Please, someone, rather than getting distracted by all sorts of nonsense, please answer my question:
Since the spaceman moving at constant velocity perceives himself to be at rest, would he observe time slowing down on earth, since, relative to him, the earth is moving at 0.98c?
What? The first link explains what you clearly don’t understand about how the time dilation effect works.
The second tells of all the effects that have to be taken into account to keep GPS accurate, including dilation. Would you prefer I linked to another experiment instead? Try these.
One of these being the use of sound to illustrate the behavior of light at relativistic speeds as I remember. Adds a bit of gravitas to my example I guess.
Yes, relativity does explain what you can expect to observe from a certain frame of reference.
Now please, someone answer my original question:
Since the spaceman moving at constant velocity perceives himself to be at rest, would he observe time slowing down on earth, since, relative to him, the earth is moving at 0.98c?
Didn’t seem to sink in, though.
You do realize there’s a fundamental difference between how sound and light works, right? Sound cannot travel at C, light can. And you can catch up to sound wave (sonic boom), you cannot with light.
I doubt the answer will help you. If he’s moving away from the earth, then he will observe time slowing on earth. Earth will observe time slowing on him. Both see slowing. The Twin Paradox site I linked to explains the apparent contradiction.
Since the spaceman moving at constant velocity perceives himself to be at rest, would he observe time slowing down on earth, since, relative to him, the earth is moving at 0.98c?
Ah, I thought you might be leading up to this. This is the infamous twin “paradox”, and eventually, anyone who looks into relativity stumbles across it (I put “paradox” in quotes, because there isn’t actually a true paradox here, once you understand it). The key to understanding what’s going on is the realization that there are not just two frames of reference, here (the Earth and the traveller), there are (at least) three: The Earth, the traveller going away, and the traveller returning. You can work in any one of those three reference frames you want, or in fact in any other reference frame (though why you’d pick some other reference frame, I don’t know), and in any reference frame, the symmetry between the Earth and the traveller would be broken. Further, the symmetry would be broken by the same amount, so that everyone, in every reference frame, will agree that when the traveller comes back, he’ll be younger than someone who stayed on Earth.
Probably the simplest place to look at it from is from the Earth’s reference frame, as you already have. In that reference frame, time on the Earth is proceeding perfectly normally. But the traveller is moving on the outward leg of his journey, so time is slowed for him then, and he’s moving on the inward leg, too, so time is slowed there, also. So from the Earth reference frame, he hasn’t aged much when he gets back.
But now let’s look at some other reference frame (as, of course, we can, since no inertial reference frame is any better or worse than any other). Suppose we choose to work in the reference frame of the traveller on his outbound leg. In this reference frame, we start off with the Earth moving away, and the traveller sitting still. So time goes slower for the Earth, but perfectly norrmally, at least at first, for the traveller. Then, after a while, the traveller leaves that reference frame, and takes off chasing the Earth at a higher speed, such that he eventually catches up to it. Now, if we stay in the same reference frame (which we must, if our answers are to make any sense), we cannot say that the traveller is still at rest, because he’s now in a different reference frame. So staying in the outbound reference frame, we now have the Earth still moving, and thus having its time slowed down, and the traveller moving even faster (because he has to catch up to the Earth), and hence his time is slowed down even more. If you go through the math, you’ll find that even though the traveller wasn’t moving the whole time, in this reference frame, his faster movement, when he does move, is more than enough to make up for that, so he still ends up with less total time passing for him, at the moment he catches up to the Earth. So in this reference frame, too, we see that he’s aged less than the folks on the Earth.
Certainly. General relativity is much more complicated, and one can’t even begin to hope to truly understand it until one has a solid grasp of special relativity, since SR is an inherent part of GR.
Ah at last and explanation! Well this kinda makes sense - let me think it over. Thanks.
EDIT: I know the twin paradox was mentioned earlier - i didn’t quite digest the relevance of the original explanation referenced.
I have a question on this topic. General relativity says that acceleration and gravity are the same, but when it says gravity, is it referring to freefalling (actual acceleration although you can’t feel it) or standing on the surface of a planet (not accelerating but feels like it)?
IANAPhysicist, but as I understand it, if it FEELS like acceleration, then it’s acceleration or gravity. You have to be in the right context to understand where it’s coming from. So, If you were in a box that completely shut out the world, you wouldn’t be able to tell the difference between the pull of earth on your body, or if you were away from any gravitational influence, yet accelerating at 1G. Same inertia… same feeling.
If you are falling… this is no different than if you were standing firmly on the ground. The earth ALWAYS has this pull on you… this acceleration. As far as you’re concerned, it could be that you’re in zero G, floating peacefully, as the earth is rushing toward you at 120 mph. The difference being, is that earth will try and accelerate your body up to 120 mph in a split second (when you hit ground). That hurts. It’s better to never have jumped from that plane to begin with… as before you left the ground, you were already “traveling” at 120 mph with the earth. That’s why parachutes are important… they decelerate you (or the earth, depending on how you look at it) slow enough where your body can handle it.
One minor detail: the earth has an atmosphere, which introduces “terminal velocity”. This is the point where the friction of the air, counteracts the acceleration of gravity. If the earth had no air… then you’d just keep accelerating faster and faster until you hit pay-dirt. No ~120 mph speed limit.
Also, I suppose then, the effects of earth’s gravitational pull on you, could be lessened or increased if you were able to accelerate the earth as well. But once you reached a constant speed/velocity, everything will feel like it’s not moving again. Just be sure to brace yourself. 
(as I am now doing for anything I may have gotten wrong here)
In the context of GR, freefalling is not acceleration and therefore doesn’t feel like it, while standing on the surface of a planet is acceleration, and therefore does feel like it. The fundamental basis for general relativity is the revolutionary notion that what an accelerometer reads is actually correct.
Of course, this implies that two people on opposite sides of a planet are actually constantly accelerating away from each other, while at the same time remaining a constant distance apart. Reconciling this is where all the heavy math and curvature of spacetime come in.
May I assure you all that if anything travels faster than light, it does not travel in time, and nor does anything else. Causality is not violated, it just appears to be so to a particular observer. If I set off in my fast jet, break the sound barrier, and land (all in a straight line), I can then listen to myself arriving. I have not arrived before I set off. Likewise, if I fly my spaceship faster than light, and then come to a stop (in a straight line), I can see myself arriving. I have not arrived before I set off.
I think we can all agree that two clocks which are experiencing 1G run at the same rate, and therefore stay in sync. This is still true if one is experiencing 1G because it is on the surface of the Earth, and the other is undergoing an acceleration of 1G. Einstein’s equivalence principle and the experiment with the man in the chest :- “Relativity The Special And The General Theory”, Methuen and Co 1920, chapter XX .
I set off in my spaceship to Alpha Centauri with the rocket accelerating at 1G. At the half way point it turns round and decelerates at 1G. It comes to a stop at AC, and without cutting the motor, is immediately accelerated back towards Earth at 1G, again turning and decelerating at the half way point, coming to a halt at Earth. The total journey time was 7.8 years, and the total distance covered was 8.8 light years. The clocks on the spaceship were always subject to 1G as were those on Earth, therefore keeping in sync with each other. I certainly did not arrive at AC before I set off, and did not arrive back at Earth before I set off.
The above scenario is allowed. As the rocket and the rocket motor are in the same reference frame (FR), there is no mass increase between the two, and I can use the Lorentz transformations to show this.
Remember that the v in these equations refers to the velocity of the rocket relative to a different FR, which the observer is in (and by inference the propulsion force : the only experiments which have been done to show mass increase with velocity have been under those circumstances). The applicable equation is m = m0 / sqrt (1-(v/c) ^2 ). Because v = 0 (the motor is in the same FR as the rocket, so there is no relative velocity), v/c = 0, and (v/c) ^2 = 0. The square root of 1 - (v/c) ^2 = 1, and m = m0 / 1. Therefore m = m0. As the acceleration is held to 1G for a distance of 2.2 light years before turning round to decelerate, the space ship will reach a speed greater than that of light (the velocity in meters per second at turn around will be 63.87 X 10e7 [ c = 30 X 10e7] ), and time on this space ship will pass at exactly the same rate as back at home on earth.
I urge you to look up :- http://myweb.tiscali.co.uk/carmam/Hollings.html by Tom Hollings
And :- http://www.aquestionoftime.com/ by Hans Zweig
Sweet Zombie Einstein!
tomh4040, do you agree that light travels at the same speed in every reference frame? If not, how you do explain the Michelson-Morley experiment?
I don’t agree.
ETA: And of course, anything you derive by assuming this is suspect as well.
The two cases are significantly different in the eyes of mainstream science, which holds that nothing can go faster than light. Thus, according to mainstream science, the first case is quite possible, and the second is quite impossible, and therefore nothing can be proven or even demonstrated simply by waving your hand and asserting:
You’re gonna need more evidence than you’ve shown so far.
Nope. It only works if the 1G is in the same frame of reference, as was Einstein’s example, where they were both on Earth. But if we are in free fall above the Earth, or in free fall above the Moon, or in free fall above Pluto, all will experience the same 0G, but because of the difference frames of reference, which are traveling at different velocities, mainstream science says that they will be experiencing time at slightly different rates, and the clocks will NOT be in sync.
tomh4040, you’ve refuted a particular argument that FTL is equivalent to time travel. Unfortunately, the argument you’ve refuted is an incorrect one used only by laymen, and is not the actual physical reason why they’re equivalent.
Before I even read any more in this thread, I must reply: Phaemon, thank you relatively massively very much for this link. This particular question in particular, standing out amidst Mr. Jackal’s commentary, is one that I have long wondered about, in my non-technical lay ignorance. (And yes, I did note your correction to the link in the following post.) I never heard of the paradox under the term “Twin Paradox” before. I just took at a quick glance there, and I’ve bookmarked it for a more thorough perusal at my leisure. I am gathering that the non-intuitive asymmetry in their aging profiles is due to the fact that, for all their relative relativity, the fact is that one is accelerating WRT the other and can detect that, while the other (on earth) sees himself as “stationary” with the other (in the ship) as accelerating, and can detect that. This, after all the math is done, leads to the asymmetry in their aging when they finally meet again? Have I got at least this much right?