Answer number two:
Relativity is a scientific theory born of empirical observations. Presentism is a metaphysical interpretation of time, not a scientific theory at all. It has zero falsification tests, as do all interpretations. If such a test (a difference between 4D block and 3D universe) could be proposed and performed, then it could be elevated beyond interpretation and one or the other could be falsified. Meanwhile, relativity would stand because it works the exact same way in both interpretations.

And you don't think that simultaneity is a frame dependent phenomenon refutes the idea of there being an objectively correct answer to whether A is before B? Why or why not? — fdrake

Your question can be interpreted different was, so I pick this one: Time as used in physics equations is what simultaneity is about, and relativity describes that. The second definition of time is from presentism, which is the rate of advancement of this 'present', which has no units, not even seconds per second since the two are different things. So I will say that presentism posits a different definition of simultaneous altogether, and there is no refutation of any part of the presentism because presentism is irrelevant.

That's the key word: irrelevant. It is an invisible pink unicorn, and not refuted for the same reason.

Do you conclude that relativity thus refutes presentism? — fdrake

Again, no.
Relativity says the math works with or without the existence of magical invisible pink unicorns, but it doesn't refute said unicorns. Presentism is such an addition: Something irrelevant, undetectable, and unrefuted.

There are real trajectories with which the expansion of the universe looks different.

Yes, but I think that from any such trajectory, the universe appears younger than it would if it were a comoving object, and an observer on that trajectory would be aware of the deviation from the local mean.

What problem is the Many Worlds Theory of Hugh Everett a solution to? In other words, why was it necessary for Everett to propose an hypotheses comprising the apparently radical speculation of ‘infinitely branching universes’? — Wayfarer

You misrepresent what Everett proposes. To quote a paper on this point:

• EVERETT POSTULATE:
All isolated systems evolve according to the Schrodinger equation d/dt |ψ> = - H|ψ>
.
Although this postulate sounds rather innocent, it has far-reaching implications:
1. Corollary 1: the entire Universe evolves according to the Schr¨odinger equation, since it is by definition an isolated system.
2. Corollary 2: there can be no definite outcome of quantum measurements (wavefunction collapse), since this would violate the Everett postulate.

• What Everett does NOT postulate:
At certain magic instances, the the world undergoes some sort of metaphysical “split” into two branches that subsequently never interact. This is not only a misrepresentation of the MWI, but also inconsistent with the Everett postulate, since the subsequent time evolution could in principle make the two terms in equation (2) interfere. According to the MWI, there is, was and always will be only one wavefunction, and only decoherence calculations, not postulates, can tell us when it is a good approximation to treat two terms as non-interacting.

No proposal of new universes. It is not an ontological assertion.
I disagree with the author's proposal of quantum suicide to test the theory since other interpretations predict the same results.

I was meaning something like the following: the equivalence principle in SR is essentially that motion is always relative motion - which introduces coordinate transforms - constrained by a cosmic speed limit -which introduces the scaling factors. In GR the equivalence principle is essentially between gravitation and an accelerated (that is curvilinear) coordinate system, and that intrinsic curvature is introduced by mass.

One of the motivating examples for the equivalence principle is the elevator thought experiment. Someone in an elevator could not tell the difference between the elevator moving down with constant acceleration due to a cord and the elevator moving down with constant acceleration due to a gravitational field. If you ignore tidal forces, there's nothing the person in the elevator could do to see if their acceleration is cord based or gravitation based. — fdrake

Right. Tidal forces is effectively a non-local experiment. Make the box big enough and the mass close enough, and tides can be felt. In SR, it doesn't matter if one of the frames is special since that special nature is undetectable, and thus moot just like it doesn't matter to the elevator guy how the force being applied to his box is linear acceleration or bent space. Either way he holds his cup this way to prevent the drink from spilling. That's my point, that the reality behind the experience doesn't matter. It makes no useful predictions either way.

I was trying to say that the undetectability of the difference between the relata in any equivalence principle should not be interpreted as an epistemic property, the equivalence in descriptions should be interpreted to be as real as its consequences - such as the relativity of simultaneity and length contraction. These things really happen and are not mere artefacts of coordinate system choice.

I find myself resisting this. Is my length really contracted if in my frame, it's the length of everything else that's contracted? Seems like an artifact of of choice. On the other hand, the twin really does come back younger, despite the stay-home twin aging slower during both legs of the journey, from the frame of the rocket-twin. No mere arithmetic games can do that.

A foliation of space-time is a lot different from a foliation of time, you were referring solely to the latter?

Don't know what the latter is. Events are points in spacetime, not in time. Not trivial to order them, but it would be trivial to order moments in time.

I don't understand how this is possible, given that in some reference frames event A can happen before B and in some event B can happen before event A - and there can be no strict total order (like <) with this property. How would you construct a foliation to produce a time which obeyed this?

Different frames foliate space differently. That's what frames do. They specify an ordering, but not otherwise a coordinate system or an origin. An actual present would imply an objective foliation instead of a relative one, but SR is all about the physics in relative terms and isn't affected by a possible objective foliation.

One possibility would be to say that if there exist two events A and B, that they occur at the same time if and only if there exists a coordinate system in which they do occur at the same time.

Actually, under relativity, there exists a frame such that any two (reasonably local) events are simultaneous with only spatial separation, are at the same location with only temporal separation, or right on the edge between the two (on the edge of each other's light cone) in which case separation is 0/0 or undefined. From event A, all events outside its light cone are the first sort, all inside are the second sort. There can be no two points that don't meet one of those 3 cases. This is pure relativity, and has nothing to do with 3D space or absolute time.
So as for your comment above, no, A and B are not simultaneous just because some frame exists where they are. They're only simultaneous in that frame, and not in some other frame where they're ordered A first or B first. One can rotate the paper at will to put C above or below B in the time dimension (my events B and C were potentiall simultaneous in my paper example. A and B were inside each other's light cones and B is unambiguously after A).

Or that there exists a coordinate system in which A is before B and B is before A. Of course coordinate systems exist in which B can be said to have occurred any time before A or B by adopting the frame of a particle with a particular motion (you can solve the Lorentz equations for v). But I think that this conception of time inappropriately quantifies over reference frames, and destroys the relativity of simultaneity. That is to say, simultaneity in SR is simultaneity in a reference frame, and the solvability of the Lorentz transform for arbitrary t shows that the ordered pairs of events in any such order are incompatible with a total order; unless time is trivialised in the sense that all events occur at the same time (which isn't presentism or a block universe).

All true. Presentism just says that there is an objective correct answer as to which of A or B happens first. Relativity supplies frame dependent answers, not objective ones.

So, the question is whether an order produced by such a foliation would resemble anything like a universal time. I'm not convinced that there is such an ordering, could you provide some references for where you're getting this from? I think you're losing too much detail when thinking of foliations as an order.

Comoving time is such an ordering. Essentially, for every event in spacetime, the actual time there is the age of the universe in the frame that maximizes that age, or in which the red shift of distant objects (most notably the CMB) is isotropic. Same thing. That age is an objective one, and provides an objective ordering of all events.

So that's the 'frame' referenced when they say our galaxy is moving at about 0.2%c. Our solar system is on the side that cancels out some of that, so we're actually cruising at about 0.12%c. I put 'frame' in quotes because it is not an inertial reference frame, and is different for every point in space due to expansion.

I don't think an undetectable in principle difference should be elevated to a difference in practice. — fdrake

What difference can an undetectable thing make to practice? In what way is the latter 'elevated'?

I'm assuming 'foliates' here means, essentially, 'providing a coordinate system for'.

It is an ordering of events, and not otherwise specifying full coordinates. This event is simultaneous with that one, and prior to that third one over there. A foliation of the universe must order all events, not just local ones like an inertial reference frame does.

And the way in X foliates Y is always done differentiably (my differential geometry-fu isn't particularly strong). So I'm thinking of a foliation as the thing which describes the rate of change of an application of a coordinate system to a locality with respect to infinitesimal shifts in its origin.

Foliation specifies no origin. Just relations, and only temporal relations at that.

So at time t they were in the Hubble volume, and at some time t' they expanded out of it? That's the picture?

Pretty much yes. Time t' would be the event of that thing increasing its proper distance from us at the speed of light. Like from beyond the Hubble Sphere can still reach us by crossing back and eventually getting here. So maybe the image of it we see is one already outside that Sphere. There is an event horizon beyond which objects are undetectable from here even in infinite time.

About t', I speak of proper distance. In reality, time is frozen for it in our frame, and t' is unexpressible in our reference system, so t' represents the local time of both here and there when the contracting Hubble Sphere no longer includes that distant place. Something like that.

What implications do you draw from this? I've said previously that there are still things which can be said about spacetime in general with respect to increasing time - like the expansion of space when the metric tensor is an increasing function of time. I interpret foliations as ways of setting up for questions like this - they will provide a system of coordinates in which the evolution with respect to some variable, probably time in this case, can be indexed.

Well, IF presentism is true, AND the foliation suggested by GR happens to match the geometry of this 'present' boundary, then there is an actual velocity and location of all things. So from what I read, this 4D metric tensor means in part that the distance between two events is path dependent, and none of the paths is straight or obviously the actual separation. In 3D, a lot of that falls away, and two events need to be simultaneous to have a defined spatial separation. Not sure how much I'm addressing your question, or if I'm being accurate here.

I don't think this makes length contraction or time dilation go away, but it does implicate some notion similar to universal time in the pre-theoretic sense. Regardless, how would you think of this time without destroying the relativisation of time/space through motion? I doubt the right answer is through an assertion against the relativisation of simultaneity (which screws with time = the succession of events), or against the way space expands/contracts relative to motion (which screws with its identification with pure extension).

Of course this 3D view still works under relativity. The twin comes back younger because time progresses slower if you move faster. Clocks do not measure time in that view since there is no way to know if it is stationary. So they just measure local process rates. Relativity of simultaneity is an illusion then. As I said, the platform guy is using incorrect data to determine the two events were simultaneous. They're simultaneous in his frame, which is all he cares about. He cares not that his frame is not actually stationary, since that distinction makes zero difference.

Aha, I see what you mean. You're providing a demonstrative example of motion in 1 spatial dimension and 1 temporal dimension, not saying space and time can be thought of as physically 1 space 1 time in general. — fdrake

No, ours is 3+1, but the concepts are the same. The coordinate system (all four axes) can still be oriented any way, so long as they stay perpendicular. Radial systems sometimes work better for the cosmological scale where SR is completely irrelevant.

The rest was just an example of the conservation of proper time.

I don't think this is true. If it were legitimate to axiomatically posit a preferred frame of reference with which to define all motion relative to, it'd be a consequence. I think the absence of a preferred reference frame is an implication of the equivalence principle - what would be the point in stressing the transformability of motion to equivalent forms if the only purpose was to index all motion again to an arbitrary origin point? Why should any one ordering of events be more true than another?

Undetectable is what the equivalence principle states, no?. Just because something is undetectable doesn't mean it isn't there. Hey, I'm not arguing for it, just against this being a proof against it. I personally favor a block view, and no ontology to it at all.

In other words, nothing changes about relativistic computations if there is a preferred reference frame for any given motion, so there being a preferred reference frame is something out-with the influence of the theory. An arbitrary decision about space-time should not structure how we think about it.

Correct. Something undetectable makes no difference to what is an empirical theory.

Your post takes the view that a predicate equivalent to 'is the true reference frame' is something that can be appended to a reference frame, this is something SR and GR prohibit from having any ontological import.

If I've understood you and it, anyway.

No GR prohibitions anyway. SR perhaps not, but it describes a flat massless spacetime that doesn't correspond to reality. I.E. no inertial reference frame foliates the universe, so none can be the correct one. Inertial frames are local, and the universe is not. There are objects that can actually be seen that do not exist in our inertial frame since they are, in our frame, simultaneous with a time before the big bang. Talking about stuff near the edge of the visible universe that "has since" (<-- questionable use of verb tense) passed beyond the Hubble Sphere which confines events even remotely valid in our reference frame. Hence the curved foliation with is not a reference frame at all, but covers all the universe.

Velocity is the slope of the worldline of some object. Relativity works in block or in 3D view, so the ontological difference is interpretation with no empirical difference. Relativity was born of the observation <of fixed light speed>. That fact is not a necessary property of Minkowski spacetime, so block universe is not necessarily relativistic. — noAxioms

So you're saying that a block universe is neither implied by or implies either relativity? I think I agree with this, but I don't understand how you're using four-velocity in the presentation. Can you give me some more words please? — fdrake

Pictures are hard to post. Consider a simple spacetime of 2D, one of space, the other of time. Lots easier to visualize. Twins experiment requires only 1D of space for instance. So it can be done on 2D paper, preferably circular paper so there is no preferred orientation.

Draw a dot A somewhere, and B somewhere else. This represents 2 events, say the start and stop of a journey. Straight line between the two is its worldline, unaccelerated. A curved line denotes acceleration. So now superimpose a vertical axis S (space) and perpendicular horizontal axis T(time), with origin at A. If you orient the paper so the line is at an angle, the vertical space displacement of B is nonzero and the slope is the (positive or negative) velocity. If you assume a different frame and orient the paper so the T axis followsthe worldline, then the space displacement is zero, T is at a maximum value at event B. There is no motion in this frame since spatial displacement remains zero for the length of the worldline. Angle the paper a lot and the space displacement gets large and the T displacement starts to shorten, but regardless, the unitless separation between A and B (called the interval) remains fixed.
If there is a third event C which is directly above B at a certain orientation of the paper, then B and C are simultaneous, but only in that frame. Orient the paper different and the events become ordered differently.

All this is pretty much a description of flat Minkowski spacetime. At no point does something move across the paper, and orienting the paper different does not make any real change to what is drawn on it.

I'd also really like to see an abbreviated form of the post you made on another forum.

Found a bit of it: Context is the train experiment, where two lightning strikes occur, one at each end of the train, leaving a mark on the platform (and train ends) as it strikes. An observer on the platform and on the train each make their assessment of the simultaneity of the two lightning events.
----
Under the 4D model, the platform guy notices the two strikes at the same time, and after measuring the distance from where he was standing to each of the platform strike marks, determines that the two strikes were simultaneous. The train guy detects the strike at the front of the train first, and afterwards the rear strike. He also measures his distance to the two marks on the train, and is equidistant. He thus concludes that the front strike happens before the rear strike. Two frames, two different but valid ordering of events.

3D model, with 3D space and separate absolute time:
Two events are not ambiguously ordered. If one frame orders them differently, that frame is not the preferred one and it orders events incorrectly. Two events simultaneous in that frame are not in fact simultaneous, and thus there are no future events that exists. The frames that put you simultaneous with those future events are simply wrong about their designation of simultaneity.

So in my examples, I always pick the unintuitive stationary guy. So it turns out that the train guy is the one actually stationary. The platform observer is on the moving ground.
Lightning flashes go off, hitting the front of the train first, and the back later.
The train observer is midway between the two events, and records the front strike first. Being equal distant from the two events, the observer knows the front strike happens first.

The ground observer is moving towards the rear of the stationary train, and by the time the light from the two signals meet, he is at the point where they meet, so he measures the two signals as arriving simultaneously, but one has traveled further than the other, so this is expected. His clock also runs slow, but since he didn't use it, nobody cares.

The guy not actually stationary is incorrect in his assessment of two events being simultaneous. So the guy on the platform is basing his simultaneity assessment on the false fact that the two marks on the ground are where the lightning struck. Since the ground is moving, this is clearly not true. The marks are not the point in space where the strikes took place. The endpoints of the train are the actual spot where the strikes took place.

This is a description of the 3D scenario, and I hope is free of inconsistencies.

BTW, I also saved a post describing the twin experiment with only SR rules, no acceleration, and using a tag team. It is more for illustration purposes, and argues no philosophical points.

Well, in block universe, there is no motion, just worldlines, straight (inertial) or otherwise. The dimensions of those worldlines can be different depending on the choice of coordinates, but that change (the separation (interval) of any two events, say the event of some twin's departure and the event of his return) is a fixed value, and not frame dependent. — noAxioms

I think it's strange to say that there's no motion in special relativity, — fdrake

I meant nothing moves through the block of Minkowski Space time. Time is built in. This is about the block view, not SR or GR. Velocity is the slope of the worldline of some object. Relativity works in block or in 3D view, so the ontological difference is interpretation with no empirical difference. Relativity was born of the observation that the worldline of a photon has the same slope regardless of assignment of coordinate system. That fact is not a necessary property of Minkowski spacetime, so block universe is not necessarily relativistic.

A 3D model of the universe works, despite the 4D Minkowski spacetime model that SR suggests. — noAxioms

I really doubt this, since this trivialises space-time curvature. The Einstein and Riemann tensors are 4-tensors, and the metric derivatives and Christoffel Symbols they consist of interact to give 4 tensors., They need to maintain the number of indices they have so that they can be contracted through identification or multiplication by another tensor to derive the Einstein field equations. 4D space-time can't be removed from SR or GR without drastically changing their character.

But, if you have a reference or previous post on this, I'd be happy to read it. — fdrake

My post was using SR case, which admittedly has bunk to do reality except in a local sense, away from significant spacetime curvature. So perhaps the field equations do indeed require 4D spacetime.

The posts I refer to is not in this forum. Took a long time to figure out why I was in read-only mode here. Essentially I ran the train thought experiment in 3D absolute space and ran into no contradictions. At least one observer is simply wrong about his assessment of the simultaneity of certain events.

With regard to the block-universe that this thing seems to imply. The block universe is essentially conceiving of the vector space (x,y,z,t) as a space-time manifold - as if when all components were free to vary along their ranges, we have a continuous set of snapshots of all events. This isn't implied, what is implied is that for a given equation of relativistic motion there is a space-time 'block' corresponding to its trajectory over space through time. It would be odd to consider space time an invariant block when the things within it can distort all of its motions with their particular properties. — fdrake

Well, in block universe, there is no motion, just worldlines, straight (inertial) or otherwise. The dimensions of those worldlines can be different depending on the choice of coordinates, but that change (the separation (interval) of any two events, say the event of some twin's departure and the event of his return) is a fixed value, and not frame dependent.

Actually I don't see any ontological necessity from relativity theory. A 3D model of the universe works, despite the 4D Minkowski spacetime model that SR suggests. I did an advocatus diaboli piece about the universe being 3D, and the train-thought-experiment being considered in that light. It works in either model, and thus I find no ontological implications. One thing that I did find is that no inertial frame can be the correct one because no inertial frame foliates spacetime. So a curved foliation (not an accelerated frame) such as the comoving system may be a description of the ontology. I don't buy that, but I cannot disprove the view. The comoving frame functions locally as an inertial frame.

Well, as I said previously, numbers are in some sense only identity. It's not that they have an identity - '7' can't be anything other than '7'. And '7' says all there is to know about it - you can carve the symbol in stone, draw it, or represent it in binary code, but at the end of all that, 7=7. So perhaps what I meant by 'having an identity' is 'being an individual existent'. But I admit, it's blurry. — Wayfarer

That seems more like identity than anything with this temporal existence for which you are reaching. 7=7 is pretty pure. But OK, you using 'exists' to describe I guess 'objects' within this universe, despite their having questionable identity. A piece breaks off a rock. Is it still the same rock? 7, having a more solid identity, seems more immune to that sort of questioning.

I would say 7 exists, but not in an ontological Platonic sort of way, but rather more like existential quantification. You are using the word differently, that's all.

The domain of natural numbers is real - but where does it exist? Only 'in the mind'? — Wayfarer

The domain of this universe is also real, but similarly has no 'where' to its existence. North of the next universe on God's shelf? (the natural numbers are kept in his box of playing cards)

Have not yet read all the replies to this, but the definition and examples of 'exist' don't seem to match, and I think need to be clarified.

'Exist' is derived as follows: 'ex-' to be apart, apart from, outside (as in external, exile), and '-ist', to stand or to be. So to 'exist' is to be 'this as distinct from that', to have an identity. In my heuristic, the 'domain of existents' is basically the realm of phenomena. 'What exists' are all the billions of compound objects that are composed of parts and have a beginning and end in time. Also, ‘existence’ refers to the human life considered longitudinally through time, 'our life', and the phenomena that we encounter within that context. — Wayfarer

The definition would seem to include numbers: they have identity, being distinct from each other. The example seems to include only temporal objects, of which the definition makes no mention. I think the definition needs rework since you seem to group numbers as real, but not existent.
And wouldn't it be noumena, not phenomena? Do stars on the far side of the galaxy not exist because we can't experience them? That would be an idealistic notion that doesn't seem represented in the definition.
My own investigation keeps pushing me more to idealism when pressed about the nature of an existent thing-in-itself, as opposed to the identity that I give it as a phenomenon. So I'm actually quite open to the example as phenomena, and not as a noumena.

Your example would accept the existence of the universe only if time is put outside the universe, since only then can the universe be a temporal object with a time before which it was not in existence.


Real: I'm fine with your 'real' definition. My own view is that given that the universe is the manifestation of what are 'real' laws, the universe is real. That's just me though. Your definitions of 'exist' and 'real' both seem to lack an ontological statement, with which I can again relate. You seem possibly to reserve that distinction for 'being':

The 'be' of 'be-ing' is of a completely different nature to the existence of objects. This is the distinction basic to ontology.

OK, a possible ontological statement, but it seems to go in a personal direction from there:

But Being is prior to knowing, in the sense that if we were not beings, the cosmos would be nothing to us, we would simply react to stimuli, as animals do.

So we're different than animals, despite the lack of evidence for this? I don't find it offensive to include my species among them. Anyway, it seems to have stopped being an ontological statement, and again been reduced to a relation: Things exist only as phenomena a specific 'being', and are real only as understood by said special 'being'. I'm probably making a strawman of this, but that's how it came across to me.

Our grasp of rational principles, logic, and scientific and natural laws mediates our knowledge of the Cosmos, that comprise the basis of ‘scientia’. However what has become very confused in current culture, is that the mind, which in some sense must precede science, is now believed to be a mere consequence or output of fundamentally physical processes - even though what is ‘fundamentally physical’ is still such an open question.

Why is that stance 'confused'?

Anyway, my primary point was about the 'exists' definition seemingly not matching the examples following it.

— Jonathan AB

First consider gravity to be instant as Newton theorized; then consider it to travel at the velocity of light as Einstein proposed. — Instant Gravity Proof

The problems start right there. Einstein did not propose gravity to propagate at all. Gravity waves, yes, which act as the particle equivalent of excitations in the quantum field, but gravity itself (the sort that attracts two orbiting stars to each other) is just an effect observed by spacetime being curved by the two masses. There are no gravitons involved, and no propagation of anything.

Here is my proof that gravity is instant:
http://www.flight-light-and-spin.com/proof/instant-gravity.htm
(my answer in short)
(ranked #1 at most search engines for 'instant gravity proof') — Jonathan AB

Didn't read it all, but the nature of the proof is pretty obvious in the initial diagram, and yes, it (speed-of-light gravity) would seem to inject energy into a closed system, with action not being balance by an opposite reaction.

The physics of instantaneous gravity seems flawed as well since it requires a simultaneity that is undefined without a frame. So OK, the frame of the mutual center of gravity is used, but that means that in different frames, the force on one object from another is different, which is contradictory. How can object X pull on me in different directions depending on reference frame? It could be measured, and the direction of force be used to determine an absolute reference frame.

Bottom line is I think your physics is off in the SOL example that spirals out, but I cannot yet put my finger on it. Such a simple proof must have been critiqued by the physics community.

You mean the force of gravity. Yes, that is pretty much everywhere. — Rich

No, I mean the force of the "Spaceship engines".

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.