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Author Topic: Length Contraction and Time Dilation Invalidated by Experiment - MMXII  (Read 10276 times)

Offline David Cooper

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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.

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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.

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You're making exactly the same mistake as you did last time...arm is halved in length,... the length of the perpendicular arm...

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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:-

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        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...

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         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.

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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.

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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...

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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.
 

Offline butchmurray

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Please provide the math that illustrates the errors I made when you get a chance.

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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.

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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
 

Offline David Cooper

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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.
 

Offline David Cooper

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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
 

Offline butchmurray

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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
 

Offline David Cooper

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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.

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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.

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   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.
 

Offline butchmurray

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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?
 

Offline David Cooper

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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.

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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.

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.
« Last Edit: 07/10/2012 19:44:39 by David Cooper »
 

Offline butchmurray

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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
 

Offline David Cooper

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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).

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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.]

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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).
 

Offline butchmurray

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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:
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Yes, except that it's three different speeds

What do you think?

Thanks,
Butch
 

Offline David Cooper

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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.

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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.
 

Offline butchmurray

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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
 

Offline David Cooper

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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.
 

Offline butchmurray

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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
 

Offline David Cooper

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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.

Quote
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.

Quote
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.

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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.
 

Offline butchmurray

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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”.
 

Offline David Cooper

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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:-
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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:-

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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.

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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.

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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.
 

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