Say everything in the universe, becomes half of its spatial dimension overnight, will we able to notice it ? (Relativity people - assume the event occurs at midnight and propogates in all direction at the speed of light).
Do you mean that I go from a 6 foot Kamandi to a 3 foot mini-K? In other words, are all three dimensions halved? Or will I go from 180 lb to 90 lb?
Would the distance between the planets, stars, galaxies, etc. be halved as well? If not, I suspect that the reduction in weight of all the stars, etc., coupled with no change in orbital distance would cause substantial changes in orbital periods.
…and the change occurs at midnight? Midnight where?
If it propagates at the speed of light, or any finite speed, you would most certainly notice it. Imagine if Jupiter were twice as close and half as massive–the attraction between it and our planet would double, and that would probably be bad.
If it happened instantly, no, nobody would notice because there would be no point of reference.
If it spread at a finite speed, like the speed of light, yes, we’d notice because the universe would start going to hell.
Well, the OP said that everything would be reduced by one-half in its “spatial dimension”, so presumably scientists would notice when photons which had previously taken mind-bogglingly short time period x to pass from point A to point B in their sophisticated laser gizmos now started taking mind-bogglingly short time period 1/2 x to traverse the same distance. (Time periods x and 1/2 x could still be measured by some gadget based on radioactive decay which would be unaffected by the whole spatial-dimension-halving thing, right?)
Would, for instance, the speed of light change? That’s not really a linear distance, but if photons seemed to be going twice the speed, that would be a giveaway. But maybe the speed of light is tied in with some linear distance that I’m unaware of. I think this is a good question, but requires a deeper knowledge of physics than you might think.
I have heard the reverse question asked… if everything doubled would we notice.
It was many many years ago… I thing the answer had something to do with area and volume being figured out differently hence no Giant ants.
Of course time, piss poor memory and they might have been feeding me a load of bull… hope that helps.
The way it was discussed in the philosophy course I took, you’d notice because if everything doubled in size, but not in mass, gravity would be halved.
I guess that if all linear distances went halfsies, then in order for us not to notice, we’d have to have the following transformations too:
c -> 1/2 c
h -> 1/4 h
G -> 1/8 G
And we’d be talking about stuff shrinking on a lot of scales. Not only would the distances between atoms have to shrink, but the size of the protons would have to as well. All forces would be cut in half, so either the constant in the Coulomb Force Law would change (by a factor of 8, just like G) or the charge of the electron (and everything else) would drop by a factor of sqrt(8). Come to think of it, that would have to happen anyway if you wanted the fine structure constant to stay the same.
Think of it this way: you have a cube that’s one meter on a side, and therefore has a volume of 1 cubic meter (1 meter x 1 meter x 1 meter = 1 meter[sup]3[/sup]). If you double the dimensions of the cube’s sides to 2 meters, you don’t wind up with a cube with a volume of 2 cubic meters, but one with a volume of 8 cubic meters: 2 meters x 2 meters x 2 meters. (And mass is dependent on volume; if both cubes are filled with water it will take eight times as much water to fill the second cube as the first, so it’s going to weigh eight times more.)
The area of the first cube is equal to (1 meter x 1 meter = 1 meter[sup]2[/sup]) x 6, or 6 square meters; the area of the second cube is (2 meters x 2 meters = 4 meters[sup]2[/sup]) x 6, or 24 square meters, or only 4 times greater than the first cube.
Something like the strength of a support column (like an organism’s leg bones) is dependent on the cross-section (assuming you’re continuing to use the same material as you scale up, which in the real world you may not be able to do, for this very reason), which is a function of area, or length squared, not volume. But the weight which the support column must support–including the support column’s own weight–is a function of volume again, length cubed. Thus, an elephant has legs which are not only (obviously) thicker than those of a mouse, it must have legs which are thicker in proportion to its own body than those of a mouse (or else it must have leg bones made of titanium or something biologically improbably like that). Various scaling problems crop up either shrinking or enlarging everything, such as in lung capacity (which is why the insides of our lungs are so physically complicated–to pack more area into the volume of our chests).
So, thinking about this a bit more and actually remembering stuff that I really should have thought of to begin with, the answer to the question posed in the title of the thread is “No”, because we’d all be dead.
Wouldn’t a change like this require so much energy that it would blow everything up and nobody would notice because there would be nobody around? Or are we doing this with magic? 
Isn’t there a gradual version of this happening all the time, namely the expansion of the universe? I’ve read on threads here that EVERYTHING - us, all the atoms, molecules, and the space between them, is still expanding from the Big Bang.
I’ve heard people ask in threads here whether what you describe is true, DarrenS, but I think the answer is always no.
Would my terminal velocity be lower? Would I be able to lift giant objects over my head? Leap tall builings in a single bound?
True Achernar - I found a couple of threads where Chronos and JS Princeton both state categorically that the expansion of the universe doesn’t happen below the megaparsec scale:
http://boards.straightdope.com/sdmb/showthread.php?threadid=32365
http://boards.straightdope.com/sdmb/showthread.php?threadid=127309&pagenumber=4
If those two agree on it, I think it’s a safe bet 
No need to trouble Hawking to confirm it for us.
You will notice, because your mass will be 1/8 of what it was before, and your weight will be a lot less still.
Another thing that you will notice is the solar system flew apart. Since gravity is directly proportional to mass and inversely to the square of the distance, in this case the mass will be 1/8 and the distance 1/2, with a net decrease of 1/2, or 50%.
height, mass, energy EVERYTHING, is ALL dependant on the speed of light. It all depends on what your asking, if your asking whether everything becomes half as big RELATIVE to the speed of light, will it be noticable, hell yes, its the reason we dont have elepahnt sized cockroaches and cockroach sized elephants.
If oyu asked if we would notice if the speed of light halved. Well, no because our rules are based on the speed of light. The speed of light could be anything it wants to be and we would never notice.
I suspect the most dire problem in the first instance would be that every single atom/molecule would be split apart by the sudden change in scale.