Lectures on Faster-Than-Light Travel and Time Travel
arxiv.org
arxiv.org
I was always under the impression that time as we know it is merely an idea and variable we add to equations to explain the motion we perceive. We see one thing happen after another thing, and conjure up the idea of time to capture a duration between the two occurrences. This duration of course only being relevant to us in our shared reference frame of earth, and because we have the ability to form memories, and experience duration.
Computation is a potential source of a definition of time - a computation naturally introduces an order of successive operations, which happens to match our observation of time very well (you can extend computation to a continuous process if needed, though of course we don't know if time is necessarily continuous).
On the other hand, both GR and QM are also consistent with an interpretation where the universe with its entire Time-line is a fixed object, where we can imagine the past and future exist just as much as distant galaxies. In this view, the concept of time travel makes some intuitive sense, as you can imagine closed loops where you can reach (here, yesterday) just like you can reach (other city, tomorrow).
> (since the distance metric is x²+y²+z²-ct²)
and you just have the line-element for flat (Minkowski) spacetime in Minkowski coordinates.
Change to polar coordinates, and you have to write the line-element down differently (even in SR). Change from flat spacetime and you have to write the line-element down differently. Change the metric signature for convenience from +++- to ---+, and you have to write the line-element down differently. The line-element depends on a choice of how one is putting down coordinates on a spacetime, and the choice of the spacetime itself.
Handily, we can turn to the lecture notes linked at the very top of this discussion. My paragraph above is essentially the content of §2.1.1 (Basic concepts, Manifolds and Metrics) of the lecture notes linked at the top, but I guess the section is just not basic enough to have found its way into this thread. See eq (2.3) for where to stuff in the "d"s and the paragraph after eq (2.1) about why they're ds rather than ∆s (or nothings). Also see equations (5.1) and (5.2), (5.41, footnote 57) for examples of line-elements for non-flat spacetimes; eqns (5.6), (5.35), (6.1) for more exotic line-elements; and (5.37-5.40) for examples of 1+1 line-elements. See footnote 10 for a pithy comment on choice of metric signature. ("Some people." Gee, thanks. cf. footnote 12.)
> In SR/GR we also see time as separate from space
is, unfortunately, almost entirely incorrect. The closest we can get to repairing this notion is by a procedure such as slicing or threading and introducing operators to knit the resulting hypervolumes together in some orderly way. This is discussed to an extent in §§5.1-5.2, or in most numerical relativity textbooks (like, especially given the content of §5 of the lecture notes linked at the top, Miguel Alcubierre's excellent introductory textbook! ISBN-13: 978-0199656158).
I'm sorry to snipe at you, but this comes after reading the discussion here in which you assert and then retract numerous statements about the content of relativity theory. All that sure has confused me, and I'm sure I'm not alone.
You're right of course about the missing ds or deltas in the Minkowski metric, and there's also a missing square, since that is the square of the 4-distance, not the 4-distance.
However, on the basic point that Minkowski spacetime is different from a Cartesian 4-dimensional space, and thus time can be seen as fundamentally different in nature than the space coordinates, in not sure why you claim I am mistaken. Maybe the specific wording I chose, "separate", was the issue?
Time and space are of course tied together in SR&GR, whereas they are more firmly separated in Newtonian mechanics. But "separate" can also mean "different", and I think it is corect to say they are still different things even in GR, though they are tied to each other.
Do we need a "definition of time"? Maybe there are certain fundamental aspects of reality which cannot be broken down into anything more fundamental, and time is one them? If that were true, then "time" could not really be defined (at least not intensionally), we could only point out the fact that it exists. We could never say what it is, if saying what it is is understood as requiring explaining it in terms of something else.
> On the other hand, both GR and QM are also consistent with an interpretation where the universe with its entire Time-line is a fixed object,
GR and QM also appear to be consistent with idealism (Berkeley-style) – all that exists are minds and their experiences, and the physical universe (including physical laws such as GR and QM) are simply patterns in those experiences. Time then might be said to be a fundamental part of the essence of what it is to be a mind. GR and QM could not really tell us anything about what time actually is–they would merely be tools which minds can use to predict what kinds of experiences they will have under various circumstances.
I don't understand how idealism can be a complete theory of the world. What are the minds made of? What are the physical laws that govern their working? How do we know there are more kinds not just one, my own (and arrive at solipsism)?
The Standard Model at least posits a simple world, made of a relative handful of basic elements that follow some simple laws. Minds are extremely complex objects, and it seems very hard to accept them as irreducible - especially if you chose to believe that other people and their minds exist as well.
Edit: Having read a bit about Berkeley's idealism from the Stanford Encyclopedia of Philosophy [0], to me it seems that it is simply a re-stating of mind-matter dualism with other terms. He posits that the world is made up of spirits and ideas. Ideas are perceived by the spirit, but they are not caused by it, as the spirit cannot choose not to perceive them. But then what is causing the ideas? According to him, a special spirit called God. Why are ideas regular and casually linked at all, and why is a dream different from an apple? Because God has willed it so. So basically "ideas" for all intents and purposes behave like matter (because God willed it so), and spirits are the minds that perceive this matter.
Honestly I don't know how anyone can find such arguments convincing.
Ask an M-theorist "what are strings and branes made of?" They'd probably say something like "in M-theory, they are fundamental entities, they are not made out of anything more basic". Well, an idealist can say the exact same thing about minds. Different minds have different properties, just as different strings and branes can have different properties, but for both theories they are entities which cannot be reduced to anything more fundamental.
> What are the physical laws that govern their working?
From an idealist point of view, I'd say physical laws are regular patterns which exist in the experiences of minds. So, your question then becomes: What regular patterns in the experiences of minds govern the working of minds? The question doesn't make a lot of sense; the best sense I can make of it is – exactly the physical laws you are familiar with. They govern the workings of minds, for (as far as we know) minds always have experiences compatible with the truth of those laws.
> How do we know there are more kinds not just one, my own (and arrive at solipsism)?
I would say that the existence of other minds is an innate idea, an a priori concept. It is a belief which does not require any evidence to justify – because the entire idea that "beliefs require evidential justification" is part of an epistemic value system which has the existence of other minds as one of its unquestionable presuppositions.
> The Standard Model at least posits a simple world, made of a relative handful of basic elements that follow some simple laws. Minds are extremely complex objects, and it seems very hard to accept them as irreducible - especially if you chose to believe that other people and their minds exist as well.
But how are you defining "simple" and "complex" here? From another point of view, the physicalist world is enormously more complex than the idealist world. If we assume there are no omniscient minds, then the universe must contain a vast quantity of irreducibly complex information which no mind will ever know – I've read one physicist suggesting that the information-theoretic complexity of the observable universe is on the order of 10^120 bits – whereas a (non-theistic) idealist can say that no mind will ever know the vast majority of that information, and if no mind ever knows that information it never actually exists, so in a (non-theistic) idealist worldview the infomation-theoretic complexity of the observable universe is likely to be substantially less, meaning the universe is substantially simpler. (Whether the same would hold in a theistic idealist worldview is a more complicated question which I suggest we leave to the side.)
Now, you might object to how I am defining "simple" and "complex" here; but the terms have no precise and unique definition – and even if some theory is simpler than another by some specific definition of "simple" and "complex", why should we care? Even if preferring theories which are "simpler" in some specific way turns out to be the most productive approach to the natural sciences (compared to preferring theories which are "simpler" in some other way) – why should we assume that the same must be true for other disciplines with quite distinct methodologies, such as philosophy?
> Having read a bit about Berkeley's idealism from the Stanford Encyclopedia of Philosophy [0], to me it seems that it is simply a re-stating of mind-matter dualism with other terms
I'm sympathetic to Berkeley-style idealism, but wouldn't defend every detail of Berkeley's views. Some idealisms do contain some degree of dualism – the mind itself vs the contents of the mind, experiencer-vs-experiences, my own mind vs the minds of others – but I don't agree that any of those dualisms can simply be reduced to or identified with the dualism of mind-vs-matter – and there is no single mind-matter dualism, since mind-matter dualism exists in multiple varieties: substance dualism, property dualism, hylemorphic dualism, etc, which disagree with each other about what mind and matter are and how they are related to each other.
> But then what is causing the ideas? According to him, a special spirit called God
This is one element of Berkeley's views I definitely disagree with. I think he is too quick to resort to God as an answer to questions which I believe can be answered without invoking the concept of a divine being. (You can be an idealist without being a theist – McTaggart is a famous example of an atheist idealist – and even a theistic idealist might prefer to invoke the concept of God more sparingly than Berkeley does.) In my view, causation is simply another kind of pattern which exists in the experiences of minds – to ask "what causes experiences" becomes equivalent to "what experience-patterns of the particular type we call 'causation' do experiences participate in?" – the obvious response to which is "the answer will be different for every experience". An idealist can provide a theory of causation without bringing God into it.
Well, here is where we get to my claim about complexity. The important point about strings or branes or particles in the SM is that they are characterized by extremely few parameters. I'm less familiar with string theory, but particles in the SM have electrical charge (+1 or -1), color charge (red, green, blue), anti-color charge(antired, antigreen, antiblue), spin (0, 1/2, or 1) and mass (this can take 16 possible values). There are 17 fundamental particles, and the theory describes all of their possible interactions based on the numbers above.
Contrast this with the minds of idealism: to be in any way recognizable as the concept we call mind in our daily lives, minds must be characterized by probably thousands of parameters. If a particular version of idealism recognizes other people and the broad strokes of the world as we know it, it must at least allow for tens of billions of different "fundamental constituents", the different minds of all humans that have ever lived, if not an unbounded number given that more humans will be born in the future.
But even then, if we accept minds as irreducible as we must with fundamental particles or strings, we should still be able to come up with a theory of the properties of minds, and dynamical laws that describe their interactions with other minds and/or ideas or other constituents of the idealistic universe. Are there any philosophers or scientists who have attempted to do so?
And I don't think it's fair to say you accept all physical laws as describing the universe, as the physical laws describing two electrons exchanging a photon have no room for "a mind" in that picture.
So, if you don't accept materialism (that is, don't accept that minds are an emergent phenomenon, with physical reality being fundamental and irreducible) then you don't have a complete description of reality until you also have a different set of laws which explain the functioning of minds.
You seem to be espousing the following principle: "All else being equal, prefer the theory whose fundamental entities are described by the fewest parameters". But why should anyone accept this principle? Even if it turns out to be the most productive methodology for the discipline of physics, why should we expect it to also be the best choice for other disciplines with rather different methodologies, such as philosophy?
> Contrast this with the minds of idealism: to be in any way recognizable as the concept we call mind in our daily lives, minds must be characterized by probably thousands of parameters.
I think your philosophy just moves the complexity elsewhere. You claim that the experiences of everyday life are somehow either reducible to or emergent from the Standard Model (a claim which is actually a philosophical interpretation of the Standard Model rather than part of the Standard Model proper), but you cannot give a complete explanation of how to do so – I'm sure you could provide some extremely high-level outline, but in doing so you must skip over innumerable details. Even just what we know of those details, is so enormously complex that I don't think anyone in the world could possibly know or understand all of it, only some little corner of it in which they've built up expertise – and there remain massive gaps all over our collective knowledge. It seems very doubtful we'll ever assemble a complete picture – indeed, the idea that we ever will is a rather massive leap of faith. And yet, it is claimed, this unimaginably complex complete explanation must exist in theory, even if it will never be fully known in practice. Why aren't you counting that complexity? I expect you'll claim that all that complexity is "hidden in" the simplicity of the Standard Model, waiting to emerge from it – but how can you actually know that is true? It looks to me like a gigantic unproven and unprovable assumption.
> we should still be able to come up with a theory of the properties of minds, and dynamical laws that describe their interactions with other minds and/or ideas or other constituents of the idealistic universe
Why ought we expect to be able to do that?
> And I don't think it's fair to say you accept all physical laws as describing the universe, as the physical laws describing two electrons exchanging a photon have no room for "a mind" in that picture.
Absolutely there are minds in that picture. How do you know those laws are "true"? Well, certain minds derived some testable hypotheses from them, minds performed some experiments and observations to confirm or disconfirm those hypotheses – and then communicated the results to other minds, and convinced other minds to repeat those experiments/observations who in turn also communicated their results, and eventually there is enough experimental/observational data to convince a sufficient supermajority of minds who possess the property of being members of the relevant scientific community that the law is "true". And when we say that law is "true", all we are really saying is that minds have done the things I mentioned in the preceding sentence; and also, since minds have in the past found the law a useful conceptual tool for predicting (certain aspects of) their future experiences, it is reasonable for minds to expect the law will continue in the future to be a useful tool for so doing.
That sounds like block time, but in that case I think the operative part is "fixed object", so there would be no concept of changing the past or having multiple time lines. If there were a loop, it would "always" have been there.
One interpretation I quite like is the idea that objects travel through time just as they do through space, and so if you went back to a past time there would be nothing there. All the matter is in the 'now' on a trajectory into the future, and both the past and future are the time equivalent of empty space.
Yes, if the universe is fixed, anything in it has always been there. Basically it would be like a recording of a movie - both the intro and the ending exist at the same time, and the film could be circular.
That is true as far as we know, but we also thought all laws of nature are P and C and T invariant, and that turned out to be wrong: the weak interaction is not time invariant or, equivalently, not CP invariant (though it is CPT invariant as far as we know) [0].
That is, if you look at two particles with the same parity forwards in time, they will interact differently than if you look at them backwards in time. However, if you look at two particles with the same parity acting forwards in time, and you look at their anti-particles backwards in time and with opposite parity, you will still see the same interaction.
Also, I don't understand what you mean when you say "there is no separation of future and past in thermodynamics" - the second law clearly states that entropy increases with time in a closed system.
But that is also problematic for many reasons. So nobody really knows why we perceive changes in the world as if coming from a state of low entropy to the state of high entropy. From pure probability reasoning and symmetry of time (even if the latter is not 100% true, it does not matter, since the error will not affect the statistical reasoning) if a system at some moment in a state with a low probability then both in the future and the past it is more likely to find the system in a more probable state with a higher entropy.
Of course, it's also possible that we have not yet discovered some other law of nature that is deterministic, but breaks CPT symmetry, that might define an arrow of time at the microscopic level as well. After all, QM still has the measurement problem, where the Born rule I believe also breaks CPT symmetry.
Regarding CPT violation. Even if it was so, it would not imply that one could use it to justify the existence of the time arrow. Asymmetry would imply that one could distinguish the past from future, but it would not explain why what we perceived as the past is the past and not the future.
An analogy is a bar that gradually changes from black to white. Surely there is a color gradient. But that alone does not imply that there is a preferred direction from black to white as the choice of the direction is arbitrary.
The measurement problem arises when one tries to use QM to predict empirical observations. The concept is fundamental to QM as a physical theory - remove it, and QM can no longer be said to agree with experimental observations (in fact, it contradicts them), so it can no longer be verified to be a physical theory.
> But everything is quantum at the end. So there are no classical devices.
This remains a supposition. It is possible that the classical world is indeed an emergent phenomenon, as in the many-worlds interpretation for example, but we don't yet have a full, experimentally verifiable account of how that would work. Decoherence has shed some light on aspects of the problem, but it is not enough (it does not account for the choice of observable to measure, the preferred basis problem).
> Asymmetry would imply that one could distinguish the past from future, but it would not explain why what we perceived as the past is the past and not the future.
Yes, that is a good point. However, moving from the future to the past in SR requires something that can move faster than light (faster than c). Such a particle is in principle possible, but it has negative energy. As such, if such a particle could actually exist, QM would predict that pairs of this particle and regular particles would form all the time in the void, and thus the universe would quickly become pure chaos (this prediction comes from the observation that energy is conserved if in a region of 0 energy you create a particle with energy E and one with energy -E).
So, if we can establish that the future and the past are distinguishable, then relativistic quantum mechanics requires that movement is only possible from the past to the future, and this should give us an arrow of time even at the microscopic level.
That makes about as much sense to me as claiming that space is merely an idea we've invented to account for our perception that things are in different places.
It reminds me of the Plank (sp) constant, a minimum unit of distance (? unsure if I remember / ever understood this correctly).
A pure (parallel) event driven model of time might be seen as the propagation of energy with some form (information). In that model folded dimensions, gravity, even the concept of space or time can distort as relationships strain. That's how space and time could be 'affected by gravity'.
Yet even with that framework I can't imagine time travel anywhere remotely like it exists in fiction. I would really like to think that it's just my very non-expert knowledge, and the general immaturity of even our knowledge as a species that keeps the universe such a mundane place. Any form of FTL, time travel, or similar fun scifi concept would keep life interesting.
?? Given that photons which transmit energy are 'timeless' that's a strange claim.
Understanding Relativity means embracing certain paradoxes and that just happens to be one of them. I mean yes, absolutely, the world of a photon would be something akin to a mathematical point with no distance or time. That knowledge is important but it's not always useful.
> I was always under the impression that time as we know it is merely an idea and variable we add to equations to explain the motion we perceive.
This seems non-sensical to me. How can you have motion without time?
> We see one thing happen after another thing, and conjure up the idea of time to capture a duration between the two occurrences
How can you have duration without time? They seem like the same thing to me.
About motion without time: it depends on the definition of distance. Some physicists are proposing that space is an emergent feature and particles are closer (in the space we perceive) if they are more entangled. If particles A and B are entangled but then B gets entangled with C and says goodbye to A, we would see B moving from A to C. We would also perceive time because of that change, but there is no time at all.
So the idea of space is required for the idea of time. It might well be possible that the idea of space is sufficient and time is just a derived perception.
Not really, since the observed behaviors of physics require an extra dimension that is different in nature to the three spatial dimensions. You can't explain the behavior of light in a universe with 4 space-like dimensions, for example.
I can conceive of the idea of a disembodied mind who exists in time, who experiences auditory qualia without any directional component, but does not experience other kinds of qualia such as visual or tactile qualia. I don't think such a scenario requires any space – some might say that auditory qualia require sound waves which require space, but a disembodied mind by definition does not have physical sense organs and their auditory qualia cannot be directly produced by physical sound waves–otherwise, they would not be disembodied (their auditory qualia would have to be hallucinations, dreams, direct telepathic communication with other minds, divine revelations, etc.) So, if I can conceive of a mind existing in time but not space, who naturally could have an idea of time but would struggle to have any idea of space (since it has never experienced it), and if conceivability is prima facie evidence of possibility, it is reasonable to conclude that it is possible for such a being to exist, and hence possible to have an idea of time without having any idea of space. Therefore, the idea of space is not required for the idea of time.
If you were to ask this mind to answer that question (or it were to spontaneously put the question to itself, whether the auditory qualia is "your" voice or its own), what do you expect its answer would be?
Why do memories and thoughts require "storage"? Why would such a being think that they do? Even for us humans, if that question seems natural to us, it may be because our ideas about the mind have been heavily influenced by materialist/physicalist/computationalist assumptions, which people at other times in human history (and even people in radically different cultures today) would not necessarily share. If you asked an educated person in mediaeval Europe or classical antiquity "where are memories and thoughts stored", the majority would probably have objected that your question makes no sense: "Memories and thoughts are immaterial, only material objects can be 'stored' in containers"
> If you were to ask this mind to answer that question (or it were to spontaneously put the question to itself, whether the auditory qualia is "your" voice or its own), what do you expect its answer would be?
Since it has no idea of "space", why would it have any idea of "storage", or that memories and thoughts are or ought to be stored "somewhere"? Your question assumes the idea of space, when that is an idea it lacks.
Are you going to stand firm on the claim that your disembodied's friend's answer to the question "where are your memories held?" is only ever going to be https://en.wikipedia.org/wiki/Mu_(negative) ?
I don't buy your claim that an educated (implying literate) person would not understand the idea of storage of information. Indeed, even less educated humans scratched out what we now call graffiti, or counting marks, on surfaces that have endured for millennia, or even longer (paleolithic cave art, petroglyphs, and so on). How do you help yourself remember some number of items that you need to account for? You write it down. Ancient Egyptians did that.
> heavily influenced by materialist/physicalist/computationalist assumptions
Guilty/guilty/guilty, sure. But I also have the dubious advantage of -- for abstruse reasons -- having worked with metric signature (++++...+), 1+1, and n+2 spacetimes, and know just how weird they are compared to the one we inhabit. So here I am stuck thinking of a brain that has some spatial extent but does not realize it, while avoiding pressing a claim that no remotely brain-like process can exist without at least two spatial dimensions.
Brains that have some feature but don't realize it pop up in cosmology (and real life) with some aplomb. The most popular example from cosmology is Boltzmann brains, which exist only extremely momentarily, but have encoded within them false memories and perceptions. Keeping BBs from appearing practically everywhere in the universe turns out to strongly limit a number of features of the not-full-of-false-brains universe we appear to inhabit, if we also want to keep thermodynamics.
Amusingly, Boltzmann brains are the opposite of what you are proposing: they have extent (and spatial structure) but vanishingly short duration. They can "remember" having an extensive dialogue with you in which they answer in great detail where their memories are kept, but the memory is false.
I agree they'd understand we can store information in written documents, etc. But I don't see why they'd make the leap from information can be stored somewhere to all information must be stored somewhere. The later is a modern view rather than an ancient/mediaeval one. But, absent the belief that all information must be stored somewhere, my hypothetical disembodied mind has no reason to assume its own thoughts/memories/etc must be stored somewhere.
> Keeping BBs from appearing practically everywhere in the universe turns out to strongly limit a number of features of the not-full-of-false-brains universe we appear to inhabit
I think BB arguments are dubious, because they all involve disputable philosophical assumptions (about the nature of consciousness/etc). If you subtract those philosophical assumptions, BB arguments no longer work as justifications for rejecting those physics theories which produce "too many" BBs. Also: if combining a philosophical assumption with a scientific theory produces absurdity, why treat that as an argument against the scientific theory, when instead you could use it as an argument against the philosophical assumption?
In physical cosmology, the Boltzmann brains issue is: how can the sky full of many galaxies (in which solar systems form) instead of many many many more complicated things (automobiles? space probes?) that were not produced by the operation of processes within galaxies? Why isn't the sky full of gazillllions of space probes with nearly zero galaxies? Instead, in practically every direction we look, we see trillions of galaxies, and (at least for now) very few space probes. (That these galaxies may end up being populated with lots and lots of space probes eventually is the point.)
We can coarsen and run into the same problem: why are stars organized in galaxies (and clusters of galaxies) rather than appearing randomly throughout the cosmos? The latter is much much much more likely in fluctuation theory.
You can substitute a sparse cold non-self-interacting and generally non-interacting gas that occasionally condenses briefly into patterns that look like a small snowman, compared to much larger and more complicated patterns (perhaps whole armies of snowmen aligned rank-and-file) if you prefer not to think too hard about intermolecular and similar forces, and want to whittle down some your objections about how thought and memory might work.
> my hypothetical disembodied mind has no reason to assume its own thoughts/memories/etc must be stored somewhere
Which is why I asked you to imagine putting the idea to your friendly disembodied mind in order to get said mind to consider that and reply with its thoughts on the matter. Having been asked, it then has a reason to ponder (admittedly not assume) that its own thoughts/memories/etc must be stored somewhere.
I don't think most people view "time" as anything in particular. They just live it. Whether or not time is composed of "infinitely many infinitesimal sequences" is the kind of highly abstract question which most people will never ask.
> I was always under the impression that time as we know it is merely an idea and variable we add to equations to explain the motion we perceive.
Who can really say what time is – is it a basic category, and as such incapable of being explained in terms of anything more basic? Or is the temporal reducible to or emergent from the non-temporal? Some have opinions – most people don't – but who can really know whether anyone's opinions are right?
> We see one thing happen after another thing, and conjure up the idea of time to capture a duration between the two occurrences.
Do we "conjure up the idea of time"? Or is it an "innate idea", an "a priori concept", etc? Rather than something we "conjure", I think all thought, having any ideas at all, even being a mind, has time as a necessary precondition. To form the idea of time is simply to recognise something which has been there from the very beginning of one's existence, something which is an essential part of being what one is, being the kind of being which one is. To know that there is time is part of mind's ability to recognise what it is to be a mind.
Perhaps it is a construct for human consciousness, because time cannot exist without consciousness. There must be a perceptor to preceive the universe and the notion of time.
However, how can time dialation be explained? Would we actually age slower when we travel close to speed of light? That throws a wrench into the concept of time being just a construct and not an actual facet of our universe.
Technically, from your point of view you will never age slower. Depending on your speed compared to others, those others may age faster or slower than you, but you yourself will never experience time at a different rate. Say you were somehow guaranteed to live 120 years. Then, no matter what you did, whether you stayed perfectly still in empty space or moved at almost the speed of light, or got infinitesimally close to a black hole, you will only ever experience 120 years of life.
In the thought experiment, in two frames of references moving at different speeds but close to speed of light, how do molecules, cells and enzymes know how fast to age?
"Time dilation" only comes into play when comparing the clocks of two different things moving at different speeds or accelerations relative to each other, or existing in two different gravitational fields (which is equivalent).
If you're floating around in the void, no, everything is stationary relative to each other, and experiencing the same acceleration, so no real difference. There would still be some small difference between the cells closer to your center of mass than the ones farther away, because you also have your own gravitational field, but it would be so weak it would almost not matter at all.
From the perspective of the force or system required to produce a discontinuous temporal displacement, what "are" any of the objects being displaced? How could such a system differentiate between "me" and "my chair" and "the ground objecting to my chair's and my motion towards the nearest significant centre of gravity"? Zoom in further... how could the "time travel machine" identify the atoms at the very edges of the dead skin cells resting between the hairs of my arms and the atoms of the myriad gasses and pollutants beside them in order to alter their temporal position. Which bits are "me"? What gets left behind? What is "me" from the perspective of a temporal displacement system?
Then zoom out a bit... "here" in space isn't "here" in time, yesterday. "here" in space yesterday was actually "over there" because the object we're riding on has moved around its orbit around ITS nearest centre of gravity since then.
For example, it's in principle perfectly possible for someone from another galaxy who lives for 100 years from their own point of view to visit the time of Jesus, and then to visit us today and tell us what they saw happen. But it's not possible as far as we know for someone from Earth to do so (or even for someone who lived on Pluto). Also, it's not possible for that same someone to do the opposite - if they visit us today, they can't then visit the time of Jesus and send him a message from us.
To me, that's just moving myself in space, not in time. (but I'm pointing this out because perhaps embedded here is some understanding of space-time I've not got yet).
> For example, it's in principle perfectly possible for someone from another galaxy who lives for 100 years from their own point of view to visit the time of Jesus, and then to visit us today and tell us what they saw happen. But it's not possible as far as we know for someone from Earth to do so (or even for someone who lived on Pluto). Also, it's not possible for that same someone to do the opposite - if they visit us today, they can't then visit the time of Jesus and send him a message from us.
Your example's tickling some imagination/understanding... thanks.
Otherwise they could just stay with you in your past and wait until their past self joins the party later.
[edit: Maybe you were not saying that in this comment. But other comments of yours are wrong so I can’t tell what are you saying, really.]
As you say, they could be events that happened in the past and are in your past light-cone. (As long as they happened far enough from each other - or close enough in time.)
But one of the events could be your meeting now and here and the other event could be elsewhere. You may disagree on whether that event has happened already or not. Without having any direct confirmation yet, of course. But you may determine later that it was before and after your meeting at t=0.
If the other person can travel to "my past", can their point of departure be said to be "in my present"?
Does this fulfil the math?
At T[0][theirs] and T[0][ours], they decide to travel very fast towards us. At T[42][theirs], they meet us, but it's T[-23][ours] At T[42][ours], we remember meeting them
It bends my head out of shape, which is fun... but is it "right"? And is it even possible to say T[0][theirs] === T[0][ours]?
Is it all better modelled by using T-theirs[0] and T-ours[0]... and some rule like "T-theirs[n] can never = T-ours[n]" ?
We will disagree on how much farther in the past, but we will agree that it is in the past. For example, if they are moving at almost the speed of light, and zipping past us, to them it may seem that they left their planet a few seconds ago, and only traveled a few meters; but to us and to their friends back home, it may seem like it took them 1 million years and they moved almost 1 million light-years.
We will also disagree on the order of some events, but only those that have already happened from both our perspectives.
If you can get there it was never in the past, by definition. It was necessarily in your future. The rocket is just a distraction. What you say is not fundamentally different from saying that tomorrow I can visit the past of the New Yorkers of Thursday. And then I can also visit their present and tell them what happened the day before.
If one is in your past light cone and the second is in your future light cone, it does indeed mean that they can't be the reverse for any observer.
Edit: the answer to my second question is also no - that would require them obviously moving faster than the light of the star...
But, what is possible is that from their point of view the star exploded before my birth, while from my point of view it exploded after my birth. Still, by the time they arrive, we will both agree that the explosion of the star is in the past.
If you're arguing you can only visit a point in time when some kind of 'clock' is showing the same time then you're begging the question w.r.t to time travel.
Without time and space:
Everything would happen at the same time at the same place.[0][1]
[0] A universe in a single event.
[1] Every word in that sentence should be individually in quotes.
The big bang doesn't answer that afaik since it requires a singularity (I think), which is something (I think).
> Well, why not?
-- Stanford Encyclopedia of Philosophy, "Nothingness" (https://plato.stanford.edu/entries/nothingness/)
Either there's 'eternal' nothingness - an option which we have excluded empirically - or something always must have existed. We're trying to work out the nature of that something, and the meaning of 'always' (did time begin at the big bang, making the question of 'before' as meaningless as the question of what's north of the north pole; is our universe just the lastest stage in a possibly eternal cycle; does the singularity hide a mirror universe with an arrow of time pointing in the opposite direction; ...).
Physics answer "How" things are, if you want to know "Why" the answer is to be found in philosophy or religion.
This particular question also seems most nonsensical to me - nothing can be said about a "universe" where nothing exists, so why even discuss it?
Why are there stars in the sky?
Nothing could be said about stars in the sky if there were no stars in the sky, so why even discuss it?
etc ad infinitum
But the phrase "something exists" is tautologically true, while the phrase "nothing exists" is a logical contradiction (since the phrase itself and the speaker and the listener must exist). So it's logically impossible for the whole universe not to exist, as long as we can have this conversation or even thought. It's like discussing why 1+1=2 and not 0.
It is nicely organized, and while most HN readers would find §2 pretty steep, the content of §2.1.4 (Massless particles), §2.3.2 (Geodesics and affine parameters) and §2.3.4 (Massless particles and the Speed of Light) are concise technical answers to a HN FAQ which is essentially "according to relativity, do photons experience no time?". Really frequently "asked". (tl;dr answer: yes, they certainly do, you just write their "time" down differently from that of massive particles. The difference in their time ("affine time") tells you observable things -- for instance the difference in quantum wavefunction phase, or the difference in redshift, just as does the difference in proper time for electron (anti)neutrinos when e.g. leaving the cores of stars or neutron stars, or traversing cosmological distances).
(The missing pieces here are defining a momentum p^\mu = \dot X^\mu where the \dot is the derivative with respect to the affine time, much as the author has actually done in §2.3.3 (Massive Particles), and one of the energy-momentum relations like de Broglie's E = hc / \lambda or \lambda = h / p).
§2.3.5 is another good trio of answers to the HN FAQ about the twin paradox, and I agree with the author that the geodesic analysis is more attractive, namely "both Alice and Bob's paths in spacetime begin and end at the same point, but Alice follows a timelike geodesic, while Bob follows a timelike path which is not a geodesic" (emphasis mine). "Since timelike geodesics are exactly the timelike paths which maximize proper time, the proper time experienced by Alice must be larger than the proper time experienced by Bob. Therefore, Alice must be the older twin." That's really all it takes to resolve the apparent paradox. (However, c.f. "Too Many Analyses" in the excellent <https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinPar...>).
I'm slightly surprised that in skimming the later sections (which I plan to peruse) I did not notice the author discussing the <https://en.wikipedia.org/wiki/Causality_conditions> and the causal ladder discussed therein, and only engaged directly with with (in §3.1.3) global hyperbolicity, although some of the many references in §7 might. I suppose that at 60ish pages the author did not want to commit into turning an extensive set of lecture notes into a comprehensive textbook, which is fine.
Finally, it has been several years since Bob Geroch's "democracy of causal cones" Faster Than Light? paper <https://arxiv.org/abs/1005.1614>, and exposure to that likely would affect the end of this paper's §4.3 ("Tachyons and Time Travel") which deals specifically with faster-than-light.
P.S.: (2019)
Skimming quickly through, the Wheelerian text around eq (53) is fascinating, although I think I prefer an ADM-ish IV approach to thinking about the spacetime "suffering" from objects with these worldtubes, and thinking about the presence of a researcher reading a book by candlelight, all of which has worldlines similar to what is discussed in that part of Recami's paper.
In that approach, a "Eulerian" snapshot observer notes two "copies" of the researcher on some slice, each with different candle-sizes and page numbers, while a more patient Eulerian observer may note one copy is reading backwards near a growing candle. However, Recami's consideration of a "Lagrangian" observer is certainly provocative if one starts to wonder what happens to his "traveller" across cosmological distances -- in that regime, one encounters arrow-of-time/statmech problems that sharpen in nonvacuum. (I will however need some time to absorb the points about apparent vacuum decay in Recami §7.7, among other goodies in the paper).
Finally, yes, it was behind a paywall, but <https://sci-hub.se/https://link.springer.com/article/10.1007...> of course -- it's even easier to read that way, even if one has springerlink access. :-)
Heck, maybe the universe was born out of failed time travel attempts as they all ended up at 0time at space coordinates 0,0,0 and the culmination of all those failed attempts gave us the big bang. Extremely unlikely, but equally, something you can't fully dismiss based upon our current understanding to the point of saying there is 0 chance of this could happen.
I think the point of GP was that any time travel device you build, calculations/projections you make, will all be built around a frame of reference where the planet IS in a fixed position, as far as you are concerned. Since you don't know any other frame of reference, the machine won't either.