Quote: Original post by mikeman

Quote: Original post by Way Walker
I think time dilation is an "illusion" in the same sense that centrifugal force isn't "real". They're both artifacts of the chosen frame of reference.

Again: There have been experiments that confirm that, when placed inside a moving body, high-precision clocks will actually, factually, tick slower:

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment

You can't get any more "real" than that. Someone mentioned the GPS. Which is also true.

Time dilation is only an "illusion" if time itsel is an "illusion". Which I can't comment on, but seems a different matter entirely.

I didn't say anything that contradicts that; I just said they both depend on the frame of reference. The paradox in the twin paradox is that the twin which is aging slower depends on which one you fix the frame of reference on (you could even choose a frame of reference where they're both aging at the same rate). Similarly, if you choose a rotating frame of reference, there will be a centrifugal force.

Quote: Original post by Way Walker

Quote: Original post by mikeman

Quote: Original post by Way Walker
I think time dilation is an "illusion" in the same sense that centrifugal force isn't "real". They're both artifacts of the chosen frame of reference.

Again: There have been experiments that confirm that, when placed inside a moving body, high-precision clocks will actually, factually, tick slower:

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment

You can't get any more "real" than that. Someone mentioned the GPS. Which is also true.

Time dilation is only an "illusion" if time itsel is an "illusion". Which I can't comment on, but seems a different matter entirely.

I didn't say anything that contradicts that; I just said they both depend on the frame of reference. The paradox in the twin paradox is that the twin which is aging slower depends on which one you fix the frame of reference on (you could even choose a frame of reference where they're both aging at the same rate). Similarly, if you choose a rotating frame of reference, there will be a centrifugal force.

I don't think so...as I said, special relativity is only valid in inertial frames, and only those are interchangeable...the twin on the rocket is accelerating, and acceleration is not relative. The twin of the rocket can easily test and see that he is *not* in an inertial frame of reference: If he takes an object in his hand and let it go while the rocket is accelerating, he will witness the object moving backwards. This is because he can't make any the same kind of (special) relativistic transformations as the Earth observer; if he does the results will not be valid. In any 2 arbitrary inertial frame of reference, measurements are relative, but laws of physics are not(according to special relativity); they are the same in both. In a non-inertial frame of reference, laws of physics are dependend of the frame: thus the emergence of 'ficticious' forces like centrifuge in a rotating frame of reference(which is non-inertial). Any observer in an inertial frame of reference just as valid as the Earth, would make the same prediction: That when the twin returns to Earth, he will be younger.

Quote: Original post by mikeman

Quote:
No, it would appear to be burning the same amount of fuel in both frames of reference, since a clock (attached to the rocket) as viewed from the rocket's reference would be ticking along normally, while the clock as viewed from the other reference would be ticking along at a slower speed. Therefore when you calculated the amount of fuel burned (using the clock as observed by either frame of reference) they would still be correct.

I have trouble understanding this: If you do measurements in one frame of reference, you must stick to it for all measurements(velocity,time,mass,length,etc). If an Earth observer measures the speed and position of the rocket relative to his own fixed frame, thus deducing that it does have a speed greter than zero and predicts time dilation, it follows that he should also measure time by a clock stationed on Earth. When you come down to it, the Earth observer measures the time difference between 2 events happening at (x,y,z,t) and (x',y',z',t'): the first event being when we start to measure the burning of the fuel(t=0), and the second event being when X amount of fuel has burned. Since (x,y,z) and (x',y',z') are measured relative to Earth, it seems logical that t and t' are also measured by an Earth clock.

I shouldn't say "the same" the two values will be different. Which clock you use doesn't matter. What matters is that you use the same clock for all of your calculations. However, whichever clock (in whatever frame of reference) you use, will require the other side to do the calculations with adjustments for the acceleration of the other side.

Now, as the clock on the rocket appears to slow down (from your perspective on earth) it will appear to burn less and less fuel (according to your local clock), however you will also note that its acceleration also decreases lower and lower (as it approaches c).

Now, if both parties are using the clock on the rocket, and both parties wait for the clock to tick for one second, then they will show that the same amount of fuel has burned. However the person on earth will have had to wait longer for that second to tick.

Now for the tricky question: If you use a clock on earth, and the guy on the rocket and the guy on earth do the same thing (wait for the clock to tick 1 second), who has to wait longer?

Quote: Original post by Washu

Quote: Original post by mikeman

Quote:
No, it would appear to be burning the same amount of fuel in both frames of reference, since a clock (attached to the rocket) as viewed from the rocket's reference would be ticking along normally, while the clock as viewed from the other reference would be ticking along at a slower speed. Therefore when you calculated the amount of fuel burned (using the clock as observed by either frame of reference) they would still be correct.

I have trouble understanding this: If you do measurements in one frame of reference, you must stick to it for all measurements(velocity,time,mass,length,etc). If an Earth observer measures the speed and position of the rocket relative to his own fixed frame, thus deducing that it does have a speed greter than zero and predicts time dilation, it follows that he should also measure time by a clock stationed on Earth. When you come down to it, the Earth observer measures the time difference between 2 events happening at (x,y,z,t) and (x',y',z',t'): the first event being when we start to measure the burning of the fuel(t=0), and the second event being when X amount of fuel has burned. Since (x,y,z) and (x',y',z') are measured relative to Earth, it seems logical that t and t' are also measured by an Earth clock.

I shouldn't say "the same" the two values will be different. Which clock you use doesn't matter. What matters is that you use the same clock for all of your calculations. However, whichever clock (in whatever frame of reference) you use, will require the other side to do the calculations with adjustments for the acceleration of the other side.

Now, as the clock on the rocket appears to slow down (from your perspective on earth) it will appear to burn less and less fuel (according to your local clock), however you will also note that its acceleration also decreases lower and lower (as it approaches c).

Now, if both parties are using the clock on the rocket, and both parties wait for the clock to tick for one second, then they will show that the same amount of fuel has burned. However the person on earth will have had to wait longer for that second to tick.

Now for the tricky question: If you use a clock on earth, and the guy on the rocket and the guy on earth do the same thing (wait for the clock to tick 1 second), who has to wait longer?

What I'm saying is, if you use a clock moving along with the spaceship to measure time, then you should also use a spatial frame of reference moving along with the spaceship to measure distance, in order to be consistent. Which means that, well, you're just not using the Earth as a reference frame at all, but the ship's. Which is perfectly fine, but the fact is that a frame of reference that *is* stationed on earth should make the same predictions about the engine rate. Note that this is a misunderstanding: If you are stationed on earth and you measure time based on the clock moving along with the spaceship, then you are just using the spaceship as frame reference, and not the earth. And if you use the earth as a frame for space but the spaceship clock as a frame for time, you're just inconsistent.

When we say 'we use Earth as a frame of reference', we of course mean that we measure distance with a spatial frame that is at rest relative to earth, and with a clock that is also at rest. If you're just stationed on Earth but do measurements with instruments that are in motion relative to you, it's just that: You just happen to be on Earth, but your frame of reference is *not* Earth.

Quote: Original post by Plasmana
If I was a betting man, I would guess that in a 1000 years our present understanding of the the way the universe works will seem archiac and shallow at best; if not completely ignorant. Just because we don't see how it's possible now, doesn't mean it won't be.

I share this oppinion and I also hope so.

Quote: Original post by mikeman

Quote: Original post by Way Walker
I didn't say anything that contradicts that; I just said they both depend on the frame of reference. The paradox in the twin paradox is that the twin which is aging slower depends on which one you fix the frame of reference on (you could even choose a frame of reference where they're both aging at the same rate). Similarly, if you choose a rotating frame of reference, there will be a centrifugal force.

I don't think so...as I said, special relativity is only valid in inertial frames, and only those are interchangeable...the twin on the rocket is accelerating, and acceleration is not relative. The twin of the rocket can easily test and see that he is *not* in an inertial frame of reference: If he takes an object in his hand and let it go while the rocket is accelerating, he will witness the object moving backwards. This is because he can't make any the same kind of (special) relativistic transformations as the Earth observer; if he does the results will not be valid. In any 2 arbitrary inertial frame of reference, measurements are relative, but laws of physics are not(according to special relativity); they are the same in both. In a non-inertial frame of reference, laws of physics are dependend of the frame: thus the emergence of 'ficticious' forces like centrifuge in a rotating frame of reference(which is non-inertial). Any observer in an inertial frame of reference just as valid as the Earth, would make the same prediction: That when the twin returns to Earth, he will be younger.

Granted in the current situation we're talking about a constantly accelerating rocket, but in the canonical twin paradox that I was referring to both are in approximately inertial frames for most of the trip (and, for most of the trip, this approximation is better for the traveling twin than the one that stayed on Earth). The paradox is that for the non-accelerating portion of the trip the experiences should be symmetric.

Even for the accelerating portions, each twin sees the other accelerate as they sit still. It's more complicated than the experiment you mentioned (if I let go of an object, I expect it to fall as if I were on rocket accelerating at 1g in space). My understanding is that you can do the calculation from the traveler's frame of reference if you treat the fictitious acceleration (i.e. acceleration arising from a non-intertial frame of reference) of the twin on Earth as if it were gravitational acceleration. This makes sense given my understanding that in general relativity gravity is also a fictitious force (arising from a the purely mathematical transformation between curved and Euclidean spaces, just like the centrifugal force arises from transforming between rotating and non-rotating spaces).

Quote: Original post by Way Walker
Granted in the current situation we're talking about a constantly accelerating rocket, but in the canonical twin paradox that I was referring to both are in approximately inertial frames for most of the trip (and, for most of the trip, this approximation is better for the traveling twin than the one that stayed on Earth). The paradox is that for the non-accelerating portion of the trip the experiences should be symmetric.

Well, not so much...think about it, for the rocket to reach relativistic speeds it has to either accelerate slowly for a very long time(which is probably what's going to happen in reality, since the human body can't stand accelerations much greater than G for a significant time), or, if we accept that it travels with constant velocity most of the trip, perform a huge acceleration for a short time. As you said, and I agree, this would be equivalent to a very large gravitational field in general relativity(in SR, spacetime is flat). I think both those options throw the 'inertial frame' out of the window for the spaceship twin.

Think about it: We have a situation where the second twin boards a rocket, makes a trip with great speeds, and returns home to meet his other twin. There aren't 2 solutions here; when they meet either the first is gonna be older or the second. There is no relativity here; it's not like when they both meet in Earth, the first will be in a reality that he's older, and the second will be in an alternative realtity in which he is the older one. The paradox is only a 'paradox'(not even then, really, but anyway) if both twins make their calculations based on special relativity. The one not in an inertial frame will have the largest errors in his results, ie predict that when he meets his brother, he(the brother) will be younger, when it isn't so.

Notice that there exists a 'paradox' only if the twin returns on earth, ie they compare ages at simultaneously, in the the same frame of reference. If the situation was a bit different: Say the second twin is already in a rocket travelling with 0.9c, and they are both 30 when the rocket passes very close to earth. Who will age faster? In other words, who will celebrate his,say, 35th birthday first? Here comes into play the relativity of simultaneity: Events can happen at the same time for one observer, one event can happen after another for a second observer, and the reversed for another observer. For example, if both twins are 30 at the start, the 35th birthday of the Earth twin will happen after the 35th birthday of the space twin, *from the reference of the space twin*, and the opposite from the reference of the Earth twin. The events can be reversed, since in this case they don't breach causality. If you express the problem properly, as a series of (x,y,z,t) events and their comparison, you won't have a paradox.

Anyway, since general relativity deals with accelerating frame of references too, if they use that as a tool(in the accelerating rocket situation), the equations they will use will be significantly different than the equations of SR; naturally, there will be no paradox, both will reach the correct results.

[Edited by - mikeman on March 4, 2010 3:51:13 AM]

Quote: Original post by mikeman

Quote: Original post by owl
The ilussion that the engine works at a slower rate, is just that, an ilussion. It is working exactly as if it was on earth. The guy analysing how the engine works should use the space-time frame the engine is working into, not his own.

It's not an 'illusion'. It's very very real. For example, it has been observed that the half-life of a fast moving particle is increased for static observer. That's because time moves slower for the particle, so it decays slower. Look here under 'Time Dilation For Particles'. That's how muons reach the surface of the earth before decaying. It's a real phenomenon alright.

http://www2.slac.stanford.edu/vvc/theory/relativity.html

I just noted a major flaw in the logic of that experiment.

Is time dilating, and actually traveling 'slower' for the high speed frame of reference? Or does the added energy given to the particle to accelerate it to that speed increase the stabilization of the atomic structure, and increases the halflife?

I just hope we/they will figure out a way to upload the contents of my brain before I die. After that, the time spent traveling to a star won't be quite so much of a factor.

Quote: Original post by Silvermyst
I just hope we/they will figure out a way to upload the contents of my brain before I die. After that, the time spent traveling to a star won't be quite so much of a factor.

Yeah, sadly enough there is no guarranty that those contents will be you (as in being)... If it was possible to transfer brain functions one by one in such a way that at some point most of your thought and motor functions are processed by the computer, then, maybe, your self being could be considered to be the same.

Only continuity could guarranty identity me thinks.