Question on simultaneous events.

[gnome]

Where are you finding tx, ty and tz? Every reference to Lorentz transformations in Modern Physics (Serway, Moses & Moyer) and in Special Relativity (A.P. French) mention only
x -> x'
y -> y'
z -> z'
t -> t'

 

[Eyesaw]

Time is treated as a variable that is dependent on relative velocity
in SR. Since velocity is a vector with 3 components, there should be
3 transformation equations for time as well.

 

[gnome]

Relative velocity of one frame of reference compared to the other.

How you set up your coordinates is entirely arbitrary. The "easy" way is to set them up so the relative motion is along the x axis. Then you only need one transformation equation for time.

If you set up your coordinates in such a way that you have 3 components of velocity, you just make the calculations more complicated -- probably hopelessly complicated -- but the end result will be the same. There is still only 1 time axis each coordinate system.

 

[Eyesaw]

Originally posted by gnome
Relative velocity of one frame of reference compared to the other.

How you set up your coordinates is entirely arbitrary. The "easy" way is to set them up so the relative motion is along the x axis. Then you only need one transformation equation for time.

If you set up your coordinates in such a way that you have 3 components of velocity, you just make the calculations more complicated -- probably hopelessly complicated -- but the end result will be the same. There is still only 1 time axis each coordinate system.

You have no choice, things do not move in one dimensional space. It's implicit in the one dimensional Lorentz transformation that
the V is the x component of V where the y and z components are 0. If time is a function of Vx, it is also a function of Vy and Vz simultaneously. Or rather, not simultaneously since we believe
in SR.

 

[gnome]

What are you talking about?

The transformation is not concerned with various objects moving in various directions in 3 dimensions. It is merely translating the coordinates of an event in one frame of reference to the coordinates of the same event in another frame of reference. The motion of one frame in relation to another frame can always be described by a single vector, and you can always position your coordinate axes so that vector is parallel to the x-x' axes.

 

[Eyesaw]

"..it is merely translating the coordinates of an event"... in other words, something moving through space. You would be better of saying Special Relativity is only valid for one dimensional objects moving in one dimensional, field free space. In other words, never.

 

[gnome]

Dude, your invention of an x-component of time and a y-component of time makes as much sense as a y-component of x and a z-component of x. In other words, no sense at all.

As to
"there should be 3 transformation equations for time as well":
When are you publishing your book? Everyone else seems to manage just fine with only 1 transformation equation for time. The difficulty of the calculation is a function of how you set up the problem. As I said, you probably could set up a problem with one frame moving along some skewed line relative to the other, but you still wouldn't have three SEPARATE time transformation equations. You would have one hopelessly complicated time transformation equation dealing with three components of velocity, and then about ten hours later (relatively speaking ) you would end up with the same result for t' as you would have gotten with the common, simple time transformation equation had you set up the problem sensibly -- if you didn't screw up the calculations.

In other words, setting up a problem such that the relative velocity of the S' frame is parallel to the x-axis is NOT saying that this method is only useful for motion in 1-dimension. It's only saying, I don't want to do 10 hours of calculation when I can solve the same problem in 10 minutes instead. Note that within those two "well-behaved" reference frames you can have objects moving in many different, not necessarily parallel, directions (and speeds), and the same, simple translation equation works for all of them.

 

[Eyesaw]

Originally posted by gnome
Dude, your invention of an x-component of time and a y-component of time makes as much sense as a y-component of x and a z-component of x. In other words, no sense at all.

As to
"there should be 3 transformation equations for time as well":
When are you publishing your book? Everyone else seems to manage just fine with only 1 transformation equation for time. The difficulty of the calculation is a function of how you set up the problem. As I said, you probably could set up a problem with one frame moving along some skewed line relative to the other, but you still wouldn't have three SEPARATE time transformation equations. You would have one hopelessly complicated time transformation equation dealing with three components of velocity, and then about ten hours later (relatively speaking ) you would end up with the same result for t' as you would have gotten with the common, simple time transformation equation had you set up the problem sensibly -- if you didn't screw up the calculations.

In other words, setting up a problem such that the relative velocity of the S' frame is parallel to the x-axis is NOT saying that this method is only useful for motion in 1-dimension. It's only saying, I don't want to do 10 hours of calculation when I can solve the same problem in 10 minutes instead. Note that within those two "well-behaved" reference frames you can have objects moving in many different, not necessarily parallel, directions (and speeds), and the same, simple translation equation works for all of them.

Erm, no. Have you tried throwing a baseball at a 45 degree angle? If so, how did you make the reference frame of the ground parallel to the motion of the baseball? I suppose it's ok for SRists to move
the whole Earth in the direction of the baseball to accomdate the
one dimensional Lorentz Transformation.

Obviously velocity between two frames has 3 components,
and since time dilation and length contraction are a function of relative velocities in SR, time is also a vector with 3 components
so that there should be 3 transformation equations for time in
SR and not 1. Therefore, every object in SR has 3 time dimensions.

 

[Doc Al]

I can't decide whether this is hilarious or sad. No offense, Eyesaw, but have you even glanced at a relativity book before?

Originally posted by Eyesaw
Erm, no. Have you tried throwing a baseball at a 45 degree angle? If so, how did you make the reference frame of the ground parallel to the motion of the baseball? I suppose it's ok for SRists to move
the whole Earth in the direction of the baseball to accomdate the
one dimensional Lorentz Transformation.

Erm, yep. You do realize that this SR thing just happens to depend on the relative velocity, right? You also realize that "SRists" don't actually have to "move the whole earth", right? It's just a mathematical convenience.

Obviously velocity between two frames has 3 components,
and since time dilation and length contraction are a function of relative velocities in SR, time is also a vector with 3 components
so that there should be 3 transformation equations for time in
SR and not 1. Therefore, every object in SR has 3 time dimensions.

The relative velocity only has three components if you choose the wrong coordinate system. Unless you are a masochist (or, more likely, an idiot), you will wisely choose a coordinate system that aligns with the direction of velocity, making all but one component zero. (You do realize that velocity is an "arrow" with only one real dimension, right?) And if you don't, then your (single) time coordinate will merely be a messy function of four variables instead of just two. Have fun with that.

 

[Peterdevis]

Eyesaw,

I don't think that you understand SR.
In SR we have 4 dimensions (time and the tree space coördinates)
Then you define a frame (it must be inertial)(existing of four axes)
You can call them t,x,y,z. When you construct another frame with a relative velocity (0,v1,v2,v3) to the first frame. To transform the first frame to the second frame you need only four transformation rules.

If you choose (0,v1,0,0) as velocity, you become the traditionel time dilatation, and x contraction

 

[Eyesaw]

Originally posted by Doc Al
I can't decide whether this is hilarious or sad. No offense, Eyesaw, but have you even glanced at a relativity book before?

Erm, yep. You do realize that this SR thing just happens to depend on the relative velocity, right? You also realize that "SRists" don't actually have to "move the whole earth", right? It's just a mathematical convenience.
The relative velocity only has three components if you choose the wrong coordinate system. Unless you are a masochist (or, more likely, an idiot), you will wisely choose a coordinate system that aligns with the direction of velocity, making all but one component zero. (You do realize that velocity is an "arrow" with only one real dimension, right?) And if you don't, then your (single) time coordinate will merely be a messy function of four variables instead of just two. Have fun with that.

Two spaceships in space, one traveling at a 22 or 55 degree angle from the other. So, how do you set one reference frame parallel with respect to the other to perform a Lorentz transformation? Don't tell me we are just going to ignore the velocity components in the directions not parallel to the x direction for the sake of performing the Lorentz transformation? High school students had no problems working in 3 dimensional space-time prior to the advent of SR, but now we have PHDS who have problems believing cars can go up freeway onramps.

Time was made into a dependent variable in SR. Dependent on the the relative velocities between two frames in the x direction in 1 d space so that in 3d space, it becomes dependent on 3 velocity components, in contrast to Galilean transform where t is assumed to be an independent variable. Perhaps it would be easier to understand this in layman's terms: length contracts and time dilates in the direction of motion, thus with three different directions in space, length has the potential to contract in 3 spatial dimensions and time has the potential to dilate in 3 temporal dimensions.

 

[Doc Al]

Originally posted by Eyesaw
Two spaceships in space, one traveling at a 22 or 55 degree angle from the other.

Statements of angles are meaningless until you've defined a coordinate system. Nothing is preventing you from choosing a coordinate system that makes calculation easier. Nothing you do will change the physical fact that length along the direction of motion is frame dependent. If you wish to choose a coordinate system that makes the direction of motion 22 degrees from your x-axis, no problem; the results won't change! Length along that direction will still "contract", just like always.

So, how do you set one reference frame parallel with respect to the other to perform a Lorentz transformation?

By choosing a coordinate system that best matches the reality you are trying to model. But you don't have to choose a coordinate system that makes the equations easier.

Don't tell me we are just going to ignore the velocity components in the directions not parallel to the x direction for the sake of performing the Lorentz transformation?

If you (unwisely) choose a coordinate system in which the relative velocity is at 22 degrees with the x-axis, then of course you'll have to include the y and z components. But don't blame that on anyone but yourself!

You seem to think something special happens if you pick a coordinate system in which the velocity is not parallel to the x-axis. Nope. You still define an event by the same old four coordinates (t, x, y, z). All you've done is make the transformation equations connecting one frame to another more complex. The physics doesn't change. You don't magically get new x,y,z "components" of time---whatever that might mean.

If you want to get nuts, don't stop with the relative velocity at an angle. Why not have one coordinate system rotated and with a different origin as well? Let's make those equations really difficult!

High school students had no problems working in 3 dimensional space-time prior to the advent of SR, but now we have PHDS who have problems believing cars can go up freeway onramps.

You are in a dream world, my friend. Your approach is like trying to calculate the time it takes for a ball to fall, but insisting on using components that aren't parallel to the gravitational field. The ball doesn't care what coordinates you use. Do it the hard way, if you wish: you'll still get the same answer.

 

[Eyesaw]

You are in a dream world, my friend. Your approach is like trying to calculate the time it takes for a ball to fall, but insisting on using components that aren't parallel to the gravitational field. The ball doesn't care what coordinates you use. Do it the hard way, if you wish: you'll still get the same answer.

What kind of analogy is this? So there are no satellites orbiting in space?

Time was made into a dependent variable in SR- so what does it depend on? Velocity between two frames of reference. What is velocity? A vector with 3 components. I did not invent this ok? There are 3 dimensions in space so there has to be 3 velocity components that describes something in space- if you choose to ignore it so you can suit some dumb math formula, fine but don't drive a car near my town. You can have a 4 variable transform in Galilean transform because time is not a dependent variable but once you make it dependent, it's inexcusable for there not to be a separate time transformation for each spatial component.

Really, why do you think the Lorentz transformation was never written into a vector form like all other physical equations
prior to SR?

 

[Doc Al]

Originally posted by Eyesaw
What kind of analogy is this? So there are no satellites orbiting in space?

Huh?

Time was made into a dependent variable in SR- so what does it depend on? Velocity between two frames of reference. What is velocity? A vector with 3 components. I did not invent this ok? There are 3 dimensions in space so there has to be 3 velocity components that describes something in space- if you choose to ignore it so you can suit some math equation, fine but don't drive a car near my town.

What's your point? Time is dependent on velocity. No one is ignoring anything.

You can have a 4 variable transform in Galilean transform because time is not a dependent variable but once you make it dependent, it's inexcusable for there not to be a separate time transformation for each spatial component.

A meaningless statement. There are only four variables (Galilean or Einsteinian): t, x, y, z.

If you choose a dopey coordinate system, then t' = f(t, x, y, z). So what? Choose a better system, then t' = f(t, x). Your choice.

Rather than continue this silly discussion, why don't you derive your version of the lorentz transformations using an arbitrary velocity and whatever coordinates you like?

 

[selfAdjoint]

Two spaceships in space, one traveling at a 22 or 55 degree angle from the other. So, how do you set one reference frame parallel with respect to the other to perform a Lorentz transformation

The group of motions in special relativity is the Poincare group, consisting of the Lorentz transformations AND the 3-dimensional rotations. Since the ships are inertial (not accelerated) they keep a constant bearing toward each other. Rotate you coordinates until the x-axis points along that bearing and then do your Lorentz boost.

 

[Eyesaw]

Originally posted by Doc Al
Huh?

Huh, what?


What's your point? Time is dependent on velocity. No one is ignoring anything.

No it's not.



A meaningless statement. There are only four variables (Galilean or Einsteinian): t, x, y, z.

If you choose a dopey coordinate system, then t' = f(t, x, y, z). So what? Choose a better system, then t' = f(t, x). Your choice.

Rather than continue this silly discussion, why don't you derive your version of the lorentz transformations using an arbitrary velocity and whatever coordinates you like?

Just use the Lorentz transformations for x, and t but substitute
x and t for y and ty in the y direction and z and zt in the z direction. If you plugged in 0 for the velocity components, you get y = y', ty= ty', and z = z' tz = tz'. If they were non zero,
you get 3 sets of Lorentz transformations that's all.

Making time a variable leads to physical nonsense.

 

[gnome]

Just use the Lorentz transformations for x, and t but substitute x and t for y and ty in the y direction and z and zt in the z direction. If you plugged in 0 for the velocity components, you get y = y', ty= ty', and z = z' tz = tz'. If they were non zero,
you get 3 sets of Lorentz transformations that's all.

Making time a variable leads to physical nonsense.

Did you learn all this at the Ralph Cramden Institute of Physics, or is this your own discovery? You really have a profound misunderstanding of the concept of special relativity (or any relativity, for that matter). For example, the idea of a 4-dimensional universe has clearly escaped you entirely. Even worse, you seem to be suffering from a rather shaky concept of the meaning of "dependent variable", you can't seem to distinguish between the relative motions of frames of reference themselves and the motions of objects within those frames, and you appear to be laboring under the misconception that all motion must be described in relation to some set of UNIVERSAL COORDINATE AXES, aligned with the ether and with its origin presumably identified by the location of the GREAT PUMPKIN.

In short, you really ought to learn to crawl before you try to fly.

 

[Doc Al]

Originally posted by Eyesaw
Just use the Lorentz transformations for x, and t but substitute
x and t for y and ty in the y direction and z and zt in the z direction. If you plugged in 0 for the velocity components, you get y = y', ty= ty', and z = z' tz = tz'. If they were non zero,
you get 3 sets of Lorentz transformations that's all.

You can substitute the word "pizza" for t, and "banana" for x, if you want, but it's just nonsense.

How do I measure tx,ty,tz? Do I need a special watch (three special watches?) or do I just have to be facing the right direction?

 

[Doc Al]

Originally posted by gnome
Did you learn all this at the Ralph Cramden Institute of Physics...

Now that's funny.

 

[Eyesaw]

Originally posted by Doc Al
You can substitute the word "pizza" for t, and "banana" for x, if you want, but it's just nonsense.

How do I measure tx,ty,tz? Do I need a special watch (three special watches?) or do I just have to be facing the right direction?

Same way we currently measure time dilation and length contraction
in SR of course. That is to say, we assume it a priori. When did you ever try to measure the speed of light or any other speed in someone else's inertial frame? This whole notion of observing events in someone else's inertial frame is laughable. Where are these special SR telescopes on Ebay?

 

[Eyesaw]

Originally posted by gnome
Did you learn all this at the Ralph Cramden Institute of Physics, or is this your own discovery? You really have a profound misunderstanding of the concept of special relativity (or any relativity, for that matter). For example, the idea of a 4-dimensional universe has clearly escaped you entirely. Even worse, you seem to be suffering from a rather shaky concept of the meaning of "dependent variable", you can't seem to distinguish between the relative motions of frames of reference themselves and the motions of objects within those frames, and you appear to be laboring under the misconception that all motion must be described in relation to some set of UNIVERSAL COORDINATE AXES, aligned with the ether and with its origin presumably identified by the location of the GREAT PUMPKIN.

In short, you really ought to learn to crawl before you try to fly.

No, you are the one who thinks only 1 spatial dimension is necessary to describe the movement of objects in 3 dimensional space. LOL. I guess the fact has escaped you for all these years that objects take up volume and things move in the universe in other than parallel directions. You are the one using some special coordinate scheme that magically aligns arbitrarily to every other object in space, and that completely ignores or removes all other existing velocities between frames except those in that very special x dimension.

 

[Peterdevis]

Dearest Eyesaw,

Obvious you don't know very well wat SR is about.
I sugest that you first learn SR (you don't have to believed, but studying it), and then say what's wrong with SR.

In SR we always speak about objects who doesn't accelerate. So forget sattelites , falling balls etc.

Second we always measure in our own frame of reference.
When a object is moving, we measure time dilitation for that object.
In the reference frame of the object there is no time dilitation to maeasure.

 

[geistkiesel]

Am I correct to conclude that the 2 light bulbs are indeed turned on simultaneously, as if viewed by a stationary observer, since that the speed of light is constant to all observers, regardless of their motion?

Doc AI in response to Icky

Everyone agrees that the light from each bulb arrived at the ship at the same time. But they disagree on whether the lights were switched on at the same time.

The fact that the two flashes reach the midpoint at the same time is evidence that they were turned on simultaneously according to observers in the rest-frame of the light bulbs. Observers in the ship will disagree that the lights were turned on at the same time. Observers in the ship will conclude that light B must have turned on first, since it is moving towards the ship.

Geistkiesel to Icky and Doc AI

If the moving platform merely detects the position of two pulses of light no assumptions about when the pulses left the sources can be made. If the stationary and moving observers know of the experiment then the detection of the pulses at the same place removes any ambiguity of when they were turned on. Only if the stationary observer triggers the pulses on does the experimental question have any relevanceThe mere fact of measuring the point two light pulses meet is insufficient to determine the respective positions of the pulse sources or when the sources emitted the pulses.

Let us assume the stationary and moving platform detectors are located within an x-ray wavelength from each other when measuring the arriving pulses. Here, all must agree that the simultaneous arrival of two light pulses measured by two light detectors were spatially equivalent and only if the stationary observer triggered the pulses simultaneously is there a thread to any discussion o 'relativity theory'. If moving observers then conclude the pulses were turned on at different times the basis of that conclusion is faulty. The mere fact of motion of a detector does not insert any ambiguity into the equation. There is simply a point in space where the pulses meet, where thestationary detector is located and whee th moving platform detector is located. Motion is not an issue. If the moving observers know the pulses were turned on by the staionary observer all must agree that the point the pulses meet is the midpoint of the sources.

Or would the motion of the ship have any effect on this simultaneity?

To which Doc AI responds:

Simultaneity is relative to the observer's frame. Observers at rest with the bulbs and those in the ship will disagree on what is simultaneous.

Geistkiesel to Icky and Doc AI

Doc AI cannot be correct.

Nobody is counting time. The measurement is purely a spatial determination ofwhere the light pulses meet. Here the pulses and all detectors are spatially equivalent. Watches aren’t relevant. Unless the participants know of the experiment do we have a quesion of simultaneity.

Or I am incorrect to assume that the midpoint of my journey means light has to travel the same distance for both the cases of points A and B?

Doc AI answers Icky saying:

The light from each bulb is only seen to have traveled the same distance according to the observers at rest with the bulbs. Folks in the ship disagree.

Geiskiesel to Icky and Doc AI

Neither the stationary observer or the moving platform observer can make any assumptions of when the lights were turned on. Two colliding pulses do not provide sufficient histories of their respective emissions. We can eliminate the stationary observer by saying she sent light pulses to A and B simultaneously from her midpoint position which triggered the pulses leaving A and B at the same time.

Now if her little sister in the moving platform knows the outbound pulse to A triggered the light that subsequently arrived from A (she could have measurd the wave front passing her ship to A behind her) and then she subsequently detects the light triggered from A and B at the same point and time she must conclude that she is also at the midpoint of the sources even with respect to her moving frome, otherwise all motion is ambiguous. Any calculation that disagrees with the measured event is theoretically faulty.

If the little sister on the spaceship knows of the experiment, knows the lights are equal distant from the stationary observer, knows about the triggering pulses arriving at A and B, then the simultaneous positions of moving and stationary platform detectors and light pulses unambiguously assures the moving platform observer that her measurement was also at the midpoint of the lights at the instant of detection.

 

[Doc Al]

Geistkiesel to Icky and Doc AI

If the moving platform merely detects the position of two pulses of light no assumptions about when the pulses left the sources can be made.

No need to assume anything: when the pulses were emitted can be deduced.

Only if the stationary observer triggers the pulses on does the experimental question have any relevanceThe mere fact of measuring the point two light pulses meet is insufficient to determine the respective positions of the pulse sources or when the sources emitted the pulses.

Nonsense. Remember that everyone knows where A and B are located. And that everyone agrees that the pulses arrive simultaneously at the midpoint. Both observers have all the information needed to calculate when the pulses were emitted.

Let us assume the stationary and moving platform detectors are located within an x-ray wavelength from each other when measuring the arriving pulses. Here, all must agree that the simultaneous arrival of two light pulses measured by two light detectors were spatially equivalent and only if the stationary observer triggered the pulses simultaneously is there a thread to any discussion o 'relativity theory'.

Again, the stationary observer (at the midpoint) doesn't have to "trigger" anything. (A and B have clocks, you know. )

If moving observers then conclude the pulses were turned on at different times the basis of that conclusion is faulty.

Wrong again. When the pulses were turned on can be deduced and is frame dependent.

The mere fact of motion of a detector does not insert any ambiguity into the equation. There is simply a point in space where the pulses meet, where thestationary detector is located and whee th moving platform detector is located. Motion is not an issue. If the moving observers know the pulses were turned on by the staionary observer all must agree that the point the pulses meet is the midpoint of the sources.

The fact that the observers are at the midpoint between the sources is known from the start. They don't deduce that from the fact that the light arrives simultaneously.

Doc AI cannot be correct.

Perish the thought.

Nobody is counting time. The measurement is purely a spatial determination ofwhere the light pulses meet.

They aren't "measuring" location--they both know they are at the midpoint; they are detecting that the light arrived simultaneously. Time is very relevant.

Here the pulses and all detectors are spatially equivalent. Watches aren’t relevant. Unless the participants know of the experiment do we have a quesion of simultaneity.

I have no idea what you mean by "spatially equivalent". And the issue is when the signals were emitted, which they both can deduce from their knowledge of how light works.

Neither the stationary observer or the moving platform observer can make any assumptions of when the lights were turned on.

They don't have to assume anything.

Two colliding pulses do not provide sufficient histories of their respective emissions.

Sure they do: We know where they started and how fast they move.

We can eliminate the stationary observer by saying she sent light pulses to A and B simultaneously from her midpoint position which triggered the pulses leaving A and B at the same time.

Whether the stationary observer triggers the pulses by sending a signal to A and B--or not--is irrelevant.

Now if her little sister in the moving platform knows the outbound pulse to A triggered the light that subsequently arrived from A (she could have measurd the wave front passing her ship to A behind her) and then she subsequently detects the light triggered from A and B at the same point and time she must conclude that she is also at the midpoint of the sources even with respect to her moving frome, otherwise all motion is ambiguous. Any calculation that disagrees with the measured event is theoretically faulty.

Again you seem confused about the assumptions of the problem: Everyone knows and agrees that: both observers are at the midpoint and that the light arrives there simultaneously. That's all anyone needs to know. If someone tries to "calculate" travel times with other assumptions, they will get nonsense.

If the little sister on the spaceship knows of the experiment, knows the lights are equal distant from the stationary observer, knows about the triggering pulses arriving at A and B, then the simultaneous positions of moving and stationary platform detectors and light pulses unambiguously assures the moving platform observer that her measurement was also at the midpoint of the lights at the instant of detection.

Again the moving observer doesn't have to know anything except that the light was emitted by A and B, which are equidistant from her. You have come full circle. Was there a point you wanted to make?

Realize that the moving observer, if she knows anything about how light works, will insist that according to her the signals were emitted at different times. And if (as you insist, but is irrelevant) the stationary observer triggered the light emissions at A and B by sending her own signal to A and B, realize that the moving sister will disagree that those signals arrived at A and B simultaneously. There is no way around it: Simultaneity is frame dependent. And that is the point of this exercise.

 

[geistkiesel]

All observers will agree that the light arrives simultaneously at the ship. So, the observer on the ship would see the the two light beams arrive simultaneously. This does not mean that observers would agree that the lights were turned on simultaneously; that is a deduction, not a direct observation.

See my comments above. No one "sees" the lights turned on simultaneously. But observers at rest with A-B will insist that they were turned on simultaneously. Observers in the ship will not.

I was under the impression that the problem started out with evryone knowing that M was the midpoint between A and B and that the pulses met at M simultaneously. O, knowing he is at the midpoint and seeing the pulses meet there at the same time deduces the lights were turned on at the same time. If O' also knows he is at the midpoint and that the pulses are detected simultaneously with O, there can be no relativity significance to the problem. The mere fact that O' is moving at the instant the lights were turned on does not mean the O' conclude that B must be turned on first in order that O' see them meet at the midpoint.

In a hypothetical automobile race. A and B are equidistant from the finish line heading toward each other at the same speed. The automobiles meet at the finish line, at the same time, obviously. When we rewind the race and insert a slower automobile, O', moving in the same direction as A at such a speed and distance from the finish line that all three meet at the finish line at the same time, what theory is there that insists O' must conclude that B cheated on A and started out earlier in order for all of them to meet at the same place at the same time?


The point of all this, as was originally asserted, regards the question of, "would O' think the lights started out at different times?"

Answer: No, and further, this is not an SR problem.

 

[Janus]

I was under the impression that the problem started out with evryone knowing that M was the midpoint between A and B and that the pulses met at M simultaneously. O, knowing he is at the midpoint and seeing the pulses meet there at the same time deduces the lights were turned on at the same time. If O' also knows he is at the midpoint and that the pulses are detected simultaneously with O, there can be no relativity significance to the problem. The mere fact that O' is moving at the instant the lights were turned on does not mean the O' conclude that B must be turned on first in order that O' see them meet at the midpoint.

In a hypothetical automobile race. A and B are equidistant from the finish line heading toward each other at the same speed. The automobiles meet at the finish line, at the same time, obviously. When we rewind the race and insert a slower automobile, O', moving in the same direction as A at such a speed and distance from the finish line that all three meet at the finish line at the same time, what theory is there that insists O' must conclude that B cheated on A and started out earlier in order for all of them to meet at the same place at the same time?

In this case, the addition of velocities therom:

w=\frac{u+v}{1+\frac{uv}{c^{2}}}

In which case w would be the relative velocity of O' to A or B when u is the velocity of the finish line with respect to O' as measured by O' and v is the relative velocity of A or B to to the finish line with from the respect of the finsh line as measured by the someone at the finish line.

The result of which will show that according to O', A and B will not have the same velocities with respect to the finish line, And thus, since they start an equal distance from the starting line, one must have started earlier in order for them both to reach the finish line at the same time as O'.

Of course at normal every day speeds, this difference is so small it is not noticeable, it isn't until the velocities involved reach a good fraction of c that it becomes measureable.

 

[Doc Al]

please read the entire thread!

I was under the impression that the problem started out with evryone knowing that M was the midpoint between A and B and that the pulses met at M simultaneously. O, knowing he is at the midpoint and seeing the pulses meet there at the same time deduces the lights were turned on at the same time.

Right.

If O' also knows he is at the midpoint and that the pulses are detected simultaneously with O, there can be no relativity significance to the problem. The mere fact that O' is moving at the instant the lights were turned on does not mean the O' conclude that B must be turned on first in order that O' see them meet at the midpoint.

Sure it does, if you think about it. Did you actually read the previous posts in this thread? We've discussed this in excruciating detail. Ask yourself this: In O's (moving) reference frame, where were A and B when they switched on their lights? Were they equidistant from O' at that time? (We all agree that they are equidistant from O' at the moment that O' passes the midpoint--but so what? We need to know where A and B were when they flashed their lights.)

In a hypothetical automobile race. A and B are equidistant from the finish line heading toward each other at the same speed. The automobiles meet at the finish line, at the same time, obviously. When we rewind the race and insert a slower automobile, O', moving in the same direction as A at such a speed and distance from the finish line that all three meet at the finish line at the same time, what theory is there that insists O' must conclude that B cheated on A and started out earlier in order for all of them to meet at the same place at the same time?

Of course, for ordinary cars moving at ordinary speeds, nothing special happens. But get those cars moving at light speed (or an appreciable fraction of light speed) and things are quite different. The theory that describes how lengths, times, and simultaneity changes from one fast moving frame to another is called Special Relativity.

The point of all this, as was originally asserted, regards the question of, "would O' think the lights started out at different times?"

Answer: No, and further, this is not an SR problem.

Please take the time to study the previous posts in this thread. Not only is this an SR problem, it is a canonical SR problem!

 

[geistkiesel]

Everybody knows the lights wee turned on at the same time . . .

Only if the stationary observer triggers the pulses on does the experimental question have any relevance.The mere fact of measuring the point [the] two light pulses meet is insufficient to determine the respective positions of the pulse sources or when the sources emitted the pulses.

Doc AI responds
Nonsense. Remember that everyone knows where A and B are located. And that everyone agrees that the pulses arrive simultaneously at the midpoint. Both observers have all the information needed to calculate when the pulses were emitted.

OK, you win a point. I had the parameters skewed. Everybody knows that the meeting of light pulses and the observer O' is simultaneous. O knows he is at the midpoint and knowing the speed of light he determines when the light was turned on. ["when" the lights were turned on is not the issue, only that they were turned on simultaneously is within the limits of the problem] O' also knows he is at the midpoint of the sources, but because the O' speed is slower than c, he must have been moving to M before the pulses left A and/or B. If the speed of O' were too slow, then the light from A would pass him and later he would see the oncoming light from B. Similarly if the 0' speed were too fast O' would cross the midpoint and then see the light from B before he saw the light from A and would then know he had passed the midpoint of A and B, because only by simultaneous meeting of the pulses at M can O' know he is at the midpoint, unless there is a litle flag there, which is within the parametric limitations of he problem.

If O' were moving at just the correct speed, such as the problem states, then the simultaneous meeting of pulses, O and 0', would tell O' that he had intercepted the pulses at M, which is given [he can verify this by seeing the midpoint flag]. The problem states that everybody knows where A and B are and that all met at M, the half way point at the same instant. In the too slow and too fast cases O' would therefore know if he were short of M or had passed M, which would all be suppored by O' seeing the flag at M..

The problem clearly stated that O' was at the midpoint of A and B when the pulses met. Without any relativity calculations by O', the fact that he knew he was in the midpoint in the O frame, he knows that the lights were turned on simulataneously in the O frame. Now, if O' makes any calculation that informs him the lights were turned on at different times in the O' frame then the O' theory used in making this calculation is flawed.

The calculations that are discussed in this thread all have O' moving at some speed less than C. If O' is moving at 1% of c or 99% of c the given limitations of the problem change nothing. I have struggled to determine what calculations O' can make that would change his observation and knowledge that all pulses and detectors were in a simultaneous configuration from beginning to end.This is because everybody knew the light left A and B at the same time and met at M at the same time.

In maintaining his mathematical instincts intact O' must offer a hearty "ho ho" to O, "we disagree on the math, but we agree on the physics."


Doc AI, please tell us what are the mechanics of the theory, SR I presume, that dictates O' must conclude the lights were turned on at different times?

 

[Doc Al]

Apparently you haven't read the previous posts in this thread.

The problem clearly stated that O' was at the midpoint of A and B when the pulses met. Without any relativity calculations by O', the fact that he knew he was in the midpoint in the O frame, he knows that the lights were turned on simulataneously in the O frame.

Right. Everyone agrees that the lights were turned on simultaneously as observed in the O frame.

Now, if O' makes any calculation that informs him the lights were turned on at different times in the O' frame then the O' theory used in making this calculation is flawed.

Nonsense. O' knows what he observes and he knows how A and B are moving and he knows how light behaves. He knows that with respect to his own frame the lights must have been turned on at different times. This is no big deal to O', since he understands that time, length, and simultaneity are relative to the frame making the observations.

... I have struggled to determine what calculations O' can make that would change his observation and knowledge that all pulses and detectors were in a simultaneous configuration from beginning to end.

O' does not directly "observe" that A and B were turned on simultaneously. (In fact, no one does!) In fact, based on what he knows about how the world works, he would vehemently disagree that the lights were turned on at the same time! The light from A and the light from B travel very different distances to get to O'--so they must start out at different times according to O's clocks. Otherwise things just don't make sense. (The light from A and the light from B only travel the same distance in Os frame.)

This is because everybody knew the light left A and B at the same time and met at M at the same time.

Not everybody! Only the frame in which A and B are at rest (the O frame) did the light leave A and B at the same time.

In maintaining his mathematical instincts intact O' must offer a hearty "ho ho" to O, "we disagree on the math, but we agree on the physics."

No. O', being sophisticated and wise, would say "We agree on the math and the physics, but since we are in relative motion we disagree on the times that the lights were turned on." You will, I hope, forgive me for assuming the validity of special relativity. After all, this is the Relativity forum.

Doc Al, please tell us what are the mechanics of the theory, SR I presume, that dictates O' must conclude the lights were turned on at different times?

I'm not about to give a class in relativity. There are many good books and web sites where you could learn the basics. The math of special relativity is easy. The hard part is believing it. We believe it for many reasons, not the least of which is that its consequences have been experimentally verified over and over again.

In a nutshell, start with this fact: Light always moves with the same speed (c) with respect to any observer, no matter what the observer's speed (relative to some other observer). Wrap yourself around that strange fact. If you consistently apply that fact you can deduce the consequences of special relativity: moving clocks are observed to slow down, moving sticks are observed to be shorter, and clocks that are in synch (in their own frame) are observed to be out of synch.

 

[geistkiesel]

All observers will agree that the light arrives simultaneously at the ship. So, the observer on the ship would see the the two light beams arrive simultaneously. This does not mean that observers would agree that the lights were turned on simultaneously; that is a deduction, not a direct observation.

See my comments above. No one "sees" the lights turned on simultaneously. But observers at rest with A-B will insist that they were turned on simultaneously. Observers in the ship will not.

Geistkiesel responds to Doc Ai thus:
If the ship is at the midpoint of the sources of light, there is one spot in the universe where the pulses first meet and this is at the midpoin M. It seems Doc AI finds disfavor with the word "deduction", well, so be it. There is no way that the observer on the ship can manipulate reality and have the light pulses start out at different times and meet at the mid point. This is a physical impossibility, but mathematics can manipulate the best of experimental results. If the ship's crew "disagrees" with the stationary observers we must concede to them their very deep and inalienable right to be in error.

What does Doc AI replace the word "deduction" with? And why does he want to discard what someone deduces? I was under the impression this is what scientists do in their proffesion. Doc AI has mentioned a number of times that the people on the ship willl "not agree" the lights were turned on at the same time and his argument isn't through the principals of physics, rather it is something else that I am unable to properly catagorize. I have some deep doubts regarding the literal reality as expressed by SR, but using SR as it is understood will not change the reality of this particlular situation.

Everybody knows what the answer is at the instant the lights meet at M.

As it was pointed out to me in no uncetain terms (by Doc AI no less) the parameters of the problem are that everybody knows the light meets at the midpoint. If someone wants to manipulate numbers to obfuscate the unambiguous experimental result to dscard a distastful "deduction", this I can understand when coming from the dogmatcally inclined.

Who was it who remarked: "The enemies of truth. Convictions are more dangerous enemies of truth than lies."