Lorentz transformations


One of you mathematical specialists could help me probably. I have recently renewed my interst in theoretical physics. As a result, the Lorentz transformations worry me again.

Would you be willing to to point me to some gentle reading on that history? For example, did they precede Einstein's search for solutions of relativity or devised to make the theory work? Not being a math or physics major in school, I had developed a certain suspicion about the need to explain why kinetic energy, E=Mc^2 instead of the integration of momentum, 1/2Mc^2. I can see how Lorentz makes the difference when the velocity of the relative frames is near the speed of light and that they would not change Newton's perspective at the speed of a horse race or a steam engine, even a shooting star.

I am not working on a challenge, certainly not a 100 years after the fact. Better reason - I'm not qualified. Probably my igorance that allows me to question things like this anyway. Lots of things about math seem a little convenient to me anyway, like we do indeed "manage the errors" when doing numerical analysis, calculus for sure. What about regression, especially if we use it for cause and effect or extrapolated predictions (HP instructions and menus for regression even use keys for "Pred" which is an extrapolated projection of some curve, no telling what R is, or which is impied cause or effect.

We are sometimes too inventive about creating an explanation (hypothesis) for things we leave outside the box or sphere like dark matter. Ether served scientists of Einstein's time, even him. Why isn't the prevailing explanation for too much mass that we can't see the other side of galaxies, even our own? Didn't we find a bulge in the moon when we finally saw it?

I just want to understand Einstein a little better before this old frame passes on, hopefully with some recognition of the truth.



Hi Ron.

Not being a:

One of you mathematical specialists

I am not entitled for helping :-) but I just thought you could look at:


and especially at the section "External links", which might provide you with some helpful information.

Hope this helps.

Best regards.




The subject is fraught with traps, but it also loaded with serious thinkers with plenty of room for amateurs like me. I took a quick look at some of the references you shared and can see that they should measure up to the challenge while some might not pass the threshhold for "gentle." I'm certain that you all are familiar with the fact that "amateur" means something like "lover of the activity, the game, the endeavor, " etc. An amateur in photography, for example, could very well perform much better than his professional neighbor measured for quality versus quantity.

Whoah, Sam, I didn't mean to step on a nerve. Maybe I should not have been too quick to draw a conclusion of my own by asserting that too many people have access to some pretty powerful stuff in these calculators. Correct me if I am wrong, but isn't a regression analysis a quick study of the existing relationship between or among pairs or groups of historical data, optimized by fitting them in a linear or quasi linear fashion to a group of curves from which to see the historical relationships and to suggest a lead with variable significance of the results. No doubt there are many examples of "winners" in regression curves that qualifies the method to be joined with other methods of reaching good leads into solid trouble-shooting type activities. As I understand it the residuals have meaning also, which is one of the reasons I believe that regression has its limited place. I am more inclined to push the idea that the dice have no memory, especially after hearing of so many stories from Las Vegas about sure fire betting schemes. I do believe that regression has its place but that statement was made to point out the fact that even a respected company like the one we buy from, makes the published error in a user document that implies a definite cause and effect relationship by labeling it "Pred." I think some trouble-shooters who trust their instincts can abandon an existing problem after losading their logical engine with data and then go into a rest mode like a cup of coffee and talking about football or some other distraction and suddenly experience brilliance when their subconscious returns the answer. That probably describes you in which you have included some regression statistics for final analysis. Foolish question - if predictive nature is prevalent in the model, why do they throw out the "outliers?"

Not sure I understand, "REPLACE THIS TEXT WITH YOUR LISTING," But I like the odds that it is a challenge for me to respond with a program to out-perform regression curves in a controlled environment.


Thanks again to all of you and your stimulus. I have Parkinsons and need all the stimulation I can get. Keeps the fog at sea.


Extending Giancarlo:
Concise derivation of E=mc^2:

Wikipedia Four-Vector entry


From what I remember from college, H. A. Lorentz derived his transform to account for the bizarre results of the Michelson-Morley experiment -- this was the famous experiment that led to the discovery of the invariability of the speed of light. What Michelson and Morley were trying to do is to measure the speed of the Aether (the hypothetical medium through which electromagnetic waves were then thought to travel). Lorentz' assumption was that Michelson's and Morley's negative results were caused by their apparatus being distorted by its own motion through the aether, in such a way as to cancel out the expected differences in the speed of light depending on the relative motion of the observed light source, and his transform described how spacetime would have to be altered for this to account for the observed results. His assumption turned out to be wrong, but he got the transform right, for the Special case of relativity anyway. And, perhaps most importantly, the Lorentz transform reconciled the inconsistencies between Newton's laws of motion and Maxwell's laws of electricity and magnetism.

I don't remember the title of my college textbook for this subject, which is probably just as well, because, while I did ace the test, I was just as confused at the end of the course as at the beginning.

However, for a gentle introduction on just about any subtopic of physics, for people who really want to know the nitty-gritty, you can't beat The Feynman Lectures on Physics. What you're looking for is in Volume 1, Chapter 15, "The special theory of relativity", but I recommend getting the whole set. Great stuff.

- Thomas

Edited: 27 May 2007, 1:21 a.m.


Thomas, I think this is responding to your input. Thansk, even if I got the wrong position. I'm refering to the four vector input. Hope it gets me without getting me. Looks good though, thanks again.



<What about regression, especially if we use it for cause and effect or extrapolated predictions (HP instructions and menus for regression even use keys for "Pred" which is an extrapolated projection of some curve, no telling what R is, or which is impied cause or effect.>
There was a problem involving a gas law which has 2 companies stumped. I had a new calculator and entered the data into an exponential analysis. The correlation was 0.384 . I retried it with a power law regression and obtained a correlation of 0.996 . A gas leakage problem that was assumed exponential turned out to be an outgassing of adsorbed helium, I made a log-log plot of the data which fit correctly. There was a point almost off the graph from an unusual data point, but it fit the power law plot extended.
With a programmable calculator I made fits to all sorts of difficult curves; thermistors and other electronic curves.
It is an addiction of mine. I enjoy reducing intractable data to a formula. Sam


re: "Why isn't the prevailing explanation for too much mass that we can't see the other side of galaxies, even our own? Didn't we find a bulge in the moon when we finally saw it?"

We can, in fact, "see" the other side of the galaxies (and our own Galaxy, too). Infrared, X-rays, and radio waves all pass right through. We don't see anything out of the ordinary "on the other side." Plus, the real indicator that there really is "missing mass" (meaning mass we can't "see") is its gravitational effect, which is not affected by lack of transparency in any part of the electromagnetic spectrum.

There's no extra bulge on the other side of the Moon, either. The core of the Moon does seem to be somewhat offset, but that is completely explainable by tidal effects as the molten, newly-formed Moon cooled down under the influence of the Earth's gravity.


Dave, thank you so much for responding to my ignorance about Dark Matter. Your straight forward, no nonsense explanation of my misinformation has already awakened me to more discipline in my efforts to understand. It has been a few years since I fell more naturally into the good lab habits. You've been a great help and I look forward to more exchanges.

Hopefully it won't be too long before I start making a contribution in the subject matter, maybe even approach parity, or close enough to carry my side of a decent argument. (If there is ever a "side" beyond a devil's advocate's position in a mock debate.) In the meantime I shall remain content to have people of your qualifications willing (hopefully) to critique my efforts.

Sincerely, Ron


Hi Ron,

You've picked an interesting topic, indeed!

If you are interested in how the transforms are derived, I can scan my derivation and send it to you. The Lorentz equations are surprisingly intuitive when you see them and you'll get a nice moment of clarity! There doesn't seem to be any easily understood algebraic derivations out there on the internet... Unfortunately, many of the science / math Wiki entries tend to confuse many folks that aren't already knee deep in it!

If you want to know where all that mass is, do a search for 3 degree cosmic background radiation.

A searchable online version of Einstein's Relativity can be found here: Relativity

If you want my opinion, go forth and read my so-called "holy trinity of space, matter, and time." This includes:

...Einstein's "Relativity"
...Martinus Veltman's "Facts and Mysteries in Elementary Particle Physics"
...Steven Weinberg's "The First Three Minutes"

Tony, AB9IO
The Plastics Guy


Hi, Plastics Guy - good of you to jump in with your advice. You sound very much like a professor or doctoral candidate at a really good institution with time to inspire thinking. I'm currently enjoying the non-technical biography, "Einstein." I have some time I can use to ask some reasonably pertinent questions that go to the central issues of Relativity, Quantum, String Theories, and other topics within the realm of "Theoretical Physics or possibly philosophy.

It would be ideal if there was a University close by with an honors class I could audit and participate or at least listen to arguments. I don't imagine anything of that nature will be forthcoming in my area soon. I may be relocating to the Huntsville vicinity by fall. There could be such an opportunity sponsored by N.A.S.A near there. Even if not, the chances of creating or joining an existing group or "club" for a subject like that would be the next best thing to having M.I.T. or Cal Tech in my back yard.

Thanks again for your encouragement and your references. I especially appreciate being set straight as to the current status of Dark Matter.



Hi Ron,

Thanks for your comments, but I am neither/nor! Actually, I work full-time in a plastics reycling plant and have decided to go back to school to finish my degree and get a minor in physics along the way. My best wishes to you in your journey of knowledge. One can gain a great deal by checking out the modern physics classes at any local university. Of course, you'll find many reasons (excuses?) for using your trusty HP in class!

Have fun!



Hi, Plastic Guy,

I catch the connection - recycle, guy (male persuasion) well-read in physics and astro physics self educated for the most part. You are the epitome of my definition of a student. That person who somehow realizes that a large part of their education is dependent on a qualified faculty with reasonable resources (library, visiting professors, an inspirational environment all focused on the customers, the student base. Yet they are more dependent on themselves setting goals, finding ways to make every course interesting, partipating in and out of the classroom, socializing with other individuals and groups, taking advantage of what resources they have and expanding resources by access through other means such as the internet. Sure, you'll have to take some structured courses for basic liberal eduation, but the real student taking the opportunity to become a better-educated individual will study some of Shakespear's plays along with the English majors instead of survey courses mandated and designed to meet minimum degree requirements. I am a strong advocate for a minimum exposure to liberal arts and science degree at the BS or BA level with graduate study at the professional or specialty level.

A BS will get you a stacks pass at the library, a better chance to audit classes you want to sit for, a chance for graduate school and the opportunity to contribute to the alumni fund along with the chance to get in line for a pair of season tickets. Liberal arts will make you a better Supreme Court Justice, Holistic MD, Teacher, Writer or, as indicated, a well-educated person probably parking cars at your favorite Restaurant.

I have to tell you that like you, I went BACK to college and found it to be a real challenge because of time constraints, but I managed to squeak into first place by something like a hundredth of a point for graduation.

Best of luck, Prof.



I would be a happy Dude indeed to see the scans of your derivations of the Lorentz transforms. (anything else you care to share). Are they derived through fairly simple 1st or 2nd order linear DEQs? I use Mathcad Release 13.1 which has a few options for DEQs with parameters, initial boundaries plus partials and systems. Several options are included for interpolation. Release 13 of Mathcad changed the solve block design to facilitate solutions with parameters, symbolic in some cases, numeric in every one I have solved. The other major improvement in the solve block design allows you to place a block inside a loop to assist in solving all DEQs.

In case you aren't familiar with the software, it is built around some Maple modules with CAS assistance. Some of the logic is illogical and it can be a hard one to program, but it can interface with scripted controls from C++ or AS An ADDIN WITH EXCEL.
I am begining to sound like a sales person for Mathsoft, not intended. Just wanted you to know that I'm not limited to that one relative weakness of the 50g vs laptop. I use the 50g for integration or differentiation any time I want to show steps. Needless to say, but I am very pleased with my 50g and Mathcad.



Hi Ron,

Check your mail...



Giancarlo, thanks for helping me out - excellent referal. I forgot about Wiki. That backup from Bob Wang on the four vector looks promising for accelerated enlightenment involving frames of refernce. Links you provided are going to help me tremendously!


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