The Pugilistic Albert - Round 2

  • Thread starter OneEye
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In summary, the conversation discusses the possibility of constructing an experiment using firecrackers and a train to demonstrate the relativity of simultaneity as described in Section VIII of Relativity. However, it is pointed out that the speed of sound may not be precise enough to show a difference in measurements, and other methods such as interference principles may be more suitable. The conversation also delves into the concept of absolute time and the relativity of simultaneity, with one participant suggesting a re-reading of Section VIII to fully understand the principles. Ultimately, the conversation ends with the idea that constructing such an experiment may not be necessary and may be better suited for a thesis project.
  • #1
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?
 
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  • #2
How do you expect to transmit the "reports" of the two firecrackers?
 
  • #3
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
ahrkron said:
How do you expect to transmit the "reports" of the two firecrackers?

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
russ_watters said:
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.

...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? :rolleyes:

(But I find the concept exciting!)
 
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  • #6
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
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 accommodate 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.
 
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  • #8
russ_watters said:
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.

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

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
turin said:
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.

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.

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

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
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
outandbeyond2004 said:
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.

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
OneEye said:
Light operates independently from the frame of reference of the observer, ...
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:
OneEye said:
... and so obliges us to perform the Lorentz transform between inertial frames of reference.
From this I would infer your consideration of the speed.




OneEye said:
Sound (operating within an inertial fram), however, does not.
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.




OneEye said:
So (as far as I can tell), SR predicts a simulaneity discrepancy between sound and light effects.
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.




OneEye said:
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.
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.
OneEye said:
An observer on the embankment would see the explosions as simultaneous, ...
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.




OneEye said:
Light from the two flashes tells us that the events were not simultaneous, ...
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.
 
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  • #13
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
OneEye said:
... I am not sure where you are going, nor how this really impacts the question under consideration.
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.




OneEye said:
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.
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.




OneEye said:
... I am shocked at how close Minkowski space is to Hawking's i-time - so much so that I fail to grasp the distinction. ...
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.




OneEye said:
... 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.
I don't know anything about that.
 
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  • #15
turin said:
I appologize. I did ramble a bit, didn't I.

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).

turin said:
Herein lies what I believe is your misconception. The relativity of simultaneity in SR is not posited as an epistemic process.

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.

turin said:
The events exist independently of the signals they produce... 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 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.

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.

turin said:
...Minkowski space-time is not Euclidean...

...as expressed and considered in relation to our one concrete model of space-time (the universe, that is :smile:). 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.

turin said:
The more general concept of a metric is used, which obviates the Pathagorean theorem, when one advances to the consideration of Minkowski space-time.

Hmmm. Wouldn't it be more like [tex]c=\sqrt { g_{11}a^2 + 2g_{12}ab + g_{22}b^2 }[/tex]? (I cheated and looked back at the book. Sorry.)
 
  • #16
OneEye said:
Whether ... 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 ...
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).




OneEye said:
We can probably have a grand go-round over this, but it's ... falling more into the "Philosophy" category.
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).




OneEye said:
The Lorentz transform applies to measurements between two inertial reference frames; ...
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.




OneEye said:
... 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.
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 occurred 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.




OneEye said:
... 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.
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.




OneEye said:
Wouldn't it be more like [tex]c=\sqrt { g_{11}a^2 + 2g_{12}ab + g_{22}b^2 }[/tex]?
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.
 
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  • #17
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
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:
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.
, but then:
... the scorch marks on the carriage floor will show that the lightning bolts were equidistant.
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.
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, ...
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.
 
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  • #19
turin said:
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:

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:

turin said:
My conclusion is that you do not understand the Lorentz transformations... 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.

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.

turin said:
1) The 90o mirror apparatus was good to consider... but I suggest that we not worry about such details at this point.

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.

turin said:
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?

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.

turin said:
How do you propose that the observer on the embankment can see the distance to the two flashes?

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.

turin said:
5) I am assuming two distinct regions of air.

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

turin said:
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?

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

turin said:
THE MAJOR INCONSISTENCY:
My conclusion is that you do not understand the Lorentz transformations... 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.

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 traveling 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:

[tex]x^\prime=x-v[/tex]
[tex]y^\prime=y[/tex]
[tex]z^\prime=z[/tex]
[tex]t^\prime=t[/tex]​

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
One more seed thought

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

Relativity, p. 26
If an observer sitting in the position M' in the train did not possesses [his] velocity [relative to the embankment], then he would remain permanently at rest at [midpoint] M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e., they would meet just where he is situated. Now in reality (considered with reference to the embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).

This piece of reasoning from Dr. Einstein forms a large part of the basis for the thought experiment I am here explaining.
 
  • #21
You have all along contended that sound measurements ought to be synchronous with light measurements.
It seems we have suffered a grave miscommunication on this issue. It was never my intent to hold such a contention. These two types of measurements suffer drastically different delay times from the generation of the respective signals. It would have been absurd for me to declare that sound and light measurements ought to be synchronous.




We are both completely agreed, I think, that simultaneity, ... must be judged primarily by reception (epistemic) rather than generation (ontologic).
Actually, this dictates to me a stark disagreement in our opinions of observed simultaneity. When I refer to the simultaneity of two events, I do not require them to be events of reception by some observer. In fact, if the idea were thusly restricted, then simultaneity would be (trivially) absolute (or meaningless, whichever you prefer). For the simultaneity of two events to be relative, they must have a space-like separation. This is tied into the non-Euclidean nature/causal structure of space-time that I brought up in a previous post. There is no frame of reference into which you can transform two events that have time-like separation (such as any two detections by the same detector that occur at different times) to be simultaneous. Alternatively, if two receptions occur simultaneously at the same point in space, then they are strictly coincident (the exact same event). Thus they are simultaneous in every reference frame (the simultaneity cannot be transformed away).





One wants to use parallax, say, or possibly something more subtle, measuring the time difference between two staggered light sensors and then triangulating.
I will need to give this more thought. I was thinking in stricly 1+1 dimensional terms. This will add another dimension (pardon my pun) to my considerations. It seems unnecessarily complicated to me.





I mean, measure the distance using light (rather than pacing it out with a tape measure.)
Do you feel there should be some fundamental difference between the two methods in the context of SR, or is this whince you now wish to deviate from SR?




... the cars are ten meters long, ...
I will assume that you intend this measurement to be made in the rest frame of the train.




What distances would the bridge observer measure (a) between the strikes on the embankment; (b) between the strikes on the train?
Both (a) and (b) have the same answer in SR: 86.6 m.
 
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  • #22
turin said:
It seems we have suffered a grave miscommunication on this issue. It was never my intent to hold such a contention. These two types of measurements suffer drastically different delay times from the generation of the respective signals. It would have been absurd for me to declare that sound and light measurements ought to be synchronous.

Quite right, and terribly sloppy terminology on my part. If you will allow me a correction, I meant only that you have said all along that both light and sound will present a coherent portrayal of the relative simultaneity of the events in question.

turin said:
Actually, this dictates to me a stark disagreement in our opinions of observed simultaneity. When I refer to the simultaneity of two events, I do not require them to be events of reception by some observer. In fact, if the idea were thusly restricted, then simultaneity would be (trivially) absolute (or meaningless, whichever you prefer). For the simultaneity of two events to be relative, they must have a space-like separation. This is tied into the non-Euclidean nature/causal structure of space-time that I brought up in a previous post. There is no frame of reference into which you can transform two events that have time-like separation (such as any two detections by the same detector that occur at different times) to be simultaneous. Alternatively, if two receptions occur simultaneously at the same point in space, then they are strictly coincident (the exact same event). Thus they are simultaneous in every reference frame (the simultaneity cannot be transformed away).

Fair enough. This is not how Einstein is using the term "simultaneous", but I find this definition much more specific and rigorous.


turin said:
Do you feel there should be some fundamental difference between the two methods in the context of SR, or is this whince you now wish to deviate from SR?

Not as far as I know.

turin said:
I will assume that you intend this measurement to be made in the rest frame of the train.

Yes, and this was the consideration at which I had earlier hinted which led me to see some light in your position. Still not sure that I can throw my weight in that direction, but time will tell.

turin said:
Both (a) and (b) have the same answer in SR: 86.6 m.

I got 115.5m. Please fix my math!:

[tex]{ x - vt } \over { \sqrt { 1 - { v^2 \over c^2 } } } [/tex]

x=100
v=.5c
t=0 ("snapshot")​

[tex] { 100 - v \cdot 0 } \over { \sqrt { 1 - { ( { c \over 2 } ) ^2 \over c^2 } } } [/tex]

[tex] { 100 - 0 } \over { \sqrt { 1 - { { c^2 \over 4 } \over c^2 } } } [/tex]

[tex] { 100 } \over { \sqrt { 1 - { 1 \over 4 } } } [/tex]

[tex] { 100 } \over { \sqrt { .75 } } [/tex]

[tex] { 100 } \over { .866 } [/tex]

=115.5m

(Sloppy treatment of significant digits, but that's not the disagreement.)

Help me out here, please! :confused:
 
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  • #23
OneEye said:
... I meant only that you have said all along that both light and sound will present a coherent portrayal of the relative simultaneity of the events in question.
I suppose so. I have really been trying to promote the independence of simultaneity from any given signal that would be used to determine it.




OneEye said:
This is not how Einstein is using the term "simultaneous", ...
This actually surprises me; I'll have to take your word for it. I do not have a copy of Relativity on hand at the moment.




OneEye said:
I got 115.5m. Please fix my math!
I think you just have it backwards in your mind. If it is 100 m when measured at rest, then it will be contracted by the Lorentz factor to give 86.6 m in the embankment frame in which it is observed to travel at 0.5c. Your math is fine (after all, it's just algebra :wink: ). But your interpretation and application are off, it seems (and quite a bit more complicated than need be; for instance, that first step in your calculation is for an event, not an interval). Notice that, if you take the inverse of the Lorentz factor that you used, you would get 86.6 m, though even this adjustment is somewhat of a coincidence. I'll tell you basically how I did it:

I let the distance between strike points be d' in the embankment frame. When measured at rest, d = 100 m. d is the magnitude of the proper distance between the worldlines of the scortch marks along a now line in the train frame. So, basically, d' = d / γ = d √{1-β2} = d √{0.75} ... Think this through: Are the carriages longer or shorter than 10 m in the embankment frame? Then, would ten carriages be longer or shorter than 100 m?

I never use the strict idea of length contraction, though, because I would often get it backwards. I actually draw it out on a space-time diagram. It's a crutch, but I'm new to this game.
 
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  • #24
turin said:
So, basically, d' = d / γ = d √{1-β2} = d √{0.75} ... Think this through: Are the carriages longer or shorter than 10 m in the embankment frame? Then, would ten carriages be longer or shorter than 100 m?

I never use the strict idea of length contraction, though, because I would often get it backwards. I actually draw it out on a space-time diagram.

Well, in my first think-though, I had expected there to be a foreshortening effect - thus supporting x'<x. When I carried out the Lorentz transform, though, I ended up with x'>x. So, I gave it another think-through. As I thought it out, it seemed to me that the foreshortening should apply to things approaching the observer, while things departing the observer would experience a lengthening effect. This accords well with the mental model which Dr. Einstein suggests of pacing out the measurement, and also coincides well with the Doppler effect. On the other hand, in relativity, velocity implicitly has no direction (as opposed to Newtonian mechanics).

I may be doublethinking myself here. I have never seen a reference to a space-time diagram. Will you please direct me to a reference on this subject? I am a concrete learner, so for me, a picture paints more than a thousand words.
 
  • #25
OneEye said:
... it seemed to me that the foreshortening should apply to things approaching the observer, while things departing the observer would experience a lengthening effect.
Aha! You have finally come right out and said it. This is not in accord with SR, but, if it makes you feel any better, that is exactly how I considered it when I first learned this stuff, and everyone with whom I have discussed SR in an introductory setting has had this same ill-conceived consideration. This is the crux of the misconception. This is also the reason why I have emphasized that SR posits an ontology, that ontology being the events themselves, not the reception thereof. I wonder if it will ever be possible to communicate this position of SR, saving the student from this difficulty. I have tried conveying this in several different ways, but they never seem to make the point clear. A stubborn cleaving to the Gallilean conception of space and time seems quite inevitable, and only after a somewhat painful abandonment can an appreciation of the Minkowski character be gained.

Length contraction and time dilation are part of the solution to the principle of relativity (in the restricted sense) playing nicely with the constant isotropy of c. Of course, as you obviously realize, this leads to problems exactly in the instance of simultaneity. The answer that every serious student seems to naturally conjure: length contraction must be anisotropic. Einstein's answer (if you read way into it): simultaneity is (ontologically) relative. Of course, at the same time, Einstein, being somewhat of a physicist, confounds the distinction between a theoretical ontology (which most certainly exists in SR as the events in space-time) and a physical ontology (of which the discipline of physics is absolutely devoid, always admitting mere physical epistimology in its results, and never extending itself to the philosophical bost of ontology).




OneEye said:
This accords well with the mental model which Dr. Einstein suggests of pacing out the measurement, and also coincides well with the Doppler effect.
I will superficially agree with you. I occasioned to read Relativity last night from the beginning through Chapter IX: "The Relativity of Simultaneity." I now quite understand your position. Were I to be trying to understand SR from these writings, I would be so completely confounded by not only his wandering style (I suppose this is to what you were referring with "peripatetic"), but also by the manner in which he attempts to elucidate the conceptual problems, the theoretical conflicts, and the solutions. With particular attention to Chapter VIII, the opening remarks present the reader with a problem:

from Chapter VIII
Lightning has struck the rails ... I make the additional assertion that these two flashes occurred simultaneously.
The text goes on with a concourse between Einstein and some imaginary you for whom he takes the privelage of speaking. Finally, the two of you come to a tentative agreement on the mechanism for determining simultaneity. Unfortunately (and this is one of the many things that I believe he has underemphasized) Einstein still maintains some subtle residual disagreement:

from Chapter VIII
I feel constrained to raise the following objection: "... if only I knew that the light ... travels along ... A --> M with the same velocity as along ... B --> M. But an examination of this suposition would only be possible if we already had at our disposal the means of measuring time."
In my opinion, this is quite obsesively picky. Even Einstein admits in the next few lines:

from Chapter VIII
After further consideration you cast a somewhat disdainful glance at me--and rightly so...
But, it is nevertheless the absolutely necessary removal of this final inevitable residue at the end of the chapter that presents the solution to your problem, I believe:

from Chapter VIII
... this definition can be used to give an exact meaning ... to as many events as we choose, ... independently of the positions ...
...
... we suppose that clocks ... are placed at the points ... of the railway line ... and ... that the positions of their pointers are simultaneously ... the same. Under these conditions we understand by the "time" of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event.
I do not believe that Einstein endows that last bit (that I have put in bold) with sufficient emphasis. This is a huge part of understanding the structure of relativity, and it presents you with an alternative to your thought experiment, an you would so allow. I suggest that you maintain your embankment with clocks, so nearly adjacent as to form a virtual continuum line of them, and that their tick markings form a virtual continuum to the limit of the practical purposes of this experiment. (Let us assume, further, that this stipulation is always possible to achieve in principle.) Then, have two clocks on the train (separated by as great a distance as is practical).

Make two further arrangements:

1) All clocks on the embankment are synchronized, and the two clocks in the train frame are synchronized. That is, they all simultaneously display the same tick mark in their corresponding frames.

2) Each embankment clock is set to stop at some common tick mark (so that they all stop simultaneously in the embankment frame) and, in so stopping, send a trigger pulse through some mechanism (the details of which are forfit in this thought experiment in the interest of clarity, and the only stipulation is that the transmission path of the triggering signal is negligible for the timescale of the experiment) to the point in the train directly above it that effects a clock at that point in the train (should there be one present) to also stop.

Now, let us imagine that this experiment has run its course, and we are to assess the outcome. The train comes to a halt at the station, we board it, and proceed on our long walk to examine the aft clock. We can do this by obvious means of simply walking to its location on the train and visually inspecting its face. It gives us some reading (frozen by the experiment and so allowing us to take our time, no pun intended) which we write down on our clip boards. Then, we proceed to examine the fore clock, which can be accomplished in the same manner. Upon examination of these two records, we find that the fore clock had stopped previously to the aft clock (in the thought experiment). Thus, without any intimate connection to a particular type of signal, we have (thought) experimentally demonstrated the relativity of simultaneity.




OneEye said:
I have never seen a reference to a space-time diagram. Will you please direct me to a reference on this subject? I am a concrete learner, so for me, a picture paints more than a thousand words.
Absolutely. Space-time diagrams are absolutely indespensible, if for nought else than their pedigogical utility. I do not believe that SR can be properly communicated without somewhat of an appeal to geometry. And, in this special case (that is, this "special theory of relativity"), the geometry may delightfully be concretely associated with graphical representation. Perhaps this site may be a tremendous help to you:
http://casa.colorado.edu/~ajsh/sr/sr.shtml
 
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  • #26
turin said:
Aha! You have finally come right out and said it. This is not in accord with SR, but, if it makes you feel any better, that is exactly how I considered it when I first learned this stuff, and everyone with whom I have discussed SR in an introductory setting has had this same ill-conceived consideration. This is the crux of the misconception. This is also the reason why I have emphasized that SR posits an ontology, that ontology being the events themselves, not the reception thereof. I wonder if it will ever be possible to communicate this position of SR, saving the student from this difficulty. I have tried conveying this in several different ways, but they never seem to make the point clear. A stubborn cleaving to the Gallilean conception of space and time seems quite inevitable, and only after a somewhat painful abandonment can an appreciation of the Minkowski character be gained.

Well, actually, the motivation for my statement was not (as far as I can tell) "a stubborn cleaving to the Galliean conception of space and time". Rather, I simply applied the Lorentz transform in the fashion which seemed most obvious, got an answer other than that which I expected, verified my math, and then attempted to reconcile the verified answer with what I thought I knew about relativity.

The essential difference between your answer and mine is that my answer was (d'=dγ), while yours was (d'=d/γ). Rather than a coincidental correspondence, our results were different because you used the inverse of the Lorentz transform. Your d was my d', and vice versa. Why, exactly, you did this this way remains a matter of some contemplation for me, and (perhaps) has other ramifications for my consideration of SR.

It seems, though, that the original question was derailed. Here is what I was getting at all along:

Based on the idea that the on-board observer is "hastening toward the beam of light coming from B [the forward strike], whilst he is riding on ahead of light coming from A [the rearward strike]," and since this anisotropy is due to the unmediated nature of light (travelling without a medium which can be affected by momentum), and since sound travels in a medim which is affected by momentum, should we not expect a different estimation of simultaneity (as Dr. Einstein uses the term) from sound measurements than we do from light measurements?

The resolution to this question is based on the deeper philosophical question, "Are the contractions and dilations of the Lorentz transform a measure of 'reality' or 'appearance'?" I.e., in SR, is space actually "deformed" by velocity, or does it only appear so because we are using light to measure time and distance, and because light has the peculiar property of isotropy?

One way to determine the answer to this question would be to conduct an experiment based on the considerations indicated above.

That was the original question. And, I would submit that the answer to the deeper philosophical question is undecided and unobtainable within the bounds of SR as it stands, apart from considerations such as those given above.

I hope that I have clarified this. I feel that your input has been helpful - and I have been grateful for your investment of time - so I am interested in your reflections on the above question.
 
  • #27
OneEye said:
... the on-board observer is "hastening toward the beam of light coming from B [the forward strike], whilst he is riding on ahead of light coming from A [the rearward strike]," and since this anisotropy is due to the unmediated nature of light ...
In the embankment frame, this hastening towards and away from the light signals is true, but this is not due to the unmediated nature of light. Sound from the strikes travels through the air outside the carriage at the speed of sound, isotropically in the embankment frame as well. So, the on-board observer is also hastening towards and away from those signals in the embankment frame. The embankment observer could further observe that the sound signals inside the train travel from the scortch marks anisotropically, since the air is moving in a particular direction at 0.5c. This is subject to the Lorentz transformations just as everything else.

In the train frame, SR says that the on-board observer is not hastening towards or away from the light signals (fundamental postulate). And, since the air in the train is moving with the train, the on-board observer is neither hastening towards or away from the sound signals.




OneEye said:
The resolution to this question is based on the deeper philosophical question, "Are the contractions and dilations of the Lorentz transform a measure of 'reality' or 'appearance'?"
An experiment will not verify a philosophy. The Lorentz transforms have a bit more complicated effect on appearance than we have been considering. If you meant observation, then physics (including SR) is not allowed the distinction, and no experiment can accommodate the question. SR has been proven correct in its predictions (in its domain of validity) for the last century, though, I don't think anyone has ever cared to investigate this particular sonic verification.
 
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  • #28
turin said:
The embankment observer could further observe that the sound signals inside the train travel from the scortch marks anisotropically, since the air is moving in a particular direction at 0.5c. This is subject to the Lorentz transformations just as everything else.

Which is the point which I found dubious to begin with.

turin said:
SR has been proven correct in its predictions (in its domain of validity) for the last century, though, I don't think anyone has ever cared to investigate this particular sonic verification.

And I am not trying to say that SR is incorrect. My question is, "Does SR apply only to photonic phenomena?" And I think there's room for doubt about this question. (See Round 1.)
 
  • #29
turin said:
I don't know what else to say about it. Sorry. I shall now proceed to consider "Round 1."

BTW, the discussion has been a real pleasure, and I hope to continue as long as you're willing. I will try to concede to your arguments as I understand them.

turin,

You have been a gentleperson. Thank you for your considerations as well. Your contributions have been most elucidating.
 
  • #30
I just read the short "Round 1" thread, and did not gain any insight into your dilemma.

Were you able to follow that link to Alexander Hamilton's page? Do you disagree with anything that he has posted there? Are you skeptical of the experimental evidence to date?

BTW, the discussion has been a real pleasure, and I hope to continue as long as you're willing. I will try to concede to your arguments as I understand them.
 
  • #31
turin said:
In the embankment frame, this hastening towards and away from the light signals is true, but this is not due to the unmediated nature of light. Sound from the strikes travels through the air outside the carriage at the speed of sound, isotropically in the embankment frame as well. So, the on-board observer is also hastening towards and away from those signals in the embankment frame. The embankment observer could further observe that the sound signals inside the train travel from the scortch marks anisotropically, since the air is moving in a particular direction at 0.5c. This is subject to the Lorentz transformations just as everything else.

You are correct, the anisotropy is not due strickly to the existence or non of a medium but the relative motion of the observer frame with the "frame" in which the speed of a propagating phenomena (e.g light and sound) is constant. I think the mistake the etherists and Einstein made back in the 19th and early 20th century is in assuming a stationary ether. If the ether is at rest with respect to the lab (i.e. moving at the same velocity as the lab through space) or if propagating phenomenon are source dependent (in the case of no ether), isotropy of propagating phenomenon inside different inertial labs would be obtained. E.g. sound waves propagating thru the air inside a "moving" train would be detected as isotropic (since the "ether" is at rest with respect to the train) while sound waves propagating through the atmosphere outside the train would be detected as anisotropic by the lab inside the "moving" train, since the "ether" is "moving" with respect to the train.

In the train frame, SR says that the on-board observer is not hastening towards or away from the light signals (fundamental postulate). And, since the air in the train is moving with the train, the on-board observer is neither hastening towards or away from the sound signals.

The part about sound is similar to my explanation. You can't be right about the light though. Again, reread chapter 9. The train is supposed to be one inertial frame since all the parts, including the observer, are at the same velocity, so how can shrinking the train prevent the light signals traveling from the rear to the observer in the middle and from the front to the same observer from arriving at different times, if the light flashes happened simultaneously inside the train frame and then traveled at a constant c relative to the vacuum? Even Einstein acknowledges this anisotropy, except he called it "the relativity of simultaneity".
 
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  • #32
turin said:
Aha! You have finally come right out and said it. This is not in accord with SR, but, if it makes you feel any better, that is exactly how I considered it when I first learned this stuff, and everyone with whom I have discussed SR in an introductory setting has had this same ill-conceived consideration. This is the crux of the misconception. This is also the reason why I have emphasized that SR posits an ontology, that ontology being the events themselves, not the reception thereof. I wonder if it will ever be possible to communicate this position of SR, saving the student from this difficulty. I have tried conveying this in several different ways, but they never seem to make the point clear. A stubborn cleaving to the Gallilean conception of space and time seems quite inevitable, and only after a somewhat painful abandonment can an appreciation of the Minkowski character be gained.

Length contraction and time dilation are part of the solution to the principle of relativity (in the restricted sense) playing nicely with the constant isotropy of c. Of course, as you obviously realize, this leads to problems exactly in the instance of simultaneity. The answer that every serious student seems to naturally conjure: length contraction must be anisotropic. Einstein's answer (if you read way into it): simultaneity is (ontologically) relative. Of course, at the same time, Einstein, being somewhat of a physicist, confounds the distinction between a theoretical ontology (which most certainly exists in SR as the events in space-time) and a physical ontology (of which the discipline of physics is absolutely devoid, always admitting mere physical epistimology in its results, and never extending itself to the philosophical bost of ontology).




I will superficially agree with you. I occasioned to read Relativity last night from the beginning through Chapter IX: "The Relativity of Simultaneity." I now quite understand your position. Were I to be trying to understand SR from these writings, I would be so completely confounded by not only his wandering style (I suppose this is to what you were referring with "peripatetic"), but also by the manner in which he attempts to elucidate the conceptual problems, the theoretical conflicts, and the solutions. With particular attention to Chapter VIII, the opening remarks present the reader with a problem:


The text goes on with a concourse between Einstein and some imaginary you for whom he takes the privelage of speaking. Finally, the two of you come to a tentative agreement on the mechanism for determining simultaneity. Unfortunately (and this is one of the many things that I believe he has underemphasized) Einstein still maintains some subtle residual disagreement:


In my opinion, this is quite obsesively picky. Even Einstein admits in the next few lines:


But, it is nevertheless the absolutely necessary removal of this final inevitable residue at the end of the chapter that presents the solution to your problem, I believe:


I do not believe that Einstein endows that last bit (that I have put in bold) with sufficient emphasis. This is a huge part of understanding the structure of relativity, and it presents you with an alternative to your thought experiment, an you would so allow. I suggest that you maintain your embankment with clocks, so nearly adjacent as to form a virtual continuum line of them, and that their tick markings form a virtual continuum to the limit of the practical purposes of this experiment. (Let us assume, further, that this stipulation is always possible to achieve in principle.) Then, have two clocks on the train (separated by as great a distance as is practical).

Make two further arrangements:

1) All clocks on the embankment are synchronized, and the two clocks in the train frame are synchronized. That is, they all simultaneously display the same tick mark in their corresponding frames.

2) Each embankment clock is set to stop at some common tick mark (so that they all stop simultaneously in the embankment frame) and, in so stopping, send a trigger pulse through some mechanism (the details of which are forfit in this thought experiment in the interest of clarity, and the only stipulation is that the transmission path of the triggering signal is negligible for the timescale of the experiment) to the point in the train directly above it that effects a clock at that point in the train (should there be one present) to also stop.

Now, let us imagine that this experiment has run its course, and we are to assess the outcome. The train comes to a halt at the station, we board it, and proceed on our long walk to examine the aft clock. We can do this by obvious means of simply walking to its location on the train and visually inspecting its face. It gives us some reading (frozen by the experiment and so allowing us to take our time, no pun intended) which we write down on our clip boards. Then, we proceed to examine the fore clock, which can be accomplished in the same manner. Upon examination of these two records, we find that the fore clock had stopped previously to the aft clock (in the thought experiment). Thus, without any intimate connection to a particular type of signal, we have (thought) experimentally demonstrated the relativity of simultaneity.




Absolutely. Space-time diagrams are absolutely indespensible, if for nought else than their pedigogical utility. I do not believe that SR can be properly communicated without somewhat of an appeal to geometry. And, in this special case (that is, this "special theory of relativity"), the geometry may delightfully be concretely associated with graphical representation. Perhaps this site may be a tremendous help to you:
http://casa.colorado.edu/~ajsh/sr/sr.shtml
Read Chapter 9 again. The relativity of simultaneity he speaks of is the effect due to the propagation delay of light so it's really a misnomer. He begins his thought experiment by assuming event A + B (lightning flashes) happened simultaneously for both observers M and M' then demonstrates that because point M' is moving towards the signal reflected at point B and away from the signal from point A, the event (A+B) is recorded as non-simultaneous by M' but simultaneous by M. In other words, this chapter which was supposed to help resolve the incompatibility between the two postulates in SR, is entirely irrelevant. If anything, since he argues that two light signals emitted from the front and rear of a moving train at the same time to a photomultiplier in the middle of the train will be detected at different times, he actually proves in his gedanken experiment that SR's two postulates ( that light propagates through the vacuum independent of source at a constant c and that physics is the same inside all inertial frames) are contradictory.

Only the later chapters on time dilation and length contraction has anything to do with resolving the logical contradiction in SR. Einstein's strategy basically was to rescale the sizes of time and space coordinates in such a way that what should be c+v and c-v in relatively moving frames becomes c.
This strategy fails because regardless of how much you shrink a set of coordinates (or expand them), there will always be anisotropic effects of light inside different inertial frames since its speed is source independent.

When Einstein says then in Chapter 9 that his so called relativity of simultaneity removes the incompatibility between the two postulates in SR, what he actually did was changed his second postulate- that the principle of physics is the same in all inertial frames- to mean only that the value c is a constant when all inertial frames measured the path of the light using the coordinates of the vacuum, that is, by taking into account their own velocities through space. He basically removed the inconsistency between his two postulates by removing the second postulate and replacing it with its logical opposite (anisotropy, but called by Einstein "the relativity of simultaneity"). It becomes a big mess by chapter 10 though when he goes back to his first renditions of his two postulates by introducing the Lorentz Transformations, which was supposed to make physics the same inside different inertial frames by rescaling the sizes of the time and space coordinates.
 
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  • #33
Eyesaw,
I'm sorry, but you are incorrect (to say that I am). Of this I am very certain, for I have chosen my statements carefully. Firstly, I will point out my initiation of "SR says..." You are neglecting the postulate of invariant c, which is what separates SR from other forms of relativity to which Einstein's appeals in the antecedent text. I believe your primary blunder may be your assumption that SR has been concluded by the arguments only through Chapter IX. There is subsequent development of the theory.

I do NOT rely on Einstein's Relativity to understand SR. I know that sounds paradoxical, but if you try to understand SR from the Minkowski perspective, which Einstein did in order to develop GR, then you may realize that Relativity is only intended as an attempt to demonstrate Einstein's process of development. For instance, if you are really after SR, you should read Chapter 2 in The Meaning of Relativity (along with the corresponding appendices) rather than the first ? chapters of Relativity (which are full of rambling prose and very little math).

For your own sake, if you truly wish to learn and understand SR, find a supplementary text. There is nothing fundamentally wrong with Relativity, but you could save yourself much time and effort by entertaining an alternative source that is more directed to exposing the theory instead of the process of development.
 
  • #34
turin said:
Eyesaw,
I'm sorry, but you are incorrect (to say that I am). Of this I am very certain, for I have chosen my statements carefully. Firstly, I will point out my initiation of "SR says..." You are neglecting the postulate of invariant c, which is what separates SR from other forms of relativity to which Einstein's appeals in the antecedent text. I believe your primary blunder may be your assumption that SR has been concluded by the arguments only through Chapter IX. There is subsequent development of the theory.

I do NOT rely on Einstein's Relativity to understand SR. I know that sounds paradoxical, but if you try to understand SR from the Minkowski perspective, which Einstein did in order to develop GR, then you may realize that Relativity is only intended as an attempt to demonstrate Einstein's process of development. For instance, if you are really after SR, you should read Chapter 2 in The Meaning of Relativity (along with the corresponding appendices) rather than the first ? chapters of Relativity (which are full of rambling prose and very little math).

For your own sake, if you truly wish to learn and understand SR, find a supplementary text. There is nothing fundamentally wrong with Relativity, but you could save yourself much time and effort by entertaining an alternative source that is more directed to exposing the theory instead of the process of development.

Invariance of c. Ok, a rest frame determines the velocity of light to be c. Now, use Galilian transformation for a frame moving in the direction of the light, you get c-v. So, add v and you get c as invariant. The space the moving observer and the light emitted from the rest source gets mixed together in a Galilian Transformation, so you get c-v. Once the space the observer moved through is separated from the space the light moved through, i.e. adding v to (c-v), every inertial frame determines the speed of light as invariantly c. Where's the need for the Lorentz Transformation? SR confuses the summed path of the light and the inertial observer with actual changes in space-time for the observers.

To make matters even more confusing, SR has two opposite definitions for its second postulate, the principle of relativity. The first definition only requires that c be invariant in all inertial frames, this is easily achieved by assuming source independence, then filtering out the velocity of the observer with respect to the rest frame, in lieu of the dumb way (the Lorentz Transformation) proposed by SR. The second definition requires that every inertial lab obtains the same results for experiments, which can only happen if propagation phenomenon were source dependent; just take the example with sound- inside a jet airplane going at Mach 2, a sound source in the middle of the jet would be heard loudly in the rear of the jet but the front receiver would hear nothing, if the propagation speed of sound was source (actually in the case of sound, medium speed) independent.
 
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  • #35
Eyesaw said:
... a rest frame determines the velocity of light to be c. Now, use Galilian transformation for a frame moving in the direction of the light, you get c-v. So, add v and you get c as invariant. The space the moving observer and the light emitted from the rest source gets mixed together in a Galilian Transformation, so you get c-v. Once the space the observer moved through is separated from the space the light moved through, i.e. adding v to (c-v), every inertial frame determines the speed of light as invariantly c.
I think I'm missing some subtle point. Why are you adding v? In what way do the Galilean transformations call for this adjustment?




Eyesaw said:
To make matters even more confusing, SR has two opposite definitions for its ... principle of relativity. The first definition only requires that c be invariant in all inertial frames, ... The second definition requires that every inertial lab obtains the same results for experiments, which can only happen if propagation phenomenon were source dependent;
This is not correct. The invariance of c is a separate postulate from the principle of relativity. Together, these two postulates generate the (kinematical) special theory of relativity. If the speed of light were observed to be frame dependent in the same way as sound, then we would most likely still use the Galilean transformations.




Eyesaw said:
... this is easily achieved by assuming source independence, then filtering out the velocity of the observer with respect to the rest frame, in ... the Lorentz Transformation ...
But this is not at all a representation of thet Lorentz transformation. The velocity of the observer (wrt some frame) is very much a (nontrivial) part of the Lorentz transformation, and it cannot be inserted nor removed by a mere addition.




Eyesaw said:
The second definition requires that every inertial lab obtains the same results for experiments, ...
This is a gross misconception. The principle of relativity requires that the form of the physical laws is the same in every inertial frame. To require the absolute identity of the results of experiment would be absurd. The results can be transformed from frame to frame, but they are only identifiable in this sense.




Eyesaw said:
... just take the example with sound- inside a jet airplane going at Mach 2, a sound source in the middle of the jet would be heard loudly in the rear of the jet but the front receiver would hear nothing, if the propagation speed of sound was source (actually in the case of sound, medium speed) independent.
I am having trouble putting this example together. How would an observer explain the anisotropy of the sound? Would the observer postulate this as a fundamental law for sound. Would the observer be allowed the consideration of the fact that he/she is in a jet traveling at Mach 2 (wrt the atmosphere/suface of the earth)? Would the observer be allowed to conduct any other experiments?
 

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