I didn't make much of the 'timeless space' paper, — 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. — noAxioms
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.I think it's strange to say that there's no motion in special relativity, — fdrake
A 3D model of the universe works, despite the 4D Minkowski spacetime model that SR suggests. — noAxioms
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.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
I wasn't referring to anything like that. I suppose what I'm trying to say is that relativity doesn't necessitate a 4D block universe. It is certainly possible for us to view time in the traditional sense, as a 3D world that changes via. the passage of time though there are costs to that sort of view.
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.
Just a side note in the convo: I remember SR being treated as a minor point to GR in my physics class. SR was the sort of thing which we learned to do in order to be able to accept GR, or understand it. We, however, did not delve into GR since it required mathematics beyond what the SR class required. I only mention this because my take away was that SR wasn't meant to be taken ontologically (from a scientific realist perspective), only GR was -- in some sense GR reduced to or was "in line" with SR. I wish I could say more than that but alas I was a chemist (interested in philosophy, I hope thats obvious) and not a physicist.
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
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.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
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.I'd also really like to see an abbreviated form of the post you made on another forum.
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.
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.
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.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
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.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?
Correct. Something undetectable makes no difference to what is an empirical theory.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.
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.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.
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.
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.
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.
Hence the curved foliation with is not a reference frame at all, but covers all the universe.
What difference can an undetectable thing make to practice? In what way is the latter 'elevated'?I don't think an undetectable in principle difference should be elevated to a difference in practice. — fdrake
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.I'm assuming 'foliates' here means, essentially, 'providing a coordinate system for'.
Foliation specifies no origin. Just relations, and only temporal relations at that.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.
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.So at time t they were in the Hubble volume, and at some time t' they expanded out of it? That's the picture?
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.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.
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.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).
What difference can an undetectable thing make to practice? In what way is the latter 'elevated'?
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.
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 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
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.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.
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.A foliation of space-time is a lot different from a foliation of time, you were referring solely to the latter?
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.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?
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.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.
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.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).
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, 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.
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.
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.
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 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).
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.
Again, no.Do you conclude that relativity thus refutes presentism? — fdrake
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.There are real trajectories with which the expansion of the universe looks different.
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.
No, I just don't trust you or Rich to have anything I would find worthwhile to say on the topic — 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.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
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.
I don't see how these two things can be compatible:
(1) There is a unique order of events induced by the idea of the present in presentism.
(2) Events A and B can be ordered differently depending on the motion of a particle.
I don't understand how you can say 'presentism is independent because it's metaphysics', when one of its implications is negated by how time works in SR. — fdrake
I certainly think it's possible to think that there is a real unique ordering of events by rejecting relativity. But I don't think it's possible to think that there is a real unique ordering of events while accepting relativity. — fdrake
I see it as intellectually lazy to posit metaphysics as independent from science, much more interesting to attempt a naturalistic metaphysics which is informed by current scientific theories. Rather than, say, dogmatic adherence to Aristotelian physics or New Age Quantum Woo. — fdrake
The first speaks of objective ordering, and the latter means that the observer is free to order events differently, and physics will still work without detectable differences, rendering any potential objective ordering undetectable. The latter is about empirical observation, not about an interpretation of what actually is. And #2 should be "depending on the reference frame", not depending on particle motion. Motion.I don't see how these two things can be compatible:
(1) There is a unique order of events induced by the idea of the present in presentism.
(2) Events A and B can be ordered differently depending on the motion of a particle. — fdrake
Presentism doesn't comment about how time works in SR. Presentism was around well over a century ago, and SR was not in any way suggested by it. Not sure when the term was coined, since the interpretation is far older than the name needed to distinguish it from alternative interpretations.I don't understand how you can say 'presentism is independent because it's metaphysics', when one of its implications is negated by how time works in SR.
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