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Offline butchmurray

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Special Relativity MMXII.1
« on: 22/07/2012 12:06:24 »
Thorntone E. Murray
July 22, 2012

PROBLEM:
In the 1887 Michelson Morley experiment a half silvered mirror split the light emitted from a monochromatic light source into two light beams half the intensity of the original. Within the moving frame that mirror was set to the exact angle necessary to perform the experiment. The Theory of Special Relativity hypothesizes length in the direction of motion in the moving frame is contracted judged from relative rest and length perpendicular to the direction of motion is not. Under those circumstances in relation to the direction of motion the angle of the half silvered mirror was greater judged from relative rest than the exact angle which was set within the moving frame.

HYPOTHESIS:
Within the moving frame the half silvered mirror in the interferometer of the Michelson Morley experiment was set to the exact angle necessary to perform the experiment. The instrument operated as specified. There can be no doubt the instrument operated as specified judged from relative rest. Therefore, the angle of the half silvered mirror in the interferometer in the moving frame was the same angle judged from within the moving frame and judged from relative rest.

DATA:
The Theory of Special Relativity hypothesizes length in the direction of motion in the moving frame is contracted judged from relative rest and length perpendicular to the direction of motion is not. Then, judged from relative rest the angle of a rigid rod or any other straight rigid body in the moving frame oriented at an angle which is greater than parallel to the direction of motion but less than perpendicular to the direction of motion varies directly with the relative velocity of the moving frame judged from rest.

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 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 applicable to the rod. This can be visualized by construction of a rectangle for which the sides are perpendicular to and parallel to the direction of motion and the angular rod is a diagonal. When the rectangle is contracted in the direction of motion only, the angle of the rod in relationship to the direction of motion is increased. Undoubtedly the angle of the half silvered mirror is increased in the same manner judged from relative rest. This visualization concurs in all respects to length contraction as hypothesized by the Theory of Special Relativity.

For example, when the half silvered mirror is set to 45 degrees within the moving frame, at the relative velocity of .866c the angle of the mirror is 60 degrees judged from relative rest. In that scenario the experiment was perfectly operational within the moving frame but was not operational judged from relative rest. Allowance for that dichotomy does not exist in the environment of special relativity. The cause of any such contradictory reality, in this case length contraction, is contrary to the laws of physics and therefore invalid. Obviously, because the experiment operated properly within the moving frame it operated properly judged from relative rest. The example depicted in Diagram 1 is indicative of the deviation of the reflected light path at relativistic velocities.

CONCLUSION:
Length contraction as hypothesized in the Theory of Special Relativity is invalid.

PREDICTION:
Additional proof that length contraction and time dilation as hypothesized in the Theory of Special Relativity will be discovered.

Thorntone E. Murray


 

Offline butchmurray

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Re: Special Relativity MMXII.1
« Reply #1 on: 30/07/2012 18:53:14 »
The attached diagram is a depiction of the Michelson Morley experiment as observed from within the moving frame and as observed from relative rest as hypothesized in the Theory of Special Relativity. In the close-up view of the half silvered mirror as observed from relative rest it is clearly demonstrated that the angle of the mirror increased in relation to the direction of motion due to length contraction in the direction of motion and the angle the normal of the reflective surface of the half silvered mirror decreased. The experiment which was operational as observed from within the moving frame must violate the law of reflection (the angle of reflection is equal to the angle of incidence) to be operational as observed from relative rest. Therefore, the experiment was not operational judged from relative rest.

The experiment cannot be operational for one observer and not operational for another observer
 

Offline David Cooper

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Re: Special Relativity MMXII.1
« Reply #2 on: 30/07/2012 22:40:55 »
The mistake you're making is to think that the angle of reflection won't still be at 90 degrees to the incoming beam when the mirror is angled at angles other than 45 degrees. You really need to imagine the beam of light as vertical bars heading towards the mirror. One end of each bar will hit the mirror before the other end, and by the time the other end hits the mirror the mirror will have moved. If you map out the points where different parts of that bar intersect with the moving mirror, that will trace out a line at 45 degrees every time, regardless of the angle of the mirror, so it will always behave as if the mirror is at 45 degrees from the point of view of the light hitting it.
 

Offline butchmurray

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Re: Special Relativity MMXII.1
« Reply #3 on: 31/07/2012 00:18:38 »
Sorry,  there is no mistake. There are at least 3 laws of physics that govern this circumstance as hypothesized in the Theory of Special Relativity.

1. The laws of physics are the same for all observers.

2. The speed of light is constant and the same for all observers.

3. The angle of reflection equals the angle of incidence.

When you envision the vertical bars, the mirror is not moving away from them. They are in the same frame. Relative to the bars or light waves, the mirror is in the same place when the bottom of a bar contacts it as it is when the top of that bar contacts that mirror. No matter the relative velocity of the moving frame the mirror is not moving away from the light waves.

It is a good rule of thumb to just add “for all observers” to any rule of physics when in the environment of special relativity. So in this case: The angle of reflection equals the angle of incidence for all observers.

Thank you,
Butch



 

Offline David Cooper

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Re: Special Relativity MMXII.1
« Reply #4 on: 31/07/2012 01:14:58 »
There was an error in my previous post, but I'll get to that in a moment.

When you envision the vertical bars, the mirror is not moving away from them. They are in the same frame.

If they are in the same frame, the angle of the mirror must be 45 degrees. You only see the angle of the mirror as some other angle if you're viewing the thing from a different frame, in which case you have to take into account the speed the mirror is moving at in the frame you're observing it from in order to work out how the light will interact with it. Any diagram showing the mirror at 60 degrees is showing a moving mirror (in a moving apparatus).

Quote
Relative to the bars or light waves, the mirror is in the same place when the bottom of a bar contacts it as it is when the top of that bar contacts that mirror. No matter the relative velocity of the moving frame the mirror is not moving away from the light waves.

But the mirror is moving away from the light waves if you're viewing the mirror as moving within your frame. You cannot ignore that aspect - you can time the speed of light and work out how much the mirror will have moved by the time the light has covered that extra distance, and that enables you to work out the effective angle of the mirror. Get paper, a pencil and a calculator and work it out yourself - it's a good exercise. It's by doing that in my head that I've spotted the error in my previous post.

Quote
3. The angle of reflection equals the angle of incidence.

It is a good rule of thumb to just add “for all observers” to any rule of physics when in the environment of special relativity. So in this case: The angle of reflection equals the angle of incidence for all observers.

That's fine, but that doesn't mean you don't have to account for the mirror moving. I've never found a textbook that spells this out - that's probably because very few people are bright enough to stop to question the details in the way the you have done. Those who do question the details eventually work out that the mirror behaves as if it is the shape which the light "thinks" it is according to where and when it contacts it. It should be obvious that this is the way things must work if you draw out the progress of the light moving along at c and the mirror moving along at a high proportion of c - the effective slope of the mirror cannot be as it appears to the observer. If the mirror is moving to the right, sloping upwards from left to right and the light is hitting it from the left before bouncing upwards off it, the effective angle of the mirror will be less than 45 degrees (and not at 45 degrees as I wrongly stated earlier) - for a mirror which looks as if it's angled at 60 degrees it will behave as if it is a lot less than 45 degrees due to its movement, and the light will reflect off it upwards and to the right, though its progress to the right will then be at exactly the same speed as the mirror. If you then look at the angle at which the light hits the effective mirror and the angle at which it reflects off it, they should match and not violate the rule.

While you're exploring all this, you might also like to think about the headlights effect of relativity where light is concentrated forwards if a light source is moving at high speed - if you take some of the light that's going out sideways from the light source and try to bounce it forwards off a flat mirror to cheat the system, the mirror will behave as if it is curved and concentrate the light forward.
 

Offline butchmurray

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Re: Special Relativity MMXII.1
« Reply #5 on: 01/08/2012 06:18:50 »
First: Thank you for the complement.

But, I’m afraid this is one of the fatal flaws in your argument:

Quote
But the mirror is moving away from the light waves if you're viewing the mirror as moving within your frame.

If the mirror is moving away from the light waves under any circumstance, the mirror is moving at a speed greater than light. We all know that is not allowed.

Thank you,
Butch
 

Offline David Cooper

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Re: Special Relativity MMXII.1
« Reply #6 on: 01/08/2012 22:16:34 »
Quote
But the mirror is moving away from the light waves if you're viewing the mirror as moving within your frame.

If the mirror is moving away from the light waves under any circumstance, the mirror is moving at a speed greater than light. We all know that is not allowed.

The issue here is an ambiguity. You're reading what I wrote in a way which I didn't expect you to. To help you understand the intended meaning, consider this:-

A Thompson's gazelle is running away from a cheetah which is chasing it - there is no intention in this sentence to suggest that the gazelle is actually opening up a wider gap between itself and the cheetah (which may actually be gaining on it). "Away from" is being used here to indicate direction of travel and is not to be taken as any kind of comentary on the separation (or change of the separation) between the two players.

In the case of the mirror, the mirror is moving away from the light which is closing in on it. The mirror is moving to the right at a high percentage of c, while the light is chasing it at c. The bottom of the wavefront of the light will catch the bottom of the mirror first and begin to reflect off that at the location where it hits it. The mirror continues to move to the right for some distance before the top of the wavefront of the light catches up with it and reflects off it. The effective angle of the mirror will thus, from the point of view of the wavefront of the light that hits it, be different from the actual angle of the mirror. [Warning: "effective angle" may not be the official term for this - it's just my invented way of distinguishing between that and the actual angle, so there could be some other scientific usage of the word "effective" in relation to mirrors and lenses which I don't know of that could cause confusion if you were to use the expression elsewhere.]
« Last Edit: 01/08/2012 22:22:32 by David Cooper »
 

Offline butchmurray

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Re: Special Relativity MMXII.1
« Reply #7 on: 03/08/2012 05:19:51 »
Quote
In the case of the mirror, the mirror is moving away from the light which is closing in on it. The mirror is moving to the right at a high percentage of c, while the light is chasing it at c. The bottom of the wavefront of the light will catch the bottom of the mirror first and begin to reflect off that at the location where it hits it. The mirror continues to move to the right for some distance before the top of the wavefront of the light catches up with it and reflects off it. The effective angle of the mirror will thus, from the point of view of the wavefront of the light that hits it, be different from the actual angle of the mirror.


Within the moving frame containing the Michelson Morley experiment the mirror was stationary in relationship to the light contacting it. Then, judged from the position of the mirror in the relatively moving frame, the speed of the light when it contacted the mirror was c. The speed of the light when it contacted the mirror was always c notwithstanding the relative velocity of the frame which contained the experiment and the mirror because c is constant and the same for all observers. Therefore, there was no difference in the manner light contacted the mirror for any observer.

Alternatively, the relative velocity of the frame had absolutely no influence on the experiment or the angle of the mirror as observed from within the moving frame. The moving frame had a certain velocity relative to one rest frame, a different velocity relative to another rest frame and so on. Judged form within the relatively moving frame the angle of the mirror in the experiment was not different for each possible rest frame. However, because the contraction factor is unique for each relative velocity the angle of the mirror was unique as judged from each unique rest frame.

Of importance is that in the Michelson Morley experiment the angle of the mirror was constant and the angle necessary for the experiment to be operational judged by the observer in the frame with it, no matter the relative velocity of the frame in relationship to any rest frame. But, the relative velocities of the moving frame were different and the angles of the mirror were not the same as the angle judged from within the moving frame, which was the angle necessary for the experiment to be operational, when judged from frames that were at relative rest. Therefore, the experiment which was operational judged from within the moving frame was not operational judged from frames which were at relative rest. In the arena of special relativity either the experiment is operational or the experiment is not operational, not both.

Thank you,
Butch

 

Offline David Cooper

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Re: Special Relativity MMXII.1
« Reply #8 on: 04/08/2012 01:23:04 »
Quote
Within the moving frame containing the Michelson Morley experiment the mirror was stationary in relationship to the light contacting it. Then, judged from the position of the mirror in the relatively moving frame, the speed of the light when it contacted the mirror was c. The speed of the light when it contacted the mirror was always c notwithstanding the relative velocity of the frame which contained the experiment and the mirror because c is constant and the same for all observers. Therefore, there was no difference in the manner light contacted the mirror for any observer.

But it isn't constant - if you measure the speed of light relative to you (and your measuring equipment), it will always be c, but if you try to measure it for something in a different frame from yourself (and your measuring equipment), it will not be constant and it will also be different in different directions. It's difficult to imagine how this works if the object is moving towards you or away from you as there are awkward delays in being able to see what's going on, but they can be minimised if you imagine the object moving past you, but passing at a great distance from you such that all the events are seen by you with near-identical delays.

Imagine a version of the MM experiment with two two-metre-long arms moving at 86.6% the speed of light such that one of the arms appears to be only one metre long. Let's add little light scatterers into it so that we can send a single laser pulse of light through the apparatus and see flashes when the light hits the light-splitter (the semi-silvered mirror) and the mirrors at the ends of the arms. If we do this, we'll get a flash when the light is split, then a flash from each mirror at the far end of the two arms when the light reaches them, and then a final flash from the light-splitter when both lots of light return there. With this setup, you will actually see four flashes at different times from your distant, stationary viewpoint. You will see the first flash when the pulse of light gets split on the mirror, then the second pulse of light will appear at the end of the two-metre arm once the light has travelled four metres (the light having to travel four metres to reach that mirror because the mirror is moving - the light has to travel at 30 degrees to the direction the apparatus is moving in in order to hit that mirror), then a third flash will be visible once the light has travelled nearly seven and a half metres forwards along the arm which has been contracted to one metre long, and then a fourth flash of light will be seen once the two lots of light have returned to the light-splitter, both of them getting there at the same time - light has returned a little more than half a metre along one the arm that appears to be one metre long and light has also returned four metres down the two-metre arm (again moving at 30 degrees to the direction of travel of the apparatus). The total light path is eight metres on both arms. The length of the arm seen by you as one metre is actually two metres long from the point of view of the apparatus, so the length of the journey if the equipment was stationary would only be four metres along both arms. Given that you're seeing the equipment as moving, you can see that light is taking twice as long to move along the arm and back as it would if the equipment is stationary, which is fine - a clock travelling with the MM apparatus will be running at half the normal speed and will record the time for the light to complete the trip as being exactly what it should be for a four-metre journey.

So, we see a mismatch in the timings of the 2nd and 3rd flashes - they are not simultaneous.

Quote
Alternatively, the relative velocity of the frame had absolutely no influence on the experiment or the angle of the mirror as observed from within the moving frame. The moving frame had a certain velocity relative to one rest frame, a different velocity relative to another rest frame and so on. Judged form within the relatively moving frame the angle of the mirror in the experiment was not different for each possible rest frame. However, because the contraction factor is unique for each relative velocity the angle of the mirror was unique as judged from each unique rest frame.

If I'm reading that the right way, it looks correct, but it's hard to tell if I'm reading it the right way.

Quote
Of importance is that in the Michelson Morley experiment the angle of the mirror was constant and the angle necessary for the experiment to be operational judged by the observer in the frame with it, no matter the relative velocity of the frame in relationship to any rest frame. But, the relative velocities of the moving frame were different and the angles of the mirror were not the same as the angle judged from within the moving frame, which was the angle necessary for the experiment to be operational, when judged from frames that were at relative rest. Therefore, the experiment which was operational judged from within the moving frame was not operational judged from frames which were at relative rest. In the arena of special relativity either the experiment is operational or the experiment is not operational, not both.

The angle of the mirror is always correct for all frames, so there is no problem with it at all. As the length of one arm contracts, the mirror's angle changes to match, and so does the effective angle of the mirror in relation to how the light interacts with it. It will always reflect off the mirror in such a way that it will be angled towards where the mirror at the end of the uncontracted arm will be when the light has travelled the right distance to connect with it. Draw out some diagrams to test that for yourself. Do it with the MM apparatus moving at 86.6% c. The mirror will not be at 45 degrees to the horizontal, but 64.3 degrees. Now imagine the light moving along from the left and reaching the bottom of the mirror. Measure the horizontal component of the distance of the top of the mirror from the bottom of the mirror and calculate how long it will take for light to cover that distance. Now work out how far the mirror will move in that time and draw the mirror that distance further on, then repeat the process as many times until you find yourself drawing the new position of mirror on top of previous one - that will be more or less the point where the light actually catches the top of the mirror. Now draw a line from the bottom of the mirror in its original position to the top of the mirror in its latest position - this line is the effective angle of the moving mirror. The light needs to reflect off this mirror at 30 degrees to the horizontal in order to meet up with the moving mirror at the end of the vertical (uncontracted) arm. This means that the effective angle of the mirror must be 15 degrees. Does that fit with the line you've drawn?

Let me check it for myself. If the top of the mirror is one cm to the right of the bottom of the mirror, it will move nearly seven and a half cm to the right before the light can reach it (after light has reached the bottom of the mirror). If one cm is the horizontal component of the angle of the mirror when the mirror's at 64.3 degrees, the vertical component will be 2 cm. Tangent of the effective angle will therefore be approximately 2 divided by 7.5 (should be slightly less than 7.5), and that gives us 14.93 degrees. That's close, but it needs to be done with the correct value for the horizontal component to make sure. Starting from 15 degrees, it needs to be 7.4641016, so is that exactly the same value we get for how far light has to travel to get from the light splitter to the mirror at the end of the contracted arm? I need to calculate that precisely, so the mirror is moving at 0.866 of c and the light is chasing it at c. How far does the mirror travel before the light catches it if it starts a metre ahead of it? I don't know how to do this calculation - it probably needs calculus or something [please demonstrate, anyone, if you know how it should be done] - but I can do it a slow way by starting at 1 and then adding sin 60 to it repeatedly. If I divide sin 60 by ten first, I then have to add it 75 times before the light overtakes the top of the mirror, but I'd like to do it a lot more accurately than that. If I divide sin 60 by 100 it'll be a ten times more accurate (and that should do), so it should take 747 additions of that to 1 before light overtakes the mirror, but I'd probably lose count, so that's no good. Ah, found a compromise, and it overtakes at exactly the right point - I typed the following into a calculator: 60, sin, +, +, 1, =, =, =, =, =, =, =, and that gave me 7 additions of sin 60 to 1, then I typed "M in" to store the value at that point in memory. Then I did this: 60, sin, /, 100, =, +, +, MR (memory recall), = = = = ... and it was 47 presses of "=" before the light overtook the top of the mirror. Exactly the result we need, so that's it confirmed: the effective angle of the mirror is indeed exactly 15 degrees for something moving at 0.866c.
« Last Edit: 04/08/2012 01:38:55 by David Cooper »
 

Offline butchmurray

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Re: Special Relativity MMXII.1
« Reply #9 on: 04/08/2012 23:58:20 »

Quote
But it isn't constant - if you measure the speed of light relative to you (and your measuring equipment), it will always be c, but if you try to measure it for something in a different frame from yourself (and your measuring equipment), it will not be constant and it will also be different in different directions.

Here are the words of Einstein himself. This is on line at http://www.bartleby.com/173/

Albert Einstein (1879–1955).  Relativity: The Special and General Theory.  1920
Section XIV.  The Heuristic Value of the Theory of Relativity

Paragraph 1
“OUR train of thought in the foregoing pages can be epitomised in the following manner. 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.”
Paragraph 3
“Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables x, y, z, t of the original co-ordinate system K, we introduce new space-time variables x', y', z', t' of a co-ordinate system K'. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.”


Quote
The angle of the mirror is always correct for all frames, so there is no problem with it at all. As the length of one arm contracts, the mirror's angle changes to match, and so does the effective angle of the mirror in relation to how the light interacts with it.

Copy an image of the instrument into an application that allows you to only change the width of the image as the Theory of Special Relativity hypothesizes. The angle of the mirror is increased when the contraction is increased. The angle of incidence is decreased and the angle of reflection is increased (in respect to the “normal”). That is a violation of the law of reflection caused by length contraction on the moving frame as observed from relative rest.

Paragraph 4
“This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.”

So, Einstein said that contraction occurred which changed the angle of the mirror which violated a natural law and as such a general law of nature was found which did not satisfy this condition and at least one of the two fundamental assumptions of the theory was disproved.

Thank you,
Butch
 

Offline David Cooper

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Re: Special Relativity MMXII.1
« Reply #10 on: 05/08/2012 20:30:10 »
Hi Butch,


Quote
But it isn't constant - if you measure the speed of light relative to you (and your measuring equipment), it will always be c, but if you try to measure it for something in a different frame from yourself (and your measuring equipment), it will not be constant and it will also be different in different directions.

Here are the words of Einstein himself. This is on line at http://www.bartleby.com/173/

Albert Einstein (1879–1955).  Relativity: The Special and General Theory.  1920
Section XIV.  The Heuristic Value of the Theory of Relativity

Paragraph 1
“OUR train of thought in the foregoing pages can be epitomised in the following manner. 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.”

In this paragraph Einstein is chucking out some aspect(s) of Galilean relativity which don't match up with reality, favouring the Lorentz transformation instead. The bit you've underlined simply says that light travels at c, and that is not disputed.

Quote
Paragraph 3
“Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables x, y, z, t of the original co-ordinate system K, we introduce new space-time variables x', y', z', t' of a co-ordinate system K'. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.”

That appears to say that you can translate between frames by applying the Lorentz transformation and the same law will then apply in the new frame.

In my quote at the top (the one which you're responding to) I made the point that when you look at a different frame from the one you are in, you will see light colliding with moving (relative to you) objects at combined speeds greater and less than c. I don't know if you are objecting to that, but if Einstein was trying to ban this he would require all objects to be in a single frame such that none of them move relative to each other. I don't think he's making any such requirement, though he is insisting that when you account for an object's motion (relative to you) and apply the Lorentz transformation accordingly, you will determine that light collides with that object at a speed which from its point of view will be c.

Quote
Quote
The angle of the mirror is always correct for all frames, so there is no problem with it at all. As the length of one arm contracts, the mirror's angle changes to match, and so does the effective angle of the mirror in relation to how the light interacts with it.

Copy an image of the instrument into an application that allows you to only change the width of the image as the Theory of Special Relativity hypothesizes. The angle of the mirror is increased when the contraction is increased. The angle of incidence is decreased and the angle of reflection is increased (in respect to the “normal”). That is a violation of the law of reflection caused by length contraction on the moving frame as observed from relative rest.

If you measure it from within its own frame, the mirror is always at 45 degrees. If you measure it from some other frame and see the mirror as having some other angle, you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror (in which case it will be at 45 degrees) or you have to analyse what's going on with the interaction between light and mirror in the way that I have described in previous posts - the effective angle of the mirror is the real angle of the mirror as far as the light is concerned, so it behaves accordingly.

Quote
Paragraph 4
“This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.”

So, Einstein said that contraction occurred which changed the angle of the mirror which violated a natural law and as such a general law of nature was found which did not satisfy this condition and at least one of the two fundamental assumptions of the theory was disproved.

If you analyse what's going on carefully, the mirror reflects light correctly because the actual angle of a moving mirror is not the angle that counts - it's the angle which the light "thinks" the mirror is at that counts, because that represents the angle of the mirror which the light experiences. Einstein must have understood that as he wasn't completely stupid, though I've never actually seen him address the issue - it may be that his approach was always to eliminate the movement by applying the Lorentz transformation such that the analysis is always done from the same frame as the thing being analysed.
 

Offline butchmurray

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Re: Special Relativity MMXII.1
« Reply #11 on: 07/08/2012 09:46:48 »
Quote
In this paragraph Einstein is chucking out some aspect(s) of Galilean relativity which don't match up with reality, favouring the Lorentz transformation instead. The bit you've underlined simply says that light travels at c, and that is not disputed.

Quote
But it isn't constant - if you measure the speed of light relative to you (and your measuring equipment), it will always be c, but if you try to measure it for something in a different frame from yourself (and your measuring equipment), it will not be constant and it will also be different in different directions.

http://einstein.stanford.edu/SPACETIME/spacetime2.html
Stanford University:
By 1905 he had shown that FitzGerald and Lorentz's results followed from one simple but radical assumption: the laws of physics and the speed of light must be the same for all uniformly moving observers, regardless of their state of relative motion. For this to be true, space and time can no longer be independent. Rather, they are "converted" into each other in such a way as to keep the speed of light constant for all observers. (This is why moving objects appear to shrink, as suspected by FitzGerald and Lorentz, and why moving observers may measure time differently, as speculated by Poincaré.) Space and time are relative (i.e., they depend on the motion of the observer who measures them) — and light is more fundamental than either. This is the basis of Einstein's theory of special relativity ("special" refers to the restriction to uniform motion).


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That appears to say that you can translate between frames by applying the Lorentz transformation and the same law will then apply in the new frame.

“…Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.”

The general laws of nature are the laws of physics. To be co-variant is to exist without conflict. Its another way of saying the Lorentz transformations, in all aspects, obey the laws of physics for all observers as required by the Theory of Special Relativity.


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If you measure it from within its own frame, the mirror is always at 45 degrees. If you measure it from some other frame and see the mirror as having some other angle, you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror (in which case it will be at 45 degrees) or you have to analyse what's going on with the interaction between light and mirror in the way that I have described in previous posts - the effective angle of the mirror is the real angle of the mirror as far as the light is concerned, so it behaves accordingly.

Could you please clarify “you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror”



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If you analyse what's going on carefully, the mirror reflects light correctly because the actual angle of a moving mirror is not the angle that counts - it's the angle which the light "thinks" the mirror is at that counts, because that represents the angle of the mirror which the light experiences.

Please clarify this as well.

I really mean this-
Thank you,
Butch
 

Offline David Cooper

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Re: Special Relativity MMXII.1
« Reply #12 on: 08/08/2012 02:13:37 »
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If you measure it from within its own frame, the mirror is always at 45 degrees. If you measure it from some other frame and see the mirror as having some other angle, you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror (in which case it will be at 45 degrees) or you have to analyse what's going on with the interaction between light and mirror in the way that I have described in previous posts - the effective angle of the mirror is the real angle of the mirror as far as the light is concerned, so it behaves accordingly.

Could you please clarify “you know that you either have to apply the Lorentz transformation to what you're seeing to convert it into a form which allows you to see it as if you are in the same frame as the mirror”

If the angle of the mirror doesn't look as if it's 45 degrees, the mirror must be moving relative to you, so if you're going to work out how light interacts with it you're going to have to do one of two things: (1) apply the Lorentz transformation according to the way the mirror is moving relative to you so that you can see the MM apparatus in its undistorted form, at which point it will turn out that the mirror is actually at the 45 degrees it should be at; or (2) analyse the way light interacts with the mirror without removing the distortions, in which case you have to work out the effective angle of the mirror by taking into account the way light reaches different parts of the mirror at different times while the mirror moves. Both these approaches work.

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If you analyse what's going on carefully, the mirror reflects light correctly because the actual angle of a moving mirror is not the angle that counts - it's the angle which the light "thinks" the mirror is at that counts, because that represents the angle of the mirror which the light experiences.

Please clarify this as well.

I've been through it all in earlier posts - At 0.866c the mirror will appear to be angled at 64.3 degrees but will behave as if it is at 15 degrees because it takes a lot longer for the light to catch the top of the mirror after it has reached the bottom of it due to the movement of the mirror. Of course, if the apparatus is moving in the opposite direction the mirror will behave as if it is at 75 degrees instead because the light will take less time than you might expect to hit the top of the mirror after hitting the bottom of it, this time because the mirror is moving rapidly towards the light. In the former case you end up with an effective 15 degree mirror reflecting the light up at 30 degrees to the horizontal, while with the latter case you have an effective 75 degree mirror reflecting the light up at 30 degrees to the horizontal but in the other direction (towards the left instead of the right). In each case the light will move with the horizontal vector component of its motion equal to that of the mirror, so it will stay in vertical alignment with it as it moves along, thus enabling it to contact with the mirror at the top of the arm.
 

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Re: Special Relativity MMXII.1
« Reply #12 on: 08/08/2012 02:13:37 »

 

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