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Simultaneity of event in different frames


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Speed of light is constant if it travels from object in one frame to an object in the same frame.When light travels from approaching frame it is slower.When light travels from escaping frame it is faster.Round-trip shows constant speed.

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I have now idea what you mean by "approaching frame" and "escaping frame".

 

But simultaneity in different frames can be demonstrated like this:

 

Imagine you have two clocks, they are set to the same reading and designed to start running when a light flash reaches them. You originate a flash form a point hlafway between them.

 

To anyone at rest with respect to the clocks, events unfold like this:

 

synch1.gif

 

The light exapnads outward from the origin at c, and strikes both clocks at the same instant. the clocks start and from that moment on always read the same time.

 

One thing of importance here is that is does not matter whether or not the source of this flash is moving with respect to the clocks or not, all that matters is that it is halfway between the two clocks when it produces the flash.

 

Now consider the same flash and clocks according to someone moving with respect to the clocks. Events now unfold like this:

 

synch2.gif

 

The light still originates at a point halfway between the two clocks and expands outward at c. However the two clocks no longer maintain the same distance from the origin. (again, it does not matter as what the velocity of the source is with respect the clocks or to the observer)

 

As a result, the light strikes one clock before it strikes the other and one clock starts running before the other. As a result, both clocks will read different times once they are both running with the clock on the right lagging behind the clock on the left.

 

Thus according to someone at rest with respect to the clocks, the running clocks are in sync, and according to someone moving with respect to the clocks, they are not. The events of the clocks reading 1:00 are simultaneous in one frame, but not simultaneous in the other.

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Speed of light is constant if it travels from object in one frame to an object in the same frame.When light travels from approaching frame it is slower.When light travels from escaping frame it is faster.Round-trip shows constant speed.

It sounds like you're talking about the separation rate of photons and their source, as measured in the observer's frame, but that's not "speed of light".

 

 

I think that round-trip might show an average separation rate relative to a moving object that is a constant and equal to c if the object has a constant velocity. That is: Light from observer takes time t to reach object, and is reflected back and returns in a time of t. At constant v, the closing rate of the signal and object is c - v for time t, and the separation rate of the return signal is c + v for time t, and the average of the two rates is c. Not necessarily so if v varies over the duration of the signal.

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Speed of light is constant if it travels from object in one frame to an object in the same frame.When light travels from approaching frame it is slower.When light travels from escaping frame it is faster.Round-trip shows constant speed.

 

This is a rehash of that tired and never taught alternative to special relativity called Lorentz Ether Theory. This has been debated countless times at this and other fringe science sites. Beloved by anti-relativistic crackpots, it is nonetheless experimentally indistinguishable from special relativity.

 

Physicists don't bother with LET at all. It never gained traction for three key reasons. One is aesthetics. LET is an ugly theory compared to special relativity. LET makes a number of ad hoc assumptions; special relativity on the other hand, only makes a small number of simple assumptions. Another is that many of these ad hoc assumptions, most notably yours, is untestable. It's metaphysics, not physics. Finally, the key motivating factor behind LET, that electromagnetic radiation is a wave phenomenon and therefore needs a medium, died with quantum mechanics. Photons are particles. They don't need a medium to travel through empty space.

Edited by D H
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This is a rehash of that tired and never taught alternative to special relativity called Lorentz Ether Theory. This has been debated countless times at this and other fringe science sites. Beloved by anti-relativistic crackpots, it is nonetheless experimentally indistinguishable from special relativity.

 

Physicists don't bother with LET at all. It never gained traction for three key reasons. One is aesthetics. LET is an ugly theory compared to special relativity. LET makes a number of ad hoc assumptions; special relativity on the other hand, only makes a small number of simple assumptions. Another is that many of these ad hoc assumptions, most notably yours, is untestable. It's metaphysics, not physics. Finally, the key motivating factor behind LET, that electromagnetic radiation is a wave phenomenon and therefore needs a medium, died with quantum mechanics. Photons are particles. They don't need a medium to travel through empty space.

Excuse me.I was some wrong up.Light has constant speed and different path between frames.Lorentz defines length contraction of moving frame,but doesn't define path length of light between objects in different frames.This causes delusion about non-simultaneity.

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  • 2 weeks later...

Twin at rest in gravitation.Twin' is the traveler in gravitation.

dt=gamma * dt'

v=v'

dx/dt=dx'/dt'

then dx=gamma * dx' in any frame

Twin' sees extended distance of twin.However light of twin has the contracted path for twin',because light has own speed and nature.

And so I made right math for simultaneity.

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There I was wrong.

Let's consider right math.Twin and twin' are traveling to each other.

dx'=gamma * dx

dt=gamma * dt'

Then time until collision of the twins

in twin frame=dx/v

in twin' frame = dx'/v'

Twin radiates light,twin' recieves the light.Then time between the reception of the light and collision of twins is:

in twin frame dt - dtl=dx/v - dx/c

in twin' frame dt'-dt'l=dx'/v' - dx'/c

dx/v - dx/c = gamma * (dx'/v' - dx'/c)

Then twin' sees their speed as

v' =gamma * vc/(c+v(gamma -1))

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  • 5 weeks later...

I incorrectly took length contraction.I should define v' in first place.Twin and twin' are moving to each other.Twin is radiator of two photons to twin'.Twin' atomic clock recieves the photons.The first photon includes the clock.The second photon switches off the clock.


dx - distance between the twins in twin frame


dti - time between radiation of first photon and radiation of second photon in twin frame


dx/(c+v) - time of travel of first photon in twin frame


(dx-v * dti)/(c+v) - time of travel of second photon in twin frame


[dti+(dx-vdti)/(c+v)-dx/(c+v)]/gamma=dtic/[(c+v)gamma] - indication of the clock predicted by twin


dx' - distance between the twins in twin' frame


dti/gamma+(dx'-dtiv'/gamma)/c-dx'/c=dti(c-v')/(gamma*c) - indication of the clock predicted by twin'


then dtic/[(c+v)gamma]=dti(c-v')/(gamma*c)



then v'=cv/(c+v)



Now let's define length contraction factor


dx/v - dx/c = gamma * (dx'/v' - dx'/c)



dx'/dx=(c-v)/(gamma*c)



I make particular predictions in two frames.Are they right?


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Here is a good explanation of the relativity of simultaneity

 

 

https://www.youtube.com/watch?v=kGsbBw1I0Rg

Don't look down to my exploring. I do make mathematical predictions of indication of clock in my experiment for two frames. You don't make. Einstein wasn't making also. Explanation without mathematical prediction is nonsence.

I was mistaken with length contraction factor. Really it is;

 

dx/v - dx/(c+v)=gamma(dx'/v' - dx'/c)

 

v'=cv/(c+v)

 

then dx/dx'=gamma(c+v)/c

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Of course neutrino (which is in gravitational field of Earth and the gravitational field is dominant) can't see speed of the Earth faster than 1/2c. Because speed of counter neutrino should be much faster . Therefore the neutrino has different Lorentz's factors for calculation of energy of the Earth and of energy of neutrinos.The neutrino has usual Lorentz's factor for calculation of neutrinos energy. The neutrino has another Lorentz's factor for calculation of the Earth energy ;

 

the Lorentz's factor~1/(1-v2/[c/2]2)1/2 tongue.png

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  • 3 weeks later...

I have now idea what you mean by "approaching frame" and "escaping frame".

 

But simultaneity in different frames can be demonstrated like this:

 

Imagine you have two clocks, they are set to the same reading and designed to start running when a light flash reaches them. You originate a flash form a point hlafway between them.

 

To anyone at rest with respect to the clocks, events unfold like this:

 

synch1.gif

 

The light exapnads outward from the origin at c, and strikes both clocks at the same instant. the clocks start and from that moment on always read the same time.

 

One thing of importance here is that is does not matter whether or not the source of this flash is moving with respect to the clocks or not, all that matters is that it is halfway between the two clocks when it produces the flash.

 

Now consider the same flash and clocks according to someone moving with respect to the clocks. Events now unfold like this:

 

synch2.gif

 

The light still originates at a point halfway between the two clocks and expands outward at c. However the two clocks no longer maintain the same distance from the origin. (again, it does not matter as what the velocity of the source is with respect the clocks or to the observer)

 

As a result, the light strikes one clock before it strikes the other and one clock starts running before the other. As a result, both clocks will read different times once they are both running with the clock on the right lagging behind the clock on the left.

 

Thus according to someone at rest with respect to the clocks, the running clocks are in sync, and according to someone moving with respect to the clocks, they are not. The events of the clocks reading 1:00 are simultaneous in one frame, but not simultaneous in the other.

I already made math of approaching twins to each other.Let's consider math of escaping twins from each other.

Indication of twin' clock in twin frame=tic/[(c-v)gamma]

indication of twin' clock in twin' frame=(tiv' +tic)/(gamma*c)

 

tic/[(c-v)gamma]=(tiv'+tic)/(gamma*c)

v'=vc/(c-v)

 

v' is negative relatively of light speed therefore v has negative value

 

I don't see any problem in my idea.

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Janus,

 

Math aside, in your first diagram with the central point eminating a signal that starts both clocks, we are viewing the situation from a point equal distant from both clocks. What if we are off to the right, where the expanding circle of the starting signal reaches us at the same moment that the right hand clock starts, but we will not see the left hand clock start for the time period that it takes light to travel the distance between the clocks. The left hand clock will forever forward, be this time period behind the right hand clock.

 

Regards, TAR2

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Janus,

 

Math aside, in your first diagram with the central point eminating a signal that starts both clocks, we are viewing the situation from a point equal distant from both clocks. What if we are off to the right, where the expanding circle of the starting signal reaches us at the same moment that the right hand clock starts, but we will not see the left hand clock start for the time period that it takes light to travel the distance between the clocks. The left hand clock will forever forward, be this time period behind the right hand clock.

 

Regards, TAR2

Where the observer is postioned has no bearing on this example, all that we are concerned about is the relative motion with respect to the clocks. It is when the light strikes the clocks, not when a particular observer "sees" the light strike the clocks.

 

For example, if you are halfway between two lightning strikes, and you see them simultaneously, you will determine that they happened simultaneously. However, you do not have to see the flashes simultaneously to determine that the the strikes occured simultaneously. If you are closer to one strike, you will see it first, but you also know that you are closer to this strike and that it took less time for the light to reach you. By knowing exactly how much closer to the strike you are, and measuring the time difference between your seeing of the flashes, you will still come to the conclusion that the strikes took place simultaneously.

 

This is also true with the animations I presented. The first shows what anybody at rest no matter what his position with respect to the clocks will determine in terms of when the clocks are struck by a light originating halfway between the clocks.

 

The second animation shows what would be concluded by anyone moving with respect to the clocks, no matter what his postition is

 

IOW, we factor out any light propagation delay for light traveling from clock to our eye, so we can concentrate purely on the light traveling from originating flash to the clocks.

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Janus,

 

But why is light propagation delay not important?

 

Its the propagation of light that "defines" everything else. C is always central to equations. Setting it to 1 and factoring it out and such, seems to me to be quite missing the point.

 

Take the clock in Colorado, that we are all going by. Are we adding, subtracting, or factoring out the propagation delay of the signal to our position on the Earth...when we talk of similtaneity.

 

I am always confused on this point. How can you take a realistic view of a situation where two observers are separated by distance, as if you have a vehical of observation that is instantaneous in nature, when nothing in fact, other than thought, is faster than the speed of light?

 

Regards. TAR2

Edited by tar
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Janus,

 

But why is light propagation delay not important?

 

Its the propagation of light that "defines" everything else. C is always central to equations. Setting it to 1 and factoring it out and such, seems to me to be quite missing the point.

 

Take the clock in Colorado, that we are all going by. Are we adding, subtracting, or factoring out the propagation delay of the signal to our position on the Earth...when we talk of similtaneity.

 

I am always confused on this point. How can you take a realistic view of a situation where two observers are separated by distance, as if you have a vehical of observation that is instantaneous in nature, when nothing in fact, other than thought, is faster than the speed of light?

 

Regards. TAR2

In this example, the propagation delay between the origin of the flash and the light striking the clocks is important. What isn't important is the propagation delay between the light striking either clock and any particular observer actually seeing this event take place.

 

For example, if I was an observer sitting at the left clock, I would see my clock start first and then see the right clock start, but this does not mean that I will conclude that the right clock started after my clock. If the two clocks are separated by 299,792,458 meters, and I see the right clock start 1 sec after my own, I know that the right clock actually started running 1 sec earlier than my seeing it start, and thus actually started at the same time as my own. This is the same conclusion that an observer stting halfway between the clocks makes due ot the fact that he see both clocks start at the same time. The observer's position with respect to the clocks has no bearing on their final conclusion as to the simultaneity of the starting of the two clocks.

 

As a results all observers that share the same inertial frame ( are at rest with respect to each other) come to identical conclusions as to the when the two clocks start ticking. The animation just shows what that shared conclusion is.

 

Here's a different example. In this case, our observers are a person standing along the train tracks and someone riding in a train car. The switch here is that the flashes occur such that the light from them strikes the embankment observer( who is halfway between the flash origins) at the same moment that the car observer is abreast of him. Thus both observers see the light from both flashes simultaneously.

 

train1.gif

 

The above animation shows how thing occur according to the embankment frame. The embankment observer sees both flashes, and since he knows that he is halfway between the sources, he knows that they originated at the same time.

 

According to the railcar observer, things happen differently. He still sees the light from both flashes at the same time, but comes to a different conclusion as to the simultaneity of their origin. Since the speed of light is invariant, the light from both flashes must travel towards him at the same speed as measured by him. However, he isn't halfway between the origins until he sees the flashes, this means that the flashes actually left the sources when he was closer to one than the other. That being the case, the flashes couldn't have originated at the same time and still reached him at the same time. Thus according to him, this is what must have happened:

 

train2.gif

 

The flashes reach him and the emebankment observer at the same time, but the flashes originated at different times.

 

This is all done by considering where each observer is with respect to the source of the flashes and how long it takes light to propagate from source to observer according to each observer.

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Janus,

 

So anyone in the same frame, can agree, in retrospect, on the order of events, calculate everything back and agree on times and distances, once they agree on a time and place to act as a reference point. If the train were to stop at the embankment observer, then the moving observer could reference everything that recently happened to her, and everything she experienced to link up exactly with the actual order of events that have now been normalized by her arrival at the same time and place of the embankment observer. She can work backward and see what happened, and everything is back in order, once the two observers are both in the same place. Either actually or imaginarily.

 

But while any two observers are actually separated by distance, the time it takes light to propagate between, is an actual separation, that cannot be removed from the situation by thought.

 

So in the first diagram, my hypothetical observer, off to the right, would NOT see the clocks start similtaneously. He might be able to know that the clocks started similtaneously to an observer half way between, but he would actually see the near clock start, before the distant clock, and run forever ahead of the distant clock, until he moved to a position equidistant to the two clocks. To see the two clocks as showing the same time, he would have to reach the center point, either physically or by mentally undoing the propagation of light consideration. In reality, the observer to the right, even though he might "know" the clocks started at the same time to any observer on the plane perpendicular to the line between the clocks, also knows he sees the clocks offset in ticks by the actual distance between the clocks.

 

Swansont,

 

I certainly could be wrong, but I thought everybody had agreed to go by the cesium clock in Colorado.

 

Regards, TAR2

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So anyone in the same frame, can agree, in retrospect, on the order of events, calculate everything back and agree on times and distances, once they agree on a time and place to act as a reference point. If the train were to stop at the embankment observer, then the moving observer could reference everything that recently happened to her, and everything she experienced to link up exactly with the actual order of events that have now been normalized by her arrival at the same time and place of the embankment observer. She can work backward and see what happened, and everything is back in order, once the two observers are both in the same place. Either actually or imaginarily.

The first sentence is correct but not the rest. In the first sentence "in the same frame" would need to be understood as "*while* in the same frame", and "in retrospect" would not apply to what happened in other frames, before coming to relative rest.

 

Coming to relative rest (sharing an inertial frame) does not change an observer's history, or sync it up with the other observer. Two reunited twins can still have different histories, having measured different orders of past events, etc.

 

 

I would not recommend trying to figure out special relativity while adding additional complications of different observers and additional delays of light. It would be easier to learn what SR says of the train example, and when you got that, you can add other observers and see that everything remains consistent when additional delays of light are considered.

 

Another thing to consider is that if all the observers you consider remain in a single frame, then a classical Galilean/Newtonian description of things works, in which everyone agrees on the timing and order of events. Yet, different observers can see events happen in different orders due to different delays of light. Differences in what is seen is considered separately from differences in what is measured. If you really must understand this all in terms of differences of observed delay of light, it might help to first understand all that can happen for different observers in a single inertial frame, before special relativity is even thrown in.

Edited by md65536
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md65536,

 

Well I do admit I have trouble understanding the implications of length contraction and time dilation.

 

Its important to me that the story of one observer "trues up" with the story of another observer, and the two can be taken together to understand the script of the greater story, that the combination of the two would tell.

 

Certainly the propagation delay of light is extremely important, or everything would be happening at the same time, at the same place. This "distance" is crucial to maintain in my understanding. The equations of relativity exchange time and distance for each other, and this may be true and doable in some regards, but make no sense to do in other regards. If things are to be understood, or "put in place" in ones mind, the implications to the one frame of reference of the events observed in the other frame of reference need to be able to be understood, in an attempt to reach an "objective" sense of it.

 

What continually complicates my personal understanding goes back to my first readings of Einstein's lightning strike and train.

 

What makes the lightning strike a single event that happens several places at once? Any small area of the flash, is happening at a particular place, at a particular time. The entire lightning stike is thus a series of particular events and the first event in the chain of events that make a lightning strike, happens before the next event, in a different location than the next. The lightning strike itself does not provide a small enough duration or happen in a confined enough space, to be used as if the propagation of light should not be considered, even within the conception of the total strike.

 

Regards, TAR2


P.S. Perhaps its inadvisable to mix psychology and philosophy with physics, but it appears to me, that we are all already bound to the same moment, that proceeds rather in lockstep to become the next moment. The Mars rover may be 14 minutes away, but there is only one instance of it currently in the solar system, in the Milky Way, and in the universe. The fact that an observer on a planet 100 light years from here will not even see the launch for quite a while, does not erase the fact that the Mars rover is operating currently on Mars. The observer on that planet will be able to mentally subtract or add the 100 years, as surely as we are able to subtract or add the 14minutes. It still is doing what its doing only one thing at a time. Then it does the next. And it never gets unattached from the rest of the universe. The universe is already bound to itself.

Edited by tar
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md65536,

 

Well I do admit I have trouble understanding the implications of length contraction and time dilation.

 

Its important to me that the story of one observer "trues up" with the story of another observer, and the two can be taken together to understand the script of the greater story, that the combination of the two would tell.

And they always do in Relativity . If an event happens at a certain point when a clock at that certain point reads a given time, everyone agree to this fact. If all such observers are at rest with respect to this point, they also all agree that this event happened at that same given time according to their own clocks.

Certainly the propagation delay of light is extremely important, or everything would be happening at the same time, at the same place. This "distance" is crucial to maintain in my understanding

Then your "understanding" is flawed. If there were no propagation delay, IOW the speed of light was infinite, everything would not be happening at the same time. I really don't get how you came to this conclusion. An infinite speed of light would mean that we revert to a Newtonian view of the universe, but you still will have separate events

The equations of relativity exchange time and distance for each other, and this may be true and doable in some regards, but make no sense to do in other regards. If things are to be understood, or "put in place" in ones mind, the implications to the one frame of reference of the events observed in the other frame of reference need to be able to be understood, in an attempt to reach an "objective" sense of it.

 

What continually complicates my personal understanding goes back to my first readings of Einstein's lightning strike and train.

 

What makes the lightning strike a single event that happens several places at once?

Nothing. Relativity doesn't imply that it is

Any small area of the flash, is happening at a particular place, at a particular time. The entire lightning stike is thus a series of particular events and the first event in the chain of events that make a lightning strike, happens before the next event, in a different location than the next. The lightning strike itself does not provide a small enough duration or happen in a confined enough space, to be used as if the propagation of light should not be considered, even within the conception of the total strike.

Here's Einstein's train experiment wiht length contraction taken into account:

 

First here's what happens in the embankment frame.

 

trainsimul1.gif

 

Lightning strikes hit the red dots on the embankment when the ends of the trains are aligned with them, and the two observers are next to each other.

 

As the flashes travel towards the center point, the train moves to the right. The light from the right hits the train observer, then both lights reach the embankment observer, and finally the light from the left hits the train observer. The train observer is next to a particular point of the tracks when each light reaches him, and the observer is next to a particular part of the train when the lights reach him. Since the train is moving, it is length contracted. IOW, it is the contracted length of the train that just fits between the red dots.

 

Now here is what happens according to the train's frame.

 

trainsimul2.gif

 

First off we must note that since it is the embankment that is now considered as moving, Thus the train is its "normal" length, while the tracks are length contracted. This means that the train can no longer fit between the red dots. The front of train hits the red dot before the rear hits the left dot.

The lightning strikes still occur when the ends of the train align with the red dots. The light from the right still hits the train observer first, and while he is next to the same point of the tracks. Both lights reach the embankment observer at the same time when he is next to the same point of the train, etc. The difference is that the lightning strikes don't occur at the same time. They can't if the train frame is going to agree with the embankment frame as to what events happened where.

 

If we were to add clocks and time dilation to the situation, you would find that everyone would agree to the clock readings on any two clocks as they passed each other. For instance, everyone agrees as to what time reads on the clock at the front of the train and what time reads on the clock at the right red dot, when the lightning strikes there.

 

In addition, Anyone, no matter where they are stationed along the tracks or train will come the same conclusions.

You can imagine an infinite number of observers lined up on both the tracks and train each with his own clock sychronized to the others in his frame (all the train clocks are synced to each other and all the embankment clocks are in sync.) All any of these observer have to do to determine when an event happens is to read the time off the clock in his frame that is next to that event. Thus for any observr on the train to tell whether or not the light strikes take place simultaneously or not, all he has to do is compare the reading the rear clock when it is next to the left red dot, to the reading on the front clockwhen it is next to the right red dot. If these two reading are identical then the strikes are simultaneous (they will not be so, menaing the strikes will not be silumtaneous.

 

The point here is that it is not important how long it takes for this information to get to him from the ends of the train, only what the information is, The light progation delay from end of train to observer can be ignored.

P.S. Perhaps its inadvisable to mix psychology and philosophy with physics, but it appears to me, that we are all already bound to the same moment, that proceeds rather in lockstep to become the next moment. The Mars rover may be 14 minutes away, but there is only one instance of it currently in the solar system, in the Milky Way, and in the universe. The fact that an observer on a planet 100 light years from here will not even see the launch for quite a while, does not erase the fact that the Mars rover is operating currently on Mars. The observer on that planet will be able to mentally subtract or add the 100 years, as surely as we are able to subtract or add the 14minutes. It still is doing what its doing only one thing at a time. Then it does the next. And it never gets unattached from the rest of the universe. The universe is already bound to itself.

Relativity is concerned with relative motion, You seem to be obsessed with relative position.
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In this example, the propagation delay between the origin of the flash and the light striking the clocks is important. What isn't important is the propagation delay between the light striking either clock and any particular observer actually seeing this event take place.

 

For example, if I was an observer sitting at the left clock, I would see my clock start first and then see the right clock start, but this does not mean that I will conclude that the right clock started after my clock. If the two clocks are separated by 299,792,458 meters, and I see the right clock start 1 sec after my own, I know that the right clock actually started running 1 sec earlier than my seeing it start, and thus actually started at the same time as my own. This is the same conclusion that an observer stting halfway between the clocks makes due ot the fact that he see both clocks start at the same time. The observer's position with respect to the clocks has no bearing on their final conclusion as to the simultaneity of the starting of the two clocks.

 

As a results all observers that share the same inertial frame ( are at rest with respect to each other) come to identical conclusions as to the when the two clocks start ticking. The animation just shows what that shared conclusion is.

 

Here's a different example. In this case, our observers are a person standing along the train tracks and someone riding in a train car. The switch here is that the flashes occur such that the light from them strikes the embankment observer( who is halfway between the flash origins) at the same moment that the car observer is abreast of him. Thus both observers see the light from both flashes simultaneously.

 

train1.gif

 

The above animation shows how thing occur according to the embankment frame. The embankment observer sees both flashes, and since he knows that he is halfway between the sources, he knows that they originated at the same time.

 

According to the railcar observer, things happen differently. He still sees the light from both flashes at the same time, but comes to a different conclusion as to the simultaneity of their origin. Since the speed of light is invariant, the light from both flashes must travel towards him at the same speed as measured by him. However, he isn't halfway between the origins until he sees the flashes, this means that the flashes actually left the sources when he was closer to one than the other. That being the case, the flashes couldn't have originated at the same time and still reached him at the same time. Thus according to him, this is what must have happened:

 

train2.gif

 

The flashes reach him and the emebankment observer at the same time, but the flashes originated at different times.

 

This is all done by considering where each observer is with respect to the source of the flashes and how long it takes light to propagate from source to observer according to each observer.

Approaching objects and escaping objects have different length contraction factors. I already made length contraction factor for approaching objects,it is

R/R'=gamma*(c+v)/c

 

Let's make length contraction factor for escaping objects.

Time of travel of light in twin frame on the first animation

t=R1/(c-v)=R2/(c+v)

R1 - distance between source1 and twin' in twin frame

R2 - distance between source2 and twin' in twin frame

R2/R'2=gamma*(c+v)/c

R'2 - distance between source2 and twin' in twin' frame

R'1 - distance between source1 and twin' in twin' frame

R'1=R'2=R2*c/[gamma(c+v)

R2=t(c+v)

R'1=R'2=t(c+v)c/[gamma(c+v)]=tc/gamma

 

R1/R'1=t(c-v)gamma/ tc=(c-v)gamma/c

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Janus,

 

Yes, I am position obsessed. When the two observers are at the same point, the foward wave from the rear strike is reaching that point. Both will see the photons or wave arriving at that point similtaneously. When the forward wave of the lead strike reach that point both observers see it at exactly the same time. Your diagrams show the wave front from the front strike hitting first the moving observer, then the stationary observer, then the position of the rear strike. This is not the information given at the start. The information was that the wave fronts of two similtaneous strikes, from the vantage point of the standing observer, reach the standing observer similtaneously. The moving observer, not being blind, will experience both wavefronts arriving at that point, because, at that point, he is halfway between, exactly as the standing observer.

 

Who does not see the strikes at the same time are the observers standing at the position of the front strike and the position of the rear strike. The fellow standing at the position of the front strike, sees his strike, and then the speed of light later, sees the rear strike. The fellow standing at the rear strike, sees his strike, and then the speed of light later, sees the front strike.

 

The similtaneousness of the strike, applies only to observers halfway between, since this is the definition of similtaneousness. You can't then expect that the fellow standing at the front strike would see the back strike at the same moment he saw the front of the train pass, and his lightnings strike. He sees the front strike, then the rear strike, then the observer pass, knowing full well that the moving observer experienced the rear strike, moments before him, and the front strike moments after.

 

Since the order of events at the rear stationary observer was, moving observer passes, trailend of train occurs similtaneously with the rear lightning strike, then the front strike is observed, the only thing that trues up when the front observer and the real observer compare notes with the moving observer and the stationary observer, is that the forward wave from the front strike reached both the standing observer, and the moving observer when the moving observer was halfway between the front strike and the rear strike. And that the forward wave from the rear strike, reached the midpoint between the strikes, likewise, when the moving observer was there.

 

Regards, TAR2

Edited by tar
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Swansont,

 

I certainly could be wrong, but I thought everybody had agreed to go by the cesium clock in Colorado.

The military's clocks are mostly in Washington DC. (I work on some of them). Colorado implies NIST. Those are the other guys.

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