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Zoraprime wrote: Time is a thing a clock measures But the thing about time, is that we don't know what it is really, we just have an idea. Typically, we say that time is another dimension like space, in the sense you cannot adequately describe your movement in space relative to another object without taking into account how fast your 'clock' ticks. Now, whenever I say 'clock,' I really mean how fast time is moving around you, it's just easier to think in terms of clocks. Loosely speaking, if I'm earth, and a very fast rocket passes by me at a constant speed, I would say that spaceship looks shorter and the clock seems to be running slow relative to someone on that spaceship. That being said, time isn't like spacein particular, in the spacetime interval, it's actually the difference between time^2distance^2 that remains preserved (if you want to be pedantic, it's the produce of time and the speed of light, but I consider such normalization constants a minor nuisance). I bring up the spacetime interval because it shows that time isn't the same as spacein particular, there's a minus sign in front of distance^2 where there isn't one in front of time^2. I should mention, most laws of physics are actually valid in a timereversed system. The only one I can think of is the second law of thermodynamics which is invalid in a timereversed system (as it would imply entropy decreases in a closed system), but I'm too lazy to look up what the laws of physics lack time symmetry right nowI only know that it's a small handful. You'll tend to find physicists are obsessed with symmetries, over and over and over. Which brings up my question for you... why is 'time' the thing that's different and unintuitive here? What is 'space'? After all, not all reference frames agree on the same clock, or the same space, so if the only thing that observers *DO* agree on are invariant quantities like the invariant interval, then why should we consider 'space' as our standard? If we were blind, and with circular shaped ears, we probably would have a weak concept of 'space' compared to a very strong concept of 'time'. (Can't we consider hearing to measure time in the same way eyes measure sight?) I find it strange when people say we don't know what time is but omit that we don't really have an intuitive sense of space either. Theoretical physicists these days want to describe the universe in absence of spacetime entirely, which who knows what symmetries we will emphasize over the next twenty years. I feel questions like 'what is time' have thousands of answers each of which depend on the context. Like Richard Feynman's Why Questions. https://www.youtube.com/watch?v=36GT2zI8lVA 



You'll tend to find physicists are obsessed with symmetries, over and over and over. Which brings up my question for you... why is 'time' the thing that's different and unintuitive here?
Because we don't have a really good way to define it. I tend to joke when I say that time is what a clock measures, but even then, that's about as far as most physicists define time. Beyond that, it's like listing details. But that's what it is: we can only really list details. Now, I didn't say that time was more or less intuitive than space. I said time is different from space, in that time isn't treated as a 'dimension' in the same way space is. I cited the spacetime interval as an example where time is treated different from space mathematically. The other fact is that certain quantities are symmetric in space but asymmetric in time. My main point is, we can't expect time to be like space because time does not play the same role as space in general relativity (and subsequently, special relativity). We know that time affects what space is, but it's not the same thing. What is 'space'? After all, not all reference frames agree on the same clock, or the same space, so if the only thing that observers *DO* agree on are invariant quantities like the invariant interval, then why should we consider 'space' as our standard? If we were blind, and with circular shaped ears, we probably would have a weak concept of 'space' compared to a very strong concept of 'time'. (Can't we consider hearing to measure time in the same way eyes measure sight?) We live in a qausinonrelativistc worldwhich is to say, for humans, our day to day experience are reasonably approximated by Galilean relativity. Even if our sensory organs were different, we would not be able to measure changes in time. The important fact about Galilean transformations is that they are a mapping form a Euclidean space to another Euclidean space, in which the invariant is the distance squared. Here, by distance, I literally mean the amount of 'centimeters' between two objects. Mathematically, we can define the metric g(i,j) of a nonrelativitic world to be equal the Kronecker delta, if you really want to be precise. In special relativity, the distance between two objects is no longer invariant under transformation, but it's still defined the same (e.g. by the distance formula) But to answer your question why space is our standard, it's because only changes in space matter when measuring objects relative to each other because our world is qausinonrelativistic. The fact we can see certainly helps, but that's not the reason. In particular, there's nothing that says we can't sense time. After all, I know what was yesterday and I know tomorrow is a thing. We have some internalized sense of time. We just don't realize that time and space are intermingled because we never see them intermingle at any significant level, and as such, we treat them as two other things until Einsteinian relativity mandates we intermingle them. I find it strange when people say we don't know what time is but omit that we don't really have an intuitive sense of space either. Theoretical physicists these days want to describe the universe in absence of spacetime entirely, which who knows what symmetries we will emphasize over the next twenty years. I'm gonna need a source that says theoretical physicists want to do away with spacetime entirely. If you mean that we want to describe things with more dimensions than the usual threespace and onetime, sure I can see that, but those avenues are being pursued to provide a consistent theory not because physicists think space and time are silly concepts. Whatever symmetries we want is usually given on what's conserved. In particular, most symmetries are found through Noether's Theorem, which still applies to the modern definition of action (which is defined by Feynman's Path Integral Formulation of Quantum Mechanics). IN short, symmetry in time implies conservation of energy; symmetry in space implies conservation of momentum; symmetry of rotation implies angular momentum. And there are probably other symmetries in modern physics, but I'm too lazy to remember them. 

FOR SCIENCE!


Zoraprime wrote: But that's what it is: we can only really list details. Now, I didn't say that time was more or less intuitive than space. I said time is different from space, in that time isn't treated as a 'dimension' in the same way space is. I cited the spacetime interval as an example where time is treated different from space mathematically. The other fact is that certain quantities are symmetric in space but asymmetric in time. My main point is, we can't expect time to be like space because time does not play the same role as space in general relativity (and subsequently, special relativity). We know that time affects what space is, but it's not the same thing. But time IS treated as a dimension, at least to the extent that it scales in the same ways and the only real 'difference' is its orientation. It's not hard to make a 2D spacetime plot with one axis space and one axis time, even intuitively that's treating both space and time as dimensions and if you want feel free to flip the axis, isn't that treating the same? We live in a qausinonrelativistc worldwhich is to say, for humans, our day to day experience are reasonably approximated by Galilean relativity. Even if our sensory organs were different, we would not be able to measure changes in time. The important fact about Galilean transformations is that they are a mapping form a Euclidean space to another Euclidean space, in which the invariant is the distance squared. Here, by distance, I literally mean the amount of 'centimeters' between two objects. Mathematically, we can define the metric g(i,j) of a nonrelativitic world to be equal the Kronecker delta, if you really want to be precise. In special relativity, the distance between two objects is no longer invariant under transformation, but it's still defined the same (e.g. by the distance formula) But we DO measure changes in time, that's exactly what hearing is, we're mapping a frequency domain onto a time domain. Not that I mean we can perceive time dilation on our scale, but rather that hearing to me seems just as much if not more 'measuring time' than our eyes 'measure space'. One could then say 'well to measure frequency you need some space to vibrate in' but to measure space you need some time for light to enter your eye, the further the light, the longer. The louder the sound, the higher the amplitude, but our ears are still measuring primarily timing information. But to answer your question why space is our standard, it's because only changes in space matter when measuring objects relative to each other because our world is qausinonrelativistic. The fact we can see certainly helps, but that's not the reason. In particular, there's nothing that says we can't sense time. After all, I know what was yesterday and I know tomorrow is a thing. We have some internalized sense of time. We just don't realize that time and space are intermingled because we never see them intermingle at any significant level, and as such, we treat them as two other things until Einsteinian relativity mandates we intermingle them. I think part of the problem with people coming to grasp spacetime is specifically that we think too much that we have an intuitive sense of space, and that we don't have enough of a well defined sense of time, when thought experiments alone are generally sufficient to hint that 'one isn't as strange as you thought, or at least, the other is weirder than you thought'. I like emphasizing symmetries more than differences. I'm gonna need a source that says theoretical physicists want to do away with spacetime entirely. If you mean that we want to describe things with more dimensions than the usual threespace and onetime, sure I can see that, but those avenues are being pursued to provide a consistent theory not because physicists think space and time are silly concepts. No I meant more like ArkaniHamed's somewhat popular 'spacetime is doomed' slogan. https://www.youtube.com/watch?feature=player_detailpage&v=_kMkYVm_GeY#t=4719 "Spacetime" as he'd argue must be emergent rather than built in. Whatever symmetries we want is usually given on what's conserved. In particular, most symmetries are found through Noether's Theorem, which still applies to the modern definition of action (which is defined by Feynman's Path Integral Formulation of Quantum Mechanics). IN short, symmetry in time implies conservation of energy; symmetry in space implies conservation of momentum; symmetry of rotation implies angular momentum. And there are probably other symmetries in modern physics, but I'm too lazy to remember them. I think the whole point of talks like the above, on the other hand, is that perhaps we've been emphasizing the wrong symmetries for too long, which could obscure deeper underlying structures. Or at the very least, prove PROFOUNDLY useful for computing scattering amplitudes :P Edit: As is always the case with youtube, don't read the comments, they're depressing, but otherwise a decent lecture from a very well respected physicist, that has NONE of the implications the new age fanatics will typically shout when seeing the words 'quantum mechanics', no matter what youtube comments say. 



SilvaZoldyck wrote: But time IS treated as a dimension, at least to the extent that it scales in the same ways and the only real 'difference' is its orientation. It's not hard to make a 2D spacetime plot with one axis space and one axis time, even intuitively that's treating both space and time as dimensions and if you want feel free to flip the axis, isn't that treating the same? It's only difference is not its orientation. Few things, just a few things I always hit  Time always marches on. That is, a change in time is always positive. Changes in spatial coordinates can be negative.  Time does not have parity in the spacetime interval. It's time^2position^2, not time^2+position^2 or time^2position^2  In Maxwell's Equations (which are inherently consistent special relativity and more or less responsible for Einstein's paper in the first place), the ∇ operator always deals with spatial derivatives exclusively; i.e. they do not include a temporal component. There are probably more, but here some more: http://web.mit.edu/bskow/www/research/temporality.pdf Moreover, just because I can make a 2D plot doesn't mean much. I can make a 2D plot of energy vs position; that doesn't mean energy is suddenly a dimension in the same way space or time is. But we DO measure changes in time, that's exactly what hearing is, we're mapping a frequency domain onto a time domain. Not that I mean we can perceive time dilation on our scale, but rather that hearing to me seems just as much if not more 'measuring time' than our eyes 'measure space'. I'm saying rules measure space; the fact we read rules with our eyes hardly matters. If you want a more technical definition, a lightsecond can be defined by the distance a light ravels in a second in the direction of its wavevector; from there, appropriate conversion factors can be used to convert from lightsecond to whatever units our ruler uses. I suppose if you want to be specific, clocks are measured in terms of frequencies, but all clocks use frequencies as a time tracking device, so I suppose it's a moot point. Granted, out definition with time relied on what a second is, so in that sense, the definition of time and distance are intermingled. Nevertheless, the reason we draw analogies between space and time is because time needs to be treated like space in Einsteinian relativity. One could then say 'well to measure frequency you need some space to vibrate in' but to measure space you need some time for light to enter your eye, the further the light, the longer. The louder the sound, the higher the amplitude, but our ears are still measuring primarily timing information. Our ears do read frequency of sounds waves, but that isn't how we conceptualize sound. All our senses our organized into memories, and the chronological order of those memories define our perception of time. think part of the problem with people coming to grasp spacetime is specifically that we think too much that we have an intuitive sense of space, and that we don't have enough of a well defined sense of time, when thought experiments alone are generally sufficient to hint that 'one isn't as strange as you thought, or at least, the other is weirder than you thought'. I don't have an issue with spacetime. I'm simply making a point that time is different form spaceeven though the two are intermingled in order to successfully describe transformations between two coordinate systems. I like emphasizing symmetries more than differences. You do know what symmetry means? Time is asymmetric; space is insofar as we can tell symmetric. Like, literally, that's all there is to it. Specifically, symmetry means that under a particular transformation, certain quantities remain unchanged. Galilean relativity says that from mapping between inertial frames of reference, forces do not change and velocity only changes by an additive constant; i.e. the relative speed of the two reference frames. Time is asymmetric because you cannot map time to negative time and get the same laws of physicsmost famously, the Second Law of Thermodynamics is violated. No I meant more like ArkaniHamed's somewhat popular 'spacetime is doomed' slogan. https://www.youtube.com/watch?feature=player_detailpage&v=_kMkYVm_GeY#t=4719 "Spacetime" as he'd argue must be emergent rather than built in. I'm pretty by emergent, he simply means that spacetime is an approximation to a greater theory that fails at high energy and short distances. That is, he is saying is that what we call spacetime is a subspace, or an approximation thereof, of a greater space of a higher dimension. That isn't to say time doesn't exist; but rather, time is just one of more than four dimensions. By analogy 3D spatial coordinates were a subspace of Einstein's 4D spacetime. That doesn't mean space no long exists; but rather, transformations from one set of 3D spatial coordinates to another has a time dependence, and as such, the transformation is only linear the fourvector of spacetime. Also, I stopped giving Arkani Hamed undivided the attention the moment I saw "quantum gravity," since this isn't about any experimentally verified physics, just random guesses. Probably a string theorist or something trying to reconcile the inconsistently between quantum mechanics and general relativity. If it's string theory, then all it's saying is that spacetime are a subspace of a larger space and time. And given that his wiki page says string theory immediately following highenergy physics, I'm pretty sure all he's saying is that we need something more than spacetime. I think the whole point of talks like the above, on the other hand, is that perhaps we've been emphasizing the wrong symmetries for too long, which could obscure deeper underlying structures. Or at the very least, prove PROFOUNDLY useful for computing scattering amplitudes If we've been emphasizing the wrong symmetries, so what? Symmetryinsofar as time is concernedsimply matter insofar as time is asymmetric in the mapping t>t and position vectors are symmetric in the mapping x > x as one of a few examples that time is different from space. That's literally all we care about insofar as the discussion of time is. 

FOR SCIENCE!


Zoraprime wrote: It's only difference is not its orientation. Few things, just a few things I always hit  Time always marches on. That is, a change in time is always positive. Changes in spatial coordinates can be negative.  Time does not have parity in the spacetime interval. It's time^2position^2, not time^2+position^2 or time^2position^2  In Maxwell's Equations (which are inherently consistent special relativity and more or less responsible for Einstein's paper in the first place), the ∇ operator always deals with spatial derivatives exclusively; i.e. they do not include a temporal component. There are probably more, but here some more: http://web.mit.edu/bskow/www/research/temporality.pdf Moreover, just because I can make a 2D plot doesn't mean much. I can make a 2D plot of energy vs position; that doesn't mean energy is suddenly a dimension in the same way space or time is. Time asymmetry is observed but hardly built into QM or relativity as a fact of time, that's the whole point of the entropy problem. What do you mean by 'time doesn't have parity'. To try to keep things ordered, I=t^2r^2, or I=r^2t^2, both descriptions are equivalent, time is treated no differently than space, it's just we've changed the orientation. https://www.fourmilab.ch/etexts/einstein/specrel/www/ Einstein treated time *exactly* the same way he treated all of his other coordinates, he just picked his axis to be easy. " At the time t=0 let all three origins coincide, and when t=x=y=z=0 let the time t' of the system K' be zero." t' at time t=0 naturally wouldn't be 0, and he presents the transformation, likewise he presents the transformation for each of the spacial coordinates. I see nothing 'different' really about his treatment. I suppose however I was a bit careless in haphazardly saying 'look we can make a plot!' but if we just think as dimension as a property of sets, then yeah anything we can consider a 'set of points' qualifies as a dimension. Energies aren't points, nor are they comprised of points (They're evaluated Hamiltonians) but *time* is and has always been easily describable as a collection of discrete points. Prior to relativity time was still a dimension. Galilean relativity certainly didn't start treating time as a scalar to spacial components. I'm saying rules measure space; the fact we read rules with our eyes hardly matters. If you want a more technical definition, a lightsecond can be defined by the distance a light ravels in a second in the direction of its wavevector; from there, appropriate conversion factors can be used to convert from lightsecond to whatever units our ruler uses. I suppose if you want to be specific, clocks are measured in terms of frequencies, but all clocks use frequencies as a time tracking device, so I suppose it's a moot point. Granted, out definition with time relied on what a second is, so in that sense, the definition of time and distance are intermingled. Nevertheless, the reason we draw analogies between space and time is because time needs to be treated like space in Einsteinian relativity. Yes, exactly, time needs to be treated like space. Treated exactly the same. That was my whole point, that any attempt to portray 'time' as a mystery seems to either ignore many of the exact same mysterious elements about space, or to overhype the mysterious elements about time. In practice both are needed to gain any kind of understanding of objective reality, but obsession with space over time, or time over space, is exactly missing the point. Our ears do read frequency of sounds waves, but that isn't how we conceptualize sound. All our senses our organized into memories, and the chronological order of those memories define our perception of time. Couldn't you say the same thing about our eyes? We never 'directly observe' anything after all, which is why it's so easy to trick either the eyes or the ears. I don't have an issue with spacetime. I'm simply making a point that time is different form spaceeven though the two are intermingled in order to successfully describe transformations between two coordinate systems. I am quibbling what you mean by 'different'. Different in that it is 'unusual' seems awkward, different in that it 'is not equivalent to space' is obvious. If you mean it should be treated differently from space, that seems wrong in the relativistic limit. (Classically I can fully get behind the idea of considering time as entirely separate from space and not including it with your spacial transformations of getting from point A to point B. Lorentz transforms are tiring.) You do know what symmetry means? Time is asymmetric; space is insofar as we can tell symmetric. Like, literally, that's all there is to it. Time asymmetry isn't built into relativity. That time asymmetry is observed is *confusing*, not an expected consequence of the physics. This is partly why we know we need more complete models, because physicists generally want pastcomplete models. Specifically, symmetry means that under a particular transformation, certain quantities remain unchanged. Galilean relativity says that from mapping between inertial frames of reference, forces do not change and velocity only changes by an additive constant; i.e. the relative speed of the two reference frames. Time is asymmetric because you cannot map time to negative time and get the same laws of physicsmost famously, the Second Law of Thermodynamics is violated. ... The second law of thermodynamics is built around statistical mechanics and not a function of general relativity. General relativity doesn't deal in probability theory* [Note]. Yes you can take statistical mechanics and scale up to thermodynamics, but that doesn't change the fact that time asymmetry is the confusing part, some people take the "spacetime is doomed" approach, others like Carroll take the "well in Everettian physics, everything is solved immediately" approach. So far as relativity is concerned, time IS EXACTLY LIKE SPACE, so why the heck do we observe a time asymmetry? This is the famous entropy problem. I don't think the solution of the entropy problem is going to suddenly tell us "time is like totally different and weird from space and must be treated unique", rather, I expect deeper underlying connections, like how we went from Galilean invariance to Lorentz invariance. No I meant more like ArkaniHamed's somewhat popular 'spacetime is doomed' slogan. https://www.youtube.com/watch?feature=player_detailpage&v=_kMkYVm_GeY#t=4719 "Spacetime" as he'd argue must be emergent rather than built in. I'm pretty by emergent, he simply means that spacetime is an approximation to a greater theory that fails at high energy and short distances. That is, he is saying is that what we call spacetime is a subspace, or an approximation thereof, of a greater space of a higher dimension. That isn't to say time doesn't exist; but rather, time is just one of more than four dimensions. In that the 'greater theory' doesn't use any description of spacetime at all, but rather, spacetime falls out as a consequence. By "falls out" I do of course mean "reverts to the quantum mechanical limit" which then can be said to "revert to the classical limit" but it's still describing the underlying structure *without* spacetime entirely. It's useful to describe the world classically, but that doesn't mean you are required to do so. It's not a 'higher dimension', it's emphasizing different invariant quantities, different symmetries that don't involve spacetime... but rather, apparently only scattering amplitudes? By analogy 3D spatial coordinates were a subspace of Einstein's 4D spacetime. That doesn't mean space no long exists; but rather, transformations from one set of 3D spatial coordinates to another has a time dependence, and as such, the transformation is only linear the fourvector of spacetime. 3D spacial coordinates were a subspace of Galieleo's 4D spacetime as well, it's just all reference frames had the same clock, and mass was the only invariant quantity. Einstein's relativity just said 'well... no... mass isn't invariant, and everyone has their own clock too'. Einstein didn't go treating time as some foreign thing different from space, he treated it the same way he'd treat any other coordinate. Also, I stopped giving Arkani Hamed undivided the attention the moment I saw "quantum gravity," since this isn't about any experimentally verified physics, just random guesses. ... There's a reason I stipulated 'theoretical physicists' but even still, we have VERY important reasons to take very seriously theoretical physicists; the standard model doesn't tell us where to go next. There are very fundamental reasons that physicists need to continue developing models of quantum gravity and addressing the underlying issues still present in physics. It'd be great if the LHC shows us something new, or totally unexpected, but lets not kid ourselves that we don't have incredibly big bugs that theoretical physicists need to reconcile. ... Also, the amplituhedron serves as an incredibly useful tool; that usually means something, even if we don't know what yet. Probably a string theorist or something trying to reconcile the inconsistently between quantum mechanics and general relativity. Eh... he certainly can delve into string theory, and finds it useful as a toolbox, but moreover, he's just an incredibly well respected physicist whose recent work has, as I mentioned, been incredibly useful as a tool for computing scattering amplitudes. Again this isn't just 'some random string theorist', nor is this a lecture you really should ignore if you care at all about the big questions in physics mostly because he's really, really interesting. But if you prefer something less dramatic than "spacetime is doomed!" here's one of his collaborators doing a guest post on preposterous universe. http://www.preposterousuniverse.com/blog/2014/03/31/guestpostjaroslavtrnkaontheamplituhedron/ It's at the very minimum a cool tool, and hints at much much deeper stuff. If it's string theory, then all it's saying is that spacetime are a subspace of a larger space and time. And given that his wiki page says string theory immediately following highenergy physics, I'm pretty sure all he's saying is that we need something more than spacetime. Well, yes, you could say "more than spacetime" but that isn't using spacetime as a requirement. Spacetime isn't built in, that's the whole point, it comes out. Honestly if this topic is up your field of interest (I'm not sure what your interest in physics is, but you've clearly had more than just a first year exposure) then it really is worth your time to look at what physicists actually are saying about GR and QM. It's too important a topic to avoid. If we've been emphasizing the wrong symmetries, so what? Symmetryinsofar as time is concernedsimply matter insofar as time is asymmetric in the mapping t>t and position vectors are symmetric in the mapping x > x as one of a few examples that time is different from space. That's literally all we care about insofar as the discussion of time is. I am still not sure what you mean by the word 'different'. I am not saying that time IS space, but rather that relativity itself mandates we talk about them as if they are essentially the 'same', with different orientations. Now I'm happy to say "yes oh god yes the entropy problem is hard" but the entropy problem is a function of the problem of the sameness of time not being expressed, not something relativity expects or predicts. Edit: If you're a graduate student or even a 4th year I'm going to probably be torn apart for saying this but I'll stand by it by virtue of solutions of time evolution governed by equations of state don't challenge time symmetry in GR. Still, since I'm clearly talking to someone who has had exposure to formal material, I *REALLY* should be careful about saying something so casually. 



SilvaZoldyck wrote: Time asymmetry is observed but hardly built into QM or relativity as a fact of time, that's the whole point of the entropy problem. You do realize that entropy, as understood by modern physicists, is a quantum mechanical phenomenon, and as such, time asymmetry is built into quantum mechanics. Given a closed system with an initial distribution of energy among particles, that system always evolves in one direction, namely towards equilibrium. Oh sure, there always exists a nearly infinitesimal chance it can evolve from equilibrium. Another example in QM is the wavefunction collapse. Basically, once you collapse the wavefunction, you can't collapses it. As such, you can't expect the system back in time and expect the same results. But more to the point, QM is actually littered with timeasymmetry. You can read more here: http://arxiv.org/pdf/1109.0598v1.pdf The fact relativity is time symmetric is hardly surprising: relativity is all about mapping between different frames of reference. It shouldn't really make a difference if time is mapped to minus time, since all what relativity is (fundamentally) is a communication tool. Granted, there's that awkward fact that we must always says we're doing things relative to something with mass which then creates a bit of annoyance because that massive object bends spacetime, but that's a minor detail in the larger picture. What do you mean by 'time doesn't have parity'. To try to keep things ordered, I=t^2r^2, or I=r^2t^2, both descriptions are equivalent, time is treated no differently than space, it's just we've changed the orientation. Flipping a minus sign doesn't mean anything. Time would only have parity with space if the spacetime interval was t^2+r^2 or t^2r^2. Put another way, the metric for the spacetime interval is +1 for time and 1 for spatial coordinates; or alternatively, 1 for time and +1 for spatial coordinates. In the fourvelocity, the temporal component is always c; int he fourmomentum, the temporal component is basically energy divided by c. In the relativistic equation, it's again the difference of E^2p^2 (where p is the fourmomentum) that's invariant, just like the spacetime interval. This isn't terribly interesting, because the relativistic equation is only a more useful version of the spacetime interval, just requires a lot of shitty mathematics to derive. The main point is that the metric corresponding to the time component does not equal the metric corresponding to the spatial components no matter how you define the spacetime interval. https://www.fourmilab.ch/etexts/einstein/specrel/www/ Einstein treated time *exactly* the same way he treated all of his other coordinates, he just picked his axis to be easy. " At the time t=0 let all three origins coincide, and when t=x=y=z=0 let the time t' of the system K' be zero." t' at time t=0 naturally wouldn't be 0, and he presents the transformation, likewise he presents the transformation for each of the spacial coordinates. I see nothing 'different' really about his treatment. I get it. The Lorentz Transformation mapping between two inertial frames of reference with different relative speeds is linear in {t, x}. Just because a transformation is linear in all those coordinates doesn't mean that the coordinates are treated the same. I suppose however I was a bit careless in haphazardly saying 'look we can make a plot!' but if we just think as dimension as a property of sets, then yeah anything we can consider a 'set of points' qualifies as a dimension. Energies aren't points, nor are they comprised of points (They're evaluated Hamiltonians) but *time* is and has always been easily describable as a collection of discrete points. Prior to relativity time was still a dimension. Galilean relativity certainly didn't start treating time as a scalar to spacial components. Even in Minkowski space, time and spatial coordinates do not have parity. IN particular, such as this [url=http://www.daviddarling.info/images/Minkowski_spacetime.jpg]image shows, there's a thing called a light cone over which information can't be communicated. As such, physics can only happen in half of the Minkowski Space (i.e. those satisfy the system of inequalities x<ct and x>ct). This is of course things like tachyons exist, but given there's no experimental evidence for anything timelike, I consider this a minor detail. And in Galilean relativity, the basis was still {t, x}. The only interesting fact of Galilean relativity was that t>t' was governed by t=t', i.e. it treated time as absolute. However, the spatial transformation x==>x' was x'=xvt, and thus that necessitates including time in our basis in order to have a linear transformation. And, from my understand, a point just means some vector of a given vector space. In that case, energy can be considered a point of particular phase space. The only difference between phase space and Minkowski space is that we generally regard Minkowski space as the one we live in. But even though we live in a Minkowksi space doesn't mean that time and space are interchangeable; rather, it means all events in space need to be specified by {t, x}. Just because we need to use time to catalog events still doesn't mean time and space interchangeable. Yes, exactly, time needs to be treated like space. Treated exactly the same. That was my whole point, that any attempt to portray 'time' as a mystery seems to either ignore many of the exact same mysterious elements about space, or to overhype the mysterious elements about time. I said treated like space. Not treated exactly the same. The only new thing in Einsteinian relativity is that a transformation from one inertial frame to another inertial frame for t>t' is no longer t=t' (rather, it's t'=(t/sqrtxv/c^2)/(1v^2/c^2))which, if you look, isn't the same transformation law of space (where x>x' is given by x'=(xvt)/sqrt(1v^2/c^2)). Even if you use the vector {ct, x}, you might convince yourself that the Lorentz Transformation looks symmetric for all coordinates (time and space), except the Lorentz factor only depends on the threevector velocity representing how fast the frames of reference or moving w.r.t. to each other. The reason why the Lorentz factor only cares about the spatial components of the threevector velocity v is because the metric for time and spatial coordinates are offset by a minus sign. In practice both are needed to gain any kind of understanding of objective reality, but obsession with space over time, or time over space, is exactly missing the point. I suppose I can agree we need to treat spacetime together to get an understanding of reality; but we still try to explain time in terms of space because we live in a quasinonrelativistic world where time is absolute, and as such, can be considered separate from space. It's easier to explain time in terms of space rather than explaining space in terms of time because how time changes under the Lorentz transformation is far more interesting than how space interacts. In particular, the spatial mappings in Lorentz transformation are equal to the corresponding Galilean transformation times the Lorentz factor. Couldn't you say the same thing about our eyes? We never 'directly observe' anything after all, which is why it's so easy to trick either the eyes or the ears. The point I was making is that we 'sense' time via memory. We actually have different receptors in our brain for spatial organizations (which, ironically, is mostly done by our ears). I don't remember my biology terribly well, so I can't name what specific parts of the brain control what. I am quibbling what you mean by 'different'. Different in that it is 'unusual' seems awkward, different in that it 'is not equivalent to space' is obvious. If you mean it should be treated differently from space, that seems wrong in the relativistic limit. (Classically I can fully get behind the idea of considering time as entirely separate from space and not including it with your spacial transformations of getting from point A to point B. Lorentz transforms are tiring.) By different, I mean we can't regard time and space as the same thing. They are necessary to fully describe relationships between different frames of reference in that we can't regard either as absolute; but there's clearly a difference between how time and space are used to define the 'vector space' (i.e. the universe) we live in. Time asymmetry isn't built into relativity. That time asymmetry is observed is *confusing*, not an expected consequence of the physics. Relativity is just a tool physicists use to get from one coordinate system to another where it's easier to do physics. We shouldn't expect it to be be time symmetric since, after all, it's not a physical theory in the same vein that quantum mechanics is; rather, it's just saying how a quantity in this reference frame will differ from a quantity in that reference frame. In other words, we could (although it would be a very bad and otherwise impractical idea) just all agree to use one reference frame: say set the origin at earth with the initial tangent vectors forming an orthonormal righthanded system with the ztangent vector pointining along earth's axis of rotation. At this point, the system would be nonEuclidean because mass only exists on Riemann manifolds. We can't do something similar with quantum mechanics, say, model everything as a particleinabox and expect our physics could work even at a theoretical level. This is partly why we know we need more complete models, because physicists generally want pastcomplete models. The only area that seems to really care about having a grand unified theory beyond satisfying philosophical interests are people looking at cases that would require both general relativity and quantum mechanics in which there are no theoretical models. Otherwise, so long as a particular model works, well, use it. After all, an area of research such as Computational Fluid Dynamics isn't going to start replacing their classical laws with quantum mechanical laws just because they could; they're already having a field day dealing with NavierStokes equations. ... The second law of thermodynamics is built around statistical mechanics and not a function of general relativity. General relativity doesn't deal in probability theory* [Note]. Yes you can take statistical mechanics and scale up to thermodynamics, but that doesn't change the fact that time asymmetry is the confusing part, some people take the "spacetime is doomed" approach, others like Carroll take the "well in Everettian physics, everything is solved immediately" approach. So far as relativity is concerned, time IS EXACTLY LIKE SPACE, so why the heck do we observe a time asymmetry? Because for some reason, time loves to move forward. Even in relativity, again, time and space have different corresponding metrics and as such are treated exactly the same. Yes, we need a temporal axis to describe the vector space of our universe, but that doesn't suddenly mean time=space. This is the famous entropy problem. I don't think the solution of the entropy problem is going to suddenly tell us "time is like totally different and weird from space and must be treated unique", rather, I expect deeper underlying connections, like how we went from Galilean invariance to Lorentz invariance. I do feel that entropy is saying time is different from space, and yes, must be treated differently in particular because time always marches on. Entropy is the place where it's most evidence, but it's not the only place. Even under relativity, time and space are treated differentlythe only difference is that time is no longer absolute. Because space was never absolute, we tend to group time with space and saying it's more like space because it's no longer absolute. But they are not, by any measure, *identical.* They're similar, they are *like* each other, but they are different. Also, perchance, do you consider energy and momentum to be exactly the same? n that the 'greater theory' doesn't use any description of spacetime at all, but rather, spacetime falls out as a consequence. By "falls out" I do of course mean "reverts to the quantum mechanical limit" which then can be said to "revert to the classical limit" but it's still describing the underlying structure *without* spacetime entirely. It's useful to describe the world classically, but that doesn't mean you are required to do so. String theorywhich is probably in part where he's coming fromjust says that spacetime doesn't span the entirety of 'our universe,' and you have to add in all these extra dimensions. If nohting else, spacetime *must* be an approximate subspace of whatever greater theory there is, and thus, time would probably not disappear altogeter. It's not a 'higher dimension', it's emphasizing different invariant quantities, different symmetries that don't involve spacetime... but rather, apparently only scattering amplitudes? If there is a higher dimension, of course the inner product would change because there's more components. Depending on what he's talking about, there may or may not be symmetries. Remember, we don't care about symmetries in relativity: it's just mapping between more convenient coordinate systems and as such, the laws of physics within a given coordinate system must be derived elsewhere. 3D spacial coordinates were a subspace of Galieleo's 4D spacetime as well, it's just all reference frames had the same clock, and mass was the only invariant quantity. Einstein's relativity just said 'well... no... mass isn't invariant, and everyone has their own clock too'. There's consensus on whether or not mass is in/variant in special relativity. In particular, the relativistic equation only references rest mass, which makes it's more useful. Usually when mass shows up, so does a Lorentz factor, and as such it's sometimes helpful to think of mass as getting heavier. That said, there's still an ongoing debate within physics on whether or not mass is relativistic and, if not, if relativistic mass is just something that's made up for convenience sake. That said, I'm not sure if mass is invariant in general relativity since I haven't looked at GR as much as I have looked at SR; but I'd imagine it's the same story there.What is often referred to as 'the invariant' are various inner products you can construct. The spacetime interval is an invariant in S.R. whereas the distance is invariant in Galilean relativity. Energy is invariant in Galilean relativity too; but it's variant in SR. Einstein didn't go treating time as some foreign thing different from space, he treated it the same way he'd treat any other coordinate. Which is to say he assert time wasn't absolute. Sure, I agree with that. But again, time has its own unique transformation law and its own distinct associated metric. ... There's a reason I stipulated 'theoretical physicists' but even still, we have VERY important reasons to take very seriously theoretical physicists; the standard model doesn't tell us where to go next. There are very fundamental reasons that physicists need to continue developing models of quantum gravity and addressing the underlying issues still present in physics. It'd be great if the LHC shows us something new, or totally unexpected, but lets not kid ourselves that we don't have incredibly big bugs that theoretical physicists need to reconcile. ... Also, the amplituhedron serves as an incredibly useful tool; that usually means something, even if we don't know what yet. Yes, string theory does gives us a sort of backdoor to solving a lot of otherwise nasty math present in the standard model. That doesn't mean it's a unique predictions; howeverunless it can only be explain in terms of string theory, it's just a mathematical shortcut. For example, there are times when you can use the Heisenberg uncertainty principle in order to find the lifetime and/or rest mass of a particle if you know the other by implying that the particle disappears and the rest energy is 'borrowed' but this argument can fail manyatimes. Eh... he certainly can delve into string theory, and finds it useful as a toolbox, but moreover, he's just an incredibly well respected physicist whose recent work has, as I mentioned, been incredibly useful as a tool for computing scattering amplitudes. Again this isn't just 'some random string theorist', nor is this a lecture you really should ignore if you care at all about the big questions in physics mostly because he's really, really interesting. But if you prefer something less dramatic than "spacetime is doomed!" here's one of his collaborators doing a guest post on preposterous universe. http://www.preposterousuniverse.com/blog/2014/03/31/guestpostjaroslavtrnkaontheamplituhedron/ It's at the very minimum a cool tool, and hints at much much deeper stuff. All I'm getting from Sean Carroll's piece is that this amiplituhedron has both unitary and locality which are the pillars of QFT. And again, my next question is how has this been used in experimentsin particular, has the amilituhedron been used in experiments in a way that the QFT cannot in principle predict, or is it just a mathematical backdoor to otherwise complicated and hairy mathematics. I don't particular care about the big questions in physicsin particular, looking at experimental physics, I care about more practical approaches. Well, yes, you could say "more than spacetime" but that isn't using spacetime as a requirement. Spacetime isn't built in, that's the whole point, it comes out. What does 'come out' mean: that spacetime isn't a subspace of our universre or what? Honestly if this topic is up your field of interest (I'm not sure what your interest in physics is, but you've clearly had more than just a first year exposure) then it really is worth your time to look at what physicists actually are saying about GR and QM. It's too important a topic to avoid. I'm looking towards experimental physics, so I really don't care what's going on in the theoretical world. Which isn't to say theoretical physics isn't important, however, it's more of a 'I'll look at it when I need it sort of things.' Physicists in general as a whole don't take string theory terribly serious eitheragain, probably because they don't need it. So, yeah, I'll mostly ignore it. I am still not sure what you mean by the word 'different'. I am not saying that time IS space, but rather that relativity itself mandates we talk about them as if they are essentially the 'same', with different orientations. Now I'm happy to say "yes oh god yes the entropy problem is hard" but the entropy problem is a function of the problem of the sameness of time not being expressed, not something relativity expects or predicts. Again, relativity is useless if we want to examine why time moves forward because, if we really want to, we could avoid using relativity altogether (that said, not using relativity makes life pretty hard so we use it). The entropy problem isn't particular hard: a wavefunction will evolve towards a state of uniform distribution in a closed system. Saying it's hard is like saying why do we flip a million coins and expect more or less the same number of heads and tails is hard. Edit: If you're a graduate student or even a 4th year I'm going to probably be torn apart for saying this but I'll stand by it by virtue of solutions of time evolution governed by equations of state don't challenge time symmetry in GR. Still, since I'm clearly talking to someone who has had exposure to formal material, I *REALLY* should be careful about saying something so casually. Eh, I wouldn't let my education get to you. I'm exposed to a lot of formal material, yes, but I'm still an undergraduate so I've mostly seen a little of everything without specialization. If you really want to know, I'm a fifth year undergraduate, but eh, I wouldn't let that get to you. 

FOR SCIENCE!


Zoraprime wrote: You do realize that entropy, as understood by modern physicists, is a quantum mechanical phenomenon, and as such, time asymmetry is built into quantum mechanics. Given a closed system with an initial distribution of energy among particles, that system always evolves in one direction, namely towards equilibrium. Oh sure, there always exists a nearly infinitesimal chance it can evolve from equilibrium. Another example in QM is the wavefunction collapse. Basically, once you collapse the wavefunction, you can't collapses it. As such, you can't expect the system back in time and expect the same results. But more to the point, QM is actually littered with timeasymmetry. You can read more here: http://arxiv.org/pdf/1109.0598v1.pdf Fair enough, I was more or less referring to the SR features of QFT, in that you can rotate any feynman diagram which is effectively the same as saying 'well an interaction that occurs one way occurs the other', if I'm careless, which I shouldn't be, that can easily be turned into 'clearly macroscopic events are reversible!', which I mean, is sorta true, a broken vase given enough time will eventually magically spontaneously return to normal, but not on any reasonably observable timescale. The fact relativity is time symmetric is hardly surprising: relativity is all about mapping between different frames of reference. It shouldn't really make a difference if time is mapped to minus time, since all what relativity is (fundamentally) is a communication tool. Granted, there's that awkward fact that we must always says we're doing things relative to something with mass which then creates a bit of annoyance because that massive object bends spacetime, but that's a minor detail in the larger picture. I'm not sure I like the phrase 'communication tool'. I get what you're trying to say, since you expanded on it later, but 'communication' seems a bit like exchange of signals when relativity is describing more basic features than that. Dilation effects I suppose you could consider results of 'communication' in spacetime, which it is, but also a bit awkward to think about in that way. What do you mean by 'time doesn't have parity'. To try to keep things ordered, I=t^2r^2, or I=r^2t^2, both descriptions are equivalent, time is treated no differently than space, it's just we've changed the orientation. Flipping a minus sign doesn't mean anything. Time would only have parity with space if the spacetime interval was t^2+r^2 or t^2r^2. Put another way, the metric for the spacetime interval is +1 for time and 1 for spatial coordinates; or alternatively, 1 for time and +1 for spatial coordinates. In the fourvelocity, the temporal component is always c; int he fourmomentum, the temporal component is basically energy divided by c. In the relativistic equation, it's again the difference of E^2p^2 (where p is the fourmomentum) that's invariant, just like the spacetime interval. This isn't terribly interesting, because the relativistic equation is only a more useful version of the spacetime interval, just requires a lot of shitty mathematics to derive. The main point is that the metric corresponding to the time component does not equal the metric corresponding to the spatial components no matter how you define the spacetime interval. "The main point is that the metric corresponding to the time component does not equal the metric corresponding to the spatial components no matter how you define the spacetime interval." I wouldn't claim anything different under any circumstance. That's why I wrote the interval both ways, strictly to make clear that t and r have opposite signs, but my point was more that because it is simply convention which to start with, as defining a positive charge is simply convention, there's no reason why we must think of time as something 'other' than space. I don't think of positive charges as something 'other' than negative charges, I can't think of heads on a coin as something 'other' than tails on a coin. It's the separation of ideas that irks me about it... time is 'like' space, at least so far as relativity is concerned. They aren't the same, but they can be thought of them in the same ways. Positive and negative charges certainly aren't the 'same thing' but you can think of a positive charge in the same way you can think of a negative charge. (Though I suppose since there are three spacial dimensions whereas only one timelike dimension, time will always be inherently more restrictive than space, try living as a 2 dimensional creature and you can't do a lot of things we as three dimensional creatures can... like have an open digestive tract.) I get it. The Lorentz Transformation mapping between two inertial frames of reference with different relative speeds is linear in {t, x}. Just because a transformation is linear in all those coordinates doesn't mean that the coordinates are treated the same. I suppose I should be more rigorous with my use of the word 'same', perhaps. The idea that you can form a linear mapping *does* mean that the coordinates are treated as the 'same', not that the individual components will all share the same transform as other coordinates, but that you're using the same structure to create your mapping in the first place. Not to say 'time is space', but you really can't transform one coordinate without transforming the other. Even in Minkowski space, time and spatial coordinates do not have parity. IN particular, such as this ___ shows, there's a thing called a light cone over which information can't be communicated. As such, physics can only happen in half of the Minkowski Space (i.e. those satisfy the system of inequalities x<ct and x>ct). This is of course things like tachyons exist, but given there's no experimental evidence for anything timelike, I consider this a minor detail. I think you mean physics can only affect an observer at the centre of that particular light cone, not that physics can only happen, since there's no reason you couldn't chose to look at the light cone of another observer which could have a totally different overlap from, say, a third observer, but all of them still see physics happening as totally naturally and normal as the others. That we are prohibited from accessing information isn't to say 'physics can't happen in regions we have no access to'... since there's no reason another observer won't have access to it. We can never go past the speed of light and look back at the earth to see dinosaurs, but some other alien might be able to see them still. And in Galilean relativity, the basis was still {t, x}. The only interesting fact of Galilean relativity was that t>t' was governed by t=t', i.e. it treated time as absolute. However, the spatial transformation x==>x' was x'=xvt, and thus that necessitates including time in our basis in order to have a linear transformation. And, from my understand, a point just means some vector of a given vector space. In that case, energy can be considered a point of particular phase space. The only difference between phase space and Minkowski space is that we generally regard Minkowski space as the one we live in. But even though we live in a Minkowksi space doesn't mean that time and space are interchangeable; rather, it means all events in space need to be specified by {t, x}. Just because we need to use time to catalog events still doesn't mean time and space interchangeable. It's been way too long since I've had any exposure to set theory (Though I'd like to pick up a textbook I've got limited time these days... I wanted to read Carroll's text instead since I love his author's voice) so I am deeply afraid of muddling too deep with the word 'dimension'. I was happy to consider phase space higher order dimensional objects but agree I never considered them very 'real', rather than just useful. I said treated like space. Not treated exactly the same. The only new thing in Einsteinian relativity is that a transformation from one inertial frame to another inertial frame for t>t' is no longer t=t' (rather, it's t'=(t/sqrtxv/c^2)/(1v^2/c^2))which, if you look, isn't the same transformation law of space (where x>x' is given by x'=(xvt)/sqrt(1v^2/c^2)). Even if you use the vector {ct, x}, you might convince yourself that the Lorentz Transformation looks symmetric for all coordinates (time and space), except the Lorentz factor only depends on the threevector velocity representing how fast the frames of reference or moving w.r.t. to each other. The reason why the Lorentz factor only cares about the spatial components of the threevector velocity v is because the metric for time and spatial coordinates are offset by a minus sign. By definition you can't express velocity without still effectively taking a time derivative, I think we're quibbling over lexicon... which often seems the case, since I don't disagree that time isn't the same, but that it doesn't, and never really did make sense, to think of spacial components without timing components, at least not in our universe. (Or at least, not in the fact of relativity... we worked perfectly fine before we had even the vaguest concept of mathematics period) In practice both are needed to gain any kind of understanding of objective reality, but obsession with space over time, or time over space, is exactly missing the point. I suppose I can agree we need to treat spacetime together to get an understanding of reality; but we still try to explain time in terms of space because we live in a quasinonrelativistic world where time is absolute, and as such, can be considered separate from space. It's easier to explain time in terms of space rather than explaining space in terms of time because how time changes under the Lorentz transformation is far more interesting than how space interacts. In particular, the spatial mappings in Lorentz transformation are equal to the corresponding Galilean transformation times the Lorentz factor. This is the heart of what I was arguing for, that just because we live in a quasinon relativistic world doesn't mean our intuition about the quasinon relativistic world should be our default starting position. If we want to ask questions like 'what is time' then we need to shake off our perception of a nonrelativistic world, and see time as something much more like space than it is different. The point I was making is that we 'sense' time via memory. We actually have different receptors in our brain for spatial organizations (which, ironically, is mostly done by our ears). I don't remember my biology terribly well, so I can't name what specific parts of the brain control what. If what my brother tells me from cognitive psychology is to be concerned, what we even mean by 'spacial organization' is also very muddled. Human brains are weird. By different, I mean we can't regard time and space as the same thing. They are necessary to fully describe relationships between different frames of reference in that we can't regard either as absolute; but there's clearly a difference between how time and space are used to define the 'vector space' (i.e. the universe) we live in. Wouldn't try to challenge this in a million years, at least not within the scale that it is appropriate (which happens to be most of perceivable reality, which is kinda nice) Relativity is just a tool physicists use to get from one coordinate system to another where it's easier to do physics. We shouldn't expect it to be be time symmetric since, after all, it's not a physical theory in the same vein that quantum mechanics is; rather, it's just saying how a quantity in this reference frame will differ from a quantity in that reference frame. In other words, we could (although it would be a very bad and otherwise impractical idea) just all agree to use one reference frame: say set the origin at earth with the initial tangent vectors forming an orthonormal righthanded system with the ztangent vector pointining along earth's axis of rotation. At this point, the system would be nonEuclidean because mass only exists on Riemann manifolds. We can't do something similar with quantum mechanics, say, model everything as a particleinabox and expect our physics could work even at a theoretical level. If I were to throw an offhand stone at Carroll it'd be "model the universe under the schrodinger equation and just see how it evolves!" But honestly if we don't have an actual interpretation of what QM means, then in what sense is it more of a physical theory than relativity? At bare minimum SR is a fundamental feature of QFT and essential in the derivation of it. The only area that seems to really care about having a grand unified theory beyond satisfying philosophical interests are people looking at cases that would require both general relativity and quantum mechanics in which there are no theoretical models. Otherwise, so long as a particular model works, well, use it. After all, an area of research such as Computational Fluid Dynamics isn't going to start replacing their classical laws with quantum mechanical laws just because they could; they're already having a field day dealing with NavierStokes equations. Or people who want better ways of computing cross sections. Because for some reason, time loves to move forward. Even in relativity, again, time and space have different corresponding metrics and as such are treated exactly the same. Yes, we need a temporal axis to describe the vector space of our universe, but that doesn't suddenly mean time=space. No but heads on a coin isn't the same as tails, they are both the same coin. It's difficult to think about or describe one without thinking about or describing the other. I do feel that entropy is saying time is different from space, and yes, must be treated differently in particular because time always marches on. Entropy is the place where it's most evidence, but it's not the only place. Even under relativity, time and space are treated differentlythe only difference is that time is no longer absolute. Because space was never absolute, we tend to group time with space and saying it's more like space because it's no longer absolute. But they are not, by any measure, *identical.* They're similar, they are *like* each other, but they are different. I'm not really arguing against that, but holy crap the words different and similar don't contain nearly enough nuance in the English language. Also, perchance, do you consider energy and momentum to be exactly the same? To the extent that the two are always linked and it makes no sense to think of them as independent stand alone quantities or properties, yes. To the extent that measured values of momentum will equal energy, or that they will always scale the same, no. String theorywhich is probably in part where he's coming fromjust says that spacetime doesn't span the entirety of 'our universe,' and you have to add in all these extra dimensions. If nohting else, spacetime *must* be an approximate subspace of whatever greater theory there is, and thus, time would probably not disappear altogeter. But by approximate you are already ceding that there are realms which it *doesn't* approximate. Within relativistic limits Newtonian physics does a very crappy job approximating anything. There's consensus on whether or not mass is in/variant in special relativity. In particular, the relativistic equation only references rest mass, which makes it's more useful. Usually when mass shows up, so does a Lorentz factor, and as such it's sometimes helpful to think of mass as getting heavier. That said, there's still an ongoing debate within physics on whether or not mass is relativistic and, if not, if relativistic mass is just something that's made up for convenience sake. That said, I'm not sure if mass is invariant in general relativity since I haven't looked at GR as much as I have looked at SR; but I'd imagine it's the same story there.What is often referred to as 'the invariant' are various inner products you can construct. The spacetime interval is an invariant in S.R. whereas the distance is invariant in Galilean relativity. Energy is invariant in Galilean relativity too; but it's variant in SR. Which is why it's just way easier to say 'massenergy is conserved' rather than worry about what is meant by 'mass'. As long as you are careful with dimensional consistency at least... none of this 'mass was converted into energy' stuff, lest Griffiths has a fit. Which is to say he assert time wasn't absolute. Sure, I agree with that. But again, time has its own unique transformation law and its own distinct associated metric. Also would agree. Yes, string theory does gives us a sort of backdoor to solving a lot of otherwise nasty math present in the standard model. That doesn't mean it's a unique predictions; howeverunless it can only be explain in terms of string theory, it's just a mathematical shortcut. For example, there are times when you can use the Heisenberg uncertainty principle in order to find the lifetime and/or rest mass of a particle if you know the other by implying that the particle disappears and the rest energy is 'borrowed' but this argument can fail manyatimes. Good thing unitary and locality provide a good check on the math, seriously, it's an awesome lecture. All I'm getting from Sean Carroll's piece is that this amiplituhedron has both unitary and locality which are the pillars of QFT. Yes but what was remarkable was that unitary and locality were not assumed in the construction of it, and so if you do your computations wrong, you don't get them. They serve as a check on the mathematics. (Also the piece wasn't written by Sean Carroll, it was Nima's collaborator Jaroslav Trnka) And again, my next question is how has this been used in experimentsin particular, has the amilituhedron been used in experiments in a way that the QFT cannot in principle predict, or is it just a mathematical backdoor to otherwise complicated and hairy mathematics. If Nima is to be believed then yes, it has already been used to compute two loop and three loop scattering amplitude calculations which had never been computed before because the old QFT using Feynman diagrams was simply too cumbersome and unmanageable to do so. I don't particular care about the big questions in physicsin particular, looking at experimental physics, I care about more practical approaches. Then this should be especially relevant to you eventually because it appears to be genuinely useful for doing experiments. What does 'come out' mean: that spacetime isn't a subspace of our universre or what? Emergent in the sense that spacetime only forms in the limits, at a certain (small enough) scale, spacetime seems to cease to be a useful method of describing the world. There'd be a scale by which you can start to describe the universe as having spacetime, just as there's a scale by which its useful to describe the universe as being classical, but beyond that scale it is no longer a useful description of what goes on. Spacetime itself, at that scale, is doomed. So says Nima... Is this true? Hell if I know, but the fact that it seems useful in providing computational solutions for scattering amplitudes is at least interesting. I'm looking towards experimental physics, so I really don't care what's going on in the theoretical world. Which isn't to say theoretical physics isn't important, however, it's more of a 'I'll look at it when I need it sort of things.' Physicists in general as a whole don't take string theory terribly serious eitheragain, probably because they don't need it. So, yeah, I'll mostly ignore it. Particle physicists take novel and easier approaches to computing scattering amplitudes rather seriously, Nima has been having quite the lecture circuit trying to describe these findings because they are useful independent of their motivations in seeking deeper physics. Good data is good data. Again, relativity is useless if we want to examine why time moves forward because, if we really want to, we could avoid using relativity altogether (that said, not using relativity makes life pretty hard so we use it). The entropy problem isn't particular hard: a wavefunction will evolve towards a state of uniform distribution in a closed system. Saying it's hard is like saying why do we flip a million coins and expect more or less the same number of heads and tails is hard. It's hard when you have to consider how the universe could have started in a lower entropy state in the first place. The starting entropy of the universe was extraordinarily low, so in any timecomplete spacetime we need to describe why it would look like entropy was getting lower before it was getting higher. It's a nontrivial problem, but an answer is beyond what we generally need for coherent experiments. Eh, I wouldn't let my education get to you. I'm exposed to a lot of formal material, yes, but I'm still an undergraduate so I've mostly seen a little of everything without specialization. If you really want to know, I'm a fifth year undergraduate, but eh, I wouldn't let that get to you. I figured you'd either be a 4th (or 5th) year or a first year graduate student. I graduated in 2012 and have textbooks painfully gathering dust so I know exactly what material you've studied but you also clearly have it much more fresh in your mind so I figured you'd have to be currently in school. Because you've made it rather obvious what types of courses you've taken, and because undergraduate physics education is so god damn standardized, I also know what comments I'm making that are far FAR too casual given proper formal education. It's astoundingly easy to spot people who have had basic formal undergraduate education compared to people who have had no exposure whatsoever. 

