Mathematical Obscurities in Special Relativity

kc3mx,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">So the Lorentz transform does not give unique answers. That means it is not one-to-one.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

It is readily shown that the Lorentz Transformation (LT) is one-to-one, really. Like I said, the map T(v) has a 4-dimensional range for 0&lt;=v&lt;c. This is a mathematical fact and is not open for discussion I'm afraid. []

To proof this once more, observe that

Ker T(v) = 0,

meaning that the kernel, or nullspace, of T only contains the zero vector. This implies the one-to-one property. Note that the LT is used between frame S and S' for one single event.

If it so happens that two different answers are obtained, then this is not caused by the LT. Instead, other considerations must have been used for some problem dealing with two events. Perhaps Dingle was referring to two different asnwers for a complete problem.

That is very nice. It just puts one more contradiction into the already confused and obscure mess that the theory consists of. Since the proof shows that there can be no contradiction, then why is there a contradiction? So the refutation is invalid since it explains nothing other than that there is a mistake that hasnt been found.

So where is the mistake? The burdon must be on the theory and not on the critics. The critics are asking for a theory that doesn't contain contradictions and inconsistencies. To exibit a proof that ignores this problem isn't very helpful.

If as you say the Lorent transform is mathematically one to one, then the problem must be elsewhere. So, where is it? Since the theory is based on the use of the Lorentz transform and this produces inconsistent answers then either the theory is based on false postulates or the mathematics derived from the postulates is false. Since you have ruled out the second possibility, then the only other conclusion must be that the postulates and the theory derived from them must be wrong.

[/quote]Perhaps Dingle was referring to two different asnwers for a complete probem.

No. Dingle is not mistaken. This problem arises when the Lorentz transform and its inverse are applied to the solution of the same problem that is physically the same situation. The two mathematical solutions give different results. McCrae admitted there was no mistake in Dingle's math. In fact no one has found a mistake in the two different solutions. Both are correct. Dingle concluded from this that the theory was faulty.

kc3mx,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">This problem arises when the Lorentz transform and its inverse are applied to the solution of the same problem that is physically the same situation.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


It is plausible that problems arise due to obscure considerations in the theory. The reciprocity within SR is probably the culprit.

<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>
<br />kc3mx,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">This problem arises when the Lorentz transform and its inverse are applied to the solution of the same problem that is physically the same situation.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


It is plausible that problems arise due to obscure considerations in the theory. The reciprocity within SR is probably the culprit.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


The most important issue is still whether light is source
dependent or not, which was sidetracked by
SR's inertial frame crap. SR doesn't help one whit in
understanding the properties and behaviour of
light imo and is pretty much a failure as an
interpretation of physical reality.

123,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The most important issue is still whether light is source
dependent or not, which was sidetracked by
SR's inertial frame crap. SR doesn't help one whit in
understanding the properties and behaviour of
light imo and is pretty much a failure as an
interpretation of physical reality.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

The source dependency is a vague point. When saying that light is independent of its source, we certainly need to specify what aspect of light has independency. Are we merely talking about speed? But what about source "dragging"? We certainly have a dependent component here.