Why is relativity so hard to learn?[1]

[Dave_Oblad]

Hi Folks,

I'd like my above post to remain in this thread "Asis". But I have been asked not to jump so far ahead (sorry). So I will take a back seat and watch (and learn). Hopefully, when the time is right, we will return to the above questions. Maybe the answer to my two questions above will become obvious en-route. I'll wait and see.

Jorrie appears to have a stepped plan for this presentation of which I'm scrambling the desired order. I apologize for such. I'm sure I will still have many questions along this presentation, but will ask such within a structured presentation at the correct time.

Best wishes all,
Dave :^)

[BurtJordaan]

So how did isotropy 'magically' return after the acceleration stopped? In order to understand that, we must turn to the spacetime structure - not to time (yet), because we did not really use time in the interferometer experiment. Spacetime structure will be topic of the next part.

Most readers have probably seen Minkowski spacetime diagrams, which are an attempt to show spacetime structures for two relatively moving inertial observers. It is non-controversial, scientifically correct, but at the same time very intimidating to many readers, so I do not want to dwell on them too much.

Minkowski spacetime

The 'normal' orthogonal axes x and ct, with the squares formed by the dotted lines represents the spacetime structure for the reference observer (say it is Bob). The oblique axes x' and ct', with the 'parallelograms' instead of squares are the spacetime structure for the relatively moving observer (say Alice), as seen by Bob. This is a crucial caveat, because Alice could just as well have been chosen as the reference observer, because she would have seen her own structure as orthognal and Bob's as parallelograms, just slanted in the opposite direction.

To make things easier to swallow, Lewis Carrol Epstein has developed (c.a. 1981) a type of diagram called "space-propertime diagram", nowadays simply referred to as an Epstein diagram. It is a clever mix of Bob's space and Alice's time (or vice versa) that creates a perfectly symmetrical view of the spacetime structures of both, from either perspective.

Epstein Spacepropertime

If we take the blue structure as Bob's and the red structure as Alice's, it is easy to see that we could just rotate both of them around the origin so that Alice's +cT points upwards on the page and Bob's more to the left, and things will essentially 'look' the same. In fact, we can rotate the two structures together in any direction, through any angle and as long as we do not change the angle between them, things will still essentially look the same, wherever we leave them to point.

The moment we rotate one structure relative to the other, we lose the perfect symmetry, because now we will have a curved cT axes for at least one of the participants. This is what acceleration does. It is the process of changing the angle between two structures. Once the acceleration stops, the asymmetry remains, unless we erase this history and set up a new structure with a new constant angle between the two structures.

This is where the scientific side of this thread meets the philosophical side. Unless we know the dynamics history of Alice and Bob, we have no way of establishing which one is going to "age less" in the first part of the so-called "twin-paradox" (meaning the part until Alice turns around to head back home, where she obviously have to accelerate). In fact, "aging" is a slight corruption of the science, it is really about who measures the least elapsed propertime when and where. In the next piece, I will attempt to show this on an Epstein diagram.

I know this is still very unsatisfactory (and patchy) for many readers, and I should spend much more time on explaining the diagrams, as well as on the philosophy of the science behind it. I have limited time to spend on making progress, so I appeal for patience. Please ask questions about the diagrams used and any spacetime structure issues. I would like to get some guidance from readers as to what aspects they perceive as the most unclear, so that we can patch it up together. In the end it might be a useful community project. ;)

-Jorrie

[mitchellmckain]

Hi all,
Given:
Ship(A) & Ship(B) are at right angles with Zero Velocity. (Ref=CMB)
Ships are separated by 300,000 Km (one light second).
Ship(A) shoots Laser Beam at Right Angle Mirror.
Beam hits Mirror and bounces 90' to Ship(B) perfectly on Target.

Given:
Both ships then accelerate identically to 86% Light Speed simultaneously and go inertial.
Both ships are still at a perfect 90' angle from each other, coasting, on perfect parallel paths.

...

So let's start the discussion on a SHARED FRAME with this simple example provided.

Question-1: Why does Ship(A) observe Ship(B) to still be located at a perfect right angle?

Because ship B is not moving with respect to ship A.

Question-2: Why does Ship(A) not need to lead the Target to make up for the Light Transit Delay?

Because ship B is not moving with respect to ship A.


The interesting thing to ask in special relativity is what does someone in a different inertial frame see? So introduce another observer C who is watching these two ships pass him at that 86% of the speed of light. According to C, Ship A DOES lead the target in order for his beam of light to reach ship B. How is this possible? Lorentz contraction shortens the lengths of ship A in the direction of motion (according to observer C) and thus changes the angle of the mirror, and thus the direction of the beam of light according to observer C.

[hyksos]

I just realized that friendly forum users were showing Epstein diagrams to Dave O ... on this forum, 4 years ago.

Four years ago. I mean uh.. no offense but my-face-when. My-face-when four years ago.

[bangstrom]

The interesting thing to ask in special relativity is what does someone in a different inertial frame see? So introduce another observer C who is watching these two ships pass him at that 86% of the speed of light. According to C, Ship A DOES lead the target in order for his beam of light to reach ship B. How is this possible? Lorentz contraction shortens the lengths of ship A in the direction of motion (according to observer C) and thus changes the angle of the mirror, and thus the direction of the beam of light according to observer C.

Lorentz contraction is essentially a rotation through space so, if observer C is between the two passing ships, C should observe both ships to be rotated as if traveling a bit sideways with the tail ends of the ships closer and the nose ends pointed away. From that perspective, both ships would appear shorter and the rotation would redirect the mirror.

[BurtJordaan]

Lorentz contraction is essentially a rotation through space so, if observer C is between the two passing ships, C should observe both ships to be rotated as if traveling a bit sideways with the tail ends of the ships closer and the nose ends pointed away. From that perspective, both ships would appear shorter and the rotation would redirect the mirror.

Lorentz contraction is not a rotation through space, but can be viewed as a rotation in spacetime. There is huge difference between the two. Lorentz contraction do not "redirect" any mirrors.

[bangstrom]

Lorentz contraction is not a rotation through space, but can be viewed as a rotation in spacetime. There is huge difference between the two. Lorentz contraction do not "redirect" any mirrors.

Yes, you stated it more precisely than I did. Lorentz contraction is a rotation through 4-D spacetime and the rotation of the spaceships is how they appear to remote observer C but not an actual rotation.

[BurtJordaan]

If we take the blue structure as Bob's and the red structure as Alice's, it is easy to see that we could just rotate both of them around the origin so that Alice's +cT points upwards on the page and Bob's more to the left, and things will essentially 'look' the same. In fact, we can rotate the two structures together in any direction, through any angle and as long as we do not change the angle between them, things will still essentially look the same, wherever we leave them to point.

More on the Epstein Diagram

Despite the above statement: "can rotate the two structures together in any direction, through any angle", it is always easier to point the reference observer's cT vector upward and cT of the other observer to the right. The angle between them be must smaller than 90 degrees, because 90 degrees would represent the cT vector of light, relative to the reference observer. We will talk about light on the Epstein diagram below, but first take a good look at the situation with a relative speed of 0.6c.

Epstein for relative speed 0.6c

We can easily see the reciprocal nature of space and time for inertial observers, because each observes the others space and time components as a projection onto their own spacetime structure. This is what is meant by "time dilation and length contraction are relative and reciprocal". It is a rotated view in spacetime (not in space alone).

A common misconception of Epstein diagrams is that the (black) grid represents Newton's "absolute spacetime" and that anything that moves relative to this grid must somehow experience slower clocks and length contraction, depending on how fast they move relative to this spacetime. This is incorrect and the grid marks are only there for convenience. All motions are purely relative and no clocks tick faster or slower than any others. All inertial observers are treated as equivalent in all respects and everything is reciprocal, as long as no acceleration is involved (i.e. the relative angle between frames do not change).

Finally, how is the propagation of light being depicted on Epstein diagrams? The simplest view is that Blue observes light to move along (or parallel to) the blue x axis and Red observes light to move along (or parallel to) the red x axis. In general, Epstein diagrams contain a meta-physical element here,^[a] because it should be interpreted that light spreads out in a circle in a 2-D space-propertime^[b], but that the different observers can only observe its effects along (or parallel to) their own spatial axes.

More philosophically, it's as if light is the only dimension existing, but we are bound to see it as space and time, with 3 spatial dimensions and one of time. But, one must be careful not to draw to many physical conclusions from this philosophy. Enough food for thought for now...


-Jorrie

[a] Epstein himself called the space-propertime diagram a "myth", albeit a very useful one. I would rather call it just a "view of spacetime". All relativistic diagrams are no more than attempts to make the unintuitive aspects of relativity more palatable.

[b] We know that relative to any point source, light spreads out spatially as a sphere in 3-D space. In an Epstein diagram, if we could portray all 4 dimensions on paper, light spreads out as a 4-D 'hypersphere'. The whole concept then boils down to 5 dimensions, 3 of space, one of time and one around which points on the hypersphere can be rotated to indicate observable relative speed. Such a concept requires complex math, so should be outside the scope of this discussion. The 2-D Epstein is however rather intuitive.

[Faradave]

Hi Dave_O,

Question-1: Why does Ship(A) observe Ship(B) to still be located at a perfect right angle?

Here's one more version of the answer.

Because when you say both ships are "moving" in parallel, it's the same as saying they are at rest, with the observer who declares them to be "moving" is traveling in the opposite direction. The ships see and aim at each other exactly as if they are in the same inertial rest frame because they are.*

If you personally perceive the rockets to be moving, you should consider the photons exchanged between the rockets to have gone along for the ride, picking up a horizontal velocity component to compensate. The situation then becomes Einstein's light clock with the "moving" perspective seeing a diagonal light path and the clock's resting perspective seeing a straight light path.

*Accelerations (i.e. changing inertial frames) by gravity or by applied force will alter things.

[Dave_Oblad]

Hi all,

Yep, as Hyksos noticed, Jorrie has been tutoring me for quite some time. I came to this site with zero understanding of SR and GR. And the first time I saw these diagrams, the look on my face would be best described as Zombie-Like.. lol. But, Jorrie created a monster. I started to see some issues and took off into left field (a bit) with my Own Model, which I won't bring up here.

Mitch was going to use Lorentz contraction to explain the beam path leading the Target. But it would still (effectively) lead the other Ship(B), even if the Laser and Mirror were switched (Laser pointing forward to the Mirror). In that case such contraction would aim the beam far behind Ship(B) and that doesn't happen.

Anyway, I don't want to derail Jorrie's plan, so let's drop my Problem until it's time by Jorrie's watch.. lol.

Anyway, for those of you that also got that Zombie look in your eyes when Jorrie displayed his diagrams, let me give a simple paraphrase of what has transpired in his post (hopefully, without introducing a bunch of errors needing corrections.. lol).

Jorrie introduced Alice and Bob. Both are heading towards a starting line. When they cross the line at the same time, the Race starts and both Alice and Bob click their start/stop watches (get their clocks in sync). While Bob, who is going very slow, continues straight on towards the Finish Line, Alice (who was gong very fast) takes the long scenic route. Ultimately.. Alice returns and manages to cross the Finish Line at the exact same time as Bob. They both click their stop watches at the same time when they cross the Finish Line.

So we know the same trip from start to finish took the same amount of time as witnessed by the Audience watching the Race. (talk about the Turtle and the Hare?)

We know (now anyway) that Alice and Bob are non-identical Twins.. born at the same time and were the same age.

We also know that Alice took a much longer scenic route than Bob. For both to have started at the same time and for both to have finished with a tie, that Alice had to be going a whole lot faster than Bob (she is the Hare and Bob is the Turtle). We know that the path Alice took was a lot longer (the scenic route) than Bob's straight path.

But if we look at both Alice's and Bob's Stop watches we see something very strange. Bob's stop-watch says the Race took 1 hour but Alice's stop-watch says the Race lasted only 45 minutes. Somehow, Bob got older than Alice by 15 minutes during the Race. Why?

The answer is that Alice took a much longer path than Bob and of course.. much faster than Bob. I'll let Jorrie fill you in on why Alice aged slower than Bob. But for you dummies out there (like me) suffice it to say that Alice was exposed to a lot more Space-Wind than Bob.. in the same amount of Time. Again, this Space-Wind is called Space-Time for those of you keeping up.

I might also mention that the Audience thought the Race lasted a little over an hour. So whose clocks are right? The Audience or Bob or Alice? They all are right.. lol.

This is called Time Dilation in Relativity (although I prefer Clock Dilation, for personal reasons). The Alice and Bob (Race) example is called: the Twin-Paradox.

Oh.. Hi Faradave. Not bad.. since the speed of light didn't change and the diagonal path would have to take longer, we might say that a local stationary observer would say it took a bit longer than a second for the light to bridge the diagonal gap between Ships. Also, if both Ships synced their personal clocks at the start, then both Ship's clocks would still be in sync.

If Ship(A) send a signal on his Laser Beam that had a Time-Stamp, the receiver at Ship(B) would see that their Local Time is a bit ahead of that from Ship(A). The same would be true in reverse. Both Ships would notice that their local Clock Time as being a bit ahead of the other. Right? Any counter argument would only be true.. if the Information travel time between Ships were instantaneous.. and that's not going to happen.

Best wishes all,
Dave :^)

[Faradave]

since the speed of light didn't change and the diagonal path would have to take longer, we might say that a local stationary observer would say it took a bit longer than a second for the light to bridge the diagonal gap between Ships.

You've given the basis for "time dilation", though I don't care for that particular term.

if both Ships synced their personal clocks at the start, then both Ship's clocks would still be in sync.

Yup!

If Ship(A) send a signal on his Laser Beam that had a Time-Stamp, the receiver at Ship(B) would see that their Local Time is a bit ahead of that from Ship(A). The same would be true in reverse.

You'd find a delay consistent with finite speed limit c. To the extent you accept the synchronization scheme, you would have done a "one-way speed of light" measurement.

If Earth and Mars happen to be close and aligned at a point where instantaneous velocities are essentially equal (parallel), it will still take about 14 minutes to get a signal from either one to the other. In a situation where the bodies are (momentarily) relatively at rest, they can point their antennae directly at each other.

[Dave_Oblad]

Hi Faradave,

To the extent you accept the synchronization scheme, you would have done a "one-way speed of light" measurement.

Wow, I hadn't realized that. That gives me a host of new ideas.. but not here of course.

Best Regards,
Dave :^)

[BurtJordaan]

Jorrie introduced Alice and Bob. Both are heading towards a starting line. When they cross the line at the same time, the Race starts and both Alice and Bob click their start/stop watches (get their clocks in sync). While Bob, who is going very slow, continues straight on towards the Finish Line, Alice (who was gong very fast) takes the long scenic route. Ultimately.. Alice returns and manages to cross the Finish Line at the exact same time as Bob. They both click their stop watches at the same time when they cross the Finish Line.

Dave, you are doing it again... ;) Running ahead, mixing in things not touched in what I'm trying to bring across here. Alice and Bob cannot "both click their stop watches at the same time when they cross the Finish Line", because Alice is still going one-way only. Neither of them are going "slow or fast", they are just moving relative to each other. Do you see the problem?

I guess that you haven't read my piece no [5] yet when you wrote your post?

[BurtJordaan]

If Earth and Mars happen to be close and aligned at a point where instantaneous velocities are essentially equal (parallel), it will still take about 14 minutes to get a signal from either one to the other. In a situation where the bodies are (momentarily) relatively at rest, they can point their antennae directly at each other.

FD, I don't follow what you are saying here. Given that there is a 14 light-minutes distance between them, wouldn't they have to be at relative rest for at least that 14 minutes?

[BurtJordaan]

Epstein diagrams and acceleration (edited)

The moment we rotate one structure relative to the other, we lose the perfect symmetry, because now we will have a curved cT axes for at least one of the participants. This is what acceleration does. It is the process of changing the angle between two structures. Once the acceleration stops, the asymmetry remains, unless we erase this history and set up a new structure with a new constant angle between the two structures.

Epstein acceleration

The figure shows the Space-Propertime (SPt) path of an object (or person, say Alice) that is accelerated to the right at a constant acceleration^[a] according to Bob, who is an inertial observer. The curve shown is a perfectly circular arc around a point on Bob's x-axis. If that point is about one light year from Bob, the initial force felt by Alice would be about the same as the "pull" of gravity here on earth's surface. More about that later.

The first important thing is that the acceleration has changed Alice's spacetime structure - it has gradually rotated relative to Bob's structure. Even more importantly, the length of the space-propertime arc that Alice has traversed (her SPt path), is of the same length as the up-arrow of Bob's structure (which is Bob's SPt path). But the vertical spacetime displacement that Alice has traversed (i.e. the vertical distance from the x-axis to the end of the arc) is obviously less than both Alice and Bob's actual SPt paths (which are of the same length).

So does this mean that the acceleration has 'slowed down' Alice's clock relative to Bob's? No, it simply means that Alice ended up with less displacement in the direction than what Bob has. The clocks were not influenced by the acceleration. The vertical SPt displacement is called the spacetime interval in relativity - in this case it is the spacetime interval between the two events: "Alice fires her rocket to depart" and "Alice switches off her rocket to coast".

Logical conclusion: their clocks ran the same, but they recorded different times because their SPt vertical displacements were different. This holds the key to the so-called "twin paradox". Before we go on to discuss that, (as "homework" ;)) please consider what would have happened if, instead of switching off the rocket, Alice has rapidly turned around and applied the exact same (reverse) acceleration for exactly the same time on her clock. And then switched off the rocket to coast again.

-Jorrie

Note [a]: A constant acceleration from Bob's perspective is actually an increasing acceleration from Alice's perspective. It is impossible to maintain for long, because the acceleration (the g's) on Alice would increase exponentially and so would the energy required to deliver it. After considering the solution to the the 'twin paradox', we can turn to a more realistic acceleration scenario.

PS. This is fairly brief and perhaps overly terse, but one has to eat this elephant one piece at a time... ;)

[Faradave]

Given that there is a 14 light-minutes distance between them, wouldn't they have to be at relative rest for at least that 14 minutes?

I think you're right, Jorrie. It was a mistake to change the analogy, especially to one where the bodies are constantly (and differently) accelerating.

[BurtJordaan]

Epstein diagrams and acceleration (Continued)
Before we go on to discuss that, (as "homework" ;)) please consider what would have happened if, instead of switching off the rocket, Alice has rapidly turned around and applied the exact same (reverse) acceleration for exactly the same time on her clock. And then switched off the rocket to coast again.

I'm not going to answer the "homework" question, but rather discuss the case where Alice just switches off the rocket and coasts further, as shown below. This is where many a newcomer have difficulties.

Epstein accelerate and coast

It is easy to see and accept that during Alice's acceleration phase, things were not symmetrical and not reciprocal. But once that rocket has been shut down, things are symmetrical again, i.e. both are inertially moving relative to the other and should view the other one as "aging less". Yet we know that the longer this coasting phase lasts, the more the difference in elapsed time becomes between the two. How does relativity get out of this conundrum?

Many quite reasonable answers to this question exists, among them: "just look at the Epstein diagram and judge the vertical heights of the final arrow heads". One can build long arguments around this one, but what is the best way to wrap ones head around it? For me the best (non-mathematical) answer lurks in the change in spacetime structure. It is easy to see that before the acceleration, Alice and Bob have shared the same spacetime structure. During the acceleration, only Alice's spacetime is distorted and her measures of space and time are changed. She now measures less time and less distance between events than what Bob does.

Should Alice apply "rocket braking" until she is stationary in Bob's structure again, her structure and her measures return to be the same as Bob's again. But in the meantime, her elapsed time and spatial displacement have accumulated differently during the relative movement, and this includes both the acceleration and the coasting phases. So even if there was no final "rocket braking" and she coasted on, the conclusion is the same: Alice experienced (and physically measured) less elapsed time and spatial displacement than what Bob measured between the same two events.

I'm sure there remains many questions, because it is a difficult concept to wrap ones head completely around.

-Jorrie

[Dave_Oblad]

Hi Jorrie,

Sorry, I didn't realize your point was Acceleration and Deceleration. I thought you were just showing the usefulness of the Diagrams to represent the Relative differences at different Relative velocities between travelers.

Usually, one avoids the issues of Acceleration and Deceleration with such shortcuts as saying "If Alice could instantly jump from one Speed to the next Speed" then the diagrams can show you how things had changed.

Thus my contribution avoided the Acceleration and Deceleration aspects.. by having everyone holding a constant velocity as coasting (being inertial) with the only difference between Alice and Bob being their different path lengths for a test that had identical start and stop points.

Remember the Title of the OP?

If your intention was to teach Relativity to College Graduates, you are doing fine. But if your Target audience was middle school children, then the sudden introduction of such large words and concepts kind of exemplifies the OP.

Yes, I get the concepts so far are rather basic.. to you. But for us Dummies, most of us would have tuned out when you jumped from a Space Lab (good start) to the Twin-Paradox.. without delving deeper into Frames first.

The 'normal' orthogonal axes x and ct, with the squares formed by the dotted lines represents the spacetime structure for the reference observer (say it is Bob). The oblique axes x' and ct', with the 'parallelograms' instead of squares are the spacetime structure for the relatively moving observer (say Alice), as seen by Bob. This is a crucial caveat, because Alice could just as well have been chosen as the reference observer, because she would have seen her own structure as orthognal and Bob's as parallelograms, just slanted in the opposite direction.

I was going to highlight terms used in your above quote.. that have little meaning to the average "Joe on the street", until I realized I would be highlighting almost the whole paragraph. So I selected just a small piece as an example of college level language.

So, I guess what I'm saying is that I don't understand what your Target Audience was intended to be. It almost seems like your intended audience are those that already know this stuff. Meanwhile, the much larger audience of folks passing through, hoping to get some education on Relativity, are going to tune out as soon as they start feeling dumb and don't understand the language and terms you are using.

Even I didn't get you were jumping directly into Acceleration and Deceleration, which are usually avoided in SR.. until the basics are better understood. How did we get from a "Lab floating in Space" to your "Minkowski spacetime diagrams" in one sudden post leap?

Most readers have probably seen Minkowski spacetime diagrams, which are an attempt to show spacetime structures for two relatively moving inertial observers. It is non-controversial, scientifically correct, but at the same time very intimidating to many readers, so I do not want to dwell on them too much.

Most readers? Minkowski Diagrams? Spacetime structures? Twisting Alice's Space-time structure to match Bob's Space-time structure?

Logical conclusion: their clocks ran the same, but they recorded different times because their SPt vertical displacements were different.

From the above quote I would have to conclude that we are not comparing Alice's Clock to Alice's Clock, as that would be silly. So.. we must be comparing Alice's Clock to Bob's Clock. So how can they run the same and yet be different?

Is it statements like this that make Relativity so hard to learn?

Is it the intent of this thread to educate dummies like myself?

Diagrams make perfect sense if one has laid down a decent foundation first. (IMHO)

I personally thought it a good idea to explain the mechanics behind Frames before showing how Frames are represented in diagrams.. but that's just my preference it taking it real slow so folks like me can keep up.

Anyway, since my "Meat and Potatoes" approach appears at odds with the Purity you wish to maintain, I should just take a back seat and see how this goes.

Oh, I see we cross posted. Ok, your last post was a bit better, but I would still have dummied down the language a bit more.

Truly.. best wishes and highest regards,
Dave :^)

[Dave_Oblad]

Hi Jorrie,

For me the best (non-mathematical) answer lurks in the change in spacetime structure.

Can we clear this up a bit?

Did the structure of Space-Time itself physically change because Alice accelerated? Or was it Alice and her clocks that changed structure because she accelerated through Space-Time?

Best Regards,
Dave :^)

[BurtJordaan]

Hi Dave. Thanks for the inputs. This is exactly what I'm after, a critique of the current teaching methods and of the approach that I propose here. A fresh way of helping people that have already battled with relativity, to wrap their heads around it. And we have many of them on this forum, but none are 'dummies'!

Remember the Title of the OP?

If your intention was to teach Relativity to College Graduates, you are doing fine. But if your Target audience was middle school children, then the sudden introduction of such large words and concepts kind of exemplifies the OP.

I may not have stated it clearly, but the intention is to get all levels interested. Those who already know can help with the pedagogy, those who have just started can say what they do not understand (either of the present paradigm or in my proposal) and the middle group can test the paradigm(s) against their interpretations and where different, question the paradigm/interpretations.

Even I didn't get you were jumping directly into Acceleration and Deceleration, which are usually avoided in SR.. until the basics are better understood. How did we get from a "Lab floating in Space" to your "Minkowski spacetime diagrams" in one sudden post leap?

As I mentioned in the OP, Nigel Calder did something even more sever in his "Layman's guide" - he jumped straight into gravity and the cosmos and then worked his way down to SR. Now he is good and he was writing a book. It may be a little ambitious for a chat forum, but I thought acceleration could perhaps be a sort of middle ground. But it seems that you reckon it would be too much for beginners? Perhaps should be written a bit better and more explanatory? Yes, I can live with this, but is the concept really that bad?

Logical conclusion: their clocks ran the same, but they recorded different times because their SPt vertical displacements were different.

From the above quote I would have to conclude that we are not comparing Alice's Clock to Alice's Clock, as that would be silly. So.. we must be comparing Alice's Clock to Bob's Clock. So how can they run the same and yet be different?

It is exactly this sort of conundrum that I want to help people to wrap their heads around. And if you say that you did not follow the logic, then I must try harder. You may not be a typical learner, because you know a lot and have your own 'private model' that is here and there in conflict with relativity, but so have many participants on this forum.

It seems to me that most of the relativity discussions on this forum are initiated by people that already know quite a bit of relativity, but then decided that they can do better - or at least have an interpretation that they feel more comfortable with. Unfortunately, most (not all) of those interpretations seem to fail when put to the acid test.

[BurtJordaan]

Did the structure of Space-Time itself physically change because Alice accelerated? Or was it Alice and her clocks that changed structure because she accelerated through Space-Time?

The larger structure of spacetime can't change due to whatever Alice does, but isn't it reasonable to argue that her own, private spacetime structure has changed relative to Bob's? Remember that they have started with identical structures. These "identical structures" could have been different to the universe's spacetime structure, which happens to be undetectable. :(

That is if the universe even has a spacetime structure...

[Faradave]

The larger structure of spacetime can't change due to whatever Alice does, but isn't it reasonable to argue that her own, private spacetime structure has changed relative to Bob's?

I refer to the underlying structure as "the continuum" upon which various spacetimes may be drawn, with no particular one privileged.* The continuum is thus, like a table top upon which graph paper may be laid in a great variety of orientations (i.e. reference frames). The continuum provides separation of events, which are then mapped according to each observer's reference frame. Though the table top is understood to be 4D, it is convenient and much simpler to consider it in 2D slices. Any slice which is to depict action will have one coordinate with unidirectional freedom (proper time) and one with bidirectional freedom (proper space).

*That doesn't mean we can't have some personally "preferred" frames, just none that are somehow preferred by the laws of physics. For example, I prefer the universality of the cosmic background radiation rest frame.

[BurtJordaan]

The continuum provides separation of events, which are then mapped according to each observer's reference frame.

Well, pure SR and GR seem to not agree with you. Such an unobservable continuum is no better than an absolute spacetime of Newton. It is the individual spacetime structures that keep individual events separate for each of us. And we all disagree on "how separate" they are. We each have our own unique table to put our cards on.

[TheVat]

I took (perhaps wrongly) FDave's "tabletop" to be a continuum in the sense of a model that explains variation as involving gradual quantitative transitions without abrupt changes or discontinuities. IOW, a reminder that GR/SR are non-quantum. A marble rolls smoothly on this "table." A continuum provides a certain kind of separation (non-"jumpy") without dictating anything about a personal FoR. It is not observable, because it's really only a nebulous kind of "permission" to move smoothly. I have no idea if this would be any help to the thread purpose, but it does give me a chance to say that Jorrie has become, in my eyes, a thoroughly awesome person - and teacher of relativity. Wow. I am going back to read the whole thread, something I do too rarely.

[BurtJordaan]

A continuum provides a certain kind of separation (non-"jumpy") without dictating anything about a personal FoR. It is not observable, because it's really only a nebulous kind of "permission" to move smoothly.

Yes, very interesting. At the risk of running things ahead (like I asked others not to do), and perhaps philosophizing a too much, it seems to be only a "permission to move uniformly". The moment something is accelerated by applying a force, it resists that change. Question: is it the continuum that resists, or is it the private spacetime structure that resists? My favorite PoV is that it's the matter itself resisting the change to its own spacetime structure. And that it takes energy to force such a change. No Mach's principle needed, i.e. inertia of matter is not dependent on the distant matter of the universe, according to this PoV.

I know that this is taking things way too far for people learning relativity. I did not intend to bring inertia and energy into this thread at all. But, I could not resist this temptation...

[BurtJordaan]

I can see that the 'private spacetime structure' have caused quite some interest. A better grip on it would benefit everyone, myself included.

It is easy to see that before the acceleration, Alice and Bob have shared the same spacetime structure. During the acceleration, only Alice's spacetime is distorted and her measures of space and time are changed. She now measures less time and less distance between events than what Bob does.

What does it mean that Alice's "measures of space and time are changed"? Instead of a philosophical view on it, I would like to propose a "real-life" inertial navigation view. The inertial navigation system (INS) of passenger and military aircraft allows them to fly 'blind' between (say) Cape Town and New York and arrive within tens of meters from where they are supposed to be.

Simplistically stated, an INS achieves this by reading a very accurate accelerometer and a very accurate clock.^[1] Every few milliseconds, its computer dead-reckons how far it has traveled in what direction. This it compares to (or 'plots on') a map in memory and voilà! Note that only an accurate clock and accelerometer were needed (ok, plus a computer and some peripherals, but you know what I mean).

Aircraft fly too slow and too low for relativity to have any impact on the required accuracy, so it is just ignored. Take a long, fast spaceflight and relativity does impact where you are and when. When Alice departs from Bob by being accelerated by her rocket, she and Bob (plus their computers) could have done the same as for the aircraft's case.

As we have seen, the acceleration changes the spaceship's spacetime structure and Alice's dead-reckoning would progress differently than Bob's. Bob's INS would read him as sitting in one place, no accelerations and just progressing in the time component of spacetime. Alice's INS would detect the acceleration and dead-reckons that she covers some spatial distance away from Bob as her time progresses.

The temptation here is to say next: because of the speed after the acceleration, Alice's clock is 'ticking slower' than Bob's and therefore her INS would add less distance per millisecond in the dead-reckoning than what Bob would have reckoned with his 'faster clock'. This 'explains' both time dilation and distance contraction.

Not so - Alice's clock was not influenced by the acceleration and still ticks like Bob's. But her spacetime structure is different in the sense that she had less distance to cover and did it in less ticks of her clock. Her INS computer would have been programmed to automatically adjust the scale of the map in its memory and would have told her exactly at what time on her clock she arrives at her destination. How cool is that?

[Dave_Oblad]

Hi all,

To describe this structure on a more simple level, we might start by agreeing both Space-Time and Matter have real structure, and such is interactive between them. I imagine taking two Bowling balls into our coasting lab out in deep flat space and putting them about 1 foot apart with no motion towards each other and release them to just float.

The Balls are having an effect on Space-Time structure. Science calls this Curving Space. (But I don't like the term curving but maybe that can come up later). Anyway, this slight space curvature surrounding and internal to the Balls has an effect that spreads far outside each Ball. This curvature affects the Structure of the other Ball causing the other Ball to have an internal Structure virtually identical to what the Ball would have.. if it was Accelerating.

This Curvature is Gradient by nature.. meaning.. the Space curvature is greatest nearest the Ball and gets weaker the further from the Ball. In this case both Balls are curving Space-Time Structure. Both Balls adopt some of the Space-Time curvature from each other and take on the internal Structure of Acceleration.. towards each other.. where the curvature becomes greater (gradient) the closer they become.

This is of course: Gravity. The Balls are not pulling on each other, as is often said.

Each Ball is changing the Curvature of its local Space-Time in a Gradient fashion that extends outwards from the Balls. Each other Ball is exposed to this Gradient from the other Ball and adopts a change in their personal Structure that is identical to the structure they would have.. if they where being accelerated towards each other. They physically react to their internal acceleration structure and accelerate towards each other. Of course they will bounce off each other, but after many bounces, they will settle down in full continuous contact.

So what is this Curvature? Specifically.. it is the Gradient effect each Ball is having on the local Space-Time Structure that surrounds the Balls. Bottom line.. if Space-Time didn't have a Structure of its own, there would be no Gravity effects.

So a common phrase is: Matter tells Space-Time how to Curve (concentrate) and Space-Time tells Matter to how to Move.

Anyway, not meaning to jump ahead into Gravity but the subject was about Structure, so it seemed appropriate to touch on what the effects Structures have on each other between Matter (Alice) and the Space-Time around her.

Again, I hope I haven't deviated too far from Jorrie's purity and Presentation Train, but Structure is the current topic and an important one.

Oops, cross posted with Jorrie.. but we seem to share a common concept about Structures. Jorrie's post is pretty good.

Best wishes,
Dave :^)

[BurtJordaan]

Hi Dave, yes, there are obviously some correspondence between the spacetime structures caused by gravity and acceleration, but I think you are missing the plot here and there.

To describe this structure on a more simple level, we might start by agreeing both Space-Time and Matter have real structure, and such is interactive between them.

The modern view is somewhat different. It is only at cosmological scales that the background spacetime has structure of its own. In the realm of bowling balls, planets, stars and even galaxies, the spacetime structure 'belongs' to the individual masses - and it extends outside the mass all the way to infinity.

Yes, the individual structures do interact in a complex way, far more difficult to understand than the purely accelerating objects in flat spacetime. So I'm not too keen on bringing it into the main discussion at this stage. Alice and Bob interacts only by means of light, provided that they do not come too close to each other, but we ignore gravity in any case for the discussed scenarios.

Both Balls adopt some of the Space-Time curvature from each other and take on the internal Structure of Acceleration.. towards each other.. where the curvature becomes greater (gradient) the closer they become.

So what is this Curvature? Specifically.. it is the Gradient effect each Ball is having on the local Space-Time Structure that surrounds the Balls. Bottom line.. if Space-Time didn't have a Structure of its own, there would be no Gravity effects.

Yea, sort off, but gravity is not dependent on a spacetime that has "a Structure of its own". Spacetime has structure (and curvature) because of mass and energy, so it belongs to the individual bits. The cosmic scale "background spacetime" (a.k.a. 'dark energy') does not affect the ordinary masses that we can directly observe.

So maybe we should defer this added complexity to a later stage.

[bangstrom]

Not so - Alice's clock was not influenced by the acceleration and still ticks like Bob's. But her spacetime structure is different in the sense that she had less distance to cover and did it in less ticks of her clock. Her INS computer would have been programmed to automatically adjust the scale of the map in its memory and would have told her exactly at what time on her clock she arrives at her destination. How cool is that?

Your comment doesn’t say exactly what Alice’s INS computer is adjusting.

Alice is headed to a predetermined point in space a fixed distance from the Earth. This distance is not a vector on a Minkowski diagram rather it is a space-like separation of two entire world lines, specifically those of the Earth and a point in space a fixed distance from the Earth. So, she is headed for a destination that is not an event but a location. Alice’s spacetime structure may tell her that she now has less distance to cover so, she may think she has arrived, but she is still short of the mark.

If I understand your statement correctly, her computer adjusts Alice’s scale of the map to conform to Bob’s scale map in Bob’s time so she arrives at the destination correctly.

[vivian maxine]

The larger structure of spacetime can't change due to whatever Alice does, but isn't it reasonable to argue that her own, private spacetime structure has changed relative to Bob's? Remember that they have started with identical structures. These "identical structures" could have been different to the universe's spacetime structure, which happens to be undetectable.

I know what "relative to" means. Therefore, I think I know what relativity means. Measurements from each observers' position. This is what Bob and Alice are seeing - each according to his/her own position. Now we look at what you call the "larger spacetime structure". I think I have to say no observers or my question won't hold water. I take it that you mean "real spacetime's structure". Am I right? If so, can it ever change? And does it even enter into the description of "relativity".

There is more going on in my head but I don't want to go there yet. Just tell me about the universe's spacetime structure as regards relativity. (Ignore for now your statement "if it has a structure".)