SR #0: What’s so Special?

classOkay, if you’ll all take your seats and quiet down we can begin. I’ll keep this very short today because I know it’s Spring and many of you are eager to get out there and walk Frisbees and throw dogs… I mean — well you know what I mean.

The point is, that in keeping with spring, I’m aiming to keep these posts light and breezy. Unfortunately, I have terrible aim, so we’ll see how that goes. I never met a paragraph I couldn’t make longer!

Ready? Let’s go…

Today begins a series of posts discussing Special Relativity. I’m going to start off by explaining what makes it “special” as well as what we mean by “relativity.” (And note that, from now on, I’ll usually just write “SR” — “Special Relativity” is a lot to type!) I’ll also introduce you to a few other important basic concepts.

special relativity

By the time we finish this series of articles, this diagram should make complete sense to you!

Last Saturday I gave you an overview of some of the consequences of SR. By the end of the series, I hope to have given you a good explanation of how those things occur. It will take us a while to get there, but every journey starts with a single step, so let’s take those first steps now.

Basically, this is about motion and, in particular, about relative motion. That’s the “relativity” part of the name right there.

If Al is “standing still” and Em is “moving past” then Al sees Em moving relative to himself. But how can we be sure Al actually is the still one while Em is the moving one?

If Al is right next to us — say we’re sitting on a bench — we can obviously tell he’s not moving closer or further away from us or the bench. We can prove this by reaching out and putting a hand on his shoulder at any time to reassure ourselves he hasn’t moved.

As we see Em pass by, we observe her distance decrease as she gets closer and then increase as she gets further. If she passes us closely enough, we might be able to “high-five” as she passes. So, clearly she’s moving.

Al train

The world passing by!

But what if that bench we’re sitting on with Al is in a train car and Em is standing on the platform. We see her (and the platform) get closer, we high-five as we pass, and then she and the platform recede behind us.

Meanwhile, Em sees that she’s standing still (relative to the station platform), and from her perspective we and Al have zipped past in the train car.

Both versions (with certain caveats) are correct versions of the event!

The important point here is that Al sees Em as moving relative to him, and Em sees Al moving relative to her. That’s exactly what we mean by “relativity.”

A key caveat here — the key caveat for the moment — is that the motion must be constant. It cannot involve any slowing down or speeding up. That is what makes the kind of motion we’re discussing here “special” (more about that next time).

Em train

The train passing by!

So long as the train is moving at constant speed — and in a straight line — it is just as correct to say Em is moving as it is to say Al is moving.

The only thing we can say about not moving is that Al is not moving relative to the train car, and Em is not moving relative to the train platform.

You may think Em has the advantage since the train platform is on the ground, which is connected to the whole Earth, so it seems silly to say that Em is moving and Al is not…

But from Al’s point of view this is exactly the case! We’re sitting next to Al, and we can see he isn’t moving. Neither is the bench inside the train car. Everything inside the car is just sitting there (while Em equally obviously is moving past us).

In fact — and this is a really important point — there is no experiment we can perform that proves otherwise. Within the train car, it is absolutely true that we are not in motion relative to the train car. If you’ve ever been riding in a car and felt like the world was zipping past, that is a completely valid way to view it.

fake train

The ‘F’ train — as in Fake!

A minor caveat is that the sound and vibration of the train running along the tracks provides a clue that we’re moving.

But if you watched the old Mission: Impossible TV show, you may have seen that episode where they trick their target into believing he’s on a moving train using sound and mechanical effects.

For that matter, some amusement park rides do a pretty good job of tricking you into thinking that you’re moving using the same kinds of effects.

Conversely, if the train car is sound proof and has a smooth suspension, you may feel no sense of motion. Consider what it feels like to ride on a commercial aircraft. You can walk down the aisle with no sense that you’re really hurtling through the air at hundreds of miles per hour!

fake motion

Not actually moving (much).

An important term here is frame of reference. It’s a technical term for “point of view” but it includes the idea that — for example — you, Al, the bench you’re sitting on, and the entire train car, are part of one thing: a frame of reference.

Em also has a frame of reference: the platform and the train station and — in her case — the entire Earth.

But having that larger frame of reference — even one as big as the Earth — doesn’t make hers “better” or preferred. It only means there are a lot more people who share her view that Al and the train are moving.

That’s all I want to cover for today. Let’s review:

  • Special Relativity is about motion of one observer relative to another.
  • It’s special because that motion must be constant; no slowing down or speeding up.
  • In this situation, both observers can make equally valid claims they are standing still while the other is moving.
  • Both can also make the equally valid claim that they are moving and the other party is standing still.
  • Every observer has their own frame of reference.
  • There is no preferred frame of reference; all are equal.

Now go out and play!

dog frisbee

Just keep in mind that some dogs have injured themselves doing this!

 

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

23 responses to “SR #0: What’s so Special?

  • SelfAwarePatterns

    You weren’t kidding when you said bite sized chunks. But I’m sure the complexity will come soon enough.

    Within the context of special relativity, I thought the “special” in the name referred to flat spacetime, as opposed to the curved spacetimes of general relativity? (Feel free to tell me to shut up and wait for you to get to that point 🙂 )

    • Wyrd Smythe

      Since this is oriented toward a general audience, I want to take it very slowly. If nothing else it gives the reader a chance to digest each idea before moving on to the next. Einstein did the same thing in his (very readable, and surprisingly brief, book) Relativity; The Special and the General Theory. (On the other hand, it was written in 1916, and in German, so the (translated) language has that density of older writing. He lets you connect a lot of the dots.)

      I’m pretty certain “special” applies to inertial frames of reference. For one thing, curved spacetime is a consequence of the general theory rather than a prerequisite, whereas constant versus accelerated motion are input conditions in SR versus GR. I found a couple quotes from his book (thank heavens for indexes!) that seem to support this:

      “…it became evident that in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity to distinguish it from the extended theory, with which we shall deal later.”

      That’s from the end of chapter 7 [emphasis his]. In chapter 18 (which is only about halfway through — gives you an idea how short the chapters are — the whole paperback book, including five appendixes is only 178 pages):

      “But in addition to K, all bodies of reference K’ should be given preference in this sense, and they should be exactly equivalent to K for the formulation of natural laws, provided that they are in a state of uniform rectilinear and non-rotary motion with respect to K; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (e.g. those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity.”

      I think his book is freely available at Gutenberg [Emphasis again his]. My copy is a 15th edition released in 1952 and copyrighted 1961.

      As it happens, the difference between SR and GR, and accelerated frames, is tomorrow’s topic! 😀

      • SelfAwarePatterns

        Thanks for the reference! It looks like it is available on Gutenberg, but without the images, which I suspect is pretty crucial in a book like this.
        http://www.gutenberg.org/ebooks/search/?query=albert+einstein
        It’s also available on Amazon Kindle for 99 cents, with images, so I just picked up a copy, just in case I decide to read it.

        On “special”, maybe we’re saying the same thing but from different angles. It seems like I remember reading some time ago about this breakdown.
        1. Galilean relativity: all motion is relative.
        2. Special relativity: 1 + the speed of light is always constant, which effectively makes time, length, and mass relative.
        3. General relativity: 2 + acceleration is relative, which is explained via warped spacetime

        But I may be showing my own misconceptions.

        Looking forward to the next post!

      • Wyrd Smythe

        The only actual image is a drawing of Einstein, but if they also didn’t include the formulas and a couple tables, that would make it pretty useless. But for 99 cents, you can’t go wrong, so good choice, I’d say.

        Incidentally, my edition has a typo. The first formula in chapter 13 should be x’ = wt’ (not x = wt’). The paragraph that follows references x’ (which will confuse you until you realize the typo), plus it’s repeated as the fourth formula in that chapter, so it’s clearly a typo.

        Your [1], [2], [3] works fine. (A quibble: I believe the mass is more tied to the energy involved, though. The famous E = MC^2 is a reduction of the full mass-energy equivalence formula when velocity is zero. (This is different from time and length changes which follow the Lorentz equation.) But I think it’s still true that what makes SR “special” is that it is restricted to inertial frames of reference — that is, frames moving with constant velocity.

        As I’ll mention tomorrow, supposedly (or, at least, I’ve heard that) Einstein wanted to call his theories “equivalence” theories. SR is based on the equivalence of light speed (to all observers). GR is based on the equivalence of gravity and acceleration.

        You probably have a good enough sense of SR that you might want to jump to chapter 18 and begin with GR. As Einstein takes you through the reasoning, some of this might come into sharper focus for you. I’m touching on GR tomorrow, mostly in contrast to SR, and plan near the end of the series to write one (maybe two) post(s) lightly covering the same material Einstein does. So you can get a jump on the rest of the class if you want. 🙂

      • SelfAwarePatterns

        Thanks for the info. While I do understand the basics (particularly why it makes FTL likely not feasible), I’m not confident I have as good of sense of SR as you may be thinking, not the extent that I’d skip Einstein’s description of it, or yours, and I’ve never been able to get the twin paradox straight in my head.

      • Wyrd Smythe

        I can relate, actually. I spent a lot of time going over the Twins Paradox — lots of diagrams on graph paper, lots of calculations (even a small Python program). The traveling twin isn’t that hard; it’s the stay at home twin that was so twisty to figure out when trying to nail down exactly what happens.

      • SelfAwarePatterns

        The biggest hangup I currently have is understanding what happens when the traveling twin decelerates and arrives at the remote destination. Every diagram I saw assumed the twin immediately returned, and exactly where the simultaneity is when they’re stopped at the destination isn’t really addressed. I keep thinking, what happens if the twin stays at the destination? Certainly there is a delay in messaging between the twins, but it should be a known quantity and therefor reconcilable, and so at what point in their timelines will they now be simultaneous?

        I don’t expect you to answer that now. I’ll wait until you get to that point. But that’s my current hang up. I fully understand it’s a hang up since SR has far too much experimental evidence behind it for it not to be reality, or at least an extremely close approximation of it.

      • Wyrd Smythe

        The key basically lies in that the traveling twin re-enters the stay at home twin’s frame of reference upon stopping at the destination. At that moment the paradox in their ages resolves, and the traveling twin is seen to be younger. (If the traveling twin kept on traveling, and the stay at home twin jumped into a spaceship traveling in the same frame of reference as the first traveling twin, that second twin would, in fact, be the younger one. Exactly how that happens was a big part of what was really hard to figure out.)

        The trip back is really just a repeat of the trip out and doubles the time difference.

      • SelfAwarePatterns

        Thanks for the explanation.

        That must mean, from the traveling twin’s perspective, as they are decelerating, the at home twin’s aging speeds up dramatically, to a rate that is faster than the traveling twin’s rate. It’s the opposite of what the traveling twin has observed on the trip up to that point. Why that happens is what I’ve struggled to understand.

      • Wyrd Smythe

        I’ll make you wait for the detailed answer, but if you’ve encountered the idea of a “surface of simultaneity” with regard to SR, what happens is that the traveling twin’s perception of what is simultaneous lags further into the Earth twin’s past as the trip progresses (although ahead of what light signals would indicate). Upon stopping and re-entering the same frame of reference, that surface catches up. So in a sense, yes, the Earth twin ages rapidly as that surface moves from the past to the present.

  • dianasschwenk

    And never mind that the earth is moving around the sun and turning on its axis. 🙂
    Diana xo

  • rung2diotimasladder

    Nice job! I appreciate your breaking this down for people like me.

  • Hariod Brawn

    As with Tina, I appreciate the way you’re assuming nothing on behalf of the reader Wyrd, which in my case is always wise.

    • Wyrd Smythe

      The goal is just one new idea per post. That means those with good familiarity may find the series slow, which is unfortunate, but it’s mainly oriented at opening doors for those with no familiarity with it (but a willingness to be fascinated by it).

  • mlhe

    This blog appears to be special. I just discovered that a lot of people are relating to it quite well! Thank you…on the curve!

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