You won't find "Spaceship engines" as a variable in any Relativity equations. — Rich

What about the F? Sounds pretty much like a variable to me.

Nothing more to say. — T Clark

I hear you.

Had nothing to do with GTR. — Rich

That's right. It has to do with knowing what acceleration is.
You're confusing it with velocity. Yes, in the frame of the fast moving ship, Earth has the high velocity, but from any point of view, it is the ship, or the frame of the ship, that does the significant accelerating.
Just throwing GTR term around or labeling as science fiction the description of others isn't helping.

Gravity plays a trivial role in the scenario being discussed. We're not computing it to 7+ digits here. You only need to do that if you're actually writing the navigation software that needs to get the ship to its target.

Look at the equation. — Rich

Yes, you should do this. It is covered in 7th grade physics. F=MA or A=F/M which still works even under relativity.
The force on Earth is primarily the weak gravitational fields of the moon and sun, which actually cancel out over a month/year respectively. Net vector of almost zero. The space craft has much greater acceleration due to orders-of-magnitude greater force to mass ratio, and it is applied in a consistent vector (at least until mid-trip where it turns around), unlike the gravity.

You describe the ship/earth as symmetrical cases, each moving away from the other's point of view, but that isn't acceleration. If it was a symmetrical situation, one twin would not be older when they are reunited. The difference is acceleration, or more precisely, the moment of acceleration. Both twins can accelerate equally (for control purposes if you like), but the one with the greater moment will be younger when the reunite.

Pretty sure this is wrong. Doppler changes wavelength/frequency of light. Relativity changes rate of time. Unrelated. — T Clark

Go through the example, ignoring relativity or not.

Does the half-lightspeed pulse generator not take 18 minutes (in Earth frame) to travel 9 light minutes? Does the first pulse not take 9 minutes to be seen, and the last not get seen immediately? What part isn't clear?

Still don't understand. This should have nothing to do with Doppler. That changes the wavelength of the light but won't change the frequency of the flash. — T Clark

Same thing. See the example above with the sun. Let's say it flashes 10 times a minute (every 6 seconds).
Without relativity, the trip takes 18 minutes, so the Earth observer sees 180 flashes in 9 minutes, twice the actual rate. Relativity says the fast-moving clock is dilated and only flashes 156 times (my guess was off) in those 18 Earth minutes. Still appears faster to the Earth observer. At 0.5c, the Doppler effect doubles the pace, and relativity removes only about a sixth of the pace.

I'm thinking about this and I'm not sure. Why would the rate of flashing be different when it is approaching vs. moving away from me? The only difference I can see is that, as it gets closer to me, the angle between my line of sight and the direction of travel increases. — T Clark

For simplicity, assume it is coming directly at you/directly away. No angles to complicate it.
This is Doppler effect, the same reason a train horn pitch is higher when approaching. The effect is far greater at a given point of observation than that of time dilation.

Suppose we flash once a minute. Sun is 9 minutes away, and the flash source is coming at us at half lightspeed. The trip takes 18 minutes, but only 9 minutes to the Earth observer since the first flash is delayed by the 9 light-minute distance.
Time dilation might take one of those flashes off (I'm guessing), so you count 17 flashes in 9 minutes.

I think this is not correct. Why do I only get one peek? Let's say the clock on the ship is constructed to flash a light at an established frequency. I can just measure the times between flashes as it passes. — T Clark

Right. It will flash faster as it approaches and slower after it goes by. This is why Andromeda is blue shifted when we look at it. Relativity says it should be a little red shifted since it's processes are slower in our frame. Point is, you're not getting accurate timings when you're not in the presence of the source of the signal. You can compute the delay if you know the distance, but the distance to the source is frame dependent, so still ambiguous.

If you want to get picky, the Earth revolves about its axis, not the sun. It orbits the sun.
— noAxioms

I love being picky. It is appropriate to say that he Earth revolves around the sun. In the definition of revolve I looked up, it was one of the examples used. It would also be appropriate to say the Earth revolves around it's axis, but I would probably use "rotate."

Fair enough. I got this from http://wikidiff.com/revolve/orbit:

As verbs the difference between revolve and orbit is that revolve is (label) to orbit a central point while orbit is to circle or revolve around another object. — wikidiff

What's the "less" part? — T Clark

I didn't like the wording of this part. Each clock is dilated slower in the frame of the other, but that cannot be directly observed.

If two space ships travelling a significant fraction of the speed of light (c), but not accelerating, pass each other going opposite directions and check each other's clocks, each will observe that the other's clock has slowed down.

They only get one peek at each other's clocks as they pass. You can't observe the dilation. If you're watching a moving clock, it appears to run faster if it is approaching. The Doppler effect is far more significant than the dilation.

If you want to get picky, the Earth revolves about its axis, not the sun. It orbits the sun.

Reciprocity of Special Relativity says there is no privileged frame of reference. If there is a privileged frame of reference, STR is wrong and Einstein's T is wrong. There is no T in GTR
-- Rich
I didn't mention a frame, privileged or otherwise. I was commenting on your statement about Earth accelerating.
— noAxioms — T Clark

Fixing the quote. I didn't say the 'Rich' part above.

If two space ships travelling a significant fraction of the speed of light (c), but not accelerating, pass each other going opposite directions and check each other's clocks, each will observe that the other's clock has slowed down.

If, on the other hand, there are two space ships at rest relative to each other and one accelerates away from the other up to a significant fraction of c then turns around and comes back and then the clocks are checked, both will observe that less time has passed on the accelerating ship.

This is called the "clock problem" or "twin paradox." Look Twin Paradox up on Wikipedia and you'll see the kind of unsatisfying explanation I was talking about. Please don't think I think that "unsatisfying" is the same as "wrong."

More or less, yes.
I don't think relativity goes into explaining why our universe has this geometry. It just does, and the theory predicts what will be measured.

How does someone on the Earth know that they are not accelerating from the spaceship? — Rich

The guy in the ship is plastered into his seat when doing the massive acceleration. The guy on Earth is not. OK, a black-hole sort of gravitational field could do that to Earth, but there is none in the scenario discussed.

The Earth is accelerating. It is always accelerating (remember gravity?). — Rich

Trival acceleration to non-relativistic speeds that cancel out over a year. See the part about the wobble around the sun I posted above.

The guy in the ship needs special technology to not die from the massive acceleration needed to get him up to enough speed to notice his age discrepancy, and he needs to do it 4 times (out, stop, start back, stop at end) before he dies of old age. The experiment is not practical even if we had a ship that could do that.

In any case, there had to be deceleration somewhere to even check the clocks. — Rich

Clocks can be unambigously compared when in each other's presence, and need not be stationary relative to each other. In short, you can look at each other as you pass by at speed if you like.

Why is that? We can just get on the radio and ask what time it is. — T Clark

See above. Comparisons of spatially separated clocks are ambiguous and yield different answers depending on the reference frame chosen. The radio doesn't help. This ambiguous ordering is the best explanation of the twins experiment.

I had put together an illustration of the twins experiment which kept things quite simple, involves no acceleration (using instead a tag team), and thus no GR complications. I can post it again if you like.

In terms of measurement either viewpoint is equivalent. Either body can be accelerating away from the other. — Rich

Completely false. You seem to not understand the distinction between velocity and acceleration.

Earth might be moving away from the ship, but it is not ever accelerating away from it.
— noAxioms

There is no privileged frame of reference under STR? Either viewpoint is coherent according to STR. STR doesn't allow for exceptions when it is convenient for a science fiction story. — Rich

All true, but again, I was talking about your use of 'acceleration'. In no frame does Earth accelerate beyond its annual wobble around the sun. It would be quite the science fiction story if it did (and yes, I've read such stories).

— Rich

...because of Special Theory of Relativity's Receprocity one can say that Earth is accelerating away from the spaceship, — Rich

Earth does not accelerate away. That would require a massive force on Earth, sending it out of the solar system.
— noAxioms

Reciprocity of Special Relativity says there is no privileged frame of reference. If there is a privileged frame of reference, STR is wrong and Einstein's T is wrong. There is no T in GTR.I didn't mention a frame, privileged or otherwise. I was commenting on your statement about Earth accelerating.

Earth might be moving away from the ship, but it is not ever accelerating away from it.

Those people that leave earth for this trip will never see anyone they know from earth again due to time dilation. They will leave for a 50 year trip (for example) and hundreds and hundreds of years could have past here on earth, — David Solman

If the trip takes 50 years (ship time), they're not exactly expecting to see their relatives again anyway. Human life span is not that long. So why is this a problem? A trip like that can only be one way. You kiss your family goodbye.

Not necessarily. Because of Special Theory of Relativity's Receprocity one can say that Earth is accelerating away from the spaceship, so it is the clocks in the Earth that are slowing down. — Rich

Earth does not accelerate away. That would require a massive force on Earth, sending it out of the solar system.

They would die because the gravity, temperature, air mixture, water mixture, or whatever environment they need is probably not what Earth has. Translation, they'd decompress, fry, suffocate, or get poisoned quickly, just like we would on every single one of the planets in this solar system except our own.

That said, the microbes probably would be the least of their worries since the microbes are equally not evolved to invade the alien host.

And then there's the inevitable greeting the humans would give. I have little faith in humanity's likely response to a visitor displaying obvious superior technology.

It's as big as 'here', so of course it fits in the sleigh. All timelord technology anyway. Anybody ever check Santa for a double heartbeat or wonder where he finds all those off-world companions he's got up there?

I suspect the present is about as big as 'here' is in size.

This is simply false. — tom

Could be. You need to reply to those who know this subject better than I. I've been a ball of disproven opinions on this point throughout this thread.
Comment on my QM thingy instead. I just stated that there is a copy of us quite nearby, to the point of giving a fairly specific figure for it.

Superposition states are states too (they are also called "mixed" states, as opposed to "pure" states). But I think I get your point: if we haven't been in contact with some remote region of the universe, then within that interval of time its wavefunction has been evolving independently from us, and there is no coherence between us and any one of its branches. — SophistiCat

A type-1 alternate universe is just like a type-3 in that we might share a common portion of past history, but we can effectively no longer interact, ever. One is a past statement, and one is the future. The future makes it type-1, and that indeed is a mixed state. But for there to be a copy of Earth, we need a reasonably identical past, which would be a pure state since nothing can come from outside.

Neither are bounded by the Hubble-Sphere. The type-1 universe is bounded by the event horizon (which IS frame dependent, despite my expressed hesitancy in the prior post), but the Earth copy requires that pure quantum state which is bounded by the particle horizon.
The former is a ball about 31 Glyr in diameter (units in proper distance), but the latter is a frame-independent ball about 92 Glyr in diameter, beyond which all quantum states are pure from our standpoint. That means the nearest copy of us is only 92 Glyr away There are closer ones, but there is no coherence between us and them, so they don't really exist in a type-1 sense.

We need another assumption. the cosmological principle, which says in effect that there are no measure zero misbehaviors! — fishfry

I think the cosmological principle allows such exceptions, but just says that the probability of us being that exception is sufficiently infinitesimal to preclude explanations that require us to be that exception.

As such, it is, as you say, an assumption, not some mathematical certainty that we're not unique.

The case of a simple bound system, such as a hydrogen atom, is easier to analyze than a more general case: we can actually solve the quantum equations and enumerate every possible state. — SophistiCat

Not sure which post brings on this reply. I brought up an insanely complex quantum equation in my prior post, but never suggested it was in need of being expressed or solved.

There is, however, a theorem for the general case in quantum mechanics, which puts a limit on the number of possible states, or degrees of freedom, given a volume and energy density within that volume.

We're talking a hubble-volume in this case, which has a finite but large degree of freedom. My wave function was based on that. Interestingly, I think it was a mistake to specify an inertial frame in my description. The full wave function of the one event is enough. If another event somewhere has the same wave function, it defines a clone Hubble sphere to ours.
It is also a definition free from tom's concern about the two universes staying identical. The definition is of an event which doesn't become something else.
My definition breaks down with Bill Clinton's oddly applicable statement: "It depends on what your definition of 'is' is". How can anybody assert that the state of some event outside our sphere 'is' in any particular state? Our definition sort of assumes a measurement taken from 'here', and by that definition, those distant events have no measurement and are in complete superposition. The nearest Earth clone is massively closer than the figure Tegmark quotes where the number of finite states is computed and divided by distance, something that seems invalid without a measurement being taken, from here no less.
The distance then becomes a function of the furthest historic matter that made a difference to our state now. That's further out that the Hubble-Volume, which is defined as the stuff that can make a future causal difference to here, not that which has made a past causal difference.

The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that moment. Even in a purely deterministic universe, as these systems transition from one state to another, they may end up in the same state at some point simply by chance. What that chance is - high, low, "almost surely" - will depend on a more detailed analysis.

Agree with this. Yes, I think I alluded to the opposite at first, but you're right. This was pointed out to me in a prior post.

Let's be rigorous about our definition of the state of a type-1 universe, that with which we would need to have copied.

I think all you need is a specification of an event, frame, and state. The frame is there for future state only, not present state. So:

Earth CoG at stroke of midnight Y2K, in the arbitrary frame of Earth CoG at that moment, in the state that is the direct causal history of me making this post 17 years later. That defines a temporal line of that point in space that goes out forever. A different Hubble Volume is identical to that one if the wave function of any point along that line is the same in both volumes.
Does that work? It totally leaves out the definition what is the 'current state' of our volume, and I think it might even be independent of QM interpretation.

If you perform a quantum measurement - e.g. a measurement of z-spin of a particle prepared in x-spin-up configuration, and choose your spouse based on the result, in half your futures you are married to Mary, in the other half it's Jane. Same past different futures.

Determinism is dead. Long live Unitarity! — tom

I thought you pushed the view that you're married to both of them, a deterministic view.
I just now see Michael's edit where he notes the same view shift.

No it doesn't. You can't count your clones. Physics tells us that the cardinality of your clones is Aleph_0.

If you think it is possible to count your clones, I urge you to try. — tom

I did in the post to which you replied. Perhaps you think that countable means you can know how many there are, but then the integers are not countable, so you're working from a different rule book.

I said the Hubble Volumes are INDISTINGUISHABLE not identical.

I think you need to expand on what you mean by these terms since we seem to be talking past each other.

If they have the same history, and if determinism is the case, then wouldn't they also have the same future? — Michael

That's why I brought up QM interpretations.
Copenhagen is in theory nondeterministic, but involves faster than light action, and thus destroys the limits of the Hubble volume. It also leaves states in superposition if not measured from an arbitrary observation point. Pull back the camera so to speak and Copenhagen becomes as deterministic as any other interpretation.

You might explain for us hoi polloi how indistinguishable things can be counted, because we would have thought that distinguishing something is a prerequisite for counting it.
— Wayfarer
I didn't say you could count them. You can't count them. — tom

You're being illusive. Wayfarer has a point, and you know the next question.
Countable means you can assign a number to any of these volumes, and to do that they must be distinguished. If they can't be, they're not countable. So volumes like ours, we're (arbitrarily) 1 and the nearest copy is 2. It is distinguished by being nearest. Of course the copy of me over there considers his volume to be 1 and ours (of which he is unaware) to be 3 because there happens to be another one closer to him. We're both unaware of the actual locations of those copies, so identical state is maintained. It is an objective ordering. Anyway, they're identical in state, but still objectively distinguishable and thus objectively countable.
I think it is a mistake to say this then:

There are a countable infinity of INDISTINGUISHABLE Hubble Volumes, which diverge. — tom

They must be distinguishable but have at least identical state. If identical state, how can they diverge? You must consider the full set of worlds as the one state, else there is no 'current state' with which another volume can be identical. To do so presumes a QM interpretation like Copenhagen with real chance and action at a distance and a bunch of baggage that muddies the statement that the two volumes are actually identical.

Heck, with that definition, maybe every Hubble Volume is identical state, and yes, that would mean uncountable.
Sorry for this post. Just thinking out loud.

They’re both metaphysical issues which physicalists are trying to solve by infinite ad hoc additions to physical theory. — Wayfarer

Funny, I see them as subtractions.

The short version: the ‘many worlds theory’ is based on avoiding the philosophically unsavoury implications of the observer problem.

The multiverse - ditto for the unsavoury implications of the fine-tuning problem.

I find them elegant solutions. The unsavory feeling you get seems to be a challenge to a religious view of what you are. Yes, I would find that unsavory, and cause for further investigation, not a terminus because it threatens my biases.

Not going to happen.
— noAxioms

You are passing up a valuable learning opportunity! Go on, give it a try! — tom

I mean the 1m3 expanding to infinity is not going to happen. OK, I worded it ambiguously, and you took it to mean that I'm not going to attempt the math.

I cannot think of anyone who has put forth a scientific hypothesis that mermaids don't exist. You have a link to such a proposal?

In practice, we don't need to worry about a time zero for either a spatially finite or a spatially infinite universe, because the General Theory of Relativity, which is used to do the backwards projection, loses validity as the scale becomes very small, and we have no theory to replace it. We can't use quantum mechanics because it ignores gravitational effects and in a very dense universe those cannot be ignored. — andrewk

I don't know my cosmology enough to describe the actual workings of our big bang. Inflation theory says there was different physics for a short time, low temperature, and perhaps the usual notions of 'density' wouldn't apply. The mass of the universe, if existing in some sort of finite volume, would form a black hole and never get off the ground.

Suffice it to say that for the purposes of this thread, the declaration that space is infinite implies it was always infinite ever since it was space. The material/energy probably never fully interacted. There is stuff that never was part of our causal history, even going all the way back. No reason to worry about it anyway since the Earth contains finite state and thus has no need of that history to be identical to another Earth.
We do have history though. If an exact duplicate Boltzmann Earth suddenly popped into existence in orbit around a plausible star, I would be on it and that 'me' would notice damn fast that it wasn't the native Earth.

I haven't gone through this idea carefully, but I'm moderately confident there is no 'reasonable' mathematical model in which a spatially infinite universe contains a time zero. If that's correct then there is no question of whether the universe was infinite or a single point at that time, since there is no such time. — andrewk

If the model has a event 0, there is no space to have a size. That's what makes it a singularity.

Maybe you should show your working? — tom

I did. I took the question for sarcasm and responded in kind when you persisted.

Given an initial 1m3 of space-time, what expansion rate is required to turn it into literally infinite volume in any finite time?

Not going to happen. Universe was never 1m3 it seems.

So, what rate of expansion do you think might be required to turn a subatomic spec into a literally infinite universe in 13.8 billion years? Have you done the calculation? — tom

You persist with this. Is it a serious question? 6 days, after which enough expansion took place to qualify as infinite. On the 7th day, the expansion rested. I really don't know how else to answer that.

The rate of expansion may be static, increasing, or decreasing. As long as there is a +ve Hubble constant, there will be Hubble Volumes.

A Hubble volume is not a type-1 universe. It is just the volume containing the matter whose distance from us is growing at sub-lightspeed. The Type-1 universe is bounded by the event horizon, beyond which things cannot ever have a causal effect here. It is something like 16BLY in radius at this time (comoving coordinates again).
About the Hubble constant, it is not a constant since the expansion rate is increasing. The constant is just what the value is now, and thus can only be measured to so much precision.
I looked at its description on space.com and found text more worthy of the New York Post:

As of March 2013, NASA estimates the rate of expansion is about 70.4 kilometers per second per megaparsec. A megaparsec is a million parsecs, or about 3.3 million light-years, so this is almost unimaginably fast. — space.com

km/sec per megaparsec is not a velocity, so not sure how this could be unimaginably fast. 70km/sec is not much more than the orbital speed of Mercury, and I think I can manage the imagination of it. Sorry. I was hoping for better from a site like that.

Sure, your Hubble volume and my Hubble volume might be slightly different in 14 billion years. In the mean time, there are an infinite number of Hubble volumes that were never in causal contact with ours. — tom

The example was about the nearby overlapping ones, not the countless more distant ones.

Why do you think Hubble Volumes were ever in contact or overlap? — tom

Another note: Level 3 universes overlap as well. There is amazing symmetry between the level 1 and level 3 concepts.
Level 1 is just Schrodinger's box implemented with distance instead of technology.

How much expansion is required to produce a literally infinite universe from a point in a mere 13.8 billion years? — tom

The comment here only makes sense if interpreted as sarcasm. It implies that there might have been finite hubble volumes, and after enough time, that goes to infinite. The greater the expansion, the less time it takes to do this. No, not my view.
The way I see it: If the geometry is such that the universe wraps (like the sphere of the balloon analogy), then there are finite Hubble-volumes. Assuming not, then if the expansion rate is increasing, there are infinite such volumes. If the rate is not increasing, light will eventually get from anywhere to anywhere else, and the universe is a single Hubble volume. At no point does "13.8 billions years" play into that.

Why do you think Hubble Volumes were ever in contact or overlap?

Why do you think they don't? We are at the exact center of our Hubble volume. Isn't that amazing? From the perspective of a planet 10 BLY away to the left (all this is in comoving coordinates BTW), they are centered on a different volume that encompasses us way to the right. Their volume ends further to the right of us, but not a whole lot further. Some distant galaxy to our right can be seen from here but can never ever be seen by them. It is outside their Hubble Volume. Our volumes overlap else we couldn't see each other.
To say they're all nonoverlapping implies there are discreet chunks of disjoint space with one preferred point in each of them which is their center. My model doesn't look like that.

There are also Level 2 multiverse earths.

I would think so, yes. Level 4 as well.

Thanks guys. Didn't think it would work. A few holes to point out, but in the end, the state of Earth does not require all the universe to have been this and thus.

Now, an atom has a finite number of configurations, or states that it can possibly be in (10 for hydrogen, I think). — SophistiCat

One atom has no position, velocity, or other relations. But a group does, and each atom has innumerable additional states that make up its relationships with the others. Really innumerable??? Maybe not.

Our visible universe may well have been the size of a point at the Big-Bang, but the entire Level 1 Multiverse was not. — tom

Maybe my model is incorrect, but this seems wrong. Since the level-1 spheres overlap, they're all points in the beginning, and all the same point at that, else they'd not overlap. I don't totally grasp eternal inflation theory, where perhaps the inflation stuff rips away as normal space forms in the bubble, but that is not a description of a point except the point where the bubble first began, not necessarily being the point that represents our hubble sphere.

As I've mentioned several times, the Bekenstein bound severely limits the number of states available to any volume of space. — tom

Limits it given finite energy. If the initial infinite universe was actually a point, there is infinite energy/information there. But this actually kills my idea. Earth is a limited space with limited energy. The bound applies. Earth cannot be in a unique state that requires the history of the entire set of material that was once in its causal past. Tegmark was working on a bound such as this, and then just computed how much space was required to make it likely that a good majority of those (valid) states were realized.

Information must be preserved, but like other conserved things, it need not all be conserved here. Most of that information is shipped off elsewhere.

The number line has to be both continuous yet discrete at the same time. — apokrisis

I just picked this out. Agree with your post. My history-of-everything assumes no discreetness at all. Any tiny difference way below Planck constant would still yield a measurable difference after chaos gets to do its thing. Sort of invalidates the Planck concepts.
I hate discreet anything. How slow can something go? If it moves one Planck length each hour, what does it do while it waits for the next one? A discreet universe would exhibit jaggies. Ewww....

The set of possible outcomes from an infinite sequence of coin tosses is uncountable. — andrewk

Right. Can count only the finite ones (trivially at that). The coin model works, and thus 1 followed by all zeros is possible. Shot down again.

Am still enjoying the concept. Perhaps a proof that no copy is possible then? The distant Earth might be outside our causal cone now, but it wasn't always. All matter (or whatever it was back then) was at the big bang and is part of the causal history of this planet. Since information is preserved, a perfect copy has it all. Thin ice there. Maybe the info was shipped out of reach, even if preserved.
Anyway, if that works, Earth (or just an apple say), contains the history of its entire causal cone in the past and cannot be recreated without that entire past, which is infinite stuff.
Tegmark assumes Earth can be represented with finite state, and computes the distance needed to get the probability of a repro up to about 1. If if the state is no finite number, then no copy.

In an infinite sample space, Probability zero is not the same as Impossible. The term 'almost surely' was invented to cover exactly this case. It is applied to an event that is in the sample space (ie 'possible') but has zero probability. — andrewk

I realized that I had made an error and backed off my 'certainly' claim pending a redo. In the end, I decided that no-Earth was not in sample-space. It's not the same as stabbing at an infinite list of impossible to hit things, inevitably hitting one of them.
That math might not be right either (I didn't show it), but it seems to hold the probability of hitting a specific countable number in random sample of the uncountable reals.
I am basing a lot of my claims on another thread debating why 0.999... is 1, not just infinitesimally close to it. It was explained by someone who knows their stuff far better than I.

With the usual binomial model of fair coin tossing, the event of an infinite sequence of heads is one that 'almost surely' will not occur, which is not the same as saying it cannot occur. — andrewk

Not sure if a model of fair coin tossing applies. In an uncountable sample space, the one you actually hit cannot be represented by any number of coin tosses.

Does anyone here disagree that speed is a measurement defined as velocity = distance/time? — AngleWyrm

Speed is distance/time. Velocity is a vector, so it has a directional component. One can accelerate (also a vector quantity) and change velocity without changing speed.
Speed and velocity are not absolute properties of objects. They are relations between things.

If distance loses it's meaning of 1 lightyear = 1 lightyear then I suggest that isn't science it's some sort of perspective modification that is creating meaninglessness.

It is still distance, but Meta's post above is correct. Distance is a local measurement that begins to alter meaning for significantly separated things.