If we could perceive time as a spatial dimension, what would the world appear to us as? Would people appear as long ribbons (beginning at birth and ending at death)? Or would we find time as a spatial dimension too confusing? How would the past look to us then, if we could look backwards into the “time” dimension? The oft-perceived “flow” of time-would time appear to be static, if perceived as a spatial dimension? Is there a PC simulation that can accomplish this?
It’s difficult simply because conceptualising a fourth spatial dimension is difficult.
Try it for Flatland characters and it becomes a lot easier - Flatland is a plane with width and length, but no height - with time as the third spatial dimension, Mr A Square becomes a mostly-vertically aligned, twisted and bent square prism as he moves (of course nothing actually moves any more, because time is only the measure of how high or low a planar slice of the 3D world you choose).
Turn on “Display Pointer Trails.”
More seriously, note that different people will have occupied the same physical space at different times. If you were to perceive time as a spatial dimension, when you looked at my desk, you would have to have some way of simultaneously perceiving me and all of the other functionaries who previously sat here or will sit here after my demise.
No, because you and them weren’t at this desk at the same position in space-time. By analogy, in three dimensional space, there’s no problem with you being just behind me, even though it would mean that we’re at the “same place” if projected on a plane parallel to our backs.
We already perceive in four spatial dimensions. Time is not often needed and is understood (since it often isn’t important).
But, say, you want to locate an airplane flying from Denver to Chicago. The plane is located at 50,000 feet (dimension one), 501 miles (dimension two) east northeast of Denver (dimension three*) at 3:24 pm CST (dimension four).
So we do perceive things in four dimensions all the time. We just tend to skip dimensions when they aren’t needed. For instance, “travel six miles on route 66” gives only one dimension – length – but the other three are there, just unnecessary.
*In this case, “east northeast” is a stand-in for 67.50 degrees on the compass.
I don’t feel as though I perceive of time as a spatial dimension. I can point north, east, and up, but I can’t point towards 3:24pm CST.
Right; I don’t disagree. I just mean that if we were to perceive time as a spatial dimension, as the OP suggests, we would have to have a way of perceiving it that does not conflict with the existing spatial dimensions.
Isn’t time, technically, three dimensions? I saw it on a website, once.
You see a lot of funny things about time on websites. You can have as many spatial dimensions as you like, but any more than one time dimension, and things start getting really screwey.
What? You can’t trust the Internets?
I wouldn’t say time is a spatial dimension. After all, time is relative, spatial dimensions are absolute.
IANA Physicist, but from what I understand with my limited physics background, to all observerers a 12 inch ruler looks like a 12 inch ruler regardless of it’s relative speed. However, it’s velocity (which is a product of the time dimension) is going to be very different depending on which relativity plane you’re on.
ETA, I should say, assuming the speed is less than the speed of light. At the speed of light the ruler become for all intents and purposes dimensionless energy.
You can go in any direction you want in space, but only forward in time.
However, once inside the Event Horizon of a Black Hole, you can only go forward in space (toward the singularity) but any direction you want in time.
:dubious:
Something to do with gravity knocking Light-Cones sideways.
This thread made me think of the fates, measuring out our lives and deciding where to cut the strings.
“If I could save time in a bottle,”
We are so wrapped up in what we feel and own in every moment that we consider the “present”, and then we have to constantly change and lose the person that we were when we move forward to the future, I think it could be very damaging to anyone to see time like that, to see other people occupy your former space, using the things you used, walking through the spot of sunlight that you walked through, at the same time as you did, and so in a way canceling out your former ownership of those things.
And what a scary idea, too, that others could see the ribbon of my life stretching out behind me, looking at my past actions, but without the benefit of my “softening filter” of self-forgiveness.
I think our relationship with time is so profound, the way we use it to measure our lives is done with so much more emotion than the other dimensions, we could never and will never treat it the same.
You might measure your wealth in how many square feet you own, or your health in how much you weigh, but no measurement can equal the amount of time you think you will have or that you have had with your loved ones.
Anyway, I don’t think we could percieve time in the way that we do the 3 dimensions, because isn’t time wholly an invention of ours, one of if not the most prized invention of our species.
Incorrect. Space and time separately are both relative. It’s only spacetime as a whole which is absolute. Your 12-inch ruler will not be 12 inches to all observers: To observers moving relative to it, it’ll be shorter. Effectively, moving relative to something is equivalent to a rotation of the object through space and time.
By way of analogy: Suppose I ask you how tall a stick is. You can measure the height of one end of the stick, and measure the height of the other end, and take the difference. But this is not an absolute measurement of the stick, since you can tip the stick over, and it’ll be shorter. Likewise, if you measure the X positions of the ends of the stick, or the Y positions, you’ll also get non-absolute measurements of the stick, since rotating the stick can change those, too.
However, suppose you take all of those measurements, and then calculate the value L[sup]2[/sup] = (x[sub]2[/sub]-x[sub]1[/sub])[sup]2[/sup] + (y[sub]2[/sub]-y[sub]1[/sub])[sup]2[/sup] + (z[sub]2[/sub]-z[sub]1[/sub])[sup]2[/sup] . This value L, which we would call the length of the stick, will be the same no matter how you rotate the stick.
Well, when we introduce time as a dimension, things work much the same way: If we measure just the X coordinate difference between two events, or just the T coordinate difference, then what we measure will depend on our reference frame, but we can combine all of those measurements into something that doesn’t depend on reference frame. The only odd part is that the time component gets subtracted, instead of added. So the formula for “proper interval”, as it’s called, looks like tau[sup]2[/sup] = (x[sub]2[/sub]-x[sub]1[/sub])[sup]2[/sup] + (y[sub]2[/sub]-y[sub]1[/sub])[sup]2[/sup] + (z[sub]2[/sub]-z[sub]1[/sub])[sup]2[/sup] - (t[sub]2[/sub]-t[sub]1[/sub])[sup]2[/sup] . With tau defined in this way, it also doesn’t depend on what reference frame you’re in.
Okay, here’s the problem. You’re still thinking in terms of there being some direction that’s “time”. Really, everyone has their own direction of time, and you can only ever move forward in that direction no matter what.
If you find the light-cone thing a little confusing, try this: gravity pulls the “future direction” of any observer towards the gravitating body. And when you’re close to a black hole (inside its event horizon) your future direction always points closer to the singularity. Since you can only move forward in time, you’re forced to move closer to the singularity, until it shreds you all up.
Okay, we have the Slaughterhouse 5 reference, but no one has yet mentioned Donnie Darko? What is wrong with you people?
As Chronos notes, spacetime is invariant; an observer’s speed might chance his perception on one or more dimensions (i.e. things outside his reference frame get shorter) but time is correspondingly stretched out. If you look at this as the interval, s across time t and position r, you find that [symbol]D[/symbol]s[sup]2[/sup]=[symbol]D[/symbol]r[sup]2[/sup]-c[sup]2[/sup]*[symbol]D[/symbol]t[sup]2[/sup] (which is just a different formulation of the last equation Chronos posted, except that he normalized the spatial dimensions in terms of c). Turning this around, you get [[symbol]D[/symbol]s[sup]2[/sup]-[symbol]D[/symbol]r[sup]2[/sup]]/[symbol]D[/symbol]t[sup]2[/sup]=c[sup]2[/sup]. If we take a unit time interval, [symbol]D[/symbol]t drops out, leaving only the numerator, [symbol]D[/symbol]s[sup]2[/sup]-[symbol]D[/symbol]r[sup]2[/sup], which equals c[sup]2[/sup]. In effect, what this means is that your total “velocity” over any interval s in spacetime, which is comprised of a set of spatial components and a time component, is c, or you are always moving at c, just mostly in the time component.
Time is a bit funny in that, at least if you think James Clerk Maxwell had his head on straight about thermodynamics, that it doesn’t go backward, or rather, things don’t go backward in it and make retroactive interactions. This gets kind of bent by quantum electrodynamics, because some of the permitted paths of, say, an electron-photon interaction permit the electron to go back in time and absorb a photon after having released one in the future, all in order to make the books balance. However, this occurs, or rather we should say, is predicted and appears to occur, on a very limited scale and is not the sort of thing that is likely to give rise to dead grandfather and crushed butterfly paradoxes. Even experts in the field of quantum field theories generally agree that the reality of what is occurring there is probably far stranger than anything we can conceive of, but the math of the theory works very, very well, and that’s all that matters to the dissertation board. There are some indications that QED has a forward preference for time as well (despite the monkey business about backwards travelling electrons and other sillyness about anti-particles just being normal particles going the wrong way down a one way street), and in general we’re all more comfortable with a universe that advances in time in only one direction.
Stranger
I’m not a physicist either, but I did fairly well in the relativity chapter in the college course, and also stayed at a Holiday Inn last night.
Anyway, I think you’ve got it backwards; The thing about Einstein’s theory was that there was no “ether” background to propagate light. In other words, we ha no intrinsic frame of reference against which to measure its velocity. Every frame of reference measures light’s velocity the same.
So, to make a long story short (and because I don’t know the long story) the relative velocity between two objects (A and B) moving at relativistic speeds is supposed to be identical, whether A is measuring B, or B is measuring A (and we are all actually correct in assuming we’re sitting still, and the rest of the universe is passing us by).
However, for this to be true, both time and distance have to be measured differently by A and B. There’s time dilation, and length contraction, and, mass distortion too, I guess. So your ruler’s length will be observed differently, depending on how fast you’re zooming by it.
Further understanding is limited, because our professor explicitly told us that our coverage of the subject applied only to objects which were NOT accelerating (or decelerating, or turning, or rotating)
seriously? Cool! When I was 13, I figured if a “particle” formed a circle in time, it would appear to be a pair of particles separating, colliding, and annihilating to the rest of us. What if the particle has “it’s own” sense of continous time where everything is rocking back and forth in this process, while the rest of us travel in a straight line and see it as an isolated incident?
This is almost exactly what happens, and we’ve even seen it!
Certain excitations of 2-dimensional media called “anyons” can be created and destroyed in pairs. If you take a picture of these excitations every instant and stack them up, you’d see the particles tracing out closed loops. If you pick one kind as a “particle” and the other kind as an “antiparticle” you can draw a direction around the loop so the particles are moving up and the antiparticles are moving down. And the quantum physics describing these loops actually depends only on the kind of knots the loops form – if you deform the path a little you get the same amplitudes. This gives what we call “topological quantum computation”.