"Time is Not the Fourth Dimension"

[blobru]

That's actually a space dimension, not an additional time dimension - space is imaginary time.

...dude, you just blew my mind.
My very limited layman's understanding is that real time would come from the collapse of the wave function, when the sum of quantum states is described in imaginary time (never having done that calculation, I don't know how much sense that makes, if any). And that for that calculation, one can describe things moving forward or backward in imaginary time. When you say "space is imaginary time", do you mean the three dimensions of space we experience are reduced to a point in imaginary time (that's not my layman's understanding, but that doesn't mean much); or that, because you can go forward or backward in imaginary time, same as you can in space (but not in real time), by definition "imaginary time is space": a spatial dimension? (Or something else? Again, layman asking, hope this makes sense.)

 

[Pi_314]

I've come to the understanding that time and space are one and the same. Space has three dimensions and so does time, same, same, all the same, and spacetime is ... drumroll .... absolutely nothing.

 

[Beerina]

As far as I can tell, they're saying that calling time another dimension is just making stuff up out of the three dimensions that do exist.

But I could be wrong.

Nevertheless, treating it mathematically as a dimension (but not a spacial one) works out to eight billion decimal places accurately. That's a little too convenient if you ask me.

You travel through the spacetime continuum at the speed of light, which includes a time factor moving forward in time. Most of the time you have very little speed, and are thus moving forward at about 1s per s. Move faster through space, and something has to give, specifically your speed through time, which must therefore slow down to compensate.

Gravity warps this 4D whatever-it-is, leaving you in a bizarre state where you must accelerate to stay in place. Hence gravity isn't just a similar phenomenon to the feeling of being pressed into your seat by acceleration, it is the exact same phenomenon. Now what that exactly means is getting beyond me -- how is it distorting, and how are you "accelerating" and why can this acceleration happen apparently indefinitely, are curious questions, and I'm not even sure they're valid questions.

Acceleration is change in speed through space. But that is just m/s/s, and we've already segregated the two types of dimension into old-school interpretations. We would need a common unit to re-write distance and time so they're just one measurement. Eh I wish I had gone this route instead of computers some days...

 

[sol invictus]

That makes me wonder, is there a way to tell the difference between a universe with 1 time dimension and 3 space dimensions and one with 3 time dimensions and 1 space dimension?

Mathematically, there is a very simple change one could make (a single over-all minus sign) that would make those two absolutely identical. Indeed, some physicists work in a convention where time is real and all three space dimensions are imaginary (the "mostly minus" sign convention), and some in the opposite ("mostly plus"). So, the best answer to your question is "no".

...dude, you just blew my mind.
My very limited layman's understanding is that real time would come from the collapse of the wave function, when the sum of quantum states is described in imaginary time (never having done that calculation, I don't know how much sense that makes, if any). And that for that calculation, one can describe things moving forward or backward in imaginary time. When you say "space is imaginary time", do you mean the three dimensions of space we experience are reduced to a point in imaginary time (that's not my layman's understanding, but that doesn't mean much); or that, because you can go forward or backward in imaginary time, same as you can in space (but not in real time), by definition "imaginary time is space": a spatial dimension? (Or something else? Again, layman asking, hope this makes sense.)

It's closest to the bolded part.

Mathematically, the only fundamental difference between time and space is a relative minus sign in the metric of spacetime (the function that determines distances between spacetime points). Points separated in time are an imaginary distance away from each other; those separated in space are a real distance away from each other (or the reverse of that; see above).

So, when you multiply time by the square root of minus 1 (i.e. the procedure you referred to in your previous post), you remove the entire distinction between time and space - time becomes the 4th space dimension.

 

[blobru]

-It's closest to the bolded part.

Mathematically, the only fundamental difference between time and space is a relative minus sign in the metric of spacetime (the function that determines distances between spacetime points). Points separated in time are an imaginary distance away from each other; those separated in space are a real distance away from each other (or the reverse of that; see above).

So, when you multiply time by the square root of minus 1 (i.e. the procedure you referred to in your previous post), you remove the entire distinction between time and space - time becomes the 4th space dimension.

I see: whatever your convention, multiplying by i must make the time dimension space-like. Great explanation; thx, sol.

 

[Roboramma]

That's actually a space dimension, not an additional time dimension - space is imaginary time.

Hey Sol, thinking about this a little more, does this mean that 1 second = i(x)meters, where x is some constant, probably related to the speed of light? Is it possible to make a simple formulation of that nature?

 

[sol invictus]

Hey Sol, thinking about this a little more, does this mean that 1 second = i(x)meters, where x is some constant, probably related to the speed of light? Is it possible to make a simple formulation of that nature?

Sure - x = 1 second/(i meters) .

But more seriously, there's no need for the "i", because the unit "second" already tells you you're measuring a distance in time, and "meters" a distance in space. As for the numerical value of x, the meter is in fact defined by the speed of light c and the second, see http://en.wikipedia.org/wiki/Metre.

 

[Beerina]

So, when you multiply time by the square root of minus 1 (i.e. the procedure you referred to in your previous post), you remove the entire distinction between time and space - time becomes the 4th space dimension.

There is an argument I make that time must, however, actually exist, and that it's not an illusion.

It's a computational argument, though. In computer science, there are certain computations that there is no known solution better than trying all possibilities. Or, if you prefer, simulating it and "running time forward", so to speak.

Assuming there is no general-purpose shortcut, then time must exist because we see such calculations all around us -- they are built into the power of general computer processing.


So "you can't get there from here", or, more accurately, "you can't get here from there", where here is the current state and "there" is a simpler state, without actually "doing" the calculations of atoms and whatnot moving about. This requires time and actual bouncy-bouncy of atoms.


A complex pool table with balls bouncing around for eons -- you can't write a formula for the location of all balls after x time*.










* Perhaps you can, I can't recall for sure. But there are other calculations where this cannot be done, so to speak. Pool table bouncing is an interesting concept as most spots on the table (in a real number sense) will never be rolled over, but that's a different subject.

 

[gnome]

I may have lost it in the complex technical and mathematical discussion if someone already said it... but could it be as simple as... time is A dimension, and putting it fourth is just a counting convention, but nothing that has consequences to the model?

I mean, we might just as well say time is the first dimension, would it affect anything?

 

[sol invictus]

There is an argument I make that time must, however, actually exist, and that it's not an illusion.

I've never been able to figure out what people mean when they say that, so I can't comment on your argument.

I may have lost it in the complex technical and mathematical discussion if someone already said it... but could it be as simple as... time is A dimension, and putting it fourth is just a counting convention, but nothing that has consequences to the model?

I mean, we might just as well say time is the first dimension, would it affect anything?

No.