Mathematical Obscurities in Special Relativity

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br />All the chatter in the world is not going to change to speed of light. What you get by adding or subtracting velocity to the speed of light is the redshift. By doing this there is no time problem-no twins to ponder or sticks to measure. That is the real advantage.
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No, if light speed is source dependent then its displacement through
space is different for light from sources moving at different velocities- this is not redshift or blueshift but actual differences in velocity through space.

I don't think you have followed the issues very carefully so unless you put some more effort in thinking about the topic, I will stop my responses here.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
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Yes it does when measured with respect to a frame at rest in a vacuum. Assume you are squatting or standing "still" on Earth. Call
your velocity with respect to the Earth inertial frame c. Now if you
were then transported to an airplane flying at 543 miles in the easterly direction with respect to a ground observer, your velocity
in your new frame is still c- i.e. you are still standing or squatting "still", but inside an airplane. This c however has a value of c+v or c-v with respect to the coordinate system of
the observer on the ground which we have taken to be the rest frame
to compare all motion. Finally, assume your speed in your frame represents the speed of light with respect to the rest frame. Obviously then, it is different when you are on the plane (c+v and c-v) then when you are on the ground (c), even if the value c is the same for all inertial frames when measured using the coordinates of your inertial frame to measure your velocity through space. That is the effect of source dependency.
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If I understand you correctly, then I think I agree with you.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
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If sound or light is depicted as wave motion then
obviously its speed through space depends on how fast energy is transfered between the molecules in the medium. But more
than that, if the medium is itself moving through space, the waves
traveling through the medium should also obtain the velocity of the medium through space, and the speed of the waves are c relative to the motion of the medium through space (i.e. c+v in the direction of the medium and c-v against the motion of the medium). <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I think I understand what you are talking about.

Here is something that might help. When I first started studying this stuff, every time I looked up the Doppler effect in a book, the stories usually talked about the train or the ambulance moving through the air (moving emitter), but they almost never talked about a moving observer or both a moving emitter and moving observer.

So, one time I was on a steam train that had a real steam whistle, and I wondered what the mechanics of the Doppler effect were, such that I heard the normal pitch of the train whistle while I was moving along with the train.

When I got home, I worked it all out on graph paper, and to my surprise, I found two different types of causes of Doppler effects. The physics books rarely mention the second major cause.

Here, take a look at this Doppler diagram:

im1.shutterfly.com/procserv/47b4da24b312...518a681e040000001610

The three long lines on the left represent a stationary train at three different times.

The three long lines on the right represent a moving train at three different times.

The small lines represent sound waves.

Note that on the left the sound waves in front and in back of the train whistle are the same length, and they move at the same speed away from the whistle.

Note that on the right, the sound waves at the rear of the whistle are “stretched out” in the air and they move away from the whistle rapidly, due to the combined speed (the additive speed) of the train and the speed of sound in air, i.e. c + v.

Not that on the right the sound waves at the front of the whistle are “compressed” in the air and they move away from the whistle slowly, due to the combined speed (the subtractive speed) of the train and the speed of the sound in air, i.e. c – v.

Note also that a moving passenger at the rear of a moving train will NOT hear any shift in the tone of the whistle, even though the sound waves he hears are “stretched out” in the air. He will hear the normal tone of the whistle.

Why?

Because basically there are two different causes of Doppler effects: 1) an emitter moving through a medium causes waves to be either stretched out or compressed, 2) an observer moving through a medium will encounter waves at faster or slower than the normal speed of the waves in the medium.

Thus, the First Doppler Effect (the stretched out waves of the sound) are canceled out by the Second Doppler Effect (the observer moving through the medium and encountering the stretched out wavelengths at a rate that is faster than the normal speed of sound through the medium).

The moving observer on the moving train encounters the stretched out waves at c + v, with c being the speed of the waves in the air, and v being the speed of the train. The observer encounters the stretched out waves at about 1,100 fps (the normal speed of sound in air) PLUS about 88 fps (the speed of the train through the air if the train is moving at 60 miles per hour).

So, the rear moving observer perceives the stretched out waves to NOT be stretched out, because he is encountering them at FASTER than the normal speed of sound.

Light must work in a similar manner and observe these Doppler Laws. Thus, an observer and a light beam converging at c + v can produce observed blueshifts, and c – v can produce observed redshifts, just as much as “compressed” and “stretched out” light waves can produce them, and even if the light waves are not “compressed” or “stretched out” in deep space.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by DAVID</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
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If sound or light is depicted as wave motion then
obviously its speed through space depends on how fast energy is transfered between the molecules in the medium. But more
than that, if the medium is itself moving through space, the waves
traveling through the medium should also obtain the velocity of the medium through space, and the speed of the waves are c relative to the motion of the medium through space (i.e. c+v in the direction of the medium and c-v against the motion of the medium). <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I think I understand what you are talking about.

Here is something that might help. When I first started studying this stuff, every time I looked up the Doppler effect in a book, the stories usually talked about the train or the ambulance moving through the air (moving emitter), but they almost never talked about a moving observer or both a moving emitter and moving observer.

So, one time I was on a steam train that had a real steam whistle, and I wondered what the mechanics of the Doppler effect were, such that I heard the normal pitch of the train whistle while I was moving along with the train.

When I got home, I worked it all out on graph paper, and to my surprise, I found two different types of causes of Doppler effects. The physics books rarely mention the second major cause.

Here, take a look at this Doppler diagram:

im1.shutterfly.com/procserv/47b4da24b312...518a681e040000001610

The three long lines on the left represent a stationary train at three different times.

The three long lines on the right represent a moving train at three different times.

The small lines represent sound waves.

Note that on the left the sound waves in front and in back of the train whistle are the same length, and they move at the same speed away from the whistle.

Note that on the right, the sound waves at the rear of the whistle are “stretched out” in the air and they move away from the whistle rapidly, due to the combined speed (the additive speed) of the train and the speed of sound in air, i.e. c + v.

Not that on the right the sound waves at the front of the whistle are “compressed” in the air and they move away from the whistle slowly, due to the combined speed (the subtractive speed) of the train and the speed of the sound in air, i.e. c – v.

Note also that a moving passenger at the rear of a moving train will NOT hear any shift in the tone of the whistle, even though the sound waves he hears are “stretched out” in the air. He will hear the normal tone of the whistle.

Why?

Because basically there are two different causes of Doppler effects: 1) an emitter moving through a medium causes waves to be either stretched out or compressed, 2) an observer moving through a medium will encounter waves at faster or slower than the normal speed of the waves in the medium.

Thus, the First Doppler Effect (the stretched out waves of the sound) are canceled out by the Second Doppler Effect (the observer moving through the medium and encountering the stretched out wavelengths at a rate that is faster than the normal speed of sound through the medium).

The moving observer on the moving train encounters the stretched out waves at c + v, with c being the speed of the waves in the air, and v being the speed of the train. The observer encounters the stretched out waves at about 1,100 fps (the normal speed of sound in air) PLUS about 88 fps (the speed of the train through the air if the train is moving at 60 miles per hour).

So, the rear moving observer perceives the stretched out waves to NOT be stretched out, because he is encountering them at FASTER than the normal speed of sound.

Light must work in a similar manner and observe these Doppler Laws. Thus, an observer and a light beam converging at c + v can produce observed blueshifts, and c – v can produce observed redshifts, just as much as “compressed” and “stretched out” light waves can produce them, and even if the light waves are not “compressed” or “stretched out” in deep space.




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I don't think this is correct. Since you are referring to the speed of sound in the air outside, the moving detector of the soundwaves in the rear would detect the waves from the source earlier than the moving detector in the front (if the source is placed in the middle of the train). Since this would happen for each pulse generated by the source, the detector at the rear will detect more waves per time interval than the detector in the front. Comparing the results to that of the stationary frame would yield differences in frequency of the waves. So in source frame velocity independent model of wave propagation, the waves should be detected as Doppler shifted inside different inertial frames. The simplest way to look at it is to separate the velocities of the medium, the source, and the detector into three parts. If all three are not at rest with respect to each other, there will be a Doppler shift.


If c is a source frame velocity independent phenomena, be it the speed of light or sound, physics cannot be the same inside different inertial frames (because the "medium" in which the phenomena propagates at c is only at rest with respect to the source and detector in one frame- the absolute rest frame). This is the contradiction of the two postulates of SR. Einstein was fully aware of the contradiction and in his 1920 book of Special Relativity (online version), he spent half the chapters trying to resolve this "incompatibility", as he called it through the introduction of the concepts of relativity of simultaneity, time dilation and length contraction. His solutions didn't work because the only way to resolve a logical contradiction is by switching premises or changing definitions in the middle of the syllogism. That's what happened in SR.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
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I don't think this is correct. Since you are referring to the speed of sound in the air outside, the moving detector of the soundwaves in the rear would detect the waves from the source earlier than the moving detector in the front (if the source is placed in the middle of the train). Since this would happen for each pulse generated by the source, the detector at the rear will detect more waves per time interval than the detector in the front. <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">



The onset of the first pulse will be fast at the rear of the train, at a combined relative speed of 1,100 fps + 88 fps, so a rear observer will hear the tone first, when compared to a front observer (assuming the whistle is in the middle of the train). But that is just the onset, the beginning of the first pulse. This is part of the whole Doppler phenomenon.

But because the whistle is moving through the air, a single wave “cycle” will be “deposited” into the air over a longer than normal distance (than if the whistle were stationary in the air). Thus, the wavelength of the tone, to the rear of the whistle will be “stretched out”, i.e. longer.

But the rear observer will hear the wave as being the normal tone, since he is encountering the stretched out wave at 1,188 fps, instead of 1,100 fps.

If the whistle is in the middle of the train, the front observer would hear the normal tone of the whistle because he is hearing a contracted wavelength over a longer period of time, since that short wave is traveling toward him at a combined relative speed of 1,012 fps, which is 1,100 fps – 88 fps.

A stationary observer on the track at the front of the train will encounter the short wavelength at 1,100 fps, and a stationary observer on the track at the rear of the train will encounter the longer wavelength at 1,100 fps, so the front track observer will hear a higher tone than normal and the rear track observer will hear a lower tone than normal, while both moving train observers will hear the normal tone of the whistle, because one kind of Doppler effect cancels out the other kind of Doppler effect.

This is “classical” Doppler effect, not “relativistic” Doppler effect.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
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Einstein was fully aware of the contradiction and in his 1920 book of Special Relativity (online version), he spent half the chapters trying to resolve this "incompatibility", as he called it through the introduction of the concepts of relativity of simultaneity, time dilation and length contraction. His solutions didn't work because the only way to resolve a logical contradiction is by switching premises or changing definitions in the middle of the syllogism. That's what happened in SR.

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The book was published in 1916 and translated into English in 1920. He desperately didn’t want to admit the 1905 theory was wrong, because some of his biggest German physicist critics had also been “racists”, and he never wanted to give them the satisfaction of him admitting publicly that they were right about his SR theory being wrong.

Today we have inherited the big myth about SR theory because he didn’t want to fully and openly admit that it was wrong, although he did alter it quite a lot in his 1918 paper, but that paper was not translated into English or published inside the US until the year 2002, and very few physicists or physics professors today know about it. He essentially converted the SR theory into the GR theory in 1918 by adding atomic clocks, accelerative effects, and gravity fields to it. When that paper was published in 1918, the original SR theory literally disappeared from the earth. The so-called “proofs” of SR theory today are actually proofs of the 1895 Lorentz theory, which is what Einstein based his 1905 SR theory on, but he altered the Lorentz theory too much, and that’s why the SR theory contains errors.