Relativity made simple

[A-wal]

The light beam is travelling vertically to anyone at rest relative to it but if the ship is moving relative to the observer then the light beam will be moving horizontally at the same speed, but the speed of light is always constant to any inertial observer so its speed horizontally has to decrease by the same amount to keep its overall speed through space-time constant. That means that the two observers see each other as slowed through time. There's also length contraction in the direction that it's moving. The angles of the zigzag path of the light beam narrows as length contracts as its relative velocity increases. The two together (always split evenly between time and one spatial dimension because you can always draw a straight one dimensional line between any two objects) make it impossible for the light beam to follow a directly horizontal path (moving through space at the speed of light and being frozen in time).

 

If you look at the path of the light beam of an accelerating object you'll see that it follows a curved path. It's this curved path through space-time that's responsible for the difference in ages in the twin paradox. All inertial objects move through time at the speed of light and aren't moving through space at all from their own perspective. If you imagine that all objects are travelling vertically upwards at the speed of light to represent their speed through time then you can view objects with a different relative velocity as moving at the same speed but at an angle to each other. Each experiences time as vertical from their own perspective because the dimension that's perceived as time is frame dependent. In reality there's no difference at all. To other inertial observers their horizontal velocity is subtracted from their vertical velocity so that their speed through space-time stays constant. Each observer views the other as time dilated so the situation is symmetric, but an accelerating object is following a curved path and so will always have to travel less distance over space-time to reach the same point when it meets up with any object that was inertial when they meet up. Relativity is really all about geometry.

Edited December 14, 2012 by A-wal

[phyti]

The light beam is travelling vertically to anyone at rest relative to it but if the ship is moving relative to the observer then the light beam will be moving horizontally at the same speed, but the speed of light is always constant to any inertial observer so its speed horizontally has to decrease by the same amount to keep its overall speed through space-time constant.

You say the light aquires the speed of the clock, and the vertical component adjusts to maintain constant speed of c. This would establish an angle for the light path at that specific speed.

Now we make one alteration by moving the distant mirror closer by half the distance. The speed and angle remain the same. How does the light intercept the mirror?

[A-wal]

I don't understand the question. The two mirrors are always the same distance away from the observer. The distance between the two mirrors is irrelevant because the angle stays the same, like you said, so what do you mean?

[altergnostic]

May I just remind you all that the path of the beam between mirrors is not seen by any distant observer? That beam is invisible in any frame other than the source/receiver frame. If you want to solve for an observer in a moving frame, you must define an origin, keep the observer there and send light rays from the path of the beam directly towards him via scattering or signaling or something. Then you take note of the reception times and distances and observed speeds and the like.

Otherwise, we are doing calculations from an absolute aether frame, in which information travels instantly (that's the only reason we would be excused not to consider the time separation between each scattering event).

 

If that isn't clear, ask yourselves how is the beam observed by a moving observer and where is he after all. Then ask if placing this observer in different positions would yield different numbers, provided we set up a mechanism that allows him to observe the beam's path. Remember that to measure the speed of light we need a two-way trip, in which the light bounces off a mirror at some distance and returns to our receiver. Meaning, light must come directly to us, else we can't define either it's own position neither the position of whatever it is we are trying to see with light.

[A-wal]

Yea I'm not taking into account the time it takes for the light to reach the observer. It's not a problem. They compare as the pass each other so that the distance is short enough for the time delay to be negligible. I should have said that though.

[ydoaPs]

If an object is stationary in space and it sees another object coming towards it at half the speed of light then you could just as easily say that it's moving towards the other object at half the speed of light and the other object is stationary. There is no distinction between which one is moving. The only statement you can make is that they moving towards each other at half the speed of light. All the laws of physics remain the same in any inertial frame, meaning all frames are equal and no frame can be said to be unique in any way. Having said that, you could use the cosmic background radiation as a frame of reference for all others, but you could do that with any frame of reference. If you're in a car and you throw a ball into the air then it doesn't go flying backwards because the laws in all non accelerating frames are the same, including the speed of light. You can't measure your speed relative to light because you'll always get the same answer of 186,000 miles per second. So if two objects are heading away from Earth at different relative velocities and you shine a flash light then the light beam will pass both of them at the same speed, meaning all three observers measure time and space differently to keep the speed of light the same for all of them. Velocity is just a measurement of distance over time. There's one spacial dimension involved because you can always draw a straight line between any two objects, and time. Both shorten from the perspective of an accelerating observer to keep the speed of light constant. This is called length contraction and time dilation.

 

If a ship were flying away from Earth and a signal was sent from Earth to the ship and from the ship to Earth then would both signals take the same amount of time to reach their destination? Yes, but both Earth and the ship would say no. Both observe outgoing signals taking longer than incoming signals because outgoing signals have to catch up to the receding destination. Outgoing signals have to travel further and take longer than incoming ones do to make the same journey, because outgoing signals are measured to when they arrive while incoming signals are measured from when they're released. Signals sent by the other observer would be travelling a shorter distance and wouldn't take as long to reach the destination as a signals sent from themselves to the other observer because outgoing signals are travelling to where an object is going to be and incoming signals are travelling to where an object is and the difference is length contraction and time dilation. Objects are always travelling through space-time at the speed of light from all frames of reference. In your own frame your stationary and moving through time at the speed of light. Objects also see other objects with a different relative velocity moving at the speed of light because they're moving through time slower (time dilation) from each others perspective and their total velocity through space-time will always equal the speed of light.

 

Imagine two ships moving at different velocities, both with a light beam moving up and down between the ceiling and the roof. It takes one second for the light to travel up or down from mirror to the other. Each would see the light on the other ship move in a zigzag as its relative velocity is added to the lights vertical motion. Light doesn't speed up to make up the difference, so it takes longer than one second for the light to get from one mirror to the other on the others ship from both perspectives. A second for either is a shorter amount of time than a second for the other, so each sees the other moving in slow motion because the light on the other ship has further to go. Now one is stationary relative to a tunnel which the other ship travels though. The ships front end comes out one second after its back end enters, but space is length contracted in the direction that it's travelling in, making anything in the other frame including the tunnel length extended by comparison. Its front end emerges before the back end enters from the perspective of the ship at rest relative to the tunnel. From this frame, the ship is longer than the tunnel.

 

If you (A) flew away at half the speed of light while your twin (E) stayed on Earth then you would change your frames of reference relative to each other. You're always stationery from your own perspective and light is always moving at the same velocity ©. Everything else is relative. From both perspectives the other will be travelling at 0.5c but each sees themselves as stationary. A travels one light-year in two years, but a light-year has changed from As perspective relative to Es because they've moved into a different frame where the speed of light is the same relative to both of them despite their different relative velocities. It moved further from As perspective in the time it took for the light to get one light-year from Earth from Es perspective and the same is true from As perspective of E. So the distance that the other ship covers wont seem like far enough from each perspective over any given unit of time, and if the distance that the other is covering decreases then the space and time separating them must decrease by an equal amount split evenly between the two (there's one time and one spatial dimension as we're moving in straight lines to keep things simple). The measurement of the others space-time has lessened because the other ships time will appear to be in slow motion (time dilation) and there will appear to be less space (length contraction) along the one spatial dimension (straight line) that they are moving from the perspective of both frames and lengthens each ships perception of anything in the others frame, which keeps the speed of light constant from the perspective of both frames. This removes the discrepancy of the speed of light from the persecutive of different relative velocities because it isn't travelling as far in space or in time, and therefore as fast as in other frames as it would if it wasn't for length contraction and time dilation, and bringing it right back to c relative to every frame of reference.

 

Everything up until now has been symmetric, so each twin sees the same affects on the other, and in exactly the same way. The twin paradox (not actually a paradox at all) is that the one leaving Earth will be younger than their twin when they return. To start with we'll give both twins a rolling start and finish. The twins pass Earth moving in opposite directions at just over half the speed of light relative to an observer on Earth who sees them moving away from each other at over the speed of light, which is fine as long as no one sees themselves moving above light speed relative to anyone else. Each twin sees themselves moving at just over half light speed relative to Earth (Earth sees them moving at that speed so the same must be true in reverse) and each twin sees the other moving at below light speed because of length contraction and time dilation. But this isn't a real affect because each sees the other one moving in slow motion and length extended (because the space is contracted), which stops anyone from moving faster than light relative to anyone else. When they turn round they have to accelerate in the opposite direction (there's no such thing as deceleration in relativity because it's just acceleration in the opposite of some arbitrary direction). If one is at rest and the other accelerates and comes back then it becomes a real affect and one twin is literally younger than the other one.

 

A uses one unit of energy to travel up to half the speed of light relative to E. A is now static in its new frame of course. A then uses another unit of energy to again reach half the speed of light relative to an object in its new frame. From Es frame that second unit of energy didn't accelerate A as much as the first one did, but from As perspective it did because of length contraction and time dilation. So if the same energy is needed to move over a relatively smaller amount of space-time then the mass of A has increased from Es frame, and Es has from As frame as well. So the others energy requirement to accelerate increases from both perspectives as their velocity relative to each other increases, so your mass increases the faster you move relative to something else from their perspective. Energy becomes mass as you accelerate relative to the speed of light from the perspective of other frames of reference. That's how matter and energy are interchangeable, E = mc^2. What separates them is the fact that A has accelerated and E hasn't. If E were to accelerate into As new frame then they'd be the same age again. Length contraction and time dilation would lessen as their speeds become relatively closer to each other. When their relative velocities match they'll be in the same frame again and the only apparent time lag will be caused by how long it takes for light to cover the distance separating them (light hours/days/years).

 

You can effectively travel as fast as you like, there's no such thing as absolute velocity and there's no speed limit because you will be in a new frame every time you stop using energy to accelerate and the speed of light and your energy requirement for acceleration relative to c is always the same in every possible inertial (non-accelerating) frame. If you accelerated to half the speed of light from your starting frame then you'd be in a new frame when you stop accelerating and you'd now be static from your own perspective and the energy requirement to accelerate to half speed of light would be the same as it was in your starting frame. If accelerated again up to half the speed of light relative to an object in your new frame then you wouldn't be travelling at the speed of light from your starting frame because you are length contracted and time dilated from the perspective of your starting frame and so you're moving slower through time and space. Time and space aren't fixed. As you accelerate towards something, it gets closer to you beyond what you would expect from the increased velocity. You can move infinitely fast, but as far as the rest of the universe is concerned you can't. So if you were to accelerate away from Earth and then return, you would be younger than your twin who stayed home because you were travelling slower through time and space from Earths perspective.

 

Gravitys strength is directly proportional to mass and inversely proportional to the square of the distance to the mass. That just means that its strength is divided by four if the distance is doubled and multiplied by four if the distance is halved. In zero dimensions (point/singularity) it's infinite. In one spatial dimension (straight line) its strength would remain constant over any distance. In two dimensions (flat plane) it would be directly proportional to the distance. In three dimensions it's an inverse square. It's proportional to the volume it fills. We feel our own weight on Earth but it's not gravity that we feel, it's the electro-magnetic force between the atoms that are resisting gravity and pushing us upwards by the same amount that gravity is pulling us down. Neutron stars are heavy enough to collapse past this resistance and are held up by the resistance of the neutrons. Black holes are so heavy for their size that nothing can hold them up and they collapse completely. We feel the difference in the amount of force being applied to our points of contact with the ground and the rest of our bodies, which is why it's more comfortable when this difference is spread over a larger area when we lay down. The difference in the strength of a gravitational field is also all that can be felt rather than the strength of the field itself, because it's relative. The relative difference in the strength of gravity is called tidal force. On Earth that difference is very small and can't be felt but in a strong enough gravitational field it's enough to rip solid objects apart.

 

Relativity explains how electricity and magnetism are actually the same force (electro-magnetism). A magnetic field can turn into an electric field if you accelerate relative to it because length contradiction moves the electrons closer together giving the field a negative charge, so the magnetism from the previous frame is felt here as electricity.

Quick question for A-wal: what's the difference between a covariant and a contravariant tensor?

[A-wal]

Oh no you don't, not in this thread. If you have an actual question or you think that I've said something that's inaccurate then please by all means speak up. What's a tensor?

Edited January 3, 2013 by A-wal

[ydoaPs]

What's a tensor?

Why should we listen to you about relativity if you don't even know the language in which the theory is written? It's like someone trying to give a 'simple' explanation of "The Count of Monte Cristo" when your only exposure is English translation Cliff Notes.

 

You're trying to give a book report when you've not even tried to read the book.

[A-wal]

I do know what a tensor is. I was making a point. It's a way of describing curvature, but I wouldn't recognise it as a tensor if I saw one. What point were you trying to make exactly? That I don't know what I'm talking about? Then how come I can explain what happens under any given circumstances without any errors? Blind luck?

[imatfaal]

Just for your further guidance - Tensor

 

The reason your explanations do not fail from your perspective is that you mix recitation of well known ideas with non-checkable unmathematical verbage.

 

As soon as you venture into more precise wording you say things like this "In three dimensions it's an inverse square. It's proportional to the volume it fills." Surely the first sentence means that relationship would be inversely proportional and to the second power not the third (like the volume).

 

When I followed your other post in speculations and actually drew the diagrams you explained - and reported my problems with them, you didn't bother to reply; the thread ended up being closed for these very reasons. This is the point many of have been trying to make - your posts are a mixture of the already explained and the untestable; thus whilst there isn't gonna be an easy way to show fault - that doesn't mean there aren't any.

[A-wal]

It IS proportional to the volume that it fills! In zero dimensions it would be infinite. In one its strength would never fall off. In two, if you doubled the distance the strength would be halved. In three special dimensions it's an inverse square.

 

I said that I accidentally missed the comments between my last two posts and that I was going to answer them and that I was going to make a list of definite predictions. Then the thread got locked (I think that's why it got locked to be honest, talk about fixing the fight) and my last post got mysteriously edited, with all the most important bits taken out. It wasn't that I couldn't be bothered to reply. If I do it here I'll probably get told off or even banned. Are you setting a trap for me?

 

I know I was out of line a few times when I first came here and maybe I've brought this on myself but I really do feel like I'm being treated very unfairly.

[imatfaal]

It IS proportional to the volume that it fills! In zero dimensions it would be infinite. In one its strength would never fall off. In two, if you doubled the distance the strength would be halved. In three special dimensions it's an inverse square. ..../snipped

This is why we ask for more precision - I would interpret "the volume it fills" as follows; firstly two points do not make a volume, they form a unique straight line but not a volume. However (if you make the distance from Point A to Point B equal r) you can imagine a volume that is bounded by a surface that is always the same distance r from Point A. This makes sense in terms of gravitation as there is such a spherical surface of equal gravity around a mass. The volume of this sphere is 4/3 x pi x radius^3. the volume is proportional to the third power of r. The force due to gravity in newtons way is Force = G x Mass1 x Mass2 / radius^2 The force is proportion to 1 divided by the second power of r,or as we say inversely proportional to the second power of r. If you double the distance the force due to gravity is divided by four - but the volume is multiplied by 8

 

Now what definition of volume are you using that decreases when r increases (that the importance of the inversely which you missed). And what definition of volume changes with r^2 not r^3.

[A-wal]

I used the term volume because it covers the greatest number of dimensions. I know it implies three dimensions (or four?) but don't you think you're being pedantic rather than thorough? I suppose that means you couldn't find anything better to pick apart, so that's good. I really think you've missed the point of this thread.

Edited January 4, 2013 by A-wal

[imatfaal]

I used the term volume because it covers the greatest number of dimensions. I know it implies three dimensions (or four?) but don't you think you're being pedantic rather than thorough? I suppose that means you couldn't find anything better to pick apart, so that's good. I really think you've missed the point of this thread.

 

ok - normal service has been resumed. Possibly I haven't been able to spot the meaning of this thread - but you seen to have missed the point of science

[altergnostic]

I used the term volume because it covers the greatest number of dimensions. I know it implies three dimensions (or four?) but don't you think you're being pedantic rather than thorough? I suppose that means you couldn't find anything better to pick apart, so that's good. I really think you've missed the point of this thread.

Maybe its a good idea to briefly reestate the point of this thread, since there was too much digression.

Edited January 5, 2013 by altergnostic

[A-wal]

And whose fault is it that this thread's been hijacked by resentment? I would have thought the point of this thread was obvious. The clue's very much in the title. This is a scientific thread about the mathematical relationship of relativity. Not using equations doesn't change this fact. You can claim it's not true but no matter how many times you call a Doberman a duck it's still a dog. I'm proving that it's not necessary to learn any of the equations to understand relativity, and you can't stand that. That's why you've got such a problem with me. The fact is you can't refute what I've said in this thread, all you can do is criticise my methods. You do it your way and please let me do it mine. You're the ones who keep giving me attitude. I'm just countering. Are you now going to delete the parts of this paragraph that you dont like you did the other one I wonder.

Edited January 6, 2013 by A-wal

[ACG52]

 

This is a scientific thread about the mathematical relationship of relativity. Not using equations doesn't change this fact

 

 

So It's about the math, but you don't know the math, so you simply serve word salad.

 

 

 

I'm proving that it's not necessary to learn any of the equations to understand relativity, and you can't stand that.

 

 

But you don't understand relativity, and therefore have been totally unable to come up with any kind of explanation.

[elfmotat]

And whose fault is it that this thread's been hijacked by resentment? I would have thought the point of this thread was obvious. The clue's very much in the title. This is a scientific thread about the mathematical relationship of relativity. Not using equations doesn't change this fact. You can claim it's not true but no matter how many times you call a Doberman a duck it's still a dog. I'm proving that it's not necessary to learn any of the equations to understand relativity, and you can't stand that. That's why you've got such a problem with me. The fact is you can't refute what I've said in this thread, all you can do is criticise my methods. You do it your way and please let me do it mine. You're the ones who keep giving me attitude. I'm just countering. Are you now going to delete the parts of this paragraph that you dont like you did the other one I wonder.

 

If you understand relativity then you should have no issues at all resolving the following "paradox":

 

A meter stick lies along the x-axis of the laboratory frame and approaches the origin with velocity v_rel. A very thin plate parallel to the xz laboratory plane moves upward in the y-direction with speed v_y as shown in the figure. The plate has a circular hole with a diameter of one meter centered on the y-axis. The center of the meter stick arrives at the laboratory origin at the same time in the laboratory frame as the rising plate arrives at the plane y=0. Since the meter stick is Lorentz-contracted in the laboratory frame it will easily pass through the hole in the rising plate. Therefore there will be no collision between meter stick and plate as each continues its motion. However, someone who objects to this conclusion can make the following argument: "In the frame in which the meter stick is at rest the meter stick is not contracted, while in this frame the hole in the plate is Lorentz-contracted. Hence the full-length meter stick cannot possibly pass through the contracted hole in the plate. Therefore there must be a collision between the meter stick and the plate." Answer unequivocally the question, will there be a collision between the meter stick and the plate?

Edited January 6, 2013 by elfmotat

[A-wal]

So It's about the math, but you don't know the math, so you simply serve word salad.

Explanation for what? What are you talking about? Every single post I've seen of your is exactly the same. Do you even know how to say anything else?

 

But you don't understand relativity, and therefore have been totally unable to come up with any kind of explanation.

Making clearly false statements like that implies one of two things. Either you can't read or you know so little about the subject that you're in no position to pass judgement. If I don't understand relativity then how do you explain this thread? If what you're saying is true then I must have made lots of false statements. Since your so clearly an expert and your reputation must be so high that you don't need to clarify anything and it's enough for you just to say everything is "word salad" I was wondering if I might impose on you to share your great knowledge and tell me what it is I've got wrong?

 

If you understand relativity then you should have no issues at all resolving the following "paradox":

 

A meter stick lies along the x-axis of the laboratory frame and approaches the origin with velocity v_rel. A very thin plate parallel to the xz laboratory plane moves upward in the y-direction with speed v_y as shown in the figure. The plate has a circular hole with a diameter of one meter centered on the y-axis. The center of the meter stick arrives at the laboratory origin at the same time in the laboratory frame as the rising plate arrives at the plane y=0. Since the meter stick is Lorentz-contracted in the laboratory frame it will easily pass through the hole in the rising plate. Therefore there will be no collision between meter stick and plate as each continues its motion. However, someone who objects to this conclusion can make the following argument: "In the frame in which the meter stick is at rest the meter stick is not contracted, while in this frame the hole in the plate is Lorentz-contracted. Hence the full-length meter stick cannot possibly pass through the contracted hole in the plate. Therefore there must be a collision between the meter stick and the plate." Answer unequivocally the question, will there be a collision between the meter stick and the plate?

 

 

No. I can't see the diagram but I think I know what you mean. They're travelling in different directions so are being contracted along a different axis. There won't be a collision because the second argument is irrelevant since the length contraction in that frame is making the plate thinner but not changing the size of the hole. Edited January 8, 2013 by A-wal

[imatfaal]

Explanation for what? What are you talking about? Every single post I've seen of your is exactly the same. Do you even know how to say anything else?

 

Making clearly false statements like that implies one of two things. Either you can't read or you know so little about the subject that you're in no position to pass judgement. If I don't understand relativity then how do you explain this thread? If what you're saying is true then I must have made lots of false statements. Since your so clearly an expert and your reputation must be so high that you don't need to clarify anything and it's enough for you just to say everything is "word salad" I was wondering if I might impose on you to share your great knowledge and tell me what it is I've got wrong?

 

Trouble is that whenever anyone does that you accuse them of hijacking with extreme prejudice and being pedantic!

No. I can't see the diagram but I think I know what you mean. They're travelling in different directions so are being contracted along a different axis. There won't be a collision because the second argument is irrelevant since the length contraction in that frame is making the plate thinner but not changing the size of the hole.

Oh dear - here's hint; what about from the frame in which the ruler is at rest, what direction is the plate moving?

[ydoaPs]

Oh dear - here's hint; what about from the frame in which the ruler is at rest, what direction is the plate moving?

You didn't know? Relativity is only an illusion. There is absolute space and absolute time; just ask William Lane Craig!

[imatfaal]

You didn't know? Relativity is only an illusion. There is absolute space and absolute time; just ask William Lane Craig!

 

 

I could be persuaded to pay for a real world set-up of the above experiment provided William Lane Craig is made to stand where Elfmotat has placed the letter x

[ACG52]

If I don't understand relativity then how do you explain this thread?

 

 

I'd say it was a thread started by a someone who doesn't understand relativity, but thinks he does and wishes to indulge his ego.

 

(All cranks who don't understand relativity think they do).

Edited January 8, 2013 by ACG52

[elfmotat]

No. I can't see the diagram but I think I know what you mean.

 

Here's a URL to the pic:

 

http://i1.minus.com/jZct9VvGyOv6n.png

 

They're travelling in different directions so are being contracted along a different axis. There won't be a collision because the second argument is irrelevant since the length contraction in that frame is making the plate thinner but not changing the size of the hole.

 

Did you even read the question? In the rest frame of the meter stick, the plate's velocity has nonzero x-component and is therefore length-contracted in the x-direction. So the hole's diameter is shorter than one meter in the meter stick's rest frame. The point of the exercise is to reconcile the seemingly paradoxical disagreement between the two frames.

 

I could be persuaded to pay for a real world set-up of the above experiment provided William Lane Craig is made to stand where Elfmotat has placed the letter x

 

. I probably should have mentioned that this exercise was taken from Taylor & Wheeler's Spacetime Physics.

Edited January 9, 2013 by elfmotat

[A-wal]

Trouble is that whenever anyone does that you accuse them of hijacking with extreme prejudice and being pedantic!

You mean the fact that I used the term volume for one and two dimensions as well as three? Thats hardly a misunderstanding of relativity.

 

I'd say it was a thread started by a someone who doesn't understand relativity, but thinks he does and wishes to indulge his ego.

 

(All cranks who don't understand relativity think they do).

I noticed.

 

You really are nothing but a spiteful and hate filled person arent you? That cant be much fun.

 

A thread started by someone who doesn't understand relativity but can still explain exactly how it works? Explain! What is it exactly that you think I dont understand? Which part? Be specific! What am I not getting? Either put up or shut up.

 

Did you even read the question? In the rest frame of the meter stick, the plate's velocity has nonzero x-component and is therefore length-contracted in the x-direction. So the hole's diameter is shorter than one meter in the meter stick's rest frame. The point of the exercise is to reconcile the seemingly paradoxical disagreement between the two frames.

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.

 

 

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?

 

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

 

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?

 

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?

 

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? 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.

 

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? 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!

 

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?

 

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?

 

8. A singularity obviously cant ever be reached by an object because it would be gone by the time the object gets there. If you work out the closest point an object can get to it you get an event horizon. 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?

 

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. 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. 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?

 

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?

 

 

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