Light shone in a train bouncing off mirrors

[JustinTime]

I have a question about a thought experiment I read about. I think the question or a similar was asked, and I'm sure others have asked this question, but I'm asking it in this way so it can be answered through the framework of my question. The framework of how I'm understanding it, and so that if there is a flaw, I can be shown what that is. I don't have a math or physics background, but have found what I've read about relativity fascinating. I got a book called Einstein's Relativity by Max Born and a lot of it is over my head but I understand bits. The thought experiment I'm listing wasn't in this book.

The thought experiment is a train is moving forward and on the top and bottom are mirrors which reflect a light up and down. It is said that for the person on the train, they will see the light go straight up. But an an observer positioned outside of the train will see it traverse diagonally. What I don't understand is this: If the speed of light is constant, it moves independent of the train. So when the light is first reflected to the opposite mirror, why wouldn't both observers see the light bounce and hit the other mirror slightly *behind* where it hit the other? I understand that if a person in a train throws up a ball, to him it appears to go straight up but to the person outside it is seen as an arc. But with light, it travels independent of the speed of the train. In order for the person in the train to see the light travel a straight path, wouldn't the beam of light have to shift or travel additionally in the direction he's going?
Thank you in advance to anyone who takes the time to answer.

Justin

 

[JesseM]

The thought experiment is a train is moving forward and on the top and bottom are mirrors which reflect a light up and down. It is said that for the person on the train, they will see the light go straight up. But an an observer positioned outside of the train will see it traverse diagonally. What I don't understand is this: If the speed of light is constant, it moves independent of the train. So when the light is first reflected to the opposite mirror, why wouldn't both observers see the light bounce and hit the other mirror slightly *behind* where it hit the other? I understand that if a person in a train throws up a ball, to him it appears to go straight up but to the person outside it is seen as an arc. But with light, it travels independent of the speed of the train. In order for the person in the train to see the light travel a straight path, wouldn't the beam of light have to shift or travel additionally in the direction he's going?

Light's speed is independent of the source, but the direction of a beam of light from a laser or a flashlight is not. If the beam travels parallel to the body of a flashlight when the flashlight is at rest on Earth, as measured in the Earth's rest frame, then the beam must also travel parallel to the body of a a flashlight when the flashlight is on a train, as measured in the rest frame of the train. If it didn't work this way, then the laws of physics would work differently in different frames, and a person in a sealed windowless room could determine their absolute velocity by seeing what angle a beam left a flashlight as measured in the room's rest frame.

 

[SpazAttack]

I have a question about a thought experiment I read about. I think the question or a similar was asked, and I'm sure others have asked this question, but I'm asking it in this way so it can be answered through the framework of my question. The framework of how I'm understanding it, and so that if there is a flaw, I can be shown what that is. I don't have a math or physics background, but have found what I've read about relativity fascinating. I got a book called Einstein's Relativity by Max Born and a lot of it is over my head but I understand bits. The thought experiment I'm listing wasn't in this book.

The thought experiment is a train is moving forward and on the top and bottom are mirrors which reflect a light up and down. It is said that for the person on the train, they will see the light go straight up. But an an observer positioned outside of the train will see it traverse diagonally. What I don't understand is this: If the speed of light is constant, it moves independent of the train. So when the light is first reflected to the opposite mirror, why wouldn't both observers see the light bounce and hit the other mirror slightly *behind* where it hit the other? I understand that if a person in a train throws up a ball, to him it appears to go straight up but to the person outside it is seen as an arc. But with light, it travels independent of the speed of the train. In order for the person in the train to see the light travel a straight path, wouldn't the beam of light have to shift or travel additionally in the direction he's going?
Thank you in advance to anyone who takes the time to answer.

Justin

The idea behind this is that the laws of physics are exactly the same if you are moving with a constant velocity as opposed to you not moving at all. So although the person on the platform will indeed see the photons direction changed (like the poster above me said, direction is not independent), the person on the train would not, because from his frame of reference, he isn't even moving.

 

[JustinTime]

Light's speed is independent of the source, but the direction of a beam of light from a laser or a flashlight is not. If the beam travels parallel to the body of a flashlight when the flashlight is at rest on Earth, as measured in the Earth's rest frame, then the beam must also travel parallel to the body of a a flashlight when the flashlight is on a train, as measured in the rest frame of the train. If it didn't work this way, then the laws of physics would work differently in different frames, and a person in a sealed windowless room could determine their absolute velocity by seeing what angle a beam left a flashlight as measured in the room's rest frame.

Thank you, that is interesting. How do we know that the beam doesn't travel parallel to the body of the flashlight?

 

[JesseM]

Thank you, that is interesting. How do we know that the beam doesn't travel parallel to the body of the flashlight?

Well, it does travel parallel in the flashlight's rest frame, just not in a frame where the flashlight is moving. You can predict this just based on the fact that the equations of electromagnetism are "Lorentz-invariant", meaning electromagnetic waves and charged particles obey the same equations in different reference frames.

 

[JustinTime]

It seems strange to me that if the speed of light is constant that it would travel in a path parallel to the flashlight. If the flashlight is moving, the light would have to move as well. If the beam is observed moving parallel to the flashlight it would be moving at the same speed as the flashlight, but light moves at a constant speed. I think it would be said that the flashlight is at rest in its own inertial frame. Something just doesn't seem to add up!

 

[Xieper]

I found the theories around what happens if you assum that (in this example) the train is approaching or at the speed of light very confusing (and so I can't remember them). I must look into it again and see if I can grasp the concept of these theories now I'm a little older and now find it MUCH more interesting...

 

[ZikZak]

If the flashlight is moving, the light would have to move as well.

What criteria are you using to determine whether "the flashlight is moving?" You must be assuming the presence of an absolute reference frame against which all motion is measured. There is no such reference frame. The person in the train is entirely justified in considering the flashlight to be at rest, and it will behave exactly as if it were, because indeed, relative to the train, it is.

 

[I. N. Stine]

Light's speed is independent of the source, but the direction of a beam of light from a laser or a flashlight is not. If the beam travels parallel to the body of a flashlight when the flashlight is at rest on Earth, as measured in the Earth's rest frame, then the beam must also travel parallel to the body of a a flashlight when the flashlight is on a train, as measured in the rest frame of the train. If it didn't work this way, then the laws of physics would work differently in different frames, and a person in a sealed windowless room could determine their absolute velocity by seeing what angle a beam left a flashlight as measured in the room's rest frame.

Wow! This is fascinating!

What if the flashlight is placed on the track bed and bound with duct tape to a cross tie so that it is exactly perpendicular to the tracks according to a protractor held against it?

Then, when the train rumbles by, a hobo standing in the embankment and looking in a window can see the beam hit a hole in the train floor and go up to the ceiling, where it hits a spot behind the spot in the floor!

OK, if I understand you right, a rider in the train will see the beam come through the hole in the floor and go straight up to a spot that is not behind the hole in the floor. The spot on the ceiling is the same distance away from the rear wall as the hole in the floor! Right? Wow! I love revatitly! it is so cool!

Thank you for explaining it so good! You are a really wise fellow!

 

[michelcolman]

Wow! This is fascinating!

What if the flashlight is placed on the track bed and bound with duct tape to a cross tie so that it is exactly perpendicular to the tracks according to a protractor held against it?

Then, when the train rumbles by, a hobo standing in the embankment and looking in a window can see the beam hit a hole in the train floor and go up to the ceiling, where it hits a spot behind the spot in the floor!

OK, if I understand you right, a rider in the train will see the beam come through the hole in the floor and go straight up to a spot that is not behind the hole in the floor. The spot on the ceiling is the same distance away from the rear wall as the hole in the floor! Right?

No, both will see the spot of light behind the hole. To the observer in the train, the light moves diagonally because from his point of view the flashlight is moving backward underneath the train.

Situation 1: flashlight on board
Observer on train: flashlight is stationary, so it shines straight up
Observer on ground: flashlight is moving forward, so it shines diagonally forward

Situation 2: flashlight on ground
Observer on train: flashlight is moving backward, so it shines diagonally backward
Observer on ground: flashlight is stationary, so it shines straight up

There can never be a situation where two observers really see different things (like a spot of light in two different locations). They will disagree on many other things, like at what time the spot hit the ceiling, how long it took the light beam to travel from bottom to top, how long the train is, whether two events happen at the same time, whether two clocks in different parts of the train are synchronised or not, etc... But they would never see a spot of light hitting different parts of the train.

If they would see the spot of light in two different locations, imagine tying a light-sensitive explosive charge to the ceiling of the train exactly above the hole. As seen from the train, it would explode. But as seen from outside, it would not. This is clearly impossible.

 

[I. N. Stine]

No, both will see the spot of light behind the hole. To the observer in the train, the light moves diagonally because from his point of view the flashlight is moving backward underneath the train.

Situation 1: flashlight on board
Observer on train: flashlight is stationary, so it shines straight up
Observer on ground: flashlight is moving forward, so it shines diagonally forward

Situation 2: flashlight on ground
Observer on train: flashlight is moving backward, so it shines diagonally backward
Observer on ground: flashlight is stationary, so it shines straight up

There can never be a situation where two observers really see different things (like a spot of light in two different locations). They will disagree on many other things, like at what time the spot hit the ceiling, how long it took the light beam to travel from bottom to top, how long the train is, whether two events happen at the same time, whether two clocks in different parts of the train are synchronised or not, etc... But they would never see a spot of light hitting different parts of the train.

If they would see the spot of light in two different locations, imagine tying a light-sensitive explosive charge to the ceiling of the train exactly above the hole. As seen from the train, it would explode. But as seen from outside, it would not. This is clearly impossible.

Thanks for explaining it to me! I love retalivity but every time I think about I seem to get something backward.

I believe I read somewhere that Einstein claimed that light did not get a change in speed from the speed of a light bulb or something like that. I think Einstein said that light does not get momentum from the thing that gives off the light. Does that sound like I am remembering it right?

What is confusing me when I study your good explanation is this. If the flashlight is in the moving train, and the hobo is sitting in the embankment watching in a window, when a piece of light comes out of the flash light, it should go straight up at its regular speed. And, if Einstein is right, and I remember him right, the piece of light will not have any speed in the direction the train is going. So, while the piece of light is going from the flash light up to the ceiling, the ceiling is moving forward but the piece of light is not moving forward. It seems that the piece of light will hit a spot on the ceiling further back than the location of the flash light. The hobo sitting outside should see it that way. Come to think of it, the rider in the train should see it that way too. Am I right at all about this?

In the first post in this thread, the writer was concerned about the light beam going straight up when the train was sitting still. Whether the rider or the hobo was watching it. Then when the train is moving, the first writer was saying ( I believe I remember it right ) that the light would get left behind and hit further back on the ceiling. Whether, again, the rider or the hobo watched it.

One time I borrowed a college physics book and was reading about relavility. It had two pictures. One picture showed light going straight up and down. I guess that was what the rider was supposed to see. The other picture showed light going in a diagonal zig zag and moving along with the train. That must have been what the hobo was supposed to see. It not have a third picture. So I don't know what anybody was supposed to see when the train was still.

I am confused about why the book showed different people seeing two different ways that light moved but you are explaining that everybody must see the same thing.

Wher am i getting mixed up on this? Does light get left behind or does light get speed from the train and go forward too?

I know all of you figured all this out a long time ago. But it gets mixed up for me. Thanks!

 

[altonhare]

The guy on the ground sees the light take a diagonal for the following reason. The atom of the source excites, sends a signal to your eye, and your brain says "there's the flashlight". Your brain decides it's *exactly* 4 feet from a nearby stop sign and 1 foot off the ground. The train then moves a finite distance (delta x) to the right before an atom in the ceiling (1 foot above the source) absorbs the signal, then retransmits it to your eye. Your brain then says "There's a spot right there". This spot will be 4 feet - delta(x) from the stop sign and 1 foot above the flash light. You perceived the source to be 4 feet to the left of the stop sign and the target (ceiling) to be 4-dx from the stop sign. (4,0) to (4-dx,1) is diagonal to the two coordinate axes considered

The guy in the train sees the source, decides its 4 feet from the wall, then the train, wall, flashlight, guy, and the signal itself move dx to the right, and the guy sees the spot exactly 4 feet from the wall again, just 1 foot higher. (4,0) to (4,1) is parallel to an axis, call it vertical or horizontal.

One way to think about light is as if the atoms between the source and the target are *physically connected* by a 2 strand entwined rope or something. When an atom in the source "excites" it torques the rope, which propagates straight up to the next atom, exciting it. Both atoms torque a rope connected to your eye, too. Just as if you took two shoe strings and wrap them around each other, then at one end take the two strings and pull them laterally, you'll torque it and cause the other end to "spin". This is the idea behind the principle of ray reversibility. The light signal propagates along this permanent physical interconnection that travels along with the atoms it connects i.e. the atoms in the flash light and the ceiling.

So if you're watching the train go by the rope connecting the two atoms is still "vertical", you just see the flash light and the ceiling at two different x-axis locations which makes it appear that light traveled both "up" and along the x axis, which makes it seem like it traveled diagonally. The guy on the train sees the flash light and the ceiling at the same location on the x axis, which makes it look like the light traveled parallel to the y axis. It's just an optical illusion, a result of light's finite propagation speed.

Now the issue of the two observers measuring light's speed is "another can of worms" that has to do with the observation that a clock belonging to the guy on the train will tick fewer times than the guy on the ground. Let's analyze the situation. The guy on the ground will measure a diagonal distance. Taking the velocity of light to be irrespective of the source like any wave, we would naively expect specific x and y components of the velocity, which of course have to add up to c. Let's say the train's moving along at ~100 km/sec (fast train). We naively expect 0.999999944*c in the y direction and 0.0003 in the x direction. So we expect the observer on the ground, watching, to perceive the light to take a little longer to go from the flash light to the ceiling than the guy on the train. The guy on the train doesn't measure a diagonal, he only has a single component, 1*c in the y direction. We'd expect the guy on the ground to report that the light took 1/.999999944 longer to get to the ceiling than the guy on the train. But in reality this isn't what we see. The guy on the ground measures the same time. It seems that the clock belonging to the guy on the ground ticks 1/.999999944 faster than the guy's clock on the train, exactly making up for the extra distance he perceives due to the "diagonal". Nature is tricky like that.

Why do clocks slow down? Who knows, all we know is that they do so just enough so that we always *measure* the speed of light to be the same, no matter what situation we find ourselves in.

Yous said you "haven't had any math" but if you're interested in relativity you should, at a *minimum* learn enough math to follow the derivation of the Lorentz transformations (if you haven't done so already).

 

[matheinste]

Hello antonhare

Quote:-

---One way to think about light is as if the atoms between the source and the target are *physically connected* by a 2 strand entwined rope or something. When an atom in the source "excites" it torques the rope, which propagates straight up to the next atom, exciting it. Both atoms torque a rope connected to your eye, too. Just as if you took two shoe strings and wrap them around each other, then at one end take the two strings and pull them laterally, you'll torque it and cause the other end to "spin". -----

As visualizations go this is pretty bizarre and also misleading.

Matheinste

 

[altonhare]

Hello antonhare

Quote:-

---One way to think about light is as if the atoms between the source and the target are *physically connected* by a 2 strand entwined rope or something. When an atom in the source "excites" it torques the rope, which propagates straight up to the next atom, exciting it. Both atoms torque a rope connected to your eye, too. Just as if you took two shoe strings and wrap them around each other, then at one end take the two strings and pull them laterally, you'll torque it and cause the other end to "spin". -----

As visualizations go this is pretty bizarre and also misleading.

Matheinste

How is it misleading? The atom can only take in or release an integral number of links of this rope, which justifies quantization. The signal can only propagate rectilinear, justifying this observation. It simulates propagating perpendicular plane waves of classical EM. It's a pretty useful visualization.

Edit: Additionally, granting that it may not be perfect, is a stream of bullets or abstract 2D plane waves somehow superior?

 

[matheinste]

Hello antonhare.

In my opinion the most fundamentally misleading part is describing the difference in "views" between the two observers as an "optical illusion". The remark about quantization is quite irrelevant to the understanding of the geometry of the situation and just throws in a level of complication into the description of a simple effect that can, and has already been, adequately explained earlier in this thread.

Matheinste

 

[altonhare]

Hello antonhare.

In my opinion the most fundamentally misleading part is describing the difference in "views" between the two observers as an "optical illusion". The remark about quantization is quite irrelevant to the understanding of the geometry of the situation and just throws in a level of complication into the description of a simple effect that can, and has already been, adequately explained earlier in this thread.

Matheinste

How is it not an optical illusion? The guy on the train sees (x1,0) ; (x1,1) and the guy on the ground sees (x2,0) ; (x2-dx, 1) where dx is just the distance-traveled by the train relative to the guy on the ground. One infers a vertical path and the other infers a diagonal path, purely because light's propagation speed is finite, so the guy on the ground must wait while the train moves to the side before he can see the second photon.

The guy on the ground infers a longer distance. The distance between A and B, though, is static. When A releases the photon it travels a distance D to B, no matter who's watching, whether they're moving or not, or whether they're doing cartwheels or not. This static separation doesn't change because of testimonials or calculations.

The remark on quantization was in response to your general dislike of the visualization, to point out other reasons I like it.

 

[matheinste]

It is not an optical illusion because what either/both observers see is real for them. Both are correct and neither sees an illusion. Perspective might be a better word, but even this is inaccurate.

Matheinste.

 

[altonhare]

It is not an optical illusion because what either/both observers see is real for them. Both are correct and neither sees an illusion. Perspective might be a better word, but even this is inaccurate.

Matheinste.

Are you saying we could barely squeeze a brick between A and B but then also stick 2 bricks between A and B?

Edit: The problem here is that the "distance" calculated in SR is actually "distance traveled" (i.e. a distance-traveled by the light signal). Distance traveled is a dynamic concept whereas distance is a static concept. An observer that assumes the two are the same makes a gross logical error.

 

[matheinste]

Quote:-

---Are you saying we could barely squeeze a brick between A and B but then also stick 2 bricks between A and B? ----

I'm afraid i do not undeerstand what you are asking.

Matheinste

 

[altonhare]

Quote:-

---Are you saying we could barely squeeze a brick between A and B but then also stick 2 bricks between A and B? ----

I'm afraid i do not undeerstand what you are asking.

Matheinste

Like I said, there are two concepts here, the static concept distance and the dynamic concept "distance traveled". The latter is what we measure, not the former. .

 

[matheinste]

Quote:-

-Like I said, there are two concepts here, the static concept distance and the dynamic concept "distance traveled". The latter is what we measure, not the former. . -----

I still don't see the relevance of anything that you say. All this, whatever it might be, is an unecessary sidetrack to the very simple explanation of the observers of the moving mirror. Can't we leave out any complications. The original question has been given the standard reply, that found in any textbook that uses this example. If the questioners had to rely only upon your response i think they would have been confused and misled.

Matheinste

 

[ZikZak]

altonhare:

I am skateboarding down the street with a tennis ball in my hand. Over the course of one second, I observe the tennis ball and measure it to be at rest, to have covered no distance at all. My friend, standing on the sidewalk disagrees and claims that the tennis ball traveled quite far. Whose observation is "real," and whose is the "illusion," and how do we tell?

 

[michelcolman]

Thanks for explaining it to me! I love retalivity but every time I think about I seem to get something backward.

I believe I read somewhere that Einstein claimed that light did not get a change in speed from the speed of a light bulb or something like that. I think Einstein said that light does not get momentum from the thing that gives off the light. Does that sound like I am remembering it right?

It's not entirely correct to say that light does not get a change in speed from the speed of the light bulb. The absolute value of the speed of light is not changed (light does not go faster in the direction of movement of the light bulb), but the direction certainly can be changed. If a laser is moving sideways, it will shine diagonally. But no matter how you move the laser, the speed of the light leaving the laser will always be 299792458 m/s. That's what Einstein meant when he said light does not gain momentum from the moving bulb. It does not go faster, but it may well move in a different direction.

It's perfectly possible for one observer to see a ray of light moving vertically while the other sees it moving diagonally. The strange bit is that both will see it moving at the same speed. And since the diagonal distance is longer than the vertical distance, this means that the two observers will not agree on how long it took for the ray of light to travel from the floor to the ceiling.

The explanation for this is a bit complicated: it's not just that one observer's clock is ticking more slowly! Otherwise, you could use the flashlight in the train and the flashlight on the ground and conclude that time is ticking more slowly AND faster in the train depending on which flashlight you happen to be using. This mistake is often made, even in books about relativity that try to simplify things a bit too much.

There are many things the two observers will not agree on, and you can only make accurate calculations if you look at all of these things together.

- Clocks are ticking at different rates. Funny thing is, the observer outside will say the clocks on the train are ticking more slowly, while the observer in the train will say the clocks outside are ticking more slowly
- The two observers do not agree on what time it is in different locations. If a flash of lightning hits the front and back of the train at the same time (as seen from outside), the person in the train will say the front was hit before the back. If the train is carrying clocks on board, and an observer inside the train says the clock are perfectly synchronised, an observer outside will say the clock in the front of the train is slightly ahead of the clock in the back. Same kind of thing for clocks on the ground as seen by the moving train.
- They will not even agree on how long the train is.

So you can imagine that, if the two observers are looking at events that happen at different coordinates using clocks that don't tick at the same rate, using rulers that don't have the same length, they will arrive at different explanations for the same things.

They will never disagree on what really happened (light hit a certain spot on the ceiling), but they will disagree on speeds, distances and times.

The only way of really calculating everything correctly is by using the Lorentz transformations. You can get some simple results without them (for example, the time it took for light to reach the ceiling is the distance (vertical or diagonal) divided by the speed of light), but it's very easy to make mistakes if you try more complicated things involving events happening at different locations.

 

[altonhare]

Quote:-

-Like I said, there are two concepts here, the static concept distance and the dynamic concept "distance traveled". The latter is what we measure, not the former. . -----

I still don't see the relevance of anything that you say. All this, whatever it might be, is an unecessary sidetrack to the very simple explanation of the observers of the moving mirror. Can't we leave out any complications. The original question has been given the standard reply, that found in any textbook that uses this example. If the questioners had to rely only upon your response i think they would have been confused and misled.

Matheinste

The relevance is this. How is the distance between two objects anything like the distance-traveled by one object?

Distance:
--------
B

0
--------

Distance-traveled:
--------0
--------

--------
B--------

Dashed lines are the floor and ceiling of the train. The 0 is the flashlight and the B is the spot on the ceiling.

Distance is a static concept, in the illustration of this concept we are looking at single cross section of time. We are looking at a SINGLE location of objects. We are looking at the locations of the flashlight and the ceiling respectively.

Distance-traveled is a dynamic concept, in this illustration we are looking at 2 instants. We are looking at SUCCESSIVE locationS of objects. This requires one to remember where an object was and also to see where it is now. We are looking at the location of the flashlight, recording it, THEN looking at the location of the ceiling *after the photon arrives*.

Consider the second illustration, you're standing on the dashed line (floor of train). You see the first picture and then the second. This corresponds to the guy on the train first seeing the flashlight turn on, then seeing the ceiling spot. Now consider the guy standing on the ground outside the train. This situation looks like (S is just a spacer):

--------0
--------
GGGGGG

S--------
SB


S--------
GGGGGG

The person standing on the ground remembers where the object WAS and sees where it is NOW. Never did the distance between the flashlight and the ceiling change because distance has nothing to do with motion. Distance cannot change because "change" invokes motion i.e. is dynamic. We need only one picture/illustration to show distance, we need at least two pictures to illustrate distance-traveled.

Both the person on the train on the ground are correct in their measurements of distance traveled. Any conclusions they draw about the distance between the flashlight and the ceiling based on this measurement is equivocating two explicitly different concepts. Distance is not relative and does not depend on perspective or observers. The static separation between two objects doesn't care if you're drunk, blind, or flying an F-15.

Finally, after laying out the basic conceptual issue, the guy on the train and the ground are idiots to be surprised at getting different results. Everyone learns somewhere in their elementary education that all measurements require a reference standard. The two people are measuring distance-traveled using different references. The guy on the train is measuring the distance-traveled by the photon relative to the train and the guy on the ground is measuring distance-traveled relative to the ground. Only someone with no education or logical reasoning would be surprised by different results. Indeed the guy on the ground can get the same result as the guy on the train simply by measuring the distance-traveled by the photon relative to the train. This is elementary level stuff. I say the height of the cup is 12 and you say it's 30.48. We're using different reference standards, that's all! Would you be shocked that I got a different result when I measured in inches vs. centimeters? Shall we conclude that the cup contracts for me? Or that the space within it contracts for me?

altonhare:

I am skateboarding down the street with a tennis ball in my hand. Over the course of one second, I observe the tennis ball and measure it to be at rest, to have covered no distance at all. My friend, standing on the sidewalk disagrees and claims that the tennis ball traveled quite far. Whose observation is "real," and whose is the "illusion," and how do we tell?

Perhaps "illusion" was a poor word. What is going on here is a misintegration of concepts, a basic and fundamental conceptual error. First of all whether something is "at rest" or not is not a matter of measurements, observations, or anyone's personal opinion. Whether an object moved or not is a matter of definitions. The definition of motion is "two or more locations of an object". Where "location" is the set of distances from an object to every other object in the universe. So, if the ball is at more than one location, then it moved by definition, whether you personally saw it move or not.

The other problem is that you two are not using a common reference standard, which is a very basic and necessary thing for any measurement. You are measuring the ball's distance-traveled relative to your chest (for instance) and the guy on the sidewalk is measuring the distance-traveled relative to the sidewalk. If you two use the same reference standard, you will both get the same result. Just like if we use the same ruler we will get the same result and if you use a metric ruler and I use British we will get different results, but can reconcile our different quantities by comparing reference standards. You on your skateboard can reconcile the different result (0 distance traveled of the ball) with your friend's (X distance-traveled by the ball) by comparing your reference standards. Your friend says his reference standard is the sidewalk, on which there are even marks (as on a ruler). You say yours is your arm, on which there are even marks (as on a ruler). Now when you go back to where you started boarding and look at your *friend's* reference standard you will conclude the same as him.

Which one is "right"? All knowledge is contextual and ALL measurements involve a reference standard.

Michel:

I intentionally left out what Einstein calls the "relativity of simultaneity" because it only complicates matters. Just because I detect a photon before you has nothing to do with if an event was simultaneous or not. Differing conclusions about simultaneity are, again, due to differing reference standards and nothing deeper.

We can illustrate this. Two balls strike a table at eye level simultaneously and emit a photon as they strike it while I run toward them and you run away from them (S is a spacer b/c of the forum's parser and P is a photon): OsssssssssssssssssssssssssssssPBBPssssssssssssssssssssssssssssssO
\|/ssssssssTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTsssssssssss\|/
|ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss|
/ \sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss/ \

ssssssOssssPsssssssssssssssssssBBsssssssssssssssssssPssssssssssssssss O
sssss\|/ssssTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTssssssssssssssss\|/
ssssss|sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss |
sssss/ \sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss/ \

ssssssssOPsssssssssssssssssssssBBsssssssssssssssssssssPssssssssssssssssO
sssssss\|/ssTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTsssssssssssssssss\|/
ssssssss|sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss|
sssssss/ \ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss/ \

Left guy says,"The balls hit now!"

The guy on the right hasn't seen them yet because he's moving away from the photon. Later on he'll say,"They collided now!"

Does either of their opinions change the *physical situation*? What if one is drunk or has a mental disorder? Will that change what happened? Because a photon's speed is finite, and so people absorb them before or after other people, does the situation change *physically*? In fact, if the two are aware that light is not instantaneous, they should not be at all surprised by their differing results! This is elementary, one surprised by this result is assuming light is instantaneous or doesn't understand the concept of a measurement.

The Lorentz transforms are just a way to reconcile different reference standards. Conceptually it is no different than using a unit conversion such as 2.54 cm = 1 inch.

 

[ZikZak]

I intentionally left out what Einstein calls the "relativity of simultaneity" because it only complicates matters. Just because I detect a photon before you has nothing to do with if an event was simultaneous or not. Differing conclusions about simultaneity are, again, due to differing reference standards and nothing deeper.

That is absolutely NOT what Einstein means by "relativity of simultaneity." He means that different observers disagree on whether events were simultaneous AFTER taking the light-travel time into account.

 

[Saw]

Hello all. Although the discussion has shifted into a deeper subject I am also very interested in, I would like to focus on the original question and illustrate it with a derivation:

- SR, hence, asserts that light projected from sources like a laser gun or a flashlight always hits the target it is pointing at, if this target is in the same frame as the source, no matter the state of motion of the latter. It seems the precision about the nature of the source (laser or flashlight) is meaningful: if the source were a light bulb, it would produce a wave that spreads in all directions and so someone could say that light hits the target because it reaches everywhere. But if the source produces no or very limited light dispersion, like in the case of a laser or flashlight, the only explanation can be that light, even if it does not acquire the speed of the frame in question, does acquire its direction. Right?

- In Lorentzian relativity, it seems to me, the answer would be different. Light, in this sort of examples, would only hit the target to the extent that the frame in question were at rest wrt the aether or had residual acceleration wrt the aether in the same direction that the light source is pointing at. Is this supposition right?

It is often said that SR and LR are conceptually different but render the same practical results. But, if my above explanation is accurate, wouldn’t this be a practical difference? I am not advocating that one theory or the other is preferable. I am not qualified to do so. Just trying to clarify the scope of the difference between the two approaches.

 

[altonhare]

That is absolutely NOT what Einstein means by "relativity of simultaneity." He means that different observers disagree on whether events were simultaneous AFTER taking the light-travel time into account.

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 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.

 

[matheinste]

Simultaneity is often misunderstood by by newcomers to SR. Observers in relative motion will disagree on the simultaneity of spatially separated events. It is not just a matter of light transit time. Whether or not an obsever sees events at the same time is irrelevant. Events that are simultaneous in one frame are not simultaneous in any frame moving relative to it. Any textbook will explain this very early on. It is fundamental to SR and most of the usual "pradoxes" in SR are resolved using an understanding of it. It has also been explained many times on this site.

Simultaneity poses no problem for events happening at the same place at the same time such as collisions.

Matheinste.

 

[altonhare]

Simultaneity is often misunderstood by by newcomers to SR. Observers in relative motion will disagree on the simultaneity of spatially separated events. It is not just a matter of light transit time. Whether or not an obsever sees events at the same time is irrelevant. Events that are simultaneous in one frame are not simultaneous in any frame moving relative to it. Any textbook will explain this very early on. It is fundamental to SR and most of the usual "pradoxes" in SR are resolved using an understanding of it. It has also been explained many times on this site.

Simultaneity poses no problem for events happening at the same place at the same time such as collisions.

Matheinste.

The point is, the only reason they disagree is because they are measuring with different reference standards. If everyone picks one standard everyone agrees.

 

[matheinste]

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.

 

[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.