5 ms·

Time isn’t simply just another dimension

39 points by crhulls 4y ago

karmakaze 4y ago
> 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.
- ickelbawd 4y ago
  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.
  - admax88qqq 4y ago
    What is the length of vector [c,c,c] ?
    - random314 4y ago
      Vector [c,c,c] is not physically realizable. First postulate of special relativity is that the magnitude of the velocity vector cannot exceed c
      - admax88qqq 4y ago
        It was a rhetorical question to prompt parent poster to reconsider. > 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. But my point was if look at the magnitude or such a vector it would be >c and therefore exceed the speed limit of c.
  - wbsss4412 4y ago
    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.
    - gizmo686 4y ago
      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.
    - ickelbawd 4y ago
      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 4y ago
        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].
        rexer 4y ago
        Not quite, though, right? Because the magnitude of those two vectors is different: the magnitude of the latter one is 1.7. I agree with the rest of your statement.
  - hollasch 4y ago
    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.
  - ickelbawd 4y ago
    Whoops. Of course I had to use c for every value so the magnitude exceeds c. FTL travel!
- ravi-delia 4y ago
  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 4y ago
    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.
- gizmo686 4y ago
  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.
- mensetmanusman 4y ago
  It’s impossible to not move in space due to inflation.
  - raattgift 4y ago
    > 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 Lemaître-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-[Lemaître]-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.
- pyinstallwoes 4y ago
  So it’s really like being in a omnitreadmill and the Omni treadmill is time and any direction I move is delta to c.
- x86x87 4y ago
  one thing to consider is that c is not really the speed of light. It's the maximum speed of causality. If an even takes place at a specific point in space it cannot be observed at another space in time faster than the distance between the two point divided by the maximum speed of causality. Light is easy for us to observe so we mix the speed at which we perceive it to travel to the speed of causality. Seen through that perspective, if you are at a fix point in space, you could apply the same logic for the time dimension and because it's the same point in time you literally can claim that you travel through time at the fasted speed causality allow it. (normally it would be infinite speed, but because our world is discrete, albeit at a very small scale, the speed of causality is also limited but very large - ie C)
naikrovek 4y ago
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 4y ago
  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" :)
russellbeattie 4y ago
There is no such thing as time, there's only movement. No movement, no time.
- x86x87 4y ago
  what if all the ever existed and will exist exists suspended in a higher dimension and nothing really happens? Time present and time past Are both perhaps present in time future, And time future contained in time past. If all time is eternally present All time is unredeemable. What might have been is an abstraction Remaining a perpetual possibility Only in a world of speculation. What might have been and what has been Point to one end, which is always present. Footfalls echo in the memory Down the passage which we did not take Towards the door we never opened Into the rose-garden T.S. Eliot - Burnt Norton

39 points by crhulls 4y ago

> 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.

ickelbawd 4y ago
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.
- admax88qqq 4y ago
  What is the length of vector [c,c,c] ?
  - random314 4y ago
    Vector [c,c,c] is not physically realizable. First postulate of special relativity is that the magnitude of the velocity vector cannot exceed c
    - admax88qqq 4y ago
      It was a rhetorical question to prompt parent poster to reconsider. > 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. But my point was if look at the magnitude or such a vector it would be >c and therefore exceed the speed limit of c.
- wbsss4412 4y ago
  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.
  - gizmo686 4y ago
    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.
  - ickelbawd 4y ago
    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 4y ago
      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].
      - rexer 4y ago
        Not quite, though, right? Because the magnitude of those two vectors is different: the magnitude of the latter one is 1.7. I agree with the rest of your statement.
- hollasch 4y ago
  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.
- ickelbawd 4y ago
  Whoops. Of course I had to use c for every value so the magnitude exceeds c. FTL travel!
ravi-delia 4y ago
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 4y ago
  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.
gizmo686 4y ago
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.
mensetmanusman 4y ago
It’s impossible to not move in space due to inflation.
- raattgift 4y ago
  > 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 Lemaître-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-[Lemaître]-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.
pyinstallwoes 4y ago
So it’s really like being in a omnitreadmill and the Omni treadmill is time and any direction I move is delta to c.
x86x87 4y ago
one thing to consider is that c is not really the speed of light. It's the maximum speed of causality. If an even takes place at a specific point in space it cannot be observed at another space in time faster than the distance between the two point divided by the maximum speed of causality. Light is easy for us to observe so we mix the speed at which we perceive it to travel to the speed of causality. Seen through that perspective, if you are at a fix point in space, you could apply the same logic for the time dimension and because it's the same point in time you literally can claim that you travel through time at the fasted speed causality allow it. (normally it would be infinite speed, but because our world is discrete, albeit at a very small scale, the speed of causality is also limited but very large - ie C)

naikrovek 4y ago

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 4y ago
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" :)

russellbeattie 4y ago

There is no such thing as time, there's only movement. No movement, no time.

x86x87 4y ago
what if all the ever existed and will exist exists suspended in a higher dimension and nothing really happens? Time present and time past Are both perhaps present in time future, And time future contained in time past. If all time is eternally present All time is unredeemable. What might have been is an abstraction Remaining a perpetual possibility Only in a world of speculation. What might have been and what has been Point to one end, which is always present. Footfalls echo in the memory Down the passage which we did not take Towards the door we never opened Into the rose-garden T.S. Eliot - Burnt Norton