Why is relativity so hard to learn?[1]

[BurtJordaan]

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.

The destination is never an event, but her arrival at the destination is. It is not at a fixed distance, but at a spacetime coordinate dependent distance and for Alice it Lorentz contracts while she is accelerating.

What is the INS computer adjusting? Only the scale of the star map, and only while it reads an acceleration on the accelerometer. Alpha Centauri (say) is still in its old location on the map, just marked with a different scale.

How does the computer know they have arrived at Alpha Centauri? It reads the spaceship clock, multiplies it by her speed relative to Bob, plot the position on the map and Bob's her uncle.

The computer knows the relative speed by integrating the accelerometer reading against the ship's time. Or Alice can tune in to Bob's radio signals and calculate the speed from the amount of Doppler shift.

[BurtJordaan]

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".

Yea, I regret having mentioned the "larger spacetime structure", because it is irrelevant here. As I have explained to Dave_O, it only enters the fray when we consider general relativity at cosmological scales. Even up to the scale of Galaxies it is unobservable, so for this discussion, we can say that it does not exist.

At the very largest scales, the spacetime structure can be said to exist and it does change. We observe it as accelerated expansion of the universe.

[vivian maxine]

Thank you, Burt. It tells me plenty on the simpler level, too. I'll hold onto that for now. It can change in a way I was forgetting.

[Dave_Oblad]

Hi Everyone,

Yea, I regret having mentioned the "larger spacetime structure", because it is irrelevant here. As I have explained to Dave_O, it only enters the fray when we consider general relativity at cosmological scales.

This is where Jorrie and I may start a debate. I would say this Space-Time structure exists at every level of Scale, from the Biggest to the Smallest. It doesn't magically appear at some preset super size.

Of course this Space-Time stuff is what is called an Aether. It's just as Real as a Magnetic Field. You can't see it or smell it or taste it.. but you can tell the Magnetic Field is real by pushing a Magnet around with another Magnet, without them touching each other.

If you want to bounce back to page one for a moment:
http://sciencechatforum.com/viewtopic.php?f=10&t=32778&start=0#p320369
My argument comes from the idea of Curved Space-Time. You can't have a curvature unless there is something real that can be curved.

See, Jorrie is a Purist. They will say that the only thing Real is the Math that describes the Relationships within Relativity such as Matter, Speed and Clocks etc. That anything outside of what the Math tells us is pure Speculation.

This is completely true and Jorrie is completely correct. No argument there.

But many times, it can be easier to get an idea across if one offers a Model that is just a speculation or an Analogy. For the purpose of teaching something, such Analogies can prove very useful, even if they are not completely accurate. For many of us, the Purist view is nearly impossible to wrap ones mind around, unless you are another Einstein.

Even Einstein had no clue what Space-Time really is. But it is a useful tool for trying to imagine how things work with each other. So, for those of us that want a simple "Meat and Potatoes" view, I believe such speculative Models can serve a useful purpose in teaching those of us that fall short of being Einstein Clones.. lol.

So, if Jorrie will allow me this leeway, I'll propose explanations that translates reasonably well to what Jorrie is teaching, but is much more simple to understand. Just keep in mind that any such Model may be completely wrong, especially from a Purists point of View.

This is why I suggested that Alice and Bob had a race that started at the same time and ended at the same time. But Alice took a much longer scenic route and was traveling a lot faster than Bob to do so. So why did Alice age less than Bob? Could it be she passed through a lot more Aether Space-Time than Bob at a much greater speed than Bob? That would be the truth.. if we took the Race at face value. Did the structure of Alice change in a different way than the structure of Bob during the race? A change that caused Alice to age slower than Bob? Did flying though a lot more Space and much faster really change her Physical Structure?

My Race is different than what Jorrie had proposed. In his version, Alice had to speed up, fly away, slow down, turn around, speed up again and return to Bob while slowing down to rejoin Bob. And she still aged a bit less than Bob. Jorrie's point was that if we graphed out this scenario, that the Accelerations and Decelerations would look like Curves on the Graph, where the straight lines are when Alice was coasting.

The straight lines indicate that during that part of the trip, Alice continues to Age slower than Bob for as long as she keeps going without changing speed. If she did this long enough, such that the curved part of the graph is only a small part of the whole, that when she got back, Bob could have died of old age while Alice is still a spring chicken (so to speak).

That Epstein Graph Jorrie showed on page two is not really that scary. It is just a graph of Bob and Alice laid on top of each other (no incest intended). It shows Time (top/bottom) and Speed (left-right). If you rotate both to point straight up, then they are not moving and both are aging at the same rate. If you rotate both Red and Blue Graphs the same amount, then both are moving at the same speed and aging at the same rate as each other.

If you rotate one graph (Red one) more than the Blue one, the graph shows how each one is aging differently then the other. The exact ratio in aging is marked with a big fat Red Dot marked (1). This is showing how much Alice's clock is changing compared to Bob's clock. You may even notice that if you rotate the Red and Blue the same amount, but in opposite directions (one clockwise and the other counter-clockwise), that Alice and Bob are heading away from each other but at the same speed. So they would both have clocks ticking at the same rate as each other and, of course, they would be aging at the same rate.

Epstein Spacepropertime

Note: I asked Jorrie if I rotated the big red dot to the 3:00 position what would it tell us? He said I can't, because that would have Alice moving at the speed of light and her clocks would be stopped completely.

I hope I didn't muddle this all up about the graph above.

Ok, I have to get back to work.. catch everyone later.

Regards,
Dave :^)

[BurtJordaan]

Of course this Space-Time stuff is what is called an Aether. It's just as Real as a Magnetic Field. You can't see it or smell it or taste it.. but you can tell the Magnetic Field is real by pushing a Magnet around with another Magnet, without them touching each other.

Yes Dave, magnetic fields exist and can push around a magnet - hence it is pretty detectable. Your type of Aether is not detectable and scientists do not bother about it.

I also happen to know that you still believe that you can detect motion (and speed) through it by comparing clocks that are moving inertially. Well, that idea has been falsified by many an experiment, so why you still cling to it, I don't understand. A theory or model must be self-consistent and predict/postdict what is observed. Otherwise it is still at the level of philosophy, an idea that could maybe inspire scientists to try and find the effect that the philosopher predicts. But do philosophers ever predict things? I don't know.

Lastly Dave, your treatment of the the Alice and Bob scenario on the Epstein diagram is wrong and might be down-right confusing to everybody else. I would suggest that we leave it until my piecemeal series (now at piece [7]) gets to the round-trip scenario, and you will quite likely see your mistake. Alice hasn't even stopped yet, never mind having turned around to head home. We are still gnawing at one front foot and leg of this elephant. Once we have done the other front leg and foot, it should become clear to you.

Then you can perhaps help to put it in proper words and philosophy for our audience. You are better with words than me.

[BurtJordaan]

I previously replied to Bangstrom as follows:

What is the INS computer adjusting? Only the scale of the star map, and only while it reads an acceleration on the accelerometer. Alpha Centauri (say) is still in its old location on the map, just marked with a different scale.

Although Alice's spaceship computer will probably have done exactly that, it is equivalent to rotating the star map around an axis that keeps Alpha Centauri in the direction of travel, so that its distance projection onto Alice's +x axis becomes shorter. This is more in line with the Epstein visualization and better for the main line of thought here.

The rotation happens gradually for a long as the acceleration lasted. Alice scores a double whammy. She gets closer to the star due to her motion relative to it, but at the same time the star is coming closer to her as well! She has to travel less distance and hence gets there earlier. No "slow clock" needed.

I have programmed many such scenarios on a computer and it is easier (and takes less computer steps) to just apply a scale change (in tech jargon, divide the present Alpha Centauri distance on the map by the ship's present Lorentz factor). Perhaps more mentally challenging, but computers don't have minds to challenge (yet?)!

[bangstrom]

She has to travel less distance and hence gets there earlier. No "slow clock" needed.

Would it also work as a slow clock and no change in distance?

[mitchellmckain]

It seems that BurtJordan has left out some of the key features of the "Epstein myth" which the Epstein diagram is a part of. Perhaps he is avoiding the aspects of this which does not fit with the usual SR dogma. It is probably these features which caused Epstein to call it a myth in the first place, as well as making most scientists not take it very seriously.

First, the circle is in the diagram because the idea is that according to the myth there is a kind of simultaneity in which the different observers all travel the same interval length along their own time axis. In fact, the myth is claiming that everyone travels (must travel) in space time at the "speed of light" along their own proper time axis. This is what generates this graph where the cosine and sine of the angles give the time dilation and Lorentz contractions. Even the relativity of simultaneity is captured by a diagram by examining a space-like interval (parallel to the x axis) in the coordinate system of one observer to see how it looks in the coordinate system of another observer -- showing how the time of the two events gets reversed.

The thing to understand is this isn't telling a different story than the usual presentation of Special Relativity, and care must be taken that you do not use Epstein's diagram in a way for which it is not intended. For example, the distance over time slope of the other observer is NOT the velocity of that observer. Also the diagram only works for comparing two observer/objects moving relative to each other. You can see this, for example, by looking at the path of light (which would count as a third object), which must go along the x axis and thus would be two different rays in the coordinate systems of the two observers.

But I must admit this way of looking at things is intriguing to me for several reasons.
1. It puts the speed of light in a role similar to that of an infinite speed (along the x axis). This is intriguing to me because there are many ways in which the speed of light is in fact like an infinite speed.
2. The idea of everybody has to go at the speed of light connects in my mind with the way that mass-less particles likewise must travel at the speed of light.
3. The relationship between the Minkowsky space-time diagram and the Epstein diagram connects with the difference between hyperbolic and circular rotations.

Nevertheless, I would judge that introducing this in a beginners class on relativity is not a great idea and likely to be more a source of confusion than enlightenment.

[BurtJordaan]

She has to travel less distance and hence gets there earlier. No "slow clock" needed.

Would it also work as a slow clock and no change in distance?

Good question!
Well it would work, sort of for now, but many other things won't. If you can be patient, some of them will come out of the wash and some will have be dealt with desperately (I meant separately, but the spell checker had other considerations ;)

[BurtJordaan]

Nevertheless, I would judge that introducing this in a beginners class on relativity is not a great idea and likely to be more a source of confusion than enlightenment.

Possibly, but let's wait and see how it goes... ;)

[BurtJordaan]

The issue of the scale of the star map versus a contraction of the distance to Alpha Centauri has come up in the discussions, starting off with this remark at the end of piece [7]:

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?

Without worrying about the details, just suppose that when Alice stops accelerating, she is moving at 60% of the speed of light relative to Bob and that according to Bob, she is just one light year short of reaching Alpha Centauri. From Alice's lofty perch, Bob's spacetime structure has rotated anti-clocks and makes an Epstein angle for a relative speed of -0.6c, as shown below.

Alice's 'view' after acceleration

Now that all is back to inertial motion again, we set op a new Epstein circle, with Alice at the center and one of Bob's stationary observers (Charlie, now the blue arrow) flashing by, i.e. he and Alice are momentarily co-located at the center. Alpha Centauri, 1 light year away from Charlie, is now projected down to Alice's x-axis and was at a distance of x = 0.8 light year from Alice at the moment that Charlie flashed by.

If we assume Alpha Centauri to be stationary in the Bob and Charlie views, they will extrapolate, by simple division, that Alice will fly past Alpha Centauri in another one year and 8 months (1.66 yr). What time will Alice's INS predict? It knows the instantaneous speed, has already (mathematically) rotated the map (or applied a Lorentz factor, according to the programmer's whims), and it will proudly display a remaining time of 1.33 yr, or one year and 4 months.

The total trip of 4.4 light years distance on Bob's map must obviously have taken much more than that, with the total times for each depending how hard Alice has accelerated (how many g's) to get to a relative speed of 0.6c. More about that in the next piece, I promise. For now, did you notice that in this scenario, we never referred to either time dilation or "slow clocks". We did refer to length contraction, indirectly through the rotation of the spacetime structures, or the alternative method of using the Lorentz factor as a change in scale.

You can see where this is leading: Alice got to Alpha Centauri in less time than what Newton would have predicted, simply because during the trip, in her spacetime structure, the star was simply closer. If she had the technology to just keep that rocket blasting, she would have been out of our galaxy before she became too grey. And this is solely because the universe becomes smaller and smaller for observers that rotate structures. They can get there in less time of their own. And isn't that all that matters?

[Dave_Oblad]

Oops.. Sorry Jorrie,

I was under the impression we had already brought Alice back to Bob.. my Bad. I'd swear you had said something about Alice turning around.. but that must have been my bad memory.

As for whether or not an Aether is Real.. it doesn't matter.. but using one in a Model helps to understand how Matter can change depending on how fast it is going. In most Special Relativity discussions, speeding up and slowing down (acceleration and deceleration) are just necessary aspects of getting from one speed to another speed. It's not uncommon to avoid such by suggesting Relativity would still be valid.. even if Travelers could jump instantly from one speed to another speed.

It's all about the speed and how long one maintains that coasting speed.. that makes the big differences in how a traveler ages for the duration of their coasting. It's not like once a traveler gets to a new speed that their clocks go back to ticking at the same rate as before they changed their speed. If that were true, then Special Relativity would be all about the time spent speeding up and slowing down and forget about the time spent coasting. But that is not the case.

Bottom line: the faster you go through Space-Time, the slower you age.

That conclusion is hard to avoid. Looking at the Epstein Diagram, we see that we are trading aging with speed. If we rotate Alice's Graph to 3:00 for maximum speed (light speed) then her aging stops completely. If we rotate the graph back to 12:00, then we see that zero velocity is the maximum aging rate.

It's even labeled on the graph with the dotted lines that says that if Alice is traveling at 0.6c (60 percent of light speed) that her clock it ticking at 0.8 (or just 80 percent of the normal rate).

So, how do clocks know how much to slow down unless they are sensitive to their velocity? And how can they be sensitive to their velocity without an Aether to affect them? These clocks don't care about how fast any other clock is moving, they only care about their own personal speed to change their own personal clock rate.

Anyway, this is the subject Jorrie and I have been debating for some time now and we should shelve this debate until we are past the basics.

So.. when we last left Alice, she was coasting away from Bob at 0.6c or 60% the Speed of Light and her clock is ticking away at just 80% of the normal Rate that it would have had.. if she had no speed. Also.. she hadn't turned around yet, if I'm not mistaken.

At 0.6c: Her personal relativistic factor is 1.25 or.. 1/1.25 = 0.8 clock rate.

Here is a Relativity Calculator to play with:
http://www.1728.org/reltivty.htm
Type 0.6 in the Input Box and click (C=1) to see the Relativistic factor as 1.25.
Now type into a calculator 1 divided by 1.25 to see her clock rate is 0.8 of normal.

Take it away Jorrie...

Dang.. we cross posted again.. time for me to catch up still more.. (but later.. it's bedtime for me)

Best Regards All,
Dave :^)

[Dave_Oblad]

Hi Jorrie,

Quick comment:

Alice got to Alpha Centauri in less time than what Newton would have predicted, simply because during the trip, in her spacetime structure, the star was simply closer.

So, instead of saying Alice's clocks slowed down.. we are just keeping her clocks normal and shrinking the Universe in front of her? Since the Universe itself can't actually change just for Alice, this would mean that Alice must have gotten a whole lot longer. Doesn't SR predict she actually becomes Shorter and not Longer, relatively speaking?

Weird way of thinking, but I'll have to wait and see where this is going.

Regards,
Dave :^)

[BurtJordaan]

Yup, Dave, you may have to wait and see if it makes sense after all.

BTW, how does your observer's clocks know how fast they are moving relative to the unobservable spacetime, so that they can adjust their clock rates accordingly?

Equally weird ... ;)

[Dave_Oblad]

Hi Jorrie,

BTW, how does your observer's clocks know how fast they are moving relative to the unobservable spacetime, so that they can adjust their clock rates accordingly?

On a windless day, if I stick a fan out the window of my car and drive, I can count the revolutions of the fan and decide my speed. Of course we have an atmosphere to affect the fan.

But if Clocks count time by how fast they move through an Aether, then so be it. Clocks are like a speedometer, but the faster you go, the slower they run. To explain why, would take us off track. But basically, without an Aether, there would be no Scale for Time and Distance. No control over the size of things. Big Hydrogen Atoms and small Hydrogen Atoms.. the Universe would be crazy without an underlying fabric that controls Scale. This is why Einstein replaced SR with GR. Without Scale, nothing makes any sense.

So observable or not, we need an Aether Fabric (metric) to build upon or nothing would work. I would even go so far as to say that without the Fabric of Space-Time, there would be no resistance to Acceleration.. but now we are really getting off track.

But I need to hit the sack now.. I've got 4 hours before my student gets here for his daily lesson. I'm mentoring my replacement so I can retire.

Everyone else, forget what I just said here.. it's just part of a long standing debate.

Best wishes all and good night (my time).
Dave :^)

[dandelion]

I find this way of explanation really great! Thanks.

[TheVat]

Having aether just for the sake of a scale metric seems kind of anti-Ockham to me, DaveO. You don't need it when you have matter in a universe. Matter generates geometry. Energy makes intervals.

[mitchellmckain]

Having aether just for the sake of a scale metric seems kind of anti-Ockham to me, DaveO. You don't need it when you have matter in a universe. Matter generates geometry. Energy makes intervals.

The immediate question which came to mind when you said, "matter generates geometry," is geometry of what? The answer is of course space-time. The question isn't what generates this geometry but whether the idea of aether adds anything to space-time. The original idea of aether was something which affects things moving through space-time. But relativity blows this out of the water to say that motion is completely relative. The whole idea of aether is at odds with this, for if there were such a thing then it would make motion absolute rather than relative.

On a windless day, if I stick a fan out the window of my car and drive, I can count the revolutions of the fan and decide my speed. Of course we have an atmosphere to affect the fan.

But if Clocks count time by how fast they move through an Aether, then so be it. Clocks are like a speedometer, but the faster you go, the slower they run.

But this is completely incorrect. This is an incorrect understanding of time dilation. There is no absolute measure of speed. It is all relative. Clocks DO NOT run slower except as a completely relative calculation.

If A has a velocity of 86% the speed of light with respect to B, then BOTH of them calculate that the clocks of the other guy is going slower by a factor of two -- BOTH. Can you ask whose clock is really going slower? NO! There is no such thing. Can they end up in the same time and place with different readings on their clock? YES!
1. If A accelerates to go to where B is then the calculation of A will change and he will see that much more time has passed for B than he thought before and it is his (A's) clocks that will have less time on them.
2. If B accelerates to go to where A is then the calculation of B will change and he will see that much more time has passed for A than he thought before and it is his (B's) clocks that will have less time on them.

BUT thinking this an effect on clocks to make them run slower is WRONG. This is a completely global effect of the space-time structure. No clocks are running slower except in the relative calculations of A and B, and the time differences are not due to any clocks running slower but the relativity of simultaneity in the global structure of space time. In other words, the Euclidean picture of space-time as a bunch of instantaneous snapshots strung together is WRONG. Motion pictures work that way but not the physical universe. Instead we have the Minkowsky picture of space-time with a completely local separation of past, present and future. The only thing which is really future is relative to your present moment and location in the forward light cone. The only thing which is really past is relative to your present moment and location in the backward light cone. Everything else outside those light cones have no real temporal relation to you except in your imagination and whatever calculations are convenient at the time, all subject to change when you alter your velocity.

But basically, without an Aether, there would be no Scale for Time and Distance. No control over the size of things. Big Hydrogen Atoms and small Hydrogen Atoms.. the Universe would be crazy without an underlying fabric that controls Scale. This is why Einstein replaced SR with GR. Without Scale, nothing makes any sense.

This makes no sense. Here Braininvat's comment is relevant. Matter sets the scale! Why indeed would you need anything else. Why does scale have to have some absolute standard aside from matter? Why shouldn't scale be relative?

So observable or not, we need an Aether Fabric (metric) to build upon or nothing would work. I would even go so far as to say that without the Fabric of Space-Time, there would be no resistance to Acceleration.. but now we are really getting off track.

Incorrect. It works without aether and it does not work with aether. Every time you impose this idea of absolute motion on things your answers will come up wrong!

[Dave_Oblad]

Hi Mitch,

We should save your comment for the end, where we all might engage in a real debate.. meanwhile.. such a debate would be confusing for our readers.

But I will say this for you to think about in the meantime: You can NOT show me a real SR problem that doesn't have at least one absolute embedded or implied. In the present problem, we have Alice moving at 0.6c in the Epstein Diagram. That literally means she is traveling at 60% the speed of light. The speed of light is 300,000 Km per Second. So Alice has an Absolute speed of 180,000 Km per Second relative to a Standing Aether, or, relative to the Speed of Light, whichever you prefer. How fast other non-connected objects (witnesses) are moving around her has absolutely no effect on how slow or fast her clock will be running.

Honestly, having an Absolutist (me) and a Purist (Jorrie) sharing the same thread.. is like having the "Hatfields and the McCoys" sitting down to dinner together. Sparks are gonna fly.. lol.

So again, let's save the debates for the end, so everyone can follow (I'm not going anywhere) and I'm trying to leave Absolutism off the discussion table for now.

Meanwhile, I'm intrigued with Jorrie's latest idea and want to hear more about it.

There is a Philosophy that offers the idea that the Universe is Smart and we are all just "Brains in Vats".

That the Universe only supplies the least amount of Information to keep us believing it is real. That a room ceases to Exist until an observer enters the room.. I don't buy this.. but it would be almost impossible to disprove.

Highest Regards,
Dave :^)

[TheVat]

There is a Philosophy that offers the idea that the Universe is Smart and we are all just "Brains in Vats".

It's just me, actually, in the vat. :-)

[mitchellmckain]

Hi Mitch,

We should save your comment for the end, where we all might engage in a real debate.. meanwhile.. such a debate would be confusing for our readers.

Science is not a matter of debate. The methodology of science is not rhetoric.

But I will say this for you to think about in the meantime: You can NOT show me a real SR problem that doesn't have at least one absolute embedded or implied.

So what? Special relativity says that velocity is relative not that EVERYTHING is relative!

In the present problem, we have Alice moving at 0.6c in the Epstein Diagram. That literally means she is traveling at 60% the speed of light. The speed of light is 300,000 Km per Second. So Alice has an Absolute speed of 180,000 Km per Second relative to a Standing Aether, or, relative to the Speed of Light, whichever you prefer.

Incorrect!!! I warned about this in my explanation of Epstein's myth above. Epstein's diagram is for one purpose and one purpose only, to represent the RELATIVE velocity between two objects ONLY. Add even one more object and it all falls apart with inconsistencies. This demonstrates that Epstein's diagram most certainly DOES NOT have anyone traveling at an absolute speed.

How fast other non-connected objects (witnesses) are moving around her has absolutely no effect on how slow or fast her clock will be running.

Nothing makes any clocks move faster or slower. This is an incorrect understanding of time dilation.

So again, let's save the debates for the end, so everyone can follow (I'm not going anywhere) and I'm trying to leave Absolutism off the discussion table for now.

I am not debating. I am not interested in debates. Science is not a matter for debate. The rhetoric of debate is the methodology of lawyers, politicians, evangelists and used car salesmen -- not scientists!

[BurtJordaan]

Meanwhile, I'm intrigued with Jorrie's latest idea and want to hear more about it.

Glad to hear, Dave. We will get there quicker if you can contain yourself to making constructive comments, like 'I see a problem with Epstein diagrams or for layman coping with the way I present it' (as you have done earlier).
But it does not help if you state 'false relativity' at the same time, like that Alice has an absolute speed of 0.6c against some hypothetical Aether, or the like. Befor the acceleration, Alice and Bob could (hypothetically) have both been moving at 0.8c relative to the CMB, or whatever, with a relative speed of 0.6c and the time profile of the mission would have been exactly the same.

The end purpose is to have these principles absolutely clear. Tuning "absolute framers" in to the real science was not part of that purpose, but if we gain that as well, it will be a bonus.

[BurtJordaan]

The total trip of 4.4 light years distance on Bob's map must obviously have taken much more than that, with the total times for each depending how hard Alice has accelerated (how many g's) to get to a relative speed of 0.6c. More about that in the next piece, I promise.

OK, I'm not going to bore you with the calculations (those equations may give some of us recurring nightmares of their final math exams), but here is what they spit out via my computer (somewhat rounded).

Alice had to accelerate at a very achievable (but maybe uncomfortably low) 0.075g, meaning roughly one thirteenth of Earth's surface gravity. This gave her a "delta velocity" of 0.6c in 9.3 years of constant 0.075g acceleration, on her clock of course. It placed her 0.8 light years (lyr) shy of Alpha Centauri (AC), as per her rotated map (corresponding to 1 lyr on Bob's non-rotated map).

The trick was to find the exact acceleration that would fit the prescribed scenario, with the distance to AC and the final coasting speed fixed at 0.6c. Upon reaching that speed, she did shut down her (restartable!) rocket and coasted, that is until turnaround time comes up, of course. This will be discussed next time.

We have seen in the prior piece that it will take another 1.33 years of coasting for Alice to achieve a flyby of AC (1.66 years according to Bob)), making her total trip time 9.3 plus 1.33 = 10.63 years. Just for reference, Bob's coordinate clocks recorded Alice's time from departure to shut down as 10.1 years accelerating, plus 1.66 years of coasting, for a total of about 11.76 years. That's if I actually put the right equations into my computer, but relativistically, they look right.

Now, is this difference in elapsed times what is meant by "time dilation"? Many, even some relativists, will say yes. I say no, it is just different elapsed times recorded between two events by observers that moved through different spacetime structures, using identical, 'undilated' clocks. I hold that relativistic time dilation should be reserved for the reciprocal observations of time and distance, where each observes the other's lengths as contracted and clocks as dilated.

I know it might just be case of semantics (what is a word anyway?), but I believe that the ambiguous use of the term "relativistic time dilation" between the two cases in the literature and in discussions, is at the heart of many a misunderstanding and/or misinterpretation. I have witnessed quite a number of cases where it drove people to incorrect theories to try and make sense out of the mess. I must confess, I'm as guilty as anyone and may have created some of the mess.

That said, in the next piece we will make Alice turn around en head home, and provided that her long-playing rocket has enough fuel left, make it little swifter.

[vivian maxine]

Thank you, Burt. This beginner is following you rather well even without the diagrams. (Print is too small to read and doesn't enlarge enough here but no problem as that part is still confusion to me. I get the gist from your explanations.)

Q. Is there a reason the Epstein diagram that you just printed is turned? Or, just coincidence? I ask because it reminds me of an illustration of a table in angular momentum position that I saw last night.

[BurtJordaan]

Thank you, Burt. This beginner is following you rather well even without the diagrams. (Print is too small to read and doesn't enlarge enough here but no problem as that part is still confusion to me. I get the gist from your explanations.)

Q. Is there a reason the Epstein diagram that you just printed is turned? Or, just coincidence? I ask because it reminds me of an illustration of a table in angular momentum position that I saw last night.

I have attached a full size version. The rotation was just to stress that the orientation of the red and blue vectors does not play a role - only the relative angle between them does. The grey 'background' grid has no more significance than that it depicts Bob's 'private' spacetime structure, but Alice (red) also possesses the same, just rotated and not pictured. It would have been a faint red rectangular grid, at the same scale as Bob's, but I was too lacy to draw one in. ;)

[vivian maxine]

Ah, yes. The circle, not the square. Am I right that the circle holds the angles to exactness no matter how you turn them? Can a square do that? Perhaps.

I hope I'm not straying from your topic. Just that I'm seeing something here that I think I understand? Thank you for the larger grid. That and my magnifier brought it out. Now I need to go back and re-read from the start. Good.

[mitchellmckain]

That said, in the next piece we will make Alice turn around en head home, and provided that her long-playing rocket has enough fuel left, make it little swifter.

Actually to do this right you would have Alice spend fuel as a percentage of her total ship mass, for the more fuel she uses the less fuel she needs for the same acceleration. For example at .6c her kinetic energy will be increased to .25 times her remaining mass energy. Then you will also have to account for her increased momentum with reaction mass. That momentum will be .75c times her remaining mass. The less reaction mass you use the more energy you need to accelerated it to get this momentum, so at minimum I calculate you will have to use half her original mass to accelerate to .6c. You can use this three more times to stop, accelerate back and stop again if you want, leaving her with 6.25 percent of her ships original mass when she gets back.

[BurtJordaan]

Actually to do this right you would have Alice spend fuel as a percentage of her total ship mass, for the more fuel she uses the less fuel she needs for the same acceleration. For example at .6c her kinetic energy will be increased to .25 times her remaining mass energy.

Yup, but I did not really consider the fuel situation for this exercise. I agree with what you said, but it's too complex for this thread by far, even if gravity is ignored. I can't remember which prof. I read that said something like: if you can convert nearly all of a body into kinetic energy, you will have nearly nothing, moving away from you at nearly the speed of light.

[mitchellmckain]

Well just for curiosity and reference, my calculations give the following costs for accelerating to these velocities (or decelerating to zero from these velocities)
velocity contraction&dilation %mass used (minimum) fraction remaining
60%_______4/5_____________50%_________________0.50
86.6% c____1/2_____________73.2%_______________0.268
99.5% c____1/10____________95%_________________0.05
99.995 c____1/100___________99.5%_______________0.005
99.99995 c__1/1000__________99.95%______________0.0005
These are the percent/fraction of the remaining mass, so for more than one operation in series simply multiply the fraction remaining for each.

[BurtJordaan]

Well just for curiosity and reference, my calculations give the following costs for accelerating to these velocities (or decelerating to zero from these velocities)

Cool! Many thanks Mitchell. This shows that 60% of c is an easy to understand speed in many ways. As you have said, one can do a return trip and have a reserve fuel of 50% x 50% x 50% x 50% = 6.25% of the original fuel. That is if you have a 100% efficient mass-energy conversion, which may not be achievable, so practically one may have to settle for much slower trips.

I will continue with the 0.6c delta-v's, but just use a higher acceleration to reduce the time for Alice.