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c o n t e n t s

INTRO

KEY UNDERSTANDINGS

SPECULATIONS

A STRANGE PHENOMENON

3-DIAGRAMS

EXTRATERRESTRIALS

INTRO

One day back in the early 60s when I was 13 or 14, I took the train to London to visit a 'New Automated Living Area' at Harrods - as advertised in one of the weekend newspaper magazines. Impressive though this was, there was nothing more to it - just one big open-plan area, with all kinds of futuristic appliances and what not. But the experience was over in an hour.

Being in Kensington High St, within easy reach of the Science Museum, I decided to wander along there. Although I spent the rest of the afternoon in the museum, I remember only one exhibit from that day. I distinctly recall staring at it for some while, as I battled to assimilate and make sense of the implications. To anyone not particularly interested, this display would have appeared banal and scarcely worth a glance. It was simply a black, one metre square, waist-height table, but crucially its top was painted with a big white swirl like a catherine-wheel that reached to the four edges. It was a representation of the Milky Way galaxy.

The formidable task, as it seemed to me then, of digesting this in conjunction with the accompanying blurb, occupied me, as I say, for some while. In fact I remember having to return to the spot several times that afternoon in an attempt to consolidate what I was taking in.

The problem was one of scale. From satellite photos I knew about Earth floating in space. And I knew about the 9-planets and their moons. I had, after all, been looking into these things for a year or two by then and had studied schematic diagrams in books. So far as the Solar System was concerned, one could get a rough sense of scale - or at least, the feeling that one could - from looking at the sun, Earth and Moon in a book, and then in reality. These were within most people's experience, But what confronted me now in the museum, was on an entirely new level.

Light from the sun takes 8.3-minutes to reach Earth. In other words, Earth is about 8 light-minutes from the centre of the Solar System. If you were to locate a point 8-light-hours out you'd find yourself well beyond the orbit of Pluto - still the furthest planet (I think?). But the outer reaches of the Solar system are certainly only a matter of light-hours away, not even a light-day. (The sun's influence goes far beyond this, of course, to the outer edges of the Oort Cloud in fact, which is ~1.5 light-years... but that's another issue).

Now consider what I was staring at on that table: a spiral 100,000 light-years across, and the Solar System about a third of the way in from the edge, on the Orion arm. If I'd made a pin-prick at that point, even with the finest pin I could find, that pin-prick would make a hole in the table that would be thousands of times larger than the diameter of the Solar System. And in all probability this hole would be too small to see. But get that: a pin-prick THOUSANDS of times bigger than the Solar System, and still invisible!

To look at this another way, imagine how far on that map light from our sun would travel in a lifetime, say a hundred years - answer: ONE MILLIMTRE, scarcely more than the thickness of my thumb-nail - and ONE MILLIMETRE would be ~100x365=36,500 light-days.... how many Solar Systems is that? Which shows the true scale of things, and how invisibly microscopic the Solar System is in the galaxy.... maybe comparable to the size of a single living cell against a total animal.

While I was absorbing this, I noticed just off to the left another great hurdle for my intellect. This was a 3D open box about a meter in each direction in which hundreds of almost invisible vertical wires supported an array of pea-sized spheres. These represented galaxies. In the centre of this space was an opaque sphere slightly smaller than a ping-pong ball which represented the outer limit of naked-eye visibility from Earth at the centre - concealed in the ball together with 'local' galaxies which included Andromeda at 2.2-million light-years away. Andromeda is a similar spiral to the Milky Way though about 30% wider.

ANDROMEDA (M31)

The diagonal of this shot is ~130,000 light-years

The suspended 'peas' were the largest of the billions of galaxies beyond range of the naked eye, but detectable with telescopes. So what lay beyond the box lay also beyond range of the most powerful telescopes - and the distances involved here were in the hundreds of millions of light-years.

All the while, fairly awe-struck by all this, I was struggling to get some kind of a tangible perspective. Curious though it seems to me now, I actually achieved it - at least, I got close enough to satisfy myself at the time. I remember leaving the museum feeling extremely happy and even perhaps a bit smug. So it was a well-spent afternoon: I've never since had to tussle with these scales of space (or time). Such is the value of getting a grip on issues like this while quite young - when the brain is still maleable and receptive to profound concepts, and the imagination still fertile: one needs, I believe, an ability to 'stand back'.

 

KEY UNDERSTANDINGS

There's a couple of key ideas in cosmology that stand out for me. One is simple logic, the other owes its existence to the amazing brilliance of Steven Hawking. They are ideas, though, that I think help illuminate aspects of the Universe which are crucial to beginning to understand it. As with so many brilliant ideas - like, for instance, the theories Einstein worked on - they are developed more by logical deduction (using well-proven models and methods) than observation. Some observation nearly always plays a part initially, then subsequently (if a theory is correct) observation becomes the whole and verification by experiment can proceed. This is not always (easily) possible. And things like black-holes and the Big Bang are such cases.

Any theories that concern extremes are essentially dubious, and may be unprovable. Even so, the process here could lead to a better understanding of matter which can turn out to be of great practical use. How else but by pushing at frontiers can we find ideal methods of space travel, develop supreme artificial intelligence, solve the nuclear 'fusion' riddle,.. etc?

Anyhow, the first idea that intrigued me concerns the 'Big Bang'. The theory is that at the point of the Bang a huge amount of potential energy was instantly transformed into kinetic energy - perhaps due to instability in the containment of the 'universe' in hyper-condensed form before the Bang; or maybe it was a collision of two enormous black holes... who knows? Either way, some laws of physics may fall-down in the extreme conditions I'm examining here, but assuming 'Conservation of Energy' worked, then the kinetic energy contained in the material thrown out just after the Bang (plus the potential energy contained in that matter) must equal the total potential energy just before it happened.

Furthermore (and extrapolating this 'fact'), the energy we observe now in the universe - in the form of potential, kinetic, gravity, light of all wavelengths and particle radiations and so on, etc... all add up to precisely this same figure - which on our meagre human scale is almost unimaginably colossal. So that's one idea.

The other - cooked up by Hawking - describes what happens near black-holes. It's an ingenious notion and could explain why black-holes are so elusive - ie, they exhibit weird formerly-unanticipated properties. The idea is that space is not quite the entity (or should that be 'non-entity'?) we imagine. Rather than being simply a neat vacuum, with e-m radiation from stars and other emitters continually passing through in all directions (ie, submillimeter, infrared, visible, ultraviolet, x-rays, gamma rays... or 'The Integrated Density of Light'), it actually has properties that become significant in extreme conditions (in the same way that gravity becomes significant only when vast numbers of particles coalesce) - for instance: in the vicinity of the (an?) event-horizon of a black-hole.

The event-horizon is a kind-of 'shell' at such a distance around a black-hole (depending on its size) that once within it, light cannot escape - gravity here is just so enormous. But outside that horizon, light still can escape. At some point (perhaps the same as for light) there is an event horizon - Hawking speculates - which effectively tears the fabric of space apart. That is, it's as though space is composed of pairs of elementary Energy particles which when together (as they naturally are) they exhibit neutrality and their presence - like turnip pulp in cheap raspberry jam - is superfluous and unnoticed...

(Maybe this theory has applications in the mysterious 'dark-matter' notion people talk about these days, which is supposed to explain the discrepancy between the amount of 'observed' and the amount of calculated matter in the universe. Without dark matter several important theories break down.)

...Yet when these pairs, so Hawking postulates, get separated at the extreme conditions of an event horizon, the negative-energy particle is absorbed into the black-hole while the positive one is repelled (or at least, floats free). These then, and in huge quantities (everything is extreme near a black-hole - quantities too), are forced into a kind of envelope (like wrapping-paper around a toffee) by the super-intense magnetic field. This 'funnels' them towards the poles from where they're 'emitted' as an intense jet of particles.

This means that instead of radiating energy like light emanating from a star, there are these jets from each pole. The black-hole will doubtless be spinning - nothing in the universe is static - so perhaps the location of the black-hole will be most obviously revealed to whoever perchance is in line with one of these beams of radiation (which presumably, unlike the coherent light of a laser, would expand and weaken - an ever widening circle). This, I guess, would resemble a pulsar. Considering the stupendous distances though - as indicated in the first section of this text - the chances of locating a black-hole on this basis or on the basis of the behaviour of local matter (because it's all been sucked into the hole), or - as with neutron stars - the odd movements of stars local to such a huge gravity point, are probably low. (Not sure if any suspect objects have been actually spotted yet? I think it's been assumed for some years that the centre of spiral galaxies contain a black hole...)

At some point... who knows?... the black-hole will be drained to the extent that it will no longer support this space-tearing event horizon.... at which time the black-hole could begin to grow again as light and debris are subsequently absorbed, and then the whole process could start again, setting up a fluctuation... like the oxygen level in the atmosphere fluctuating at ~20% (if it exceeds this then spontaneous forest fires cause it to reduce). Or maybe the black-hole would instead fail to contain itself and expand, even explode into a supernova?

Most of the above could be tosh - I mean, I could just be revealing my own monumental lack of knowledge and understanding or how out-of-date I am. This doesn't matter. As long as I feel I understand it (or bits of it), then fine. Because when you think about it, a great deal of life is like that (particularly the phenomenon of life itself): you only THINK you understand it (and maybe sometimes you do), but you can then contentedly put it aside and get on with other things without having to dwell on it - whatever 'it' is?. And mostly it'll probably be some irrelevant 'mystery' that would take you a big effort to get to the nub of. So we kind-of 'pretend' we understand things - or else actually do briefly then immediately forget but retain a memory of having understood, which is good enough - hence a contented acquiescence and idleness is possible.

So, unless you're a research physicist or cosmologist, these Big Bang and black-hole theories are not THAT important: whether or not they're actually true is beside the point. I, though, enjoy contemplating them; it's like a game, an intellectual game that also calls on intuition (the creative bit). So I've watched keenly over the years as the experts have unveiled new ideas and observations on these things. Even if I am ready at any moment to revise what I 'know', I feel more contented if I think I understand what the world's best brains have come-up with SO FAR - our best contingent provisional picture... even if it does turn out to be tosh.

BUT I only pursue this interest while the effort or cost is small - by which I mean: that being an idler and true to form, I've actually, for instance, done absolutely no research for this article - it's all straight out of my head (and I guess that tells).

 

SPECULATIONS

 

Science journal

The top two-thirds of Oct '68's Science Journal

(for more on 'Machines Like Men' click here)

The last item in this edition is authored by the amazing Isaac Asimov himself... see 'The Last Question' The reason I refer to this story is because in it Asimov says more about the universe than about 'Multivac' (or 'ac' for short... standing maybe for Asimov's Computer or Analogue Computer?), and his speculations are about the most extreme in both depth and in time I've ever encountered. Maybe Douglas Adams came close? Neither, of course, were entirely serious and were really playfully and entertainingly juggling with serious concepts. As for my speculations, I'll at least keep (boringly) to the present era of the 21st Century....

 

So now for my own mad conjectures:

(Heisenberg's Uncertainty Principle permitting... )

First...

THE BIG BOING - and I mean BOING!

Preliminary aside:

It's well enough known that the phenomenon of gravity causes particles in the universe to 'fall' towards one another. Frequently these particles collide and form clusters - where the greater the cluster the steeper will be the 'fall' into it of other clusters and particles. Observations have shown that the sun's mass attracts not just planets and comets but also light, which when passing close by deflects towards it. This, say the 'experts', reveals the distortion (curvature) of space caused by gravity. It's reckoned, moreover, that the effective overall 'curvature' of the universe caused by matter (mostly in the form of stars or dead stars) forms a kind of saddle shape, which extended becomes a toroid - like the inner-tube of a tyre. This means that the universe - or our particular universe - although vast beyond what we can see, is essentially finite, existing only within this 'tube'. Of course, beyond the tube, in whatever dimensions one cares to speculate on, there may well be an infinite number of these 'tubes' - or perhaps they too, like matter in this universe, are limited by a further level of 'curvature' and so on ad infinitum?

Despite all this, 'experts' again have calculated (from the amount of matter they believe exists in the universe and the kinetic energy that's causing it to spread) that the total gravity is not strong enough to eventually return everything to its original point where the Big Bang occurred ~13.7 billion years ago. Instead, they say, the universe will suffer a 'heat-death' - which I take to mean that the 'tube' containing the universe will end-up as simply a uniform spread of cold static particles - ie, 'dust'.

This strikes me as a very strange conclusion, because doesn't dust have gravity? And won't this dust - as mentioned above - begin at some stage to gather into clusters, etc? Either way, and even if this did not happen, the subsequent instability - predicted by (and empirically demonstrated from) Chaos Theory for any homogenous mass - would lead to an evolving process that would preclude any possibility of an eternal uniform dead-space. Hence the inevitability of the formation of a new 'universe'.

Who knows?

However - and regardless of whether there's this 'tube' or whether a whole load of universes (albeit with vast gulfs of space between them) exist out there - if the dispersing galaxies are slowing (which, at least as clusters and in spite of what one would expect, they are reckoned not to be: see below), they will eventually stop. In the absence of any other matter beyond them, how can they possibly do otherwise? And having stopped, they will - however weakly - be attracted by gravity back towards one another. What alternative is there? I can think of none.

 

Is This What Caused the BIG-BANG?

As the universe approaches these final stages, there will be a period with clusters of black holes. These will absorb other matter and collide forming fewer and fewer but larger and larger black holes until finally there are just two remaining, probably a huge distance apart after each hoovering-up half the universe. All THIS taking untold aeons, perhaps hundreds of billions or even trillions of years....

BUT if these last two enormous black holes come together at great enough velocity, then instead of 'falling' into one another and becoming a single monumental black hole, the collision could result in an explosion so phenomenal that beside it a supernova would resemble a passing photon.... and hey-presto your next BIG-BANG: a new UNIVERSE is born! And so on ad-infinitum!

Well, can you come up with a better theory? I can't believe that someone hasn't already postulated this - probably they have? Or more likely, for some reason I've failed to notice, my speculations are all bonkers!

 

Second...

A STRANGE PHENOMENON

This note (added 18.5.10) seemed appropriate after watching this impressive 20-min episode of 'Cosmic Journeys' on youtube: 'When Will Time End?'.

It's suggested in the film - which includes spectacular shots from the Hubble space telescope of distant stars, supernova, gas-clouds, galaxies and other amazing phenomenon of outer-space - that the expansion of the universe is actually accelerating. This is weird indeed: that the overall speed of recession of the various galaxy-clusters and so on, is increasing seems to defy logic; yet it has been observed - see: wikipedia. Although galaxies are frequently detected to be slowing and even reversing within local clusters or regions (ie, for just one instance: in a few billion years Andromeda & The Milky Way are set to collide), the general trend apparently is that the rate of expansion increases.

The mystery this creates is rather more significant than the one implied in that film's title. Similarly for other fine questions that further episodes of this epic series pose... such as 'How Large is the Universe?'.

 

So the key questions now are...

What force is causing the acceleration? And: From where does the force emanate? (see also my little addendum)

Is there something 'beyond' the outer limits of the observable universe that's attracting matter out with a greater pulling-power than the gravity operating within - like a balloon expanding at an increasing rate? Maybe there's a straightforward logical answer? Or is it truly the monumental puzzle it seems - the next great hurdle for science? I've seen speculation that the cause could be the power of vacuum.... which I have to confess made me laugh.

But here's an intriguing detail from wikipedia:

"With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance."

If reliable, this must bring the whole question into some doubt. And at the same time the issue of Dark Matter too.

 

THE SPEED OF LIGHT:

c = speed of light (~300,000 Km/sec)

In addition, and I think entirely relevant here, is the idea that the speed of light cannot be exceeded. This will some day be recognised as the mad notion it is, and will be discarded (See below *).

What could be more obvious than that there can be no limit in reality to the speed at which something can move in the universe relative to something else? Regardless of frames of reference, the concept is logically inconsistent - I mean what about two bodies moving away in opposite directions at > half 'c'? Just because we can't measure or otherwise perceive an object moving at or faster than c due to our relative frames of reference, doesn't mean it isn't. Most of the universe, certainly the outer edges after ~13.7bn-years since the Big Bang, is beyond the range of our observation. If we on Earth are presently receding from that 'edge' at >c then the light emitted from this region can never reach us. See also time dilation. (and wikipedia.)

 

DARK MATTER

The issue of stars near the centre of the Milky Way encircling at rates that suggest far more matter (gravity) there than is observed, gives rise to the idea of 'Dark Matter'. Here's a neat little diagram I nicked from wikipedia:

wmap

If the gravity we measure for which the Dark Matter is responsible is real, then one can only wonder what makes the Dark Matter dark? Either it isn't emitting light of any wavelength, or else it's moving away from us at a speed that prevents the light from reaching us: ie, probably close to or > c. And if Dark Matter is simply matter that's receding at > c - of which there must disproportionately be vastly more near the outskirts of the observable universe - then that would certainly explain the phenomenon.

In addition, our assessment of distance may be further compromised by miscalculation through failure to take account of speed of recession - as if this has no effect on how long the light will take to reach us.

 

For instance, observe the 3-diagrams below.

I should first clarify that although not drawn incorrectly, the diagrams are drawn misleadingly. This is deliberate to emphasise the error - if there is an error - in concluding as in the previous paragraph. To be fair, I should have drawn a central vertical with the galaxies moving left and right, but instead I've chosen to fix the remote galaxy... The fact is, nothing is space is static. Only when an observer arbitrarily assumes such a vantage point can just ONE location be considered static.

 

In the top picture at Time = 0 the two galaxies at a billion light years apart are separating at ½c. That's when the supernova explodes. In the middle picture a billion years have passed so the flash reaches the point where the Milky Way was when the flash began its journey - but now the Milky Way is half a billion light-years further away. In the last picture the flash finally arrives at the Milky Way which is now twice the distance from the location of the flash when it occurred.

If the galaxies were stationary relative to one another the flash would have reached the Milky Way after a billion years, but the speed of separation has caused it to take 2-billion years.

Now, supposing we change the diagrams so the Milky Way is fixed and the remote galaxy instead is zooming away at ½ c. THEN how long would we expect the flash to take in reaching us? The situation would be identical - the perspective we choose is purely arbitrary. 

So if someone in the Milky Way sees that flash and together with other data from the vicinity of the flash calculates that it all left the remote galaxy only one billion years ago (neglecting the speed of recession - or separation), then they will assess the distance of the galaxy to have been twice as far away than it actually was when the flash took place.

This would mean that the distances of all remote objects receding from us at speeds of a significant fraction of c would be miscalculated: ie, over-estimated. If an object is receding at ¼ c then its calculated distance will be 50% further than actual (ie, substitute ¼ for ½ in the above diagrams). In this instance, the distance between the galaxies at the moment the flash occurred would be ¾ of the distance eventually calculated by an observer in the Milky Way (assuming they failed to take into account the speed of separation).

Referring now to the above indented quote stating that the measurement of distances of objects beyond 1000 parsecs is unreliable: Since 1-parsec is 3.26 light-years, if that item is correct then reliability reduces as distance exceeds 3,260 light-years, which is just one thirtieth of the diameter of the Milky Way. So where does that place the reliability of distance measurements of galaxies at the edge of the visible universe - ie, a million times further away: ie, several-billion light-years?

What could have been overlooked - surely not? - is the fact that if an object is receding at, say, ½ c, then the light from it will take twice as long to reach us than if it was stationary relative to us. What could be more obvious? The light will be Red Shifted too, of course, which would reveal that speed. But have astronomers assumed the light is STILL travelling towards us at c... erroneously assuming that c is constant regardless of the speed of recession of its source relative to them, or them relative to the source? If so, then all the listed distances of remote receding objects will (as I say) be incorrect, and the further away - or faster their recession - the greater the error.

I'm sure they're not that stupid.... but who can say? If that error has been made, though, it would certainly explain the counterintuitive, not to say bizarre, even paradoxical, notion that the universe is expanding at an increasing rate. I don't know anyone who might be able to verify this either way, and I'm definitely too idle to search around and look up the truth of the matter. It does strike me as odd, though, how rare it is to find acknowledgement of the fact that there can be no limit to the speed of an object, and that contrary to what everyone seems to think, the speed of light DOES depend on the speed of its source. I repeat, to me this is obvious, and I think many people are confused by the incorrect (and really erroneous) notion that they themselves are the ONLY reference point relative to which nothing moves at speeds greater than c.

The monumental error, it seems to me, is not the entirely correct understanding that c always measures to be 300,000 Km/s, but in the concomitant failure to recognise that as the metres vary, time must vary accordingly to maintain this (local) reading. Well, fine - let relative time vary, so what? But speed is free to be anything! How the speed of an object affects the passing of its time relative to ours as 'static' observers, is another issue. See time dilation .

Two possible methods to confirm that light-speed adds to the speed of its source might be:

ONE, speed helium atoms in the CERN accelerator to half-c then as they filter towards detectors at that speed, fire particles to make them emit photons, and at the same point fire a laser - and see which hits the detectors first. I propose it will not be the laser-beam.

TWO, if there are pulsars in space receding (or advancing) at speeds of a significant fraction of c, then if a pulse can be detected by a device in the upper atmosphere or on a satellite AND the same pulse also detected at ground level, then assuming clocks are appropriately synchronised and all other factors taken into account, the time difference for detecting the pulse should reveal speeds other than c.

(I guess I'll have an addendum too for the next - final - little section to this article when I've seen the 'Cosmic Journeys' episode on 'The Search for Earth-like Planets'.)

 

EXTRATERRESTRIAL LIFE

A couple of months ago - in one of those morning magazine progs where they give too little time to gripping stories and loads too much to boring ones - a member of the SETI (search for extra-terrestrial intelligence) team spoke of several recently discovered planets around a star about 40-light years away. Before this agonisingly brief interview was brought to an abrupt end, the scientist was able to squeeze in the fact that in their search for life they were concentrating first on planets that had a moon at a distance that would cause a total solar eclipse - as our moon eclipses our star (the Sun) for us on planet Earth.

For anyone new to, or poorly versed in, the evolution of life, this detail might have looked perplexing. The logic was immediately clear to me for the following reason (though if I'd been asked before what I'd look out for first in the search for planets most likely to support life, I'm sure it wouldn't have occurred to me):

Some while ago in a TV documentary about the lunar landings, they interviewed a guy who's job it had been for the past four decades to measure every day (using a laser emitter-receiver - probably the same device seismologists periodically use to monitor how much a mountain is shifting) the distance between a fixed point on Earth and likewise on the moon (namely, a mirror that had been set-up there by astronauts Aldrin & Armstrong in 1969).

When asked what the measurements revealed, the guy replied that the moon was receding at precisely 3-cm a year. Which means - assuming recession is linear (which it probably isn't... if I wasn't such an idler I'd research this detail) - that it's moving just 1-metre further away from Earth every 33-years - or 3,000Km in a 100 million years.

If the moon averages ~380,000Km away, then 3,000Km is a bit <1%. So if vertebrates evolved as recently as 400 million years ago, then sea tides would have been greater according with the moon being about 3% closer - and doesn't gravity change with the square of the distance? Hence (maybe?) much bigger tides back then. And the bigger the tides, the greater the opportunity for sea life - especially vertibrates - to adapt to increasingly long periods on dry land. (And it was the sea where life finally began to really take-off after a couple of billion years of struggle from the first singe-cell organisms). In other words, we probably owe our early evolution onto land almost entirely to the existence, and proximity, of the moon.

So by the time we arrived at where we are in evolutionary terms, tides have become relatively shallow and the moon is at a distance where were get a fairly precise solar eclipse. Which presumably should guide us in at least one detail of what to look out for in our search for relatively advanced life elsewhere in the galaxy... because, face it: out of the hundreds of billions of stars in the Milky Way alone (which is one of billions, at the very least), and their billions of planets.... the probability of similar conditions as happened for Earth and from which life emerged, are almost 100% certain. And most likely, as Carl Sagan has speculated, the universe is actually teeming with life. The only reason against us making contact is the colossal scale of time/distance involved. What's colossal to us is minuscule to the universe. The centre of the Milky Way is ~30,000 light-years from here, and its fringes ~20,000. There's scarcely a handful of suitable stars close enough to Earth for beings on an inhabited planet to detect our radio signals within the next 10-millennia... by which time our signals will have reached a mere half-way towards the edge of the galaxy. So it goes...

 

*Speed-of-LIGHT

From the cliffs here at Hastings on the south coast of England I can look south-east on a clear day and see France. Using a theodolite I could take readings for a distant point there then drive east to Hythe, say, take another reading for that point and calculate its distance. I guess it would be ~20-miles... so if I flew a gyrocopter across the channel to that point and back, and the whole trip (according to my watch) took an-hour, then my average speed would obviously be ~40 mph.

There are other ways than a theodolite and triangulation to calculate distance. But say you choose a star 20-light-years away - a distance that astronomers confidently calculate - then launch your super-fast futuristic spaceship towards it so you get close to the speed of light. Accounting for acceleration and deceleration the round trip takes maybe 45-years according to those you leave behind who monitor the ship. BUT according to your watch the trip takes perhaps only 5-years due to time dilation caused by the relative speed of your ship. To your estimation, you have covered 40 light-years in 5 years, an average speed of 8c.

What this means is that for you in your spaceship the speed of light has been exceeded considerably. You can observe the distance you travelled; and you've measured the time it took according to YOUR clock. Those you left behind are in no position to tell you how fast you were travelling. They can only experience their own situation, while you can only experience yours.

Who's correct, you or them?

Obviously, YOU are correct for YOU. This means there is no theoretical (nor practical) limit to speed, clearly.... confirming again that it's quite permissable for distant galaxies to be receding at > c - how could it not be? Hence the light they emit will never reach us. QED!

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