Hm...I could be wrong. But, you said that time dilation and the rest effects are an 'illusion', which are certainly not. As about the invariant(rest)/relativistic mass, it's just terminology: Most scientists believe that when we say 'mass', we mean the rest/invariant mass of the particle, and we must explicitly say 'relativistic mass' when we mean the opposite, or not talk about relativistic mass at all, but about the total energy of the moving body, which is the same.

The fact that relativistic mass is real is easily observed on particle accelerators: Particles are constantly provided with a force by magnetic fields. The force is not dependent on the mass of the particle, but on its electric charge, which is constant. If the particle's mass(the mass used in equations like a=F/m) stays the same, then the particle would have no reason not to accelerate past the speed of light. It is because relativistic mass increases by the factor gamma, that the acceleration decreases in high speeds even when the same force is applied, thus making it impossible to reach the speed of light.

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

Quote:
When an object is pushed in the direction of motion, it gains momentum and energy, but when the object is already traveling near the speed of light, it cannot move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase without bounds, whereas its speed approaches a constant value—the speed of light. This implies that in relativity the momentum of an object cannot be a constant times the velocity, nor can the kinetic energy be a constant times the square of the velocity.

The relativistic mass is defined as the ratio of the momentum of an object to its velocity, and it depends on the motion of the object. If the object is moving slowly, the relativistic mass is nearly equal to the rest mass and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass by an amount equal to the mass associated with the kinetic energy of the object. As the object approaches the speed of light, the relativistic mass becomes infinite, because the kinetic energy becomes infinite and this energy is associated with mass.

The relativistic mass is always equal to the total energy (rest energy plus kinetic energy) divided by c2.[3] Because the relativistic mass is exactly proportional to the energy, relativistic mass and relativistic energy are nearly synonyms; the only difference between them is the units. If length and time are measured in natural units, the speed of light is equal to 1, and even this difference disappears. Then mass and energy have the same units and are always equal, so it is redundant to speak about relativistic mass, because it is just another name for the energy. This is why physicists usually reserve the useful short word "mass" to mean rest-mass.

The question remains: Inside the spaceship,from the Earth's reference, clocks tick slower. We know this. It's not an 'illusion', if the spaceship would be to turn around and return to Earth, we would find that the clocks of the ship are out of sync with Earth clocks. That should mean that the engine's components also 'tick' slower. If hypothetically the spaceship would reach a velocity very very close to the speed of light, the engine of the ship would appear nearly stopped, like the clocks. How does this not result to a decrease in thrust?

Because in the engines frame of reference time is still flowing at the normal speed, thus it is still working at the same power output.

Quote: Original post by phantom
Because in the engines frame of reference time is still flowing at the normal speed, thus it is still working at the same power output.

Yes, of course that is correct. However, I'm under the impression that special relativity gives us the tools to make predictions in any valid frame of reference. If Earth is also a valid frame of reference, and if in deed time dilates inside the spaceship and the Earth observer 'measures' both the engine 'ticking' slower, but also giving the same power output, how that observer explains this? Say the ship propells by launching particles. Certainly there is some rate, a number of particles that is launched per second. If the ship is travelling near the speed of light, wouldn't an Earth observer see the number of particles 'launched' per second to be significantly decreased? How would he then explain that the thrust remains the same? Of course I haven't invented a 'paradox' about relativity, I'm certainly misunderstanding something about it, but I'm wondering what it is.

I can only think that the measured from the Earth momentum of the launched particles increases the same factor as their measured rate decreases(due to time dilation), so the total gain of momentum they give to the spaceship remains the same for both frame of references. I believe this is the deal with the relativistic/invariant mass 'debate', that when talking about relativity we should talk about energy and momentum(which becomes P=mvγ?) and not about mass to avoid confusion, and should reserve the word 'mass' for when we are talking about the rest mass.

[Edited by - mikeman on March 3, 2010 9:49:14 AM]

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.

Quote: Original post by mikeman
If Earth is also a valid frame of reference, and if in deed time dilates inside the spaceship and the Earth observer 'measures' both the engine 'ticking' slower, but also giving the same power output, how that observer explains this?

I don't know much about Einstein's relativity, but I think the simple answer is that the power doesn't remain the same. Power is energy per second. If you're moving such that I observe 10 seconds of my time for 1 second of yours, so time is a factor of 10 slower, then I would observe the power output of an engine in your frame to decrease by the same factor of 10.

we just need to build one of these :)
http://en.wikipedia.org/wiki/Bussard_ramjet

here are some numbers, acceleration == 1/g
to travel to the nearest star 4.3lt/yr == 3.6yr ship time
to travel across the galaxy 100,000 lt/yr == 12yr ship time

thus time on the ship is bugger all, pity when the ship comes back we'll be long dead

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.

It is still an "illusion" because the slowing down is only due to the frame of reference of the stationary object.

It would be just as correct to say that the fixed atomic clock increased in speed with regards to the frame of reference of the moving atomic clocks in those experiments.

From their internal frames of reference however nothing has changed; they would still be decaying at the same rate, in the same manner that the spaceship in question is also still burning fuel at the same rate within its frame of reference it would just appear to be burning less from the frame of reference of the observer due to the difference in the frame of reference.

Quote: Original post by phantom
It is still an "illusion" because the slowing down is only due to the frame of reference of the stationary object.

It would be just as correct to say that the fixed atomic clock increased in speed with regards to the frame of reference of the moving atomic clocks in those experiments.

From their internal frames of reference however nothing has changed; they would still be decaying at the same rate, in the same manner that the spaceship in question is also still burning fuel at the same rate within its frame of reference it would just appear to be burning less from the frame of reference of the observer due to the difference in the frame of reference.

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.

The problem you're encountering with the descriptions is that you're assuming that the clock is relative to whichever frame of reference you're in. To establish any sort of "rate" (which is time based) you need to specify the source of your clock. If you use a clock relative to some other frame of reference, then you have to adjust for the acceleration that the rocket is undergoing in order to properly calculate the rate of consumption.

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:

You can't get any more "real" than that.

I don't think Way Walker was denying that... It doesn't tick slower if you're sitting next to the clock, but it does tick slower if you're sitting on Earth, right? That's why illusion is in quotes.
Like with centrifugal force, if you're observing from one place it seems like an outward force, but from another place it seems like a lateral force, hence the ""illluuuussiionnn"".

Quote: Original post by phantom
It is still an "illusion" because the slowing down is only due to the frame of reference of the stationary object.

It would be just as correct to say that the fixed atomic clock increased in speed with regards to the frame of reference of the moving atomic clocks in those experiments.

I just have a problem with the world 'illusion', because it seems to suggest that only passengers in the spaceship are seeing 'reality', whereas observers on Earth are experiencing some deceptive phenomena. They are both seeing reality, both their measurements are 'real', they're just relative. Just as speed is relative, special relativity extended this to length, time and the rest. They're relative quantities, only having meaning when a frame of reference is specified. Not an 'illusion', which would imply that there is an absolute frame.

Also, the moving frame of reference(say a rocket that we have put the atomic clock inside) can't make a valid relativitistic transformation of measurements, because to compare measurements the rocket would have to accelerate to gain speed, and then deccelerate to return to Earth. Those accelerations render it invalid as an inertial frame, which are the only frames special relativity deals with. To passengers in the rocket, the clock on earth would seem to speed up, but this is contrary the theory of relativity(passengers seeing earth moving, so clock on earth should slow down, not speed up). That's because relativity is valid in an inertial frame of reference. The whole 'twin' paradox etc.

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.