The "ttec2" function [I prouounce "ttec" as "check", by the way - I use my own phonetic spelling system] changes the speeds of the light blobs at all the key points where they need to change direction. The variables a, b, c and d are for controlling the light blobs moving on the stationary apparatus on the left of the screen, while e, f, g and h control the light blobs on the moving apparatus. The speed of each light blob is always 1. When g is 0.5 (vertical speed), h is 0.866 (horizontal speed), so if you square them both, add the results and get the square root, the speed of the blob comes out as 1.
Clearly the speed the blobs are moving relative to the moving apparatus is not going to be c though - when a blob's moving to the left and the apparatus is moving to the right, the speed the blob's going at relative to the apparatus is 1.866c, and when it's on the return trip its relative speed is 0.134c, but these are not measures of the speed of light for you as you observe the screen - your measure of the speed of light in your stationary frame is the speed that the light moves across the screen, and that is always 1.
If you compare the speed of the light blobs with the speed of the moving apparatus you will never get the answer 1, but that does not count as a measure of the speed of light for a person moving with the apparatus. In the same way, if there were two objects moving across the screen in opposite directions at 0.7c, you would measure their speed relative to each other as 1.4c (which is well in excess of the speed of light), but if you were to measure things while travelling with either of those objects, you could treat the one you're with as stationary and measure the other object to be moving past you at less than c.
If you were travelling with the apparatus you would not be able to see it as contracted, so you'd be in exactly the same situation as looking at a stationary apparatus as on the left of the screen, seeing light moving across it at c at all times. What you have picked up on, though, is that SR generates contradictory accounts of things. In a Lorentzian universe the relative speeds are absolutely real - the speed of light really can be 1.866c in one direction relative to the apparatus and 0.134c relative to the apparatus in the other direction, but in SR these speeds for light that aren't c are simply ignored - SR is only interested in the speed of light as measured by an observer relative to himself, so other observers' measurements of the speed of light relative to him count for nothing.
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The take away, you must agree, is that the speed of light in the direction of motion is different than the speed of light perpendicular to the direction of motion judged from relative rest. Yes?
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I suspect that half the time we're talking at cross-purposes because I'm never sure if I'm answering the question you're trying to ask.
The take away, you must agree, is that the speed of light in the direction of motion is different than the speed of light perpendicular to the direction of motion judged from relative rest.
As I look at the screen, I see the apparatus contracted in length as it moves along at .866c. If the equipment had light scatterers added into it to show the progress of the light pulses then that progress would be visible and would look exactly like it does in the interactive diagram. Because the light blobs cross the screen at a fixed speed (of 1), the speed of light is the same in every direction.
What I think you're getting at is that if I'm seeing the true journey of the light, then the light must be moving fastest through the apparatus when it's going in the opposite direction to that of the apparatus, and slowest when returning the other way when they're moving in the same direction, while the light on the perpendicular arm is travelling at some speed between the two.
Now, if you try to measure the progress of the light while travelling with the apparatus, you will not see it behaving that way at all - you will determine that it is travelling at the same speed relative to the apparatus at all times. This means that you get contradictory accounts of how fast the light is travelling through the apparatus, but it's important to point out that it's impossible to tell in either case whether what is being measured is what is actually the reality. If the light really is moving at a constant speed through the apparatus, the apparatus must be stationary and it is the observer who is moving at .866c. If the observer is definitely stationary though and the apparatus is moving relative to him at .866c, then the light really is moving at different speeds in different directions relative to the moving apparatus.
In a Lorentzian universe there are no contradictions, but it's impossible to work out which answers are the correct ones. In Einstein's universe, all the answers are said to be right and the infinite number of contradictions is simply ignored - you're not supposed to draw attention to them. This doesn't really matter though as it's still possible to save SR by deciding that one frame is giving the true picture and the rest are wrong, the only cost being that the unnecessary dogma about all frames being equal has to be rejected. SR doesn't need that dogma or the contradictions which result from it, so it's no loss - what SR really is is a 4D Spacetime model which is vital as a base for GR, but absolutely nothing in GR depends on the dogma about all frames being equal (and it actually relies on the opposite if it wants to be a rational theory).
What we have then is a theory which is known to be wrong in parts, but that those errors are completely unimportant to physicists - they know there's a simple cure by removing the unnecessary dogma, but it provides them with no practical gain, so they don't bother. They never have the time to look down to notice that the educators actually believe the false dogma and push it relentlessly as if it's fact, confusing all the learners and deterring many of the best from wanting to study physics any further by making it look more like voodoo than science. All the physicists care about is that GR is a fantastically accurate tool for making calculations relating to gravity, so the trivial business of unnecessary contradictions in SR is not relevant to them. You could spend your life attacking SR on the basis of the contradictions, but if you actually managed to make the physics world take notice and accept your objections, they would simply tell you that they know about them already and it probably means that there is a slowest frame in SR, similar to a preferred frame in LET, and that this does no damage to SR whatsoever while removing all the contradictions at a stroke. And then the educators would continue to push the dogma as before because it simply doesn't matter to physics - it makes no difference to their sums and is merely an affront to reason.
Going back to the situation where the light is moving at different speeds relative to the moving apparatus and yet the scientist travelling with the apparatus measures the light's speed as c relative to the apparatus at all times, it is important to understand that his measurements are incapable of measuring the speed of light on anything other than a round trip - there is no possible way to measure the speed of light in a single direction only, so it could easily be much faster in one direction than the other without that showing up.
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OK
Right now I don’t think our purposes are important.
You did an impressive job of creating the animation from the mathematics.
That second animation depicts the MMX at relative velocity .866c observed from relative rest.
That second animation shows that observed from relative rest light traverses the arms at 2 different speeds.
Please, before you offer further explanation, is the statement above true? Yes or No, then give your explanation, PLEASE.
Thanks,
Butch
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You did an impressive job of creating the animation from the mathematics.
Thanks, but it was actually fairly straightforward. The real difficulty was all the trial and error "relative position" HTML coding which always takes ages to get right, and which frequently only works for one browser (though fortunately it didn't require any browser-specific customisation in this case).
That second animation depicts the MMX at relative velocity .866c observed from relative rest.
It's actually the one labelled with the id of "mm" that goes with the second diagram, though they move at the same speed as each other. [I wrote the code for the second diagram first, then added "x" to the end of all the variables and id's to use as a starting point for the first diagram, so the code at the top doesn't appear in the same order as the diagrams.]
That second animation shows that observed from relative rest light traverses the arms at 2 different speeds.
Please, before you offer further explanation, is the statement above true? Yes or No, then give your explanation, PLEASE.
Yes, except that it's three different speeds - one speed for the journey to the left along the horizontal arm; another speed for the journey to the right along that same arm, and a third speed for the journey up and down the other arm. When you average out the speeds for the two journeys along the horizontal arm, you then get the same speed of light along that arm and back as you do for the journey up and down the other arm. It's only the round trip that really counts because it's impossible to measure the speed of light in just one direction unless you also know which is the preferred frame (and that depends on such a thing existing).
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When you average out the speeds for the two journeys along the horizontal arm, you then get the same speed of light along that arm and back as you do for the journey up and down the other arm. It's only the round trip that really counts because it's impossible to measure the speed of light in just one direction unless you also know which is the preferred frame (and that depends on such a thing existing).
David,
Take a look at your animation again.
You get the same time in the direction of motion and perpendicular to the direction of motion.
However, the lengths are different, therefore, the speeds are different.
Contraction in the direction of motion causes the constant speed of light not to be constant.
Actually you said:
Yes, except that it's three different speeds
What do you think?
Thanks,
Butch
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Take a look at your animation again.
You get the same time in the direction of motion and perpendicular to the direction of motion.
However, the lengths are different, therefore, the speeds are different.
Ah yes - I got that bit wrong. It's half the distance so the average speed of the light relative to the apparatus is twice as high on the vertical arm as on the horizontal arm.
Contraction in the direction of motion causes the constant speed of light not to be constant.
The speed of light is only always constant (or giving the appearance of being constant) within the frame in which you're measuring it. In this case it clearly is - it always moves across the screen at c, and the screen represents our frame of reference as we observe it. If we were moving with the apparatus, we would not see the contraction of it, so it would appear to behave exactly like the uncontracted apparatus on the left of the screen. The only cases in which you can measure a speed of light as being higher/lower than c [ignoring situations where it's slowed by gravity or movement through gas/liquid/solid] is where you're reading the speed of light through your frame (i.e. across the screen) and then adding it or taking it away from the speed of something else that's moving through your frame (i.e. across the screen) - in such cases you will obviously get speeds of light relative to other moving things which are not c. Those speeds may indeed be the actual speeds which light would be measured at by someone travelling with the moving apparatus if it was possible for him to measure the speed of light in one direction instead of on a round trip, and if it was possible to see that contracted lengths have been contracted and clocks slowed, but it's impossible for a person in such a position to make such measurements. It's possible for us to make the measurements from our vantage point, but we can't trust them to be true as we may be the ones moving at 0.866c while the apparatus which we think is moving is actually stationary.
Think about this: you are measuring two speeds of light for the same event, one of them being the speed of light across the screen (which always gives you c) and then another speed for that same piece of light relative to something else that is moving across the screen (which always gives you c +/- x), so of course the speeds you're getting which involve comparisons with other moving things are not going to be c: no theory requires them to be c, and if a theory tried to require it it would automatically have to ban everything from moving across the screen at all (unless it's light or another thing that travels at the speed of light). It's only the speed of light across your frame (the screen) that you must always measure as travelling at c.
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The speed of light is only always constant (or giving the appearance of being constant) within the frame in which you're measuring it.
Daaavviiidd, :0 only always constant????
We both know that we both know better than that!
“The speed of light is CONSTANT and the same for ALL observers.” NO EXCEPTIONS!!!
That is the mantra.
Right?
That was cute, trying to trick me like that. But I didn’t fall for it.
BIG SMILE!!
Butch
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“The speed of light is CONSTANT and the same for ALL observers.” NO EXCEPTIONS!!!
That is the mantra.
Right?
But it is the same for all observers - they all measure the speed of light in their frame (or across their screen) as being c. That is all the mantra means. What you're trying to do is extend its meaning to cases which it simply isn't intended to cover: i.e. those cases where you add c to (or subtract c from) the speed of other objects moving through your frame where you will then necessarily produce values that aren't c.
What these non-c values represent are the speeds for light which you might expect people on those moving objects to get as their measurements for the speed of light within their frame, just so long as you fail to account for length contraction and time dilation. If you understand relativity properly though, you understand that they cannot measure those non-c values for the speed of light passing them because length contraction and time dilation cancel out the differences and ensure that the answer they get will always be c.
What these non-c values may also represent are the possible real speeds of light across moving objects if you happen by luck to be observing from the preferred frame, but a person who is moving cannot make those measurements to confirm them as they will always get the value c instead.
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What you're trying to do is extend its meaning to cases which it simply isn't intended to cover: i.e. those cases where you add c to (or subtract c from) the speed of other objects moving through your frame where you will then necessarily produce values that aren't c.
Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.
http://www.bartleby.com/173/6.html
Section VI. The Theorem of the Addition of Velocities Employed in Classical Mechanics
There is only one paragraph.
This is what Einstein said:
“We shall see later that this result, which expresses the theorem of the addition of velocities employed in classical mechanics, cannot be maintained; in other words, the law that we have just written down does not hold in reality. For the time being, however, we shall assume its correctness.”
http://www.bartleby.com/173/14.html
XIV. The Heuristic Value of the Theory of Relativity
Paragraph 1
This is what Einstein said:
“Experience has led to the conviction that, on the one hand, the principle of relativity holds true, and that on the other hand the velocity of transmission of light in vacuo has to be considered equal to a constant c. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates x, y, z and the time t of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from classical mechanics, the Lorentz transformation.”
http://www.bartleby.com/173/11.html
XI. The Lorentz Transformation
Paragraph 2
This is what Einstein said:
“In other words: Can we conceive of a relation between place and time of the individual events relative to both reference-bodies, such that every ray of light possesses the velocity of transmission c relative to the embankment and relative to the train? This question leads to a quite definite positive answer, and to a perfectly definite transformation law for the space-time magnitudes of an event when changing over from one body of reference to another.”
Do you disagree?
Thanks,
Butch
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What you're trying to do is extend its meaning to cases which it simply isn't intended to cover: i.e. those cases where you add c to (or subtract c from) the speed of other objects moving through your frame where you will then necessarily produce values that aren't c.
Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.
http://www.bartleby.com/173/6.html
Section VI. The Theorem of the Addition of Velocities Employed in Classical Mechanics
There is only one paragraph.
This is what Einstein said:
“We shall see later that this result, which expresses the theorem of the addition of velocities employed in classical mechanics, cannot be maintained; in other words, the law that we have just written down does not hold in reality. For the time being, however, we shall assume its correctness.”
Right, so the addition of velocities is actually being rejected, though he continues to entertain the idea for a while before ruling it out again later. You are not allowed to add the speed of light across your frame (or screen) to the speed of an object through your frame (or screen) and to assert that that represents the speed of light across that object. You have to apply corrections to it to calculate the speed of light across that object properly.
http://www.bartleby.com/173/14.html
XIV. The Heuristic Value of the Theory of Relativity
Paragraph 1
This is what Einstein said:
“Experience has led to the conviction that, on the one hand, the principle of relativity holds true, and that on the other hand the velocity of transmission of light in vacuo has to be considered equal to a constant c. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates x, y, z and the time t of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from classical mechanics, the Lorentz transformation.”
And that bit gives you a clue as to how to make those corrections.
http://www.bartleby.com/173/11.html
XI. The Lorentz Transformation
Paragraph 2
This is what Einstein said:
“In other words: Can we conceive of a relation between place and time of the individual events relative to both reference-bodies, such that every ray of light possesses the velocity of transmission c relative to the embankment and relative to the train? This question leads to a quite definite positive answer, and to a perfectly definite transformation law for the space-time magnitudes of an event when changing over from one body of reference to another.”
And this bit asserts that once you've made those corrections you will then calculate the real speed of light across the object to be c.
Do you disagree?
I imagine that it must work as claimed, though I've never been able to work out how to apply it. Using my method, when I take into account the slowing of time for the object moving through my frame of reference and the length contraction which will be generated by its movement, I then calculate that the speed of light on a round trip across that object will be c when measured by an observer travelling with that object, and that amounts to much the same thing except that my method generates different speeds for different directions with only the average being c. This method of Einstein's (which he took direct from Lorentz), however, must by the sound of it be able to generate the right answers for light travelling in a single direction and not just over a round trip, so it must be doing some extra work to even things out and I haven't managed yet to work out how it performs that trick because I don't know how it's meant to be applied.
Perhaps you can show me, though I imagine that if you aren't getting the right numbers out of it you can't be applying it correctly either.
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Perhaps you can show me, though I imagine that if you aren't getting the right numbers out of it you can't be applying it correctly either
David, I’m crushed.
Just kidding.
http://www.bartleby.com/173/11.html
XI. The Lorentz Transformation
XII. The Behaviour of Measuring-Rods and Clocks in Motion
Here Einstein gives all you need to know.
Be aware that in section XII: this is a mistake!
“The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod. For the velocity v = 0 we should have”
It should read:
“The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod. For the velocity v = c we should have”
If v=0 the result of the calculation below this sentence would be 1 and not 0.
I thought I should point that out to avoid confusion.
The reason I am not getting the same numbers is because I strongly disagree.
The Theory of Special Relativity only addresses length contraction of rigid bodies in the direction of motion and not the light and the consequences to light in the light paths delineated by those contracted lengths which is part and parcel of the Michelson Morley experiment.
I can guarantee that this thread is the only place on the planet that ever explained the details and ramifications of this issue.
As they say these days “Google it”.
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http://www.bartleby.com/173/11.html
XI. The Lorentz Transformation
XII. The Behaviour of Measuring-Rods and Clocks in Motion
Here Einstein gives all you need to know.
It's part of XI that looks most relevant:-
A light-signal is sent along the positive x-axis, and this light-stimulus advances in accordance with the equation
x = ct,
i.e. with the velocity c. According to the equations of the Lorentz transformation, this simple relation between x and t involves a relation between x' and t'. In point of fact, if we substitute for x the value ct in the first and fourth equations of the Lorentz transformation, we obtain:
This is followed by some maths voodoo which I can't paste here, followed by:-
from which, by division, the expression
x' = ct'
immediately follows. If referred to the system K', the propagation of light takes place according to this equation. We thus see that the velocity of transmission relative to the reference-body K' is also equal to c. The same result is obtained for rays of light advancing in any other direction whatsoever. Of course this is not surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.
So, when the voodoo is applied to x = ct it produces x' = ct', thereby showing that light will travel along the object at c relative to that object even in a single direction once you've done the transformation stuff, though the last sentence appears to admit that the voodoo was specifically contrived to produce that result. The voodoo itself can't be wrong, but I'd like to see the justification for using that voodoo. It appears to be an attempt to sideline the contradictions in how fast light travels past a moving object, but it looks as if it could just be a conjuring trick.
The reason I am not getting the same numbers is because I strongly disagree.
But if you apply their voodoo, you should get the same numbers as they do. If you don't agree with the use of their voodoo, that's a different issue.
The Theory of Special Relativity only addresses length contraction of rigid bodies in the direction of motion and not the light and the consequences to light in the light paths delineated by those contracted lengths which is part and parcel of the Michelson Morley experiment.
The x = ct --> x' = ct' section appears to be directly addressing the behaviour of light relative to moving objects.