Dale said:
@tophatphysicist
Any further posts mentioning consciousness will be deleted. It is not a relevant topic for this thread.
I would regret that, because I find Tophat's note on consciousness very interesting, for the simple reason that Tophat probably -unintentionally?- solved the issue I had in this thread! His latest posts all of a sudden make me realize why "3D object" indeed doesn't make sense. Because a 2D section through a rock is NOT the same as a slice (being 3D) of the 3D rock, hence a 3D section through 4D spacetime is not the same as a slice (being 4D) out of/part of full 4D object. I thought the difference is rather nitpicking, but I bet this is why we didn't understand each other, isn't it, Dale? We probably do have the same special relativity analysis in mind, but because of this 3D section not being same as 'slice', we couldn't get agreement. I think I now also understand all the other posts :-) Let's see...
tophatphysicist said:
If you think about it, our perception delivered by the brain after receiving
information from the optical nerves is an averaged out "image", average over
somewhere around the last 300,000 miles or so of travel along the 4th dimension
(if you set a mode of consciousness watching the continuous sequence of 3-D
cross-sections of the neuron 4-fibre bundle as it advances along the observer
world line at the speed of light -- and assuming some conscious response time).
One way of interpreting that might be to say that consciousness observes a running
average of 4-D sections (3-D cross-sections extending 300,000 miles along the
4th dimension). In a sense you might say that we are actually observing 4-D objects.
tophatphysicist said:
Actually, I could understand if you wish to make a point out of we, as observers, when observing an object, probably are observing the result of a brain/consciousness process that presents an image of an object that includes 4 dimensions. This is in the sense that the image has probably been averaged over something like 0.3 seconds (depending on your response time). So, in reality you consider in what sense you are experiencing the mental display of a 4-D object. Consider how far the observer moves along his world line in 0.3 sec (quite a distance along the brain 4-D fiber bundle).
Very good posts, Tophat. Your comment about the 0.3 timelapse made me think, and forces me to jump in again. Actually, such a timelapse includes 4D extention. But your "averaged out image", is a 3D object without time "thickness" making it a non issue, because that 3D construct is only a mental thing of your brain, not an object out there to be/being observed. I now have to admit that when I compared a 2D section through a 3D rock with a "2D" slice of bread still being an object, I was -unintentionaly- cheating, because the slice of bread necessarily does have a small part of (extention into) the 3rd dimension. Hence the section though the rock I had in mind also needed a 'thickness' to be able to consider it the set of 3D rock atoms 'along' that section.
This indeed means that in special relativity a
3D object of simultaeous events doesn't make sense, because an object 'needs' a 4D extention. And this also makes a 3D world a non issue, because a 3D world is only an illusion (your "averaged out image") produced by your mind. The 3D world you and I had in mind does contain a slight 4D extention, making it a 4D object. From now on I should use "4D slice of simultaneous events" instead of "3D section of simultaneous events". Doesn't it make sense?
tophatphysicist said:
I won't get into the details of whether the 3-D cross-sections make up a continuum
or whether they are discrete, perhaps with Planck time sequences. But, we already
know that the optical nerves/brain system has a relatively enormously long time
constant.
For what it's worth. Your final comment in post #190 is more important for the discussion than it seems. Because if the spacetime continuum is discrete, one would be able to talk of a 3D section being a 3D object, with no 'time-lapse'/time extention?
One last thought. Just to make sure what we have in mind when considering an event. Consider a car hitting a tree. We can give the event coordinates to locate it relative to ref frames, but what about dimensions of the event itself? Because, if there is no time extention part of the event itself, wouldn't this mean that there cannot be an event, nor car, nor tree? Because when comparing with the rock: we can locate an atom inside the rock by labeling it with coordinates, but the rock atom itself is a 3D object. Wouldn't that make an event a 4D 'object'? I has to be because that's how a collection of simultaneous events is a 4D (not 3D) slice/part out of the full 4D... If we use a ref frame to locate an event, the event (absolute building block of absolute 4D spacetime) itself must have dimensions, otherwise there is nothing to be measured... (cfr atom in the rock slice: if a rock molecule has no dimensions, there is no molecue, hence there is nothing to be labeled with coordinates...).
@Dale, and @Jbriggs, ... is this getting closer to what you were trying to get across?