[HN Gopher] Time isn't simply just another dimension
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Time isn't simply just another dimension
Author : crhulls
Score : 27 points
Date : 2022-07-22 14:03 UTC (8 hours ago)
(HTM) web link (bigthink.com)
(TXT) w3m dump (bigthink.com)
| naikrovek wrote:
| Is it odd of me to not trust anyone that claims they are
| thinking? There are a few youtube channels with names like this:
|
| "bigthink", "just have a think", "undecided [whatever]"
| (indicating that they are thinking about something and providing
| evidence in their videos)...
|
| I'm sure there are more. in my limited experience, people who
| tell me that others are wrong, and that only they are thinking
| about something are about to lie to me and attempt to trick me
| into doing something that benefits them, and often damages me in
| some way.
|
| I think it may be that I grew into the internet as it matured,
| and I've seen many bad actors try new things over the years to
| swindle gullible internet users.
|
| I don't know. I just know that I do not trust anyone who centers
| their brand identity around the claim that they are thinking or
| that they are carefully weighing both sides of an issue before
| making a decision. People who say that aim to manipulate you, in
| my experience.
| ozim wrote:
| Just like people that repeat that they will give you your money
| back - while obviously not doing it.
|
| Then you get political parties or movements that claim that
| they are "true and real" or "genuine".
|
| Just like "The People's Front of Judea" :)
| karmakaze wrote:
| > However -- and this is the key point -- the faster you move
| through space, the slower you move through time. The other
| dimensions are not like this at all: your motion through the x
| dimension in space, for example, is completely independent of
| your motion through the y and z dimensions.
|
| Not the clearest way to think about this. The speed of light
| isn't the speed limit, it's the _only_ speed. If you 're not
| moving in space, you're moving through time at c.
|
| So for the above example, something moving in the x-direction at
| c, can't also be moving in the y or z components--spacial
| directions are also not independent with each other.
| ravi-delia wrote:
| It pretty succinctly expresses what makes time special; it's
| the imaginary dimension (as in numbers)! You can say you're
| always going c, and you won't be wrong for a given metric, but
| time is special _because_ it 's where the "velocity" gets sunk
| into when all the spacial dimensions are grouped as one.
| Obviously none of this is any different from what you said, but
| since the article is about what makes time special it's not
| unfair to think about velocity components in time and space
| differently.
| mikewarot wrote:
| The Electromagnetic Vector Potential field, usually labeled
| _A_ is also something that many treat as merely a
| mathematical convenience. However, it can be directly
| observed using a Superconducting QUantum Interference Device
| (SQUID).
|
| It is fitting that we use a similar quantum phenomenon,
| oscillations of the Cesium atom to measure time.
| mensetmanusman wrote:
| It's impossible to not move in space due to inflation.
| raattgift wrote:
| > It's impossible to not move in space due to inflation.
|
| Do you mean cosmic inflation? If that happened at all, it
| must have been before the formation of the cosmic microwave
| background. The (standard) concordance cosmology provides a
| calculation for the PVF photon visibility function (PVF) --
| when the surface of last scattering became transparent to
| photons. From detailed observation of the CMB (by the
| Wilkinson Microwave Anisotropy Probe among many others), we
| have data strongly supporting that the PVF's interval from
| opacity to transparency is about 110 000 years, opaque at the
| early time of about 370 000 years after the electroweak
| epoch. (The splitting of electroweak into electromagnetism
| and the weak force gave rise to electrons and other leptons,
| photons, and neutrinos, and their respective antiparticles;
| consequently there is also a Cosmic Neutrino Background).
| Prior to the start of the PVF, matter in the universe was too
| hot to form electrically neutral structures like atoms, and
| prior to the end of the PVF these structures would be broken
| apart by electromagnetic interactions.
|
| Or do you mean the metric expansion of space? That's an
| ongoing observable, unlike cosmic inflation, which ended
| hundreds of millions of years before the formation of the
| first galaxy clusters, while the metric expansion continues
| to cause all galaxy clusters to drift apart from one another.
|
| "Cosmic inflation" doesn't do anything to the motion of an
| object today; it switched off more than thirteen billion
| years ago.
|
| How about expansion, then?
|
| The universe at scales where galaxy clusters are like fine
| grains of dust or microscopic elements of a fluid is well
| represented by a set of equations -- the Friedmann equations
| -- that describe an expanding spacetime (the Robertson-Walker
| metric (R-W), if we subtract out all the galaxy clusters
| leaving only vacuum behind). However, the R-W metric is not a
| good description for galaxy clusters themselves, nor
| individual galaxies, nor individual stars, etc. Those are
| best described by a _collapsing_ spacetime, with a metric
| like Lemaitre-Tolman-Bondi (LTB), adapted for hierarchy and
| non-spherically symmetrical lumpiness of the collapsing
| matter. (You are on a lump right now! There is obviously a
| lot of dense mass in one direction, below you, but not so
| much above you). We can combine R-W and LTB into a "swiss-
| cheese" model, where the name is evocative of holes (the LTB
| collapsing spacetimes) embedded in the otherwise smooth,
| homogeneous, isotropic Friedmann-[Lemaitre]-Robertson-Walker
| spacetime).
|
| Our galaxy is in a "hole", and so there is no metric
| expansion within our galaxy.
|
| (Or alternatively, and commonly put forward in popsci
| descriptions of dark energy, the expansion is so small within
| our solar system that we can ignore it. We have checked for
| local expansion experimentally, because if we could measure
| local expansion we might choose to explore otherwise-
| superfluous theoretical ideas. All measurements so far are
| consistent with _no_ expansion in our solar system.)
|
| Is it impossible to not move in _space_ , as you say? I don't
| know. One can prove whether one is in gravitational free-
| fall, using highly sensitive accelerometers. One can then set
| down coordinates that freely-fall with you and your always-
| reading-no-acceleration accelerometers. In _those
| coordinates_ , one could say that the rest of the universe is
| in motion about the coordinate origin, which is you. However,
| one would tend to reject the notion for reasons similar to
| the rejection of geocentrism.
|
| It is however impossible to hold still in our _spacetime_.
| Our universe has a strong time-oriented causality and for
| good reason (including the behaviour of subatomic particles
| in countless laboratory experiments and astrophysical
| observations) we represent it as Lorentzian spacetime with
| certain constraints and energy conditions, and while that
| remains the best most fundamental representation of our
| universe it is safe to say that everything physical _must_ be
| in constant motion _through spacetime_. So our freely-falling
| self-centred astronaut is only always at the 3-dimensional
| _spatial_ origin of a set of 4-dimensional coordinates, one
| dimension of which is timelike. Indeed we can even say that
| minimizing the movement against spacelike axes, one must
| maximize the movement against the corresponding timelike
| axis. We are of course free to set down any set of
| coordinates we want -- doing so does not change the physical
| arrangements of matter, only how one represents those
| arrangements.
| gizmo686 wrote:
| More importantly, the concept of speed itself is confusing when
| you try treating time as just another dimension. Traditionally,
| speed means how many units of space do you move in a unit of
| time. Asking about your speed through the x dimension is as
| simple as asking for dx/dt. Asking about your speed in the time
| dimension is even simpler, it is just dt/dt, which probably
| isn't what you where actually interested in.
|
| You can ask for your overall speed in all spatial dimensions
| with dX/dt where dZ^2 = dy^2 + dx^2 + dz^2.
|
| By analogy, you could say that your speed through all of
| spacetime is dS/dt, where dS = dx^2 + dy^2 + dz^2 - dt^2. You
| could then say that your speed through time us dT/dt, where
| dT=1-dS. Although this quanity is really measuring the
| difference between proper time and coordinate time, which is
| just time dilation. An equivalent derivation works for length
| contraction as well.
|
| Importantly, all of these qualities are dependent on your
| choice of reference frames. Only dS and dT are frame
| independent, so (in some sense) they are the only true
| quantities. Both of them also rely on merging time and space to
| a single quantity.
|
| Of course all of what I wrote applies to special relativity
| (flat spacetime). Once you get to curved spacetime, your metric
| gets more complicated, but the general ideas still apply.
|
| Really, I don't see how you can make sense of general
| relativity as anything other than a 4 dimensional geometry with
| a really weird metric.
| pyinstallwoes wrote:
| So it's really like being in a omnitreadmill and the Omni
| treadmill is time and any direction I move is delta to c.
| ickelbawd wrote:
| Is this really true? I can imagine a vector, [1,1,1] in
| cartesian space. Scale that vector by c and you are now going
| light speed in all three spatial dimensions.
| ickelbawd wrote:
| Whoops. Of course I had to use c for every value so the
| magnitude exceeds c. FTL travel!
| admax88qqq wrote:
| What is the length of vector [c,c,c] ?
| wbsss4412 wrote:
| Said vector doesn't span all of 3D space though. It is a one
| dimensional vector.
|
| x, y, and z are just shorthand for orthonormal basis vectors.
| What you've described isn't "traveling in all three
| dimensions" simultaneously, it's traveling along on of the
| dimensions with a different basis.
| ickelbawd wrote:
| That might be true from my own frame of reference but not
| so to an observer, right? How can we say there are 3
| spatial dimensions at all if what you say is true? What
| you're describing suggests there are an infinite number of
| dimensions based on the different frame of reference for
| all observers. Why do we then believe there to be 3
| dimensions? Is this just one of the cases where 3
| dimensions is a useful model for calculation but not really
| true in reality?
|
| Undoubtedly there must be something I'm missing here--I've
| taken physics courses but clearly I'm no expert. :)
| wbsss4412 wrote:
| Unfortunately I am not well versed in relativity, my
| response was completely rooted in linear algebra.
|
| That is, any vector is going to be inherently one
| dimensional, regardless of its coordinates. Dimension is
| a property of a set of vectors, dependent upon how many
| are linearly independent of the rest of the vectors in
| the set. What I described doesn't imply that there are
| infinite dimensions.
|
| The vector [0,0,1] is traveling through three dimensions
| just the same as [1,1,1].
| gizmo686 wrote:
| But this is true in relativity as well. In an appropriate
| coordinate system, you are also moving in only 1 of the 4
| dimensions. If you are not accelerating, then this
| coordinate system is an inertial reference frame, and the
| fact that you appear to be a stationary object moving
| through time is not mere mathematical curiosity, but the
| core insight of relativity.
| hollasch wrote:
| You are assuming that we can alter our speed, which isn't
| true. Our speed through spacetime is c. If you are at a fixed
| point in X,Y,Z, then your velocity is c in the direction of
| time. You can change _direction_ in spacetime, but you can't
| change your speed.
|
| If you set your velocity to [1,1,1,x], then x (your speed in
| time) MUST be sqrt(c^2-3). And still, once you've done that,
| you cannot "scale your velocity", because you cannot change
| your speed. We can only change direction.
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