Food for thought with respect to relativistic phenomena!

[Doctordick]

I started this as a new thread as I think it brings up a number of issues not discussed anywhere else.

 

Hi Anssi, once again I am moved to answer a private note with a public post. You seem to invariably bring up issues which ought to be presented to most everyone involved in this forum. Your comments consistently deal with issues central to the fundamental problems extant in common misunderstandings of physics.

 

Yes I did receive an e-mail from Stewart which I have not answered as I do not get the impression that his knowledge is up to the problem he wants to discuss. Essentially, I feel there are many people much more prepared to correct his misunderstandings than I am. Stewart, I think Anssi and I have been discussing issues much more fundamental than are the problems you are having. Anssi's lack of mathematics may seem to be similar to your lack; however, his understanding of the fundamental issues is much more adroit than even some of the best physicists I have met.

 

But back to Anssi's note; directly from the opening post on the physicsforums thread you quote,

As many of you know, Newton used a thought experiment to prove the existence of absolute space. He argued that the curvature of the water inside a bucket while rotating, demonstrates the the true motion of the water in reference of what must be absolute space. (he used a similar thought experiment using two spheres connected by an ideal rope in an empty universe. If these spheres rotate, a tension force is created on the rope, which indicates the "real movement" in reference to absolute space).

 

Mach argued that curvature of the water was due to the rotation in reference of the fixed stars, and even further, he argued that if we rotate the "fixed" stars around the bucket we will obtain the same result, concluding that space is relative.

 

Of course we will never be able to rotate the whole universe around the bucket to prove mach's theory.

 

I wonder if anyone knows better arguments, specially under the light of recent scientific evidence, to disprove Newton's absolute space. Please provide links if research papers are available.

What pilopais clearly misses here is that “rotation of the whole universe around the bucket” is a very easy task to accomplish.

 

Making the presumption that the entire universe is rotating around a bucket at rest is as easy as making the presumption that the bucket is rotating and the entire universe is at rest. What is difficult is figuring out what your expectations should be if it is the universe which is rotating. I won't go into the problem as it requires a good understanding of some rather subtle general relativistic considerations but excellent arguments can be made that your expectations should be identical to the other circumstance (that is in fact the central issue of Mach's relativistic principle; by the way you should be aware that the modern tendency is to refer to this idea as the “principal of equivalence”). The distortion of the waters surface can be seen as a mathematical consequence of gravitational forces due to the apparent relativistic mass distribution of the entire universe.

 

To see this result, consider a universe consisting of the bucket and two identical stars in opposite directions from the bucket. If it is the stars which are rotating around the bucket, their masses will be increased by the fact that they are moving close to the speed of light. The gravitational forces of the two stars still cancel at the origin of the coordinate system (the center of the bucket) but no longer cancel as one looks at short distances from that origin (because their masses have become so large). Of course, you are going to point out that the apparent velocity of the two stars easily exceeds the speed of light (apparently invalidating the picture); however, what you are actually pointing out is that you have failed to take into account the Lorentz contraction of the moving reference frame of the stars. The apparent circumference of the universe must go towards zero as large radii are encountered. The mathematics is far from trivial and calculating your expectations is a very involved process.

 

The important fact is that there is no way to prove that it is the bucket which is rotating and not the background universe. Since both views must be seen as equally valid, the laws of physics must be consistent with the change in view (that is exactly the issue of the “principal of equivalence” and is fundamental to Einstein's deduction of general relativity).

 

In other words, standard physics makes the “assumption” that there is no difference between the two views; an issue you cannot prove is correct. My work is subtly different. My fundamental equation is based upon symmetry principals and results in three independent constraints upon any epistemological construct. I then use the defined alpha and beta operators to define a single equation (what I define to be my “fundamental equation”) containing all three elements. Having postulated that relationship I then prove that it reduces to exactly those three independent constraints only so long as the coordinate system within which that equation is displayed is explicitly at rest with the entire universe. (Note that I also show that a transformation exists which will transform any solution to that equation into a solution in a frame which is not at rest with the universe. Thus the fact that the equation is only valid in such a frame is not a real constraint on the applicability of the equation.)

 

Under normal circumstances, physicists presume the principal of equivalence is valid and use a frame of reference essentially at rest with the distant stars because it is much much easier than using one in general relativistic motion with respect to the distant stars. My equation is explicitly valid only if the frame of reference is at rest with respect to the distant stars; quite a different statement. Of course, my equation covers the entire universe. The physics community has never even considered the possibility of such a representation being of any value at all and thus no one has even made the slightest effort to even examine such a thing; many body equations are simply regarded as insoluble and thus a waste of time to consider. The professional position is that the examination of an equation representing the entire universe is pure quack baloney.

 

Oh btw, one funny and little bit disturbing thing I noticed about a month ago. If you google "co-accelerating spaceships" or just "accelerating spaceships" to find out about that SR thought experiment (which I suppose a lot of physics student come across at some point), the first result is to an old Physics Forums thread that I started :I

I read your post and it is quite a good presentation of the fundamental difficulty of establishing general relativistic transformations. In classical physics, the transformations required for changing from one moving coordinate system to another are quite easy to work out because time is not an issue. The true difficulty here is to establish exactly how the various measurements have to transform in a general transformation. You should note that even Einstein's deduction of general relativity does not provide a unique transformation (that is what that cosmological constant is all about).

 

Because, in my approach, time is again an evolution parameter and not a dimension, the general relativistic effects become, once again, a rather simple (and unique) transformation. If we continue with our communications, we will get to that issue and, though the mathematics is once again rather outside your experience, the process is far simpler than Einstein's approach. (Just a little tid-bit to keep you interested.)

 

By the way, your examination of "co-accelerating spaceships" reminds me of a thought problem I proposed back when I was a graduate student. I always thought it was a very interesting problem but could get no interest in it from anyone. I think the real problem is that educated people don't like to think and avoid such problems whenever they can.

 

Here is the problem. We have a powerful galactic war lord who has, through his brute powers, has caused to be built a immense number of interstellar battle cruisers. They are powered by means beyond his conception (invented by scientists of the galaxy; think in terms of the supposed ZPM from the star-gate series). Essentially, how they work is outside this problem. When it comes to scientific issues, this war lord is relatively ignorant and he quite often orders acts which simply are not scientifically achievable. He has no interest in that impossibility. From his perspective, scientists do impossible things all the time. As a result, failure to obey simply results in the death of whomever he holds responsible for that failure.

 

This war lord has always demanded that his fleet of battle cruisers maintain an orderly formation whenever they move as a unit from one star system to another. One of his major interests is that they remain exactly where they are supposed to be in the formation when the fleet changes direction. This was no big thing back in the days when the fleet was small but now that the fleet is so large, relativistic effects (which he does not accept a real) have begun to become important. Essentially the ship navigators, who do clearly understand the relativistic effects (at least special relativity) are beginning to have difficulties fulfilling their orders since the actual request of the war lord violates relativity. They don't want to die so their only solution is to at least appear to be fulfilling those orders.

 

So here are the constraints of the problem. Anytime the war lord gives an order for a specific maneuver (a turn or an acceleration) that order is sent by a radio message to the entire fleet. Thank god he understands that the speed of the signal is finite as at least everyone in the fleet knows what the maneuver is to be before the maneuver is actually begun. Since there is actually no way for the war lord (or his trusted agents) to check the positions and clocks aboard the various ships unless the entire fleet is in the same rest frame (they need time to go about their examinations throughout the fleet), the real need is for the ship navigators to be able to demonstrate that they were indeed in formation throughout the entire maneuver.

 

Their computer records must show the correct position for every time during the maneuver and their clocks must agree with the war lords clock both for the actual moment that the maneuver starts and for the exact moment the maneuver finishes. All the personnel on board the ship must agree that the timing of the acceleration is in accordance with the computer records and that there has been no tampering with the data: i.e., the computers can be programed to yield the desired results (intermediate times during acceleration can be faked) but cannot be reprogrammed to adjust to a new maneuver. The trajectories resulting from those programs must end up being an internally consistent set.

 

Just as an aside, high acceleration is no problem as scientists have created acceleration couches capable allowing survival in spite of practically infinite accelerations.

 

Of course, what we have here is the definition of a supposed solid object's behavior under relativistic rotations and accelerations. Since the only time any of these states are checked the entire system is in the same rest frame, only special relativity is required to solve the problem. In my opinion there are some very interesting consequences of the picture and it is well worth the time for anyone interested in relativity to work out the details of the data which needs to be presented to the war lords authority.

 

Oh, I just received the latest issue of “Scientific American”. On the cover page, there is “Naked Singularities” in red letters which of course drew me to look at the article (starts on page 36). I get a kick out of the statements in that article made by the “noted professional physicists”. “Assuming that no new forces of nature intervene, horizons should be governed purely by general relativity, a theory that is based on well-understood principles and has passed 90 years of observational tests.” Boy is that a long time; it's almost 20 more years than I have been alive. My god, there can't be any error there.

 

“Stephen Hawking and Roger Penrose proved that singularities were, in fact, unavoidable.” And exactly how did they “prove” that? By assuming Einstein was right? I think they did indeed make that assumption. Personally, I am of the opinion that the “singularities” themselves are evidence of error in the theory. Of course, that's a quack opinion.

 

Have fun -- Dick

[arkain101]

As many of you know, Newton used a thought experiment to prove the existence of absolute space. He argued that the curvature of the water inside a bucket while rotating, demonstrates the the true motion of the water in reference of what must be absolute space. (he used a similar thought experiment using two spheres connected by an ideal rope in an empty universe. If these spheres rotate, a tension force is created on the rope, which indicates the "real movement" in reference to absolute space).

 

It just so happens that I developed an animation of this exact scenario! The purpose was for reasons unrelated. Although, I think it surely has a place in this particular topic, just as a visualization tool for discussion of thought.

 

Hopefully this will work.

 

http://11-11.tv/phpbb2/download.php?id=350

[AnssiH]

Anssi's lack of mathematics may seem to be similar to your lack; however, his understanding of the fundamental issues is much more adroit than even some of the best physicists I have met.

 

Well it's nice to hear that you think so :shrug:

 

To see this result, consider a universe consisting of the bucket and two identical stars in opposite directions from the bucket. If it is the stars which are rotating around the bucket, their masses will be increased by the fact that they are moving close to the speed of light. The gravitational forces of the two stars still cancel at the origin of the coordinate system (the center of the bucket) but no longer cancel as one looks at short distances from that origin (because their masses have become so large). Of course, you are going to point out that the apparent velocity of the two stars easily exceeds the speed of light (apparently invalidating the picture); however, what you are actually pointing out is that you have failed to take into account the Lorentz contraction of the moving reference frame of the stars. The apparent circumference of the universe must go towards zero as large radii are encountered. The mathematics is far from trivial and calculating your expectations is a very involved process.

 

Hmm, that's interesting, and for all I can tell, sounds valid. One thing I'd need to spend some time with still; I never really managed to understand properly the issue with Lorentz contraction shrinking the apparent circumference of the rotating universe (or rotating disk). I mean, I understand why that is expected, and I tend to look at lorentz contraction in terms of scaling, so I don't expect there to be any actual paradoxes involved, but then I don't feel I see the whole issue very clearly... I can see though that the definition of the circumference becomes somewhat ambiguous if you want to define it in a rotating frame, and when I'm avoiding the ideas of rotating frames it's... Well let's just say it's a tough nut to crack that one!

 

The important fact is that there is no way to prove that it is the bucket which is rotating and not the background universe. Since both views must be seen as equally valid, the laws of physics must be consistent with the change in view

 

...

 

My fundamental equation is based upon symmetry principals and results in three independent constraints upon any epistemological construct.

 

...

 

Under normal circumstances, physicists presume the principal of equivalence is valid and use a frame of reference essentially at rest with the distant stars because it is much much easier than using one in general relativistic motion with respect to the distant stars.

 

My equation is explicitly valid only if the frame of reference is at rest with respect to the distant stars; quite a different statement.

 

I think I understood everything you said, but not sure what the further implications are. It did make me think of couple of things. It is certainly somewhat surprising that rotating frames can be seen as symmetrical to each others as well if you consider the whole universe, that had not occurred to me quite that clearly before, even though, as you probably know, I have thought about the role of the rest of the universe in "causing" inertia, which is kind of the same issue.

 

Also, makes me wonder whether the root of such circumstance in our worldview can be traced back to those same three symmetry principles...?

 

I read your post and it is quite a good presentation of the fundamental difficulty of establishing general relativistic transformations.

 

You refer to the complications that arise because the objects in the situation undergo accelerations all the time, and with the simultaneity definitions of relativity two different accelerations (i.e. starting from different positions) can look identical only in one inertial frame?

 

In classical physics, the transformations required for changing from one moving coordinate system to another are quite easy to work out because time is not an issue. The true difficulty here is to establish exactly how the various measurements have to transform in a general transformation. You should note that even Einstein's deduction of general relativity does not provide a unique transformation (that is what that cosmological constant is all about).

 

I.e. how to properly read the measurements when the measurement devices are also undergoing accelerations all the time?

 

Because, in my approach, time is again an evolution parameter and not a dimension, the general relativistic effects become, once again, a rather simple (and unique) transformation. If we continue with our communications, we will get to that issue and, though the mathematics is once again rather outside your experience, the process is far simpler than Einstein's approach. (Just a little tid-bit to keep you interested.)

 

Yeah, I'm interested. I think I have an inkling of understanding to that issue after skimming your threads regarding your treatment of relativistic time relationships, but definitely have to concentrate on that issue properly after the Schrödinger Equation bit.

 

By the way, your examination of "co-accelerating spaceships" reminds me of a thought problem I proposed back when I was a graduate student.

 

...

 

Their computer records must show the correct position for every time during the maneuver and their clocks must agree with the war lords clock both for the actual moment that the maneuver starts and for the exact moment the maneuver finishes. All the personnel on board the ship must agree that the timing of the acceleration is in accordance with the computer records and that there has been no tampering with the data: i.e., the computers can be programed to yield the desired results (intermediate times during acceleration can be faked) but cannot be reprogrammed to adjust to a new maneuver. The trajectories resulting from those programs must end up being an internally consistent set.

 

Hmmm, okay, so if we have identical ships performing identical acceleration procedures, starting at the same moment in the "initial frame", then according to SR the distances between the ships would be stretched after the acceleration due to changed simultaneity.

 

To avoid that stretching, the ships at the rear need to accelerate harder or longer. And in that case the computers of the front ships and of the rear ships don't produce similar trajectories (albeit the product of acceleration * time (covered distance) would be the same?)

 

So what we would then like to see is how the data should be recorded so it would produce identical trajectories? Hmmm, I'm not sure how to proceed from here.

 

And interesting enough, if we have a single object tracing the trajectory at its front and at its rear (with an accelerometer and a clock), then with the definitions of SR we would say the front and the rear followed different trajectories while the geometry of the object didn't change at all?

 

Oh, I just received the latest issue of “Scientific American”. On the cover page, there is “Naked Singularities” in red letters which of course drew me to look at the article (starts on page 36). I get a kick out of the statements in that article made by the “noted professional physicists”. “Assuming that no new forces of nature intervene, horizons should be governed purely by general relativity, a theory that is based on well-understood principles and has passed 90 years of observational tests.” Boy is that a long time; it's almost 20 more years than I have been alive. My god, there can't be any error there.

 

“Stephen Hawking and Roger Penrose proved that singularities were, in fact, unavoidable.” And exactly how did they “prove” that? By assuming Einstein was right? I think they did indeed make that assumption. Personally, I am of the opinion that the “singularities” themselves are evidence of error in the theory. Of course, that's a quack opinion.

 

Well, objectivity is a difficult business :friday:

 

I got somewhat stuck today on this post, hopefully I'll have time to reply to the Schrödinger Equation thread soon...

 

-Anssi

[Doctordick]

Hi Anssi, I didn't mean to lead you down another complex path.

I can see though that the definition of the circumference becomes somewhat ambiguous if you want to define it in a rotating frame, and when I'm avoiding the ideas of rotating frames it's... Well let's just say it's a tough nut to crack that one!

It most certainly is. The only solution is to be very careful with your definitions and then pretty well ignore your intuitive conclusions. Then your results depend directly upon your definitions and can be different depending on exactly how you decide to define things.

It is certainly somewhat surprising that rotating frames can be seen as symmetrical to each others as well if you consider the whole universe, that had not occurred to me quite that clearly before, even though, as you probably know, I have thought about the role of the rest of the universe in "causing" inertia, which is kind of the same issue.

I have heard people make such statements before and my complaint is always the same, “exactly how are you defining “inertia”? Most people seem to work under the belief that their intuition gives them the correct answers and this is a logical error. As I commented to Bombadil, I think it would be worthwhile for you to at least read the opening to my thread where I define “logical” and “squirrel” thought. I think it is a very important observation difficult for a lot of people to comprehend.

Also, makes me wonder whether the root of such circumstance in our worldview can be traced back to those same three symmetry principles...?

I think the roots of our world-view lie within the realm of “squirrel thought” and, as such, essentially defy logical analysis. On the other hand, the resultant world-view had better be in accordance with those symmetry principles or logical errors would arise; however, I would point out that most people have little concern with errors in their world-view: they believe what they believe and are not really interested in logical conflicts.

You refer to the complications that arise because the objects in the situation undergo accelerations all the time, and with the simultaneity definitions of relativity two different accelerations (i.e. starting from different positions) can look identical only in one inertial frame?

I am not sure what you are referring to here.

I.e. how to properly read the measurements when the measurement devices are also undergoing accelerations all the time?

Reading the measurements is not the problem; the problem is inferring the proper “simultaneity” you should be using to actually plot the temporal positions. Just for your education, let us look at a ring rotating at relativistic speeds. The question is, how do we reconcile Lorentz contraction with the circumference being given by [imath]2\pi r[/imath]. If we are in the rest frame of the distant objects (we see the ring as rotating) we would expect the elements making up the ring to appear contracted towards one another; however, that would imply insufficient total length to accommodate the required circumference. Clearly the space between the elements is too large. But isn't that exactly what you should expect? Because of centrifugal force the ring is trying to expand so it must be stretched. Likewise, a ring rotating at relativistic speeds should be severely stretched unless the forces holding it together are infinitely strong. In the final analysis, what you will actually get depends explicitly on the forces which hold the ring together. These forces simply can not be neglected.

Hmmm, okay, so if we have identical ships performing identical acceleration procedures, starting at the same moment in the "initial frame", then according to SR the distances between the ships would be stretched after the acceleration due to changed simultaneity.

Most certainly; but the war lord doesn't want that.

To avoid that stretching, the ships at the rear need to accelerate harder or longer. And in that case the computers of the front ships and of the rear ships don't produce similar trajectories (albeit the product of acceleration * time (covered distance) would be the same?)

No, the covered distance cannot be the same in any actual rest frame because the formation must be Lorentz compressed in the original rest frame. Neither can the start and stop times be the same: the start times have to be the same in the original rest frame but the stop times must be the same in the finish frame.

 

I solved this problem a long time ago and I am not sure I remember the solution correctly but as I remember it, there is a single acceleration profile for the entire fleet. If the war lords ship is in the middle of the fleet and he sets up the desired acceleration (i.e., his own acceleration) of the fleet, the actual required acceleration depends upon how far behind or ahead of his ship you are. There exists a point behind the war lords ship where the required acceleration goes to infinity (anybody behind that point might as well desert as there exists no possibility they can fulfill the lords orders). As I remember the solution, the required acceleration of the ships in the fleet is a rather simple function of the distance forward of that singularity (if no one can figure it out, I will work out the solution myself). Since the positions of every ship in the fleet remains the same (so far as the war lord is concerned) the clocks in every ship need to read exactly the same a the war lords clock (with a constant correction which is exactly equal to the length of time a signal needs to cover that constant distance). Reminds me a lot of the clock settings on the geocentric navigation satellites as referenced to Colorado.

 

Turning the fleet is a more complex problem.

I got somewhat stuck today on this post, hopefully I'll have time to reply to the Schrödinger Equation thread soon...

I think that would be best. These other things can wait.

 

Have fun – Dick

[AnssiH]

I have heard people make such statements before and my complaint is always the same, “exactly how are you defining “inertia”? Most people seem to work under the belief that their intuition gives them the correct answers and this is a logical error. As I commented to Bombadil, I think it would be worthwhile for you to at least read the opening to my thread where I define “logical” and “squirrel” thought. I think it is a very important observation difficult for a lot of people to comprehend.

 

When reading that post, I once again got the feeling that we indeed think very much alike :) I see the human worldview as a self-coherent set of assumptions, i.e. self-coherent in the sense that different assumptions are glued together with little bit of logic. And since they are so tied together, it seems our (squirrel) assumptions are quite rational (other assumptions considered), when actually they are simply a function of those other assumptions we have made (and multiple different self-supporting sets of assumptions can be made to explain any set of data)

 

When I said "It is certainly somewhat surprising that rotating frames can be seen as symmetrical to each others as well if you consider the whole universe", I meant it is surprising on the squirrel thought level, because it seems for most everyone that inertial effects would reveal which frames are rotating. It is surprising that under a careful logical analysis you find there's no way to tell which frame is rotating (that the expectations are the same). I understand your commentary on why that is so to a certain level, albeit I don't have the chops to actually perform that sort of logical analysis rigorously myself (with all the involved details).

 

My comment about "the role of the rest of the universe in causing inertia" had to do exactly with thinking about the possibilities of defining "inertia" in specific ways to end up with specific conclusions. Just never were able to think out very far how different routes could unfold exactly, and it is certainly interesting observation that with current physics definitions there's no difference whether it's the bucket or the universe that is rotating.

 

I think the roots of our world-view lie within the realm of “squirrel thought” and, as such, essentially defy logical analysis. On the other hand, the resultant world-view had better be in accordance with those symmetry principles or logical errors would arise; however, I would point out that most people have little concern with errors in their world-view: they believe what they believe and are not really interested in logical conflicts.

 

Yeah, what I was wondering was whether this specific "ignorance" about rotating bucket vs. rotating universe is also - under careful logical analysis - tautologous to those three symmetry principles.

 

I am not sure what you are referring to here.

 

You commented the co-accelerating spaceships post was a "good presentation of the fundamental difficulty of establishing general relativistic transformation", and I was not sure what you meant by that, so just made a blind probe :)

 

Reading the measurements is not the problem; the problem is inferring the proper “simultaneity” you should be using to actually plot the temporal positions. Just for your education, let us look at a ring rotating at relativistic speeds. The question is, how do we reconcile Lorentz contraction with the circumference being given by [imath]2\pi r[/imath]. If we are in the rest frame of the distant objects (we see the ring as rotating) we would expect the elements making up the ring to appear contracted towards one another; however, that would imply insufficient total length to accommodate the required circumference.

 

That's exactly the problem that I got stuck on, as it was brought back into my mind when you mentioned the 2 star universe. I have this squirrel thought in my mind which tells me it should be possible to understand that situation without contradictions even when supposing a perfectly rigid rotating disk. Looking at the history of that problem, seems like many very smart people have had the same squirrel thought (I suppose for the purpose of making the problem simpler to handle in ones mind) and on the other hand many suggested solutions have had something to do with taking into account the realistic properties of any real disk.

 

In the attempt to figure that out, I did try to approach the problem from many different angles, while trying carefully to not picture the situation "from a rotating frame" (defined as "a frame where inertial effects are felt") since with the definitions of SR, from every point of that "rotating frame" the situation would look different (different simultaneity). Also I think I have convinced myself that the radius most certainly cannot shrink or there would be insurmountable trouble...

 

At any rate, I certainly cannot deny that...

 

Clearly the space between the elements is too large. But isn't that exactly what you should expect? Because of centrifugal force the ring is trying to expand so it must be stretched. Likewise, a ring rotating at relativistic speeds should be severely stretched unless the forces holding it together are infinitely strong. In the final analysis, what you will actually get depends explicitly on the forces which hold the ring together. These forces simply can not be neglected.

 

...in the final analysis the forces holding the object together are also subject to the definitions of time and space and cannot be expected to live a life independent of those definitions... It's a very tough nut to crack that one! :O

 

No, the covered distance cannot be the same in any actual rest frame because the formation must be Lorentz compressed in the original rest frame.

 

I meant, the covered distance as measured by the onboard computers that measure the strength of the acceleration and elapsed time. If the ships at the rear accelerate harder than the ones at front by the exact amount that keeps the fleet intact, then I suppose all onboard computers would calculate the same covered distance(?) As that's the same situation as measuring the covered distance of the front and the rear of a ship during an acceleration procedure.

 

Or are there ambiguities (hidden from squirrel thought) when it comes to "covered distance of an accelerating object, as measured by the object itself"? Hmmm....

 

I solved this problem a long time ago and I am not sure I remember the solution correctly but as I remember it, there is a single acceleration profile for the entire fleet. If the war lords ship is in the middle of the fleet and he sets up the desired acceleration (i.e., his own acceleration) of the fleet, the actual required acceleration depends upon how far behind or ahead of his ship you are. There exists a point behind the war lords ship where the required acceleration goes to infinity (anybody behind that point might as well desert as there exists no possibility they can fulfill the lords orders).

 

That, btw, is also quite surprising conclusion and not really obvious from a squirrel thought level.

 

It seems to imply that

- The larger the fleet, the slower acceleration maneuvers it can complete without breaking up.

- If you have a long enough pole, it cannot accelerate without breaking up even if you have individual engines attached along the length of the pole and starting to accelerate at the same time; the engines at the rear end would have to produce an infinite thrust to keep the pole intact while the engines at the front only produce a tiniest thrust.

 

Is that correct? It sounds... ...interesting.

:I

 

I think that would be best. These other things can wait.

 

Well I replied anyway, but I wouldn't like to get into tons of math while still struggling with the Schrödinger bit :)

 

-Anssi