Timey-wimey Wibbly-wobbly Stuff

[pzkpfw]

Fair enough

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.

You arrive at your interpretation by trying to bend what is written to meet what you have pre-detrmined to be "true". That's backwards. It's a natural assumption that simultaneous events are simultaneous for everyone. In that paper Einstein was showing this to be an incorrect assumption. You, however, wish to hold to that assumption, so come up with your own (almost) unique interpretation.

Since your interpretation is at stark odds with current science (which has existed for quite a while) you certainly are trying to "disprove" something.

I'd point out that Einstein didn't vanish after writing this paper. He was active in academic circle for a while longer. If the interpretation of his work was so wrong, he had plenty of time to correct it!

Why not, it is after all, only relative.

No. You still have not explained how events in a single location can occur at different times for different observers. That is not something that is "only relative". You may as well look at a bat hitting a ball, and say that one observer might see the bat miss!

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!

Not at all. Things do happen in the Universe, that those things happen is no "(super) frame". When a beam of light hits an object, that's something that either occured or it didn't, to say it occured, when it did, is not placing any special meaning on any frame.

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.

I don't really see what you are getting at here, or why you bring it up.

I would however note that the relativity of simultaenity does preserve cause and effect. If the lightening flashes make a tree catch fire, no observer will see the tree catch fire before the lightening strikes it.

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?

Not at all. Distance and time are "bendy" in relativity, but a location is a location. You may see the lamp post 0 metres away from you, it may be 100 metres away from me. You may think the time is 4 o'clock, I may think the time is 5 o'clock. You may think the distance between it and the next lamp post is 50 metres, I may think it is 40 metres. But a single location is a single location. We can both see that lamp post. Whatever we call it's location, it has a location. And any events that occur at that location can only be seen the same way by both of us.

If I see the bat hit the ball, you will see the bat hit the ball.

(You could argue that from some frames, the ball hit the bat, not the bat hit the ball, but you'd agree they hit.)

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.

Yeah, I just don't see how you can twist it that way. The two flashes of light either hit the single object at the same time, or different times. No observer can disagree with that.

What you describe is basically the reason the two flashes can be simultaneous for one observer but not the other, but certainly doesn't "explain" why you think the two observers can disagree about what happened for one of them.

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 you are not making "everything" work out, and your interpretation raises more contradictions and requires much more twisting of words to achieve. All to preserve the "truth" that you assume and wish to hold - an absolute defintion of simultaneous.

(Besides, I'd argue that "easy, simple and logical" is not necessarily the best judge of accuracy. Some things are "rocket science".)

But why do you say this?

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.

What observers see is due to the reality of what occurs.

The light from A and B travel to the observer in the centre of the train. Those flashes of light reflect, including to the direction of the embankment observer. Those photons then travel to the eyes of that embankment observer. That allows him or her to be able to actually measure when the beams of light hit that train observer. It's about actual physical photons. Those same beams of light, with their same leading edge of photons are what went to that train observers eyes. Those actual photons either hit that central observer at the same time, or they didn't. Both the train observer and embankment observer must agree. It's about actual real photons, it's not simply an illusion.

Here you are again assuming ("stipulating") the outcome you want, and then trying to describe the situation to achieve that. It's not what Einstein did. He looked at the situation, figured out what would actually occur, and came to a startling conclusion.

[Grimble]

From the OP:


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:

Again interpretation.

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.

Experiments have indeed shown that clocks will read different times but there has been nothing to show why! Lots of experiments that are proclaimed conclusive because the [b[expected[/b] results are achieved. That is not science unless all other possible factors are eliminated and for relativity that is impossible.
For instance: length contraction – is the body that has been measured to be contracted actually changed size, or is the measurements that have been changed by the conditions under which they have been taken?


We can certainly prove cases where clocks differ but can we say, definitively why?

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?

That statement is fine. I have no problem with it. But in relativistic terms, which clock is moving. Movement is only relative. Whether or not an observer in a particular frame can determine whether his frame has any forces acting upon it we know that from his frame he will consider it to be so.

What Einstein's theory predicts is that the 'moving' clock will be slow as read from the 'stationary' clock. And that has to be reciprocal, the maths says it has to be. Movement is only relative. Movement can only be relative. Or we are going back to saying that there is a fixed Frame of Reference, an Ether, against which movement can be judged?


I wish you could see how the arguments used go round and round until the accepted reading finishes up shooting itself in the foot.

That is what bothers me so much. I don't want to change Special Relativity as Einstein proposed it. But when you spend a lot of time just concentrating on it it becomes much clearer simpler and neater and every bit fits with all the others.

I know you (I am talking to you generally, not you specifically Rob) will never accept what I am saying but you are giving me lots of examples of points that need to be dealt with in the draft.

So once again Thank you one and all

[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'. ...

No, you are mixing things up.
When we look at the flashes meeting at M, we are looking at the flashes meeting at M.
When we look at the flashes meeting at M', we are looking at the flashes meeting at M'.
M can look at M' just as M' can look at themselves.
M' can look at M just as M can look at themselves.
What occurs at M is of course different to what occurs at M', but...
everyone will agree about what occured at M,
and everyone will agree about what occured at M'.

[RobA]

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.”

OK, so let's compare systems, to see which which best matches the criteria of :

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.

We say:
1) Embankment and Train are each in their Inertial Frame of Reference
2) The observers on each have their own take on whether the strikes were simultaneous
3) Each observer can calculate the other's answer to (2)

Your model says:
1) Embankment and Train are each in their Inertial Frame of Reference
2) The observers on each say the strikes were simultaneous
3) Each observer can calculate the other's answer to (2), puts that answer aside, and declare the answer to (2) would actually be yes.

You tell me which is simpler

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? ...Every bit of science is always open to be reinvestigated.

Great - but have you considered that if Relativity were a movie, the bits that are "not visualized", "fuzzy", etc are not problems with movie itself, but with the glasses that you're looking through? We're already fixing one area up, where you hadn't realised that "Frame of Reference" was always simply the good old "Inertial Frame of Reference". That's a major chunk of fuzziness right there! I'll tell you right now that the next chunk is your concept of time

And absolutely every bit of science is always open to reinvestigation. Some of extremes that experiments in Relativity (and Quantum Mechanics) are phenomenal. For example, Gravity Probe B uses the worlds most perfect gyroscopes, built around super accurate spheres. No, testing of Relativity hasn't stopped.

I don't want to should drag Hefele-Keating and co into this.

I wasn't referring to Hefele-Keating. I was just after your response to Einstein's statement about the clocks - but more in my next post.

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.

No, we wouldn't. The requirement for simultaneity is not just that the lights reach the observer at the same time, but also that that observer is midway between where the strikes happened. That is not the case for the train observer. Remember, he measures his distance to the scorchmarks on the train, not the embankment. Sorry, I went though this in Post #44 - is it unclear, or are you disputing it?

(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?)

Exactly - the three reference points come together to form a single Event, which is a single point in spacetime. That's true for both A and B. How can they not be simultaneous? Because a point only gains its coordinates in a Frame of Reference (yes, the Inertial Frame of Reference). One attribute of that coordinate is the Time coordinate - which brings us back to your OP that I quoted in Post # 173.

[caveman1917]

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.

It doesn't depend on any relativity. What each "version" of relativity does is basically tell you how to change your axes to go from one observer to another, this way of changing axes is different in different "versions". What however none of them will do is say that a single point will suddenly become two different points, irrespective of how you change axes.

[RobA]

From the OP:

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.
... It is the whole of Space where every point has the same time.

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

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

Again interpretation.

No. Sorry, but No Way. It is impossible to reconcile "every point has the same time." with "the travelled clock ... will be ... slow". (I'd have thought especially so for someone who distinguishes "with reference to" from "relatively to" )

This is the next issue that must be addressed. You are fixed on the idea that the Time axis is separate from the Space axes. That's understandable - it's our natural, intuitive world, and sure enough, everybody on earth shares the same experience. However, that is insufficient reason to assume it must be universally true. I remember discussing "Up" and "Down" with my Dad - being from the UK, he always thought it was a miracle that people didn't fall off Australia (even after I moved here, and he came to visit!) He never really grasped that "Up" and "Down" were just Relative terms.

I think you're making a similar mistake between Time and Space. Remember that quote I've thrown at you "One man's space is another man's time"? That's not just pithy, but we actually mean it in a literal sense.

That is not science unless all other possible factors are eliminated and for relativity that is impossible. We can certainly prove cases where clocks differ but can we say, definitively why?

Firstly, can you state definitively why light moves at c for all Inertial Frames of Reference? Nope, neither can I.

However, given that it does - and every experiment to date supports that statement - then there are certain inevitable consequences .... and that's basically all that Relativity is. Once you accept that the universe behaves according to the postulates (that the Laws of physics hold in all Inertial Frames of Reference, and light travels at c in all Inertial Frames of Reference), then you must accept Einsteins Relativity since that is simply the mathematical working out of the consequences of those postulates. Subsequent experiments simply support that he didn't make a mistake

One of the consequences is that every Inertial Frame of Reference will reckon that clocks in every other Inertial Frame of Reference run slower. Why? Again, it's a mathematical consequence - but you have to tell us if you're up to the math. It's spelt out and derived in "On the electrodynamics of moving bodies".

That statement is fine. I have no problem with it. But in relativistic terms, which clock is moving. ... What Einstein's theory predicts is that the 'moving' clock will be slow as read from the 'stationary' clock. And that has to be reciprocal, the maths says it has to be.

Again, we've covered this. One clock remains stationary in it's Inertial Frame of reference. The other changes it's Inertial Frame of Reference to turn around and return. The two cases are not reciprocal - and the maths support that. If you dispute that, then you will have to show where Einstein got his maths wrong (as I said, it is derived in "On the electrodynamics of moving bodies" from first principles from the postulates). Sorry, he does use a mathematical discussion, so you will have to show maths to support your position - but seriously, take a read. The statement is in section 4 "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks".

I wish you could see how the arguments used go round and round until the accepted reading finishes up shooting itself in the foot.

That is what bothers me so much.

But look at why they're going around. In post 44, I covered why the train observer wouldn't regard the strikes as simultaneous, in #177 you bring it up again. In post #156, I tell you that the clocks aren't reciprocal because one changes Inertial Frame of Reference, and you just brought that up again.

I don't want to change Special Relativity as Einstein proposed it. But when you spend a lot of time just concentrating on it it becomes much clearer simpler and neater and every bit fits with all the others.

Actually, I think the Relativity I've leant is a really nice picture. Two Inertial Frames of Reference, each with light travelling at c, and Relativity lets me translate coordinates of events from one into the other. Yes, it requires me to let go of things like a universal time axis, but I can understand that. After all, if speed of light is so unusual, and speed is simply distance / time (eg. miles per hour), then I would expect unusual things to happen with distance and time. I see that as a lot neater than the need to add clauses like "both see two events as simultaneous, but reckon that the other doesn't", or "putting results aside".

[cjameshuff]

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"

Those "unnecessary additions to Einstein's theory" you have so much of a problem with are Einstein's theory. You keep trying to reduce things to Newtonian physics with absolute space and time, with some hodge-podge ad-hoc handwaving about relativistic effects being illusions or some other unexplained effect, rather than exactly what relativity predicts. You are twisting Einstein's words around and claiming he meant something completely different from what he clearly stated and mathematically showed. You most certainly are denying relativity.

A purely spacelike separation in one frame can be a timelike separation in another frame, and vice versa. Space in one frame maps to time in another. Simultaneity can only be defined locally, for events with no significant spacelike or timelike separation (in other words, the very conditions where you evidently imagine different observers will for some reason disagree). It's really quite simple, and internally consistent, and verified with measurements. Your approach is more complicated, inconsistent, illogical, self-contradictory, and in conflict with observation, all because you are fixed on preserving your intuitive understanding of space and time.

[Grimble]

OK, so let's compare systems, to see which which best matches the criteria of :


We say:
1) Embankment and Train are each in their Inertial Frame of Reference
2) The observers on each have their own take on whether the strikes were simultaneous
3) Each observer can calculate the other's answer to (2)

Your model says:
1) Embankment and Train are each in their Inertial Frame of Reference
2) The observers on each say the strikes were simultaneous
3) Each observer can calculate the other's answer to (2), puts that answer aside, and declare the answer to (2) would actually be yes.

You tell me which is simpler

The second as it is the same for whoever is considered. For the first one has to know what each saw before being able to deduce simultaneity.

Great - but have you considered that if Relativity were a movie, the bits that are "not visualized", "fuzzy", etc are not problems with movie itself, but with the glasses that you're looking through? We're already fixing one area up, where you hadn't realised that "Frame of Reference" was always simply the good old "Inertial Frame of Reference". That's a major chunk of fuzziness right there! I'll tell you right now that the next chunk is your concept of time

And thank you for that, but that wasn't a confusion about relativity, only about what is the meaning of a term used in describing it.

No, we wouldn't. The requirement for simultaneity is not just that the lights reach the observer at the same time, but also that that observer is midway between where the strikes happened. That is not the case for the train observer. Remember, he measures his distance to the scorchmarks on the train, not the embankment. Sorry, I went though this in Post #44 - is it unclear, or are you disputing it?

No, I am sorry but I seem to have missed reading that post (there can be a lot to get through at one time:redface). I was wondering what you meant when you referred to scorch-marks in a previous post.
Now I have read it I still don't see how you can say the observer on the train was not midway between the scorch-marks on the train?

For the train observer, the lightning strikes happened*at the scorchmarks on the train. They are the ones stationary relative to him. So, was he equidistant to those? No - he can't be. When the strikes happened, a certain amount of time passed until the light reached the middle of the embankment. During that time, the train was moving, bringing that observer level towards the middle - which means that observer must have been closer to the left at strike-time.

But I don't understand why you say

During that time, the train was moving,

Not according to the passenger on the train it wasn't! You even say yourself

They are the ones stationary relative to him.

He must be and remain exactly midway between them as he has never moved relative to them.

Exactly - the three reference points come together to form a single Event, which is a single point in spacetime. That's true for both A and B. How can they not be simultaneous? Because a point only gains its coordinates in a Frame of Reference (yes, the Inertial Frame of Reference). One attribute of that coordinate is the Time coordinate - which brings us back to your OP that I quoted in Post # 173.

But in relativity all movement, any movement is relative. It can only be relative. So each clock moves and each clock must show the same difference when viewed from the other. That is fundamental to Relativity.

To claim that experiments show that this is not so and that two clocks do indeed show a difference, is proving that relativity is wrong!

And not just Special relativity, but the very concept of relativity itself! For that aspect is just as true of Galileian relativity!

There is no possible mechanism, within relativity, by which the clocks could be different.

So those experiments that show it are showing it for another reason other than relativity.

Just think about the simplest possible form of relativity, two points moving relative to one another.
Whatever one measures, the other will too! It has to be. that is what relativity means.

But I am sure that someone will show me how that simplest of views is mistaken?

[Grimble]

It doesn't depend on any relativity. What each "version" of relativity does is basically tell you how to change your axes to go from one observer to another, this way of changing axes is different in different "versions". What however none of them will do is say that a single point will suddenly become two different points, irrespective of how you change axes.

No, thinking about that you are right and one dot on a sheet of paper can never become two points, whatever one does to the axes. But that is not the point here. What we have are two separate, distinct points on separate sheets of paper.
On the one hand the lightning strikes are reflected by mirrors on the track, while on the other hand they are reflected by mirrors on the train. Separate mirrors, different individual photons reflected by different mirrors meeting at different places.
So it is not like one lamppost and two cars but more like two lampposts and two sets of cars.

[RobA]

No, I am sorry but I seem to have missed reading that post (there can be a lot to get through at one time:redface). I was wondering what you meant when you referred to scorch-marks in a previous post.

Awww - I was so pleased with coming up with that, and you entirely missed it Not to mention I've lost count how many times I've been referring to the scorchmarks !

Still, you know what they are now, though - yes? They've the visual representation of the space coordinates of where the lightening strikes hit. They graphically show how observers in differing inertial frames of reference view the same event.

But I don't understand why you say <the train was moving >

OK, let's say a train is moving from Left to Right relative to the embankment (and that the train extends beyond the embankment both front and back), and we have three observers :
- Edward in the middle of the Embankment
- Tom, on the train directly facing Edward when the strikes hit (or more precisely, who is midway between the scorchmarks on the train)
- Tara, on the train directly facing Edward when the light from the strikes meet (ie. like Edward, she gets the light from the strikes at the same time).

So, Tara must be sitting further towards the back of the train than Tom. This is because - as everybody agrees - there is a period of time between when the lightening strikes at A (say), and the light from that strike reaches Edward. During that time, the train has been moving forward relative to Edward (or, if you prefer, Edward has been moving back relative to the train). So, when the lightening strikes A, Tom was opposite Edward. By the time the light of the strike reaches Edward, Tara was opposite him - and meanwhile, Tom is now closer to the front of the train than Edward is.

So how does this work from the trains inertial frame of reference? OK, the train is stationary, and the Embankment's (and Edward with it) is flying Right to Left toward the back of the train (just as you see when you've been on an express train). Again, when the lightening hits A, Tom is opposite Edward. Then, during the time that the light is spreading out, the Embankment - and Edward with it - is still flying toward the back of the train. By the time the light reaches Edward, Edward has flown back to be opposite Tara.

So, all natural, symmetrical operations, each stationary in their own inertial frames of reference, and a consistent view of the events that are happening to them.

I still don't see how you can say the observer on the train was not midway between the scorch-marks on the train?

OK, in this example, we've got two observers on the train - Tom and Tara. In their inertial frame of reference, they're quite happy to consider that they're stationary.

- Tom IS midway between the scorchmarks on the train. So, does he reckon the strikes were simultaneous? No - because he doesn't receive the light from the two strikes at the same time. We know that for certain, since it's Tara (along with Edward) who did get the light from the strikes at the same time. So Tom is midway between the scorchmarks, but gets the light from the front BEFORE the light from the strike in the back. By definition, therefore, he reckons the strike in front happened BEFORE the one in the back.

- Tara receives the light from both strikes at the same time, so does she reckon the strikes were simultaneous? No, because when she measures the distances to the scorchmarks, she finds that she's not in the middle (she can't be, since that's where Tom is). Actually, she measures that she's closer to the scorchmark at the back. Since she got the light from front and back at the same time, then by definition she reckons the strike in front happened BEFORE the one in the back (since it had further to travel).

- Edward, of course, gets the light from both strikes at the same time, and subsequently measures that he also happens to be directly in the middle of the scorchmarks on the embankment.

Again, all natural, symmetrical operations, stationary in their own inertial frames of reference, and a consistent view of the events that are happening to them.

So, Edward reckons the strikes were simultaneous in his embankment's inertial frame of reference, but both Tom and Tara reckon the strike in the front happened BEFORE the one in the back in their train's inertial frame of reference. The reckoning of simultaneity is therefore dependent on the inertial frame of reference.

But in relativity all movement, any movement is relative. It can only be relative. So each clock moves and each clock must show the same difference when viewed from the other. That is fundamental to Relativity.

Yes, for any two inertial frames of reference, that is certainly the case. In fact, each clock will reckon all clocks in other inertial frames of reference to be running slower. However, when you break the symmetry by having just one of the clocks change it's inertial frame of reference (as per Einstein's example), then you can get a difference in time.

But I am sure that someone will show me how that simplest of views is mistaken?

Yes, Einstein did in that passage I quoted . So have you read Section 4 of "On the electrodynamics of moving bodies"?

[RobA]

It is the whole of Space where every point has the same time.

Interesting. If everywhere has clocks that are all synchronized, then there's none of this pesky length contraction and stuff, is there? After all, as light always takes 1 second to travel 1 light second of distance, then as everyone's clocks agree, then their lengths must agree as well. So everyone agrees on their seconds, and therefore their metres as well - right?

Hey, do you like quizzes ; I've got one I want us to try.

OK, I'll go first:

At 3pm, Alice and Bob see a white car go past them at 100 kph. Alice immediately chases after it at 90kph, leaving Bob standing.
Q1) How fast does Alice reckon the car is travelling away from her?
ANS: 10 kph

Q2) When Bob sees it's 4pm, how far does he reckon the car is from him?
ANS: 100km

When Alice sees it's 4pm,
Q3a) how far does she reckon she is from Bob?
ANS: 90km

Q3b) How far does she reckon she is from the car?
ANS: 10km

Q4) Add the answers to Q3a and Q3b, to give a distance that Alice reckons the car is from Bob
ANS: 100km

Q5) Compare this answer to Q2
ANS: They're the same

OK, your turn :
-------------------------
NOTE: For this quiz, assume a value of 300km per sec for the speed of light. All answers are to be in km per second, not fractions of c.

At 3pm, Alice and Bob see a beam of light go past them. Alice immediately chases after it at 290,000 km per sec, leaving Bob standing.
Q1) How fast does Alice reckon the beam is travelling away from her?
ANS:

Q2) When Bob sees it's 3:00:01 , how far does he reckon the beam is from him?
ANS:

When Alice sees it's 3:00:01,
Q3a) how far does she reckon she is from Bob?
ANS:

Q3b) How far does she reckon she is from the beam?
ANS:

Q4) Add the answers to Q3a and Q3b, to give a distance that Alice reckons the beam is from Bob
ANS:

Q5) Compare this answer to Q2
ANS:

Fun, eh? Thanks

[Grimble]

No. Sorry, but No Way. It is impossible to reconcile "every point has the same time." with "the travelled clock ... will be ... slow". (I'd have thought especially so for someone who distinguishes "with reference to" from "relatively to" )

Ah yes, apparently so, but indulge me for a moment. When we say 'the travelled clock' what do we mean? It cannot be the one in our frame as that, by definition, is stationary, so we are talking of a clock in another frame. Yes?
And we must be reading it from our frame, for if we were reading it from its frame it still would not be travelled.
So we are reading a clock from another frame and in doing so we find it is slow compared to what? - To our clock in our frame. So we have the clock measured in another frame, indeed the time measured in another frame is slow, is different from our local time.
Now taking that, together with the statement that every point has the same time, we are left with the inevitable conclusion that times measured in one frame from another frame read differently from times measured within the same frame. [b] That the act of measuring in another frame leads to an alteration in the time read, as a function of the relative velocity of those two frames.

This is the next issue that must be addressed. You are fixed on the idea that the Time axis is separate from the Space axes. That's understandable - it's our natural, intuitive world, and sure enough, everybody on earth shares the same experience. However, that is insufficient reason to assume it must be universally true. I remember discussing "Up" and "Down" with my Dad - being from the UK, he always thought it was a miracle that people didn't fall off Australia (even after I moved here, and he came to visit!) He never really grasped that "Up" and "Down" were just Relative terms.

I think you're making a similar mistake between Time and Space. Remember that quote I've thrown at you "One man's space is another man's time"? That's not just pithy, but we actually mean it in a literal sense.

I believe that there may well be truth in that quote, and that in certain circumstances it can no doubt be interpreted in such a way. But that does not make it a universal rule, so can you put it in context and give an example of where it might be used?

Firstly, can you state definitively why light moves at c for all Inertial Frames of Reference? Nope, neither can I.

Yes, it falls out quite naturally from the theory of relativity and the structure and nature of Space-time! (without the need for any esoteric maths, by simple logic and reasoning – surely one must question any interpretation of the theory where that is not so?)

However, given that it does - and every experiment to date supports that statement -

As I say it is a necessary conclusion that it has to be so.

then there are certain inevitable consequences .... and that's basically all that Relativity is. Once you accept that the universe behaves according to the postulates (that the Laws of physics hold in all Inertial Frames of Reference, and light travels at c in all Inertial Frames of Reference), then you must accept Einsteins Relativity since that is simply the mathematical working out of the consequences of those postulates. Subsequent experiments simply support that he didn't make a mistake

Agreed, I have always said so. I take pride in being a stout supporter of Einstein and his Theory.

One of the consequences is that every Inertial Frame of Reference will reckon that clocks in every other Inertial Frame of Reference run slower. Why? Again, it's a mathematical consequence - but you have to tell us if you're up to the math. It's spelt out and derived in "On the electrodynamics of moving bodies".

clocks in every other Inertial Frame of Reference run slower.

This is important; this means clocks that are moving with respect to our clock and measured to be slow compared to our clock. (We know that in their own frame that will not be the case as in their own frame they are the stationary clock.) So it is a clock in another frame, measured from our frame. So yes, any moving clock will be measured to run slow.
[quote]Again, we've covered this. One clock remains stationary in it's Inertial Frame of reference. The other changes it's Inertial Frame of Reference to turn around and return. The two cases are not reciprocal - and the maths support that. If you dispute that, then you will have to show where Einstein got his maths wrong (as I said, it is derived in "On the electrodynamics of moving bodies" from first principles from the postulates). Sorry, he does use a mathematical discussion, so you will have to show maths to support your position - but seriously, take a read. The statement is in section 4 "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks".
And he describes it very lucidly and I have no problem with that; but I still ask which clock is moving? . In relativity, movement is relative, nothing can be moving except relative to another body or coordinate system. So one can say one is moving just as one can say the other is moving. If one says that the moving clock is stationary then its frame is inertial and the other changes frame. It can be no other than reciprocal.
Look at what you are saying yourself.

One clock remains stationary in it's Inertial Frame of reference. The other changes it's Inertial Frame of Reference ...

But look at why they're going around. In post 44, I covered why the train observer wouldn't regard the strikes as simultaneous, in #177 you bring it up again. In post #156, I tell you that the clocks aren't reciprocal because one changes Inertial Frame of Reference, and you just brought that up again.

Because being reciprocal doesn't mean that they are the same. It means that if one takes the viewpoint of one or the other, the situation is the same.
That one can swap the labels and leave all else unchanged.
The one that is stationary has a single inertial frame of reference, while the moving one swaps frames or at least has a non-inertial frame. And either one can be taken as the stationary one and the other as the moving one.

Actually, I think the Relativity I've leant is a really nice picture. Two Inertial Frames of Reference, each with light travelling at c, and Relativity lets me translate coordinates of events from one into the other. Yes, it requires me to let go of things like a universal time axis, but I can understand that. After all, if speed of light is so unusual, and speed is simply distance / time (eg. miles per hour), then I would expect unusual things to happen with distance and time. I see that as a lot neater than the need to add clauses like "both see two events as simultaneous, but reckon that the other doesn't", or "putting results aside".

Yet you say that why the speed of light is constant is a puzzle to you.
Let me repeat that I have spent a long time studying and pondering these things, and that I agree with most of what you say. I don't agree that the constancy of the speed of light and its consequences are any more than simple mechanics that fall out quite naturally from Einstein's theory. His theory brought the elements into focus, that was his genius. After all it was there all along, it only required the genius of Einstein to recognise it.

[pzkpfw]

No, thinking about that you are right and one dot on a sheet of paper can never become two points, whatever one does to the axes. But that is not the point here. What we have are two separate, distinct points on separate sheets of paper.
On the one hand the lightning strikes are reflected by mirrors on the track, while on the other hand they are reflected by mirrors on the train. Separate mirrors, different individual photons reflected by different mirrors meeting at different places.
So it is not like one lamppost and two cars but more like two lampposts and two sets of cars.

In the part of the thought experiment with light from the ends of the train (depending on frame of reference) hitting the observer in the middle, that's an irrelevant quibble; and is the reason why an earlier poster introduced the idea of the detector worn by the train observer.

(Or in other words, yes, in the overall thought experiment the two observers are like two different dots on the paper; but in that part of this thread we were talking about what both observers see occur to one observer. As in, how both dots see what occurs to one of them. When the two flashes of light hit one dot on the paper, would the other dot disagree with that dot, about whether those flashes hit that dot at the same or different times? No.)

We are trying to explain (in that track of this thread) why you interpret the situation with the train observer incorrectly; mixing in what happens with the embankment observer at that point is a distraction. The crux of the paper is that the embankment observer must know the flashes to hit the train observer at different times. Since this can't contradict what the train observer sees (the train observer considered as a single location) this means the flashes can't have been simultaneous for the train observer. That's it for that part of the paper. We are looking at the train observer.

To re-cap that simplification:

The detector worn by the train observer is the thing at "one location". (Just as the observer themself is considered, in the basic thought experiment).
Photons hit the forward input of the detector and photons hit the rear input of the detector. (There is no separate track and train detector here. Those inputs are the same for all observers. They are the same photons in everyones version of the Universe.)
So when the detector lights green or red, all observers will see that same green or red.
So all observers (just as in the current understanding of the relativity of simultaenity) will agree whether or not the flashes hit the train observer at the same time; after all - they were the same photons hitting the same inputs of the same detector.

There is simply no room for your idea that the train observer would see the flashes at the same time (detector=green), and consider them simultaneous while at the same time the embankment observer would see the flashes hit the train observer at different times (expecting detector=red) while some how actually seeing detector=green.

(I'd add that observers agreeing with what occured in one location works in all directions. If the embankment observer is wearing a similar detector, and sees the flashes at the same time and therefore sees their detector shine green, the train observer will agree with those observations. He or she will see the flashes hit the embankment observer at the same time, and won't be surprised to see the detector light green. (Of course their interpretation will be that the flashes were simultaneous in the frame of the embankment, not the frame of the train.))

[RobA]

(Einstein' quote reinstated in full):

No. Sorry, but No Way. It is impossible to reconcile "every point has the same time." with
"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".

Ah yes, apparently so, but indulge me for a moment. When we say 'the travelled clock' what do we mean?

You know, I read the whole post, where you explain emphatically and clearly, that when you have two clocks in two frames, that what applies to one must be reciprocal and also appply to the other. So if our clock reads one in the other frame as slow, then the one in the other frame must read ours as slow as well.

And you know what - You're absolutely right. I totally agree with you ! Which just left me pondering one question - when were you going to address Einstein's quote above?

Then I came across this :

The one that is stationary has a single inertial frame of reference, while the moving one swaps frames or at least has a non-inertial frame. And either one can be taken as the stationary one

NO! You're using one of your pet definitions of Frame of Reference again, aren't you?

Let's reiterate the point from my Post #156
PLEASE: Forget any other definitions or usages of the terms "Frame" or "Frame of Reference".
In Special Relativity, we are ONLY concerned with Inertial Frames of Reference. Einstein was quite explicit about that.

So no, a clock that changes it's inertial frame of reference CANNOT be taken as stationary, and that situation is NOT reciprocal with a clock that does remain stationary in its inertial frame of reference.

Firstly, can you state definitively why light moves at c for all Inertial Frames of Reference? Nope, neither can I.

Yes, it falls out quite naturally from the theory of relativity ... Yet you say that why the speed of light is constant is a puzzle to you.
Let me repeat that I have spent a long time studying and pondering these things

No - the fact that "light moves at c" does not fall out from the Theory of Relativity. It is the initial postulate, the "Given", the "Starting Assumption". It does not come FROM the theory - the theory comes from IT.

You know, looking at all your posts, I'm wondering if you've fallen into the "Optical Illusion" trap. Time dilation is commonly demonstrated solely by looking at two clocks separating, and so both observers see eachothers clocks running slowly. The trap is that people can think that that is all that time dilation is - some simple observational effect, but time and clocks "really" all progress normally and at the same rate. In fact, time dilation is what happens with the clocks after allowing for observational factors.

Einstein made this quite clear, including the statement above. Clocks that were once synchronized, but are now side-by-side showing different times, are not just some observational effect. His preceeding example is also interesting.

Neptune is around 4 light hours from Earth. Suppose Edith on Earth performs the synchronization procedure with Ned on Neptune, by sending a radio signal at 1am. Ned gets this signal, adds the 4-hour flight time, and so sets his clock to 5am. This means that at 6am, Edith and Ned are happy that their clocks are synchronized - this it is "now" 6am in both places. You would say that that is the universal time, I would say that it's only for that Frame of Reference.

Now, at 7am, Sarah blasts off in a ship from Earth to Neptune, travelling at 0.9c. This means her trip takes her 266 minutes, according to both Edith and Ned. So, when she lands at Neptune, the local clocks are reading 11:26.

What time is her ship's clock reading? Well, Einstein has the answer - he says the clock will have been running slow by the good old 1/2 t v² / c².
So, with t=266 minutes and v=0.9, this works out that it's slow by 108 minutes, which means her clock is showing 9:38.

So all the clocks were synchonized, but now the Neptune clock showing 11:26 is side-by-side with the ship's clock showing 9:38. They're both correct, and there is no such thing as a universal time.

[Grimble]

Excuse me Gentlemen but I have an announcement to make.
As a result of all the questions and different scenarios and what is more your different views of those scenarios I have had to do some hard thinking!

One particular aspect of the train scenario has bothered me from the outset.
That was the idea, first proposed by Einstein himself, that the moving train is, or can be considered to be, moving away from one strike and toward the other.

This bothered me, as I say, for at first view it seems to fly in the face of the speed of light being constant. As in, how can it be? For it must then be faster toward one light and slower toward the other.

That this is resolved by saying one light struck before the other, still feels a little uncomfortable for that seems to be the only evidence for that happening.

Anyway having spent some time in deep contemplation, I have an admission to make: I have it all wrong!

I have fallen into the same trap as many and have been unable to clearly separate Special Relativity from Galileian Relativity.
I have been looking at the train and embankment, principally in Galileian terms! I have failed to appreciate that the train's Frame of reference, already having light travelling at the speed of light in it, is then subjected to another vector - the relative velocity of the train!

And we cannot just add that to the speed of light, can we? Do we not have to take into account the concept of 'rotation' of the frames?
Is that rotation with respect to the embankments frame?
In which direction(dimension?) is that rotation?
And how does that rotation affect what is seen, both for the non-rotated stationary frame and from the rotated frame itself?
So how would you describe it?
How does rotation work and what does it achieve?

And should tat be a different thread, for I think this one is done with as far as all that has gone is concerned?
What do you think PZKPFW?
What is the Moderator's view?

[Strange]

Anyway having spent some time in deep contemplation, I have an admission to make: I have it all wrong!

Hang on, chaps. I think it might be a trap.

Seriously, well done Grimble. It takes a brave person to make an admission like that.

One particular aspect of the train scenario has bothered me from the outset.
That was the idea, first proposed by Einstein himself, that the moving train is, or can be considered to be, moving away from one strike and toward the other.

This bothered me, as I say, for at first view it seems to fly in the face of the speed of light being constant. As in, how can it be? For it must then be faster toward one light and slower toward the other.

The key thing here is that by the time the light reaches the arrives, the observer has moved towards the location of one flash and away from the other. In other words, the observer can have a "closing speed" toward the source even though he sees the constant spped of light from the source.

That this is resolved by saying one light struck before the other, still feels a little uncomfortable for that seems to be the only evidence for that happening.

I don't think I would say it is "resolved" by saying that one light arrives before the other. Rather this is a consequence of the closing speed of the observer and the source plus the constant speed of light.

I'm not sure I understand your point about rotation but you are probably right that it should be a new thread.

[pzkpfw]

What do you think PZKPFW?

I think if you still come up with an odd personal interpretation that is different from current science, then you've not finished figuring this thing out.

(In the trains frame, the train is not moving, so the relative velocity of the train does not come into it.

From the embankment point of view, the train is moving and since the speed of light is not infinite, the train must (from the embankment point of view) move towards the approaching photons ahead and away from the approaching photons behind. So (from the embankment point of view) the train can't see the two flashes at the same time. After all, the train observer may have been adjacent to the embankment observer "when" the flashes occured, but won't be by the time the flashes reach them.

That view can't be contradicted by the train observer, as the flashes reaching him or or her are simply events that occur at his or her location - the leading edge of photons arriving at his or her body/eyes/whatever.)

What is the Moderator's view?

First up, you're done with arguing against the current science on the simultaenity of relativity. You've already had more than your share of ATM threads on the topic.

As for your new idea, the ATM forum is not the place for developing claims, it's for presenting fully formed claims. So - if you do happen to keep working on this new interpretation of yours, if you come back and present it it needs to be significantly different to this and your previous threads.

[RobA]

I have an admission to make: I have it all wrong!
I ... have been unable to clearly separate Special Relativity from Galileian Relativity.

First off, let me also congratulate you you being able to re-evaluate your position, make a change, an publicly state it.
Good work, and that's why we're here to help.

Having said that, that admission was not the admission that struck me most. Do you know what did?

This bothered me, as I say, for at first view it seems to fly in the face of the speed of light being constant

But the fact that both the Embankment and the Train view the same light as travelling at 'c' is the very embodiment of "The speed of light is constant for all observers". Exploring the implications of this (including resolving this type of counter-intuitive "paradox") is the very reason that Special Relativity was developed in the first place. If you're only now just getting comfortable with it, then that's great, but it's just the start.

For example, does "I have it all wrong!" mean that you now agree that events that were simultaneous for the Embankment observer are not simultaneous for the Train observers? Do you understand that this blows "every point has the same time" out of the water, and so you must let go of that nice universal-time-dimension visualisation? As I said before, it's all a direct consequence of the speed of light being constant.

Last but certainly not least, you must still train yourself to accept that in Special Relativity the terms "Frame" and "Frame of Reference" ALWAYS and EVERYWHERE mean INERTIAL Frame of Reference. Read that into all documents, and use ONLY that definition when you write. You spent the whole of post #192 based on a wrong definition, and you just have done so here as well ("the train's Frame of reference ... is then subjected to ... the relative velocity of the train!" - I don't think so!)

So please, before you go tearing off to explore rotations and other stuff, make sure that you have the foundations right first.

(and I'd still like to see your answers to my quiz in Post #191 )

[Grimble]

First off, let me also congratulate you you being able to re-evaluate your position, make a change, an publicly state it.
Good work, and that's why we're here to help.

Having said that, that admission was not the admission that struck me most. Do you know what did?



But the fact that both the Embankment and the Train view the same light as travelling at 'c' is the very embodiment of "The speed of light is constant for all observers". Exploring the implications of this (including resolving this type of counter-intuitive "paradox") is the very reason that Special Relativity was developed in the first place. If you're only now just getting comfortable with it, then that's great, but it's just the start.

For example, does "I have it all wrong!" mean that you now agree that events that were simultaneous for the Embankment observer are not simultaneous for the Train observers?

I have realised, with the help of 'scorchmarks' and lights that turn to green when hit by two photons, that my position was untenable! What one observer sees, all observers must see. So if the embankment observer sees simultaneity, the train observer must also see simultaneity for the embankment observer rather than for himself. (and that if one sees two cars hit the same lamppost then everyone will see the same two cars hit the same lamppost.

Do you understand that this blows "every point has the same time" out of the water, and so you must let go of that nice universal-time-dimension visualisation? As I said before, it's all a direct consequence of the speed of light being constant.

That is where I feel rotation may come into the picture, for if something is rotated, it cannot still be the same as it was ...

Last but certainly not least, you must still train yourself to accept that in Special Relativity the terms "Frame" and "Frame of Reference" ALWAYS and EVERYWHERE mean INERTIAL Frame of Reference. Read that into all documents, and use ONLY that definition when you write. You spent the whole of post #192 based on a wrong definition, and you just have done so here as well ("the train's Frame of reference ... is then subjected to ... the relative velocity of the train!" - I don't think so!)

Sorry, Rob, you are quite right my terminology is suspect at times. lol

How about if I say 'the train's frame of reference', observed from the embankment has the additional relative velocity to be taken into account'.

I am visualising (as I am very much a visual thinker) a frame of reference as being a set piece in the puzzle that is fixed, being either stationary (from its self-view) or moving with a constant velocity (from an external view).

So please, before you go tearing off to explore rotations and other stuff, make sure that you have the foundations right first.

(and I'd still like to see your answers to my quiz in Post #191 )

[Strange]

That is where I feel rotation may come into the picture, for if something is rotated, it cannot still be the same as it was ...

Did you see this comment, earlier; is this what you are thinking of?

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.

The transformation between one frame of reference and another is a rotation which changes "space" (distance) for one observer to "time" for another. This is also what the Minkowski diagrams you referred to earlier show.

[Grimble]

Interesting. If everywhere has clocks that are all synchronized, then there's none of this pesky length contraction and stuff, is there? After all, as light always takes 1 second to travel 1 light second of distance, then as everyone's clocks agree, then their lengths must agree as well. So everyone agrees on their seconds, and therefore their metres as well - right?

Hey, do you like quizzes ; I've got one I want us to try.

OK, I'll go first:

At 3pm, Alice and Bob see a white car go past them at 100 kph. Alice immediately chases after it at 90kph, leaving Bob standing.
Q1) How fast does Alice reckon the car is travelling away from her?
ANS: 10 kph

Q2) When Bob sees it's 4pm, how far does he reckon the car is from him?
ANS: 100km

When Alice sees it's 4pm,
Q3a) how far does she reckon she is from Bob?
ANS: 90km

Q3b) How far does she reckon she is from the car?
ANS: 10km

Q4) Add the answers to Q3a and Q3b, to give a distance that Alice reckons the car is from Bob
ANS: 100km

Q5) Compare this answer to Q2
ANS: They're the same

OK, your turn :
-------------------------
NOTE: For this quiz, assume a value of 300km per sec(300,000km per sec?) for the speed of light. All answers are to be in km per second, not fractions of c.

my addition highlighted.

At 3pm, Alice and Bob see a beam of light go past them. Alice immediately chases after it at 290,000 km per sec, leaving Bob standing.
Q1) How fast does Alice reckon the beam is travelling away from her?
ANS: 300,000km/sec

Q2) When Bob sees it's 3:00:01 , how far does he reckon the beam is from him?
ANS: 300,000km

When Alice sees it's 3:00:01,
Q3a) how far does she reckon she is from Bob?
ANS: 290,000km

Q3b) How far does she reckon she is from the beam?
ANS: 300km

Q4) Add the answers to Q3a and Q3b, to give a distance that Alice reckons the beam is from Bob
ANS: 590,000km

Q5) Compare this answer to Q2
ANS: Yet this is the answer that Alice has to agree is correct for that is the answer that the speed of light, relative to Bob, gives

Fun, eh? Thanks

[Grimble]

Did you see this comment, earlier; is this what you are thinking of?


The transformation between one frame of reference and another is a rotation which changes "space" (distance) for one observer to "time" for another. This is also what the Minkowski diagrams you referred to earlier show.

Yes, possibly, rotation(s) is a term that occurs quite often in descriptions of one frame viewed from another, but it seems quite tricky to actually pin down to what they are referring, I have some ideas but I would rather find out the real meaning. Can you help? (Please?)

[cjameshuff]

Yes, possibly, rotation(s) is a term that occurs quite often in descriptions of one frame viewed from another, but it seems quite tricky to actually pin down to what they are referring, I have some ideas but I would rather find out the real meaning. Can you help? (Please?)

This page has an applet demonstrating the transform:
http://webphysics.davidson.edu/apple...owski_FEL.html

Also: http://en.wikipedia.org/wiki/Squeeze_mapping

[Grimble]

This page has an applet demonstrating the transform:
http://webphysics.davidson.edu/apple...owski_FEL.html

Also: http://en.wikipedia.org/wiki/Squeeze_mapping

Thank you, I have had a look at them but while I can see how those relationships match exactly with what I, in my more workaday thinking have concluded, I have difficulty understanding how what is said in those links relates to relativity. The processes seem to be spot on, yet the association is left a little vague.

Perhaps I should start a new thread to address this?
But don't worry I am not going against any received wisdom - as far as I can see, so it won't be an ATM thread, merely one to check my understanding is correct.

Yes I think that would be the best way to do it.

[RobA]

I have realised, with the help of 'scorchmarks' and lights that turn to green when hit by two photons, that my position was untenable! What one observer sees, all observers must see. So if the embankment observer sees simultaneity, the train observer must also see simultaneity for the embankment observer rather than for himself. (and that if one sees two cars hit the same lamppost then everyone will see the same two cars hit the same lamppost.

Exactly right It takes a lot of getting used to, and you have to keep your wits about you, but it's fascinating to see how things which appear impossible (like simultaneity being different) actually work together just right, to remain consistent for everyone. And 100% on the quiz, by the way ! A number of people think they accept that light is at c for all observers, but then answer 10,00km/s on Q1.

Sorry, Rob, you are quite right my terminology is suspect at times. lol

Yes, you have to watch that (otherwise you might find yourself thrown back in here for all the wrong reasons ). Seriously, you've seen how easy it is to get one wrong idea in something like this, and then when that gets built upon, it's a pain to unlearn.

I am visualising (as I am very much a visual thinker) a frame of reference as being a set piece in the puzzle that is fixed, being either stationary (from its self-view) or moving with a constant velocity (from an external view). That is where I feel rotation may come into the picture, for if something is rotated, it cannot still be the same as it was ...

As you know, 4-d spacetime is impossible to visualise, so the simplest thing to do is lose a dimension. Imagine a sheet of paper glued onto the bottom of a glass cube, so the paper is Space and the z-dimension is actually a t "time" dimension. Now, thanks to this thread, you'll appreciate that since all the points on the paper are at the same time (t=0), then this cube models a single frame of reference. Say this is Alice's FoR.

So what happens when Bob's FoR goes by? My mental picture originally was that the cube was tilted - so the Y axis (or edge of the cube) was still along the ground, but the X axis (ie. in Bob's direction of travel) was raised off the ground ("the ground", of course, being synonomous with Alice's paper). So 1 metre along Bob's X axis is shortened compared to 1 metre in Alice's, with the difference being accounted for by being raised in Alice's Z (or time). Remember that quote "One man's space is another man's time"? Also, Bob's Z (or time) axis is tilted compared to Alice's, so his passage of time differs.

Looking at some other sites (including those good ones from cjameshuff), I'd modify that to say rather than Bob's cube being rotated, it's actually squeezed, so as the X axis gets raised, the Time axis drops.

But GREAT BIG DISCLAIMER here - this is the visualisation that I've built up, but I'm a layman and much less sure on this than my other posts - ie. I may have it wrong (any corrections gratefully received).

So yes, best thing to do is post in Q & A, and you'll get lots more useful links.

[Bob Angstrom]

As you know, 4-d spacetime is impossible to visualise,

Some nineteenth century artists discovered a clever aide for visualizing 4-D space. A mirror is a 2-D surface but the images we see in a mirror are 3-D. A reflecting sphere is a 3-D surface but the images we see may be the closest we can get to visualizing 4-D space. Picasso and Dali worked with 4-D space but nobody does 4-D better than Escher. Here he demonstrates the technique.
http://images.search.yahoo.com/searc...lecting+sphere

[Tobin Dax]

Some nineteenth century artists discovered a clever aide for visualizing 4-D space. A mirror is a 2-D surface but the images we see in a mirror are 3-D. A reflecting sphere is a 3-D surface but the images we see may be the closest we can get to visualizing 4-D space. Picasso and Dali worked with 4-D space but nobody does 4-D better than Escher. Here he demonstrates the technique.
http://images.search.yahoo.com/searc...lecting+sphere

The surface of a sphere is two-dimensional, like every other surface in 3-d space. The only difference between a flat mirror and a spherical mirror is the geometry.