Good question. My thought-experiment explanation of why time distorts as objects approach the spped of light: Imagine a single particle of light bouncing back and forth between two points on a platform. The point of the viewer is a relatively motionless platform in space. As the platform with the point of light begins to move, the path of the particle of light becomes more and more horizontal. As the pythagorean theorem shows, the distance required to travel that triangular space is now longer than before, when the platform is stationary. And because the speed of light remains the same in all frames of reference, the time that is required for the light to travel that distance is more than before. Thus, the time distortion seen as anything approaches the speed of light. This explains time distortion, but not space distortion, although I suspect that they are based on a similar thought process.
Yes. I underdstand the equation and how it is derived, but is there a theoretical or observable reason that it can be explained without an equation?
I am reading the theory of relativity by Albert, but he does not seem to theoretically explain this occurence. He only shows an equation
It would be a similar scenario. Consider that c is constant regardless of relative speed, opps looks like you have. Well that is what messes with the distance calculation, each observer has their own proper time to calculate distance. Remember that in both FoR proper time ticks at the same rate (i.e. c is constant, 1 sec is 299,792,458m). If the 1 second is "distorted" then the299,792,458 meters is "distorted".
Okay, now Albert also talks about how anything can be refrenced as at absolute rest compared to other things. Such as a cup on a table. Everything moves around this cup. But now lets place the cup in the air 100 meters above the table. We still hold true the fact that the cup is at absolute rest, and we let go. Albert states that instead of saying gravity has effected the cup, he states the earth accelerates at upward at 9.8 m/s. But then we have an explinaton that anything that has a push or pull cannot be at rest and then is therefore in motion and not in absolute rest. How does he institute this possibility of a explainable counter-effect of gravity?
Be careful with feeling you understand it and how it was derived. I only have a very basic understanding of SR, and it is enough to reply to your questions. I suggest thinking about what speed really means. From there consider how there is a maximum speed, and that all inertial observers measure it to be the same. distance / time whether staying at rest relative to me or if you travel at 0.5c relative to me, you will always have the same proper time. your time measurement appears the same to you. To me, your proper time appears dilated (slow). I know that your calculation of the value of c will be the same as me. I have to conclude that in addition to your proper time being dilated, your measurement of distance is effected as well. An easy way to visualize it is to imagine you are piloting a disco ball ship in space at some speed close to c relative to me. you emit a "pulse" of light in all directions around you. Because c is constant, your perspective will be that the light around you is all equal distance away from you (as in your ship is right in the middle of the light pulse circle) despite the fact that you are moving towards the light pulse infornt of you and away from the light pulse behind you. However because c is constant, my perspective is the light you are traveling towards is less distance to you then the light you are travelling away from.
I'd suggest staying away from GR. It will only muddy the SR concepts jumping back and forth. I have no idea what GR intuition would be but it definitley is not as intuitive as SR. I don't know when it comes to GR, but from an SR perspective free fall, like the space station (people and things floating around in the spacestation are in free fall) is a way to "ignore" gravity, said differently free fall is a way to counter effect gravity.
Yay! I find it fun. I just wanna mention that ( edited my post to include this) I only have a very basic understanding of SR. because most of that understanding is with the concepts I could answer you. But yea, keep that in mind. i.e. this is the more intuitive stuff. Things like the doppler effect while intuitive, layers ontop of this concept described. But in my opinion that's what makes this stuff fun. oohhh that's geeky.
I agree. Also, do you know anything about what is said about the size of the universe? I was reading about how it is tied to the average density in the universe?
Sorry I don't. But continuing with SR there is a great annimation by a helpfull forum member ghwellsjr in this thread here Alot can be learned from that annimation. It takes a while to really grasp.
R^{2}=2/k*p p is the average densityof the matter and k is a constant connected with the Newtonian constant of gravitation Can anyone explain why this is true, or how Einstein came up with such an equation?
Einsteins definitions question distances, time and what we call gravity and motion. In SR he defines 'speeds' to exist relative inertial frames. A inertial frame generally speaking will then be any object uniformly moving, following a geodesic (slightly diffuse also called 'free falling'). A ball thrown up in the air can not be said to strictly follow a geodesic as I understand, but the same ball instead leaving the atmosphere will follow it. And there it has to do with 'time'. Each second of that balls trajectory can be expressed through the constant 'c', in where light travels proximately 300 000 km per second in a vacuum. And expressed as such the path taken by the ball thrown on Earth do get influenced by SpaceTime, even though not being a geodesic. That in its turn has to do with how Einsteins defined it as SpaceTime, instead of splitting it in a '3D-space' and a '1D-time'. Try to use that concept on a quantum level :) Very few manage, although I personally think they need too if they want it to fit. Speeds on the whole becomes a very weird definition in Relativity, and distances too. IN SR you locally is the one defining both a 'speed' and a 'distance'. In GR it seems as even that definition loses its meaning. "In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime | that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at dierent points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very denition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime." Too see how I think. Assume that you're on a planet (Earth) relatively, and uniformly, moving at half the speed of light, as measured relative the CBR (Cosmic Background radiation). That we now define as your 'inertial frame' loosely speaking. Take two rockets, identical in all aspects. One accelerating in the direction of Earths motion relative the CBR. The other accelerating opposite Earths motion as measured relative the CBR. Assume them to have identical accelerations relative Earth, then ask yourself which one of those, according to their own 'local' definition of time (clock at rest with rocket) first will reach 75% of lights speed in a vacuum. Keep on assuming that everything, from start, all the way accelerating, to that final 'speed', is the exact same for both rockets, as their invariant mass etc as measured relative their own local clocks. Will the motion we measured relative the CBR play a role? Then tell me how they know that they reached the speed, relative what frame of reference? And finally, is that a absolute 'speed' they define then. How?
Let us presume that Earths 'relative motion' (versus CBR) did count in, a little as the hangar-ships speed will do for a aircraft taking of from its deck. Then it also should become logical to assume that depending on in which direction we shoot up a rocket from Earth, it should either reach a 'speed' faster, or slower depending on what side we choose, relative Earths motion versus the CBR. As well as assuming that you can 'gain fuel' by accelerating in that 'relative motion' we defined relative the CBR. Do we find it to be so on Earth? How Fast Are You Moving When You Are Sitting Still? But feel free to answer the questions before. I'm quite interested in how you would define it.