Thursday, May 26, 2011

Musing about Physics: Feynman and time dilation

Special Relativity is one of those topics that looks simple on the surface of things but gets really really complicated once you get under the hood.

The math is simple, trivial even, but the meaning gives a normal person headaches. What are we to make of "slowing clocks, contracting length" and other oddities that come once you accept the basic premise that c is a constant for every inertial observer.

Of course I have time, and since I started thinking about "Spring Theory" I decided to revisit classics see if I could make progress. Working on the Feynman book, I rediscovered basic SR.

I still stumble somewhat at the Dingle paradox, which is a version of the twin paradoxes. For those initiated with the paradoxes, I am OK with twin paradoxes (which involve acceleration) but still struggle with inertial versions of the twin paradoxes. (2 clock in inertia with V relative intersect, what do they read, assuming they were synchronized at some point, what do they read?). So I went over to sci.physics.relativity. The old usenet group. Funnily the "simple question" generated about 200 answers, which you can read here .

The answers were confusing, some plain wrong, taken as a whole completely contradictory, some saying I got the result right but the interpretation wrong, some saying I got the result wrong and the interpration wrong, some just don't waste time and call me a motherfucker, most just say I am stupid for not understanding the basics and so the joke goes on with SR. What is "trivial, basic" concepts still generate this amount of controversy 100 years from the inception of theory. In all fairness there are also well meaning folks that actually provided real information.

Clocks and Clicks

I recently I a bit of a breakthrough thanks to the Feynman book. I could finally put my finger on a few things.

In his book "Feynman lecture" (vol 1, 15-6) Feynman covers basic SR. In typical Feynman fashion it is highly readable and entertaining. He clearly presents C constant for all observers as a postulate of the framework. Says that with C postulated this way one must adopt the Lorentz transformation of coordinates as the proper transformation. Shows Lorentz has the Galilean transformation as limit as v tends to 0.

In there he has a very interesting paragraph about Clocks that Tick. Basically he imagines a setup where the "clock" is keeping count of the number of "clicks" a light beam bouncing off parallel mirrors separated by a distance d, makes. See the scanned image straight from the book (that is a bad bad thing to do). Imagine a photon going back and forth and count every time it bounces at the source.

If the mirrors are moving, the photons are making a zig-zag between the mirrors. (the mirrors move while the photons travel). So the photons will take more time to go back and forth. If we admit that the speed of light is C in the rest frame then the time it takes for the photons is longer as we are doing a zigzag. The "moving time" corresponds to the time it takes for a photon to cover the zig-zag, as seen from the rest frame.

It is trivial to see that the distance travelled by the photon is the hypothenuse of a triangle that has d on one side and v*t-m/2 on the other. So the distance is longer. OK, then the time it takes is longer as well because the distance was longer. You work out the math, I will spare you the math, which is frankly boring and straightforward and you find that the time it takes for the photon in the moving framework to reach the mirror is t-rest(1/sqrt(1-v/c^2)). Meaning the EXACT FORM of lorentzian transform in this case.

Reflections on Ether and Muon decomposition

So what is very interesting is that this explanation by Feynman, does give us a sense of why a "clock" like this would show lorentzian contraction. He uses this to say "every clock behaves like this" (a bit of a non-sequitur, but whatever, great prop). Of note it depends on the orientation of the mirrors, if you rotate them by 90 degrees, then there is no zig-zag and we would show the same time than at rest. But it is essentially a very "classical" explanation. If fact you can almost picture an ether, where the ACTUAL distance has increased and where the speed is limited to C and you get actual time dilation. In other words, a muon moving at the speed of light would indeed take the proper SR time to decompose (more than at rest) as it falls to the earth. I find that absolutely fascinating because in fact MUON DECOMPOSITION IS COUNTED AS ONE OF THE BIG EXPERIMENTAL VALIDATIONS OF SR. But taken as is, it can also be accounted by simple "classical" views.

Of course a big difference is that unlike SR, this theory only works ONE way. SR posits that the result be true for any inertial movement. In other words, the muons travelling would see the muon at rest decomposing more slowly due to the symmetry. Otherwise the travelling muons would know they are travelling (they decompose more slowly) which is in violation of the SR postulate.

In short, while amusing and entertaining (at least to me) the above only replicates half the predictions of SR, but, as far as I know, we have not measured the point of view of the muon.

Musing about time

But the big shortcut I do in reasoning here, is assuming that "time" is defined by the number of clicks. I don't know why or how, but let's assume that the smallest of oscillations is used as a 'reference' for all other oscillations. In this case time is defined in a relative way with respect to this "basic oscillation". It is the "reference". Well then time is an emergent property. You count other events with reference to this basic event. And if your basic event shows "time dilation" then you time reference has just dilated.

So what is evolving is the 'philosophical' definition of time. Time, far from being an ontological reality, is just a highly localized entity that entirely depends on the movement of the particle in consideration. If the muon is moving, it bases it's "time" on the basic oscillation and that oscillation just showed "time dilation" due to movement to a relative "rest media".

Every point of matter will therefore have a time. Related to its speed relative to a resting media. If we imagine that for some reason the most basic oscillation is always perpendicular to the movement (something to do with less resistance in that direction compared to the direction of propagation, I guess) then it is straightforward to see that your "moving time" follows exactly a Lorentzian transform. I find that thought particularly amusing.

The problem with velocities

If it wasn't speculative enough, let me dive some more into this "time". There is no time. Time is an emergent construct. There is no time "dimension", we are just counting clicks, and if you are moving it takes more 'time' for your clicks to happen. Or more strictly for every 1 click of the main clock you will have a fraction of 1 click (gamma from relativity) for the moving clocks. Simple.

The problem with velocities is that it is defined as a ratio of "distance by time" but time itself is an emergent property and I suspect that the way we "intuitively" understand velocity is erroneous because we assume a universal "time". But is a locally emerging construct and every moving body has a different time.

At least muons agree :)

A word to the wise

Please do not take the above too seriously. I don't take it seriously at all, altho I must admit to being tickled pink. In essence it is a simple way to pass time and entertain myself. For example the lack of symmetry (it assumes a medium, ergo a privileged frame) is anathema to most modern science. I just find it amusing that one of the canonical experiments (mentioned by Feynman himself as "proof SR works!") the decomposition time of muons as seen here is in fact trivially explained by classical mechanics. It also implies things about what "time" really is. An emergent property of movement.


pcleddy said...

what do you think about the first ten pages of this book? does it relate? (ahem)

glad i'm not crazy, always claiming there is "no time", so no "time travel".

the question is, can we drop time out of all equations then? have a new physic so simply?

pcleddy said...

while i'm asking you to "take a look", what do you think of the first 40 pages of this?

i've got some strange ideas about trying to explain existence from a devolution/evolution perspective. or, at least, i used to think about these things. now, i learn german.

Marcf said...

Pcleddy, browsed teh first pages of the book. Sounds interesting, but not sure what the 'theory' is. Time in this view looses its "special dimension" status, it is just an 'index" on events. The way the index evolves is dependent on speed.

pcleddy said...

ya, i just had the idea that 'time' was nothing other than the relation of objects to each other -- for example, the moving of objects back to the same exact relation to each other is a kind of timelessness or time loop. and had never seen it presented so simply before. then, you were saying something similar. i was surprised.

plus the point about scale is fascinating.

i havent read it in a while. like four years ago. dont have it handy. not available in kindle form either.

i need to take some time and re-think some things from about 15 years ago and send you a note.

so then, you'll know i'm totally insane.

or way ahead of my time. er.

well, you know what i mean.

kenhughes said...

'Very ineresting account and also, completely accurate. I can't help but take this seriously, sorry, I'm a bit of a nerd when it comes to relativity.
SR makes one fundamental error and that is to ignore the unidirectionality (asymmetry) of time as compared to the bi-directionality (symmetry) of physical dimensions. It draws silly little diagrams of ships passing each other to prove that time dilation is reciprocal, (looks the same between ships), but in doing so, it ignores this fundamental difference.
In 1971, they flew an atomic clock around the world in both directions and left another behind. In accordance with SR, the moving one had lost time by the end of the journey. This proves the moving clock ran slower during its travels. This is also in contradiction with SR since there must be a redshift observed from the Earth clock but a blue shift observed from the moving one due to the different relative time rates.
As you rightly point out, no one has yet taken the position of the muon, or indeed of any moving entity which has a significant enough time dilation to be observable. I predict this red/blue shift non reciprocality and encourage an experiment to test this hypothesis. Any takers?

Marcf said...

Ken, thanks for your thoughts on this.

I did study briefly the Hafele-Keating experiment you refer to. It has SR and GR components. But really it is a GR thing since the clocks have acceleration. If you have an experiment in mind to test please do share.

Marcf said...

Are you this kenhughes?

Further thoughts on the HK experiment. SR really has nothing to say but "both clocks are slow compared to each other" which is non-sensical once you bring the clocks back together (twin class experiments) but again this assumes non-inertial movement as there must be acceleration and then all bets are off with respect to SR. I have learned to 'embrace' SR for the silly thing that it is, there is no contradiction in the Lorentz special group, you can draw all the silly diagrams.

In reviewing SR it is really the first postulate that is problematic that every inertial OBSERVER would see C. But HK/ MMX type experiments are very disturbing. If you do not accept SR 1st postulate then you are left with a preferred frame of reference. I have no problem with a preferred frame of reference conceptually but still struggling.

I am focusing on MMX at the moment. I think, unfortunately, time dilation is not enough, you do need length contraction. Which means you have half the lorentz transform (from stationary to moving). It is the reciprocity of the lorentz transform that is problematic (for me) at a conceptual level and leads to a funky definition of time and space.

As an aside, not sure what you meant by "unidirectionality of time". Yes, there is unidirectionality but that is not part of SR, you have "contraction" not reversal (at this stage).