Relativity made simple

[elfmotat]

I know what you mean now. I didn't look at the diagram, I don't normally find them helpful, I just suddenly realised what you meant. The answers obvious. If the ruler can get through the hole in one frame then it can in all frames. It can either go through or it cant. You cant change reality by changing perspective or by switching coordinate systems. Well start with the labs frame. Lets say the ruler can just make it through without touching the sides but with absolutely no room to spare. Now if we go to the rulers frame it gets longer because its not length contracted any more, but time gets longer by exactly the same amount because its not time dilated either in this frame, giving its extra length just enough time to pass through the hole, and of course the same thing happens if we switch to the disks frame. Youre going to have to do a lot better than that. This is what I mean when I say space and time are interchangeable and there really is no difference between them. I hate it when one of says time-like or space-like. My turn.

 

While what you say is certainly true, the point of the exercise was to figure out how both perspectives can be correct according to SR, yet seemingly be contradictory. Since you are apparently unable to answer, I'll do it for you: in the meter stick's rest frame, the plate is tilted at an angle [math]\phi'=tan^{-1}(v_y v_{rel}\gamma_{rel}/c^2)[/math] with respect to the x-axis. This is because of the relativity of simultaneity - if all points on the plate cross the x-axis at t=0 in one frame, they cannot possibly do so in any other frame. In this frame the plate passes over the meter stick at a tilted angle, so it doesn't matter what is length contracted and what isn't.

 

As someone who apparently "understands" relativity without understanding the math, why is it that you couldn't predict this phenomenon?

 

 

1. When an object uses energy to accelerate it cant ever reach a velocity of the speed of light relative to any other object because velocities dont add together in that way. Length contraction and time dilation prevent any object from doing this, so why would it be any different when gravity is accelerating an object? If there are three objects near to a black hole , one of which is using a constant amount of energy to balance the gravitational attraction and maintain a constant distance from the event horizon while one free-falls and the other accelerates away from the hovering object, steadily increasing its acceleration at exactly the same rate as the free-falling object to keep its velocity relative to the hoverer the same as the free-falling objects velocity relative to the hovering object then at what point does gravity mysteriously become infinitely strong so that no amount of acceleration in the opposite direction is enough to accelerate away?

I'm sure you already know that the answer to this is "at the event horizon." The proper acceleration required to "hover" outside of a black hole is:

 

[math]a=\frac{GM}{r^2\sqrt{1-r_s/r}}[/math]

 

You can look at this as the equivalent of the Newtonian "g" value (which at Earth's surface, for example, is ~9.8 m/s²). As you can see, as you approach the Schwarzschild radius (the event horizon), the value of [math]a[/math] asymptotically approaches infinity. There isn't some "mysterious" (as you like to call it) jump discontinuity where, all of a sudden, [math]a[/math] shoots to infinity - it's an asymptote.

 

 

The increasing rate of change in relative velocity between the object using energy to accelerate away and the hovering object decreases as the object accelerates away because of length contraction and time dilation despite the fact that its proper acceleration continuously increases at the same rate, keeping its relative velocity below the speed of light no matter how hard it accelerates. Now if we compare this to the free-falling objects velocity relative to the hovering object, at what point does the decreasing rate of increasing change in velocity relative to the hoverer act differently to the decreasing rate of change in velocity relative to the hovering object of the object thats using energy to accelerate away, and why? In other words, why would length contraction and time dilation work differently when mass is accelerating an object than it does when energy is doing the same? When energy accelerates an object length contraction and time dilation are a consequence of the speed of light remaining constant relative to any inertial observer.

The free-falling object and the object accelerating away from the BH act completely differently from the very beginning. The free-falling object experiences zero proper acceleration, and is moving toward a region of spacetime with more and more curvature. The other object experiences nonzero proper acceleration and is approaching an asymptotically flatter region of spacetime. They're in no way equivalent.

 

Whats the length contraction and time dilation of general relativity based on if not that?

 

Time dilation and length contraction by themselves aren't well-defined in GR. You may get analogous effects in particular solutions to the EFE's, but there's no direct generalization of TD and LC to curved spacetime.

2. How can the Schwarzschild and Kruskal coordinate systems both be considered correct when they clearly directly contradict each other? You cant have it both ways. Either an object can reach an event horizon or it cant. How can both possibly be true?

They don't contradict each other. Proper time corresponds to what clocks actually measure in GR. It is the only physically meaningful type of time. All objects cross the even horizon in finite proper time according to all observers a finite distance from the BH. Schwarzschild "coordinate time" is not physically meaningful - it's just a coordinate. It actually corresponds to the proper time of an observer at an infinite distance away from the BH. A consequence of using this particular type of coordinate system is that there's a coordinate singularity at the event horizon.

 

There's no such thing as "correct" coordinates, because coordinates are not physically meaningful. It obviously doesn't matter what I decide to call a particular set of points. Why would it? Treating coordinates as physical "things" is absurd! They're just labels!

 

Your question is equivalent to asking how Cartesian and polar coordinates can both be "correct." It doesn't make any sense.

 

3. General relativity describes a black hole as have an event horizon that expands outwards at the speed of light locally, so how can any information from the black hole possibly reach any object before the event horizon does when theres simply no way for a black hole with an expanding event horizon to influence anything?

I'm not really sure what you're asking here. Could you try rephrasing the question?

 

4. How can any object possibly reach an event horizon when theres no way for an object to ever reach it from the perspective of a more distant object no matter how fast it accelerates towards the horizon or how close the more distant object gets?

Because what you just said is patently false.

 

If it were possible for an object to reach an event horizon from the perspective of a more distant object then an object thats crossed the horizon would have to move back across it from inside the black hole, which general relativity says cant be done.

I really don't understand your logic here. More distant observers can't have objects crossing the horizon because then the objects would have to escape the horizon? What? How did you come up with that?

 

5. If a hovering object and a free-falling object are attached to each other by a rope then what happens if the hovering object pulls the free-falling object away from the black hole after the free-faller has crossed the event horizon from its own perspective?

The object, and the part of the rope that crossed the event horizon will fall toward the singularity. You'd be pretty hard-pressed to find a rope that can stay together under that much tension in the first place.

 

From the free-fallers perspective no amount of energy could ever be enough to escape (yea right) but from the other objects perspective the free-faller can never reach the horizon, so it will always be possible to pull the free-faller away. Paradox!

As I already explained, all observers have the object crossing the even horizon in finite proper time.

 

6. The amount of energy needed to move away from a black hole is quadrupled every time the distance between a free-falling object and the event horizon is halved, so how can it ever reach infinity without using quantisised space-time, which general relativity doesnt do? Its supposed to be a smooth increase so how can it jump to infinity?

You're applying Newtonian gravity to a clearly relativistic scenario, so you shouldn't be surprised that you're getting nonsensical answers. I already answered this question in detail in #1.

 

7. A singularity occupies a single point in space and time, so length contraction and time dilation are infinite at the singularity and decrease as an observers distance from it increases. Length contraction and time dilation obviously increase at exactly the same rate, making the black hole a perfect four dimensional sphere from any distance that its observed from, so why is it a cone shape in general relativity?

I have no idea what you're trying to say here. A black hole is a 3D sphere, not a cone (where'd you get that from?) or a 4D sphere. An angular time coordinate (which you are implying with your "4D sphere" nonsense) implies closed timelike curves.

 

8. A singularity obviously cant ever be reached by an object because it would be gone by the time the object gets there.

What? Why would it be gone?

 

If you work out the closest point an object can get to it you get an event horizon.

This is simply not true, as I've probably explained to you half a dozen times already.

 

As an object approaches an event horizon its radius shrinks as length contraction and time dilation increase. At the event horizon length contraction and time dilation would be infinite because its the equivalent of using energy to accelerate to the speed of light, so its radius would have shrunk to a singularity at zero distance. How could an object reach an event horizon before it reaches the singularity when the event horizon is just what the singularity looks like from a distance?

As I said, LC and TD are not well-defined in GR. An object's proper length and proper time are unaffected by your choice of coordinates. Since there's a coordinate singularity at the event horizon in Schwarzschild coordinates, trying to use them to describe an object crossing the horizon is nonsensical (which is what you're apparently trying to do).

 

9. The Rindler horizon approaching from behind an accelerating object but never reaching it no matter how hard it accelerates works in exactly the same way that the speed of light horizon does in front of the accelerating object.

I've never heard of a "speed of light horizon" before, but I think I know what you're trying to say.

 

The Rindler horizon also works in exactly the same way for a free-falling object, approaching from behind it at the same rate that it does when using energy to accelerate and never reaching it, so why would the event horizon work any differently.

There is no Rindler horizon for a free-falling object, because a free-falling object isn't really accelerating. A free-falling object is essentially inertial, and light also travels along geodesics.

 

Its the equivalent of using energy to accelerate towards the speed of light so how and why would it behave any different to the other horizons?

1. Because it's not equivalent. Free-falling objects experience zero proper acceleration, whereas accelerating objects in flat spacetime obviously experience nonzero proper acceleration.

2. Because the Rindler horizon is an effect in flat spacetime. There's no reason to think that it would put any kind of restrictions on the behavior of objects in curved spacetime.

 

10. What the hell could possibly make you think that travelling along a geodesic in curved space-time is physically different to following a curved path in flat space-time?

Because they are physically different. Here are two experiments for you to try so you can prove it to yourself:

 

1. Get in car.

2. Accelerate.

3. Feel yourself being pushed back in your seat (i.e. nonzero proper acceleration).

 

1. Find cliff.

2. Jump off cliff.

3. Feel weightless (i.e. zero proper acceleration).

 

The first experiment is a curved path in spacetime. The second scenario is geodesic motion in spacetime. In one of them you feel and acceleration, and in the other you don't. If free-fall was equivalent to proper acceleration then, for example, astronauts in orbit wouldn't feel weightless.

Given all this, how can general relativity be regarded as self-consistent?

Because it is self consistent? I have a better question: do you really think you're smarter than nearly 100 years of scientists researching and testing GR? Seriously, do you honestly believe that you, someone who barely even knows what a tensor is, just shattered a century's worth of scientific consensus? Or do you think it's maybe just a little more likely that you don't understand GR, that you don't know what you're talking about, and that you're not as smart as you think you are?

Edited January 9, 2013 by elfmotat

[A-wal]

Why does this site have so much trouble with copy and pasted 's? It looks weird without them. Sorry for the late reply, I had to wait until I'd chilled out a bit. You should have seen my first reply. There's no way I could have posted that. Not so long ago I would of. Also I can't do this stuff whenever I want. I used to be able to but that time has passed. I have to wait until I'm in the right mood now.

 

 

Because it is self consistent? I have a better question: do you really think you're smarter than nearly 100 years of scientists researching and testing GR? Seriously, do you honestly believe that you, someone who barely even knows what a tensor is, just shattered a century's worth of scientific consensus? Or do you think it's maybe just a little more likely that you don't understand GR, that you don't know what you're talking about, and that you're not as smart as you think you are?

Let's find out.

 

While what you say is certainly true, the point of the exercise was to figure out how both perspectives can be correct according to SR, yet seemingly be contradictory. Since you are apparently unable to answer, I'll do it for you: in the meter stick's rest frame, the plate is tilted at an angle [math]\phi'=tan^{-1}(v_y v_{rel}\gamma_{rel}/c^2)[/math] with respect to the x-axis. This is because of the relativity of simultaneity - if all points on the plate cross the x-axis at t=0 in one frame, they cannot possibly do so in any other frame. In this frame the plate passes over the meter stick at a tilted angle, so it doesn't matter what is length contracted and what isn't.

 

As someone who apparently "understands" relativity without understanding the math, why is it that you couldn't predict this phenomenon?

What? There was no inability to predict anything. I showed you exactly why there's no contradiction between the different frames. The extra length in space is exactly balanced by the extra length in time needed to make it through the hole because time is always extended by the same amount in a frame where length is extended, so it makes no difference. You asked me to explain how the extra length doesn't cause a paradox and that's exactly what I did. You just don't like that I was able to answer your question so you used something that I didn't go into because it's not what you asked about but you used it in completely the wrong way. It's not me you're making look stupid by doing that. It doesn't tilt from the labs frame or in its own frame when its length is extended. How could it? Would the front end tilt up or down, and what would decide this? You've got it the wrong way round! It wouldn't help anyway because the tilting would make it harder for the rod to go through because it would take longer for the extra height to move through. Rotate the hole by ninety degrees if you're having trouble visualising it. The rod tilts from the hole frame because if there's no room to spare in one frame then there's no room to spare in any frame and the hole is time dilated by the same amount as the rod in the labs frame but the rod is the same length that it is in the labs frame because it's length contracted, which would give it room to spare if it wasn't tilted. The extra time it takes to move through the hole because of its tilt is identical to the extra time it takes to go through the hole in the rods frame because of its extra length.

 

[url=http://i6.minus.com/jQIveN8dhGYZ6.png]http://i6.minus.com/jQIveN8dhGYZ6.png[/url[/url[/url]

 

I'm sure you already know that the answer to this is "at the event horizon." The proper acceleration required to "hover" outside of a black hole is:

 

[math]a=\frac{GM}{r^2\sqrt{1-r_s/r}}[/math]

 

You can look at this as the equivalent of the Newtonian "g" value (which at Earth's surface, for example, is ~9.8 m/s²). As you can see, as you approach the Schwarzschild radius (the event horizon), the value of [math]a[/math] asymptotically approaches infinity. There isn't some "mysterious" (as you like to call it) jump discontinuity where, all of a sudden, [math]a[/math] shoots to infinity - it's an asymptote.

 

[url=http://i1.minus.com/jbbtqucyYBxvmZ.png]http://i1.minus.com/jbbtqucyYBxvmZ.png[/url[/url[/url]

 

You could just as easily use that argument to claim that objects can accelerate to the speed of light using energy. I don't see how there can be a smooth transition to infinity when accelerating to a relative velocity of the speed of light. The whole idea of a finite amount of one force being able to overpower an infinite amount of any other is beyond ridiculous! One moment a finite amount of energy is enough to move away and the next all the energy of a trillion trillion universe isn't. Does that really make any sense to you?

 

The free-falling object and the object accelerating away from the BH act completely differently from the very beginning. The free-falling object experiences zero proper acceleration, and is moving toward a region of spacetime with more and more curvature. The other object experiences nonzero proper acceleration and is approaching an asymptotically flatter region of spacetime. They're in no way equivalent.

Yes they are! Using different words to describe them doesnt make them different. Its the same thing. How can black holes or anything else be infinitely powerful? That's just stupid no matter how you try to justify it! So you're saying that they're never equivalent. So if an object is free-falling away from a second object then there's a different amount of length contraction and time dilation than there is when an object uses energy to accelerate away from another object at the exact same rate? I don't think so.

 

Time dilation and length contraction by themselves aren't well-defined in GR. You may get analogous effects in particular solutions to the EFE's, but there's no direct generalization of TD and LC to curved spacetime.

Saying that length contraction and time dilation are not well defined in gr is just another way of saying that gr doesn't accurately describe them. I agree.

 

They don't contradict each other. Proper time corresponds to what clocks actually measure in GR. It is the only physically meaningful type of time. All objects cross the even horizon in finite proper time according to all observers a finite distance from the BH. Schwarzschild "coordinate time" is not physically meaningful - it's just a coordinate. It actually corresponds to the proper time of an observer at an infinite distance away from the BH. A consequence of using this particular type of coordinate system is that there's a coordinate singularity at the event horizon.

 

There's no such thing as "correct" coordinates, because coordinates are not physically meaningful. It obviously doesn't matter what I decide to call a particular set of points. Why would it? Treating coordinates as physical "things" is absurd! They're just labels!

 

Your question is equivalent to asking how Cartesian and polar coordinates can both be "correct." It doesn't make any sense.

 

You're not getting it. Whether or not objects can reach an event horizon should be a coordinate independent statement. They either can or they can't. You said yourself that nothing can actually change when you switch coordinate systems, but that's exactly what happens when you switch between Shwartzchild and Penrose coordinates. No object can reach an event horizon in a finite amount of time using Shwartzchild coordinates and this is an either or statement that can't be Lorenzed away. Show me any other example of coordinate systems in direct contradiction with each other that are both considered correct. Why is it okay when it's a black hole?

 

I'm not really sure what you're asking here. Could you try rephrasing the question?

 

Sure. General relativity describes a black hole as having an event horizon that expands outwards at c locally, but information propagates through space at c so how can any information coming from the black hole possibly reach any object before the event horizon does? The closer an observer looks towards a black hole, the slower they see time moving on the watch of any object at that distance, and the event horizon and the gravitational influence of the black hole get slowed by the same amount. The event horizon and the information coming from the black hole would always move at the same speed away from a black hole with an expanding event horizon, so how could any object be influenced by a black hole before it reaches the event horizon?

 

Because what you just said is patently false.

 

That's completely wrong even according to general relativity! Another basic error. Gr describes an event horizon as unreachable from the perspective of more distant objects. When an object approaches an event horizon it slows down in time and space as its relative velocity increases in exactly the same way that sr describes. Gr then goes on to describe objects as being able to reach an event horizon in a finite amount of their own proper time, which is a complete contradiction. You can't change reality by switching coordinate systems. It's like the rod and hole question you asked. If it fits through from one frame of reference then it fits through from all frames. If objects can't reach an event horizon in one valid coordinate system then they can't in any valid coordinate system. It's not complicated at all. It should be obvious.

 

I really don't understand your logic here. More distant observers can't have objects crossing the horizon because then the objects would have to escape the horizon? What? How did you come up with that?

 

It can't ever be possible for an object to observe another object in front of it reaching an event horizon because if it was then what would happen if the more distant object moves away? Let's say that if you're within one metre of the black hole you can see objects crossing the horizon. If you then moved back to two metres away those objects would have to move back across the event horizon from the inside. If no object can reach an event horizon before you do then all objects must reach it at the exact same time, but this can't happen as long as the event horizon exists. Do you see now? This again proves beyond any doubt that an event horizon can't ever be reached. There simply can't ever be enough time to reach one because of time dilation, and it gets smaller the closer you get to it because of length contraction. Why would mass be able to accelerate objects to a relative velocity faster than light when energy can't? Why would it be any different?

 

The object, and the part of the rope that crossed the event horizon will fall toward the singularity. You'd be pretty hard-pressed to find a rope that can stay together under that much tension in the first place.

 

That's not an answer! From the more distant objects perspective it will always be possible to pull the closer object away in a finite amount of time with a finite strength rope using a finite amount of energy. Explain!

 

As I already explained, all observers have the object crossing the even horizon in finite proper time.

 

You don't know as much as you pretend to do you? I get the very strong impression that you're just googling what you want to know as you go along, but you're not understanding a lot of it and it really shows. That statement is completely false, even according to gr! If you're not going to think for yourself and you have to copy what you've read then you should at least make sure you have a basic grasp of it before you use it to pretend that you know what you're talking about. And you've got the nerve to tell me that I don't understand relativity!

 

You're applying Newtonian gravity to a clearly relativistic scenario, so you shouldn't be surprised that you're getting nonsensical answers. I already answered this question in detail in #1.

 

It's not Newtonian. It's anything but Newtonian. The energy required to move away from a black hole is quadrupled every time the distance between it and the object is halved, in exactly the same way that the energy needed for an object to increase its velocity relative to another object by the same amount as before is quadrupled every time the difference in their velocity compared to the speed of light is halved because reaching an event horizon is the same as reaching the speed of light, so why wouldn't it be just as impossible?

 

I have no idea what you're trying to say here. A black hole is a 3D sphere, not a cone (where'd you get that from?) or a 4D sphere. An angular time coordinate (which you are implying with your "4D sphere" nonsense) implies closed timelike curves.

 

4-D nonsense? Closed time-like curves? Wtf? You really don't have the first clue what you're talking about do you? Every object has a four dimensional shape! Black holes are the simplest objects in the universe because there's no internal structure holding them up, so it's not at all surprising that they have the simplest possible shape. Of course they're hyperspheres! Why would their length in time be any different to their length in the other three dimensions? General relativity describes a black hole as a sphere in three spatial dimensions but as a cone in four dimensions, which doesn't make sense. It has to be the same length in all four dimensions, making it a hypersphere with an event horizon that contracts at the speed of light locally but slower the more distance there is between it and the observer as the local space-time around it gets extended the further away it's viewed from. Start with a singularity. It obviously can't be reached because as well as having no length in the three spatial dimensions locally, it has no length in time locally so only exists for an instant. If we switch to the perspective of a more distant observer it gets length extended equally in all four dimensions. The closest any object could have gotten to the singularity at a particular time is marked by the event horizon. If you worked it out like this would you get the same radius as the event horizon?

 

What? Why would it be gone?

 

Because a singularity is a single point in time as well as space. If it doesn't exist for any length of time then how can there ever be enough time to reach one before it's gone?

 

This is simply not true, as I've probably explained to you half a dozen times already.

 

You haven't explained anything! All you're doing is parroting back what gr says without even attempting to justify it. You can't use the conclusions of gr as evidence of its validity.

 

As I said, LC and TD are not well-defined in GR. An object's proper length and proper time are unaffected by your choice of coordinates. Since there's a coordinate singularity at the event horizon in Schwarzschild coordinates, trying to use them to describe an object crossing the horizon is nonsensical (which is what you're apparently trying to do).

 

There's a coordinate singularity at the event horizon in Schwarzschild coordinates for a very good reason!

 

I've never heard of a "speed of light horizon" before, but I think I know what you're trying to say.

 

Super.

 

There is no Rindler horizon for a free-falling object, because a free-falling object isn't really accelerating. A free-falling object is essentially inertial, and light also travels along geodesics.

 

Of course there's a Rindler horizon behind a falling object! So you think that a signal would catch up to any free-falling object from any distance away given enough time then? A Rindler horizon marks the furthest point that anything could ever catch an accelerating object at that rate of acceleration. Whether the acceleration is being caused by energy or mass is completely irrelevant. When an object free-falls towards a black hole the Rindler horizon is always exactly the same distance behind it as the event horizon is in front of it, getting closer to them as they approach the event horizon and it approaches them slower as their acceleration increases but it can never catch up to them, in exactly the same way that the Rindler horizon approaches at a progressively slower rate behind an object that's using energy to accelerate as their acceleration increases and is always exactly the same distance behind them as the speed of light horizon is in front of them. The rate that the two horizons approach an object at a slower rate in response to the same amount of acceleration as the objects acceleration increases is identical to the rate that an objects velocity relative to another object increases at a progressively slower rate as their relative velocity increases because it's preventing them from ever reaching a relative velocity of the speed of light, which is what would have to happen for an objects Rindler horizon to catch up to it and for it to reach the speed of light horizon/event horizon.

 

Just to clarify. Acceleration can be thought of as velocity relative to energy because energy has the same speed relative to all inertial objects. If an objects acceleration stays the same then its velocity relative to energy stays the same. When an object accelerates, either using mass or using energy, there's a point behind the object marking the furthest point that anything could ever catch up to the accelerator as long as it carries on accelerating at at least the same rate and a point in front of the accelerator the exact same distance away that can never be reached, which is the speed of light. These horizons get further away if the object decreases its acceleration and closer to it if it increases its acceleration. The way that it takes more energy to close the gap on the speed of light relative to another object as their velocity relative to the other object increases is identical to the way that it takes more energy to close the gap on the two horizons as their acceleration increases. In the case of a black hole the speed of light horizon is called an event horizon. The speed of light is very much a horizon. If you know what I mean by that then what happens when you apply that logic to an event horizon?

 

1. Because it's not equivalent. Free-falling objects experience zero proper acceleration, whereas accelerating objects in flat spacetime obviously experience nonzero proper acceleration.

2. Because the Rindler horizon is an effect in flat spacetime. There's no reason to think that it would put any kind of restrictions on the behavior of objects in curved spacetime.

 

Free-falling objects do experience proper acceleration. Its called tidal force. The Rindler horizon is an affect of all forms of acceleration, because theres no real difference.

 

Because they are physically different. Here are two experiments for you to try so you can prove it to yourself:

 

1. Get in car.

2. Accelerate.

3. Feel yourself being pushed back in your seat (i.e. nonzero proper acceleration).

 

1. Find cliff.

2. Jump off cliff.

3. Feel weightless (i.e. zero proper acceleration).

 

The first experiment is a curved path in spacetime. The second scenario is geodesic motion in spacetime. In one of them you feel and acceleration, and in the other you don't. If free-fall was equivalent to proper acceleration then, for example, astronauts in orbit wouldn't feel weightless.

 

If I jumped off a cliff Id miss out on all the fun of showing people like you up, and thats far too much of a sacrifice to ask me to make. You don't feel acceleration because velocity is relative and acceleration is just a change in relative velocity. What you feel is the difference in relative velocity over the different parts of your body as the accelerated parts pull the rest of you along. For example, when you're lying down it feels more comfortable than when you're standing up because the acceleration pushing you up that was focussed on your feet is spread over a larger point of contact with the ground. When you're in a car the seat is pushing you in the back which pushes the rest of you along. If every part of your body was accelerating evenly you wouldn't feel a thing. That's why you don't feel acceleration in free-fall. All you feel is the difference in acceleration over the different parts of your body, know as tidal force. Acceleration is every bit as relative as velocity. How could and why would it not be? Is there anything else that makes you think that following a curved path through flat space-time and following a straight path through curved space-time are somehow different from each other?

 

 

The fact that I don't agree with how gr describes relative motion doesn't mean that I don't understand it. It means the exact opposite. Anyone who truly understands gr would be able to spot the inconsistencies, and be able to point out exactly where I'm going wrong. Gr disproves itself, but I don't want to give them an excuse to lock, delete or move this topic to speculations so I'll stick to asking questions and if you or anyone else can provide solid and self-consistent answers I'll happily hold my hands up and say that I was mistaken. I'm not the one here who's terrified to admit that I was wrong. I don't know why you're all so keep to cling on to gr when the truth is far more beautiful and simpler.

 

Do you really think that you, someone who obviously lacks even a basic understanding of how gr describes relative motion is in any position to judge the validity of this? Do you not think it's at all possible that someone who has a much deeper understanding of relativity than you could ever hope to have has figured out something that you never could have?

 

 

If an object was actually able to reach an event horizon then it would have reached a velocity of the speed of light relative to the black hole and the event horizon would be infinitely length contracted and time dilated. A black hole is what a singularity looks like from a distance. Think about it. Velocities don't add together like that. An object can never reach a velocity of the speed of light relative to any other object. It works in exactly the same way that it works in special relativity. Why wouldn't it?

 

No diagrams, no equations, no further education and I just totally bitch slapped the most scrutinised theory ever. Who the man? (:

[imatfaal]

/ horrific salad snipped....

 

No diagrams, no equations, no further education and I just totally bitch slapped the most scrutinised theory ever. Who the man? (:

Einstein - still.

[ACG52]

 

Do you really think that you, someone who obviously lacks even a basic understanding of how gr describes relative motion is in any position to judge the validity of this? Do you not think it's at all possible that someone who has a much deeper understanding of relativity than you could ever hope to have has figured out something that you never could have?

Silly, egotistical, crank nonsense.

[md65536]

The defining feature of cranks is zealousness, as compared to eccentrics or crackpots. Zealousness leads to easy points to argue against, and all the subtle details in the pages of text end up being ignored. It's a shame, because everything is dismissed as a whole, whereas if the contentious points were simply dropped, the discussion could be about developing the details of the parts that are consistent with SR and GR.

 

"The definitive guide to relativity" is probably not a reasonable goal here.

A way of wrapping your head around relativity, for those who don't need to use it, is probably possible, as long as it's not misleading.

New ways to interpret relativity, consistent with other ways, are probably also possible to develop.

Edited January 29, 2013 by md65536

[hypervalent_iodine]

!

Moderator Note

A-wal,

 

From the looks of things, you could have done with some more time to chill out. Please try and be a bit more humble and a whole lot less discourteous and hostile in future. You'll find it goes a long way in a discussion, unless of course your aim is to pit everyone against you and end up with a permanent ban.

[elfmotat]

I simply don't have the patience to continue catering to your nonsense, so this will likely be my last response (unless for some reason I can't help myself).

 

• You "answered" the exercise by essentially rewording the question. Obviously the events can't disagree between the two frames - your job was to figure out why they don't disagree. You were unable to do so because you don't really understand SR.
• The plate certainly is tilted in the meter stick's rest frame. That's just good old SR - it falls right out of the Lorentz transformation.
• The acceleration your rocketship needs to produce in order to hover at a constant r-value asymptotically approaches infinity as you approach the event horizon, as I explained. I can't really make out the logic of your "rebuttal."
• An object free-falling into a BH and an object accelerating away from a BH are not equivalent no matter how much you bang your fists and exclaim that they are.
• Length contraction and time dilation are phenomena which are derived from a special case of GR. They don't really generalize to curved space. Claiming GR is incorrect because LC and TD aren't well-defined is like claiming arithmetic is incorrect because division by zero isn't defined.
• Whether or not objects cross the event horizon in finite time is coordinate-independent. Schwarzschild coordinates do not cover the entire manifold because they are singular at the event horizon. That means you can't use Schwarzschild coordinates to describe objects crossing the horizon. Coordinate singularities are not physically meaningful, they just restrict the domain of a particular coordinate system. This will be my fourth or so time repeating myself.
• Your statements about singularities are nonsensical. We don't know how singularities behave by definition.
• You changed your argument about geodesic motion from "geodesic worldlines and curved worldlines are equivalent" to "free-falling objects experience tidal forces, Nana-Nana Boo-Boo!" Regardless of whether or not tidal acceleration constitutes proper acceleration, that was pretty sneaky of you.
• You for some reason think that coordinate acceleration and proper acceleration are equivalent, which is quite clearly absurd.
• Acceleration isn't relative the same way as velocity because we can measure it on an accelerometer.

[A-wal]

I notice that no one is actually managing to come with answers to the questions. All you're doing is attacking me personally to try to discredit me. If you really want to discredit me the best way would be to explain why what I said was wrong and how it actually works, in other words to actually answer the questions. At least elfmotat's trying.

 

Einstein - still.

Cheap shots like that are very easy to do and make you look even worse than my bad attitude makes me look. If you really want to hurt me then you should pick apart my arguments to show why I'm wrong. The fact that you choose not to do it that suggests to me that you can't fault the arguments themselves and you're getting desperate. Maybe I'm wrong but that's how it looks.

 

Silly, egotistical, crank nonsense.

Hi ACG52.

 

The defining feature of cranks is zealousness, as compared to eccentrics or crackpots. Zealousness leads to easy points to argue against, and all the subtle details in the pages of text end up being ignored. It's a shame, because everything is dismissed as a whole, whereas if the contentious points were simply dropped, the discussion could be about developing the details of the parts that are consistent with SR and GR.

 

"The definitive guide to relativity" is probably not a reasonable goal here.

A way of wrapping your head around relativity, for those who don't need to use it, is probably possible, as long as it's not misleading.

New ways to interpret relativity, consistent with other ways, are probably also possible to develop.

I do tend to do well when everyone's against me. Conflict brings the best out of me, but I take it too far. I'm tired of constantly butting heads. I think "The definitive guide to relativity" is a very reasonable goal, but I just think that gr has it wrong and so far no one has been able to show me what I've misunderstood. I know I'm making a very big claim, but that's no reason to automatically dismiss it.

 

!

Moderator Note

A-wal,

 

From the looks of things, you could have done with some more time to chill out. Please try and be a bit more humble and a whole lot less discourteous and hostile in future. You'll find it goes a long way in a discussion, unless of course your aim is to pit everyone against you and end up with a permanent ban.

You're right. I should have waited longer. I'm really not going to get so emotional when I post from now on. It's not helping my case. In my defence I'm always getting undeserved attitude and disrespect thrown at me on this site so it's not surprising that I come across as even more of an arrogant arse than I really am. I'm not going to take the bait anymore because that's just making it easier for people to attack me and ignore my arguments.

 

 

elfmotat: I'm going to respond to your post when I'm happy with the reply. I don't want this thread to get locked or to carry on winding people up. I also want to make my thoughts as clear as possible and show exactly why I think gr has it wrong and sr has it so right.

[ydoaPs]

I notice that no one is actually managing to come with answers to the questions. All you're doing is attacking me personally to try to discredit me. If you really want to discredit me the best way would be to explain why what I said was wrong and how it actually works, in other words to actually answer the questions. At least elfmotat's trying.

 

Cheap shots like that are very easy to do and make you look even worse than my bad attitude makes me look. If you really want to hurt me then you should pick apart my arguments to show why I'm wrong. The fact that you choose not to do it that suggests to me that you can't fault the arguments themselves and you're getting desperate. Maybe I'm wrong but that's how it looks.

 

Hi ACG52.

 

I do tend to do well when everyone's against me. Conflict brings the best out of me, but I take it too far. I'm tired of constantly butting heads. I think "The definitive guide to relativity" is a very reasonable goal, but I just think that gr has it wrong and so far no one has been able to show me what I've misunderstood. I know I'm making a very big claim, but that's no reason to automatically dismiss it.

 

You're right. I should have waited longer. I'm really not going to get so emotional when I post from now on. It's not helping my case. In my defence I'm always getting undeserved attitude and disrespect thrown at me on this site so it's not surprising that I come across as even more of an arrogant arse than I really am. I'm not going to take the bait anymore because that's just making it easier for people to attack me and ignore my arguments.

 

 

elfmotat: I'm going to respond to your post when I'm happy with the reply. I don't want this thread to get locked or to carry on winding people up. I also want to make my thoughts as clear as possible and show exactly why I think gr has it wrong and sr has it so right.

You getting the wrong answers because you don't understand the theory doesn't discredit it and is hardly a "bitch slap". You refuted yourself.

[hypervalent_iodine]

!

Moderator Note

I guess I must have missed when this was moved to Speculations.

 

Anyway, this is getting tiresome. A-wal, you've said all you have to say in your other thread about why you think GR as wrong and you're right. Since that thread was closed and since this one has now become a repeat of it, I'm closing this. You're not permitted to open any more threads on the topic.