The Relativity of Simultaneity: A Fundamental Concept in Special Relativity

[mangaroosh]

Hey guys,

this might seem like yet another basic question, but I was wondering about RoS. The impression that I got from reading about relativity was that relativity of simultaneity was a consequence of Lorentz contractions, primarily time dilation. Someone else made the point [emphasis is theirs, not mine]

ROS is a subsidiary shorthand way of using distance contraction and time dilation and is not a separate stand-alone component of SR. ROS is a SUBSTITUTE for distance contraction and/or time dilation. It is NOT an additional function.

This was effectively how I understood it, but in a discussion on here I was told that wasn't the case. As with the other concepts of relativity I'm trying to get a better understanding of it.

To try and illustrate my own understanding of it: if everything in the universe was at rest relative to each other, then there would be absolute simultaneity, but I thought that if an observer started moving relative to that previous rest frame then they would encounter time dilation and relativity of simultaneity would occur. It thought that RoS was a result of the time dilation.

Just wondering what I'm missing, and if there are any online resources that clearly explain the distinction between RoS and Lorentz contractions, and how they are different from each other?

 

[Dale]

Relativity of simultaneity is a particular feature of the Lorentz transform (in units where c=1):
t'=\gamma (t-vx)
x'=\gamma(x-vt)

Here is a transform which has length contraction and time dilation, but not the relativity of simultaneity:
t'=\gamma (t)
x'=\gamma(x-vt)

Here is a transform which has the relativity of simultaneity, but not length contraction or time dilation:
t'=t-vx
x'=x-vt

 

[ghwellsjr]

You have to understand the concept of a Frame of Reference in order to understand Relativity of Simultaneity. In Einstein's Special Relativity, a scheme to create a coordinate system is defined in which you have three coordinates for specifying a location (x,y,z) and one coordinate for specifying time (t). Just like we have three coordinates for specifying a point in space, these four coordinates specify an event in the Frame of Reference. If you pick any two events and they have the same time coordinate, then they are simultaneous. If you then pick another Frame of Reference moving with respect to the first one, you can transform the coordinates for those two events using the Lorentz Transformation which will give you a new set of coordinates for the same two events. If the two time coordinates in the new Frame of Reference are equal to each other, then the events are simultaneous in that FoR. In general, two events that are simultaneous in one FoR will not be simultaneous in another FoR, but not necessarily.

So it has nothing to do with what is at rest or what is moving but simply the time coordinates of a pair of events in one Frame of Reference compared to another FoR.

 

[mangaroosh]

Relativity of simultaneity is a particular feature of the Lorentz transform (in units where c=1):
t'=\gamma (t-vx)
x'=\gamma(x-vt)

Here is a transform which has length contraction and time dilation, but not the relativity of simultaneity:
t'=\gamma (t)
x'=\gamma(x-vt)

Here is a transform which has the relativity of simultaneity, but not length contraction or time dilation:
t'=t-vx
x'=x-vt

thanks Dalespam; I think you mentioned that before. I don't fully understand it from that, but all information is helpful

 

[mangaroosh]

You have to understand the concept of a Frame of Reference in order to understand Relativity of Simultaneity. In Einstein's Special Relativity, a scheme to create a coordinate system is defined in which you have three coordinates for specifying a location (x,y,z) and one coordinate for specifying time (t). Just like we have three coordinates for specifying a point in space, these four coordinates specify an event in the Frame of Reference. If you pick any two events and they have the same time coordinate, then they are simultaneous. If you then pick another Frame of Reference moving with respect to the first one, you can transform the coordinates for those two events using the Lorentz Transformation which will give you a new set of coordinates for the same two events. If the two time coordinates in the new Frame of Reference are equal to each other, then the events are simultaneous in that FoR. In general, two events that are simultaneous in one FoR will not be simultaneous in another FoR, but not necessarily.

So it has nothing to do with what is at rest or what is moving but simply the time coordinates of a pair of events in one Frame of Reference compared to another FoR.

Thanks gh.

I think I have a decent enough understanding of what a reference frame is ["I think" being the operative words]. I suppose, when thinking about simultaneity I consider it in the sense of simultaneity in the universe, as opposed to simultaneity between a limited number of events; because absolute simultaneity would be a universal phenomenon, as well as applying to a limited number of events.


As per Dalespams example, I understand that two or more events can "experience" contractions but still be "absolutely simultaneous"; presumably it would be theoretically possible that all events could "experience" contractions and still be "absolutely simultaneous"; that, however, would mean that Absolute simultaneity, not relativity of simultaneity was a "feature" of the universe.

Is it possible for RoS to be a "feature" of the universe without time dilation?

 

[ghwellsjr]

Thanks gh.

I think I have a decent enough understanding of what a reference frame is ["I think" being the operative words]. I suppose, when thinking about simultaneity I consider it in the sense of simultaneity in the universe, as opposed to simultaneity between a limited number of events; because absolute simultaneity would be a universal phenomenon, as well as applying to a limited number of events.


As per Dalespams example, I understand that two or more events can "experience" contractions but still be "absolutely simultaneous"; presumably it would be theoretically possible that all events could "experience" contractions and still be "absolutely simultaneous"; that, however, would mean that Absolute simultaneity, not relativity of simultaneity was a "feature" of the universe.

Is it possible for RoS to be a "feature" of the universe without time dilation?

It's meaningless to consider RoS for the universe as if it is something intrinsic to the universe that we have to or could learn about or discover. This is an issue of remote time. We can't talk about it until we define what we mean and since there are an infinite number of ways to define remote time, it's not going to be something that we get from nature, rather it's something we put into nature.

Events do not "experience" anything, let alone contraction. They are numbers, three for space, one for time. If those numbers for the time coordinate are identical according to the synchronization established for that FoR, then the events are simultaneous. The reason that I limited it to two is because if you have more than two, some of them can be simultaneous with each other but not with some others.

 

[mangaroosh]

It's meaningless to consider RoS for the universe as if it is something intrinsic to the universe that we have to or could learn about or discover. This is an issue of remote time. We can't talk about it until we define what we mean and since there are an infinite number of ways to define remote time, it's not going to be something that we get from nature, rather it's something we put into nature.

Events do not "experience" anything, let alone contraction.

Please forgive the use of imprecise terminology; I used the inverted commas to try and demonstrate that I know that isn't necessarily how we would talk about them, but in the absence of proper terminology I thought they would convey the meaning. We can abandon any mention of "feature" of the universe and "experience" and replace them with whatever words make sense when talking about contractions and simultaneity.

They are numbers, three for space, one for time. If those numbers for the time coordinate are identical according to the synchronization established for that FoR, then the events are simultaneous. The reason that I limited it to two is because if you have more than two, some of them can be simultaneous with each other but not with some others.

Limiting it to two is fine, but if we limit it to two then we speak about a universe in which there are only two events; if they are simultaneous then does that mean that absolute simultaneity prevails and not RoS? In saying that they can be simultaneous with each other but not with others, we are not limiting it to two, but to an undefined number of events. Of course, if they are simultaneous with each other but not with other [undefined] events, then there RoS prevails.

Could we build on this, saying that three events are simultaneous with each other but not with [undefined] others; in that case RoS prevails again, and not absolute simultaneity. I presume we could do this exponentially until we arrive at a scenario where all events are simultaneous with each other - in this case absolute simultaneity prevail, wouldn't it.

In order for RoS to prevail, I presume there would only need to be one single event where the time co-ordinate is different from all the rest [who have the same time co-ordinate]. Is this possible without there being "time" dilation?


I see Dalespam's example seems to suggest that there might, but I'm not sure how.

 

[ghwellsjr]

Please forgive the use of imprecise terminology; I used the inverted commas to try and demonstrate that I know that isn't necessarily how we would talk about them, but in the absence of proper terminology I thought they would convey the meaning. We can abandon any mention of "feature" of the universe and "experience" and replace them with whatever words make sense when talking about contractions and simultaneity.




Limiting it to two is fine, but if we limit it to two then we speak about a universe in which there are only two events; if they are simultaneous then does that mean that absolute simultaneity prevails and not RoS?

The universe contains an infinite number of events: every different location at every different instant of time is a different event. All the events that occur at the same time are simultaneous with each other. But remember, the times are all defined according to our FoR. There is no issue of RoS within a single FoR.

In saying that they can be simultaneous with each other but not with others, we are not limiting it to two, but to an undefined number of events. Of course, if they are simultaneous with each other but not with other [undefined] events, then there RoS prevails.

This sounds like a repeat of what you just said, so ditto what I just said.

Could we build on this, saying that three events are simultaneous with each other but not with [undefined] others; in that case RoS prevails again, and not absolute simultaneity. I presume we could do this exponentially until we arrive at a scenario where all events are simultaneous with each other - in this case absolute simultaneity prevail, wouldn't it.

There's no absolute simultaneity in SR. At every instant in time, all the locations throughout the entire universe are simultaneous events, because they all have the same time coordinate but different spatial coordinates. At the next instant in time, there is a new set of events throughout the entire universe that are another set of simultaneous events. We keep repeating this forever. But if you pick one event from the first set and another event from a subsequent set, they are not simultaneous.

In order for RoS to prevail, I presume there would only need to be one single event where the time co-ordinate is different from all the rest [who have the same time co-ordinate]. Is this possible without there being "time" dilation?
I see Dalespam's example seems to suggest that there might, but I'm not sure how.

As I keep saying RoS is not a factor until you transform the coordinates for a pair of events in one frame into the coordinates for the same pair of events into another frame in motion with respect to the first frame. You can continue to transform any number of events to see which pairs remain simultaneous.

This has nothing to do with time dilation. Any clock that is moving in a Frame of Reference will be running at a slower rate than the coordinate clocks defining the Frame of Reference. You could have two clocks traveling at different speeds and in different directions and talk about the simultaneous events of where they both were at a particular time which has nothing to do with the times displayed on their two clocks. But when you consider a different Frame of Reference, all the coordinates of all the events take on a new set of values and events that used to be simultaneous in the first frame are no longer simultaneous in the second frame.

Let me emphasize once more: unless you consider two different Frames of Reference, you don't have any issue with relativity of simultaneity.

 

[Dale]

Limiting it to two is fine, but if we limit it to two then we speak about a universe in which there are only two events; if they are simultaneous then does that mean that absolute simultaneity prevails and not RoS?

The question about RoS isn't whether two arbitrary events are simultaneous or not, but whether two events which are simultaneous in one frame are also simultaneous in other frames.

 

[mangaroosh]

The question about RoS isn't whether two arbitrary events are simultaneous or not, but whether two events which are simultaneous in one frame are also simultaneous in other frames.

They are numbers, three for space, one for time. If those numbers for the time coordinate are identical according to the synchronization established for that FoR, then the events are simultaneous. The reason that I limited it to two is because if you have more than two, some of them can be simultaneous with each other but not with some others.

Sorry, I phrased that all wrong; I meant to talk about reference frames, not events, but I lost myself on that one.

Limiting it to two is fine, but if we limit it to two then we speak about a universe in which there are only two reference frames; if all events are simultaneous across those reference frames then absolute simultaneity prevails and not RoS; would that be correct? In saying that an event can be simultaneous in two reference frames but not with others, we are not limiting it to two, but to an undefined number of reference frames. Of course, if events are simultaneous across two refrence frames but not with other [undefined] reference frames, then RoS prevails.I presume we could build on this, saying that all events are simultaneous across three reference frames but not with [undefined] others; in that case RoS prevails again, and not absolute simultaneity.

I presume we could then extrapolate this exponentially [at least theoretically] until we arrive at a scenario where all events are simultaneous across all reference frames; in which case absolute simultaneity would prevail, wouldn't it? Would this only be possible if everything were at absolute rest, or perhaps at rest relative to each other?

In order for RoS to prevail, I presume there would only need to be one single event that isn't simultaneous across all reference frames; namely, where the time co-ordinate is different from all the rest [who have the same time co-ordinate]. Is this possible without "time" dilation?

I see Dalespam's example seems to suggest that there might, but I don't really understand the maths representing the logic.

If the two scenarios, mentioned above, are the only possibilities where absolute simultaneity could prevail, then presumably there would have to be relative motion in order for RoS to prevail; or am I way off on that?
An issue might be with the assumption I'm working from, namely, that if all events are simultaneous across all reference frames, then that is absolute simultaneity; if even one event is not simultaneous, that is RoS.EDIT: I think it is meangingful to contrast absolute simultaneity with RoS because without one there would be the other; is that accurate?

 

[Dale]

Limiting it to two is fine, but if we limit it to two then we speak about a universe in which there are only two reference frames;

This does not make sense. The number of reference frames is not a property of a universe. Universes don't "have" reference frames, they are mathematical devices for analyzing physics, not physical features themselves. You could use an infinite number of reference frames to describe even the simplest possible universe.

If you want to talk about something "having" reference frames, then it would be an analysis which has reference frames.

if all events are simultaneous across those reference frames then absolute simultaneity prevails and not RoS; would that be correct? In saying that an event can be simultaneous in two reference frames but not with others, we are not limiting it to two, but to an undefined number of reference frames. Of course, if events are simultaneous across two refrence frames but not with other [undefined] reference frames, then RoS prevails.I presume we could build on this, saying that all events are simultaneous across three reference frames but not with [undefined] others; in that case RoS prevails again, and not absolute simultaneity.

I presume we could then extrapolate this exponentially [at least theoretically] until we arrive at a scenario where all events are simultaneous across all reference frames; in which case absolute simultaneity would prevail, wouldn't it?

Yes to all the above.

Would this only be possible if everything were at absolute rest, or perhaps at rest relative to each other?

No. Even if everything were at rest to each other you could still analyze it in different reference frames, and if the transformation of the time coordinate included a spatial term then there would be relativity of simultaneity.

In order for RoS to prevail, I presume there would only need to be one single event that isn't simultaneous across all reference frames; namely, where the time co-ordinate is different from all the rest [who have the same time co-ordinate].

Strictly speaking, I don't think that is mathematically possible since coordinate systems are required to be smooth, but essentially yes.

Is this possible without "time" dilation?

Yes, I showed an example above.

I see Dalespam's example seems to suggest that there might, but I don't really understand the maths representing the logic.

OK, let's look at the equations t'=t-vx and x'=x-vt in a little more detail.

Suppose we have three events with coordinates (t_A,x_A)=(0,0), (t_B,x_B)=(0,1), and (t_C,x_C)=(1,0). A and B are simultaneous, since t_A=t_B, and the time between A and C is 1.

Now, transforming to the primed coordinates using the above formulas (v=0.5) gives (t'_A,x'_A)=(0,0), (t'_B,x'_B)=(-.5,1), and (t'_C,x'_C)=(1,-.5). So we see that t_A \ne t_B meaning that simultaneity is relative, and the time between A and C is still 1 meaning that time does not dilate.

Therefore, the relativity of simultaneity is possible without time dilation.

If the two scenarios, mentioned above, are the only possibilities where absolute simultaneity could prevail, then presumably there would have to be relative motion in order for RoS to prevail; or am I way off on that?

It doesn't have to do with motion, but with the transformation between different reference frames.

An issue might be with the assumption I'm working from, namely, that if all events are simultaneous across all reference frames, then that is absolute simultaneity; if even one event is not simultaneous, that is RoS.

EDIT: I think it is meangingful to contrast absolute simultaneity with RoS because without one there would be the other; is that accurate?

Yes to the above, although again mathematically I don't think that it is possible for only one event to be non-simultaneous.

 

[ghwellsjr]

Now, transforming to the primed coordinates using the above formulas (v=0.5) gives (t'_A,x'_A)=(0,0), (t'_B,x'_B)=(-.5,1), and (t'_C,x'_C)=(1,-.5). So we see that t_A \ne t_B meaning that simultaneity is relative, and the time between A and C is still 1 meaning that time does not dilate.

What happened to gamma?

The way I calculate the three transformed events, I get:

A' = (0,0)
B' = (-0.577,1.1547)
C' = (1.1547,-0.577)

So A and C do not have the same time coordinates so they are not simultaneous.

EDIT: I see that wasn't your point. I should have said, the time between A and C is not the same as before, it's longer in the primed frame. But I wouldn't call that time dilation, it's just different coordinates for a pair of events.

 

[Dale]

What happened to gamma?

I was describing this transformation:

OK, let's look at the equations t'=t-vx and x'=x-vt in a little more detail.

Which has no gamma. I was showing a transformation (not the Lorentz transform) which had relativity of simultaneity, but not length contraction nor time dilation. The transformation above is not a useful transform for physics, just an example showing that the relativity of simultaneity is not the same thing as length contraction and time dilation.

 

[mangaroosh]

This does not make sense. The number of reference frames is not a property of a universe. Universes don't "have" reference frames, they are mathematical devices for analyzing physics, not physical features themselves. You could use an infinite number of reference frames to describe even the simplest possible universe.

If you want to talk about something "having" reference frames, then it would be an analysis which has reference frames.

Apologies, I am aware of that, but don't often use terminology that makes that clear.

No. Even if everything were at rest to each other you could still analyze it in different reference frames, and if the transformation of the time coordinate included a spatial term then there would be relativity of simultaneity.

That would be another thing that I don't understand, namely how, or why, the time co-ordinate would include a spatial term.

OK, let's look at the equations t'=t-vx and x'=x-vt in a little more detail.

Suppose we have three events with coordinates (t_A,x_A)=(0,0), (t_B,x_B)=(0,1), and (t_C,x_C)=(1,0). A and B are simultaneous, since t_A=t_B, and the time between A and C is 1.

Now, transforming to the primed coordinates using the above formulas (v=0.5) gives (t'_A,x'_A)=(0,0), (t'_B,x'_B)=(-.5,1), and (t'_C,x'_C)=(1,-.5). So we see that t_A \ne t_B meaning that simultaneity is relative, and the time between A and C is still 1 meaning that time does not dilate.

Therefore, the relativity of simultaneity is possible without time dilation.

It doesn't have to do with motion, but with the transformation between different reference frames.

Yes to the above, although again mathematically I don't think that it is possible for only one event to be non-simultaneous.

Thanks for going through the above; the part I don't understand is the initial equations; I read t'=t-vx as meaning t' equals t minus the velocity along the X-axis, but I don't understand why the velocity comes into it.

and x'=x-vt I read as x' equals x minus the velocity multiplied by the time - which makes a bit more sense to me.

My interpretation of it would be that, if the clocks which give the time co-ordinates all ran at the same rate, then absolute simultaneity should prevail; and in order for RoS to prevail clocks would have to give different times (co-ordinates).


I suppose, essentially, where I have trouble is how we can go from the scenario where an event (or all events) are absolutely simultaneous across all reference frames, to a scenario where there is RoS. Presumably the initial scenario of absolute simultaneity would involve a transform (to affirm absolute simultaneity); I don't understand where a different transform could result in [the conclusion of] RoS if the initial transform leads to the conclusion of absolute simultaneity.


Hopefully that makes some bit of sense.

 

[harrylin]

[..] Thanks for going through the above; the part I don't understand is the initial equations; I read t'=t-vx as meaning t' equals t minus the velocity along the X-axis, but I don't understand why the velocity comes into it.
[..]
My interpretation of it would be that, if the clocks which give the time co-ordinates all ran at the same rate, then absolute simultaneity should prevail; and in order for RoS to prevail clocks would have to give different times (co-ordinates). [..]

Just a primer: If you start with a reference clock in your hand, how would (indeed, how could!) you determine what time it is at a distance? That has little or nothing to do with clock rate.

 

[mangaroosh]

Just a primer: If you start with a reference clock in your hand, how would (indeed, how could!) you determine what time it is at a distance? That has little or nothing to do with clock rate.

You probably couldn't, but the time at a distance would either be the same or it wouldn't; if it is the same [for all clocks at a distance] then absolute simultaneity prevails; if any of the clocks is different, then RoS prevails. What I'm wondering is, what would cause any of the clocks not to tell the same time?

 

[harrylin]

You probably couldn't, but the time at a distance would either be the same or it wouldn't; if it is the same [for all clocks at a distance] then absolute simultaneity prevails; if any of the clocks is different, then RoS prevails. What I'm wondering is, what would cause any of the clocks not to tell the same time?

Sorry, I could not decipher your method to set a distant clock "on time", such that you assume (or pretend) that both clocks indicate the same time perfectly simultaneously, even if only shortly. How would you do that? How could you make distant clocks tell exactly the same time?

 

[mangaroosh]

Sorry, I could not decipher your method to set a distant clock "on time", such that you assume (or pretend) that both clocks indicate the same time perfectly simultaneously, even if only shortly. How would you do that? How could you make distant clocks tell exactly the same time?

I mightn't be making the point very lucidly, but the intention isn't to set two distant clocks to the exact same time; the question is, how might it arise that they don't tell the exact same time?

There's only two possible scenarios: either the clocks do tell the same time, or they don't. If they do then absolute simultaneity prevails; if they don't RoS prevails; what would cause them not to tell the same time?

 

[ghwellsjr]

There's only two possible scenarios: either the clocks do tell the same time, or they don't. If they do then absolute simultaneity prevails; if they don't RoS prevails; what would cause them not to tell the same time?

We have no way of knowing if a clock remote from us has the same time on it as our local clock. That's the problem. Once you recognize that there is no test, no measurement, no way to detect, no way to determine, etc., etc., etc., the time on a remote clock, then you can follow Einstein's process. He said unless you define the time on the remote clock, it is impossible to deal with the problem. And you can define it arbitrarily in many different ways. So rather than suppose, like everyone else did, that there is an absolute universal time that nature is ticking away at, he postulated that the time on a remote clock is equal to the time on a local clock when a light signal takes the same amount of time to get from the local clock to the remote clock as it does for a light signal to get from the remote clock to the local clock. Under this defintion, RoS prevails. Under the previous assumption of an absolute universal time, RoS is not a factor.

 

[harrylin]

I mightn't be making the point very lucidly, but the intention isn't to set two distant clocks to the exact same time; the question is, how might it arise that they don't tell the exact same time?

There's only two possible scenarios: either the clocks do tell the same time, or they don't. If they do then absolute simultaneity prevails; if they don't RoS prevails; what would cause them not to tell the same time?

We understood your intention, which appears to be based on an unfounded assumption. Clocks are man-made and when you put a battery in it you can set it at any time you want. Thus, in order to have two clocks tell the same time, you have to do that.

You seem to have already a difficulty with getting two distant clocks synchronized according to yourself, despite your suggestion that all clocks will be automatically synchronized with all other clocks according to everyone. Nevertheless it was only an introduction to the next question: how can you do that in such a way that everyone will agree?

 

[mangaroosh]

We have no way of knowing if a clock remote from us has the same time on it as our local clock. That's the problem. Once you recognize that there is no test, no measurement, no way to detect, no way to determine, etc., etc., etc., the time on a remote clock, then you can follow Einstein's process. He said unless you define the time on the remote clock, it is impossible to deal with the problem. And you can define it arbitrarily in many different ways. So rather than suppose, like everyone else did, that there is an absolute universal time that nature is ticking away at, he postulated that the time on a remote clock is equal to the time on a local clock when a light signal takes the same amount of time to get from the local clock to the remote clock as it does for a light signal to get from the remote clock to the local clock. Under this defintion, RoS prevails. Under the previous assumption of an absolute universal time, RoS is not a factor.

We understood your intention, which appears to be based on an unfounded assumption. Clocks are man-made and when you put a battery in it you can set it at any time you want. Thus, in order to have two clocks tell the same time, you have to do that.

You seem to have already a difficulty with getting two distant clocks synchronized according to yourself, despite your suggestion that all clocks will be automatically synchronized with all other clocks according to everyone. Nevertheless it was only an introduction to the next question: how can you do that in such a way that everyone will agree?

Thanks guys; it hasn't clicked for me yet. It might be easier for me to outline the question by contrasting Einsteinian relativity with Lorentzian relativity; under Lorentzian relativity there is absolute simultaneity, while under Einsteinian relativity there is RoS. If both theories are indistinguishable in terms of experimental data, why is it that there is RoS in one and absolute simultaneity in the other, if both theories include clocks which tick at different rates?

 

[ghwellsjr]

Thanks guys; it hasn't clicked for me yet. It might be easier for me to outline the question by contrasting Einsteinian relativity with Lorentzian relativity; under Lorentzian relativity there is absolute simultaneity, while under Einsteinian relativity there is RoS. If both theories are indistinguishable in terms of experimental data, why is it that there is RoS in one and absolute simultaneity in the other, if both theories include clocks which tick at different rates?

Only because LET believers believe it is so. Or maybe I should say "believed" it was so because I don't think there are any LET believers left in the world.

 

[mangaroosh]

Only because LET believers believe it is so. Or maybe I should say "believed" it was so because I don't think there are any LET believers left in the world.

Would it not be more accurate to say that the theory postulates it? If there were no theory, there would be nothing to believe.

 

[ghwellsjr]

I don't think it takes a formal theory to believe that time is absolute, that just seems natural and normal, don't you think? But once you measure the speed of light to be constant, it's only natural and normal to come up with a theory that retains absolute time, don't you think?

 

[mangaroosh]

I don't think it takes a formal theory to believe that time is absolute, that just seems natural and normal, don't you think? But once you measure the speed of light to be constant, it's only natural and normal to come up with a theory that retains absolute time, don't you think?

I'd agree, it doesn't take a formal theory to believe that time is absolute, but LET appears to postulate absolute simultaneity, and if the experimental evidence doesn't distinguish between it and SR then there must be a reason why RoS prevails in SR but not LET. I'm just trying to understand what that reason is.

In the last sentence, do you mean, once you measure the speed of light to be constant, it's only natural and normal to come up with a theory abandons absolute time?

 

[ghwellsjr]

I'd agree, it doesn't take a formal theory to believe that time is absolute, but LET appears to postulate absolute simultaneity, and if the experimental evidence doesn't distinguish between it and SR then there must be a reason why RoS prevails in SR but not LET. I'm just trying to understand what that reason is.

I think I've asked you before--do you think if no one else had put forward the idea that time could be relative, that is, time actually progresses at different rates under different conditions, you would ever come up with that idea on your own? Even now, many people struggle with this concept even though the idea is so prevalent in our world at this time.

In the last sentence, do you mean, once you measure the speed of light to be constant, it's only natural and normal to come up with a theory abandons absolute time?

I only meant that just because the speed of light was measured to be constant, why should anyone connect that with time being relative? Wouldn't you do what the LET scientists did and say that the clocks moving in the ether run slow for some mechanical reason rather than say that time itself was slowing down for them? It made perfect sense that light propagated at a constant speed with respect to the ether and they just couldn't detect that fact rather than claim that light propagated at a constant speed for each inertial state.

 

[mangaroosh]

I think I've asked you before--do you think if no one else had put forward the idea that time could be relative, that is, time actually progresses at different rates under different conditions, you would ever come up with that idea on your own? Even now, many people struggle with this concept even though the idea is so prevalent in our world at this time.

That's a philosophical question without an answer I would say; history might show that no one but Einstein could have come up with the idea, but if you or I had been born in his stead and had his life experiences, we both would have come up with it.

I only meant that just because the speed of light was measured to be constant, why should anyone connect that with time being relative? Wouldn't you do what the LET scientists did and say that the clocks moving in the ether run slow for some mechanical reason rather than say that time itself was slowing down for them? It made perfect sense that light propagated at a constant speed with respect to the ether and they just couldn't detect that fact rather than claim that light propagated at a constant speed for each inertial state.

Those appear to be two differing interpretations, both equally supported by evidence; is that a fair enough comment?

According LET clocks tick at different rates for mechanical reasons, and so absolute simultaneity prevails.

According to Einsteinian relativity, clocks tick at different rates becuse "time itself slows down"; is it because "time itself slows down" in certain reference frames that RoS prevails? I presume it must be, because if time didn't slow down, and slower ticking clocks were the result of the mechanics of the clock then, as per LET, absolute simultaneity would prevail. Alternatively, if time itself didn't slow down and clocks all ticked at the same rate, then absolute simultaneity would prevail.

 

[harrylin]

Thanks guys; it hasn't clicked for me yet. It might be easier for me to outline the question by contrasting Einsteinian relativity with Lorentzian relativity; under Lorentzian relativity there is absolute simultaneity, while under Einsteinian relativity there is RoS. If both theories are indistinguishable in terms of experimental data, why is it that there is RoS in one and absolute simultaneity in the other, if both theories include clocks which tick at different rates?

In Lorentzian relativity there is absolute simultaneity that cannot be measured, as well as "local time". Poincare pointed out that clocks measure local time. This local time already had the characteristic of relativity of simultaneity before relativity, but until 1904 it was only approximate. Einsteinian relativity considers only what can be measured; consequently he calls "local time" simply "time".

A similar thing happened earlier in classical mechanics: Newtonian mechanics distinguishes absolute velocity that cannot be measured as well as relative velocity that can be measured. Classical mechanics only deals with relative velocity.

 

[mangaroosh]

In Lorentzian relativity there is absolute simultaneity that cannot be measured, as well as "local time". Poincare pointed out that clocks measure local time. This local time already had the characteristic of relativity of simultaneity before relativity, but until 1904 it was only approximate. Einsteinian relativity considers only what can be measured; consequently he calls "local time" simply "time".

That's fair enough; but if all the local clocks registered the same time then absolute simultaneity would prevail; but local clocks register different times and so RoS prevails. Why do local clocks not register the same time?

A similar thing happened earlier in classical mechanics: Newtonian mechanics distinguishes absolute velocity that cannot be measured as well as relative velocity that can be measured. Classical mechanics only deals with relative velocity.

At the risk of going off-topic, I think the idea of measuring absolute velocity is somewhat of a misnomer, because measurement is, by it's very nature, relative i.e. it is making a statement about one phenomenon by relating it to other phenomena.

Absolute velocity is a simple yes or no answer to the question, is there velocity?

 

[ghwellsjr]

I only meant that just because the speed of light was measured to be constant, why should anyone connect that with time being relative? Wouldn't you do what the LET scientists did and say that the clocks moving in the ether run slow for some mechanical reason rather than say that time itself was slowing down for them? It made perfect sense that light propagated at a constant speed with respect to the ether and they just couldn't detect that fact rather than claim that light propagated at a constant speed for each inertial state.

Those appear to be two differing interpretations, both equally supported by evidence; is that a fair enough comment?

Yes.

According LET clocks tick at different rates for mechanical reasons, and so absolute simultaneity prevails.

According to Einsteinian relativity, clocks tick at different rates becuse "time itself slows down"; is it because "time itself slows down" in certain reference frames that RoS prevails? I presume it must be, because if time didn't slow down, and slower ticking clocks were the result of the mechanics of the clock then, as per LET, absolute simultaneity would prevail. Alternatively, if time itself didn't slow down and clocks all ticked at the same rate, then absolute simultaneity would prevail.

Let me try it this way:

I'm going to stipulate, for the sake of argument, that LET is the correct understanding of the way nature works. That means that there truly is an immovable ether and light propagates at c only with respect to the rest state of that ether. Time and space are absolutes. And because of the mechanical properties of the ether and the way that matter interacts with it, when matter moves through the ether, it contracts along the direction of motion. Also, any physical clock made of matter will keep track of the absolute time correctly only if it is stationary in the ether. If it is moving, the operation of the clock makes it slow down and so it is no longer keeping the correct time. The Lorentz factor correctly describes how much a moving clock slows down and how physical objects are contracted along the direction of motion. This is the stipulated truth about nature.

Now let's suppose an observer who is stationary in that ether has some measuring rods and some accurate, stable clocks and a mirror. When he attempts to measure the round trip speed of light, he gets the correct answer because his rulers and clocks are normal since they are not moving. Now let's suppose that he gets in a spaceship and accelerates to a high rate of speed with respect to the ether. This will cause his clocks to slow down and his rulers to contract when aligned with the direction of motion. When he repeats his measurement of the speed of light, what will happen? Well we know if he aligns his experiment so that the light has to travel against the ether to get to the mirror, it will take longer than when he was stationary. After it hits the mirror and reflects back, we know that it will take a shorter time than before because it is being carried along by the ether. Furthermore, we know that when he measures the distance between the mirrors, they will be closer together. As long as his clocks and rulers are modified by just the right amount, he will get the same measurement of the speed of light as he did before. But we know why he gets the same answer and that's because of length contraction and time dilation for matter moving through the ether.

As a matter of fact, the moving observer will see everything exactly the same when he is moving as he did when he was stationary. He cannot tell that he is moving with repsect to the ether. Do you understand this?

 

[harrylin]

That's fair enough; but if all the local clocks registered the same time then absolute simultaneity would prevail; but local clocks register different times and so RoS prevails. Why do local clocks not register the same time?

Originally (before SR) this was for practical reasons as you can read here:
http://en.wikisource.org/wiki/The_Measure_of_Time
It was found that even if we wanted to, we cannot detect absolute simultaneity. But if we wanted, we could define a truly "universal time" and synchronize all clocks accordingly.

At the risk of going off-topic, I think the idea of measuring absolute velocity is somewhat of a misnomer, because measurement is, by it's very nature, relative i.e. it is making a statement about one phenomenon by relating it to other phenomena. [...]

Apparently Newton defined it to mean velocity relative to absolute space; it doesn't mean "absolute" in the secondary meaning that you think (and which probably resulted from it much later).
- http://gravitee.tripod.com/definitions.htm
(press "cancel" and scroll to "SCHOLIUM")

Harald

 

[mangaroosh]

Yes.

Let me try it this way:

I'm going to stipulate, for the sake of argument, that LET is the correct understanding of the way nature works. That means that there truly is an immovable ether and light propagates at c only with respect to the rest state of that ether. Time and space are absolutes. And because of the mechanical properties of the ether and the way that matter interacts with it, when matter moves through the ether, it contracts along the direction of motion. Also, any physical clock made of matter will keep track of the absolute time correctly only if it is stationary in the ether. If it is moving, the operation of the clock makes it slow down and so it is no longer keeping the correct time. The Lorentz factor correctly describes how much a moving clock slows down and how physical objects are contracted along the direction of motion. This is the stipulated truth about nature.

Now let's suppose an observer who is stationary in that ether has some measuring rods and some accurate, stable clocks and a mirror. When he attempts to measure the round trip speed of light, he gets the correct answer because his rulers and clocks are normal since they are not moving. Now let's suppose that he gets in a spaceship and accelerates to a high rate of speed with respect to the ether. This will cause his clocks to slow down and his rulers to contract when aligned with the direction of motion. When he repeats his measurement of the speed of light, what will happen? Well we know if he aligns his experiment so that the light has to travel against the ether to get to the mirror, it will take longer than when he was stationary. After it hits the mirror and reflects back, we know that it will take a shorter time than before because it is being carried along by the ether. Furthermore, we know that when he measures the distance between the mirrors, they will be closer together. As long as his clocks and rulers are modified by just the right amount, he will get the same measurement of the speed of light as he did before. But we know why he gets the same answer and that's because of length contraction and time dilation for matter moving through the ether.

As a matter of fact, the moving observer will see everything exactly the same when he is moving as he did when he was stationary. He cannot tell that he is moving with repsect to the ether. Do you understand this?

Sorry gh, it might be the way I'm phrasing the question; I understand the above (I think), but it isn't Lorentzian relativity I'm wondering about, it's RoS in Einsteinian relativity.

My understanding is that RoS prevails, or perhaps more accurately, RoS is a consequence of the fact that [local*] clocks tick at different rates - if they didn't then absolute simultaneity would prevail. According to LET, as you have outlined above, clocks slow down for mechanical reasons (presumably this is true even when LET is stripped of everything but the absolute rest frame). That much I understand.

The question pertains to Einsteinian relativity. My understanding is that RoS is what results when [local*] clocks tick at different rates - is that much correct? As mentioned, LET postulates that this is down to the mechanics of the clock (as outlined above) - what, according to Einsteinian relativity, is the reason that [local*] clocks tick at different rates?*Just in case the term "local" isn't used in Einsteinian relativity, what I mean is the clock at rest in a given FoR

 

[ghwellsjr]

Sorry gh, it might be the way I'm phrasing the question; I understand the above (I think), but it isn't Lorentzian relativity I'm wondering about, it's RoS in Einsteinian relativity.

My understanding is that RoS prevails, or perhaps more accurately, RoS is a consequence of the fact that [local*] clocks tick at different rates - if they didn't then absolute simultaneity would prevail. According to LET, as you have outlined above, clocks slow down for mechanical reasons (presumably this is true even when LET is stripped of everything but the absolute rest frame). That much I understand.

The question pertains to Einsteinian relativity. My understanding is that RoS is what results when [local*] clocks tick at different rates - is that much correct? As mentioned, LET postulates that this is down to the mechanics of the clock (as outlined above) - what, according to Einsteinian relativity, is the reason that [local*] clocks tick at different rates?


*Just in case the term "local" isn't used in Einsteinian relativity, what I mean is the clock at rest in a given FoR

The second postulate: that light propagates in both directions at the same speed of a round-trip measurement of its speed, is what results in RoS for SR. LET does not have that postulate. Instead, it claims that the one-way speed of light is constant only in the absolute ether.

The one-way speed of light cannot be observed and cannot be measured. That is why we are free to make any postulate regarding it. For example, let's say that we place a mirror 10 feet away from our light source and our timer. We turn on the light at the exact moment we start the timer. When we detect the reflected light and stop the timer it reads 20 nanoseconds. We have the option of dividing the times for the two trips any way we want. We can say that it took 0 time for the light to get to the mirror and 20 nanoseconds to get back or vice versa. Or we could say that it took 1 nanosecond to get to the mirror and 19 nanoseconds to get back. Or 2 and 18, 3 and 17, etc. Or we could say, like LET that we have to determine the division of the times based on how fast we think we are traveling with respect to ether when the round-trip measurement assigns the times as equal. That claim supports the idea of an absolute time. Or we could say, like SR, that those times are equal every time we make the measurement which leads to the concept of relative time which is just another way of saying Relativity of Simultaneity.

Please look again at Einstein's 1905 paper introducing Special Relativity. Look at the title of the first section. It's called "Definition of Simultaneity". Look at what he says in the third paragraph:

We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, “That train arrives here at 7 o'clock,” I mean something like this: “The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.”

Then read the rest of that section and see how he builds up a consistent definition of time in remote locations.

Please study the first half, Part I, of his paper. If you don't understand something there, please ask a question. You need to understand Einstein's presentation if you want to understand Einsteinian relativity. I don't want to entertain any more questions that aren't sourced from Einstein.

 

[harrylin]

[..] My understanding is that RoS prevails, or perhaps more accurately, RoS is a consequence of the fact that [local*] clocks tick at different rates - if they didn't then absolute simultaneity would prevail. [..] The question pertains to Einsteinian relativity. My understanding is that RoS is what results when [local*] clocks tick at different rates - is that much correct? [..]

That is wrong, as demonstrated in the reference of post #31 (in the second half of that reference). RoS was already applied without accounting for time dilation. And also the "Voigt transformation" (although he didn't intend it that way) doesn't have time dilation.

In order to obtain the Lorentz transformations from the Galilean transformations, one has to assume time dilation and Lorentz contraction (done by nature) as well as RoS (should be done by the experimentalist, by means of clock synchronization).

Harald

 

[mangaroosh]

The second postulate: that light propagates in both directions at the same speed of a round-trip measurement of its speed, is what results in RoS for SR. LET does not have that postulate. Instead, it claims that the one-way speed of light is constant only in the absolute ether.

The one-way speed of light cannot be observed and cannot be measured. That is why we are free to make any postulate regarding it. For example, let's say that we place a mirror 10 feet away from our light source and our timer. We turn on the light at the exact moment we start the timer. When we detect the reflected light and stop the timer it reads 20 nanoseconds. We have the option of dividing the times for the two trips any way we want. We can say that it took 0 time for the light to get to the mirror and 20 nanoseconds to get back or vice versa. Or we could say that it took 1 nanosecond to get to the mirror and 19 nanoseconds to get back. Or 2 and 18, 3 and 17, etc. Or we could say, like LET that we have to determine the division of the times based on how fast we think we are traveling with respect to ether when the round-trip measurement assigns the times as equal. That claim supports the idea of an absolute time. Or we could say, like SR, that those times are equal every time we make the measurement which leads to the concept of relative time which is just another way of saying Relativity of Simultaneity.

Please look again at Einstein's 1905 paper introducing Special Relativity. Look at the title of the first section. It's called "Definition of Simultaneity". Look at what he says in the third paragraph:

We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, “That train arrives here at 7 o'clock,” I mean something like this: “The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.”

Then read the rest of that section and see how he builds up a consistent definition of time in remote locations.

Please study the first half, Part I, of his paper. If you don't understand something there, please ask a question. You need to understand Einstein's presentation if you want to understand Einsteinian relativity. I don't want to entertain any more questions that aren't sourced from Einstein.

thanks gh, I'll have a look at Einstein's paper and try to base my questions on Einstein's paper.


Just one quick question though, to see if I am even in the ball park with understanding this: am I at least [some way] right in thinking that if all clocks ticked at the same rate then absolute simultaneity would prevail; but because clocks tick at different rates RoS prevails?

 

[Dale]

am I at least [some way] right in thinking that if all clocks ticked at the same rate then absolute simultaneity would prevail; but because clocks tick at different rates RoS prevails?

No, I explicitly showed that to be incorrect above, and I have stated it clearly multiple times.

 

[Dale]

My interpretation of it would be that, if the clocks which give the time co-ordinates all ran at the same rate, then absolute simultaneity should prevail; and in order for RoS to prevail clocks would have to give different times (co-ordinates).

This interpretation is incorrect. dt'/dt=1 so all of the clocks run at the same rate.

That would be another thing that I don't understand, namely how, or why, the time co-ordinate would include a spatial term.

If the transform is linear (I.e. Both frames are inertial) then the transform in general includes a spatial term. It may be that the coefficient is zero, but that is an additional assumption.

 

[Naty1]

That would be another thing that I don't understand, namely how, or why, the time co-ordinate would include a spatial term.

in some sense, it makes no sense. But this may offer a way to begin to think about it:

A simple minded thought experiment: picture an x,y plot...as two particles move around there in different paths, they experience different rates of x and y distances covered,,,right? we don't normally think much about that...each would observe the
other moving differenty through space [distance] than themselves...

now consider a plot of time versus,say, x distance: observe two particles moving differently... say straight lines with different slopes as an example...one moves faster thru time and another faster thru distance [space]. We observe the particles and each observe's the other moving differently through time and the x direction than themselves...all the
observations are 'correct' but they are also 'different'.

 

[mangaroosh]

No, I explicitly showed that to be incorrect above, and I have stated it clearly multiple times.

Hi Dalespam, are you referring to another thread, because I only saw your response on the first page of this one and had a few questions about it?

This interpretation is incorrect. dt'/dt=1 so all of the clocks run at the same rate.

If the transform is linear (I.e. Both frames are inertial) then the transform in general includes a spatial term. It may be that the coefficient is zero, but that is an additional assumption.

I'm sorry, I don't really understand what dt'/dt=1; I am familiar with the notation from high school maths but I'm not sure how to interpret it in this context.


Where I am not clear is why there is absolute simultaneity according to Lorentzian relativity but RoS according to Einsteinian. Do both not use the same transformations?

 

[Dale]

No, I explicitly showed that to be incorrect above, and I have stated it clearly multiple times.

Hi Dalespam, are you referring to another thread, because I only saw your response on the first page of this one and had a few questions about it?

I explicitly showed it to be incorrect here:
https://www.physicsforums.com/showpost.php?p=3751522&postcount=2

And I stated it clearly here:
https://www.physicsforums.com/showpost.php?p=3747625&postcount=57
https://www.physicsforums.com/showpost.php?p=3747739&postcount=59
https://www.physicsforums.com/showpost.php?p=3752737&postcount=11

I'm sorry, I don't really understand what dt'/dt=1; I am familiar with the notation from high school maths but I'm not sure how to interpret it in this context.

It means that the ratio of the time in one frame to the time in the other frame is 1, i.e. time is not dilated.

 

[mangaroosh]

I explicitly showed it to be incorrect here:
https://www.physicsforums.com/showpost.php?p=3751522&postcount=2

And I stated it clearly here:
https://www.physicsforums.com/showpost.php?p=3747625&postcount=57
https://www.physicsforums.com/showpost.php?p=3747739&postcount=59
https://www.physicsforums.com/showpost.php?p=3752737&postcount=11

I appreciate you taking the time to reply DaleSpam, but it was the comments in "the constancy of c" thread lead to me starting this thread, to try and get a better understanding. You posted a few responses in the first page of this thread, the first being post #2; I replied to that explaining that I didn't fully understand the logic as represented by the maths; your subsequent reply was an expansion on that point (post #11); to which I posted some questions in reply. From there the discussion of my reply to your post was continued with George and Harry, where I outlined my rationale; your next reply was post #36 where you said that you had explicitly addressed the issue in a previous post (in the thread) and has stated it countless times. As mentioned, however, there were subsequent questions to that clarification which lead to the conversation with George and Harry.

I do appreciate your taking the time to entertain my questions, and I'm sure you're probably addressing countless other [perhaps equally naiive] questions, so it will hopefully reduce any frustration you might be feeling by highlighting why I still haven't got my head around the issue, despite your generous attempts to clarify it.

It means that the ratio of the time in one frame to the time in the other frame is 1, i.e. time is not dilated.

Thanks for the clarification.

My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations?

If so, the trouble I have is understanding how one interpretation includes RoS while the other includes absolute simultaneity. George suggested that it is down to the different assumptions about the propagation of light, but I don't see how that would lead to RoS without some intermediary step(s).

If my understanding is correct, and the mathematics is the same for both theories, then I'm not sure a mathematical explanation will address the issue; I would imagine it has to be more of a theoretical consideration of what the maths represents.

 

[James_Harford]

Hello Mangaroosh,

May I suggest yet another way of answering your two questions about Relativity of Simultaneity [RoS]? You might find it simpler to understand, and I am confident that DaleSpam, Ghwellsir, and other posters who have been answering your questions so tirelessly will vouch for its correctness:

Your OP question is,

this might seem like yet another basic question, but I was wondering about RoS. The impression that I got from reading about relativity was that relativity of simultaneity was a consequence of Lorentz contractions, primarily time dilation.

And your latest post question is (with [SR] & [LET] inserted for clarity):

... the trouble I have is understanding how one interpretation [SR] includes RoS while the other [LET] includes absolute simultaneity. George suggested that it is down to the different assumptions about the propagation of light, but I don't see how that would lead to RoS without some intermediary step(s).

Fortunately in this case, both questions can be addressed without Lorentz transforms, clocks or rulers. The price of using this approach is that we cannot quantify RoS, but we can demonstrate its existence.

Relativity of Simultaneity means simply that two events, separated by a distance from one another, and simultaneous according to one competent observer are not (generally) simultaneous according to another moving relative to the first at some constant speed.

The simultaneity of two events can be established using a shuttered lamp on a track between two distant mirrors positioned on the track to reflect any light pulses from the lamp back to it and yourself, the observer. The mirrors need not be at rest and may move independently at arbitrary speeds along the track. Suppose that you are very quick with the shutter and send an extremely brief pulse of light towards both mirrors. If the reflected pulses from both mirrors happen to return simultaneously, what can you legitimately infer? Since by Einstein's postulate, light moves at one speed only, you know these two things:
1. the mirrors were equidistant from the lamp at the time of the reflection, and
2. the two reflections occurred simultaneously.

Now suppose that a second observer happens to be moving along the track just as you send your light pulse from the lamp. Will he agree that the reflections were simultaneous? No. By the time the two reflected pulses meet at your lamp, observer #2 has moved some distance along the track, and correctly notes that the two pulses did not "return" simultaneously to his "here", and for that reason, by Einstein's postulate he must infer that the two reflections did not occur simultaneously.

The LET interpretation predicts exactly the same phenomena, but differs from SR only in that it insists that light depends upon a hypothetical medium, or aether, Therefore the method of "simultaneous arrival" for determining simultaneity is valid only for an observer who is motionless in the aether, and there is only one "true" definition of simultaneity -- that of the motionless observer. Einstein's great insight was that the aether hypothesis was completely superfluous.

- Regards

 

[harrylin]

[..]
Where I am not clear is why there is absolute simultaneity according to Lorentzian relativity but RoS according to Einsteinian. Do both not use the same transformations?

Hi I answered that in post #28 and also, indirectly, in post #31. RoS corresponds to the "local time" concept as interpreted by Poincare but Einstein interpreted it differently. Did you study the references? Is there something unclear about it?

 

[harrylin]

[..] My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations? [..]

Apparently you missed my post here, in which I explained this in detail and with a lot of precision:
https://www.physicsforums.com/showpost.php?p=3756233&postcount=54

Harald

 

[PhilDSP]

My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations?

It would probably be fair and correct to say that the mathematics going into and coming out of the Lorentz Transformation and their usage is very different comparing Einstein-Minkowski and Lorentz-Poincare relativity. While the Lorentz Transformation itself is obviously common. For the most part, Lorentz worked with vectors, differential equations and their initial and boundary conditions. Einstein and Minkowski built a platform where those things were abstracted away in which tensors and 4-vectors are preferred.

 

[Agerhell]

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

From wikipedia:

"A popular picture for understanding this idea is provided by a thought experiment consisting of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past. It is similar to thought experiments suggested by Daniel Frost Comstock in 1910[1] and Einstein in 1917.[2][3]

A flash of light is given off at the center of the traincar just as the two observers pass each other. The observer onboard the train sees the front and back of the traincar at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the traincar at the same time.

The observer standing on the platform, on the other hand, sees the rear of the traincar moving (catching up) toward the point at which the flash was given off and the front of the traincar moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times."

Is this helpful? According to SR the speed of light on Earth is not c in relation to the gravitational field of the Earth but relative to "any inertial frame". Thus the observer on the platform sees the front- and the backside of the wagon lit up at different times but the guy on the train will think that the front and the backside of the train are lit up simultanesously, because the light coming back from the rear and the front end of the wagon walls will hit him simultaneously.

I think this type of thought experiments are always what is meant when someone talks about "relativity of simultaneity", but I might be wrong...

 

[mangaroosh]

Hello Mangaroosh,

May I suggest yet another way of answering your two questions about Relativity of Simultaneity [RoS]? You might find it simpler to understand, and I am confident that DaleSpam, Ghwellsir, and other posters who have been answering your questions so tirelessly will vouch for its correctness:

Your OP question is,



And your latest post question is (with [SR] & [LET] inserted for clarity):



Fortunately in this case, both questions can be addressed without Lorentz transforms, clocks or rulers. The price of using this approach is that we cannot quantify RoS, but we can demonstrate its existence.

Relativity of Simultaneity means simply that two events, separated by a distance from one another, and simultaneous according to one competent observer are not (generally) simultaneous according to another moving relative to the first at some constant speed.

The simultaneity of two events can be established using a shuttered lamp on a track between two distant mirrors positioned on the track to reflect any light pulses from the lamp back to it and yourself, the observer. The mirrors need not be at rest and may move independently at arbitrary speeds along the track. Suppose that you are very quick with the shutter and send an extremely brief pulse of light towards both mirrors. If the reflected pulses from both mirrors happen to return simultaneously, what can you legitimately infer? Since by Einstein's postulate, light moves at one speed only, you know these two things:
1. the mirrors were equidistant from the lamp at the time of the reflection, and
2. the two reflections occurred simultaneously.

Now suppose that a second observer happens to be moving along the track just as you send your light pulse from the lamp. Will he agree that the reflections were simultaneous? No. By the time the two reflected pulses meet at your lamp, observer #2 has moved some distance along the track, and correctly notes that the two pulses did not "return" simultaneously to his "here", and for that reason, by Einstein's postulate he must infer that the two reflections did not occur simultaneously.

The LET interpretation predicts exactly the same phenomena, but differs from SR only in that it insists that light depends upon a hypothetical medium, or aether, Therefore the method of "simultaneous arrival" for determining simultaneity is valid only for an observer who is motionless in the aether, and there is only one "true" definition of simultaneity -- that of the motionless observer. Einstein's great insight was that the aether hypothesis was completely superfluous.

- Regards

Hi James, thanks a million for taking the time to reply.

I hope I'm using the right phraseology here when I say that, under Galilean transformations we would expect the moving observer to measure a different speed of light to the pulse operator, but under Lorentz transformations this isn't the case; is that accurate?

Lorentzian relativity maintains absolute simultaneity, while Einsteinian relativity incorporates RoS. I don't think we're too concerned with Lorentzian relativity in this particular instance, what we're looking for, or rather, what I'm trying to understand, is what phenomena must occur in order for the speed of light to remain constant for all observers, regardless of their motion realtive to the source of the light; which appears to be the reason given, why RoS prevails. That was essentially the point made by George, so I presume he would agree with your statement to a similar effect.


One thing he might disagree on is that Lorentzian relativity necessarily includes the superfluous concept of an aether.

nowadays, when we speak of LET, we have striped it of everything except the idea of a preferred rest frame.

 

[mangaroosh]

Hi I answered that in post #28 and also, indirectly, in post #31. RoS corresponds to the "local time" concept as interpreted by Poincare but Einstein interpreted it differently. Did you study the references? Is there something unclear about it?

Hi Harry, the conversation with DaleSpam is in reference to mathematical transformations, while your reply in post #28 was with respect to clocks; unfortunately I don't have the nous to make the connection between the two, so I find it more beneficial to engage with the point that is raised and see where it goes.

I had a quick glance at the reference in post #31, but statement immediately following the link was something you had mentioned before, with respect to detecting absolute simultaneity (or the time on a distant clock) and which I had addressed in #18; so that affected my judgement of the necessity to go through it in detail. Is there a specific part that I can jump to that would address the issue?

Just reading back over the exchange I realize that I didn't address reply in #20 directly. I tried reformulating the question, which lead to your reply in #28, which appears to just be a reformulation of the same reply that was questioned previously.

Post #20:

We understood your intention, which appears to be based on an unfounded assumption. Clocks are man-made and when you put a battery in it you can set it at any time you want. Thus, in order to have two clocks tell the same time, you have to do that.

You seem to have already a difficulty with getting two distant clocks synchronized according to yourself, despite your suggestion that all clocks will be automatically synchronized with all other clocks according to everyone. Nevertheless it was only an introduction to the next question: how can you do that in such a way that everyone will agree?

The issue being raised appears to be the idea of detecting absolute simultaneity; but that isn't necessarily an issue that needs to be addressed. We don't need to figure out how to synchronise clocks to say that if all clocks remained synchronised then there would be absolute simultaneity; it's somewhat of a tautology. If any clock falls out of sync, and the change isn't due to mechanical processes, then RoS prevails; if the change is down to mechanical processes then absolute simultaneity prevails - that is assuming that a clock measures time, because if a clock doesn't measure time, then we have no way of measuring time, and it wouldn't necessarily be something that could be dealt with in physics - as someone mentioned in another thread on here a while ago, pertaining to the MMX.This is #28, which, as mentioned, appears to just reformulate the issue of detecting absolute simultaneity.

In Lorentzian relativity there is absolute simultaneity that cannot be measured, as well as "local time". Poincare pointed out that clocks measure local time. This local time already had the characteristic of relativity of simultaneity before relativity, but until 1904 it was only approximate. Einsteinian relativity considers only what can be measured; consequently he calls "local time" simply "time".

A similar thing happened earlier in classical mechanics: Newtonian mechanics distinguishes absolute velocity that cannot be measured as well as relative velocity that can be measured. Classical mechanics only deals with relative velocity.

 

[mangaroosh]

Apparently you missed my post here, in which I explained this in detail and with a lot of precision:
https://www.physicsforums.com/showpost.php?p=3756233&postcount=54

Harald

I didn't miss it, my reply was deleted because I used an invalid reference; although I didn't intend for it to be a reference per se, rather as a means of explaining a point that was made more eloquently than I could have done.

I'll PM you the reply, but I'd prefer to continue the discussion in an open thread. Perhaps if I PM you, you might be able to paraphrase the quote in your reply, for the posterity of the thread - that is if you deem it worthy of reply, of course.

 

[Dale]

I replied to that explaining that I didn't fully understand the logic as represented by the maths

That is fine. If you don't understand then ask new questions that will help me get at your root concern. But if you merely repeat the same incorrect claim that I answered already then all I can do is as I did above and refer back to my previous answers.

your subsequent reply was an expansion on that point (post #11); to which I posted some questions in reply. From there the discussion of my reply to your post was continued with George and Harry, where I outlined my rationale; your next reply was post #36 where you said that you had explicitly addressed the issue in a previous post (in the thread) and has stated it countless times. As mentioned, however, there were subsequent questions to that clarification which lead to the conversation with George and Harry.

You are correct, I was traveling for about two weeks with reduced time and access. However, I did find it frustrating to come back and find you repeating the same mistake that I already addressed weeks ago.

My trouble with "getting it" lies in the difference, or lack thereof, between Einsteinian relativity and Lorentzian relativity; do I understand correctly that there is essentially no difference between the mathematics of both interpretations?

I don't think that anything productive will come from a discussion of Lorentzian relativity. It is a defunct interpretation which asserts the reality of undetectable entities. All of the confusion with LET comes from the simple fact that the aether is undetectable, so in LET you continually have to make careful distinctions between measurements and what is happening in (undetectable) reality. It is a rabbit hole not worth going down.