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 wave-function collapse. Basically, once you collapse the wave-function, 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 time-asymmetry. 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^2-r^2, or I=r^2-t^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^2-r^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 four-velocity, the temporal component is always c; int he four-momentum, the temporal component is basically energy divided by c. In the relativistic equation, it's again the difference of E^2-p^2 (where p is the four-momentum) 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'=x-vt, 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 over-hype 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/sqrt-xv/c^2)/(1-v^2/c^2))--which, if you look, isn't the same transformation law of space (where x-->x' is given by x'=(x-vt)/sqrt(1-v^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 three-vector 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 three-vector 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 quasi-non-relativistic 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 right-handed system with the z-tangent vector pointining along earth's axis of rotation. At this point, the system would be non-Euclidean because mass only exists on Riemann manifolds. We can't do something similar with quantum mechanics, say, model everything as a particle-in-a-box 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 past-complete 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 Navier-Stokes 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 differently--the 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 theory--which is probably in part where he's coming from--just 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 back-door to solving a lot of otherwise nasty math present in the standard model. That doesn't mean it's a unique predictions; however--unless 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 many-a-times.

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/guest-post-jaroslav-trnka-on-the-amplituhedron/

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 experiments--in particular, has the amilituhedron been used in experiments in a way that the QFT cannot in principle predict, or is it just a mathematical back-door to otherwise complicated and hairy mathematics.

I don't particular care about the big questions in physics--in 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 either--again, 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.