Eise

You did, but not the kind I hoped for. If you cannot illustrate how the spacetime relation of certain (not causally related of course) events can even reverse timely order, your task is no yet done...

Depends on what you think is weird. If 'weird' means 'completely against our deepest intuitions', then some weirdnesses will remain forever. If you mean with 'weird' that we have no explanation, then my educated guess is that the collapse of the wave function is an unresolved weirdness. To give an example of 'weird, but explained' belongs in my opinion entanglement: the mathematics of QM is clear that entanglement exists. So we have an explanation, but it is strongly against our daily intuitions. Except that at the bottom of entanglement also lies a collapse of the wave function... If something that is not (yet?) explained is a mystery is another question. If you see some process that you do not understand, but it is repeatable, and you can even base technology on it, is this a mystery? Or is it just natural, but (still?) unexplainable.

I would suggest to add a second observer, who moves with high velocity relative to your observer to your diagram. And maybe a third one moving at similar speed in the opposite direction. Then look which event lies in the past for which observer, but in the future of another one. What can you conclude?

I am asking you to digest 'me' even better. MigL did it more or less already for you: The point is that the photo is a record of me sitting int the chair between 13:00h and 13:05h. It proves that e.g. at 13:03h the chair was occupied by me. Looking at a spacetime diagram of you I can lookup your dimensional whereabouts: so it is a map of your whereabouts. So, if I want to know where you were 13:03h, I see that you were sitting in the chair. That of course simply implies that nobody else could be sitting in the chair at that moment. Say that at 12:55h you were making coffee in the kitchen, and you enjoyed you espresso sitting in your chair. That you are sitting in the chair from 13:00h to 13:05h does not negate the fact that you really made coffee before. In the same way you being somewhere else now, does not negate that you were sitting in the chair from 13:00h to 13:05h.

The event of their death has a time coordinate that is 'lower' than that of my birth: so there is no chance that I will meet Caesar. I can go to space coordinates where he was, but I'll miss the time coordinate by about 2000 years.

OK. Except that I must also be careful with my words. 'To follow' suggests a little bit too much a footpath you can follow. It might be better to say that the 4D-Bird sees an uninterrupted line through spacetime. From every point on the line he can read the coordinates, i.e. knows exactly where you are at what moment, even for events that you will be involved in in the future. You do not see see that, that is the advantage of being a 4D bird with a 4D bird's view. Of course. The persistence is only between their births and deaths. That is what I mean with persistence: there is a continuity between e.g Caesar at one bank of the Rubycon, and a few minutes later on the other bank. He did not magically disappear on the north bank, and a few minutes later appeared at the south bank. Yes. As explained above. Single events do not persist (you are not at the mall anymore), but you, as an object, persist, only you are home now. And you existed all the time, from the time you were at the mall, to the moment you are home now.

No! When you were at the mall at t = 1, and today at t = 100 you are at home, it is still true that you were at the mall at t = 1. In a spacetime diagram time is depicted as a space coordinate. If I have the (magic) bird's view on 4D-spacetime, the question "where is Michel now" makes no sense: the Superbird does not know what 'now' means: for him you are the complete line. But you can ask the bird where Michel was at t = 1, or t = 100. Those questions make sense from the 4D perspective.

Sorry. Still friends? 😟 Well, I think that is a kind of definition of an object: something that persists in time and space. Compare with an explosion. This is a very short event, and part of its essence is that it is a (huge) change. It is essentially a process, concentrated around some narrow spacetime coordinates. But e.g. a ball persists in existing in spacetime. It can change space coordinates when travelling in time, but is still identifiable as the same ball: on one side because of its own properties (it is red, plastic, and 20 cm in diameter, with some scratches made by Tony yesterday), and on the other side by its continuity in spacetime: it follows an uninterrupted path through spacetime (except at the moments of it being made, resp. destroyed).

I cannot comment on that, because I do not know what 'is commonly assumed'. The idea of the block universe comes from physicists (Einstein also adhered to the idea), so if physicists are 'not common' then you might be right. As I said before, space and time are intimately linked in spacetime, but they do not play exactly the same role. As a simple example: one can always return to some space coordinate, but nothing can go back to a previous time coordinate. And then, as I already said in another thread, the way time appears in the flat spacetime metric is not the same as the space coordinates: d2 = x2 + y2 + z2 - (ct)2. No idea what you mean, especially that 'our past coordinates are free'. No, that is not what I mean. Objects are 3-dimensional things that persist in time. No, of course not. As I said, the evening before yesterday I was in the shop. Nothing empty. Because I am not in the shop now, does not mean I was not there that evening. If you say 'spacetime coordinate', then of course Michel is there. There is not Michel now, i.e. there is no Michel at that space coordinates there and now. I think you only get more and more confused by equating space and time too much. I do not see a difference. I fully agree with MigL, except that I would not use the expression that we are 4-D objects. But the gist of his argument seems clear to me: if it is true today that I was in the shop the evening before yesterday, so at 25.02.2020, then this will still be true at 21.06.2030. These coordinates are definitely 'occupied' (so 'not free'). Nobody else can take these exact spacetime coordinates, otherwise I would describe a collision I had with somebody in the shop; but I did not collide with anybody. Under the right coordinate transformations, the Lorentz transformations mathematically behave just as a rotation in 3D space. But without these transformations, they completely differ. Again, do not confuse the land with the map. Even if the map is perfect, you can do thing with the map you cannot do with the land (e.g. one can fold a map, but it does not follow that you can fold the land). Spacetime diagrams are maps to help orienting in Relativity Land. No. What is 'flying' in time is one and same object, persisting in time. There is a story about Thales of Milete: as an astronomer and philosopher he was walking and wondered himself about the stars in the sky. So he did not see the ditch for his feet, and he fell in. A woman standing by laughed, remarking that he was seeing the stars, but did not see the ditch at his own feet.

No, because these footprints are in space, not in spacetime. I can assure you, when your spacial- and time-coordinates are the same as that of the dog, this is a Minkowski-depiction of you colliding with the dog. The dogs steps crossing yours in your example means that the dog passed your spacial coordinates at a later point in time. Again you do as if time is just a 4th space-dimension. It is not. I think that is wrong. Objects are 3-dimensional objects. Processes are 4 dimensional objects: they can occupy a certain volume, and exist for a certain time. I mean what everybody means with 'process', see above. 'Moving' means (continuous?) change of coordinates. So if an object changes its space coordinates, we classically say it moves: movement is movement in space. But the time coordinate also changes: at the beginning of the movement it was 13:00h, when it stopped it was 13:05h. So the object does indeed move in time. The only way that this does not fit the conventional meaning of 'movement' is that even if we do not change our space coordinates, we still move in time (even more so, according to SR). E.g. if I sit still in my chair from 13:00h to 13:05h, I 'moved' in time, but not in space. So what is wrong is the kind of expressions as 'time flies like an arrow': no, we fly through time. Very poetic. And I think more or less true.

If I make a graph of the path that an object takes in time, what does 'the imprint exists' even mean? Just do it: make a graph of the movement of some particle. And? Does the imprint disappear? To say it more realistically: if I was in the shop yesterday evening, was I not there anymore today, now I am not there anymore? (Careful, do not blow your head...). Of course: it is still true that I was in the shop yesterday evening, so if I want to make a spacetime diagram of my life, I certainly will add the event 'me in the shop yesterday evening'. The idea of an imprint 'truly existing' makes no sense. In spacetime space and time are intimately related, but they are not the same. You cannot treat time just as another space dimension. So when you depict time as a distance, which you necessarily must do if you make a graph, it doesn't mean that everything you see in the graph has an exact physical counterpart. Here another example: No, of course not. Objects can overlap in time, because at the moment t + 1 the object is not at t anymore, so there is nothing there to overlap with. 2 Objects cannot be at the same place at the same time, but they can perfectly at different times. A spacetime diagram is a diagram of events, not of objects. And as a diagram it is just a simplified model of what is going on. You confuse the model with reality. The argument for the block universe goes along these lines: for observer A, two events are timely separated, one is in the past of A's observation, the other in its future. However, for an observer B, who is moving fast in relation to observer A, A's future event can be in his past. And a there are many ways other observers can move in relation to A there are many events that lie in the future for A but not for some other observer. So in a '4D-bird's view' ('God's view') A's future is already there, A just has not experienced it yet. You, as an object, are not smeared out over time, But as a process (i.e. a continuous line of events), you are.

One reason for RAGORDON2010 might be that e.g. in the well-known example of muon-decay, there is no known mechanism that controls when the muon will decay. So there is nothing that can be effected by the muon's velocity. So one has to accept that it is magic. Or propose a new kind of interaction, which would be the scientific way. What he obviously does not see is that the Lorentz transformations are rotations in spacetime. If I compare with a 'normal' rotation in space, we are used to the fact that objects themselves do not change when we look at them, even if they look shorter than their 'rest-length', when viewed under an angle. And just as we do not need to propose an interaction to explain this '3D length contraction', because for the observed object nothing changes, so we do not need one for the muon: in the muon's rest frame nothing changes. @RAGORDON2010, as a question to think about: does the muon really have a longer half-life when it approaches earth with near lightspeed? Really? But then it should have been clear from the beginning that SR is based on how EM-phenomena are described by different inertial observers (as Swansont and Strange already pointed out). Why do you present us this as such an important insight: Again: you should not teach SR to students, because it is obvious to us all you do not understand it yourself.

Dennett calls it a 'deepity'. I like that word.

Your way of formulating can be confusing. E = mc2 is valid universally, so also in chemical reactions. However, the mass differences are so small, that they cannot be weighed (or did I miss something?). That we notice it in nuclear reactions, as in fusion and fission, is because the strong nuclear force is so much stronger than the electromagnetic forces, which are involved in chemical reactions. To give a simple example: a full battery is slightly (= inmeasurable) heavier then an empty one. Not because some netto outflux of particles, but because the particles of the battery 'found' an energetic lower state, and because E = mc2 the battery is slight lighter.

AFAIK this is the way at least some neurologists see it this way, and I think it has its merits. E.g. it gives an explanation of the effect of training. Consciousness is notoriously slow, and where fast action is needed, like in sports, you must train, so that most actions really bypass consciousness. But that has no impact on the matter of free will: the origin of the 'consciousness bypassing action' is still you (that bag of water...), and you will notice when an unconscious action is blocked. Imagine Roger Federer is playing a tennis match, but then somebody comes from behind, and suddenly holds Federer's tennis racket. Federer immediately will notice that his partially unconscious 'trained tennis program' is interrupted, and will be able to report that he just wanted to play the ball in the utmost left corner, before he was blocked. This reporting maybe consciousness after the fact, but that is no problem: as long as you recognise the action as your own, see the motives behind them, you will also recognise when you are blocked, i.e. when you cannot act according your own motives. So the simplest of definitions of free will, being able to do what you want, is not touched by this. It is only the heavily metaphysically loaded definition of 'uncaused consciousness always must cause our actions (and therefore precede it) for an action to be free', that is refuted by such mechanisms. But in a naturalist world view such a definition makes no sense from the beginning. It probably makes no sense at all.

Do not forget that also in the physical 4D-world, the time dimension does not stand on equal footing with the space dimensions. Pythagoras in spacetime is: x2 + y2 + z2 - (ct)2 = d2 Note the minus-sign. So in some sense we experience a 4D world: we need 4 coordinates to define the spacetime location of events. But time- and space dimensions do not behave exactly the same.

There is so much wrong with this... In the first place, the fictional light clock and atomic clocks work on completely different principles, so I have no idea why you throw them in one bucket. Secondly, you should not forget that SR is based on 2 postulates: one is the invariance of the speed of light, and this is used in the example of the light clock. The other postulate is that there is no physical experiment that can show you that you are in absolute rest: observers in all inertial frames see exactly the same laws of physics. But if clocks based on other principles than the light clock would run at different rates, one would have a criterion to say who is at rest, and who is moving. The light clock is just a nice example to easily explain time dilation to lay people. But there are derivations of SR that are much more fundamental, than this. (Why do you think the original article of Einstein was titled 'On the electrodynamics of moving bodies'? There appears no light clock at all in this article.) Do not think that SR is based on the example of the light clock!

Don't go there. Unless you are a conspiracy theorist yourself. Then you can give your life a meaning, and join the tribe. It remembers me of the one million dollar challenge of James Randi. The idea is simple: both (Bjorkman and Randi) know that the task is impossible, therefore they can safely bet their one million. Bjorkman can then say "See nobody can prove that buildings collapse like that, they can't even build a scale model!", not bothering that a scale model never can reproduce the real collapse.

I would suggest to think about the crew of a submarine. Do they move normally, or are they lighter as soon as the submarine is under water? So what value of g would they measure?

It is at least difficult to imagine... But this brings me to another point. If it is correct what Kip Thorne says (which I strongly assume, knowing what kind of expert he is), then we have 2 completely different 'pictures' based on which interpretation we choose: gravity curves spacetime, and all free moving objects follow geodesics in spacetime gravity is a force, which affects paths of free moving objects, durations and distances But especially my use of 'force' seems to completely contradict the way GR is usually presented: that gravity is not a force. How could one formulate the second interpretation in a better way? Maybe I should stick to Mordred's view: it seems to have the least metaphysical baggage of all descriptions of GR. Word of the day... So glad that Wikipedia exists... OK, now I play for a moment devil's advocate (in this case as a Kantian philosopher): the concept of curvature only makes sense when there is a higher dimension. A line is said to be curved because there is one dimension more, namely the second (wow, that sounds stupid. And as I think to understand, for a 1-D organism there is no chance, not even with differential geometry, to discover that his universe is curved.); a surface is said to be curved, because there is one dimension more in which it is curved. But a 2-D organism can at least discover that, by measuring angles and distances. But how can he conclude that this 3rd dimension does not exist, and that the curvature of his world is intrinsic only? And of course the same questions for 3-D organisms, that discover that their world can best be described as if it is curved? Shouldn't they conclude that there is one dimension more? Or locally diffeomorphic?

Yes, it was in Thorne. He says that one can formulate GR in flat spacetime, where gravitation deforms lengths and durations, whereas the standard interpretation is that lengths and durations stay the same, but spacetime is deformed by the presence of matter/energy. The results are the same, but it seems the math is not completely, and so, dependent on the kind of problem, one can use the interpretation that makes the calculations easiest. And he explicitly says that the question if spacetime is really curved is a philosophical question that does not bother physicists.

I understand, but with some hesitation. Maybe it is because of my (stupid?) idea that intrinsic curvature is the way out for 'n-D' organisms to discover that they live in a curved space, because they cannot access the n+1th dimension to actually see it. But you are saying they cannot discover that they are living in a cylindrical universe based on its intrinsic curvature: the metrics of a flat universe and a cylinder universe are the same. Wow! And I thought one extra dimension would suffice... Obviously that is when one, like me, only has a very superficial understanding of differential geometry, and has to do with analogy arguments. (I am not @scuddyx, who talks about 'tensor force' as if he is understanding what he is talking about...). Gasho, Eise

Isn't that an example of a 2-D object with intrinsic curvature? (And for which we can make a 3-D model.) My idea (hopefully), was even simpler, say the curvature of the surface of a ball (the ball is 3-D, but the surface is 2-D). Isn't it true that one can use both descriptions? In that case we see the 3-D space in which the 2-D surface of the ball is curved, so we can describe it extrinsically. The most important lesson about this in GR, that I thought I learned, is that one can describe curvature intrinsically, and therefore, because we cannot observe 4 dimensions, the question in what the 3-D universe is curved is a metaphysical question (and therefore physics can do without it). Therefore also my 'as if' in my previous posting:

scuddyx, see this video. Much closer to what GR says than the rubber sheet analogy. Are these two types of curvature, or are these different ways to describe curvature? E.g. one can describe the curvature of the surface of a 3 dimensional object in 3 dimensional space in both ways, no? And my understanding of the 'curvature' of the universe is that it is as if it is curved. If I remember well, Mordred said that GR only says how worldlines of free moving objects in the universe look like. In some book I read that one can formulate GR without the use of curved spacetime, which for some kind of problems seems to make the calculations easier (I think this was in the book about black holes of Kip Thorne).

In line with the answers already given: if 2 particles are entangled, then they: were entangled themselves, which means at least they were interacting directly in such a way that we only can know the wave function of the two particles together, not for the particles individually ('normal' entanglement) or they share a history in which the quantum state of the particles is determined by two particles that were entangled (that would be 'quantum-teleportation') See the second point above. If they 'incidentally' share a history based on an entangled pair, then yes. And thereby it does not matter how they got entangled, by human intervention, or just some 'blind physical process'. Otherwise no. But do not forget: locally, an observer can never find out that the particle he measures is entangled with another. The entanglement only shows up when two observers compare their measurements of the entangled particles. Then it shows that their measurements are correlated.