To what extent are the "strange" features of Relativity Theory due to the latency of light?

November 23, 2011 10:41 AM

Which of the "strange" features of Relativity Theory can be accounted for by appeal to the latency of light, which cannot, and why?

By "latency" I mean the fact that light travels at a finite speed and therefore observations have to wait around for the light to arrive, at which point the observations are of the past.

Some of the standard "paradoxes" include the pole and the barn, the twins, and the fact that light appears to travel at light speed regardless of how fast one is moving with respect to it.

My question is: which aspects of such "paradoxes" can be accounted for by appeal to the latency of light, which cannot, and why?

posted by Eiwalker to Science & Nature (21 answers total)

Response by poster: I should have said, "regardless of one's velocity with respect to it".
posted by Eiwalker at 11:04 AM on November 23, 2011

Almost none of them, if I understand you right. On way to think of it is that Sound has a finite speed and whatever we "hear" was emitted at some point in the past. Yet this doesn't give rise to the same paradoxes. I could theoretically outrun a sound wave. Many airplanes do. (Note: Don't bring up Cerenkov radiation unless you understand phase velocity)

The two basic axioms of Relativity are that 1) Light is Finite and also is the same speed for everyone everywhere and 2) There is no privileged observer. Combine those two axioms and then you get the paradoxes.
posted by vacapinta at 11:14 AM on November 23, 2011 [1 favorite]

There, what vacapinta said.

The paradoxes only point out how we live in a world (the low-energy, far-from-light-speed one) where nothing in our experience and understanding makes the limit of c comprehensible to us.

They are paradoxes due to our myopic world-view of physics, if you will.
posted by IAmBroom at 11:38 AM on November 23, 2011

Response by poster: Thank you for the comments so far, but I realize that I should fine-tune by question in at least three ways.

I had asked to what extent any of it was due MERELY to the latency. That was a mistake, as part of my question has to do with some disanalogies between light and sound.

For instance, (a) nothing is faster than light; and (b) unlike a sound wave, which propagate in all directions from the source, light has a particle aspect, and probably also (c) that speed is distance over time, distance is speed times time, and that distance is itself defined partly in terms of light's speed.

Note that I'm still ignoring the second postulate, that there is no privileged observer, as basically I'm curious to what extent that is being derived from the other postulate.

So now, if you will, imagine something like this: a world where nothing is faster than sound, and where sound has a particle aspect, and where sound's speed is itself calculated by judging its distance divided by its time of travel, and where distance itself is defined partly in terms of sound's speed. Does this change anything?

Thanks.
posted by Eiwalker at 11:44 AM on November 23, 2011

The fact that light has a particle aspect has nothing to do with relativity. When Einstein came up with the formalism for special relativity, he was just using the equations of electro-magnetism which described light as a wave.

Sound waves are quantized as well.

Sorry if this sounds harsh, but your entire premise is wrong.
posted by aroberge at 12:50 PM on November 23, 2011

Eiwalker,
OK, some misconceptions here. The particle/wave duality of light (and the rest of the world, actually) has nothing to do with relativity. Indeed, special and general relativity have real problems being combined with quantum mechanics, so nothing about quantum mechanics can really inform the basics of relativity that you're asking about (though of course we've made progress since Einstein's day and can combine the two in limited areas). Also, sound can be thought of as a particle: the fundamental components are called "phonons." They're just not terribly useful outside of solid state physics.

Second, the distance and time are not in principle defined in terms of light. Practically of course, we often do that, but you could also imagine doing those measurements with, say, a ruler. It's just that the measurements you make will be different depending on the frame you're in (so you have to use a ruler/clock in your frame). That is, the differences in distance/time due to the different frames are not a trick due to the time it takes for light to propagate, but real differences due to fact that the measurements are in different frames. In the thought experiments, you can imagine filling space/time with little tick marks that tell you location and time. Making the different observations agree is a function of the finite propagation of light though; for example, in the twin paradox, the way that the two twins get to see the other age the correct amount is that the light leaving the twin who stayed behind catches up nearly all at once during the time that traveling twin accelerates to return to Earth.

Sorry I can't explain in more detail right now - I have some other things I need to do, so it's unlikely I'll be able to drop back into the thread, but suffice to say that the finite travel time of light is a way to make the observations synch up, but not in general the source of the "paradox" itself.
posted by physicsmatt at 12:52 PM on November 23, 2011

I'm still ignoring the second postulate, that there is no privileged observer, as basically I'm curious to what extent that is being derived from the other postulate.

The lack of a privileged/special frame is key; without it there would be no relativity. (Hence the name…) It's also not a postulate, it's an observation.

I find that one of the best ways to understand a physical theory is to read up on its early development. Probably any question you can think of will have been raised at the time, and answered in detail. Before relativity, light was assumed to act like a sound wave (with a probably-constant speed through some medium, called the luminiferous ether for lack of a better name) or like a particle (speed dependent on the motion of whatever emitted it). Many experiments were done to try to learn more about the ether, with the Michaelson-Morely experiment being the most famous, and utterly failing to detect an ether. Ether-based theories had to become more and more baroque in order to fit the observations; special relativity, by contrast, is fairly simple and even kind of intuitive, once you accept the lack of absolute simultaniety in the universe. Earlier generations had to accept that Newtonian mechanics threw out the notion of absolute stillness. For relativity we had throw out universal time.

that speed is distance over time, distance is speed times time, and that distance is itself defined partly in terms of light's speed.

The last part— where distance is defined in terms of light speed— does definitely smell kind of like circular reasoning, but i's really a modern definition intended to make use of the discovery that light speed is a physical constant. The development of special relativity doesn't depend on that definition at all. The usual thought experiment is to imagine space filled with a lattice of rigid measuring sticks and clocks, and sending light pulses or physical objects here and there, and making only local observations (e.g., "when the light pulse passes this clock, what time does the clock read?"). This lets you reason about the implications of relativity without having to pre-assume certain things about the nature of space or time.
posted by hattifattener at 1:51 PM on November 23, 2011

Response by poster: Big thanks for the responses so far! But I still have some lingering questions:

1. Pole and barn. If you're the guy running with the pole, why exactly does the barn seem so short? GR just implies that it will, but doesn't explain why. Any ideas on why? Maybe there's no way to know, but I'm just throwing it out there that I'm curious about it.

2. I'm under the understanding that quantum mechanics is consistent with the "growing block universe" theory of time, in such a way where the entire universe might grow (temporally) by inching along discretely, one Planck length at a time. If this might be the case (for all we know), then (for all we know) it might be that the relativity of simultaneity is at best a limitation on our observational capabilities, not a deeper truth.

It is because of the second consideration that I'm curious about why relativity seems true, and wondering to what extent it might have to do with peculiar properties of light. In fact, as a photographer, I have another question:

3. How are the light measurements to be performed?

Now both physicsmatt and hattifattener have mentioned the idea of imagining space-time as being filled with measurement devices. I'm not clear on this though. Suppose I'm the guy running with the pole towards the barn, and the barn looks too small to fit the pole. How am I measuring the barn in such a way that it looks so small? We could let the pole be my measuring stick, but we'd still have to compare the pole next to the barn doors. How are we going to do the comparison? Presumably by using light. What kind of photographic camera will suffice to perform this measurement? Particularly, what will be camera's shutter speed (how long will the sensor be recording data?), what will be the focal length and aperture of the lens, and how large will the lens and sensor be?

Now perhaps I'm totally off-track in thinking that there would have to be a camera, but if I'm wrong about that, then how will the measurement be performed? For instance, should I be imagining that there's a huge sensor that's infinitely wide and thin going the same direction as the man with the pole, and that each section of the pole has its own infinitely wide/thin sensor? If so, doesn't that make the measurement into something make-believe which has no real world consequences? Haha, I have no idea about #3.
posted by Eiwalker at 3:08 PM on November 23, 2011

The pole+barn "paradox" illustrates the fact that observers in different reference frames have different notions of simultaniety. (This is just like how, in Newtonian mechanics, observers in different reference frames— on a train vs. on a platform, say— have different notions of "the same place".) From the barn's point of view, the pole is shortened and fits in the barn with both doors shut. From the pole's point of view, it's the barn that's foreshortened— so clearly the pole won't fit inside— but from the pole's point of view the doors aren't shut at the same time. The leading end of the pole enters, the exit door shuts briefly then opens to let it out; the pole moves through for a while; once the trailing end of the pole enters, the entrance door shuts briefly behind it.

How am I measuring the barn in such a way that it looks so small?

If you're trying to be rigorous, you do it using only local measurements. You need to synchronize your clocks (in your reference frame). Then you note that the front edge of the barn passes by Clock A at 10:15; you find the clock which saw the back edge of the barn pass by at 10:15, and you count off the distance between them. Synchronizing your clocks is tricky, of course; I'll defer to someone else to explain that, or you could probably find some explanations online.

You could also just watch the barn pass by the clocks, from another vantage point (eg the camera); but then you have to figure out the speed-of-light delay between you and each thing you're looking at and correct for it. That's a pain. Physics books don't usually describe things that way because things will also appear foreshortened (or otherwise distorted) because of speed-of-light delays, and you want to keep that purely optical/illusory foreshortening separate in your mind from the somewhat less illusory SR shortening. (The optical effects are sometimes referred to as "aberrations"— I assume because the first places they were actually observable were in astronomy.)

I really think that quantum mechanics, wave/particle duality, the discretization of spacetime, etc., are distractions if what you're trying to understand is SR. They tend to get mixed together in pop science books because they're all Wacky Physics Things, but they're easier to understand one at a time.
posted by hattifattener at 4:14 PM on November 23, 2011

Response by poster: The "sync" problem seems pretty serious.

After all, if you go into the experiment wanting to know whether relativity is true, rather than simply presupposing it, you can't assume any of its postulates.

Pole and barn again. Suppose you put one camera on the front of the pole and one on the rear. Then if you want to sync up the cameras so that you can press one button to trigger both cameras, you'll have to make assumptions about the speed of the signal that triggers the cameras. Particularly, you might think that the signal, if starting from the middle of the pole, will reach the rear camera first. In that case the rear camera will start taking its flurry of pictures before the front camera does.

Now I have a visual way to make the point, although MetaFilter doesn't use a mono-spaced font, so I'm paranoid that this isn't going to work! Nevertheless I might as well try; I'll be trusting the live preview. Here goes: suppose each camera takes a number of pictures and the ordering goes as follows:

F: ---------ppppppDUpppppppppppp
R: ppppppppppppppDUpppp---------

Now MetaFilter doesn't allow indents or multiple spaces, so I'm using hyphens to stand in for spaces. That is, a hyphen means that a pictures was not taken. With that said, you can see here that the rear camera started firing first. But then you think they're in sync, so you go to the editing room and line them up like so:

F: ppppppDUpppppppppppp
R: ppppppppppppppDUpppp

Here I'm letting "D" stand for "down" and "U" stand for "up". Now here, if one thinks they're in sync, one will assume that the rear door (the one that the front camera is taking pictures of) went down and then up first, and only later did the front door (the one that the rear camera was taking pictures of) go down and then up. This is what relativity predicts.

However, if you think the signal might travel to the rear first, since after all the pole's rear was traveling towards the signal, whereas the pole's front was traveling away from it, you'll assume that the cameras were not in sync. You'll assume instead that the rear camera started taking its flurry of pictures first! In that case, the correct way to sync up the pictures might be the way I presented it the first time. In that line-up (if the font spacing was successful!), you can see that both cameras detected their respective doors as going down at the same time, and then back up at the same time, in which case there would be no disagreement with the observation performed from the barn's frame.

Thus it seems that the observation is itself theory-laden. If you assume relativity, you'll "sync" your cameras accordingly.

I'm no expert, though, so I expect that I'm overlooking something.
posted by Eiwalker at 6:35 PM on November 23, 2011

Response by poster: Well, the spacing only works if your screen resolution and zooming is just right. :(

Hopefully the idea shines through anyway!

Another way would be to just copy and paste what I wrote and convert it to a mono-spaced font, and then replace each string of hyphens with eight spaces.
posted by Eiwalker at 6:39 PM on November 23, 2011

Response by poster: I found a concise article on the circularity of judging light's speed as c.

I also found a video giving an alternative interpretation of the classic relativity experiments (and thought experiments). It accompanies a paper.
posted by Eiwalker at 9:22 PM on November 23, 2011

Light travels at the speed of time.
posted by blue_beetle at 9:40 PM on November 23, 2011 [1 favorite]

Response by poster: If the clock sync problem is handled in the way that is discussed in the article I cited above, this would make relativity theory unfalsifiable.

Basically, the observation would be theory-laden in the way I suggested above. For one would be reasoning circularly, by incorporating relativistic principles into the sync calculation. If you do that, any observation will seem to support relativity.
posted by Eiwalker at 10:09 PM on November 23, 2011

Look at it the way Einstein did. If you have two stationary electrons, they repel one another (which you can demonstrate with a plastic hair brush, and some foil). If you have moving electrons, they create a magnetic field (which you can demonstrate with a battery, wire and some paperclips).

OK, now we're in space. I'm sitting still relative to two electrons and I see a repulsion but measure no magnetic field. The electrons and I go zipping by you. You are going to measure a magnetic field, but (if we're going the speed of light) see no repulsion. WTF? (Well, WDB? because Einstein was German, but other than that....)

The thing is, nothing in this, and this was the puzzle that Einstein started with, has anything to do with light and, like I said, you can set up both conditions in the privacy of your own home if you want without having to personally undergo a lot of tedious time dilation.
posted by Kid Charlemagne at 12:20 AM on November 24, 2011

Special relativity is falsifiable. It leads to plenty of measurable effects (time dilation being one of them) that are measured daily from "exotic" environment such as particle physics laboratory and to less exotic such as people's car if they have GPS (the latter taking having to take into account also time dilation and other subtle effects from General Relativity). Anyone writing papers claiming that relativity is unfalsifiable a) does not understand relativity and b) is likely to be more appropriately described as a crackpot.

Theories are not simply judged on their merit on paper: they have to make predictions that can be observed in Nature. Special relativity is an extremely-well tested theory, whose predictions up until now have always been confirmed to great accuracy by experiments ... with the possible exception of the apparent faster than light neutrinos.
posted by aroberge at 8:55 AM on November 24, 2011

Response by poster: Thanks for more responses!

@ Kid Charlemagne, thanks for the EM example. However, although it's electrons and magnetic field instead of light, there is still a latency issue. You zip along with a couple of electrons that are judged in your frame of reference to be stationary, and I don't observe the magnetic field immediately, for EM radiation goes at the speed of light, so I have to wait for it to reach me before I can observe the magnetic effect. Moreover, by a definition of "frame of reference" whereby it's something you carry with you, you won't observe the magnetic effect, since to do that there would have to be a part of your frame of reference that "stays behind" to perform a measurement that would detect it.

@aroberge, everyone agrees that GR predicts observable consequences to an extremely high degree of accuracy, so everyone agrees it should be used when doing GPS calculations. Moreover, nobody questions the lab experiments and so forth. The only place where doubt creeps in is when one wants to interpret why the "weird"/"paradoxical" effects happen. Some physicists say, "that's outside the domain of physics: for physics is only concerned with observable consequences and doesn't even try to give a more fundamental explanation of the observable data". However, it seems at least as common for physicists, or those who have studied a lot of physics, to confidently answer the question by saying that it's because there really is no absolute simultaneity at the most fundamental level of reality, etc. However, I suspect that such confidence is misplaced if there are mutually incompatible interpretations of all of the observable data, where each interpretation tells a consistent story.

Happy Belated Thanksgiving, everybody!
posted by Eiwalker at 6:10 AM on November 25, 2011

Well, I guess I do fall in the category of physicists ... who confidently answer the question by saying that it's because there really is no absolute simultaneity. The fact that there are mutually incompatible interpretations of all of the observable data, where each interpretation tells a consistent story is not mysterious, once one gets rid of one's mistaken preconception and truly understand the theory, and is aware of the experimental data that is completely consistent with it. This last point is essential: I could come up with the most beautiful theory; however, if its predictions do not agree with observations, then that theory is clearly not an adequate description of nature.

Let me start by making a small detour/analogy (with the understanding that analogies are never perfect and that they should not be taken as having an absolute correspondance to that which they purport to illustrate): imagine being able to observe from space two people pointing "up" and "sideways/horizontally": someone living in Australia and someone living in North America. And imagine that both these people believe that the Earth is flat.

It should fairly easy to see, knowing that the Earth is not flat, that they will not be pointing in the same direction: the notion of "up" (or "sideways/horizontally") depends on where you are located on the Earth surface. Yet, each person will be able to interpret their locally observable data in a perfectly consistent manner, based on their local observations. For example, each will be able to describe the motion of a ball thrown up in the air and coming down due to gravity in a similar way. An outside observer will be able to reconcile the different definitions of what is "up" and come up with some mathematical equation that will explain how to transform ("up") as seen by someone in Australia as a combination of ("up", "sideways/horizontally") by someone in North America. [Yes, I am over-simplifying by describing "sideways/horizontally" as though it was only one direction... but please bear with me.]

Eventually, after making more detailed observations, both observers may realize that they agree on a new piece of information: that their notion of "down" varies slightly as they move, and that a common point (known as the position of the centre of the Earth) can be obtained by looking at where all these "down" directions intersect. With this observation, they will come to realize that the Earth is not flat, contrary to their preconception.

What special relativity teaches us is that what one observer describe as a "time" interval may be described by another person as being a different combination of a "time" interval and a "space" interval, based on their relative state of motion. What they would find that they have in common, is that they agree on common piece of information: the ratio of "distance travelled"/"time elapsed" for light, also known as the speed of light, is the same for both. Otherwise, the relative breakdown of "time component" and "space component" will be different.

Using their choice of definition for "time" and "space", they can each tell a consistent story. However, after careful analysis of the data, it becomes clear that this story precludes the possibility of having an absolute definition of simultaneity (i.e. universal, or "flat", time). It may not be clear for someone who relies on word descriptions to understand what special relativity describes, and who has a preconceived notion of the existence of absolute simultaneity. However, contrary to what people used to believe, the Earth is not flat and absolute simultaneity (i.e. "a unique, common direction to which time points") does not exist. There is no notion of a universal time: space and time do not exist as separate entities, but only as a combination known as spacetime.

The fact that Einstein was able to make this huge conceptual leap, in the absence of the data that we have today to confirm that this is the way Nature works, is truly remarkable.
posted by aroberge at 10:52 AM on November 25, 2011

Response by poster: @aroberge Thanks for the analogy! With that said, I have a couple of points in response.

First, I was unclear. When I raised the possibility that there may be "mutually incompatible interpretations of all of the observable data, where each interpretation tells a consistent story", I didn't mean to leave open the possibility that different interpretations might imply different observable consequences. Rather, the idea was that GR is true, and the different "interpretations" of why GR is true involve deeper speculation about what our universe might be like such that any observations will be in conformity with GR's predictions. Thus the question naturally arises: why choose one interpretation over another when there is, by hypothesis, no difference at the level of prediction?

Second, I don't see why the relativity of simultaneity in one sense of "simultaneity" should be inconsistent with absolute simultaneity in another sense of "simultaneity". Particularly, I don't see why GR should be inconsistent with the growing block universe theory of time. For instance, one option is that the entire universe grows (temporally) one Planck length at a time, and that local clocks tick at different rates relative to the incremental Planck length growth of the universe. This way, it may be that GR would be true, even though there would be a deep sense in which there would be absolute simultaneity (namely, to exist "now" would be to exist on the latest layer of Planck length temporal growth of the universe).

The only mental stumbling block I've been able to imagine is if someone were to reason as follows: "A and B might zip past each other. Then if A's frame of reference is privileged, B's frame of reference will have the odd property of including some things that don't exist yet". But the flaw in this reasoning is that no observations are of the present anyway, due to latency issues. Thus there's a sense in which to be observed as simultaneous in A's frame of reference consists in being in A's past to various degrees. Similarly, there's a sense in which, even though B's frame of reference is "tilted" with respect to A's, it may be that everything that is observed as simultaneous in B's frame of reference is stuff that happened in the past of both B and A, in which case it is consistent with the growing block theory of time that nothing ever observes events that haven't happened yet.
posted by Eiwalker at 10:53 PM on November 25, 2011

Hm. I think the suggestions you have for ways in which the clock synch could be wrong all amount to the introduction of a preferred frame (velocity or orientation), or that the speed of light depends on the circumstances under which it was emitted (that is, different apparently-identical beams of light might travel at different speeds, say, if the source was moving). Relativity does, indeed, fall apart if there's a preferred frame. And it's not absurd to postulate one— many pre-relativistic theories had preferred frames.

So, I encourage you to think like a scientist: specifically, a budget-squeezed scientist who needs to make every experiment count. You've got one shot at tenure / the Nobel / etc before you run out of money and have to become a beet farmer. Don't just look for an experiment you could propose that would support or falsify your theory; look for experiments that have already been done that would support or falsify your theory. The early 1900s would be a good place to look for such an experiment, since people were trying very, very hard at that time to investigate ether-based theories and to detect the preferred frames that those theories predicted.

At this point I fear this thread is just recapitulating a physics text, in random order and less well-written. I really think it would help you solidify your ideas to read some good histories of physics ca. 1890–1920, so that you know what parts of this road have already been well-trod.
posted by hattifattener at 12:56 AM on November 26, 2011

Response by poster: @ hattifattener I suspect that a privileged frame of reference is not in principle discoverable, although it doesn't follow from this (I think) that the growing block universe theory of time is false. If so, then looking at historical physics experiments would be futile. At any rate, the growing block theory clearly doesn't require ether.

Moreover I've never heard the growing block universe theory of time discussed in a historical overview. Rather, the only time I've heard it mentioned in a physics discussion is in a recent documentary on Time (see 4-6:30) where contemporary physicists Brian Cox and Fay Dowker briefly discuss it.
posted by Eiwalker at 7:07 AM on November 26, 2011