How to Introduce Special Relativity (Historical Detour)

I am just reading the volume titled Waves in my favorite series of ancient textbooks on Theoretical Physics by German physics professor Wilhelm Macke. I tried to resist the urge to write about seemingly random fields of physics, and probably weird ways of presenting them – but I can’t resist any longer.

There are different ways to introduce special relativity. Typically, the Michelson-Morely experiment is presented first, as our last attempt in a futile quest to determine to absolute speed in relation to “ether”. In order to explain these results we have to accept the fact that the speed of light is the same in any inertial frame. This is weird and non-intuitive: We probably can’t help but compare a ray of light to a bunch of bullets or a fast train – whose velocity relative to us does change with our velocity. We can outrun a train but we can’t outrun light.

Michelson–Morley experiment

The Michelson–Morley experiment: If light travels in a system – think: space ship – that moves at velocity v with respect to absolute space the resulting velocity should depend on the angle between the system’s velocity and the absolute velocity. Just in the same way as the observed relative velocity of a train becomes zero if we manage to ride besides it in a car driving at the same speed as the train. But this experiments shows – via non-detected interference of beam of alleged varying velocities – that we must not calculate relative velocities of beams of light. (Wikimedia)

Yet, not accepting it would lead to even more weird consequences: After all, the theory of electromagnetism had always been relativistically invariant. The speed of light shows up as a constant in the related equations which explain perfectly how waves of light behaves.

I think the most straight-forward way to introduce special relativity is to start from its core ideas (only) – the constant speed of light and the equivalence of frames of reference. This is the simplicity and beauty of symmetry. No need to start with trains and lightning bolts, as Matthew Rave explained so well. For the more visually inclined there is an ingenious and nearly purely graphical way, called k-calculus (that is however seldom taught AFAIK – I had stumbled upon it once in a German book on relativity).

From the first principles all the weirdness of length contraction and time dilation follows naturally.

But is there a way to understand it a bit better though?

Macke also starts from the Michelson-Morely experiment  – and he adds the fact that it can be “explained” by Lorentz’ contraction hypothesis: Allowing for direction-dependent velocities – as in “ether theory” – but adding the odd fact that rulers contract in the direction of the unobservable absolution motion makes the differences the rays of light traverse go away. It also “explains” time dilatation if you consider your typical light clock and factor in the contraction of lengths:

Light clock

The classical light clock: Light travels between two mirrors. When it hits a mirror it “ticks”. If the clock moves relatively to an observer the path to be traversed between ticks appears to be longer. Thus measurement of time is tied to measurement of spatial distances.

However, length contraction could be sort of justified by tracing it back to the electromagnetic underpinnings of stuff we use in the lab. And it is the theory of electromagnetism where the weird constant speed of light sneaks in.

Contraction can be visualized by stating that like rulers and clocks are finally made from atoms, ions or molecules, whose positions are determined by electromagnetic forces. The perfect sphere of the electrostatic potential around a point charge would be turned into an ellipsoid if the charge starts moving – hence the contraction. You could hypothesize that only “electromagnetic stuff” might be subject to contraction and there might be “mechanical stuff” that would allow for measuring true time and spatial dimensions.

Thus the new weird equations about contracting rulers and slowing time are introduced as statements about electromagnetic stuff only. We use them to calculate back and forth between lengths and times displayed on clocks that suffer from the shortcomings of electromagnetic matter. The true values for x,y,z,t are still there, but finally inaccessible as any matter is electromagnetic.

Yes, this explanation is messy as you mix underlying – but not accessible – direction-dependent velocities with the contraction postulate added on top. This approach misses the underlying simplicity of the symmetry in nature. It is a historical approach, probably trying to do justice to the mechanical thought experiments involving trains and clocks that Einstein had also used (and that could be traced back to his childhood spent basically in the electrical engineering company run by his father and uncle, according to this biography).

What I found fascinating though is that you get consistent equations assuming the following:

  • There are true co-ordinates we can never measure; for those Galileian Transformations remain valid, that is: Time is the same in all inertial frames and distances just differ by time times the speed of the frame of reference.
  • There are “apparent” or “electromagnetic” co-ordinates that follow Lorentz Transformations – of which length contraction and time dilations are consequences.

To make these sets of transformations consistent you have to take into account that you cannot synchronize clocks in different locations if you don’t know the true velocity of the frame of reference. Synchronization is done by placing an emitter of light right in the middle of the two clocks to be synchronized, sending signals to both clocks. This is correct only if the emitter is at rest with respect to both clocks. But we cannot determine when it is at rest because we never know the true velocity.

What you can do is to assume that one frame of reference is absolutely at rest, thus implying that (true) time is independent of spatial dimensions, and the other frame of reference moving in relation to it suffers from the problem of clock synchronization – thus in this frame true time depends on the spatial co-ordinates used in that frame.

The final result is the same when you eliminate the so-called true co-ordinates from the equations.

I don’t claim its the best way to explain special relativity – I just found it interesting, as it tries to take the just hypothetical nature of 4D spacetime as far as possible while giving results in line with experiments.

And now explaining the really important stuff – and another historical detour in its own right

Yes, I changed the layout. My old theme, Garland, had been deprecated by wordpress.com. I am nostalgic – here is a screenshot –  courtesy to visitors who will read this in 200 years.

elkement.wordpress.com with theme Garland

elkement.wordpress.com using theme Garland – from March 2012 to February 2014 – with minor modifications made to colors and stylesheet in 2013.

I had checked it with an iPhone simulator – and it wasn’t simply too big or just “not responsive”, the top menu bar boundaries of divs looked scrambled. Thus I decided the days of Garland the three-column layout are over.

Now you can read my 2.000 words posts on your mobile devices – something I guess everybody has eagerly anticipated.

And I have just moved another nearly 1.000 words of meta-philosophizing on the value of learning such stuff (theory of relativity, not WordPress) from this post to another draft.

14 thoughts on “How to Introduce Special Relativity (Historical Detour)

  1. Most people choose to be no more intelligent than an eyeball, and/or they choose to simply accept the words of credited others, and do so without question.

    For starters, as far as the eye is concerned, “MOTION” contains 2 variables.

    One is speed, and the other is distance. Any motion occurring will include motion across a distance of some measure, and at a speed of some measure. And that’s all there is to it, is what the eyeball says to you.

    Yet, variables range from zero to infinity. Thus if you instead choose to be more intelligent than an eyeball, you will choose to push both of these variables involved in motion to infinity, and do so such that you will now be able to see a bigger picture than that picture which is restricted to the limits of the eyeball.

    Variable 1) To travel across an infinite distance.
    Variable 2) To travel at an infinite speed.

    If you travel across an infinite distance, you will go on forever, since there is no end to an infinite distance.

    If you travel at an infinite speed, you will therefore cross any distance in no time at all.

    Note: If it takes time to move from point A to point B, then this means that you can still travel faster and complete the trip in an even shorter time period, and so on and so an….., thus if it takes any time to move from point A to point B then clearly you are still only traveling at a finite speed.

    Now, if you put the two variables together, thus you are traveling across an infinite distance at an infinite speed, in turn YOU WILL GO ON FOREVER, and do so IN NO TIME AT ALL.

    Thus you end up with a Time Paradox.

    If you have brought just one clock with you for the trip, there is no way that this one clock can indicate both a forever time period and a zero time period at the same time. Thus you realize that this is “ABSOLUTELY” impossible. Thus it must therefore be a relativistic phenomena since it clearly can not be an absolute phenomena.

    Following onward with this logical analysis of motion, you soon end up with the same outcome as Einstein’s Theory of Special Relativity, along with creating all of the equations involved in Einstein’s Theory of Special Relativity.

    See http://goo.gl/fz4R0I to watch videos #1 through #9 which lead from scratch to the creation of all the equations. It’s about 1 1/2 hours long, but most people, due to slacking off, stop before reaching the interesting assembly of the jigsaw puzzle concerning Relativity. This occurs at video #7. You still have to watch them all since they are strung together in a logical order.

  2. First, here’s a limerick for you:
    There was a young lady, so bright
    whose speed was much faster than light
    She went out one day
    in a relative way
    and returned on the previous night!

    I still recall first encountering the Michelson Morley experiment. It was 1979, I was just 18 and in a small class of around 10-15 or so. The course was an introduction to Modern physics. The instructor, Dr. Saudi Paddi Reddy, was one of the most caring, sincere profs I have ever had (and I am happy to say that I had quite a few excellent physics profs at Memorial University’s physics department). It was a very small room but Dr. Reddy always used his “big room” voice. He always accentuated the important stuff with, “And if I call you up at 3 in the morning and ask you this will you be able to answer it?”
    Anyway, after thinking about the M-M experiment, that he’s presented in class one day, and, becoming quite intrigued, reading up a bit more about Albert Michelson, certain things started really clicking into place for me. In particular this: what we know we must always treat as tentative; it may always be disproven. We do, though, have fantastic minds and quite ingenious ways can be found to point out flaws that lead to even greater understanding. Nothing in the world of science is beyond scrutiny.”
    That idea stays with me today, but I think it was the M-M experiment that really hooked it in in place.
    The new theme is great–and, yes it’s nice on the phone too. I was always able to read your stuff just fine on the phone, though. WordPress would default to an excellent mobile version whenever it realized I was not on a PC.
    Oh, and as far as I am concerned a 2000 word pose is twice as good as a 1000 word one. 🙂 I know that the accepted rule is keep it to around 800 words or so but I think that’s just to satisfy the lazy likers and such who don’t realy want to read YOUR stuff; they just want to put likes and such on your blog to act as click bait to theirs. There are still lots of us who only follow a few blogs–but with great interest so well developed thoughts are what we are looking for. But that’s just my opinion.

    • Thanks, Maurice! Great poem 🙂

      I can relate a lot to your story!! I had great physics teachers in high school. However, I was so eager to learn about the theory of relativity (learning about the math behind the sensationalist accounts in pop-sci books) that I read a small volume by Einstein before it was presented in class.

      What I find so amazing is that you can learn about really deep things by using using astonishingly simple math. Therefore I strongly disagree with all who say that relativity should be removed from the high school physics curriculum – in order to allow for more “practical” and “applied” physics. (This is in a nutshell what I have said / will say in the other 1.000 words I had moved to a draft.)

      My other favorite book that shaped my junior scientist’s mind was Gödel, Escher, Bach by Douglas Hofstadter. Seems I had always been into combining math / physics / computer science / philosophy … and a bit of weird art.

    • Re the layout: Yes – you are right. I have also seen this (completely different) layout on my mobile phone. What bothered me was that on online iPhone simulator that shows the current layout as really responsive (no sidebar) simply made the middle pane in Garland smaller… which resulted in the scrambled menu bar. As WP said they did not support it any longer and I didn’t want to test with all kinds of devices I thought I better move to a really responsive layout.

    • You know, I just realized, the only thing I remember my professors saying was so important we’d have to know it if we were called up at three in the morning was the Contraction Mapping Theorem. But I was only an undergraduate in physics, and went to grad school for mathematics, so there’s slightly different priorities.

  3. Not going to pretend to understand the physics, but love the new layout! My mobile devices thank you :). As for the virtual time casual, I’m sure hoards of future WP users will thank you for marking the demise of Garland. Here lies Garland with one column too many. Seriously, the blog looks great.

    • Thanks a lot, Judy! I know you choose your layouts carefully 🙂 I have read about Garland’s depreciation in a WordPress.com forum. They said modern features will not be supported and I was stuck with options for customization – as the old color picker has never been migrated to the Custom Design tools and I couldn’t fully control it with CSS.
      Yes, the third column was probably too much – although I picked it exactly for that reason 😀

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