Real life examples of simultaneity

[CLSabey]

Yes, he would see the bolts hit A and B at the same time. The light from both would reach him when t=0.5 s. Knowing he was right in the middle of A and B, he would then conclude that the bolts hit A and B at t=0 s.

You are presuming the line AB to be 300,000km then. Time is only significant when we know the reference frame for the events which we speak of. Here we could use any value for time so long as the beams of light resulting from the bolts reached M at same time, whatever that time may be from t=0 which coincides to origin of events A and B (lightning bolts). Whatever the t'= x then you can determine distance of lines AM and BM by dividng time in half and multiplying by distance in speed of light (use seconds for t).

Let's say it takes one second for light beams from A and B to reach you. The line AB is 600,000 km/s.

 

[vela]

No, they all agree that the bolts hit at t=0 s, even though they didn't know about the strikes until some time later when the light was able to propagate from the event to the observer.

The relativity of simultaneity happens between observers moving relative to each other. Since A, B, and M are all at rest to one another, they all agree that the bolts hit at the same time, even though they didn't see the bolts hit until later. Again, when an observer sees the event and when the event actually happened are two different things.

Say you had an observer C going from A to B who passes M at t=0 s, the time the lightning bolts strike. From A, B, and M's point of view, the light from B will reach C before the light from A does because C is moving toward the light coming from B and away from the light coming from A. C also agrees that the light from B reached him before the light from A, but he also knows that A and B were at the same distance from him. If the light from B reached him first, it must be because the lightning hit B before the lightning hit A. To C, the events weren't simultaneous.

 

[CLSabey]

In the stationary frame they meet at 1/3 the distance between M and B.

If you want A' too, that meets at 2 times the distance between M and A.

I want when M' and B' meet. What specifically is the number of the point they meet. No ratios or relations or descriptives just the number.

 

[vela]

You are presuming the line AB to be 300,000km then.

Yes, because that's the set-up goodabouthood made up. Something happens at A and B sees it one second later. M being in the middle would be a half light-second away from A and B.

 

[CLSabey]

Yes you are right

 

[goodabouthood]

No, they all agree that the bolts hit at t=0 s, even though they didn't know about the strikes until some time later when the light was able to propagate from the event to the observer.

The relativity of simultaneity happens between observers moving relative to each other. Since A, B, and M are all at rest to one another, they all agree that the bolts hit at the same time, even though they didn't see the bolts hit until later. Again, when an observer sees the event and when the event actually happened are two different things.

Say you had an observer C going from A to B who passes M at t=0 s, the time the lightning bolts strike. From A, B, and M's point of view, the light from B will reach C before the light from A does because C is moving toward the light coming from B and away from the light coming from A. C also agrees that the light from B reached him before the light from A, but he also knows that A and B were at the same distance from him. If the light from B reached him first, it must be because the lightning hit B before the lightning hit A. To C, the events weren't simultaneous.

This actually helps. The guy at C actually experiences the event before the others. The event of seeing the lightning B actually happens for him first.

 

[nitsuj]

Now wouldn't that be relative simultaneity because person M sees both lighting bolts at the same time but person A and person B see them at different times?

Person A and B will not agree with the person M when the bolts striked.

At least that is what I thought simultaneity was.

Well it depends on context.

With that perspective their experience is what is used to define "right Now". And your right they didn't experience each lighting strike at the same time, and in that sense wasn't simultaneous.

After the group measures how much time (this is key, they measure time the same) elapsed between events, they measure the distance between themselves and using their time and distance measurements, A, B & M calculate that the lighting strikes flashed at the same time.

 

[goodabouthood]

That is the train example. It's most likely a better example than the one I tried to give.

So events actually happen for some FoR than they do for other FoR.

 

[goodabouthood]

So let's say that the guy on the platform has a clock and the girl on the train also has a clock that are synchronized.

Special relativity tells us that even if they are reading synchronized clocks the events that happen would be different for them at particular times. They couldn't agree.

I understand this more now. Thanks.

 

[BruceW]

good. I think in your example before, you were confusing two different events: the lightning bolt hitting the ground, and the light from it going into someone's eye. These two events are different because light travels from one place to another. They are not different due to relativity of simultaneity.

 

[nitsuj]

So let's say that the guy on the platform has a clock and the girl on the train also has a clock that are synchronized.

Special relativity tells us that even if they are reading synchronized clocks the events that happen would be different for them at particular times. They couldn't agree.

I understand this more now. Thanks.

If their clocks are synchronized (adjusted for differences in measuring time) they would agree on the time of events, like with the GPS.

Another way to say it is SR/GR redifined the concept of simultaneous with the postulate c is invariant.

 

[ghwellsjr]

So let's say that the guy on the platform has a clock and the girl on the train also has a clock that are synchronized.

Special relativity tells us that even if they are reading synchronized clocks the events that happen would be different for them at particular times. They couldn't agree.

I understand this more now. Thanks.

If their clocks are synchronized (adjusted for differences in measuring time) they would agree on the time of events, like with the GPS.

Another way to say it is SR/GR redifined the concept of simultaneous with the postulate c is invariant.

In the example of the train and the platform, it is not possible to adjust the clocks so that they remain synchronized. Identical, unadjusted clocks will run at different rates in a symmetrical, reciprocal way, making it impossible to tweak them so that they can run at the same rate. The platform observer sees the train clocks ticking slower than his own and the train observer sees the platform clocks ticking slower than her own.

This is the point that has been repeated many times on this thread: clocks moving inertially (in a constant direction at a constant speed) with respect to each other run at different rates and cannot be synchronized, and Frames of Reference moving with respect to each other will have different definitions of the synchronization of the clocks at rest in their respective frames.

It's a different story with the time dilation caused by gravity where clocks at different altitudes and/or in orbit run at different rates, but there the relationship is not symmetrical and reciprocal which allows them to be tweaked so that they can display the same time and remain "synchronized". So, for example, the atomic clocks at Greenwich, England, run at a different rate from identical clocks at Boulder, Colorado, but they both agree on the difference because its not symmetrical and reciprocal, so they can both be used as standards for the second here on Earth with appropriate tweaking.

And goodabouthood, you're still confused on the meaning of "event" as used in relativity. Please study this recent https://www.physicsforums.com/showthread.php?t=543416" and see if it helps you.

 

[bobc2]

Here is a space-time diagram to help you visualize what special relativity is representing in the train-lightening example. Try to imagine a 4-dimensional universe with 4-dimensional objects (the train passenger car, the observer on the platform and the observer in the train car--these are all 4-D objects). These objects extend into the 4th dimension in the sketch below. A 4-D object corresponding to motion along X1 is slanted in the 4th dimension (the 3-D representation of the object moves along its 4th dimension at the speed of light). Google "space-time diagram" and "Block Universe" to get insight into these concepts. It's likely that you will not really get a good grasp of special relativity until you can comprehend a space-time diagram.

 

[ghwellsjr]

Wow--if I thought I had to comprehend space-time diagrams before I could really get a good grasp of special relativity, I'd have given up a long time ago, especially when you promote this 4-D "Block Universe" version which is not mainstream SR but rather a philosophical speculation. Why don't you stick with the legitimate 1-D version as described in the wikipedia "Minkowski diagram" article? And since they are inherently 1-D, how can they illustrate the difference in length contraction along a second dimension?

 

[goodabouthood]

1. My idea of an event is pretty much an instant in time where something happens.

2. The idea in my head about all of this is that the observer on the platform and the observer on the train experience one of the events together. That would be the lighting bolt that hit B.

The lightning bolt hitting A would happen at the same time as B for the observer on the platform so he would think that these events were simultaneous. The observer on the train is moving towards B so the lightning bolt from A has to catch up to him so he would not think these events were simultaneous.

Is this correct?

 

[PatrickPowers]

Wow--if I thought I had to comprehend space-time diagrams before I could really get a good grasp of special relativity, I'd have given up a long time ago, especially when you promote this 4-D "Block Universe" version which is not mainstream SR but rather a philosophical speculation. Why don't you stick with the legitimate 1-D version as described in the wikipedia "Minkowski diagram" article? And since they are inherently 1-D, how can they illustrate the difference in length contraction along a second dimension?

I'll take up the sword in defense of the Block Universe concept. I don't believe that the world is actually this way, but it is a very useful idea nonetheless. In mathematics it is quite often the case that if you can get the element of time out of the problem then everything gets easier. So it helps a lot to be able to think this way.

 

[ghwellsjr]

1. My idea of an event is pretty much an instant in time where something happens.

2. The idea in my head about all of this is that the observer on the platform and the observer on the train experience one of the events together. That would be the lighting bolt that hit B.

The lightning bolt hitting A would happen at the same time as B for the observer on the platform so he would think that these events were simultaneous. The observer on the train is moving towards B so the lightning bolt from A has to catch up to him so he would not think these events were simultaneous.

Is this correct?

No, did you study the thread I asked you to?

 

[goodabouthood]

Well I see this:

"The “time” of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock."

So if you were on the platform and saw both lightning bolts hit and your clock read 8:00pm that would be the time of the two events for said person. The two events would be simultaneous for this person on platform.

Please explain if I my interpretation of the train example is wrong.

 

[ghwellsjr]

What's wrong with your interpretation is that even though your statement in your second paragraph is correct, you then went on to talk about the observer seeing the two lightning bolts and looking at his clock and seeing a time of 8:00pm on it. The observer's clock is of no consequence. He doesn't even need a clock to see that the images of the two lightning bolts arrive at his location simultaneously. But what is important is the times on the two separate clocks located where the lightning bolts occurred when they occurred. These clocks will have an earlier time on them and they define the two events, along with their locations. The observer has no knowledge of the lightning strikes until some time later.

You have to imagine a multitude of synchronized clocks spread out everywhere in the space defined by a Frame of Reference. At each location is the spatial coordinates of each clock. The combination of the time on each clock, plus its location, is defined as an event. It has nothing to do with any observers or when they see anything that might be happening.

So, in a Frame of Reference where the ground is stationary, the event of the lightning strike at the front of the train and the event of the second lightning strike at the rear of the train are simultaneous because the two events defined by the two clocks at those two locations we are told have the same time reading on them. We are told that indirectly by virtue of the fact that the light from those two events arrives simultaneously at a point midway between them. That's the way the scenario is set up.

So given that the scenario is set up so that the events of the lightning strikes occur at the same time according to the definition of time in the ground reference frame, if we want to see what the times of those same two events are in a different Frame of Reference moving with respect to the first one, we need to use the Lorentz Transform to take the x, y, z and t coordinates of each event of interest and transform them into the second FoR.

So for simplicity's sake, let's say that the speed of light is 1 foot per nanosecond and let's say the train is traveling at 0.6c and it is 1000 feet long. We could establish some coordinates and use the Lorentz Transform to see what the time coordinates of those two events are and subtract them to see what the difference between them is but since BruceW gave you a concise formula to calculate this difference in post #3, let's go ahead and use that. In his formula, β=0.6 and Δx equals 1000 feet or in compatible units, it is 1000 light nanoseconds or 1 light microsecond. Here's BruceW's formula:
$$\frac{\beta}{\sqrt{1- \beta^2}} \Delta x$$
You can easily see that this evaluates to 0.75 microseconds.

Note that this evaluation has nothing to do with the observers in the scenario.

I think what is confusing in the video is the introduction of the observers and the "interpretations" of what they are seeing as if that is what are the events in question.

 

[bobc2]

1. My idea of an event is pretty much an instant in time where something happens.

2. The idea in my head about all of this is that the observer on the platform and the observer on the train experience one of the events together. That would be the lighting bolt that hit B.

The lightning bolt hitting A would happen at the same time as B for the observer on the platform so he would think that these events were simultaneous. The observer on the train is moving towards B so the lightning bolt from A has to catch up to him so he would not think these events were simultaneous.

Is this correct?

I can understand your attention focused on the guy in the middle of the car moving away from the point on the ground that the lightning hit. But the answer to your question is "No." The focus in this example should be on the special relativity effects relating to the relativistic speed of the train.

Did you understand the space-time diagram? You can see that the guy on the train is living in a different 3-dimensional world than the guy on the platform. They are not living in the same simultaneous 3-D spaces. That accounts for the fact that the front and rear flashes are not simultaneous for the guy in the train--those two events are literally not simultaneous in his 3-D world.

 

[bobc2]

Wow--if I thought I had to comprehend space-time diagrams before I could really get a good grasp of special relativity, I'd have given up a long time ago, especially when you promote this 4-D "Block Universe" version which is not mainstream SR but rather a philosophical speculation. Why don't you stick with the legitimate 1-D version as described in the wikipedia "Minkowski diagram" article? And since they are inherently 1-D, how can they illustrate the difference in length contraction along a second dimension?

That's not an unreasonalble response, ghwellsjr. Thanks for the comments. But, it has been my experience that the "light" has really suddenly turned on for my students who came to an understanding of the space-time diagrams. Length contraction, time dilation, constant speed of light and all of the "paradoxes" seem so obvious and easily explained with the aid of space-time diagrams. But, it does take a little persistence initially to get a handle on it, so I understand your initial reaction to my suggestion.

My approach was to never introduce the block universe concept until students began to ask about it. It was always interesting to see which students would see the implication of a block universe after much of a semester of working with space-time diagrams.

And could you describe the geometrization of the world without some equivalent to the Block Universe? Are you saying that the universe is not 4-dimensional (perhaps more dimensions if string theory pans out)?

Could you give me the link for the wikipedia article.

 

[nitsuj]

In the example of the train and the platform, it is not possible to adjust the clocks so that they remain synchronized. Identical, unadjusted clocks will run at different rates in a symmetrical, reciprocal way, making it impossible to tweak them so that they can run at the same rate. The platform observer sees the train clocks ticking slower than his own and the train observer sees the platform clocks ticking slower than her own.

This is the point that has been repeated many times on this thread: clocks moving inertially (in a constant direction at a constant speed) with respect to each other run at different rates and cannot be synchronized, and Frames of Reference moving with respect to each other will have different definitions of the synchronization of the clocks at rest in their respective frames.

It's a different story with the time dilation caused by gravity where clocks at different altitudes and/or in orbit run at different rates, but there the relationship is not symmetrical and reciprocal which allows them to be tweaked so that they can display the same time and remain "synchronized". So, for example, the atomic clocks at Greenwich, England, run at a different rate from identical clocks at Boulder, Colorado, but they both agree on the difference because its not symmetrical and reciprocal, so they can both be used as standards for the second here on Earth with appropriate tweaking.


And goodabouthood, you're still confused on the meaning of "event" as used in relativity. Please study this recent https://www.physicsforums.com/showthread.php?t=543416" and see if it helps you.

So a moving clock could not have it's measurement of (proper?) time adjusted to match the time of a stationary clock? I need to read about this "Identical, unadjusted clocks will run at different rates in a symmetrical, reciprocal way, making it impossible to tweak them so that they can run at the same rate." I don't understand what it means.

Is it because both observers see the others clock as ticking slower, so adjusting either clock to "correct" for the difference for one observer's clock would exaggerate the difference for the other observers clock?

To say it differently, does the symmetry of SR time dilation reffer to how two observers in relative motion obeserve the others clock as ticking slower?

 

[ghwellsjr]

I can understand your attention focused on the guy in the middle of the car moving away from the point on the ground that the lightning hit. But the answer to your question is "No." The focus in this example should be on the special relativity effects relating to the relativistic speed of the train.

This thread is about the meaning of simultaneity. The purpose of the train example is to show that in one Frame of Reference (where the ground is at rest), the two lightning bolt events that occur at different locations nevertheless occur at the same time, not because nature demands it, but because the clocks that are located at those two events have been previously synchronized and the problem is stated such that they are simultaneous. That's one point to focus on.

The second point to focus on is that the events defined according to one FoR need to be at different locations, otherwise two events at the same location and the same time are not two events but one event (they have the same four coordinates).

The third point to focus on is that in many other FoR's (not all, just some), those same two events, when transformed into a set of new coordinates will have a totally different set of four coordinates and the time components may be different in which case they are not simultaneous in that FoR.

Did you understand the space-time diagram? You can see that the guy on the train is living in a different 3-dimensional world than the guy on the platform. They are not living in the same simultaneous 3-D spaces. That accounts for the fact that the front and rear flashes are not simultaneous for the guy in the train--those two events are literally not simultaneous in his 3-D world.

But the gal on the train and the guy on the platform are both living in the same world. There's only one world. The issue is how we describe the 3 spatial coordinates and the 1 time coordinate that define an event--what numbers do we (and they) use? The gal on the train can use a Frame of Reference where the ground is stationary (of which there are an infinite such FoR's) and in which the two events will be simultaneous and the guy on the platform can use a FoR in which the train is stationary (of which there are an infinite such FoR's) and in which the two events will not be simultaneous. But whichever FoR is used, it includes everyone and every thing. People, other observers and objects don't own their own FoR to the exclusion of the other observers and objects. And it's the FoR that determines if two events are simultaneous not any observers or objects no matter what their states of motion are.

So it's really wrong when discussing the meaning of simultaneity in Special Relativity to link it to particular observers or especially to say that one person lives in a different 3-D world than another one and that's what determines the simultaneity of events, it should only be linked to particular FoR's.

 

[ghwellsjr]

Length contraction, time dilation, constant speed of light and all of the "paradoxes" seem so obvious and easily explained with the aid of space-time diagrams.

How do you show that length contraction only occurs along the direction of motion in a space-time diagram? How do you show the very common example of a light clock with the light bouncing back and forth at right angles to the direction of motion? How would you show that a circular set of mirrors becomes an ellipse when in motion but the light reflecting off of them follows a circular pattern like what is illustrated in robphy's animated glyph on post #9 of this thread?

And could you describe the geometrization of the world without some equivalent to the Block Universe? Are you saying that the universe is not 4-dimensional (perhaps more dimensions if string theory pans out)?

In Special Relativity, we focus on a subset of the real world, we ignore gravity and quantum effects and other theories. We model the spatial aspects of the world with three normal, ordinary, everyday, easy-to-understand dimensions and the time aspect of it as in the normal, ordinary, everyday, easy-to-understand way that everyone understands time. But then we define a Frame of Reference that combines the three spatial dimension with time to create the concept of events which are the four coordinates within that particular Frame of Reference. If we use a different Frame of Reference, even another one that is not moving with respect to the first one, we get a different set of four coordinates for each event.

Could you give me the link for the wikipedia article.

I did what you said to do:

Google "space-time diagram" and "Block Universe"

The first wikipedia hit for the first one was en.wikipedia.org/wiki/Minkowski_diagram as I said here:

the wikipedia "Minkowski diagram" article

and the first hit for the second one was en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)

 

[ghwellsjr]

So a moving clock could not have it's measurement of (proper?) time adjusted to match the time of a stationary clock? I need to read about this "Identical, unadjusted clocks will run at different rates in a symmetrical, reciprocal way, making it impossible to tweak them so that they can run at the same rate." I don't understand what it means.

Is it because both observers see the others clock as ticking slower, so adjusting either clock to "correct" for the difference for one observer's clock would exaggerate the difference for the other observers clock?

To say it differently, does the symmetry of SR time dilation reffer to how two observers in relative motion obeserve the others clock as ticking slower?

Yes. We're talking here about Relativistic Doppler.

Remember, in our discussion of simultaneity (the subject of this thread), there are not just two clocks moving with respect to each other, there are an infinite number of clocks in two different Frames of Reference. If we give preference to one FoR, it is not possible to tweak all the clocks in the other FoR to match the preferred FoR. If we want to have a preferred FoR, we just use that one and forget about any other FoR and then the issue of simultaneity becomes moot because we treat time as absolute, but that's not what we do in SR.

If you want to talk about just two clocks moving inertially with respect to each other (which has nothing to do with the subject of simultaneity and is not restricted to Special Relativity) then it's a fact of nature that each observer will see the other one's clock as ticking differently than their own in a symmetrical way. If one of them adjusts his clock so that the other one will see it as ticking at the same rate as his own (which can only be done for very restricted types of relative motion), the adjusted clock will then tick at a rate even further removed from the unadjusted clock.

Consider two clocks far removed from each other but have been ticking for a very long time and the image of each of them has reached the other. These two clocks do not have to be moving along the same line, although they could be. If they are moving along the same line toward each other, they will each see the other one as ticking faster than their own. Then when the pass each other, they will immediately see the other one as ticking slower than their own. A similar effect happens when they are not traveling along the same line but the transition is gradual instead of abrupt and they each see the same gradual transistion. The farther away their point of closest approach, the more gradual is the transition. But how in the world can you tweak one of the clocks so that it always appears to be synchronized with the other clock?

 

[bobc2]

"The non-mathematician is seized by a mysterious shuddering when he hears of 'four-dimensional' things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more common-place statement than that the world in which we live is a four-dimensional space-time continuum." Einstein, "Relativity - The Special and the General Theory" - Chapter XVII, "Minkowski's Four Dimensional Space".

From the final paragraph of that chapter: "These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski. Without it the general theory of relativity, of which the fundamental ideas are developed in the following pages, would perhaps have got no farther than its long clothes."

 

[goodabouthood]

When I first started this thread I thought I had a much better idea of what is happening in special relativity. I was wrong.

Now, are you saying each reference frame has their own set of infinite clocks? Why is this? I had thought that if two objects are moving relative to each other in uniform motion the same laws apply.

So, does the reference frame of the person on the train have a totally different set of infinite clocks than the observer on the platform? If this is the case why?

When do the two lightning bolts actually happen for each of them?

You are saying the reference frame on the ground has its own set of clocks and the reference frame in the train has it's own set of clocks? Why are they different?

 

[vela]

That's exactly what's happening. To put it in a more mathematical way, each reference frame has its own set of coordinates. If an event in reference frame S has spacetime coordinates (t, x), in another frame S', it will have a different set of coordinates (t', x'). In Newtonian mechanics, it was assumed everyone experienced time the same way, so you would have t=t'. Special relativity said that assumption was wrong.

SR says the laws of physics are the same across inertial frames. That's not the same as saying the coordinates are the same in different frames.

As far as why the universe works this way, the only answer we really have right now is "because it does." You could say it's a consequence of the postulates of special relativity, but that merely changes the question to why the postulates are true. Again, this just boils down to the fact that they're consistent with what we have observed. In other words, it's how the universe appears to work.

 

[goodabouthood]

Can you give me an example of the coordinates of the reference frame of the train and the coordinates of the reference frame of the ground?

Also, are these infinite set of clocks in each reference frame always synchronous?

 

[nitsuj]

Yes. We're talking here about Relativistic Doppler.

Remember, in our discussion of simultaneity (the subject of this thread), there are not just two clocks moving with respect to each other, there are an infinite number of clocks in two different Frames of Reference. If we give preference to one FoR, it is not possible to tweak all the clocks in the other FoR to match the preferred FoR. If we want to have a preferred FoR, we just use that one and forget about any other FoR and then the issue of simultaneity becomes moot because we treat time as absolute, but that's not what we do in SR.

If you want to talk about just two clocks moving inertially with respect to each other (which has nothing to do with the subject of simultaneity and is not restricted to Special Relativity) then it's a fact of nature that each observer will see the other one's clock as ticking differently than their own in a symmetrical way. If one of them adjusts his clock so that the other one will see it as ticking at the same rate as his own (which can only be done for very restricted types of relative motion), the adjusted clock will then tick at a rate even further removed from the unadjusted clock.

Consider two clocks far removed from each other but have been ticking for a very long time and the image of each of them has reached the other. These two clocks do not have to be moving along the same line, although they could be. If they are moving along the same line toward each other, they will each see the other one as ticking faster than their own. Then when the pass each other, they will immediately see the other one as ticking slower than their own. A similar effect happens when they are not traveling along the same line but the transition is gradual instead of abrupt and they each see the same gradual transistion. The farther away their point of closest approach, the more gradual is the transition. But how in the world can you tweak one of the clocks so that it always appears to be synchronized with the other clock?

Ah okay, SR time dilation symmetry, both see the others clock ticking slower.

Does relative simultaneity happen from gravitational time dilation as well?

would an observer on Jupiter see an Earth clock tick faster then their own, and the Earth observer see a Jupiter clock tick slower then their own (no time dilation symmetry from gravity)?

 

[ghwellsjr]

When I first started this thread I thought I had a much better idea of what is happening in special relativity. I was wrong.

Now, are you saying each reference frame has their own set of infinite clocks?

Yes.

Why is this?

Because clocks in relative motion tick at different rates.

I had thought that if two objects are moving relative to each other in uniform motion the same laws apply.

The same laws do apply and one of those laws says that physical constants will be the same in all reference frames and one of those constants is the speed of light, c, but in order for two observers in relative motion to both measure the round-trip speed of light to be the same value, c, we need to introduce time dilation and length contraction, which is the reason that clocks moving with respect to each other tick at different rates.

So, does the reference frame of the person on the train have a totally different set of infinite clocks than the observer on the platform?

Yes.

If this is the case why?

Basically, we have two choices. We can either believe in a single preferred reference frame defined by a presummed but elusive ether in which the one-way speed of light is exclusively c, which was the choice presummed by scientists prior to Einstein and called the Lorentz Ether Theory (LET) and which affirmed the notion of absolute time and space, or we can postulate that the one-way speed of light is c in any state of inertial motion (Einstein's second postulate) which then leads to the notion of relative time and space with no preferred Frame of Reference but rather any frame you want to choose with its own set of clocks and rulers defining space and time.

When do the two lightning bolts actually happen for each of them?

It is not possible to answer the question of when remote things actually happen until and unless you define a reference frame to give meaning to remote clocks and distances. The train example shows that different observers will have different opinions on when the two lightning bolts happened and nature isn't going to reveal to us what is actually happening. So we can either debate about what actually happens (which is what the LET scientists prior to Einstein did because that pesky ether was impossible to pin down) or we can take Einstein's idea and define times and locations according to his convention. That's what we're here to learn about on this forum.

You are saying the reference frame on the ground has its own set of clocks and the reference frame in the train has it's own set of clocks? Why are they different?

Because when we set up the ground reference frame, we synchronize all the clocks to have the same time on them and when we set up the train reference frame, we synchronize all of its clocks which are ticking at a different rate to have the same time on them. If all the train reference frame's clocks tick at a different rate than the ground reference frame clocks, then how could we get by with only one set of clocks? But we also have to keep in mind that the locations are defined differently too.

 

[bobc2]

Can you give me an example of the coordinates of the reference frame of the train and the coordinates of the reference frame of the ground?

Also, are these infinite set of clocks in each reference frame always synchronous?

Here are the two coordinate systems. Consider the ground as the rest system (black) and the train as the moving system (blue). The observers (black and blue) move along their respective X4 coordinate at the speed of light. Each observer carries his own clock as he moves along his respective 4th dimension. Distance moved along the X4 dimension for each observer is X4 = ct.

Now, we have an event in the 4-dimensional space, the red point, "P", in the sketch. Each observer registers a different time (t = X4/c) along his respective X4 coordinate for that unique event (red point). Likewise each observer registers a different distance along his respective X1 coordinate.

The clocks are synchronous only in this sense: From the point that the two observer pass each other (at the origins of both coordinate systems), the time lapses are the same for equal distances traveled along the respective 4th dimensions. A synchronous "proper" time can be established for both observers. Nervertheless, the instantaneous 3-D cross-section each observer lives in (his 3-D space of simultaneity) includes the clock of the other observer that displays an earlier time than his own proper time (the black guy sees an earlier time on the blue clock and the blue guy sees an earlier time on the black clock--and this has nothing to do with light travel times--we're just looking at events in 4-D space). The reason for this is evident in the space-time diagram below--it's because of the different cross-section views of the 4-D universe associated with the two different observers.

 

[goodabouthood]

Well, what exactly defines a reference frame?

Are there infinite number of reference frames?

Why do different reference frames have different coordinates?

 

[ghwellsjr]

Ah okay, SR time dilation symmetry, both see the others clock ticking slower.

Does relative simultaneity happen from gravitational time dilation as well?

No, it's not relative. As I said in post #47:

It's a different story with the time dilation caused by gravity where clocks at different altitudes and/or in orbit run at different rates, but there the relationship is not symmetrical and reciprocal which allows them to be tweaked so that they can display the same time and remain "synchronized". So, for example, the atomic clocks at Greenwich, England, run at a different rate from identical clocks at Boulder, Colorado, but they both agree on the difference because its not symmetrical and reciprocal, so they can both be used as standards for the second here on Earth with appropriate tweaking.

would an observer on Jupiter see an Earth clock tick faster then their own, and the Earth observer see a Jupiter clock tick slower then their own (no time dilation symmetry from gravity)?

As far as the gravitational contribution to time dilation goes, yes. During the long orbital times of the two planets, there would be other variations in the observed differences in the clocks but these would average out so that every time the two planets are in the same relative position in the solar system, there will be a steadily increasing time on the Earth clock compared to the Jupiter clock.

 

[goodabouthood]

http://en.wikipedia.org/wiki/File:Relativity_of_Simultaneity_Animation.gif

This one is actually pretty good.