# The Pugilistic Albert - Round 2

1. Apr 13, 2004

### OneEye

In Section VIII of Relativity (On the Idea of Time in Physics), Dr. Einstein proposes a thought-experiment in which "Lightning has struck the rails on our railway embankment at two places A and B far distant from each other." He then goes on to show that the two lightning strikes may be regarded as simultaneous or asynchronous depending on one's frame of reference - hence opening the door to a new understanding of time as relative to the frame of reference of the observer.

All very well and good. But can we not use this idea to construct an experiment?

Substitute firecrackers in carriages on the train for lightning strikes on the embankment. One explosion occurs many cars "forward", the other many cars "backward." An observer on the train is centered between the explosions. An observer on the embankment would see the explosions as simultaneous, but...

With respect to the on-train observer: Scorches on the carriage floors tell us that the firecrackers were equidistant from the observer. Light from the two flashes tells us that the events were not simultaneous, in accordance with the discussion in Section VIII. But despite the asynchronous flashes, the reports of the two firecrackers will arrive at the observer's position at the same time, telling the observer that the explosions were simultaneous. Right?

I would expect that the comparison of simultaneity of any two events using light and sound would yield measurable discrepancies precisely because light travels independently from the frame of reference of the observer, but sound travels in the frame of reference of the atmosphere.

This means that an experiment could be constructed which would provide strong validation of SR using the simultaneity discrepancy between light-based and sound-based observations.

Does anyone know of any such experiments?

2. Apr 13, 2004

### ahrkron

Staff Emeritus
How do you expect to transmit the "reports" of the two firecrackers?

3. Apr 13, 2004

### Staff: Mentor

I honestly don't see the point of this: its trivially simple. We're so far beyond the need for such an experiment there is no point to doing it.

Calling it a "simultaneity discrepancy" implies its still an open question. It isn't.

4. Apr 13, 2004

### OneEye

Sorry about that - I used the language off of the firecracker packages - "Emits showers of sparks with report."

I meant, "Bang."

We thus have two metrics: One is visual, optic, the result of light-based measurements which are subject to time and length distortion. The second is audible, sonic, and occurs within the frame of reference of the train car - so is not subject to Lorentz transformations.

The discrepancy between the two - if it can be measured (and I think it probable) - will then provide an excellent affirmation of SR.

5. Apr 13, 2004

### OneEye

...certainly not my intention to appear dubious or critical.

Perhaps you can suggest more palatable terminology. By "simultaneity discrepancy," I meant only that there should be a measurable difference between the optic and sonic measurements of simultaneity. I did not mean to imply any disagreement with SR. As you see, this proposal is intended to affirm SR, not to attack it.

As to the point of the experiment: Well, perhaps there is a MSc candidate in need of a thesis?

(But I find the concept exciting!)

Last edited by a moderator: Apr 13, 2004
6. Apr 13, 2004

### Staff: Mentor

As a practical matter, I doubt the speed of sound can be measured to anywhere near the precision necessary to show an SR related measurement difference.

7. Apr 13, 2004

### turin

OneEye,
I think you should re-read the section in Relativity on simultaneity. Try to abandon as much as you think you know about common sense. It seems as though you are falling victim to the most common misconception in SR, inevitable stubborn (I don't mean this in a condescending manner) adherence to the idea of absolute time. The relativity of simultaneity is not due to any kind of delay in the signals. It seems that way at first, because you are probably still thinking in terms of Galilean transformations. But, here's where SR starts to get interesting. Instead of considering the light signals to be fundamentally anisotropic, the "now" line actually gets tilted to accomodate Einstein's postulate that c is the same regardless of the inertial frame in which it is considered.

You admit that the light from the flashes will not arrive at the observer at the same time. But you also admit that The flashes originated from equidistant points from the observer. Since the light from each flash traveled at c to the observer, then the explosions themselves must have happened asynchronously. This could be verified by timers on the fire crackers if you like. The reports, then, also must have been emitted at different times and thus will arrive at the observer asynchronously.

Your assumption that the sound from both fire crackers arrives simultaneously at the observer is not in accord with the relativity of simultaneity.

Last edited: Apr 13, 2004
8. Apr 13, 2004

### OneEye

Quite right. Train carriages and fireworks are clearly not the right sort of apparatus for experimentation.

This sort of thing is usually done using interference principles, I gather. I was imagining the idea that a standing wave could be created using sonic emissions, and that a similar wave could perhaps be constructed with lasers at the same time. (I am noodling, off the top of my head.) It seems to me that, if constructed properly, a cusp of the standing sonic wave should be centered between the emitters, while the cusp(s) of the standing light wave should be off-center. I think. This is almost completely off-the-cuff, and pretty much fact-free. I am not used to constructing experiments along these lines.

What is important is that the sound emissions should occur within an inertial frame, but the light emissions should come from outside that inertial frame. Thinking along these lines, I now begin to doubt that the firecracker experiment would necessarily demonstrate what I imagined it would. Not sure - and I could sure use some expert guidance.

9. Apr 13, 2004

### OneEye

Yes, you are completely right. It is so difficult to get out of the prejudice of K0. It should come as no surprise that all of my progress in considering relativity has been along exactly this line.

This is exactly the question I am asking. Rather than assuming, I am working from this angle: Light operates independently from the frame of reference of the observer, and so obliges us to perform the Lorentz transform between inertial frames of reference. Sound (operating within an inertial fram), however, does not. So (as far as I can tell), SR predicts a simulaneity discrepancy between sound and light effects. (Sorry if "simultaneity discrepancy" sounds like an attack on SR - it's not - it's just the most concise phrase I have on hand. Alternative suggestions are welcome.) This may only be the case when the light originates from outside the frame of reference and the sound from within - I am not sure on this - but I think the general concept is valid, and supported by SR.

What I have found most helpful is to consider measurements of distance and time as Dr. Einstein suggests - by successive applications of a meter rod, and by the observed ticks of a clock. This sort of consideration has led me to this particular possibility.

Any insight that you could provide on this would be most helpful.

10. Apr 14, 2004

### outandbeyond2004

OneEye, I am sorry, but I think thought experiments involving sounds of low velocity (<< c) are practically and theoretically a waste of time. What could they prove? What insights into nature could they lead to? I think it is true that if the fireworks happened to be equidistant to the observer in the train (as measurement to the sorch marks would show afterwards), then the sounds would indeed arrive simultaneously at his ears. So what? If someone did an actual experiment and found different arrival times, that would not overthrow SR. Scientists would simply look for whatever caused the discrepancy.

11. Apr 14, 2004

### OneEye

Well, the point is not to overthrow SR. It is to validate and extend SR.

The idea here is that the sound/light simultaneity discrepancy substantiates SR - since the sound occurs within the inertial reference frame, and is not subject to the dilatory effects of the Lorentz Transform, while the light signal is inherently unattached to the reference frame, and so is subject to dilation.

(Mind you, it is altogether uncertain that such a discrepancy exists. turin, e.g., is convinced that it doesn't, and we have yet to come to the fulcrum upon which that disagreement turns.)

But, consider what this would imply if such a discrepancy does exist: If adequate measurements could be made, it would be possible to validate the two events as both simultaneous and non-simultaneous in the same frame - and would also allow us to derive in what frame the events were simultaneous, both visually and sonically.

To the average student of SR, these are both odious concepts. First, the idea that two different measurements in the same frame would provide two different views of simultaneity is quite annoying.

Second, the opportunity afforded to appeal to a frame in which optical/sonic simultaneity occurs smacks suspiciously of one frame being "specially favoured" over another - not the sort of thing which relativity encourages.

Still, one wonders whether such an outcome is possible...

12. Apr 14, 2004

### turin

The above statement is a little ambiguous. Light operates? Light travels, yes, and it does so at a speed c regardless of the inertial frame (assuming the validity of SR, as it is clear to me you do for the sake of argument). Light also interacts with matter, delivering work and impulse by virtue of its wavelength and frequency. These two properties are not independent of the frame of reference, so please try to be more precise. What do you mean by "operates?" I suppose I could venture a guess based on the following:
From this I would infer your consideration of the speed.

If it were not for the parenthetical, I would agree with you. However, the inclusion of the parenthetical renders this statement either inconsistent or vacuous. If you're going to talk about some transformation property, then you cannot restrict yourself to a single frame. Alternatively, restricting the consideration of the behavior of sound to a single frame trivially disallows the behavior that you have specified for light in the previous sentence.

Effects geneally do not occur at the same point in 3-D space, but I will assume for the sake of argument that you not only intend consideration of the simultaneity of two effects, but rather their full-blown coincidence. For this purpose, you do not need SR to tell you that light effects and sound effects will have a coincidence discrepancy. I will even extend further your statement to infer that you intended the luminous and sonic causes to be simultaneous in the Galilean sense (that is, my following appeal completely ignores any SR induced consequences, and you have only to accept the principle of relativity in the restricted sense). Then, there will be a coincidence discrepancy of the two effects in general, provided that the sonic medium does not have a motional accord with the frame of reference.

SR actually predicts a simultaneity discrepancy between the causes from one frame to another for the exact same signal, be it luminous, sonic, or what have you. That is something I think you may be missing in your assessment of the issue of the relativity of simultaneity.

Again, this is ambiguous. In the SR context (in which I suggest we remain for the time being), every inertial frame has an infinite extension, and so, light that originates in any given frame originates in every frame without exclusion. The concept of origination outside a frame is not supported, and is in fact meaningless in the SR context.

In light of your more recent posting, I now feel obliged to point out some ambiguities that I took for granted upon first reading of your initial post.
You say "see." I would suggest to use the term "observe." Though this can be just as semantically ambiguous, in the SR context, it implies an intelligent acquisition of data, that is, one that realizes a signal delay and therefore accounts for it. Then, if the embankment observer observes a simultaneity, this will indicate a simultaneity of the cause. This could be achieved, for instance, by the firecrackers being triggered by contact with ignition mechanisms on the embankment that had been appropriately separated at the calculated distance of the firecrackers.

I think you may be subconsciously abusing the concept of "event." In the case of a light signal, the abuse can be inadvertantly overlooked, since the light signal experiences no proper time. But if you wish to consider sound alongside light, you must appreciate the concept. An event is an occurance at a particular point in 3-D space at a particular time. There are events that represent these flashes. There are distinct events that represent the reception of light from these flashes. Neither the set of two flashes nor the set of two receptions is coincident, but there is a fundamental difference between their characteristic separation.

The two flash events have a space-like separation. The two reception events have a time-like separation. These specifications are manifestations of an absolute causal structure in SR. Let's examine the implications one step further to get an idea of how this structure applies to your light flash example.

The reception events have an absolute order. That is, both the train observer and the embankment observer will agree on which signal was received firstly and which signal was received secondly, even though they will in general disagree on the time and distance between receptions. This is why they are said to have time-like separation.

Regarding the events of the flashes themselves, both train and embankment observers will agree that neither flash event could have possibly caused the other. That is, the events are said to be causally, or space-like, separated.

This absolutely divides the space around some given origin into three distinct, and unambiguously characterizable regions: the past cone, the future cone, and the conditional present. I'm sure that you will encounter these concepts soon in your reading, so, unless there are any questions, I will defer the elaboration to the literature. I have briefly mentioned this causal structure because I think it might be part of your underlying misunderstanding.

Last edited: Apr 14, 2004
13. Apr 14, 2004

### OneEye

turin,

I appreciate your investment of time in this consideration. To be honest, I am not sure where you are going, nor how this really impacts the question under consideration. But, I will give your writing a little more consideration. I still feel that the momentum of the air in the carriage produces a different sonic concept of simultaneity than that produced by observation of light signals. And, I think that this could be important to SR and, especially, to some of the philosophical ramifications of SR. And, as you point out, I am assuming SR to be correct (and have no good reason not to), and am working within this context.

As far as event cones - yes, I came across that concept in Dr. Hawking's A Brief History of Time about ten years ago - and I see how Dr. Einstein initiates the concept in his discussion of Minkowski space. (In fact, I am shocked at how close Minkowski space is to Hawking's i-time - so much so that I fail to grasp the distinction. And, indeed, based on A Brief History of Time, I had the impression that Dr. Hawking was the one who invented the "finite, unbounded" cosmology. Now, reading Relativity, I see a surprising amount of correspondence between these two books. But all that is beside the point.)

Anyway, thank you again for your time. I will contemplate your writings further.

14. Apr 15, 2004

### turin

I appologize. I did ramble a bit, didn't I. I was trying to address what I am only assuming to be the source of your misconception from as many angles as I could imagine. I suppose I should also appologize for assuming your misconception. It's just that, when approaching SR, misconceptions can run deep. They usually result in subtle epistemic distinctions (i.e. the simultaneity of detection), but are based on dramatic ontological differences (i.e. the difference between the SR event and the Galilean occurance). I was operating under the impression that you are probably not aware of your own misconceptions, and so, it would be futile to probe you directly for them.

Herein lies what I believe is your misconception. The relativity of simultaneity in SR is not posited as an epistemic process. The events exist independently of the signals they produce. In fact, in this example, the event of a firecracker explosion (let us approximate this as an event) produces at least two totally different signals, light and sound, that eventually reach the observer. It is not the reception of either of these signals that determines its temporal relationship to any other event as observed by the train observer. The exact same temporal relationship, that is order and time ellapsed between explosions, would be determined by the train observer even if he/she were sitting right next to one of the two firecrackers as it exploded. Of course, if the observer is sitting next to the aft firecracker, then the received signals of both the flash and report would be those for that firecracker. This does not violate the position that the other event did, in fact, occur previously in this reference frame. The train observer has but to make a simple delay calculation and then measure the distance to the fore explosion to realize that it must have happened before the aft. The relativity of simultaneity is not a result of signal delay (in the strictest sense), not even that of light. I appologize in advance for my presumption, but I am assuming that this is your misconception.

I have never read this Hawking book, but I am assuming that you refer to the concept of what I have heard people call "ict space." This concept is an attempt to comfort the reader when they consider the concept of proper distance by allowing the use of their familiar Pathagorean Theorem. You should be aware, if you would like to consider Minkowski space-time, that the Pathagorean Theorem is a geometrical construct that does not apply in general, but only in Euclidean space, and Minkowski space-time is not Euclidean. The more general concept of a metric is used, which obviates the Pathagorean theorem, when one advances to the consideration of Minkowski space-time.

I don't know anything about that.

Last edited: Apr 15, 2004
15. Apr 15, 2004

### OneEye

No offense taken - please don't think of me as complaining. As you say, you covered a great deal of ground, and so it took me some time to really assimilate all that you said (assuming I have assimilated it).

I don't think that this is the root of our disconcert. Whether velocity-related time-space distortion is to be considered epistemic or ontologic is a highly dubious question. Everyone agrees, I think, that without some proof to the contrary, we should assume that the epistemic propositions are indeed ontologic - and this is where any contemplation of SR must begin (and where most contemplations end). We can probably have a grand go-round over this, but it's probably off-topic for this forum - for now, at least - falling more into the "Philosophy" category.

Yes, well, if I'm understanding you properly, then no, I am not presuming that the relativity of simultaneity is the result of signal delay. It is, as we both agree, the result of relativistic transformations of the measurements of distance and time, mediated by the relative velocity of differing inertial frames. I hope that I have expressed this in a way which we both find agreeable and thorough.

But here is my point: Light and sound behave differently in this regard: The Lorentz transform applies to measurements between two inertial reference frames; since the sound measurement occurs within a reference frame (sort of; not quite, but immeasurably close to Newtonian), then the two measurements of simultaneity should produce different results. Which, to my mind, is really interesting, and which reflects on the ontologic/epistemic question.

...as expressed and considered in relation to our one concrete model of space-time (the universe, that is ). However, I am fairly sure that you could envision a Minkowski space-time which was Euclidean - mathematically, I mean, though (probably?) not in relation to the actual universe.

Hmmm. Wouldn't it be more like $$c=\sqrt { g_{11}a^2 + 2g_{12}ab + g_{22}b^2 }$$? (I cheated and looked back at the book. Sorry.)

16. Apr 15, 2004

### turin

Well, I suppose I should be more specific. Of course, it is a trivial issue to suggest the ontology of SR within the theory itself. I meant to separate what SR takes to be epistemic from what it takes to be ontological. SR posits the events as ontological and the observation of the events as epistemic (that is, the details of the observation depend on the state of the observer, but the observation of the events themselves represents an ontology).

Yes, I understand your diversion. The termonology suggests a philosophical consideration. That was not my intent. Merely identification. Neither one of us wants to argue the validity of SR (not in this thread at any rate).

I think I know what you mean: the Lorentz transformation from one frame to another "takes the measurement with it." That is, it allows one to consider what a measurement would be in a different inertial frame. The phrase "measurements between frames" makes me uneasy.

I'm not following your logic. All measurements take place in some reference frame. If we consider the train frame, then the reception of both the sound and light signals occurs in the train frame. By "measurement of simultaneity," I'm assuming you simply mean a determination of whether or not the events were simultaneous in the frame of reference in which the determination is made, and, if not, which event occured firstly.

If the observer uses the light signals to make the determination, then he/she will find that the signals are not simultaneous; the fore signal arrives before the aft, and, since they had equal path distances, they required equal times of flight. No problem.

However, the same result will obtain if the determination is made from the sound signals. I am a little confused how you think the sound signals could arrive simultaneously. They have equal distances to travel, and therefore equal times of flight. Since the fore explosion occurs firstly, it follows that the sound signal from the fore explosion should be received firstly.

I don't see how this is possible. Though the construction and definition of Minkowski space-time was motivated by our physical universe, it is mathematically defined as having a non-Euclidean geometry. It has a Euclidean topology, but that does not allow us (without ambiguity) the physical objects we wish to discuss, such as distance and simultaneity. Once we endow the topolgy of space-time with an ict (and its specific purpose of defining an axis) or an ημν (and its specific purpose of defining a metrical relationship), we realize that the geometry is not Euclidean (in any way that I can see). Are you suggesting that math itself depends on our universe? I don't know how to think about that, but, for sure, this qualifies as a topic for the philosophy forum.

This looks like the metric for string theory (sort of). The Minkowski metric in Cartesian coordinates looks like this:

(ds)2 = ημνdxμdxν
= c2dt2 - dx2 - dy2 - dz2

whereas the Metric for a 4-D Euclidean geometry in Cartesian coordinates looks like this:

(dl)2 = δμνdxμdxν
= dw2 + dx2 + dy2 + dz2

You can see the basic similarities (the form of the definition), but the object ημν is different than the object δμν. This is precisely what makes the latter definition indicative of Euclidean 4-space and the former indicative of Minkowski space-time.

Last edited: Apr 15, 2004
17. Apr 15, 2004

### OneEye

Recapitulation

Thank you again for your kind and more-than-competent investment of time.

I think that we may be (pardon the pun) somewhat off-track. So, with your permission, I would like to offer a restatement of the thought experiment which may, perhaps offer some elucidation of this question:

A train travels on a track at significant fraction of the speed of light. An observer on a bridge, who happens to have set up a 90o mirror apparatus which allows him to see up-track and down-track simultaneously, oversees the train. Lightning strikes the track in two places along the track, passing through two of the carriages on the way to the ground . The two strike points are equidistant to the observer on the bridge - one up-track (in the direction of the train's motion relative to the bridge), the other down-track. Another observer on the train happens to have an identical mirror apparatus set up in the aisle. As a further condition of the experiment, let us stipulate that the two lightning flashes appear simultaneous to the observer on the bridge.

Let us now consider what the two observers experience. First, as specified, the observer on the bridge sees the flashes as equidistant and simultaneous. If he is alacritous, he also notices that the thunderclaps of both lightning strikes occur simultaneously. Finally, a later examination of the embankment shows that the two lightning strikes were equidistant. So, then, our observer on the bridge correctly concludes that the two lightning flashes were simultaneous.

In the train carriage, it is a different story. The two lightning flashes in the observation device appear asynchronous, the forward flash preceeding the aft flash. Were our observer able to measure the apparent distance from his seat to both flashes, he would think that the forward flash occurred much closer than the aft flash. This much is the product of the Lorentz transform, and after contemplating special relativity, it is clear that such a conclusion is the only sensible one.

Which observer has the correct observations? Well, unless we are able to claim the existence of some reference system K0 which is at rest "really," then we must say that both observations are equally correct. But a distinction exists.

The bridge observer's auditory observations corroborate his visual observations: The flashes were equidistant and simultaneous. But sound - which travels at a relatively slow velocity in the medium of the carriage's air, and which occurs completely within the carriage's frame of reference, and is thus not subject to adjustment via the Lorentz transform - will report for the carriage observer what it did for the bridge observer: That the lightning flashes were simultaneous. And, the scorch marks on the carriage floor will show that the lightning bolts were equidistant.

In order to say otherwise, we would have to say that the speed of the sound waves from the lightning bolts are subject to the Lorentz transform with respect to the observer in the carriage, and that the distances between the carriage observer and the scorch marks are also subject to the Lorentz transform. But since these physical phenomena occur completely within the context of the frame of reference of the train, such an application of the Lorentz transform would be novel - or so it seems to me.

Now, I have laid out the case as clearly as I can think to. But I am willing to go further to clarify the matter. And, perhaps it is time to begin to put a mathematical framework around these thoughts. In any case, please don't hestitate to query or critique. You are certainly helping.

P.S. As I reread this prior to posting it, I conceived a critique of the above which may dismantle my case. But please don't hesitate to respond, in any case. And again, thank you for your investment.

18. Apr 16, 2004

### turin

Perhaps this is not the critique you were expecting, but I see that you have now more nakedly exposed the inconsistency that I suspected. A few nitpicks which I am afraid cannot be avoided in order to avoid ambiguity:

1) The 90o mirror apparatus was good to consider, qualifying light as a signal to be received and giving a specific mechanism for doing so, but I suggest that we not worry about such details at this point. As a matter of fact, you would leave fewer holes in your gedanken experiment were you to use sound and light sensors themselves, oriented appropriately, with synchronized registers. Bottom line, we may take the ability to receive any given signal of any type as moot.

2) When you stipulate the appearance of simultaneity, do you intend a simultaneous reception of the signal at the observer, or do you intend a simultaneous generation of the signal at the sources of interest which can be calculated by the observer? How do you propose that the observer on the embankment can see the distance to the two flashes?

3) Thunderclaps have an extremely blurred temporal envelope. Let us assume that, instead of thunderclaps, the actual striking of the train/embankment generates the distinct sound to be considered in the experiment.

4) This is in response to your 6th paragraph. An observation and a reception are different. You don't even need SR to give you that result. For instance, I could be doing a card trick for someone. They are allowed to see the face of the card, I merely observe from careful calculation and arrangement that it is the same card that they see it to be, even thought I see only the intricate red pattern of the cyclist. Both observers made the same observations, that is, two events in space-time.

5) I am assuming two distinct regions of air. One is the air that is at rest wrt the embankment. This is the air through which the sound travels to the embankment observer. This region is all of space (for the practical purposes of the experiment) with the exlusion of the train carriages. Then, there is a sharp/abrupt schism between the regions. The other is the air that is at rest wrt the train. This is the air through which the sound travels to the train observer. This region fills the inside of the carriages. It moves with the train.

THE MAJOR INCONSISTENCY:
You say:
, but then:
This is an inconsistency in SR. I suppose I should ask: how does the train observer "measure ... apparent distance?" What is the difference between apparent and actual distance?

My conclusion is that you do not understand the Lorentz transformations.
This is not the case. The Lorentz transforms will not change the relative distance of the observer to the two flashes. The distances will contract by the same factor, and will therefore remain equidistant regardless of the trains speed. Or, conversely, as the original declaration was that the fore strike was closer than the aft strike, the scorch marks cannot be equidistant. Also, if the fore strike was closer than the aft, then the sound would have required less time to arrive from the fore, and so this must be taken into consideration.

Last edited: Apr 16, 2004
19. Apr 16, 2004

### OneEye

Well, I think that we are getting somewhere. You have all along contended that sound measurements ought to be synchronous with light measurements. Now, we have an apparatus for considering this - one to which we can apply mathematical rigor.

One note up front:

This is what you have been contending all along. Let us examine this model together and see if we can conclude whether this is the case or not. (Of course, in the end, only experiment will conclude the matter, but I would like us to at least understand the two alternative views as far as this model is concerned.)

But if you will permit me, I would like to deal with a few of your minor points, and then tackle the major question in a follow-up to the thread.

Sorry. That's one of Dr. Einstein's inventions (Relativity, 22). I borrowed it more for whimsy's sake than for necessity. It is of course obvious that much more sophisticated measuring devices exist today.

Incisive question! We are both completely agreed, I think, that simultaneity, being completely relative, must be judged primarily by reception (epistemic) rather than generation (ontologic). We may choose to project our observations into some other reference frame in order to decide whether events were simultaneous in that reference frame, but this is not the primary approach we would take.

I didn't really try to address this. One wants to use parallax, say, or possibly something more subtle, measuring the time difference between two staggered light sensors and then triangulating. Obviously, this is a challenging experiment - but not outside the ken of modern science - and some crafty method could be found. Whatever the case, I hope that we will not bog down in minutiae of experimental details. (I know, I know, I started it. But I'm not really attached to Dr. Einstein's mirrors. Just adding some color, á la Doctor Einstein.) Obviously, a real experimental construction would use neither trains nor lightning bolts.

Yes. Important. This helps the thought-experiment along tremendously. In fact, without it, the experiment is lost (I think).

I mean, measure the distance using light (rather than pacing it out with a tape measure.)

And here is the point at issue. I consider the possibility that we may be able conclude otherwise. But I will have to post this a little later - time does not permit right now. Pardon this diversion please. But please allow me to add two seed thoughts:

1) Consider the instantaneous "snapshot" of the moment of the lightning strike. Assume that the cars are ten meters long, and the strike occurs in the middle of cars (say) 50 and 60, that the trainbound observer sits in the middle of car 55, and that the train is travelling at (say) .5c. What distances would the bridge observer measure (a) between the strikes on the embankment; (b) between the strikes on the train? (For this thought experiment, we assign that lightning strikes occur at the speed of light. We know otherwise, of course, but the fact that it is a lightning strike is immaterial to the question.)

2) "If in place of the law of tranformation of light we had taken as our basis the tacit assumptions of the older mechanics as to the absolute character of times and lengths, then instead of the above we should have obtained the following equations:

$$x^\prime=x-v$$
$$y^\prime=y$$
$$z^\prime=z$$
$$t^\prime=t$$​

This system of equations is often termed the "Galilei transformation." The Galilei transformaion can be obtained from the Lorentz transformation by substituting an infinitely large value for the velocity of light c in the latter transformation." (Einstein, Relativity, 33.)

By the way, I am starting to think that you have the correct view. But that will have to wait for my next post.

20. Apr 16, 2004

### OneEye

One more seed thought

With your indulgence, one more seed thought ought to be added to this contemplation:

This piece of reasoning from Dr. Einstein forms a large part of the basis for the thought experiment I am here explaining.