[JerryLove]

I had something of an epiphiny. I suddenly understood *why* it takes more energy to accellerat from 0.2c to 0.3c than it does from 0.1c to 0.2c. And before I share it, I want to know if I've just reinvented the wheel or have something new.

So, to all you physics buffs. we know that interal mass increases with speed, but do we understand what *causes* that. Please tell me what does if we do. I just want to know if it's already known or if I have something new.

Don't worry, if it's not already known, I'll share my revelation.

[Qingu]

God causes it






(come on Jerry! Spit it out!)

[JerryLove]

Well. I'm worried I'm just showing my ignorance of an understood phenomina by repeating the obvious.

Time dilation *causes* the appearance of increased inertial mass.

Here's the problem: How fast is something moving at .9c actually moving? Of course, to an outside observer, it's crossing .9c-per-year (therefore moving at .9c), but remember that time dilation has time moving far slower for that something.

So to the object, it's crossing space at a much faster rate. It would be, in point of fact, moving far faster than light.

Say, for example, that at .9c, time moves at half speed (pulling a number out of my butt), then crossing the 4ly distance to our nearest stellar neighbor would take (from the perspective of someone moving at .9c) about 2 years. Crossing 4ly in 2y = moving 2c.

Scale this up. At c time essentially stops. Therefore c isn't the speed of light to the object in question, its actually infinate speed. How much power would it take to move a mass to infinate speed? Infinate power.

From the perspective of those of us outside the moving object, it just seems to get harder and harder to accellerate... it seems to have more mass. The reality, however, is that we are just more and more out of temproal sync with its accelleration.

Of course, the whole tihng creates some math I really don't see how it's possible (anyone want to explain it to me?). I think my classic example is when I send two photons, one forward and one backward, from a moving object (say one moving at .5c). Where will the photons be in two seconds? (for argument, from the moving object's view, though the problem exists either way).

If the object starts at point 0, and is moving at .5c, then in two seconds it will be at +1ls. Now, for the light that left two seconds earlier to have moved away at a constant speed from the observer, one will be at -1ls (+1ls-2ls) and the other will be at +3ls (1ls+2ls). So at this instanct in time, with two photons emitted from 0, one is at -1 and the other +3.

OK. How does this look to the outside observer. Certainly time passes differently, so I don't much care how many seconds it took him to watch. What I care about is this:

In one unit of time, two photons left point 0 and went to -1 and +3. This means that the forward travelling photon moved 3-times-as-far in the same aount of time as the one moving backwards.

I've looked for an snwer to this problem, but haven't found one.

[Niflmir]

Originally Posted by JerryLove

Well. I'm worried I'm just showing my ignorance of an understood phenomina by repeating the obvious.

Time dilation *causes* the appearance of increased inertial mass.

This is the old view of things. The modern view does not include the idea that mass increases with speed. It causes various problems to hold this. I believe it was originally motivated by a comparison of relativistic momentum with classical momentum and then waving hands at it.

Originally Posted by JerryLove

Here's the problem: How fast is something moving at .9c actually moving? Of course, to an outside observer, it's crossing .9c-per-year (therefore moving at .9c), but remember that time dilation has time moving far slower for that something.

In the rocket frame a clock ticks at the same speed it normally would. However people in the external frame see the rocket frame clock moving at a slower rate. Length contraction has caused the distances that the rocket sees to be greatly diminished.

Originally Posted by JerryLove

So to the object, it's crossing space at a much faster rate. It would be, in point of fact, moving far faster than light.

Say, for example, that at .9c, time moves at half speed (pulling a number out of my butt), then crossing the 4ly distance to our nearest stellar neighbor would take (from the perspective of someone moving at .9c) about 2 years. Crossing 4ly in 2y = moving 2c.

Yes and no. The rocket bound observer will never see herself travelling at 2c, when they take the observed distance and divide it by the time of travel, it will come out to the normal velocity 0.9*c. However, they can make a 4ly distance in an arbitrarily small amount of time, given the ability to accelerate.

Originally Posted by JerryLove

Scale this up. At c time essentially stops. Therefore c isn't the speed of light to the object in question, its actually infinate speed. How much power would it take to move a mass to infinate speed? Infinate power.

From the perspective of those of us outside the moving object, it just seems to get harder and harder to accellerate... it seems to have more mass. The reality, however, is that we are just more and more out of temproal sync with its accelleration.

Of course, the whole tihng creates some math I really don't see how it's possible (anyone want to explain it to me?). I think my classic example is when I send two photons, one forward and one backward, from a moving object (say one moving at .5c). Where will the photons be in two seconds? (for argument, from the moving object's view, though the problem exists either way).

If the object starts at point 0, and is moving at .5c, then in two seconds it will be at +1ls. Now, for the light that left two seconds earlier to have moved away at a constant speed from the observer, one will be at -1ls (+1ls-2ls) and the other will be at +3ls (1ls+2ls). So at this instanct in time, with two photons emitted from 0, one is at -1 and the other +3.

OK. How does this look to the outside observer. Certainly time passes differently, so I don't much care how many seconds it took him to watch. What I care about is this:

In one unit of time, two photons left point 0 and went to -1 and +3. This means that the forward travelling photon moved 3-times-as-far in the same aount of time as the one moving backwards.

I've looked for an snwer to this problem, but haven't found one.

Yes, so what you have run into is the classical problem of general relativity. Trying to compare two vectors which exist at two different locations. In a cartesian coordinate system, the basis vectors are the same everywhere, but in a system like polar coordinates (which is warped/curved) as you travel further away from the origin, the angle basis vector increases linearly with distance. So if we call the angle /theta, and /hat/theta is the basis vector, the absolute size changes from point to point. It is necessary to develop a sophisticated method of comparing vectors which are located at different points/ in different frames. You get the 2c speed because you want to use the time the rocket bound observer measures with the distance that the external universe measures.

Hope that helps.

[JerryLove]

Yes and no. The rocket bound observer will never see herself travelling at 2c, when they take the observed distance and divide it by the time of travel, it will come out to the normal velocity 0.9*c. However, they can make a 4ly distance in an arbitrarily small amount of time, given the ability to accelerate.

You've lost me. Let's start with the simple question.

If someone in a rocket travelled 4.7ly at 0.5c (a trip that would take 9.4 years for a clock on Earth?). How long would pass on a clock inside the rocket?

<9.4 years
9.4 years
>9.4 years

Yes, so what you have run into is the classical problem of general relativity. Trying to compare two vectors which exist at two different locations. In a cartesian coordinate system, the basis vectors are the same everywhere, but in a system like polar coordinates (which is warped/curved) as you travel further away from the origin, the angle basis vector increases linearly with distance. So if we call the angle /theta, and /hat/theta is the basis vector, the absolute size changes from point to point. It is necessary to develop a sophisticated method of comparing vectors which are located at different points/ in different frames. You get the 2c speed because you want to use the time the rocket bound observer measures with the distance that the external universe measures.

You seem to have expounded on the problem without offering a soultion.

I've got two photons equidistant along a single trajectory (they went in opposite directions) from a point (the ship that shot them). At the same moment, I have the same two photons equidistant from another point along the same line that is not the ship (the spot the ship was when it shot the photons).

I can think of no geometry that allows for two different points on a line to be in the exact center of two other points on a line without the former being the same point.

[Lightknight]

Have you taken into account acceleration and initial static friction?

[Niflmir]

Originally Posted by JerryLove

You've lost me. Let's start with the simple question.

If someone in a rocket travelled 4.7ly at 0.5c (a trip that would take 9.4 years for a clock on Earth?). How long would pass on a clock inside the rocket?

<9.4 years
9.4 years
>9.4 years

<9.4 years

However, the key point is that when they measure the distance traveled, they will measure a distance < 4.7ly.

Originally Posted by JerryLove

You seem to have expounded on the problem without offering a soultion.

I've got two photons equidistant along a single trajectory (they went in opposite directions) from a point (the ship that shot them). At the same moment, I have the same two photons equidistant from another point along the same line that is not the ship (the spot the ship was when it shot the photons).

I can think of no geometry that allows for two different points on a line to be in the exact center of two other points on a line without the former being the same point.

Your last point is a problem with the classical notion of simultaneity. You want to say that the photons are at +/- a certain distance at the exact same time. However, the time that you necessarily ascribe to the event of their being at such and such a location is observer dependent. The geometry that is necessary is Lorentzian. Minkowski space is the simplest example of this, for if c=1, all the points that lie along the t = +/- x lines are seperated by a distance of zero. (ds^2 = -dt^2 + dx^2 in Minkowski space).

When you change observers in Minkowski space, you don't simply shift the origin, you also must boost the basis vectors. The t=+/-x lines would stay in the same spots, the t and x axes would be pulled toward or away from these lines, depending on the changing of observers. Since the events would also not change in position in Minkowski space, you would measure the events along the new axes at different positions. This causes the time you ascribe to them (distance up the time axis) and the seperation (distance on x axis) to change. Thus depending on your choice of observer, your notion of point of centre of location will be different.

Does that make sense? The idea is that we exist in a Lorentzian space. When you change observers your coordinate axes tilt. This causes you to give them different coordinates. Since the event which was initially simulataneous will now have two different time values and no longer appear simultaneous. However, the new simultaneous positions will appear equidistant from the correct location.

Its late, and I still seem to be jet lagged to Germany time. Let me know what troubles you there. Also let me know how much relativistic theory you know, so that I can include more math and proper theoretic structure.

[JerryLove]

<9.4 years

However, the key point is that when they measure the distance traveled, they will measure a distance < 4.7ly.

Of course, the distance was not chosen arbitrarily: It's the distance from here to Alpha Centauri. When they stop and look back at their origin point, will it be 4.7ly away? If not, how can they be said to have been moving at .5c?

Its late, and I still seem to be jet lagged to Germany time. Let me know what troubles you there. Also let me know how much relativistic theory you know, so that I can include more math and proper theoretic structure.

The lack of absolute or stable values in the universe. But that seems to be more my problem than it is that of the universe. I'm just looking at the ladder paradox. Gahh!

You've given me some good terms to point at information. Right now my concern is less mathmatical than conceprual. Once I can wrap my brain around the concepts well, then I'll peek at the math.

I managed finite, unbounded spacetime, I'll manage this

[JerryLove]

From looking at the ladder thing. Let me see if I follow how dilation preserves speed:

If I was to point myself at Alpha Centauri and instantly accellerate to basically c, space dilation would cause the distance from here to there to drop to about 0, and I would then cross that near-zero distance at near-light speed (taking essentially no time to do so). When I then stopped, space would expand back out behind me, and I would find myself 4.7 light-years from where I was, and everyone back on Earth would have watched me travel for 4.7 years.

But rather than havine percieved myself as travelling faster than light, I would have simply percieved a much smaller universe and travelled through that universe at c.

Oh, and during all this, the shape of the universe isn't fixed.

Am I getting warm?

[JerryLove]

Wait. That solution doesn't work either.

Based on the fact that light is always c faster than me, my speed is always zero. But my suggestion of spacial contraction means that, if I went from "stationary" to c "instantly", then the distance from me to Alpha Centauri would drop to basically 0 instantly. That means I would percieve AC as moving faster than light, which I can't do.

So how do I travel 4.7ly in less than 4.7y without anything (me or the target) breaking the speed-of-light rule?

[Niflmir]

Originally Posted by JerryLove

Wait. That solution doesn't work either.

Based on the fact that light is always c faster than me, my speed is always zero. But my suggestion of spacial contraction means that, if I went from "stationary" to c "instantly", then the distance from me to Alpha Centauri would drop to basically 0 instantly. That means I would percieve AC as moving faster than light, which I can't do.

So how do I travel 4.7ly in less than 4.7y without anything (me or the target) breaking the speed-of-light rule?

You were correct. You don't measure your speed relative to a beam of light. It is fine to describe velocity in terms of some fraction of the speed of light, but it is impossible to measure your speed in terms of it. This is why the theory is one of relative velocities. You say that: Relative to the frame in which Alpha Centauri is stationary, the rocket frame moves at close to the speed of light. Relative to the rocket frame, it seems that Alpha Centauri is approching the rocket at near the speed of light.

In a universe where there is only the rocket, there is no velocity. If there are no "fixed" objects to measure a velocity relative to then the concept becomes meaningless, regardless of whether or not you can shoot out laser beams. Of course, once shot away from the rocket, you would never see the laser beams again. So you wouldn't be able to use them for anything.

[JerryLove]

But the quwstion still applies. Once I come to rest at AC, my point of origin (Earth) will be 4.7ly away. Travelling near the speed of light, my travel time will have been (from my frame) less than 4.7 years. I don't see how I can manage both without something moving faster than light from my frame, once I come back to relative stop.

[Niflmir]

Originally Posted by JerryLove

But the quwstion still applies. Once I come to rest at AC, my point of origin (Earth) will be 4.7ly away. Travelling near the speed of light, my travel time will have been (from my frame) less than 4.7 years. I don't see how I can manage both without something moving faster than light from my frame, once I come back to relative stop.

Heh, that's the twisted aspect of Lorentzian geometry. In 3 dimensions, we have only a few simple classes of symmetry transformations. I can rotate the coordinate axes and I still end up with Cartesian space. I can translate the origin and still end up in Cartesian space.

In Minkowski space, the 3 space like dimensions still have the rotational transformations, you can still translate your origin to wherever you would like. Then there the additional symmetries, which are boosts. If you draw any line through the origin, so long as it remains inside of the light cone you can boost the coordinate system so that that line becomes the new time axis. The rest of the light cone is necessarily warped in a way that has no real analogies to cartesian space.

I suppose I could draw you some diagrams if it would help.

[Qingu]

Originally Posted by JerryLove

Well. I'm worried I'm just showing my ignorance of an understood phenomina by repeating the obvious.

Time dilation *causes* the appearance of increased inertial mass.

Here's the problem: How fast is something moving at .9c actually moving? Of course, to an outside observer, it's crossing .9c-per-year (therefore moving at .9c), but remember that time dilation has time moving far slower for that something.

So to the object, it's crossing space at a much faster rate. It would be, in point of fact, moving far faster than light.

Say, for example, that at .9c, time moves at half speed (pulling a number out of my butt), then crossing the 4ly distance to our nearest stellar neighbor would take (from the perspective of someone moving at .9c) about 2 years. Crossing 4ly in 2y = moving 2c.

Scale this up. At c time essentially stops. Therefore c isn't the speed of light to the object in question, its actually infinate speed. How much power would it take to move a mass to infinate speed? Infinate power.

From the perspective of those of us outside the moving object, it just seems to get harder and harder to accellerate... it seems to have more mass. The reality, however, is that we are just more and more out of temproal sync with its accelleration.

Of course, the whole tihng creates some math I really don't see how it's possible (anyone want to explain it to me?). I think my classic example is when I send two photons, one forward and one backward, from a moving object (say one moving at .5c). Where will the photons be in two seconds? (for argument, from the moving object's view, though the problem exists either way).

If the object starts at point 0, and is moving at .5c, then in two seconds it will be at +1ls. Now, for the light that left two seconds earlier to have moved away at a constant speed from the observer, one will be at -1ls (+1ls-2ls) and the other will be at +3ls (1ls+2ls). So at this instanct in time, with two photons emitted from 0, one is at -1 and the other +3.

OK. How does this look to the outside observer. Certainly time passes differently, so I don't much care how many seconds it took him to watch. What I care about is this:

In one unit of time, two photons left point 0 and went to -1 and +3. This means that the forward travelling photon moved 3-times-as-far in the same aount of time as the one moving backwards.

I've looked for an snwer to this problem, but haven't found one.

Man ... the first time I read this I thought I was too high to understand it. After reading it a second time now, I think maybe I'm just not smart enough.

I'll look this over more when I'm not tired from a long day's work.

[Lightknight]

Perhaps we'll find that the energy requirements to increase speed at those extremes doesn't just increase Arithmetically. I mean, it may become geometric. It isn't so crazy to think that physics may require a bit of tweaking past light speed.