The Lorentz transformation derivation(s)

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The Lorentz transformation derivation(s)

Postby jocular on November 23rd, 2017, 8:26 am 

I have worked my way through Einsteins "simple" algebraic derivation which I assume is quite well known.

http://www.bartleby.com/173/11.html

I can hardly fail to notice that it (the derivation) is predicated on time being measured with a light clock and so the centrality of c in the final formula is apparently "built in" to this particular derivation.

I have however on many occasioned been warned against assuming that light (or its speed ) is central to Special Relativity and so presumably it is not central to the Lorentz Transformation formula.***

I assume there must be other derivations of the Lorentz Transformation that do not start with the speed of light as a way of measuring time (and they may be very advanced**).

What are they?

**well "advanced" for me as I took at le

*** I have repeatedly been told that this is just the geometry of spacetime and that the speed of light is a consequence -not causative.
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Re: The Lorentz transformation derivation(s)

Postby bangstrom on November 24th, 2017, 1:17 am 

jocular » November 23rd, 2017, 7:26 am wrote:I have worked my way through Einsteins "simple" algebraic derivation which I assume is quite well known.

http://www.bartleby.com/173/11.html

I can hardly fail to notice that it (the derivation) is predicated on time being measured with a light clock and so the centrality of c in the final formula is apparently "built in" to this particular derivation.


In relativity, c is consistently used as a spacetime dimensional constant rather than as a speed so it serves as a speed in name only. There is a disconnect in relativity between how c is used and how it is explained. Hermann Bondi claimed that c is nothing more than the length of a standard meter expressed in seconds and relativity makes more sense if you drop the notion that c is ever a speed.

jocular » November 23rd, 2017, 7:26 am wrote:I have however on many occasioned been warned against assuming that light (or its speed ) is central to Special Relativity and so presumably it is not central to the Lorentz Transformation formula.***


The use of c is central to both SR and the Lorentz transform but it serves as a dimensional constant. It is possible to derive the Einstein/ Lorentz time-dilation formula on the basis of Pythagoras’ theorem alone without having to consider c as the ‘speed of light.’
jocular » November 23rd, 2017, 7:26 am wrote:I assume there must be other derivations of the Lorentz Transformation that do not start with the speed of light as a way of measuring time (and they may be very advanced**).

What are they?

There are no derivations of the Lorentz transform that use c as the “speed of light.” As you said, c is “built into” the Lorentz transform but not as a speed. It serves as a universal spacetime constant giving us the interval of time found in every interval of space. Different observers may have different observations for units of distance and time but they all should agree that the ratio of their units of time to units of distance is always c for light related events. So c is a space/time ratio but not a speed.

jocular » November 23rd, 2017, 7:26 am wrote:I have however on many occasioned been warned against assuming that light (or its speed ) is central to Special Relativity

The use of c is central to both SR and the Lorentz transform where it serves as a spacetime dimensional constant. It is possible to derive the Einstein/ Lorentz time-dilation formula on the basis of Pythagoras’ theorem alone without having to consider c as the ‘speed of light.’
jocular » November 23rd, 2017, 7:26 am wrote:*** I have repeatedly been told that this is just the geometry of spacetime and that the speed of light is a consequence -not causative.

The "speed of light" is a universal constant giving us the amount of time found in any given interval of space. It is the "geometry" of spacetime but it is neither a cause nor a speed despite the name.
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Re: The Lorentz transformation derivation(s)

Postby jocular on November 24th, 2017, 7:01 am 

bangstrom » November 24th, 2017, 1:17 am wrote:There are no derivations of the Lorentz transform that use c as the “speed of light.”

Apologies for giving a "too general" link to Einstein's publication.

Here is the specific page where it seems to me the the derivation does start from an equation of a ray of light proceeding along the x-axis: http://www.bartleby.com/173/a1.html

The first part of the derivation states x-ct =0 (and the fourth part subsequently adds x^1+ct^1 =0 equipped with a suitable and to be determined "mu" factor)

I accept that all derivations may not start from this acceptance of the speed of light (and this is intended almost as a layman's derivation) but I have not yet come across others that do not and would be grateful to be pointed in the direction of any of them.particularly one that did not require too much heavy maths (although I am not entirely out of the practice of matrices,as convoluted as their workings can appear at first)
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