There has been the following dialogue over 2-3 posts. When you talk about meeting the light reflected from the clock, it sounds to me like you are saying that you are looking at the clock to determine how fast it is running.
Not nonsense. Consider that the escape velocity of the Earth is 11 km/s, but 1 km/hour is enough to escape if you keep your engine running long enough. Escape velocity refers to the velocity needed if you shut down your engine.
The velocity relative to the EH need only be >= 0 to avoid crossing the EH It's not very specific. If the velocity is positive away from the EH, and you have some thrust keeping your velocity from going negative, then yeah, your right. BUT, it looks like you are talking about the escape velocity, which would not be an speed above 0. Using your earth example this would be: The velocity relative to the earth need only be >= 0 to avoid crashing back to earth
I am talking about escape velocity or a better description of it. Your velocity relative to the Earth need only be > 0 to escape Earth’s gravity. At 1 km/hour you can reach an altitude where you can shut down your engine and never crash back to Earth. Likewise, near the EH, an object need not travel at nearly the speed of light to escape.
You are not talking about escape velocity. That is the velocity at which you need to apply no more force to keep on going forever. You're 1 km/hr thing is right.... you just have to reach an alititude where the escape velocity is less then 1 km/hr before you shut your engine off.
For more perspective on this see The Twin Paradox: The Doppler Shift Explanation. The free falling observer is analogous to Terrance, and the ground clock is analogous to Stella on the inbound leg of her trip.
Maybe I badly phrased my statement. I certainly agree that you don't feel gravity until you oppose it, but that gravity certainly does exist. You are in it's grip despite not being able to feel it. That is the reason you are moving (in free fall) after all. I'm pretty sure that is wrong (although I am happy to be corrected if I am wrong). The reason is because as you get closer to the hole you are being accelerated at a greater rate. This is quantifiably different to accelerating within a "constant" field. If I was falling towards earth say from 50,000 feet I would feel an accelration of more or less 1g all the way to the ground. I would be accelerated by 1g all the way down. However, as you fall towards a BH the gravity is increasing. I would feel 1g for a while but it would start to increase. At some point it will become 2g, and 4g, and 8g etc etc. ie. I am not only accelerating within the field. The field is increasing which is turn accelerates me even more. This is mildly analogous to sitting in a car where intially I accelerate at 10m/s<sup>2</sup>, and then jam my foot harder on the gas and accelerate at 20m/s<sup>2</sup>. I would certainly feel that change from 10-20m/s<sup>2</sup>. You mention spaghettification. This is precisely what spaghettification is caused by. The difference in acceleration between your head and your feet. Once there is a considerable difference in g-force between your head and feet you start to be stretched. ie. you feel that differential as the streching of your body. Before the gravity gets that extreme you feel the increase in g-force as an increase in your rate of acceleration as I describe above, and you will most certainly feel that increase. NB. Check out SR. It states that whilst in uniform motion I cannot tell I am moving, but as soon as I accelerate I know I am moving because I can feel that force on my body. In GR the equivalent scenario is falling within a constant gravity. I cannot tell if I am being accelerated until that acceleration (not my velocity but a change in the rate of change of my velocity) increases. kind regards Paul aka §lîñk€¥™
I thought about this whilst I was eating dinner and I have a few comments. All theoretical aspects of GR and SR must conform to observation. Therefore one can deduce GR and SR from observation and Einstein most certainly did use observation albeit with thought experiments. However, his ideas have been confirmed with observation. GR does say the clock is slowed when in stronger gravity. SR does state that the clock is slowed when viewed by a moving observer. However, light travels at a finite constant speed no matter which reference frame (gravitational or moving) you are in. This is why clocks would appear to speed up as you move towards them. You are meeting each photon earlier. I probably don't need to give you an example but I will give one for the benefit of people who don't understand this. Imagine I have set up a marker post in space precisely 4/5 light second from my location (I'll take myself as the rest frame). You are travelling directly (but not quite so as you won't crash into me!) towards me in your spaceship at 4/5c. You pass the marker post and it sends me a signal at the speed of light to let me know you have reached the maker. The signal takes 4/5 second to reach me. Just 1/5 second later you wizz by me because it takes you 1 second to cover that same distance. Ignoring dilation for the moment, this means that if I could see a clock on your ship it would appear to run 5 times faster than my own clock. 1 second / (1/5) second = 5. If I add dilation in, 4/5c works out to a dilation of 3/5. Therefore your clock would appear to run at 5 * 3/5 = 3 times as fast as my own. And that's even when we add in dilation. The very fact that you are moving towards me means that you would appear to run fast. kind regards Paul aka §lîñk€¥™
Sorry to burst your bubble and with all due respect, but, no, it's not. Please take note of the word relative. The EH does not move. Therefore, relative to the EH you only need to be moving at > 0 to move away from it. kind regards Paul aka §lîñk€¥™
Well, I don't know about you, but I know of no other way of observing a clock than looking at it. Please Register or Log in to view the hidden image! kind regards Paul aka §lîñk€¥™
Correct. If I fire a rocket from the surface of the earth it would need to hit 11km/s to escape the earth. If I have a constant speed of 1 km/s relative to the earth I will escape it also. kind regards Paul aka §lîñk€¥™
Thanks for the link, but no need. Been there seen it done it. Please Register or Log in to view the hidden image! Sorry if I sounded like I was teaching you how to suck eggs in my first reply above WRT spaghettification. Upon review I really didn't need to repeat what you had already said but in a different way. kind regards Paul aka §lîñk€¥™
I think we really need to agree on what the conditions are like at the EH of a BH. A clock on the EH would appear to be frozen from the perspective a stationary outside observer at infinity (if we could see it, which we could not). Agree? Disagree? How long does a black hole exist from the perspective of the clock? Strange question, but I cannot think of any other way of framing it presently. Don't forget. The BH "exists" at the bottom of an infinite gravity warp. Does time even apply here? According to Einstein nothing massive can accelerate to c. Is this postulate defied at the EH, or within it? My intuition tells me that if Einstein is correct then, no, it isn't. That's tautlogous I know, but I feel it must be said. Assuming clocks are frozen at the EH, and that nothing can move at light speed, I stick with my original conjecture. The BH ceases to exist before you reach it because it does not exist in any time frame. I guess this would be analogous to asking what the Universe would look like it you could move as fast as light. Any thoughts would be appreciated. kind regards Paul aka §lîñk€¥™
Time slows down the closer you get to the center of a Black hole. It slows down so much that someone who was in the area of a Black hole, would see the "future" of universe around you. To someone on the outside, he would lose sight of you once you passed the Event Horizon. No light can escape from this point, hence no visual confirmation can be made. Once someone passes the EH, it is theoretically impossible to contact them. I haven't kept up with it lately, but I've read reports of people thinking that they had a way to use the Hawking Radiation as a method of "listening" to the black hole and retrieving information about the BH from the radiation.
I do think you’re wrong yet I’d likewise be happy. Your description of spaghettification seems fine. Yet consider that your acceleration can increase from 1g to 5,000g whilst the differential in acceleration between your head and feet remains negligible. The differential can be negligible even as you cross the EH. The BH could be so large that you could comfortably survive for decades after crossing the EH before spaghettification killed you. Picture this: As you drive the Earth seems flat. Its surface curvature is detectable only over a vast area. Naturally this is true on a larger planet as well. Imagine that as you drive, your planet shrinks from the diameter of the galaxy to the diameter of the Earth. Would you notice the change in curvature? Would it matter how fast the diameter shrank? Replace the change in curvature with a change in acceleration to apply this to BHs. You wouldn't notice the change in curvature until the planet became sufficiently smaller than the Earth. The equivalent of spaghettification would occur when your car high-centered. I’d say the GR equivalent to SR acceleration is avoiding free fall by say, hovering. Free falling within any gravity (constant or not) is equivalent to SR uniform motion, ignoring spaghettification. (Upon re-reading this it seems that's what you were saying.) Agreed. I add: In free fall I cannot tell if I am being accelerated unless there is a tactile difference in the rate of acceleration between my head and feet. The change in the rate of acceleration (the jerk) can otherwise be any rate. Suppose a comfortable differential in acceleration between my head and feet is x%. Can I jerk from 1g to 100g in 1 second on my clock while maintaining a differential of <= x%? Yes, and I can survive if the acceleration is passive, as it is in free fall (more on this below). I will never feel the acceleration per se; only the differential may be felt. From a differential value alone I cannot compute the individual rates of acceleration that comprise the differential. And if I can’t compute the rates, I can’t feel them either. To be more precise, although the differential tells me I am being accelerated, it does not tell me if I am approaching the BH. I could orbit the BH and feel the differential. An increase in the differential would tell me I am approaching. We know the Moon spaghettifies the Earth somewhat. The Earth becomes slightly egg-shaped in the presence of the Moon. Hold the Moon in your hand, initially light years away from the Earth. Now the Earth is perfectly spherical (let’s pretend it is in the absence of the Moon). Now accelerate the Moon back to its present altitude. The Earth becomes slightly egg-shaped. Can we on the Earth feel this warping? No, the warping is too subtle to feel. Would it matter how fast you accelerated the Moon from initially light years away back to its present altitude? No, it wouldn’t matter; we’d still not feel the warping. Nor would we feel our acceleration relative to the Moon (after all, the Moon came to us, not the other way around). Recall my labels, passive and active, for acceleration. When you free fall you passively accelerate. That is like being on the Earth as above, minding your own business, while a giant hand actively accelerates the Moon towards you. No matter how fast the Moon approaches, you’d feel neither the acceleration nor the warping. (If you replaced the Moon with Jupiter, you might feel the warping, but you’d not feel the acceleration.) It is conceivable that as you read the paragraphs above you crossed an EH. During your reading our observable universe as a unit could have accelerated from 200,000 km/s to 400,000 km/s on average relative to a singularity somewhere. It might be a billion years before any spaghettification effects are felt. Dinosaur may be referring to the distinction many relativity texts make between seeing/looking and measuring/observing. For example, a ship could approach you at < c but you could see it approach at far > c. Most books would observe that the ship moves at < c and would ignore what you’d see. How can you observe differently than you see? The observation can be a measurement taken by an assistant of yours, far away from you and at rest with respect to you, who records the velocity of the ship as it passes close by. The assistant emails you the velocity, so you can ignore what you see. Your assistant might also record the passing ship’s relative rate of time and email you that, so you can ignore the ship’s rate of time that you see as the ship approaches you. (After all, you see the ship’s velocity relative to you as > c so determining the time dilation from sight is tricky.) What you see is considered by these books to be misleading or superfluous in understanding the theory. In these books observations/measurements are made locally, not from afar by sight, unless otherwise noted. It’s good to be aware that using the terms see and observe interchangeably may confuse others. Agreed. It would appear to be frozen also from the perspective of anyone hovering or rising at any altitude above the EH. But the point is moot because the clock could not stay at the EH; to do so it would have to travel at c relative to the moving space, or, if you like, relative to objects passing by that free fell from an infinite distance. I find it misleading when books say that “time is stopped at the EH.” Time stops for no one because no clock or other material object can stay at the EH; rather, they must be crossing it. The clock cannot stay at the EH, as described above. Let’s say the clock is hovering a tad above the EH. This clock might not tick off 1 second before the hole evaporates. (Explanation given before in this thread; elaboration upon request.) Yes, time applies everywhere except perhaps at the singularity. As I mentioned above, we could have recently crossed an EH, with the singularity a billion years away. Yet our clocks are still ticking. Or, a light-year-long ship could free fall across an EH, and for an entire year by the ship’s clocks the EH would move within the ship. Yet the crew might not notice. The singularity exists at the bottom of an infinite gravity warp. The EH does not, and it could be billions of light years distant from the singularity. Good question. Black hole theory does not defy the postulate; it effectively puts a wrapper around it that protects its validity. Make a frame of reference. Within the frame the postulate applies. But the space in which the frame exists may exceed c relative to the mass. Space itself may move—squeeze toward a point—at > c to seemingly allow objects to defy the postulate, or so I like to think to better understand. Clocks are not frozen at the EH due to the light speed limitation. For the reasons I gave in this thread I think: You can reach the EH before the BH evaporates, the BH can evaporate in an arbitrarily small amount of time on your clock, and life can comfortably continue for years on your still-ticking clock after you cross the EH of a sufficiently large BH. Edited to clarify some points.
Some posts to this thread reach conclusions based on what an observer sees. When dealing with situations requiring SR and/or GR, what an observer sees can be very misleading. For example, consider the following. Exactly 1000 light years away a star goes nova and ejects a planet or some other object from its system at a velocity of 20% of light speed. Image that relative to us, the object is moving along the hypotenuse of a right triangle similar to a (3, 4, 5) triangle, with the 4-side directly in our line of sight. After 5 years, the object has traveled 5 light years along the hypotenuse, and seems to have traveled 3 light years perpendicular to our line of sight. What do our astronomers see? If you count zero as the time the object started moving, we first see it 1000 years after it started. Five years later, it is almost 4 light years closer to us, and the light now takes 996 years to reach us, arriving in year 1001. Without further analysis, we seem to see an object move 3 light years in one year. Obviously, it did not, but that is what careful visual observation would indicate. The above is easily explained if you analyze the situation properly. It does not even require SR or GR reasoning. It is an example of a simple situation in which what you see is misleading. Due to such possibly misleading situations, it is not a good idea to analyze SR/GR situations based on what an observer actually sees. In dealing with time and distance contractions due to SR/GR, you must rely on coordinate transformations or other methods, not on what an observer sees. Statements like the following boggle my mind, but not because they are confusing like quantum weirdness. I am astonished because such statements are so contrary to authoritative books I have read. I do not bother to analyze the reasoning (if any) leading to those conclusions. Bold remarks are mine, paraphrasing authoritative books I have read. My intuition (heh!) seems to tell me if the above is correct then the BH would evaporate at the precise moment you would have reached it's EH. Assuming clocks are frozen at the EH, and that nothing can move at light speed, I stick with my original conjecture. The BH ceases to exist before you reach it because it does not exist in any time frame. 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. No matter how far, or near, from the EH I am, it is always a reference frame moving at c. From the point of view of an object falling toward a Black Hole, the EH is reached in finite time. It is from the point of view of a distant observer that time slows for the object falling toward the EH. Black holes cannot eat anything. In fact, I'm going to stick my neck out (and hope I don't lose my head!) and say that the current picture of black holes is wrong, and if they do exist, then they cannot "eat" and "starve to death". Black Holes grow in finite time at the expense of stars, gas, and other mass they pull in. This is why clocks would appear to speed up as you move towards them. You are meeting each photon earlier. 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? A clock moving relative to you runs slower than your clock. I am receiving a signal from you with a picture of the clock on your ship, also, I am sending you a picture of my clock too. When I look at the picture of your clock I can see it is running half as fast as mine but when you look at the picture of my clock you can see that my clock is running twice as fast as your own. While it seems counterintuitive, SR states that two observers moving relative to each other each consider the other’s clock to be running slower.
Seems to me someone has lost their rattle because a mistake of theirs has been pointed out to them, and decided to take quotes out of context in order to gain some face (like that will mean they didn't make a mistake). I'll reply to that nonsense in due course. Zanket, I've read your response and will take time to consider your points before I reply. Thanks for taking the time to reply. Please Register or Log in to view the hidden image! kind regards Paul aka §lîñk€¥™
I made an error in my previous post. The object would have to be ejected from the Nova with a speed much faster that 20% of light speed to create the apparent paradox.
