# Why Must The Lorentz Transformation Equations Be Linear?

Discussion in 'Pseudoscience Archive' started by Eugene Shubert, Oct 6, 2010.

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3. ### AlphaNumericFully ionizedRegistered Senior Member

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It is linear in the sense that if you have a space-time vector which is the linear combination of other vectors, $\mathbf{v} = a \mathbf{v}_{1} + b \mathbf{v}_{2}$ then a Lorentz transform acts like $L(\mathbf{v}) = a L(\mathbf{v}_{1}) + b L(\mathbf{v}_{2})$. In other words it doesn't matter if you add the vectors then do the Lorentz transform or if you Lorentz transform each vector and then add them, you get the same.

Incidentally that's the definition of a general linear operator so 'L' doesn't have to mean 'Lorentz', it means 'Linear'.

5. ### CptBorkRobbing the Shalebridge CradleValued Senior Member

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And as to the reason it needs to be linear: If the Lorentz transforms weren't linear, as Einstein put it, uniform motion in one frame would not translate into uniform motion in another frame. If observer A sees a certain space and time separation between two events, then the space and time separations observer B sees are independent of where A was located in space, the time at which A made their first observation, and the coordinate A arbitrarily chooses to mark as x=0, t=0. Work out the maths starting with arbitary transformations x'=x'(x,t) and t'=t'(x,t) (with the simplifying assumption that an event marked as x=0,t=0 in frame A is marked in frame B as x'=0,t'=0) and for uniform motion you'll ultimately get x'=ax+bt, t'=cx+dt, showing that they have to be linear, then the remaining postulates lead to the Lorentz transformations.

Last edited: Oct 6, 2010

7. ### Eugene ShubertValued Senior Member

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Conclusions depend on presuppositions

CptBork,

Isn't it true that conclusions depend on presuppositions? Is it your opinion that Wiley Online Library is not an authoritative source? How are the two papers in the opening post different in their hypotheses, science and conclusions?

8. ### CptBorkRobbing the Shalebridge CradleValued Senior Member

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I don't know what sources you're using or if you're interpreting them correctly, but it can be simply showed that anything other than linear transformations will lead to uniform motion seen in one inertial frame correspond to non-uniform motion as seen in another inertial frame. I browsed briefly through one of the links but didn't look into it much- does either source take uniform motion as a postulate?

9. ### Eugene ShubertValued Senior Member

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CptBork,

Both sources invoke an arbitrary simultaneity so your question of uniform motion only makes sense if it is phrased in terms of invariants. For example, “Would a clock in one inertial frame of reference move equal distances in equal proper times when compared to some other inertial frame of reference?" The answer is always yes. That is a postulate. Yet, both papers show that if proper time is defined to be linear, coordinate time can still be nonlinear.

10. ### rpennerFully WiredRegistered Senior Member

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Eugene Shubert

On Evolution: [1] [2] [3] [4] [5] [6] [7]
On Authority of Dictionaries: [1] [2]
On the structure and depth of mathematics: [1] [2]
On Relativity: [1*] [2*] [3*] [4*] [5*] [6]

From 2005:

Finally, from 2004:
http://sci.tech-archive.net/Archive/sci.physics/2004-10/7570.html

October marks at least 6 years of his inability.

11. ### NeverflyBannedBanned

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I don't know the answer to the question. This is because I don't know the math.

But on a side note... I really don't think tooting the holy livin' hell out of your own horn when you have no referenced peer reviewed work on this topic is a very good idea.

That is the most self centered and egotistical OP I've ever read on a forum.

If it's so great... Get it published in the journals and watch the actual mathematicians and scientists clap you on the back and you'll have no need to troll the internet looking for fans.

12. ### Eugene ShubertValued Senior Member

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I can easily outdo that and you might see it if you stick around long enough.

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