Sorry I've taken so long to getting round to replying to you all. Been a bit busy, but thanks for taking the time to reply all the same. Please Register or Log in to view the hidden image! Can't it be both!? Please Register or Log in to view the hidden image! This brings a big hmmmmmm out of me. I don't quite see how one is not being accelerated by the gravitational field when one is being accelerated by it! That doesn't make any sense to me. That I am in free-fall means that locally I don't feel a gravitational pull, but I most certainly am being pulled by gravity. I am therefore being accelerated even though I may not be aware of it! In fact, I would be aware of it the closer I get to the EH. As I get nearer to the EH the gravitational field is getting stronger and stronger. This equates to me being accelerated faster and faster. I would feel this increase of acceleration. That is inescapable because it is a change in the rate of change of velocity. Say I am in flat space at infinity above the BH. The EH marks a spot of a reference frame that is moving (being accelerated) at c. Let's say I fall towards the BH to the point where the gravity is equal to 1g (I'm being accelerated at 1g). The EH still marks a spot of a reference frame that is moving at c. I fall closer. I'm now accelerating at 2g. The EH is still a reference frame moving at c. I fall closer. I'm now accelerating at 4g. The EH is still a reference frame moving at c. And so on... No matter how far, or near, from the EH I am, it is always a reference frame moving at c. I'm not saying you are wrong, Zanket (you may well be right and I am just a dunce! Please Register or Log in to view the hidden image!). I'm just saying that I don't see how your explanation works. I just don't understand how falling in a gravitational field means you are exempt from the effects of that gravitational field. Sure, I remember Einstien's elevator, but he used a constant g. We're not because g increases as we get closer to the EH, and this would be noticeable inside the elevator because the roof of the elevator is in a different reference frame from the floor, and these reference frames become increasingly different the closer to the EH you get. ie. if you had a clock on the floor and one on the ceiling they would show increasingly different times. At all times I am in a different reference frame from the EH. kind regards Paul aka §lîñk€¥™
Hmmmmm. That's sounds like you contradicted yourself there in the same paragraph (but my ears may well be faulty so please don't take affront at that)! If I free-fall towards eartg it would feel like I am floating inside Einstein's elevator because I am moving at the same "velocity" as the local gravity. However, should I look out the window then I will most certainly see the ground getting nearer and nearer. One could well argue that I would see the ground accelerating towards me! Therefore if I free-fall towards an EH it would be the same as saying that the EH is accelerating towards me! Does this have no effect? kind regards Paul aka §lîñk€¥™
Continuing on the theme of my last post: Imagine I am free-falling towards earth. On the ground is a clock. As I travel towards the clock I am "meeting" the light that has been reflected from it's surface and towards myself. Would it not appear to run faster? As I fall towards a clock at the EH of BH I am being accelerated at a greater and greater rate (gravity is increasing). Wouldn't that clock get faster and faster? kind regards Paul aka §lîñk€¥™
just to BUTT in, i was looking at the last couple of posts... is free-fall not like weight-lessness? Acceleration (to or away from a black-hole) would have the same a effect as gravity. if you were accelerating in a lift to a black-hole then you would be stuck to the ceiling... If you were accelerating away from it then you would be on the floor. SRY if this has messed up your line of thought.
Free fall toward the Earth is far different from free fall toward a compact and extremely massive object like a Black Hole or a Neutron Star. The strength of the force does not change much as you fall toward the Earth, while it changes significantly as you fall toward a compact massive object. If you fall feet first, the black hole would accelerate your feet faster than your head. Get close enough and you will be pulled apart. Understanding SR & GR sometimes require that you pretend your experiments are being performed in a room with no windows. In SR, it is claimed that no experiment can distinguish between inertia frames. You cannot tell the difference between standing still and moving at a constant velocity. This is the reason you can play table tennis on a smoothly moving train and be unaware of the constant velocity motion. If you look through a window, you can obviously tell that the train is moving relative to the Earth. Prior to the Michelson/Morley experiment and the SR explanation, it was believed that only mechanical experiments were unable to distinguish between inertial frames. SR extended this to include all experiments. In GR, it is claimed that no experiment can determine a difference between being stationary in a gravitational field and being accelerated in the absence of a gravitational field. Once again, if you can look through a window at the external environment, you can obviously tell the difference. GR describes free fall in a gravitational field as equivalent to having no forces acting in the absence of a gravitational field. From inside a closed room, you cannot tell the difference until you hit the gravitating object. It is not the fall that does you in, it is the sudden stop. While falling, an observer (in a closed room) is unaware of any forces acting on him, assuming that the force gradient is neglible. From what I have read here, nobody (including myself) seems to be a reliable source of information about Black Holes. I find it hard to comment on some of the posts, because I suspect they are invalid, but I do not know enough to refute them. I have seen posts referring to the Event Horizon as being a frame of reference moving at the velocity of light. To the best of my knowledge, this is nonsense. The EH is a 2D region where the escape velocity is the velocity of light. The statement about escape velocity makes no claim about the motion of the EH, the Black Hole, or objects near the EH. Also, I do not believe that there are singularities in the GR near, at, or inside the EH. The singularity occurs at the center of the Black Hole, but I am not sure that the existence of a Black Hole guarantees the existence of a singularity. It might only imply that a singularity can (or will) exist some finite time after the formation of the Black Hole. I do not trust the posts describing what an observer sees as he falls toward the EH. The force gradient would be noticeable. Sentient entities tend to notice when they are torn apart. Aside from that problem, I do not think that the observer falling toward the EH would notice anything strange about his own environment, assuming that he is in free fall. I think that he would see the universe behind him distorted in some fashion as he got close to the EH. I think the gravitational effect on light rays from the rest of the universe would be analogous the refractive effects seen by an observer at the bottom of a still pond. From the point of view of a distant observer, an object falling toward the EH gets red shifted and has clocks which are slower. I still maintain that a distant observer can see the EH grow in finite time. He might never see any object reach or fall through an EH. I mentioned the following in a previous post. Consider an EH of radius R around a Black Hole with mass M, and imagine large amounts of mass falling toward the EH from all directions. It is obvious that a larger Black Hole with mass M+DeltaM has an EH with radius R+DeltaR. The EH of radius R will grow to R+DeltaR when DeltaM mass falls inside the radius R+DeltaR. This growth of the EH can occur without an external observer ever seeing any object reach the original EH of radius R. BTW: Even without clocks slowing, the red shift phenomena would prevent a distant observer from seeing an object reach the event horizon. In thinking about Black Holes, it should be remembered that no observer sees them or measures the radius of their Event Horizons. Distant observers infer the mass of a Black Hole by measuring the gravitational effects on nearby objects. The radius of the unseen EH is calculated from the inferred mass.
You are being accelerated by the gravitational field but not in a way you can feel or that causes clocks in your immediate vicinity to run at different rates. When I say the kind of acceleration needed to avoid free fall I mean the subset of acceleration that requires you to burn your rocket engines or be on the ground. The kind you feel against your back or feet. You describe the broader kind of acceleration, which is simply acceleration relative to something else. Perhaps there’s a label that distinguishes between these kinds of acceleration. Remember that relative to ten different objects you can be accelerating ten different ways, so there need not be a strong relationship between you and the ground when you free fall. For example, if you free fall on Earth, there isn’t a strong relationship between you and the surface of Mars, even though you are accelerating relative to Mars. Let’s examine the relationship between you and the ground when you free fall towards the ground. You are not being pulled. If you were, you’d feel something tugging on you. Instead, you can do somersaults no problem. It is as if you are staying in the same coordinates in space, just like you can imagine you would be if you did somersaults in deep space. If you like to imagine you are still being pulled by gravity, imagine as well that your surroundings are likewise pulled in such a way that none of it feels a pulling. I find it easier to imagine that space itself accelerates toward a mass. But look, the ground is accelerating towards you. What makes it do that? The ground is avoiding free fall. The ground is doing the kind of acceleration that you feel on your feet when you walk on it. It is the electromagnetic repelling force within the atoms of the Earth that keeps the Earth from imploding from the gravitational attractive force within and amongst those same atoms. This repelling outward force is felt on our feet. Squeeze a tennis ball in your hand and feel it push against your hand. Yet the ball does not enlarge. The Earth is likewise squeezed by its gravity that squeezes space itself. And the Earth likewise pushes out but does not enlarge. And we feel the push on our feet. (James R taught me this.) This is why it is said that you cannot feel the force of gravity. You can feel only the outward force which is the electromagnetic force existing in equilibrium with gravity. This outward force is analogous to that caused by the burn of a rocket’s engine. When you free fall, you can imagine that you remain at the same coordinates in space. That is, you can imagine that you are not falling but rather staying in place. The coordinates themselves are moving toward the center of the mass. Make a box around yourself, small enough to ignore spaghettification (more on this below), and call it a frame of reference. The frame is moving—accelerating—toward the center of the mass. Yet within the frame, special relativity applies, like it would inside a spaceship moving in deep space with its engine off. Two clocks stationary with respect to the frame (hence each other) tick at the same rate, even as they accelerate relative to the mass. In flat space at infinity above the BH, your velocity relative to the EH is zero and reaches c when you cross it. As you approach the EH you’d not feel the increase in acceleration. You might feel a differential in acceleration between parts of your body, which is spaghettification. Here your velocity relative to the EH is < c and increasing at a rate of 10 m/s<sup>2</sup>. The EH is moving at c relative to objects free falling across it. Different reference frames apply here because the acceleration is the kind you feel on your feet. This effectively curves the space within the elevator, as evidenced by the bending of light within. If, however, you are within a free falling elevator then light does not bend within and a clock on the floor runs at the same rate as one on the ceiling. Let’s discuss spaghettification, which I’ve explicitly ignored so far. In deep space coordinates are Euclidian in nature like we learned in beginning geometry (three axes at right angles to each other). Around a mass the coordinates have a curvilinear relationship (not necessarily at right angles). As you free fall your body is increasingly squeezed on the sides and pulled lengthwise, as the space changes from flat to curved. You can also think of this as your feet accelerating faster than your head, if you are falling feet first. Imagine the river of gravity I mentioned before. Imagine a river than goes from placid lake-like to an incline. At the incline the river will become narrower and accelerate. Imagine you are in the river entering the incline. Imagine that—unlike a real river—the shape of your body must conform to changes in the shape of the river. You likewise become narrower (squeezed on the sides) and are stretched lengthwise in concordance with the differential in acceleration at your head versus your feet. In free fall, the shape of your body conforms to the changing shape of space. That’s spaghettification. The shape of the Earth, as it rotates, conforms to the curved space created by the Moon. The Earth is slightly egg-shaped with the egg’s point pointing towards the Moon. The location of the point on the Earth’s surface moves as the Earth rotates. This conformation to the shape of space causes the ocean tides. Spaghettification is also known as the tidal force. Now while your body as a whole may feel spaghettification as you free fall, your thumb per se may not be in danger. Being within a smaller region of space the effect of spaghettification on your thumb may be negligible. In learning GR as it relates to black holes, you can choose to ignore spaghettification because a BH can be large enough that spaghettification is undetectable by instruments even as you cross the EH. A EH can for example encompass an area of space the size of a supercluster of galaxies. I’ll add one more analogy to describe how gravity accelerates without pulling. Recall the old science fiction question “If everything instantly doubled in size, could you tell?” You wouldn’t be able to, of course, because there’d be no benchmark against which to measure the doubling. Even the benchmark doubled in size. When space moves toward a mass under the influence of gravity, and you are moving with and within that space (free falling), there is likewise no local benchmark against which you may measure your movement. Neither will fixed clocks within your vicinity run at different rates for there is nothing to cause that. Now if everything instantly doubled in size except your thumb, then you’d know about it. And if space moved toward a mass at a significantly different rate at your head than at your feet, you’d know about that too; this is the tidal force.
my pointless comment I like this whole discussion about EH and BH.... <HR> As you get closer and closer to the EH you watch the clock. It starts to slow down. This is because as you get closer to the EH the gravity gradient increases. However, you will never see that clock cross the EH as described above. But dig this, not only that, but you are still above the clock. You are still farther away from the EH than the clock. So if you never see the clock cross the EH and you are always farther from the EH than the clock, then you never cross the EH. <HR> IF, you manage to get near the EH before tidal forces spaghettify you, in the case of a very large BH, you will be aware of everything up to the moment time stops. However, motion will continue in the contorted space within the BH. From the outside, we would see you get sucked in as energy waves, just as you cross the EH, accellerating perhaps to the speed of light. If it is possible to accellerate beyond that speed within the BH, you will finally make your end at the singularity. (given there really is one) All of this will take place in your experience in a matter of milliseconds once you are at the EH. We will see you stop at the EH and fade to red shift, then black suddenly when the light can no longer escape. The paradox of the clock in your hand is about light energy that cannot escape the gravity of the BH. That light will die immediately upon crossing the EH, just after a brief red shift.
Dinosaur, I'm confused by your statement: "From inside a closed room, you cannot tell the difference until you hit the gravitating object" and " While falling, an observer (in a closed room) is unaware of any forces acting on him, assuming that the force gradient is neglible". If I am in a closed room would I not be aware the neither the room nor I are experiencing the pull of gravity, realize that we're both in 'free fall'? Curious. Please Register or Log in to view the hidden image!
Originally posted by Chagur If I am in a closed room would I not be aware the neither the room nor I are experiencing the pull of gravity, realize that we're both in 'free fall'? You would both be experiencing the same acceleration, so you wouldn 't notice. At a distance, every inch closer you get pulled to the black hole, the room moves an inch too. So relative to the room, you are not moving. This would break down as you got closer to the event horizon because the acceleration on the side closer to the black hole would be much higher then the other side. And you'd get 'spagetified'.
Persol, the portion of Dinosaur's post that I was referring to was not, unless I am mistaken, referring to a black hole situation. So, my Q is still unanswered. Please Register or Log in to view the hidden image!
Oopss... sorry ChagurPlease Register or Log in to view the hidden image!... same basic reasoning though... You and the room would both be experiencing the same acceleration, so you wouldn't notice. At a distance, every inch closer you get pulled to the gravitating object, the room moves an inch too. So relative to the room, you are not moving. This is demonstrated on the 'vomit comit' when the go into free fall. You and the plane have the same acceleration being applied so you don't notice any gravity. The part of noticing gravit y at the impact is because you suddenly come to a stop. It's like slamming into a brick wall.
Okay, Persol. But, it's not like I were riding the 'vomit comet', I don't think. If I'm not mistaken, the 'vomit comet' flies a parabolic path and in so doing 'drops away' until it has to pull out of the dive it is in. That to me is not the same as, for example, being in an elevator when the lifting cable breaks, assuming the elevator is not equipped with automatic brakes, and remaining in it until it eventually impacts the bottom of the shaft. Please Register or Log in to view the hidden image!
if the lift were given a (hard enough) sideways push it would fall in a nice curve, it doesn't really matter. The acceleration to to ground is the same . Are you saying that if the floor of the lift was weakened and you were falling towards a black hole you would fall through the bottom?
Erroneous statements are being posted here. I could be wrong, but I am fairly certain that the red shift and clock slowing effects of a Black Hole are from the point of view of a distant observer. An observer falling into a black hole does not notice his clock running slower nor does he notice a red shift. What he notices is the force gradient which will rip him apart. The longer he is in the direction perpendicular the EH, the worse this effect is. If oriented properly as he fell toward the EH, a 2D SciFi fantasy creature would not notice his 2D clock slowing nor would he notice a red shift of light. All would seem normal to him, even though a distant observer would view his clock as running very slow and would view the 2D creature as being red shifted. GR (and classical physics) claim that the escape velocity at the EH is the speed of light. This statement says nothing about the actual speed of objects close to the EH. It merely states that an object near the EH must travel away from the EH at nearly the velocity of light to avoid falling into the Black Hole. GR makes no statements about the EH traveling at the velocity of light relative to objects falling through it. Imagine being inside a closed room unable to view the environment outside the room. GR claims that there is no experiment you could perform which would allow you to distinguish among the following situations. The room and observer are stationary in empty space far away from any gravitating mass. Perhaps the room is in an otherwise empty universe. The room and observer are traveling at constant velocity in empty space far from any gravitating mass. The room and observer are free falling toward a planet or star, but far enough away not to be subject to a measurable force gradient. Since the observer cannot be aware of any motion, he cannot know his velocity or acceleration. The room and observer are orbiting a gravitating mass. Also GR claims that an observer in a room cannot tell the difference between the following two situations. The room is at rest on the surface of a gravitating mass. The room is in empty space far from any gravitating mass and is being given a constant acceleration. The observer can determine the acceleration/gforce, but does not know which is affecting him. He can obviously tell the difference between being on the surface of the Earth and the surface of the moon if he is told that gravity is causing him to stay on the floor of the room. He can similarly determine the acceleration if told that inertial effects of acceleration are keeping him on the floor.
Yes, it would run faster than your clock. Yes, it would run faster and faster. I found the labels I was looking for. When you free fall, you passively accelerate towards the Earth. The Earth actively accelerates towards you. In the twin paradox, the earthbound twin passively accelerates relative to the space-faring twin, who actively accelerates relative to the earthbound twin. (I haven’t seen these labels used in a book, nor have I seen better labels.) When you passively accelerate, you don’t feel the acceleration and fixed clocks in your frame of reference run at the same rate. When you actively accelerate, you feel the acceleration and the clocks may run at different rates.
I understand that anybody avoiding straight-in free fall will observe the redshift and clock slowing effects about a lower free falling object. Suppose at a given altitude the free fall rate is x m/s<sup>2</sup>. Anybody at that altitude who is approaching the BH at less than that rate will observe the effects. That might include an actively accelerating rocket (engines on) or an orbiting planet. The altitude per se is immaterial. Using the river-of-gravity metaphor, anybody who is moving against the river’s flow observes these effects about a downstream object moving with the river (free falling). The velocity relative to the EH need only be >= 0 to avoid crossing the EH. It is relative to objects passing by that free fell from an infinite distance that the velocity must be nearly c. I agree. When I say this to §lîñk€¥™, it pertains to an example where the object free fell from an infinite distance. Such an object crosses the EH at c.
I would not trust any one posting at this forum to answer the following. GR claims that the clock on the ground is slowed by gravity. SR claims that the clock on the ground is affected by the relative motion. Both state that you must perform some coordinate transformations or run some experiment to determine the clock rates. You do not determine clock rates by looking at the other observer’s clock. In the situation described above, I have no idea what the observer would conclude about clock rates due to actually looking at the clock on the ground. I am suspicious of anyone who talks about looking at a remote clock to determine SR/GR time contraction effects.
Dinosaur, no one said it was. I asked what we would observe. I'll try and get around to responding to all the replies since my last post this evening. Right now my children are demanding some quality time. Please Register or Log in to view the hidden image! kind regards Paul aka §lîñk€¥™
Bold in the following by me. At each distance from the EH, there is an escape velocity that can be calculated from the mass of the Black Hole, the distance from the EH, and the direction of the velocity vector. Near the EH, an object must be traveling at nearly the speed of light to escape. The bolded part of the above quote is nonsense.
