Mr. Sammi

A long long time ago when I was in University the twin paradox filled my mind so much that it came to pass that there was no such paradox in my mind anymore. At this point intime SR to me and the twin paradox is just an observational hazard.

Concerning the experiment. Say a centrifuge is available in the bubble ship that can attain speeds ranging from .19c to .22c. The plutonium is seperated into 3 parcels. One goes into the centrifuge, the other stays on the lab tabletop, and the third is jettisoned out the window. Which plutonium chunk would have more energy, Parcel 1, which is in the centrifuge, Parcel 2, which is on the table, or Parcel 3, which goes out the window?



Sammi Na Boodie (being nice)

Jesse

OK, in whose reference frame are we calculating the energy of the 3 chunks? Do all three chunks have equal rest mass? Also, for the chunk that is jettisoned out the window, how fast is it going relative to the reference frame of the person who wants to calculate the energy?

The fact that it's plutonium also makes things a little more complicated than if we were just dealing with a single particle, because even when the plutonium itself is at rest in some frame, many of the particles that make it up will not be. Can we ignore that for the sake of the problem, and just treat the chunk as a point mass?

Mr. Sammi

Jesse : Can we ignore SIZE for the sake of the problem, and just treat the chunk as a point mass? OK. A minor approximation.

Would you be able to sum the results for the point mass up over all the points which consist the real mass, to achieve a higher degree of approximation? If not OK.

Calculations are done from the reference frame of the ship treating the 3 chunks as identical. We can approximate the jettison to leaving it behind, as there is a special spherical door on the ship which can swivel and expose the Mass to the exterior without causing damage to the ship, hence its initial relative velocity is zero. The person is inside the ship who is performing the experiment.

*On a somber note - Do you think if the calculations were done from EARTH using a special transmitter & reciever on board the ship, it would affect the results? OR would the results seem to have been different?


Sammi Na Boodie ()

Jesse

Mr. Sammi:
Jesse : Can we ignore SIZE for the sake of the problem, and just treat the chunk as a point mass? OK. A minor approximation.

Would you be able to sum the results for the point mass up over all the points which consist the real mass, to achieve a higher degree of approximation? If not OK.

Well, the problem is with the momentum of all the particles making up the rock, which would greatly add to its kinetic energy. The velocity of an object made up of a lot of smaller particles can be found just by adding the velocity vectors of all the particles, so if half are going in one direction but the other half are going in the opposite direction it balances out to 0 total velocity, but to get the kinetic energy of the object you ignore the direction of each particle's velocity and just look at the magnitude, so things don't cancel out in the same way. In Newtonian physics the formula for kinetic energy is K.E. = (mv^2)/2, while in SR it's K.E. = pc = (gamma*mv)*c = mvc/(1 - v^2/c^2)^1/2. Again, you'd get the wrong answer if you just plugged in the mass of the object and the velocity of its center of mass, you have to sum the kinetic energy of each particle that makes it up.

edit: actually, now that I think of it I don't think it's correct to call pc the "kinetic energy" in relativity, since the total energy is not pc + mc^2, it's the square root of (p^2*c^2 + m^2*c^4)...anyway, this doesn't affect my main point about having to sum the energy of each particle to get the total energy.

Mr. Sammi:
Calculations are done from the reference frame of the ship treating the 3 chunks as identical. We can approximate the jettison to leaving it behind, as there is a special spherical door on the ship which can swivel and expose the Mass to the exterior without causing damage to the ship, hence its initial relative velocity is zero. The person is inside the ship who is performing the experiment.

If the initial relative velocity of the jettisoned chunk is zero, aren't we assuming the ship is traveling at constant velocity and there is no resistance in space, so the chunk will just stay alongside the ship? In that case the energy of that chunk would be the same as the energy of the chunk on the tabletop.

Mr. Sammi:
On a somber note - Do you think if the calculations were done from EARTH using a special transmitter & reciever on board the ship, it would affect the results? OR would the results seem to have been different?

Yeah, in SR the amount of energy an object has depends on the reference frame you're calculating things from, just like mass or length. If the ship is not travelling at the same velocity as the earth, the answer you'll get for the energy of the three chunks will be different.

Hawkingfan

As far as whether it is possible for anything in the universe to travel faster than the speed of light, there is no definite proof. It depends on the real structure of the space-time continuum, which modern physics ignores.

Einstein was challenged on that notion time and time again during his lifetime, but experimental tests determined motion with respect to some absolute space-time frame had failed so he decided to abandon the notion of absolute time. He therefore postulated the principal that all physical laws appear according to the same laws in all reference frames. This was established by observation and experiments.
But in order for that postulate to hold, he had to assume (without proof, only thought experiments) that the speed of light is constant in all reference frames.
It implies, in contrast to Galilean Space-Time, that simultaneity is not an absolute physical quality, but a relative one, depending on the motion of the observer (ie. the reference frame). It is a fact that the existence of a physical absolute time (or, equivalently, a preferred reference frame) cannot be established by experiments.
Time travel would then be possible, since there is no absolute reference frame separating the regions of superluminal past and future, faster-than-light motion in Minkowski space-time. But because of the logical paradoxes of time travel, SR excludes faster-than-light speeds a priori.

There is no definite answer to this problem. The true structure of the space-time continuum is currently unknown. If Newton was correct and Einstein was wrong, then absolute time (and a preferred reference frame) exists, and faster-than-light speeds - and even faster-than-light travel - are possible, at least in principle. If superluminal signals are to be found in the future, then the notion absolute time will surely have to be reintroduced to physics. But until then, it won't.

cfgauss

Jesse:
Well, when you're moving down the river, you've only seen what's behind you because you haven't been to the next parts yet.
Think of a parametric graph <x(t), y(t)>, consider x & y as position and t as time. x & y are just along for the ride, they go wherever t takes them. t describes a curve in space that they follow, but the curve "moves" as t increases. (A bit of a digression, in mathematics there's some disagreement on what constitutes an "intersection" of two parametric graphs. Some say that it's wherever the curves intersect, others say that it's only where they intersect at the same t-value!)
Then just extend this thinking to a 3D parametric equation <x(t),y(t),z(t)>, as t moves along its way, x, y, & z are just along for the ride like a boat on the river. (Another digression: the best way to think of a particle's path through 3-space in time is to think of a single point at one t-value, another point at a t-value slightly after it, etc, describing a "worm" in 4-space just like you could think of the <x(t),y(t)> graph doing the same thing in 3-space (it would actually be written more correctly in this sense like <x(t),y(t),t>.)
Make sense?

Also, you've done an excellent job describing the other stuff to the others!


Hawkingfan:
You should be slapped with a physics (and math!) book! I'll bet you don't know the difference between a continuum and a set!

A continuum is what space-time is not. It almost is, but it's not quite. Current physical theories point to the idea that spacetime itself is quantized, making it certainly *not* a continuum! (Though it's quantizations are so small it can be considered a continuum for most purposes.)

As to the structure of spacetime, if you think it's been ignored, then you've been living under a rock since at least the '12s. Quantum mechanics, Relativity, and nearly every other branch of modern physics--especially theories of quantum gravity!!--deal with this!

Let me explain to you what you're talking about. Einstein realized, due to experiments like the MMX and Maxwell's equations that one's frame of reference did not appear to affect measurements of phenomenon. He also realized that this meant that the speed of light should be isotropic in a vacuum. He sat down to figure out the consequences of this and then *realized* that if these assumptions were true, the ideas of absolute space and time failed. He did not just "decide" to throw them out! Nor did he start with that to find the speed of light to always be constant!!!!!!!!!

From these simple postulates, and high school algebra one can *trivially* show that time transforms like:
t = t' / sqrt(1-v^2) where v is velocity as a fraction of the speed of light, t is time for someone at rest, and t' for the those in motion.

Remember your calculus? And I'm sure you've taken it if you feel like you can talk in any knowledgeable way about physics. There was a little theorem (the Intermediate Value Theorem) which said, essentially, that a continuous function on the interval (a,b) must pass through all the points between? (The one that provides a nice way to approximate zeros, remember? f(.9)=.1 and f(1.1)=-.1 so there's a zero between .9 and 1.1 by the IVT!)

Well, we can do the same thing with velocity. If I want to get from velocity "a" to velocity "b," then my instantaneous velocity must pass through all the velocities between to get there. This, assumes, of course, that spacetime is indeed a continuum, though we need not. Thus, since our world lines through spacetime are continuous, then to get from v<c to v>c we must pass through c! But we cannot! For: lim c->v gamma = 0! That means time slows to a halt relative to everyone else, our length contracts to nothing, and our mass-energy becomes infinite. There's not an infinite amount of energy in the universe, so we can't get to c, let alone >c!

But, of course, those of us who actualy understand physics know this.

Jesse

cfgauss:
Well, when you're moving down the river, you've only seen what's behind you because you haven't been to the next parts yet.

"Yet" already presupposes an arrow of time! The question is, why do I remember parts of my worldline which lie in the -t direction but not those which lie in the +t direction, given that the laws of physics are time-symmetric? The answer, according to most physicists, lies in the low-entropy boundary condition of the big bang (although there is no concensus on why the big bang started off in such a low state of entropy to begin with). If this is correct, then in an imaginary universe with a low-entropy boundary condition at the big crunch but no boundary condition at the big bang, people would remember events in the parts of their worldline that lie in the +t direction, but be ignorant about those which lie in the -t direction. But to see why this is true, you have to invoke an argument involving the thermodynamics of computation as Hawking did--definitely not trivial.

Do you agree with this thermodynamic explanation for the asymmetry in our memories, or do you have an alternative theory?

cfgauss (speaking to Hawkingfan):
You should be slapped with a physics (and math!) book! I'll bet you don't know the difference between a continuum and a set!

Speaking as a moderator, please try to avoid gratuitous insults.

A continuum is what space-time is not. It almost is, but it's not quite. Current physical theories point to the idea that spacetime itself is quantized, making it certainly *not* a continuum! (Though it's quantizations are so small it can be considered a continuum for most purposes.)

In GR space-time is most certainly treated as a continuum, and "space-time continuum" is standard lingo, even though most physicists suspect that GR breaks down in certain circumstances. Anyway, I don't think Hawkingfan's arguments had anything to do with the question of whether space-time is ultimately continuous or discrete (although I agree with you that relativity was based on a fair amount of existing evidence, not just some arbitrary postulates).

cfgauss

"'Yet' already presupposes an arrow of time! "
That's why it's an analogy .
I think my example with parametric equations is more clear. t starts at 0, and increases to infinity. x and y are just along for the ride.

And the laws of physics aren't symmetrical. To illustrate, think about describing to an alien on Mars left and right! How about up and down? The latter is impossible to do completely without referring to quantum mechanical asymmetries! The former is easy.

"In GR space-time is most certainly treated as a continuum"
Yes, it does! That's one of the reasons why it can't deal with quantum gravity.

And when you talk about *structure* you have to use the right terms! If he'd have been talking about something else, I wouldn't have mentioned it, but because he was arguing "It depends on the real structure of the space-time continuum, which modern physics ignores," I had to bring it up!

"Speaking as a moderator, please try to avoid gratuitous insults."

Oh, you mean like:
Please stop flattering yourself. I believe you, in fact, have difficulty understanding basics of physics. For instance, you could not identify that the original postings were talking about the 2nd LoT whenever this was totally obvious. You also did not understand the basics of relativity. You also were unfamiliar with the 3 arrows of time. I still disagree that anything can travel faster than the speed of light. I've heard this fact spoken from almost every physicist from Einstein to Hawking. E=mc^2 influenced the atom bomb, an object not at rest.

Jesse

Jesse:
"'Yet' already presupposes an arrow of time! "

cfgauss:
That's why it's an analogy .
I think my example with parametric equations is more clear. t starts at 0, and increases to infinity. x and y are just along for the ride.

But it's just an arbitrary coordinate choice whether you parametrize a worldline with the parameter increasing in the future direction or the past direction. In contrast, remembering the past but not the future is a real physical phenomenon in need of an explanation.

cfgauss:
And the laws of physics aren't symmetrical. To illustrate, think about describing to an alien on Mars left and right! How about up and down? The latter is impossible to do completely without referring to quantum mechanical asymmetries! The former is easy.

I was referring specifically to time-symmetry--if you get into quantum mechanics you have to use CPT symmetry instead, but either way, there is nothing in the fundamental laws of physics that explains why we should see any macroscopic arrows of time.

cfgauss:
And when you talk about *structure* you have to use the right terms! If he'd have been talking about something else, I wouldn't have mentioned it, but because he was arguing "It depends on the real structure of the space-time continuum, which modern physics ignores," I had to bring it up!

I'd still say it's a nitpick, since what he meant by "the structure of the space-time continuum" was the issue of whether there is a preferred reference frame, a question which doesn't really have anything to do with the question of whether space-time is discrete or continuous.

Jesse:
Speaking as a moderator, please try to avoid gratuitous insults.

cfgauss:
Oh, you mean like:
Please stop flattering yourself. I believe you, in fact, have difficulty understanding basics of physics.

I'd forgotten about that, but you're right, my comment applies to Hawkingfan as well. Try to keep it clean guys!

cfgauss

"But it's just an arbitrary coordinate choice whether you parametrize a worldline with the parameter increasing in the future direction or the past direction. In contrast, remembering the past but not the future is a real physical phenomenon in need of an explanation."
t could just as well be decreasing. But the thing is, t *is* increasing (or t *is* decreasing).

"I was referring specifically to time-symmetry--if you get into quantum mechanics you have to use CPT symmetry instead, but either way, there is nothing in the fundamental laws of physics that explains why we should see any macroscopic arrows of time."
But there are violations to many symmetries, too! In fact, there are possibly violations to *every* symmetry!
Anyway, it's, IMO, that we have some "velocity" through time, just like the velocity through a river, or the progression of t in a parametric equation.

"I'd still say it's a nitpick, since what he meant by "the structure of the space-time continuum" was the issue of whether there is a preferred reference frame, a question which doesn't really have anything to do with the question of whether space-time is discrete or continuous."
No, it would be like saying that in order to really understand math you need to understand "the field of integers, which mathematicians ignore." No, it physically hut me to type that.

"I'd forgotten about that, but you're right, my comment applies to Hawkingfan as well. Try to keep it clean guys!"
Yeah, I'll see what I can do about that. But sometimes it's hard, ya know!