Development of Special Relativity

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NoahsArk
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I'm interested in the history of thought that led to the discovery of special relativity.

Of all the equations in special relativity, e.g. the equation for the invariant interval, the equation for gamma, the Lorentz transformation equations, the equation for velocity addition, etc., which one was discovered first, and which one is the one from which all the others are derived? If I'm not mistaken, it was the equation for the invariant interval or the one for gamma that came first (and that these two are really the same thing in different form).

I've wondered how really was that first equation arrived at. The light clock is the usual example given for the gamma equation. Is that also historically how it was arrived at- through a thought experiment? Was it Einstein that came up with that example?

Also, didn't Lorentz first come up with the Lorentz transformations before Einstein came up with the light clock example/ gamma equation? That seems a bit confusing because the Lorentz transformations are more complicated and more general than than the equation for gamma. It seems like the equations should have been discovered the other way around.

Also, Einstein is considered to have been the founder of special relativity. To me, the most profound part of special relativity is that the passage of time between any two things happening is not the same for everyone, and depends on their relative motion. Lorentz could not have not understood this already, though. The Lorentz transformations show that time in one frame has a different value than time in another, so wouldn't he have understood that time is now a new dimension? I am not doubting Einstein's contributions. I know that he came up with ## e = mc^2 ## and general relativity. I just wanted to know what his contribution was to the idea of "time is relative" compared to what Lorentz's contribution was.

Finally, it is often said that Einstein's discovery of relativity is likely the greatest mental achievement ever in history. When this is said, are people referring to the discovery of special relativity or general relativity or both? Also, why exactly is it that it is the greatest mental achievement, if it is? I assume that opinion plays a part in it, but why, for example, would it be a deeper discovery than Newton's discovery of gravity, or Pythagoras' discovery of the Pythagorean theorem? Is it because special relativity was the discovery of a 4th dimension, and because the discovery of the nature of time went against all of our prior experience?
 
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  • #2
Nugatory
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Of all the equations in special relativity, e.g. the equation for the invariant interval, the equation for gamma, the Lorentz transformation equations, the equation for velocity addition, etc., which one was discovered first,
The Lorentz transformations came first, which is why they’re called ‘Lorentz transformations” instead of “Einstein transformations”. Einstein showed that these transformations followed naturally from his two postulates, so could form a complete and internally consistent alternative to Galilean relativity.

The gamma factor wasn’t “discovered”, it’s just easier to write ##\gamma## than ##1/\sqrt{1-v^2/c^2}## so we generally do the former instead of the latter. The velocity addition law is a bit of algebra starting from the Lorentz transformations; there never was anything there to “discover”.

The invariant interval and the concepts of Minkowski space and Minkowski diagrams came later. First Einstein published his SR paper in 1905, and then a year or so later Minkowski pointed out that there’s a more mathematically elegant way of describing the physics based on the fact that the Lorentz transformations preserve the spacetime interval - that’s why we call them “Minkowski diagrams” instead of “Einstein diagrams”
When this is said, are people referring to the discovery of special relativity or general relativity or both?
Maybe you should ask whoever said that?
 
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  • #3
NoahsArk
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The invariant interval and the concepts of Minkowski space and Minkowski diagrams came later.
It seems, though, like the Lorentz transformations immediately show the existence of one space-time due to the use of t's and t primes. I don't see where the further thought and work came to go from the LTs to Mikowski space-time.
 
  • #4
Nugatory
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I don't see where the further thought and work came to go from the LTs to Mikowski space-time.
Well, try to imagine yourself as a talented PhD student in 1905, reading Einstein’s just-published paper “On the electrodynamics of moving bodies” - google will find some English translations online. Do you think that you would immediately jump to Poincare’s discovery of the implications of substituting ##t\mapsto ict##? And from there to Minkowski’s 1908 paper https://en.m.wikisource.org/wiki/Tr...or_Electromagnetic_Processes_in_Moving_Bodies?

It looks like a lot of seriously non-trivial work to me.
 
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  • #5
NoahsArk
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My last question I poorly phrased. I guess my main question is about understanding in lay man's terms, if that's possible, the contributions of Lorentz vs. those of Einstein.

Is it correct to say that the novelty of special relativity is that it introduces t as being frame dependent? If so, was it Lorentz or Einstein that realized this?
 
  • #6
robphy
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It seems, though, like the Lorentz transformations immediately show the existence of one space-time due to the use of t's and t primes. I don't see where the further thought and work came to go from the LTs to Mikowski space-time.
As it is often said, hindsight is 20/20...

https://en.wikipedia.org/wiki/History_of_special_relativity

The equations and geometry underlying Minkowski spacetime and even 1+1 de Sitter spacetime are natural extensions of the work of Felix Klein.
https://www.physicsforums.com/threads/physics-mathematics-and-analogies.813201/post-5105772
https://en.wikipedia.org/wiki/Cayley–Klein_metric

Of course, due to the success of relativity, supported by a lot of experimental results,
and many pedagogical approaches, it probably seems "immediate" today
... but, as @Nugatory suggests, things might not have been so obvious in the late 1800s-early 1900s.
 
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  • #7
NoahsArk
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Maybe you should ask whoever said that?
It's something I often read. The question goes beyond special relativity to the more general idea of what makes any idea brilliant. For example, there are equations in different fields like mechanical engineering I think that are much longer than the SR equations but less famous than something like ## e = mc^2 ##. Why is Einstein considered one of if not the most brilliant?
 
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Speaking as a laymen, I think Einstein has to be considered in terms of what he was suggesting and the generally accepted wisdom at the time he made them. This is why he is remembered so fondly in my opinion, he had the biggest impact on the way of thinking at that time than other discoveries have since then.
 
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PeroK
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It's something I often read. The question goes beyond special relativity to the more general idea of what makes any idea brilliant. For example, there are equations in different fields like mechanical engineering I think that are much longer than the SR equations but less famous than something like ## e = mc^2 ##. Why is Einstein considered one of if not the most brilliant?
You can't judge a physicist by the length of his equation!
 
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  • #10
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Imagine how much nerve it took to say that time, in real-world physics, was dependent on the speed of an observer. And the intelligence to show that it explained the results of well-known experiments without creating any inconsistencies. That was the genius of Einstein. Then he worked for years to show that the consequences actually explained gravity. The nerve of Einstein was astounding! General relativity is, IMHO, an intellectual accomplishment far beyond my ability to evaluate. So I am happy to accept that it is the greatest intellectual accomplishment of mankind. The mathematical manipulations of the Lorentz transformation do not impress me nearly as much.
 
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  • #11
NoahsArk
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The mathematical manipulations of the Lorentz transformation do not impress me nearly as much.
I am trying to get an understanding of what Einstein's contribution was in order to get a deeper understanding of special relativity. I don't doubt his contribution was major. I just don't understand it, and can't say what was it that he contributed compared to what Lorentz did, or what any other person did for that matter.

Should I not even be bothering to try and learn the history of SR in order to understand SR in general? I am starting to be able to solve problems using Lorentz transformations and time dilation/ length contraction problems. I understand, I think, the basic ideas of SR: i.e. passage of time is frame dependent, length is frame dependent, and simultaneity if frame dependent. I can see how these concepts are counter intuitive and are very interesting to me. I wanted to learn the history to get a deeper understanding, but it seems like a back ground in physics is necessary to really understand it's development- at least insofar as the vocabulary used presupposed a physics back ground. I am a lawyer with an undergraduate degree in Spanish, so if the explanations of SR go beyond algebra or plain english/ logical descriptions, then it can becomes challenging.

For example, I started to read the wikipedia link on the history of SR. Here's an example of what I encounter:

"Following the work of Thomas Young (1804) and Augustin-Jean Fresnel (1816), it was believed that light propagates as a transverse wave within an elastic medium called luminiferous aether. However, a distinction was made between optical and electrodynamical phenomena so it was necessary to create specific aether models for all phenomena."

This is all Greek to me, and am wondering if there are other, non technical ways of learning the background if I need to learn it at all to understand SR. Can I obtain a good understanding of SR with just algebra and doing SR problems, or do I need a physics background with courses in things like electrodynamics, etc?

Thank you.
 
  • #12
PeterDonis
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Should I not even be bothering to try and learn the history of SR in order to understand SR in general?
Yes. If your purpose is to learn what SR says, learning its history is (a) irrelevant and (b) distracting. Every theory goes through a period where a lot of wrong turns are made and a lot of different methods are tried. All you need to know to know what SR says is the end result of that process: the modern, clean version of the theory that you will find in textbooks and modern papers.

If your purpose is to satisfy your historical curiosity, then of course you should learn the history of SR. Just don't confuse doing that with learning SR itself.

Can I obtain a good understanding of SR with just algebra and doing SR problems
IMO, yes, you can. The best way to do that is to work through an introductory textbook like Taylor & Wheeler's Spacetime Physics. To the best of my recollection it does not require any math beyond algebra and knowledge of trig functions like sine and cosine and their hyperbolic counterparts.
 
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  • #13
NoahsArk
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Thank you Peter. That saves me some frustration.
 
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  • #14
robphy
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IMO, yes, you can. The best way to do that is to work through an introductory textbook like Taylor & Wheeler's Spacetime Physics. To the best of my recollection it does not require any math beyond algebra and knowledge of trig functions like sine and cosine and their hyperbolic counterparts.
From an old post of mine ,
[The] Old edition has a discussion of rapidity (the Minkowskian analogue of "angle" between two future timelike vectors) and [in some editions] worked solutions to the problems.

[The ] New edition has some nice revised discussions of some topics. Unfortunately, the discussion of rapidity was dropped.

I would regard the old 1966 maroon edition with the solutions to be a must-have. The new edition is worth having (as a supplement to the older version) for some of the updated topics.
First (maroon) edition (1966)
http://www.eftaylor.com/download.html#special_relativity

Second edition (1992)
http://www.eftaylor.com/spacetimephysics/
 
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  • #15
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NoahsArc,

Just to add to the above ... algebra alone suffices, because the relationship between differing inertial frames is assumed to be linear, due to the observed properties of homogeniety attributed to space and time. That was stated by Einstein in his 1905 OEMB paper, near the beginning of Section 3 paragraph 5. Since linear, algebra alone can relate space and time between differing inertial systems. His 1905 paper used both algebra and calculus (partial derivitives and integration) to derive the LTs, but calculus is not required.

Best regards,
GrayGhost
 
  • #16
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In fact, you can go a long way in SR just using the math of the Pythagorean Theorem.
 
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PeroK
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Should I not even be bothering to try and learn the history of SR in order to understand SR in general?
I know you've been working through Taylor & Wheeler for a quite a while. This post from the beginning of the year says it was your third attempt at getting through the book.

https://www.physicsforums.com/threads/spacetime-physics-by-taylor-and-wheeler.963558/

To be honest, I can't see the point in trying a fourth time. If you still think it's worth the effort to learn SR you have to try something different. You could try to find a private tutor to help. And/or try a different text book.

As others have said, learning the history is not going to help.
 
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  • #18
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Should I not even be bothering to try and learn the history of SR in order to understand SR in general?
Do you need to know how the Pythagorean theorem was developed to understand it?
 
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Yes. If your purpose is to learn what SR says, learning its history is (a) irrelevant and (b) distracting. Every theory goes through a period where a lot of wrong turns are made and a lot of different methods are tried. All you need to know to know what SR says is the end result of that process: the modern, clean version of the theory that you will find in textbooks and modern papers.
Alas, while I don't really disagree, I do think that in a first approach to SR it is important to know (or at least have a good idea) of the problems the physicist at the time were facing and the inability of their classical approaches to solve them. That will let the student appreciate SR.
 
  • #20
Ibix
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I agree that the context is interesting, but not vital.

I'd summarise it by saying that Maxwell's equations were a great success and a great puzzle. You could, for example, accurately describe the fields around a charge moving near a wire. You could also describe a wire moving near a charge. But you couldn't turn one description into the other.

People assumed that this was a failing of Maxwell's equations - that they were a special case of something more general. Lorentz eventually found a mathematical patch (what we now call the Lorentz transforms) which let you transform one answer into another.

Einstein, however, had the insight that Lorentz had found a modification to Newton, not Maxwell. He showed that replacing the Galilean transforms with the Lorentz ones was self-consistent and reproduced Newtonian results in the low-speed limit - the only regime where it had been tested. And it made Maxwell's equations correct.

The only problem was that his theory was completely inconsistent with Newtonian gravity - it forbids causation from propagating faster than light, but Newtonian gravity propagates at infinite speed. Attempts to patch that failed, and Einstein eventually developed general relativity as a complete (and very different) replacement.

I don't think you really need to know more of the history than that to motivate relativity in a historical sense. And this is very much a sketch - the complete story is, of course, much more complex and messy.
 
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  • #21
robphy
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I know you've been working through Taylor & Wheeler for a quite a while. This post from the beginning of the year says it was your third attempt at getting through the book.

https://www.physicsforums.com/threads/spacetime-physics-by-taylor-and-wheeler.963558/

To be honest, I can't see the point in trying a fourth time. If you still think it's worth the effort to learn SR you have to try something different. You could try to find a private tutor to help. And/or try a different text book.

As others have said, learning the history is not going to help.
It might be that @NoahsArk 's has gotten stuck, preventing progress into the rest of the book.
@NoahsArk, is that the case?

It seems as the text being used is the 2nd edition.
I'd suggest the different textbook to try is the 1st edition [which introduces and uses rapidity, unlike the 2nd edition], preferably with the worked solutions in the back of the book.
http://www.eftaylor.com/download.html#special_relativity

Depending on what aspects are unclear, there may be other books to consider.

I think Bondi's Relativity and Common Sense ( https://archive.org/details/RelativityCommonSense ) is a great introduction because it uses operational definitions first, transformation equations later... and the mathematics and physics prerequisites are low.

I think Geroch's General Relativity from A to B ( https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20&tag=pfamazon01-20 ) is a great book on developing spacetime intuition using methods similar to Bondi. Despite its likely first impression from skimming the text, GRAB is remarkably deep in terms of the big picture of spacetime and general relativity but without the technicalities of how it's actually done. (For some of those details, one should refer to his notes for an advanced course ( https://www.amazon.com/gp/product/0987987178/?tag=pfamazon01-20&tag=pfamazon01-20 ).)

There are some newer alternatives... but it depends on what is specifically wanted.
 
  • #22
Ibix
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I think Bondi's Relativity and Common Sense ( https://archive.org/details/RelativityCommonSense ) is a great introduction because it uses operational definitions first, transformation equations later... and the mathematics and physics prerequisites are low.
Agree that this is a good book. I stumbled across a copy in a charity shop near my office, killing time during a fire evacuation.
 
  • #23
NoahsArk
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I appreciate the advice. @robphy and @PeroK I intend to continue with the Spacetime Physics book. One of the reasons I've stopped and started multiple times in the past is I've just gotten caught up with things at work and put it aside. I need to persevere more to get through it.
 
  • #24
Ibix
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If you are short on time, I'll reiterate my support for Bondi's book. It's the size of a short paperback novel - only 167 pages plus index. Then go back to Taylor & Wheeler.
 
  • #25
NoahsArk
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@Ibix Thank you- I will check that out as well.
 

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