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 DAVID</i>
<br />So if we have a star that is fixed relative to the sun, and if we assume the star’s light is traveling between the star and the sun at c, and if we send a space probe out toward the star at several hundred miles per second, and if we assume the atomic clock aboard the probe is ticking faster than it would on earth, then at what speed is the starlight meeting up with the space probe, and why is the probe seeing a blueshift in the starlight?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">In an SR context, the probe's atomic clock will be ticking slower than Earth clocks as judged by Earth observers. Because of this, Earth observers will judge that the probe will see starlight approaching at speed c and measure a blueshift.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">And if we have a star in another galaxy that is moving along with that galaxy at several hundred miles per second, what would be the speed of the light relative to the earth when the starlight moving toward us is still traveling though that galaxy?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">In SR, the speed of light is c by postulate for all inertial frames. Clocks then change accordingly to make that consistent with observations. It was long ago established that you cannot create a contradiction example. You can only accept or reject the postulate.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Einstein’s velocity addition and “speed limit” hypothesis came from Lorentz theory. Einstein didn’t invent it, Lorentz did.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The relativity principle and the Lorentz transformations were in play before the turn of the century. Einstein's only original contribution in 1905 was to find a way to get Lorentz theory to work without aether.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">There is no reason to assume that the high z galaxies are moving right up to the speed of light but not more than the speed of light, relative to us.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Look, I don't like being forced to defend relativity or the Big Bang, neither of which I support. But your objections are based on unfamiliarity with these theories and are invalid objections. I recommend you learn the theories and look into valid reasons for rejecting them.

In BB, cosmological expansion is not a motion of galaxies through space. It is caused by the continual creation of new space between galaxies that have only small motions through local space. There is no limit to expansion speed, but there is a limit to how far away we can see galaxies before their recession speed exceeds the speed of light.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">A Relativity 101 class will merely propagandize students with the usual SR myths.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">These issues have been debated by good minds for the last century. Learning a scientific theory with understanding does not "propagandize" you or disable your critical thinking ability. But it does qualify you to critique the theory and to talk with others about it.

You will find few here willing to teach you relativity or cosmology in messages when you are unwilling to pick up a book and learn them. But you are the one who decides how much time and effort a theory is worth, and whether you wish to reach the point on the learning curve where you can successfully communicate with others about it. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br />

In an SR context, the probe's atomic clock will be ticking slower than Earth clocks as judged by Earth observers. Because of this, Earth observers will judge that the probe will see starlight approaching at speed c and measure a blueshift.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

If atomic clocks slow down in gravity fields where light also slows down. A slow ticking clock will measure “c” for the speed of the slow-moving light. And if an atomic clock speeds up in a weak gravity field where light speeds up, the clock will measure “c” for the speed of light.

But in the example of the space probe moving toward a star, the relative light speed has speeded up, and you have the clock slowing down, so the probe will not only see a blueshift, but it will measure the light speed as being faster than “c”.

If you want the probe to see the star’s light moving at “c”, you’ll have to speed up its clock, not slow it down.

Hello David,

You are not revealing enough information in your examples to justify your conclusions.

===

Your first example has one frame of reference. So it seems to be OK.

Your second example has more than one frame of reference. Because of this you need to explicitly identify (label) each one so that you can specify which frame or pair of frames you are talking about when you say things like " ... the probe ... will measure the speed of light as being ..."

When you are talking about what SR predicts would be seen in one frame from the perspective of another frame, the Lorentz Transforms AND the postulates of SR must be properly applied.

If you do this (showing your work, of course) and can still find an inconsistency in Special Relativity (SR) then you will become famous. (So be careful what you ask for.)

Good Luck,
LB

BTW, note that SR does *not* have to be inconsistet to be wrong.

And, are you familliar with Lorentzian Relativity (LR)? It passes all of the same experimental hurdles that SR passes. And it fixes all the dumb stuff about SR - IOW it more or less agrees with your second example.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Larry Burford</i>
<br />Hello David,

You are not revealing enough information in your examples to justify your conclusions.

===

Your first example has one frame of reference. So it seems to be OK.

Your second example has more than one frame of reference. Because of this you need to explicitly identify (label) each one so that you can specify which frame or pair of frames you are talking about when you say things like " ... the probe ... will measure the speed of light as being ..."

When you are talking about what SR predicts would be seen in one frame from the perspective of another frame, the Lorentz Transforms AND the postulates of SR must be properly applied.

If you do this (showing your work, of course) and can still find an inconsistency in Special Relativity (SR) then you will become famous. (So be careful what you ask for.)

Good Luck,
LB

BTW, note that SR does *not* have to be inconsistet to be wrong.

And, are you familliar with Lorentzian Relativity (LR)? It passes all of the same experimental hurdles that SR passes. And it fixes all the dumb stuff about SR - IOW it more or less agrees with your second example.


<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Hi, Larry,

I was talking mainly about the classical Doppler effects in my last post. I can give you more information about them if you are interested. I worked with them all my life. There are two main causes for the Doppler effects. Most people today think there is just one cause.

The SR theory of 1905 descended from the Lorentz theory and the Lorentz book of 1895. Einstein changed a few things around in the Lorentz theory, and he made some mistakes when he tried to “improve” the Lorentz theory. For example, Einstein left out forces, accelerative effects, atomic clocks, and gravity effects.

In his 1905 paper, Einstein had his watch and his balance wheel clocks slowing down for no physical reason.

After all the criticism he received in Europe about the errors in and the stupidity of the 1905 SR theory, he finally added the forces, the acccelerative effects, the atomic clocks, and the gravity effects to the theory’s thought experiments in a paper he wrote in 1918, in which Einstein solved the “clock paradox” problem by adding real forces to real atomic clocks. He had neglected to do this in the original 1905 SR paper, and that’s how he wound up with the paradox in the first place. As far as I can tell, the Lorentz theory contains no paradox, and in fact Einstein straightened out his SR paradox with his GR theory.

1905 SR theory: Two relatively moving observers see each other’s clocks “slow down” exactly the same amount, but only one of the clocks “lags behind” the other when both clocks are united. But which one? Paradox.

1911-1916 GR theory: Two observers with their clocks in weak and strong gravity fields. The strong gravity field causes one atomic clock to slow down, and the observer with that clock sees the clock in the weak field seem to tick fast. The observer with the clock in the weak field sees the clock in the strong gravity field slow down. The atomic clock in the weak field really is ticking faster than the atomic clock in the strong field. No paradox.

You might want to get yourself a copy of Lorentz’s 1895 book and Einstein’s 1918 paper.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jan</i>
Proof:

The speed of light is the same for the observer in S and S', so x=ct and x'=ct'. Hence,

x/t = x'/t'

Using the Lorentz Transformation, we know that

x/t = x'/t' = (x - v*t)/<b>(t-(v/c^2)*x)</b> = x/t + <i>v*((x/(c*t))^2-1) + O(v^2) + ...</i>

where we have used a Taylor expansion around the point v=0. Here, O(v^2) means the rest of the expansion of order 2 and higher, and satisfies O(0)=0.
If the Lorentz Transformation, together with the postulates, is to be a well-defined mapping between spaces S and S', we conclude that v=0.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Jan, the expansion into a Taylor series has apparently led you astray here because the italic part of the last equation vanishes anyway: if you use c=x/t in the bold denominator, the latter becomes <b>t/x*(x-v*t)</b> i.e. x'/t=x/t for all v.
The Lorentz transformation is just constructed this way such as to compensate for the inconsisteny of having actually two different speeds of light in the two reference frames moving with relative velocity v. The point is that Einstein did not realize that the usual definition of 'speed' can not be applied to light (see my webpages www.physicsmyths.org.uk/relativity.htm and www.physicsmyths.org.uk/lightspeed.htm )

www.physicsmyths.org.uk
www.plasmaphysics.org.uk

Hi Thomas,

Yes, you are right. The LR leaves the curve x(t)=ct invariant <b>but no other curves</b>. Indeed, if you put c=x/t in the Taylor expansion, then the higher order terms vanish and we are left with x/t, as advertised.

Jan