You’re right, there is a finite chance that at any time pi = 3 or 5. Turns out that chance is zero, though.
BTW, I’ve never known 3 to approach 4… 
But 2+2=5 for sufficiently large values of 2.
Bah! Chicanery and balderdash, I say! Twos creeping up to be almost threes, pi deciding to be 5 sometimes, electrons having long distance conversations, space shifting universes, 10 to the minus bejesus…it’s confounding!
I wish I could understand it. Serves me right for taking business and English courses in college…I never learned the neat stuff.
In the immortal words of Jethro Bodine, “Ought plus ought is ought. One plus ought is one…”
I remember reading this years ago so I may have it wrong; but it was a proposed example of faster than light travel.
If the tip of the second hand on my watch sweeps around the dial faster than a point next to the center–that is, travels a greater distance in the same amount of time (Conservation of angular momentum? Where’s a physics book when I need it), could the tip of a “almost infinitely long (light years in length)watch hand” be rotated faster than light?
No way to test this puppy, but in theory, if it was long enough, could the tip travel faster than light?
no, it won’t work. Nothing is 100 percent perfectly rigid, which is what the second hand would have to be for the scheme to work. The forces transmitting the movement of the hand from atom to atom are the electromagnetic forces between said atoms, all travelling at c.
I don’t know if I buy that.
1). The tip of a bullwhip moves much faster than the handle, IIRC, the “crack” is the sound of the tip breaking the sound barrier. Even if it’s not, it’s still an example that it doesn’t need to be rigid, isn’t it? Say a long enough bullwhip instead of a “second hand”.
2). Even if the forces “transmitting the movement of the hand from atom to atom are the electromagnetic forces between said atoms, all travelling at c” is a correct statement; isn’t this in the direction of the length (to hold the thing together) and not in the direction that the length is traveling?
I’m grasping here, but doesn’t relativity deal with “frames of references”? The atoms of the second hand/bullwhip aren’t moving faster than light with respect to each other, are they?
Yes, they are.
Let’s say you do construct a rigid stick one lightyear long, to test your theory. You hook one end up to a very strong motor, and press a button to make it sweep through one “tick”.
The motor applies a force to your end of the stick, making the atoms there start moving. Well and good.
The atoms at your end are bonded to their neighbors. So when Atom 1 starts moving, it exterts an attraction on Atom 2, which also starts moving. Atom 2 exerts the same kind of attraction on Atom3, which attracts Atom 4, and so on down the length of this stick.
This attractive force is electromagnetism, which propagates at the speed of light. It should be obvious that the “wavefront” of movement-- the spot in which the atoms are just feeling the motive force-- propagates at the same speed.
If your stick were short, this effect could be ignored. But we’re talking about an object one lightyear long. The wave of movement cannot move faster than c, so when you push on your end of the stick, the other end doesn’t hear about it until a year later.
In short, the stick doesn’t act rigid. Instead of sweeping it instantaneously through a degree of arc, you’ve only served to bend it in the middle, and the end is never forced to exceed C.
(Does this make sense? I can’t tell, it’s 5 AM and I haven’t slept yet.)
Laugh hard; it’s a long way to the bank.
AuraSeer,
Your explanation was good. I would add that a co-ordinate system could have points that move “faster than light”, but since rigid rods cannot exist, no material is moving at faster than light locally.
Virtually yours,
J Matrix
There is nothing to prevent a circle or a globe (or any other geometric form) to increase its size faster than the speed of light. If a circle expands at the speed of light, its diameter will increase at twice the speed of light; its circumference will increase at pi times the speed of light; and its area will increase at pi times the radius squared times the speed of light. But as long as the radius increases no faster than the speed of light, no law of physics has been violated.
Here’s the exciting part: This has been observed in nature. A few years ago, National Geographichad an article on lightning that revealed that modern videography and photography had captured on tape and film forms of lightning totally different from the familiar jagged line. One looks like a fountain of light. Another of these newly-discovered forms was a ring that expanded outward at nearly the speed of light. These other forms of lightning had been seen by pilots and some scientists were skeptical of the lightning’s existence until only recently.
One should remember something when cosmologists describe the universe as expanding: They’re not necessarily saying that it’s blowing up like a balloon. They’re saying that new space is being created, and that it’s in creation all around us, not just at the so-called “edge” of the universe. Or so one theory of many states.
(We are not stationary, we are in motion just as those red-shifted galaxies are. It’s that we are each flying away from the other. Think of two cars driving away from each other, each going at 60 MPH. Their velocity of separation would thus be 120 MPH. And any visible red-shift would be identical to that observed if one car was stationary and the other was driving away at 120 MPH. It’s all relative, you see. )
Don’t bother looking for that new space; we can’t sense it directly. But we can, of course, observe those galaxies flying away.
The creation of new space seem to be the theory that best fits the observations.
Where is that space coming from? No one really knows for sure. (I need to bone up on those theories.)
Those who do not learn from the past are condemned to relive it. Georges Santayana
Cabbage sez:
Zero is not finite.
Zero isn’t infinite either. I always understood finite to mean “not infinite”, i.e. bounded.
In theory, what if you started with “short watch hand”, got it rotating, and then began extending it? Add subunits to either end like a microtubule in a cell (using Borg technology, no doubt). Since it’s already rotating, would it still bend? Could you get the tip going fast enough this way?
Nice try dasmoocher, but the watch hand would still bend. The speed of light is still the speed limit for material objects and signals.
Virtually yours,
J Matrix
“Faster than the speed of light” is a pretty sophisticated topic and there have been some damned good posts in this thread. Let me humbly submit a concept I picked up somewhere in my reading (I hope it wasn’t in a Straight Dope book):
If you have something expanding from a singularity think of it as a yeasty dough with raisins in it. As it expands in all directions it must make room and be pushed by more material from the source. As the doughball gets bigger the raisins on the outer edge are moving a lot faster than the raisins near the source. When the doughball gets really huge, as in light years across, the raisins at the outer edge are really moving. Theoretically there is no limit on their speed. They must move to accommodate the expansion even if it means moving faster than the speed of light.
I’m no Einstein but I can visualize this.
The raisins in dough analogy, while it is a good analogy, can only be taken so far. There is no dough expanding–space itself is expanding. And since it (space) is not material it can expand “faster than light”. The other problem with this image is it makes it seem the big bang was a localized phenom that flung mass-energy out into an existing universe. The bang was the entire universe (all space and all matter) expanding from the point that was the entire universe.
You have the same problem with the spots on a baloon analogy. The spots are the only physical things. The baloon surface does not exist as a physical thing.
Virtually yours,
J Matrix
DrMatrix – something just clicked. Do you have a daugher named Iva?
“Vandelay!! Say Vandelay!!”
ravenous: Doh!
But it’s still not zero.
pluto So you’ve heard of me. Martin Gardner’s reports of me are slightly exaggerated.
Konrad Zero is finite.
Dr. Matrix: Lies, lies, lies, spam and lies. But still, my point is that at that scale anything’s possible.
Unfortunately, the universe has not been refined to a limited number of mathematical models yet. So it must be based on chaos. Due to this, there is a 50% chance that Pi will equal nothing and infinity simultaneously and 50% chance that it won’t.
Whatever happens everything is 50% chance - it either happens or it doesn’t.
The universe could not have expanded at the speed of light because it would not experience time. Despite time being created by humans, it is still theoretically a recordable unit. If it did not experience time, it could not decelerate as all physicists know:
Change in acceleration is equal to change in velocity over time.
If time = 0 or infinity,
the change in acceleration would also equal 0 or infinity. Because 1/0 = 0 or infinity.
If the Big Bang occurred at the speed of light it would continue to do so, therefore due to relativity everything in the Universe would also have to travel at the speed of light. Will that do?
I am an A-Level Physics student at Reigate college UK. I am 17 and spend too much money on drugs. I also spend too much time thinking about things.
E-ME at m_sworn@hotmail.com cos i can’t get to this site on the college sever for some reason.
Remember: