Light shone in a train bouncing off mirrors

[altonhare]

You do not understand. It is not a case of picking the same standards.

Events simultaneous in one inertial frame are NOT simultaneous in another inertial frame moving relative to it. Observers in different frames can of course calculate what is simultaneous in which frame and agree on this but spatially separated events that are simultaneous in one frame will not be simultaneous in the other frame . And of course they will also agree on this.

Matheinste.

But of course it is. If the two are moving relative to each other their clocks and rulers are different. They are using different standards. It's just a matter of correcting for this difference

 

[matheinste]

You are wrong but i am afraid i cannot convince you.

Matheinste.

 

[Naty1]

Events simultaneous in one inertial frame are NOT simultaneous in another inertial frame moving relative to it.

This is absolutely correct.

The point is, the only reason they disagree is because they are measuring with different reference standards.

This is not correct...but is rather naive...relativity is far deeper !

Relativity takes time to understand and absorb and the interest to learn.

 

[altonhare]

You are both declaring me wrong without any justification. You're saying there's "something far deeper" because you want it to be so.

How is anything dependent upon an individual observer's testimonial or opinion? Shall science be decided by casting votes? What if one observer is drunk?

Since when are we shocked that different observers have to reconcile their measurements by referencing a single standard? If my left foot is assumed motionless and every object in the universe moves relative to it, and everyone uses this principle, everyone agrees on everything. My left foot is now called a "reference standard" and is a basic and crucial component to any measurement.

 

[matheinste]

You are completely on the wrong track. Sorry but this is absolutrely basic relativity as understood by any student of SR. I'm afraid there is no more to be said.

Matheinste.

 

[Mentz114]

Again, they disagree only because they are not measuring with a common reference standard. They get together, compare numbers. The numbers are different. After thinking for a moment they realize that one is measuring relative to the train and one to the ground. Once they both pick a common reference they get the same answer.

There has never been a "preferred frame" in all of human history. For every measurement ever done something had to be picked as the "standard". A specific stick, motion of the sun across the sky, whatever. People always measured things *relative* to a standard. Relativity has been around ever since the concept of a measurement was struck. I measure the height of the cave *relative* to my stick. I measure the speed of the cheetah *relative* to mine. I measure the motion of the sun across the sky *relative* to the motion of sand particles in my hourglass. If people were using different references they had to resolve the difference by finding the relationship between the two references. The Lorentz transforms are no different. If everyone picked a common reference everyone would agree. Just like if every caveman used the same stick they'd all conclude the same height for the cave!

There has never been a "preferred reference" except in the sense that kings, religious leaders, or scribes/scientists dictated one. Even if there were some kind of "aether", it would be preferred only by convention. Measurement is a human activity, Nature doesn't know anything about "reference frames" or "standard references" or "preferred references". We can take the aether as stationary but we can just as well take my chair as stationary. If we all choose the same one we all get the same answer.

The deep question here, is WHY does a clock slow down? WHY is light so special? What physically intervenes between two atoms to cause this phenomenon? What is its physical structure? How does this structure explain/justify the observations?

In this, and your later post, you completely misunderstand the idea of 'measurement' such as holding a ruler to a piece of wood, and 'relativity' which is about the laws of physics in frames of reference that are in relative motion. SR reconciles a serious problem in electrodynamics and is not a restatement of something already known.

In older times it was easy to say that one ruler was longer than another, one standard-weight bigger than another, etc. But today we have no such easy answers, the emission of radiation from a cesium clock is not understood at all. We have no idea what the structure of the radiation is or of the cesium clock's internal machinery. Such "explanations" as time dilation and space/length/distance contraction are no more than circular restatements of the observation. They say nothing new.

The emission of light from a cesium is not "not understood at all". Most of what you say here is hot air.

 

[altonhare]

You are completely on the wrong track. Sorry but this is absolutrely basic relativity as understood by any student of SR. I'm afraid there is no more to be said.

Matheinste.

Refutations with no justification. Whether I am, have been, or will be "a student of SR" in your estimation or anyone else's is irrelevant.

In this, and your later post, you completely misunderstand the idea of 'measurement' such as holding a ruler to a piece of wood, and 'relativity' which is about the laws of physics in frames of reference that are in relative motion. SR reconciles a serious problem in electrodynamics and is not a restatement of something already known.

It has always been known that measurements had to be reconciled with what the different people are measuring relative to. Relative to the motion of the sun across the sky? The motion of a pendulum? This stick? That stick? Only in the last few centuries have we realized that many more factors affect our measurements and have to be reconciled. Basically we learned that the fundamental workings of the atom on a small scale affect our measurements and follow a pattern that is quantified and correlated via the Lorentz transformations.

The emission of light from a cesium is not "not understood at all". Most of what you say here is hot air.

Could you point to where the physical mechanism of light emission is illustrated? All I've seen are particles (silly cartoon visualizations), continuous perpendicular "plane waves" (continuity inconsistent with quantization) or continuous waves that magically morph into particles "on contact". This enabled mathematical models, but still nobody knows what light *is*. We have great listings of observations/facts, but very little understanding.

"Mathematicians do not study objects, but relations between objects." -Poincare

In other words, an equation does not care what light or the atom ARE, but simply what relationships/patterns can be identified. We have correlations but not understanding.

"Science is built up of facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house." -Poincare

We know *that* light is discrete. We know *that* light propagates in an oscillatory pattern in two perpendicular directions. We know *that* about a lot of things, what we don't have is understanding.

 

[matheinste]

I was just pointing out that any student of SR, at the most basic level will be well aware that you are wrong. This was not making any comment on your level of studies but at your lack of understanding of such a basic part of SR. My justification us unnecessary because ANY textbook on SR will contradict you. It may of course require a little more effort on your part.

I wil not be drawn into arguments of this nature. The relativity of simultaneity is apodictic.

Matheinste

 

[altonhare]

My justification us unnecessary because ANY textbook on SR will contradict you. It may of course require a little more effort on your part.

But they all say the same thing, that if we measure using the same reference we get the same answer, and if we measure using different references (often called "reference frames") we get different answers which we can reconcile by using a common reference.

I wil not be drawn into arguments of this nature. The relativity of simultaneity is apodictic.
Matheinste

Apodictic? Have I offended your religion?

To "observers 1 and 2" measure two objects with the exact same ruler. 1 concludes A is bigger than B and 2 concludes B is bigger than A. 1 took his measurements in the afternoon and 2 took his at night. A and B happen to be a block of metal and a brick, respectively. Are we shocked that they got different answers?

(Materials science note: metals tend to thermally expand/contract more than brick)

In this case they had the same ruler, we can even assume the ruler is "perfectly rigid". In this case only the "conditions" of the measurement changed. Velocity is just another kind of condition. For some reason velocity induces clock slowing and meter-stick contraction.

 

[matheinste]

Quote:-
--But they all say the same thing, that if we measure using the same reference we get the same answer,---

Not with regards to simultaneity. I understand about time dilation and length contraction. Along with these goes the relativity of simultaneity. Perhaps it is harder to grasp but it is basic to SR.

Studies of relativity teaching have shown that this is the least understood aspect of SR. Even among graduates


Take another look at the standard thought experiment which most textbooks use. The embankment and train observers. This is the standard teaching aid to the relativity of simultaneity.It is not obvious without a little thought. .

Let me make it clear what this says. If someone is on the embankment midway between two events (say lightning flashes if you like) and they see them at the same time, then they regard them as simultaneous, by definition. This is of course simple geometry and has nothing to do with relativity. Of course the observer does not need to be at the midpoint to decide on simultaneity because wherever he is (As long has he is stationary with respect to the embankment), he can allow for light transit time and do a calculation. So we have an observer, for the sake of this illustration let him be at the mid point on the embankment between strikes, and so in his frame (the embankment frame) he judges the lightning flashes to have happened simultaneously.

Now introduce an observer on the train at the midpoint of the train which is passing the embankment observer at the time the strikes take place in the embankment frame.This means that when the embankment observer sees the strikes the train observer is next to him. So when the strikes took place, simultaneously for the embankment observer, the observer on the train was at the same point. However, the observer on the train at the centre of it will correctly argue " if the strikes were simultaneous in my frame , me, being a clever man who understands relativity and that the speed of light is the same for all observers, would expect to see them at the same time at my position at the centre of the train. But as i do not see this, i can correctly assume that (in my frame) they were not, by definition, simultaneous. I can of course do a calculation and agree that the stikes were simultaneous in the embankment frame, but not in my. I also realize that if the strikes were seen by me at the same time at my position at the midpoint of the train, they would be, by definition, simultaneous for me but not for the observer on the embankment."

The argument can be used reciprocally.

No amount of calculation or reasoniong can make the two observers agree on the strikes being simultaneous for both of them. And the reason is that they were not!

Matheinste

 

[altonhare]

Math,

I appreciate you're taking the care to lay out the train/embankment pedagogy, you've only reinforced what I said, I think without realizing it.

The act of measurement involves a specific reference standard that is assumed immutable. The act of comparing measurements involves premises which must be established *before* any comparisons may be meaningful. Any conclusions agreed upon by both parties are predicated on these premises.

For you and I to compare measurements we must first compare reference standards. This is because *all* knowledge is contextual. There's nothing special about "special" relativity. If you always measure this brick and this metal at midnight of the winter solstice, and I always measure them on the afternoon of the summer solstice, we have different references. The first thing we must do before engaging in *any* productive comparison or discussion is to reconcile them. The aforementioned case is reconciled (at least with quantitative accuracy) by correlating the size of a block of metal or brick with the height of a column of mercury (or water or whatever) by some constant empirical parameter unique to each material. Now we can compare results meaningfully. What is our conclusion? The brick is bigger than the metal in winter and the metal is bigger than the brick in summer. Or if we're very careful and fastidious we can pinpoint the height of a column of mercury/water at which the two are the same size. Our conclusion from the train/embankment? Relative motion is another condition that must be taken into account in your reference standard.

 

[matheinste]

Hello again altonhare.

If everything else is absolutely controlled and the same in two reference frames there will still be a relativity of simultaneity. Both frames are looking at the SAME. There are lenghth contraction on time dilation effects but again these are far more fundamental than differences in reference standars.

The issue of simultaneity is much more fundamental than reference standards.

I will try a rephrasal just to be sure what i say is clear.

Two events cannot be simultaneous in two reference frames that are moving inertially relative to each other. Observers in these two frames can agree which frame the events are simultaneous in (assuming they are simultaneous in one of them). But the two events CANNOT be simultaneous in both frames.

I make the proviso that, should i decide to say no more, that should in no way be taken as an admission of error on my part.

Dictionary corner. Apodictic:- Incontrovertible.

Matheinste..

 

[altonhare]

Dictionary corner. Apodictic:- Incontrovertible.

Matheinste..

Incontrovertible: An axiom (a statement which must be true in order to attempt to refute it), an assumption/premise (hypothesis), or a theory declared unquestionable by authority (religion).

You have not provided a single justification for your claim that it is "far deeper" than reference standards.

The brick/metal measurers I alluded to:

One guy says,"Okay so they seem to get bigger depending on how warm it feels to us, which seems correlated with the height of mercury/water/etc. There's got to be something deeper going on here"

Second guy: "I know. I wish we could crack these bricks and metal apart and see what is going on inside that causes this behavior."

First guy: "No, it's even deeper than that!"

Second guy: "What do you mean? There was obviously some effect that changed this metal more than this brick, that required us to reconcile our measurement standards"

First guy: "God (or space-time) contracts/expands the metal more than the brick."

Second guy: "What do you mean? What is the physical situation you're trying to illustrate?"

First guy: "What don't you understand? God/space-time did it!"

Second guy: "..."

First guy: "It's beyond your understanding, leave it to me though, I have the equation that "predicts" (correlates) these phenomena. You'll have to look up to me, one who understands, to tell you what's going on.

Second guy: "But we have the same equations. This isn't an issue of equations. This is a qualitative, conceptual issue of physics."Blah blah blah etc.

 

[matheinste]

You really don't get it do you.

Matheinste.

 

[altonhare]

You really don't get it do you.

Matheinste.

You're telling me that, if I measure something exactly the same way as someone else, I will come to the same conclusion as them, but if I measure it in a different way my conclusions will differ. You still haven't justified why this is so "deep" or fundamentally different than the way measurement has been done throughout human history.

Perhaps we should try to agree on one thing that may clear this up. Is it "magic" that makes one person obtain different measurements, and thus different conclusions, or is there a direct cause for it, whether we know the cause or not?

If there's a specific cause (not "magic") then how is that any different than the reconciliation of any other measurement, i.e. measuring metal and bricks? A physical effect causes us to come to different conclusions there, exactly the same as if we were measuring in the train scenario. We may not know the precise mechanism yet.

So tell me, is it magic, or a physical causal mechanism? If the latter, how is it fundamentally different (from the perspective of measurement) than the physical expansion of a block of metal?

If I don't get it, but you do, why can't you make the distinction clear?

 

[matheinste]

Quote:-
---If I don't get it, but you do, why can't you make the distinction clear? ---

I will put it down to my lack of explanatory skills and leave it at that.

Matheinste

 

[altonhare]

Quote:-
---If I don't get it, but you do, why can't you make the distinction clear? ---

I will put it down to my lack of explanatory skills and leave it at that.

Matheinste

If you can't explain it, you don't really understand it. And you accused me of not "getting it"!

 

[matheinste]

Hello altonhare.

It is rude of me to do all the talking and continually put forward the generally held views on simultaneity. Let us reverse the situation and give you an opportunity to put forward your ideas on simultaneity. You have not yet tried and it is perhaps incorrect of me to assume that your ideas are those normally accepted.

Firstly, does simultaneity have any meaning for you. That is not meant cynically

If the answer is yes, what is your definition of simultaneity.

If the answer to the first question is yes will you give me a definition of your meaning of the word in the context of physics

If your definition is not the normal one then all well and good.

If it is the normal one will you then explain to me how two observers in two systems moving inertially relative to each other can both define the same two events as being simultaneous in their systems. By the normal definition i mean that which is given and understood by the vast majority of physicists and authors on relativity.

Matheinste.

 

[matheinste]

Hello altonhare.

I should add:-

I assume that the clocks in both systems have been synchronized using Einstein's procedure.

That the two events are spacially separated.

That the direction of relative motion between the two systems is not in a direction perpendicular to the line joining the events.

Matheinste.

 

[altonhare]

Hello altonhare.

It is rude of me to do all the talking and continually put forward the generally held views on simultaneity. Let us reverse the situation and give you an opportunity to put forward your ideas on simultaneity. You have not yet tried and it is perhaps incorrect of me to assume that your ideas are those normally accepted.

Firstly, does simultaneity have any meaning for you. That is not meant cynically

If the answer is yes, what is your definition of simultaneity.

If the answer to the first question is yes will you give me a definition of your meaning of the word in the context of physics

If your definition is not the normal one then all well and good.

If it is the normal one will you then explain to me how two observers in two systems moving inertially relative to each other can both define the same two events as being simultaneous in their systems. By the normal definition i mean that which is given and understood by the vast majority of physicists and authors on relativity.

Matheinste.

Hello altonhare.

I should add:-

I assume that the clocks in both systems have been synchronized using Einstein's procedure.

That the two events are spacially separated.

That the direction of relative motion between the two systems is not in a direction perpendicular to the line joining the events.

Matheinste.

I think you may understand better if I give you my version of the boxcar gedanken experiment. If it doesn't suffice perhaps I'll try something more formal.

This one is called "Matheinste in the hot seat". In the middle of the box car is an electric chair in which we place you. On either side of the chair, equidistant, are two lightning rods connected to a circuit on the back of your chair. A team of qualified electrical engineers designed, built, and tested this circuit to allow lethal current to flow into the occupant if it receives a voltage simultaneously from both sides. It has been extensively tested to be reliable with a tiny experimental error. I am the conductor of the train and possesses the switch that activates Dr. Mad's lightning tower and sends two bolts to strike either rod simultaneously. Additionally there is a radar that measures the train's velocity relative to the Earth that is programmed not to allow any current to flow unless relativistic effects are orders of magnitude greater than the experimental error of the circuit.

Outside the boxcar, on the embankment, will be two crowds. One consisting of your family and friends, ready to testify under oath at me and Dr. Mad's murder trial tomorrow that the bolts were most definitely not simultaneous. The second group consists of trained and qualified physicists who all scored perfectly on relativity exams, equipped with photon detectors, atomic clocks, and whatever other apparatus they need so they are ready to swear on Einstein's grave at tomorrow's trial that the measurements and calculations show that the bolts were most definitely not simultaneous.

Inside the boxcar there is only me, I flip the switch while watching the two bolts strike simultaneously. You fry. We drag your smoking corpse off the train.

At the trial tomorrow I plead the 5th, as is my right. Some of your closest family, though they love you dearly, cannot put an innocent man behind bars. They either plead the 5th or state that the two bolts did not appear simultaneous. The physicists present their calculations, based on measurements using the most advanced and precise technology, calculated using the prevailing theory of relativity, showing that the bolts were most definitely not simultaneous.

The electrical engineers, having had no idea what their circuit was used for, are nevertheless relieved at the testimonies. They present their circuit to the jury and state that it would only deliver a lethal shock if the strikes were simultaneous. They state that it had been subjected to numerous tests and the odds that some kind of fluke caused an unexpected outcome are billions to one.

The defense concludes that it could not have been their circuit, Alton's hand, or Dr. Mad's lightning that killed poor Matheinste.

The jury does not deliberate long, the evidence is overwhelming. They declare me and Dr. Mad innocent and the consciences of the electrical engineers are eased. What did kill poor Matheinste? Who knows.

 

[matheinste]

Quote:-

---If it doesn't suffice perhaps I'll try something more formal.---

I prefer something more formal. How about a direct answer to my questions. As long as you avoid the questions i must assume that you cannot answer them. While you are giving youe more formal answer i will study your last post.

Matheinste.

 

[altonhare]

The "formal" answer is not as fun, but have it your way.

Whether two events happened at the same time or not is, in physics, not a matter of measurement, testimony, or or observers. It is decided strictly by rigorous definitions and logic.

Simultaneous: Happening at the same time.

Note that there are no provisions for observers in this definition. Whether bolt A physically struck before, after, or simultaneously as bolt B has nothing to do with what anyone saw. It either did or it didn't.

Fortunately for me and Dr. Mad, nobody else seemed aware of this. They insisted that, because their measurements and observations indicated one bolt struck before the other, they were not simultaneous. So we got away with murder.

 

[matheinste]

Hello altonhare

At last. That's all i wanted to know. Your last reply confirms that you have no idea of the definition(s) of simultaneity.

Matheinste.

 

[altonhare]

Hello altonhare

At last. That's all i wanted to know. Your last reply confirms that you have no idea of the definition(s) of simultaneity.

Matheinste.

I have a game show you might want to go on then. It's called:

"Matheinste in the Hot Seat, Dead or Alive?"

If you live through it, you can name your prize. Are you game?

You understand so much, and I so little, so how is it that I can get away with murder?

 

[Saw]

altonhare, I really enjoyed your thought experiment. In fact, my north in studying the subject was for some time a similar trial. A trial, yes, because that is the point: however you interpret things, you cannot have two realities and I am afraid the legal profession, mischievous as it is, would have a good case against physics if the latter favoured the multiple-reality approach. However, I left aside that modality of example (not the idea of a trial, but the type of case you have brought before the court) because it appears to have an easy solution under the framework of orthodox SR. I have another modality of trial you may enjoy yourself, which can be adapted in your honour as "althonhare, the referee, should the mob stone him for cheating or not?" (another version: "should we in the end burn Galileo, after all?"). While I prepare it, however, I wouldn't mind if you proceeded with your own development under the title, "Saw in the hot seat, Dead or Alive?", ‘cause you have already put once matheinste in that unpleasant seat.

On the other hand, we have gone a little off-thread, by way of generalisation. If anyone is interested in the specific subject of the thread, s/he can follow the one “Special Relativity, Time Dilation, Light Clock, Velocity of light”, which is about the same thing.

 

[altonhare]

altonhare, I really enjoyed your thought experiment. In fact, my north in studying the subject was for some time a similar trial.

I don't think I understand this jargon/slang. Your north? Afaik north of me is anything that's closer to where Santa Claus lives than I am.

A trial, yes, because that is the point: however you interpret things, you cannot have two realities and I am afraid the legal profession, mischievous as it is, would have a good case against physics if the latter favoured the multiple-reality approach. However, I left aside that modality of example (not the idea of a trial, but the type of case you have brought before the court) because it appears to have an easy solution under the framework of orthodox SR.

The claims I hear are contradictory and inconsistent. On the one hand I hear that rel does not propose "multiple realities". On the other hand I hear that the strikes were simultaneous for one person but not for the other. So what? One person can come to the wrong conclusion by watching from a different perspective, but we can get the same result by having him down 5 liters of beer! Suppose I'm not even watching the rods when I flip the switch, therefore nobody sees the strikes as simultaneous! Yet Mathe is still a dead man and, according to what Mathe has said so far, the audience must conclude that I'm innocent as Mother Teresa!

Edit: I'm not asking for a "solution", I know the "solution", Matheinste's dead! And if everyone on the embankment follows what Math has said they must conclude that it's not my fault and I walk.

While I prepare it, however, I wouldn't mind if you proceeded with your own development under the title, "Saw in the hot seat, Dead or Alive?", ‘cause you have already put once matheinste in that unpleasant seat.

Do you have a death wish? I will tell you ahead of time that Dr. Mad and I have set everything up carefully to so the strikes will hit either end of the train simultaneously according to us, but we will not be around to testify that they were simultaneous after the fact. The only testimony you'll get is from a crowd on the embankment. If what Mathe has said is correct, that the strikes "are not simultaneous in another frame", you'll either live and name your prize or I get away with murder.

 

[altonhare]

By the way I encourage people to use "aether" instead of "ether" because this:

R-O-R

is ether.

 

[Saw]

Yes, for sure my tone was not adequate and my English is not perfect, both for reading and writing purposes (after all, not my mother-tongue). Sorry for that.

If I have understood well your thought experiment, you are charged if the two currents meet at the mid-point simultaneously, since only in that case the lethal mechanism is triggered. If not, even if the victim is killed, we must conclude that the reason for the victim being fried up may theoretically be another. Right?

If it is so, I think that SR would not allow for discrepancy in this respect, it would just happen that, after an initial manual synchronisation, the clocks at the embankment and on the train would show different readings, but both sets of observers would agree on the fact that the currents have met simultaneously where they have. I know it sounds odd if we look at those readings as more than a pure measurement discrepancy, ok, but I just wanted to note that at least SR does not discuss the substance of the case: the current that you released was the cause of the death, in everybody's opinion.

What if you release one current and a friend of yours, with whom you have synchronised clocks releases the other one at the same time, as per the train's standard?

In this respect (distant events) SR would allow equally valid versions about the judgment of simultaneity: observers at the embankment would claim that the two switching acts were not simultaneous. There would exist two equally valid versions about whether the two actions were simultaneous. If we introduce the aether of LR, this is of little use, since its version is unknowable. But even if the aether's version were known, that would be irrelevant. For legal purposes, what matters is that you had the intention to kill and did acts appropriate to kill (in the environment where you did them), so you should be condemned for murder, if the jury is well informed.

However, there may be other scenarios where the fact that two events are simultaneous in purely relative or absolute terms is legally relevant... That is what I am thinking of. But please proceed with your arguments. Sincerely I enjoy the exchange, precisely because I am so little sure of anything! Regards.

 

[matheinste]

Hello altonhare.

My final attempt.

Here is a list of the better known authors on relativity and what they say about the relativity of simultaneity. Only the most popular are included because a full list would be very long. If you do not have access to any of these books I will be happy to transcribe passages for you. If you need to know the specific editions, printings etc. I can provide them. These are some of the books that gave me the ideas on the relativity of simultaneity with which you disagree.

Bernard E. Schutz. A First Course in Relativity. Sixteenth Edition 2004 Page 9.

Wolfgang Rindler Essential Relativity. Springer-Verlag. Second Edition. Page 28.

Rober M.Wald General Relativity. Page 4

A.P. French. Special Relativity. Page 74

G.Stephenson and C.W Kilmister. Special Relativity for Physicists. Page 37.

Eddington. The Theory of Relativity. Page 33

Hans Reichenbach. The Philosophy of Space and Time. Page 134.

Eddington. Space, time and Gravity. Page 51.

Einsstein. A. Relativity. The Special and General Theory. Project Gutenberg Ebook Page 11.

Misner Thorne and Wheeler. Gravitation. Page 296

Matheinste.

 

[altonhare]

Heya Saw,

What's your mother tongue?

Yes you understand right. If the bolts hit the two rods (situated to either side equidistant from the chair) simultaneously then they induce a current that travels to the chair, arrive simultaneously, and the chair's integrated circuit sees the logic "1-1" which tells it to allow all the electrical current to go through Matheinste's body painlessly and instantly rendering him lifeless.

The people on the embankment, if they stick to what Mathe has said, "must conclude that the bolts were not simultaneous". In which case the bolts could not have killed Mathe, the circuit would never have allowed non simultaneous strikes through.

But of course I killed Mathe. The bolts were simultaneous no matter how many observers on the embankment testify that they were not. We don't care how much beer they drank or how advanced their calculations. "None of it was worth a single hair of a woman's head" - Camus

What are their observations and calculations worth if they let a murderer go free?

Here's the deal. There is no "relativity of simultaneity" because the concept "simultaneity" only has meaning for events in their own inertial frame, i.e. in the rest frame of the train in this instance. The observers on the embankment are simply wrong if they actually conclude that the events "were not simultaneous". It doesn't matter if they tack on "in our reference frame" because such a conclusion is worthless and irrelevant to the question of *were the events actually simultaneous?*. Obviously they actually were, because Mathe is dead, so simultaneity is NOT relative. If Mathe continues to argue that simultaneity is relative he'll be happy to strap into the chair as long as nobody on the train is watching the event, and lots are on the embankment to watch the bolts be "non simultaneous"!

Mathe,

Thanks for the additional references and completely ignoring everything else I said. Wanna hop in the hot seat or not? Nobody on the train will watch the strikes, I promise! Only people who "must conclude that the strikes were not simultaneous" will watch!