1. Originally Posted by Grimble
True from the point of view of the clock at rest at A. But what about from the frame of the 'moving' clock?
From that frame it would be the 'resting' clock that would be moving in a closed curve with constant velocity, the journey lasting t seconds, then by the clock which has remained at rest (originally considered to be the moving clock) the travelled clock on its arrival at A will be 1/2 t v2 / c2 second slow.
Reciprocity.
The moving clock is covered by that quote. Let's plug some numbers in:

Two synchronous clocks at A
, so let's say they're both set to 3pm
One ... is moved in a closed curve Let's say it's moved at 0.9c
the journey lasting t seconds, Implicitly, that's t seconds by the clock which has remained at rest. Let's say 600 seconds, so when the clocks reunite, the clock at rest is now reading 3:10
the travelled clock on its arrival at A will be 1/2 t v2 / c2 second slow
So t = 600, v/c = 0.9 so v2 / c2 = 0.92 = 0.81. So slowness = 1/2 * 600 * 0.81 = 243 seconds = 4 minutes
So when the clocks reunite, the one that remained at rest will read 3:10, the one that travelled will read 3:06. Effectively, the travelling clock has traded time for distance - remember that quote "One man's space is another man's time"?

Originally Posted by Grimble
There is nothing in relativity that can specify which of the clocks is moving - they may both be moving.
Not true. Relativity says that there is nothing that can specify which of the Frames of Reference is moving. Each Frame of Reference can consider itself at rest.
For these clocks, one stays "stationary" - ie. in a single Frame of Reference. The other has travelled in a curve - it has changed direction, so it KNOWS it has been moving - ie. it has been changing Frames of Reference. The act of changing Frames of Reference is what distinguishes them. The one that changes will have the slower clock.
Last edited by RobA; 2012-May-25 at 11:59 AM. Reason: Oops, got minutes wrong!

2. Originally Posted by Strange
You have had detailed explanations, including the relevant math, in this and other threads (and other forums). You appear unwilling to work through the math so that you can understand it. You ignore all possible explanations. I have given up trying to explain it to you. I will point out when you make blatantly wrong statements - mainly for the benefit of any other readers.

The Wikipedia page has a very detailed explanation. However, as you are unwilling to follow the explanation and mathematics of how relativity works in a really simple case, I don't know how much you will get out of it.

Convinced?

The basis of that piece, is that the time difference increases incrementally at whatever rate is applicable for that time.

Unfortunately, as is quite apparent from the Lorentz Transformation Equations and the Lorentz Factor, one cannot do that.

The Lorentz Transformation is a snapshot; it enables one to transform the measurements at that moment.

The Lorentz Transformation is just that a transformation, not an accrual of those times.
It is the time period in question, transformed by the Lorentz Transformation at the current velocity. So the time since departure T, is transformed by applying the Lorentz Transformation .
So if we designate the time elapsed for the moving Twin to be T', we have
T' = T√1-v2/c2.

Think about it. Look at the Lorentz Transformation Equations and what they mean, and think about them. There is no suggestion than that they are transforming an existing quantity, as it exists at that time, as a whole, in one go, immediately, to see how it will appear at the current velocity. It matters not whether the journey up too that time had been close to c, or at walking pace! Just so long as that is the current velocity the transformation will be the same.

So please tell me where on earth the mathematically absurd idea that we need to use calculus comes from.

3. Originally Posted by RobA
The moving clock is covered by that quote. Let's plug some numbers in:

Two synchronous clocks at A
, so let's say they're both set to 3pm
One ... is moved in a closed curve Let's say it's moved at 0.9c
the journey lasting t seconds, Implicitly, that's t seconds by the clock which has remained at rest. Let's say 600 seconds, so when the clocks reunite, the clock at rest is now reading 3:10
the travelled clock on its arrival at A will be 1/2 t v2 / c2 second slow
So t = 600, v/c = 0.9 so v2 / c2 = 0.92 = 0.81. So slowness = 1/2 * 600 * 0.81 = 243 seconds = 4 minutes
So when the clocks reunite, the one that remained at rest will read 3:10, the one that travelled will read 3:06. Effectively, the travelling clock has traded time for distance - remember that quote "One man's space is another man's time"?
No sorry, I haven't come across that.
Not true. Relativity says that there is nothing that can specify which of the Frames of Reference is moving. Each Frame of Reference can consider itself at rest.
For these clocks, one stays "stationary" - ie. in a single Frame of Reference. The other has travelled in a curve - it has changed direction, so it KNOWS it has been moving - ie. it has been changing Frames of Reference. The act of changing Frames of Reference is what distinguishes them. The one that changes will have the slower clock.
No! I disagree! The one that has moved has only moved in relation to the one that has stayed at rest.

Or are you saying that there is such a thing as Absolute rest?

And I don't agree that the moving clock changes reference frames. The most one can say is that it is not an Inertial Frame of Reference. It has a reference frame that is defined by the clock. As far as that clock is concerned (to continue anthropomorphising them) it is stationary, as is its frame of Reference!

Two clocks exist in space and if A goes round B then it is just as true that from the other perspective B goes round A. That is what Relativity is all about! it is Relative!

After all any Frame of Reference may be considered an Inertial Frame of Reference. Its position in space is only determined relative to other Frames of Reference. So there is no reason why one has to say it is not inertial. It may be that it is and that the rest of space is not. Who can say?

4. Originally Posted by Grimble
No! I disagree! The one that has moved has only moved in relation to the one that has stayed at rest.

Or are you saying that there is such a thing as Absolute rest?
Good grief.

There is such a thing as "acceleration". You may have heard of it. Hence the emphasis on inertial frames of reference.

If you are in an inertial frame of reference you can't tell if you are moving or the platform in.

However, if you are accelerating you can tell. Have you noticed?

If you are in a car turning a corner you get pushed to the side. If you are on the pavement and car goes round the corner next to you, do you feel a force pushing you towards the car?

You may have noticed that when a lift starts and stops you feel a slight change in your weight. Have you ever noticed a change in your weight while waiting in the lobby for a lift to arrive?

Originally Posted by Grimble
So please tell me where on earth the mathematically absurd idea that we need to use calculus comes from.
Yes, any theory that relies on math you don't understand must be wrong.

You can treat an accelerating frame, in the limit, as a sequence of inertial frames. To do that we use something called "integration".

5. Originally Posted by Grimble
... The most one can say is that it is not an Inertial Frame of Reference. ...
Aha! He begins to grasp it.

... After all any Frame of Reference may be considered an Inertial Frame of Reference. ...
And he loses it.

6. Originally Posted by Grimble
The most one can say is that it is not an Inertial Frame of Reference.
YES Yes, yes, yes, yes, YES.

The Inertial Frame of Reference. THAT'S the Frame of Reference we've been trying to get through to you. We just didn't know what term (if any) you would identify it by. Think about it : A body is "stationary" in its own Inertial Frame of Reference. The Train and the Embankment - each has their own Inertial Frame of Reference. Do you see why I corrected you when you said "The observer, however may be moving within that Frame of reference ", and in Post 45 I said:

Originally Posted by RobA
Every observer considers themselves at rest (since we're in SR), and a Frame of Reference is the system of coordinates relative to themselves. Multiple objects not moving relative to eachother do, by definition, share the same Frame of Reference. Also by definition, observers do not move within their Frame of Reference (which is, after all, based on their position, and they are at rest).
The Inertial Frame of Reference is the "Unambiguous" definition of Frame of Reference I was driving towards in Post # 109. It is the ONLY Frame of Reference used in Relativity (which is why the "Inertial" part is taken for granted).

PLEASE: Forget any other definitions or usages of the term Frame of Reference. Forget any and all other coordinate systems. In Relativity, we are ONLY concerned with Inertial Frames of Reference, the coordinates an observer "at rest" in that Inertial Frame of Reference constructs to map it, and how those coordinates translate to another Inertial Frame of Reference (ie. for another observer who is moving relative to the first).

7. Originally Posted by Strange
Good grief.

There is such a thing as "acceleration". You may have heard of it. Hence the emphasis on inertial frames of reference.

If you are in an inertial frame of reference you can't tell if you are moving or the platform in.

However, if you are accelerating you can tell. Have you noticed?

If you are in a car turning a corner you get pushed to the side. If you are on the pavement and car goes round the corner next to you, do you feel a force pushing you towards the car?

You may have noticed that when a lift starts and stops you feel a slight change in your weight. Have you ever noticed a change in your weight while waiting in the lobby for a lift to arrive?
OK, point taken.
But what has acceleration to do with relativity? Where in the Lorentz Equations is acceleration used?
Yes, acceleration can often be detected, but so what?
Does an observer who detects a body circling round him, necessarily go to the extent of measuring acceleration before deciding whether that body is circling him or he is circling it?

Was the fact that the Earth orbits the sun discovered by measuring the Earth's acceleration?

Relativity is about the effects of the relative movement of bodies, that is if A accelerates according to B then B accelerates according to A. Why the bodies move as they do relative to one another is hardly a part of Relativity.

Yes, any theory that relies on math you don't understand must be wrong.

You can treat an accelerating frame, in the limit, as a sequence of inertial frames. To do that we use something called "integration".
Yes of course; but why apply it here?

A clock measures the time that has passed.
When a clock is displaying a time it is displaying the time that has passed since its start point. (00:00, or Midnight).

Integration would be a way of taking every incremental difference and summing them to give a total, but what total? The time the clock has measured, which is what the clock is displaying anyway
So all that needs to be transformed is the measure the clock is displaying!

I may not be a mathematician but I do have a basic understanding of calculus.

So do you understand why the use of calculus here is absurd?
A clock is not just a display of the current time, it is the measure of the time that has passed.

8. Originally Posted by Jim
Aha! He begins to grasp it.

And he loses it.
Very good

For man on the Earth the Earth appeared to be an inertial Frame of reference.
Then man discovered that it orbits the sun and then that the sun orbits the galaxy.
So we know that the Earth is not an inertial frame. Indeed the only frames of reference that we do know to be inertial are theoretical ones in thought experiments.

And if any frame can be considered to be stationary by an observer within that Frame, who is to say that it is not? Forces that may be acting upon it do not have any relation to its relative movement compared to another frame.
Consider comparing frames here on earth. All are subject to the same gravitational forces. but does that affect whether they are considered to be inertial?
I think that depends on the circumstances and what is being compared, so can a frame that is subject to acceleration ever be considered inertial?
I leave that to you to decide.

9. Originally Posted by RobA
YES Yes, yes, yes, yes, YES.

The Inertial Frame of Reference. THAT'S the Frame of Reference we've been trying to get through to you. We just didn't know what term (if any) you would identify it by. Think about it : A body is "stationary" in its own Inertial Frame of Reference. The Train and the Embankment - each has their own Inertial Frame of Reference. Do you see why I corrected you when you said "The observer, however may be moving within that Frame of reference ", and in Post 45 I said:

The Inertial Frame of Reference is the "Unambiguous" definition of Frame of Reference I was driving towards in Post # 109. It is the ONLY Frame of Reference used in Relativity (which is why the "Inertial" part is taken for granted).

PLEASE: Forget any other definitions or usages of the term Frame of Reference. Forget any and all other coordinate systems. In Relativity, we are ONLY concerned with Inertial Frames of Reference, the coordinates an observer "at rest" in that Inertial Frame of Reference constructs to map it, and how those coordinates translate to another Inertial Frame of Reference (ie. for another observer who is moving relative to the first).
Thank you, that is a great help!
I have had so many statements questioned and picked apart in previous threads that I have been unsure how much may be assumed in the use of a phrase.
So an observer will only ever be moving in another observer's frame?

10. Originally Posted by Grimble
Thank you, that is a great help!
I have had so many statements questioned and picked apart in previous threads that I have been unsure how much may be assumed in the use of a phrase.
So an observer will only ever be moving in another observer's frame?
Glad to help Correct. In fact, if the other observer has another frame, then by definition they are moving relative to eachother (and so the other observer will be moving in the first observer's frame as well). On the other hand, if the two observers are stationary relative to eachother, then they are said to share the same frame (or be in the same frame).

11. OK, now we have an agreed definition of Frame of Reference, let's go back and look at some of the examples in that light. Naturally, we'll start with Einstein's clocks:

Originally Posted by Grimble
Originally Posted by RobA
So when the clocks reunite, the one that remained at rest will read 3:10, the one that travelled will read 3:06. Effectively, the travelling clock has traded time for distance - remember that quote "One man's space is another man's time"?
No sorry, I haven't come across that.
...
OK, forget the quote (although you have come across it )

The important point is that we applied Einstein's own example and equation. Two clocks started side-by-side showing the same time. One moved around and came back. When they were back side-by-side, the one that had traveled shows a different time. There is no "from the other's perspective" here - the clocks are together showing different times. The one that moved has experienced less duration than the one that remained.

Originally Posted by Grimble
No! I disagree! The one that has moved has only moved in relation to the one that has stayed at rest. ... And I don't agree that the moving clock changes reference frames. The most one can say is that it is not an Inertial Frame of Reference.
Now that you understand that we are indeed talking about Inertial Frames of Reference, do you accept the example? Remember, this is Einstein's own example, and has subsequently been confirmed by repeated experiments. This is how the universe operates, and is a direct consequence of the second postulate - speed of light is constant for all observers.

What this shows is that observer's clocks do not all tick at the same rate; each observer's measured durations between events vary. This in turn means that there is no global time - so again, it's not surprising if different observers make different conclusions about whether two remote events happened at the same time.

And how about the Train and the Embankment : (I've added the Inertial s)
Originally Posted by Grimble
Observed from the Embankment's Inertial Frame of Reference A & B are points on the railway. The observer WHO IS STATIONARY AT POINT P is the embankment Observer at point M in his Inertial Frame of reference. He will say that in the Embankment's Inertial Frame of Reference the lightning strikes are simultaneous but that the Passenger on the train who passes point P as the lightning strikes will not see simultaneity as his motion will have taken him away from P by the time the light reaches there.
The coordinates used by the observer on the embankment are not some "static" description of universal spacetime; They're simply the ones that he uses to map out his Inertial Frame of Reference. Likewise for the observer on the train. So that's ALL we have, just two Inertial Frames of Reference - and the way the maths works out, what's simultaneous in one cannot be simultaneous in the other. There's no "from the other's perspective" here either - just each Inertial Frame of Reference being consistent.

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Originally Posted by Jim
And he loses it.
Or he suddenly jumped ahead to full blown GR where his statement is accurate, though i doubt it

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Originally Posted by Grimble
But what has acceleration to do with relativity? Where in the Lorentz Equations is acceleration used?
It isn't. Special relativity is a theory about inertial frames only (ie moving at constant velocity), it has nothing to say about accelerating or rotating frames. For that you need general relativity, but that is quite a bit more complicated, so you're probably best to just stick to special relativity and inertial frames for the moment and forget about acceleration or rotation.

14. Originally Posted by Grimble
And if any frame can be considered to be stationary by an observer within that Frame, who is to say that it is not?
This is true.

So let's say the observer on the train considers themselves at rest - which is fine. And that observer see flashes at the same time from the ends of the carriage, which are equidistant to him or her. Given that the speed of light is always the same he or she determines that the flashes were generated at the same time, and were simultaneous, in the frame of the train.

But, for this to "work", the source of those flashes, the ends of the train, immobile in the frame of the train, are not the same location as flashes that the embankment observer might have seen at the "same time".

Code:
```=====[A....M....B]====== (Train moving right, according to N)
|
----------------------------
|
C....N....D```
Say M on a train sees flashes at the same time from equidistant A and B, and observer N on the embankment sees flashes from equidistant C and D at the same time.
Both may know their own flashes to be simultaneous, but they can't have been the same flashes.
While each may considers themselves as stationary, if there is relative motion (i.e. the train isn't "sitting still") then A & C and B & D can't have been the same flashes, because they are in different places.

M, considering herself at rest, knows the flashes came from A and B, and knows these are not the same location as C and D.
N, considering himself at rest, knows the flashes came from C and D, and knows these are not the same location as A and B.

M, knows that the flashes came from A and B, so couldn't have hit N at the same time.
N, knows that the flashes came from C and D, so couldn't have hit M at the same time.

Again, observers in relative motion can not both experience the same events as simultaneous.

Both can experience simultaneous events. That's never been in question. They just can't both know the same events to be simultaneous.

(
The above scenario would work in classical physics, replacing light with bullets from guns.
Each observer would consider themselves as at rest, but would be able to consider the other observers bullets as having speed + or - the relative speed of the train/embankment.
Thus A & C and B & D might have adjacent when the shots were fired, and both M and N would be hit at the "same time", each by both of their own bullets simultaneously.

But this can only work as in classical physics the speed of the bullets, according to each observer, can be + or -. N considers the bullets to hit M as coming from C and D, which are not equidistant to M when M is hit - but that's OK according to N, because the bullets have speed + or - the speed of the train, relative to N. It all works out.

Light doesn't work that way. In all frames it's c. In all directions.
)

There is just one idea you hold on to, that simltaneous for one must mean simultaneous for all. But that then causes multiple contradictions. Accepting what is plainly meant by Einstein here, resolves all of those contradictions:

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.
Originally Posted by Grimble
Bit I believe you are creating a preferred frame by claiming that that simultaneity is special to the one frame because, and only because, from the perspective of that frame, the observer in that frame concludes that other frames will not see simultaneity.
It has nothing to do with what the other frames, from their perspective, measure, only what the first frame concludes they will measure.
The point you miss there is that it's an observation that can't be contradicted. If one observer sees flashes of light hit some (single) object at the same time, then all observers must see those flashes hit that object at the same time. If two cars hit one lamp post at the same time, no observer is going to see one of them hit it 10 seconds earlier than the other.

So when the embankment observer sees one of the flashes hit the train observer before the other flash, that's not forcing the view of the embankment onto the train observer, because that's what the train observer must have seen for themselves.

The only way you can get around that is by deciding that somehow they can all see contradictory things; like with that detector. You asserted that the embankment observer would see the detectors light shine green, even though that embankment observer would have seen one flash hit the detector before the other. That just can't work.

15. To take once again that so often quoted
Originally Posted by Einstein
Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.
Look at the wording and read what is written.
which are simultaneous with reference to the railway embankment
with reference to = as observed from
and
simultaneous relatively to the train
relatively to = with respect to not as observed from.

If he had writtenAre two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous with reference to the train? We shall show directly that the answer must be in the negative.

But he didn't, he deliberately said "relative to"

That is that the embankment observer would have seen that the lightning strokes were simultaneous to him but not to the train as he (the embankment observer) saw it.

It says nothing of what the train observer would observe, only what the embankment observer would calculate that the train observer would observe.

Do you know what really puzzles me here?

That is why my attempts to fully understand what was written causes such a furore? What difference does it make? All the calculations are unaffected; it is only a matter of visualisation.

Oh and by the way, it is nothing like two cars hitting a lamppost, as each observer has different coordinates. I will give a different analogy.
It is like a painting, such as the 'Laughing Cavalier' where the image appears to be looking directly at you, wherever you stand in front of the painting; and if two were to stand at different places, each would say that it was looking directly at him and not at the other.

16. Originally Posted by Grimble
... But he didn't, he deliberately said "relative to" ...
Well, he actually wrote it in German, and we are reading an English translation. And in any case I (and most others) don't agree with your interpretation.

"With reference to" and "relatively to" are synonymous here, both meaning the same thing - events within each frame (not just observed in the frame from another frame). It's saying events simultaneous in the embankment frame are not simultaneous in the train frame (and later he adds, of course, vice versa (via relativity, events could be simultaneous according to the train frame - but then they won't be simultaneous according to the embankment frame)).

Originally Posted by Grimble
It says nothing of what the train observer would observe, only what the embankment observer would calculate that the train observer would observe.
No, it says everything about what the train observer would observe, because they can't disagree.

Originally Posted by Grimble
Do you know what really puzzles me here?

That is why my attempts to fully understand what was written causes such a furore? What difference does it make? All the calculations are unaffected; it is only a matter of visualisation.
If you think it's just about visualisation, you are wrong. It's about the actuality of whether events which are simultaneous in a frame are simultanenous in frames which are in relative motion to that frame. (There's a reason why yours isn't the version taught at University!)

Goodness, we already know that relative motions causes differences in observation, e.g. simple things like the doppler effect. That's no big news.

Originally Posted by Grimble
Oh and by the way, it is nothing like two cars hitting a lamppost, as each observer has different coordinates.
Please explain how the observers different coordinates can affect the way they see events ocurring in a single location.

(Edit: i.e. I would expect that if you are sitting on top of the lamp post (stationary with respect to it), and I were 100 metres away riding my motorcycle at 100 km/h with respect to it, that if two cars hit that lamp post at the "same time" we'd both see that occur at the same time. There's no reason why either of us in our "different coordinates" would see one car hit the lamp post before the other.

While at it, please explain why you think this can be, when at the same time (no pun intended) you reject that events which occur in different locations can be simultaneous for one observer but not simultaneous for another observer.

That is, you demand that events which are simultaneous for one observer must also be simultaneous for another - but to "explain" this you allow events at a single location to be simultaneous for one observer but non-simultaneous for another observer! Another contradiction!)

Originally Posted by Grimble
I will give a different analogy.
It is like a painting, such as the 'Laughing Cavalier' where the image appears to be looking directly at you, wherever you stand in front of the painting; and if two were to stand at different places, each would say that it was looking directly at him and not at the other.
No, that's just an analogy about visualisation. But we are talking about actual events.

Observer M is the lamp post, observer N is watching them. If two beams of light hit observer M at different times, then observer N can't see those beams hit M at the same time; if those beams hit M at the same time, observer N can't see them hit at different times; events occuring at the same physical location must be agreed by all observers to be simultaneous or not.

You claim that one observer can see two beams of light hit another observer at different times, while that observer themself will see those beams of light hit them at the same time.

That's such a huge contradiction. It's not just some illusion, you are talking about actual photons hitting an object both at the same time and at different times. It can't be. That's the whole point of that paper.
Last edited by pzkpfw; 2012-May-28 at 12:48 AM. Reason: Add Edit:

17. Originally Posted by Grimble
To take once again that so often quoted
Look at the wording and read what is written.

with reference to = as observed from
and
relatively to = with respect to not as observed from.
Once again you are quibbling over the interpretation of words. The words are irrelevant. Look at the maths; it proves your interpretation is incorrect.

That is why my attempts to fully understand what was written causes such a furore? What difference does it make? All the calculations are unaffected; it is only a matter of visualisation.
One reason is a desire to educate and inform. Another is that it isn't just a matter of visualization: what you claim (that two events will be simultaneous to all observers) is factually wrong.

18. Originally Posted by Grimble
with reference to = as observed from and relatively to = with respect to not as observed from.
Don't you think that you're reading just a BIT too much into near-identical phrases ? Just for example, Dictionary.com lists "with reference to" as one meaning of "relatively to".

But look, you're making things unnecessarily complicated.

We have :
- An Embankment and an Observer Edward in Inertial Frame of Reference R1
- A Train and an Observer Tom in Inertial Frame of Reference R2
- Lightening strikes at A and B.

Now Edward decides whether the strikes were simultaneous in his Inertial Frame of Reference (let's say he does), and Tom decides whether they were simultaneous in his.
Each can calculate by Relativity the answers for the other - ie. they can take the spacetime coordinates from their Inertial Frame of Reference, and translate them into the spacetime coordinates of the other's Inertial Frame of Reference. In doing so, they get the answers to what the other observed.

And that's it. Two Inertial Frames of Reference, and observers in each can calculate the other's observations.

Originally Posted by Grimble
It says nothing of what the train observer would observe, only what the embankment observer would calculate that the train observer would observe.
So what's the bit that I've bolded? You say Tom would also observe the strikes as simultaneous, but Edward would calculate that Tom wouldn't have? So are you trying to say that the point of Relativity is that the Relativity calculations give wrong answers?

Originally Posted by Grimble
Do you know what really puzzles me here?
That is why my attempts to fully understand what was written causes such a furore?
Why is that a puzzle? We're here because we love the subject, and want to help others appreciate it. An essential part of that is to make sure that people have a clear and correct understanding of the subject, so they appreciate the beauty of the picture, and have a firm foundation for further exploration. That's not just for you - we've already had one poster say that they read threads like this so they can learn, so we owe it to them as well.

Originally Posted by Grimble
What difference does it make? All the calculations are unaffected; it is only a matter of visualisation.
But it's not. Two clocks side-by-side showing the same time, one moves and returns - now they're showing different times. That's not just visualisation, but physical reality - and if your calculations don't reflect that, then they are affected by your visualisation.
And how important is Simultaneity? When I started learning about Relativity, all the pop-sci started on Length Contraction and Time Dilation - maybe because they're fun and easier to understand. Einstein started with Simultaneity - both in "On the electrodynamics of moving bodies", and in "Relativity" on Bartleby. It is important.

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Originally Posted by pzkpfw
Please explain how the observers different coordinates can affect the way they see events ocurring in a single location.

{...}

Observer M is the lamp post, observer N is watching them. If two beams of light hit observer M at different times, then observer N can't see those beams hit M at the same time; if those beams hit M at the same time, observer N can't see them hit at different times; events occuring at the same physical location must be agreed by all observers to be simultaneous or not.

You claim that one observer can see two beams of light hit another observer at different times, while that observer themself will see those beams of light hit them at the same time.

That's such a huge contradiction. It's not just some illusion, you are talking about actual photons hitting an object both at the same time and at different times. It can't be. That's the whole point of that paper.
Perhaps another approach might work better for this specific aspect, by noting that there really is only a single event here, not two. Since an event is nothing more than a location in space at a specific time, the two photons hitting the lamp post at the same time don't constitute two events but a single one. Naturally a single event (just a geometric point) doesn't suddenly become two events because you change coordinates.

Unless Grimble would like to claim that when i draw a single point on a piece of paper, that point suddenly becomes two different points just by changing how i draw my axes on that paper.

20. Originally Posted by RobA
Why is that a puzzle? We're here because we love the subject, and want to help others appreciate it. An essential part of that is to make sure that people have a clear and correct understanding of the subject, so they appreciate the beauty of the picture, and have a firm foundation for further exploration. That's not just for you - we've already had one poster say that they read threads like this so they can learn, so we owe it to them as well.
At least the thread is in the right place now, as Grimble's position is certainly not the mainstream. So far as he's doing anything consistent, he's basically denying Einstein's relativity, claiming its measured effects are illusions (or apparently, mysteriously inaccurate clocks that just happen to give errors that match prediction) and that reality is Galilean relativity. He says otherwise, but that's what he's doing.

It's been tried before, but I'll try this approach again, with a bit more detail: locations and events can be described using a coordinate system of 3 spacelike coordinates and 1 timelike coordinate, defining the frame of reference of a non-accelerating (inertial) observer. Any other inertial observer at a different location or with relative velocity will have a different coordinate system, a different frame of reference, and measurements can be transformed between these two frames with the Lorentz transform. This transform is a 4D hyperbolic rotation. Like your everyday 3D elliptical rotation, it can mix one axis with another...including the time axis. What one frame sees as two simultaneous events with spacelike separation, another sees as two events with timelike separation (hence, not simultaneous), and vice versa.

21. Originally Posted by caveman1917
Perhaps another approach might work better for this specific aspect, by noting that there really is only a single event here, not two. Since an event is nothing more than a location in space at a specific time, the two photons hitting the lamp post at the same time don't constitute two events but a single one. Naturally a single event (just a geometric point) doesn't suddenly become two events because you change coordinates.

22. Originally Posted by cjameshuff
At least the thread is in the right place now, as Grimble's position is certainly not the mainstream.
And this will be the last time he starts a thread like this. After this one was moved I re-checked his posting history; he's had this thread already more than once. The site doesn't need another.

23. From the OP:
Originally Posted by Grimble
So if we were to define a particular time point by a colour, for instance, than we would see the whole of space change colour as Time progressed and we would be able to refer to simultaneous events as all being the same colour on a progressing scale.

From this it becomes evident that there is one Space-time and that synchronous events are synchronous wherever they are observed from.

It is the whole of Space where every point has the same time. Where every Space-point has a synchronous event. Think about it. It has to be!
And this is the visualisation that you are using as the basis of your calculations. This is the visualisation that forces you into believing that both the train and the embankment observers must read the same times on their clocks for the lightening strike events.

This is the visualisation that is flat-out denied by Einstein - remember:

Originally Posted by Einstein
If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be 1/2 t v2 / c2 second slow
Originally Posted by RobA
Let's plug some numbers in:

Two synchronous clocks at A
, so let's say they're both set to 3pm
One ... is moved in a closed curve Let's say it's moved at 0.9c
the journey lasting t seconds, Implicitly, that's t seconds by the clock which has remained at rest. Let's say 600 seconds, so when the clocks reunite, the clock at rest is now reading 3:10
the travelled clock on its arrival at A will be 1/2 t v2 / c2 second slow
So t = 600, v/c = 0.9 so v2 / c2 = 0.92 = 0.81. So slowness = 1/2 * 600 * 0.81 = 243 seconds = 4 minutes
So when the clocks reunite, the one that remained at rest will read 3:10, the one that travelled will read 3:06.
To recap: Two clocks started side-by-side showing the same time. One moved around and came back. When they were back side-by-side, the one that had traveled shows a different time. There is no "from the other's perspective" here - the clocks are together showing different times. The one that moved has experienced less duration than the one that remained. Remember, this is Einstein's own example, and has subsequently been confirmed by repeated experiments.

So this visualisation is not compatible with Einstein's Relativity. The questions for you remains : now that you understand that we are indeed talking about Inertial Frames of Reference, do you accept Einstein's statement?

24. Originally Posted by pzkpfw
Well, he actually wrote it in German, and we are reading an English translation. And in any case I (and most others) don't agree with your interpretation.
Fair enough

"With reference to" and "relatively to" are synonymous here, both meaning the same thing - events within each frame (not just observed in the frame from another frame). It's saying events simultaneous in the embankment frame are not simultaneous in the train frame (and later he adds, of course, vice versa (via relativity, events could be simultaneous according to the train frame - but then they won't be simultaneous according to the embankment frame)).
I admit that that is the accepted reading but as a 'word smith' (someone who is fascinated by language, prose and poetry) I maintain that my reading is a better interpretation of what was written, while accepting that it is only my opinion. I have reached that stage in my study of Relativity (and I do understand all the you and the rest are saying to me), but as I say I have reached that stage where I can examine what is accepted and look for alternative readings, not to try and disprove anything, but to try and clarify some of the rather fuzzy bits that don't sit well with the rest.

No, it says everything about what the train observer would observe, because they can't disagree.
Why not, it is after all, only relative.

If you think it's just about visualisation, you are wrong. It's about the actuality of whether events which are simultaneous in a frame are simultanenous in frames which are in relative motion to that frame. (There's a reason why yours isn't the version taught at University!)
But when you say the actuality, you can only have that if you have a single definitive (super) frame of reference which defines reality, and that is what I am repeatedly told we can't have!

Goodness, we already know that relative motions causes differences in observation, e.g. simple things like the doppler effect. That's no big news.
No indeed, I must agree with you there, but have you considered the difference between difference in observations in space (3dimensions) and time which has only one dimension. It is difficult to see how time can be viewed in the same way as space where we can view things from different angles. Time, as a single dimension has only one angle that it can be viewed from.
Show me how any observer in a single dimensional world can see events in anything but a straight sequence.

Please explain how the observers different coordinates can affect the way they see events ocurring in a single location.

(Edit: i.e. I would expect that if you are sitting on top of the lamp post (stationary with respect to it), and I were 100 metres away riding my motorcycle at 100 km/h with respect to it, that if two cars hit that lamp post at the "same time" we'd both see that occur at the same time. There's no reason why either of us in our "different coordinates" would see one car hit the lamp post before the other.

While at it, please explain why you think this can be, when at the same time (no pun intended) you reject that events which occur in different locations can be simultaneous for one observer but not simultaneous for another observer.

That is, you demand that events which are simultaneous for one observer must also be simultaneous for another - but to "explain" this you allow events at a single location to be simultaneous for one observer but non-simultaneous for another observer! Another contradiction!)
Again you are maintaining that a location is the same in every frame, is it that same single space-time that I am accused of needing?

For me that single location exists in each and every frame, but has different coordinates, and a different relationship to those coordinates, in most of them it is moving in different directions at different speeds.
Two bodies, flashes of light meet, that is true but where? At a point in space that is fixed. Yet in another frame that point is moving. So in the frames where it is moving, where the 'lamppost' is moving, it must be moving towards one of the cars and away from the other – like the train is moving toward one flash of lightning.
In the case of the lamppost the cars hit at different speeds, but light cannot do that, so it is seen to hit at different times – because we are dealing with relativistic effects.

No, that's just an analogy about visualisation. But we are talking about actual events.

Observer M is the lamp post, observer N is watching them. If two beams of light hit observer M at different times, then observer N can't see those beams hit M at the same time; if those beams hit M at the same time, observer N can't see them hit at different times; events occuring at the same physical location must be agreed by all observers to be simultaneous or not.

You claim that one observer can see two beams of light hit another observer at different times, while that observer themself will see those beams of light hit them at the same time.

That's such a huge contradiction. It's not just some illusion, you are talking about actual photons hitting an object both at the same time and at different times. It can't be. That's the whole point of that paper.
I'm sorry to appear argumentative here but that is why I am re-examining all these things to make sure that everything works out and forms the best interpretation of the theory that will provide easy, simple and logical explanations of it all.

But why do you say this?
events occuring at the same physical location must be agreed by all observers to be simultaneous or not.
Why? I would agree that, yes, there has to be one reality of what happens. That has to be the view of the observer in who's frame it happens. The one where it is stationary.
For the others, who do not see simultaneity it is due to relativity, simultaneity is relative to how it is viewed. In the same way that a moving observer measures length contraction and time dilation, relativistic effects.

25. Originally Posted by Strange
Once again you are quibbling over the interpretation of words. The words are irrelevant. Look at the maths; it proves your interpretation is incorrect.
Does it? (again a global statement with no reason)

One reason is a desire to educate and inform. Another is that it isn't just a matter of visualization: what you claim (that two events will be simultaneous to all observers) is factually wrong.
and the reason you say that is ...?

The way I am investigating, makes no difference to what you say, it only makes it general instead of specific; it makes it relative to the relation between frames, rather that making one preferred. And saying that it is so for one and not for another is giving preference.

26. Originally Posted by Grimble
Does it? (again a global statement with no reason)
Yes. You have been shown the reason several times here (and other forums). I see no point in repeating it for someone who has chosen to be blind to learning. Einstein works through it in detail in the work you cite. And yet you prefer to quibble over a translator's choice of prepositions.

27. Originally Posted by RobA
Don't you think that you're reading just a BIT too much into near-identical phrases ? Just for example, Dictionary.com lists "with reference to" as one meaning of "relatively to".

But look, you're making things unnecessarily complicated.

We have :
- An Embankment and an Observer Edward in Inertial Frame of Reference R1
- A Train and an Observer Tom in Inertial Frame of Reference R2
- Lightening strikes at A and B.

Now Edward decides whether the strikes were simultaneous in his Inertial Frame of Reference (let's say he does), and Tom decides whether they were simultaneous in his.
Each can calculate by Relativity the answers for the other - ie. they can take the spacetime coordinates from their Inertial Frame of Reference, and translate them into the spacetime coordinates of the other's Inertial Frame of Reference. In doing so, they get the answers to what the other observed.

And that's it. Two Inertial Frames of Reference, and observers in each can calculate the other's observations.

So what's the bit that I've bolded? You say Tom would also observe the strikes as simultaneous, but Edward would calculate that Tom wouldn't have? So are you trying to say that the point of Relativity is that the Relativity calculations give wrong answers?
Lol, yes I see what you mean, it could be read like that!:redface:. The problem is that the answers arrived at are relative to the specific frames of reference. If Edward were to calculate that from his point of view he would say that Tom was approaching one light and see that one first, but if he were a bit more astute, he would put that result to one side and say to himself: “Ah but, within Toms frame of reference, the train would not be moving so Tom will see the lights simultaneously.”

Why is that a puzzle? We're here because we love the subject, and want to help others appreciate it. An essential part of that is to make sure that people have a clear and correct understanding of the subject, so they appreciate the beauty of the picture, and have a firm foundation for further exploration. That's not just for you - we've already had one poster say that they read threads like this so they can learn, so we owe it to them as well.
[/quote]Which is why this is now in the right place for that in ATM. As I say I am not trying to rewrite relativity, I love it and it works fine, it is just that there are some points that I feel are – um, misrepresented? not visualised very clearly? a bit fuzzy? tend to be glossed over? - and I am suggesting how this may be done, Focussing a bit tighter on some issues …

But as I say these are only my feelings although I would defend myself by saying that this is acceptable scientific process. Every bit of science is always open to be reinvestigated.

But it's not. Two clocks side-by-side showing the same time, one moves and returns - now they're showing different times. That's not just visualisation, but physical reality - and if your calculations don't reflect that, then they are affected by your visualisation.
I don't want to should drag Hefele-Keating and co into this. I am receiving enough abuse over this already. All I will say is that experiments have indeed shown a physical difference in two clocks, but the reason why they were different is open to many interpretations.

And how important is Simultaneity? When I started learning about Relativity, all the pop-sci started on Length Contraction and Time Dilation - maybe because they're fun and easier to understand. Einstein started with Simultaneity - both in "On the electrodynamics of moving bodies", and in "Relativity" on Bartleby. It is important.
Oh, I agree, absolutely and I am not trying to change that.
But, to me, it seems that the difference, the major, if not the only difference between the embankment and the train is that in the Embankments frame, M is stationary while the lights come to it while M', moves away from that spot.
However when viewed from the train it is M' that is stationary and M that is moving and if we apply those same criteria we would naturally come to the conclusion that the strikes would be simultaneous from the train, in the train's frame.
The one thing that we can say absolutely is that from the trains frame they cannot be simultaneous to the embankments observer who is moving away from one strike and toward the other.

(And as an aside here I would point out that the lightning strike hitting A on the track and A on the train is a single event of three reference points coming together – lightning = lampost, A on train and A on embankment = cars – and, obviously the same is true for the point **. So how can they not be seen as simultaneous from each frame?)

28. Originally Posted by caveman1917
Perhaps another approach might work better for this specific aspect, by noting that there really is only a single event here, not two. Since an event is nothing more than a location in space at a specific time, the two photons hitting the lamp post at the same time don't constitute two events but a single one. Naturally a single event (just a geometric point) doesn't suddenly become two events because you change coordinates.

Unless Grimble would like to claim that when i draw a single point on a piece of paper, that point suddenly becomes two different points just by changing how i draw my axes on that paper.
It depends whether you are using Galileian Relativity - as in your example or Special Relativity, where the constant speed of light is taken into account.

29. Originally Posted by cjameshuff
At least the thread is in the right place now, as Grimble's position is certainly not the mainstream. So far as he's doing anything consistent, he's basically denying Einstein's relativity, claiming its measured effects are illusions (or apparently, mysteriously inaccurate clocks that just happen to give errors that match prediction) and that reality is Galilean relativity. He says otherwise, but that's what he's doing.

It's been tried before, but I'll try this approach again, with a bit more detail: locations and events can be described using a coordinate system of 3 spacelike coordinates and 1 timelike coordinate, defining the frame of reference of a non-accelerating (inertial) observer. Any other inertial observer at a different location or with relative velocity will have a different coordinate system, a different frame of reference, and measurements can be transformed between these two frames with the Lorentz transform. This transform is a 4D hyperbolic rotation. Like your everyday 3D elliptical rotation, it can mix one axis with another...including the time axis. What one frame sees as two simultaneous events with spacelike separation, another sees as two events with timelike separation (hence, not simultaneous), and vice versa.
On the contrary I have no problem with relativity, all I am doing is questioning some of the details that, as far as I can see, only make it far more complicated and are unnecessary additions to Einstein's theory. I may well be wrong but I want to be able to prove that in clear simple terms with none of the fudging that comes from "just because it is"

30. Originally Posted by pzkpfw
OK the meeting of the lightning strokes is a single event and has a unique set of 4coordinates, in each frame of reference. In one frame of reference they meet at the point M, in any other M is moving away from that point and the reflected lightning meets at M'.
Remember that in the Embankment's frame M is a fixed point while in the train's frame it is a worldline, that M' is a worldline while in the train's frame it is a fixed point. So in one frame they meet at a fixed point while in the other they cross a worldline.

And consider, we know that the world line passes through the point where they meet, at the moment the strikes hit but where is the point on that world line by the time the lights meet - it has passed that point and has moved on ...

I am not trying to be difficult but to sort out how this all works.

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