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Everything posted by Janus

  1. Black holes and dark matter linked?

    This is a bit and chicken and the egg question. Did the galaxy form more dispersed due to the lack of SMBH, or did a SMBH not form because the material forming the galaxy was too diffuse?
  2. Black holes and dark matter linked?

    A couple of points: The Supermassive BH at the center of the galaxy is is pretty much through absorbing matter. It cleared out the vast majority of the close-by stuff long ago. The rest of the material went into orbit around that Black hole. After you get any distance from a black hole, it gravity behaves just like that of any other object. If we look deep into the universe ( and thus into the past), we see very bright objects originally named Quasars, they turned out to be young galaxies where the Black holes at their centers were still gobbling up matter. The high speed collisions between the stuff being pulled into the BH caused the region around to to emit a lot of high energy radiation. If our BH was still actively absorbing matter like this, our galaxy would be presently irradiated to point that life would be impossible. Even if it was absorbing matter, it could not spew dark matter. The difference between DM and "normal matter" is that DM does not interact with light or electromagnetically in any way. It only strong interaction it participates in is gravity. Since it is gravity that prevents escape from the event horizon of a black hole, DM would be no more capable of escape than normal matter. Our galaxy is not expanding. It is be held together by the mutual gravitation attraction of it components. Dark matter comes into play in that the visible matter isn't enough to hold the galaxy together against the rate at which it spins. Dark matter come into play by providing the additional gravity needed to hold the galaxy together. To do this job in a way that is consistent with how stars are measured orbiting the galaxy, DM has to have a certain type of distribution, which is pretty evenly spread out through the galaxy. If DM were being produced at the center of the galaxy, then it would be much denser there and thin out as you moved outward. This would produce a much different rotation profile for the galaxy than what we observe. Another point that should be made is that sometimes people make too much out of the "supermassive" part of supermassive black hole. Yes, they are massive in terms of a typical star (The SMBH at the center of our galaxy is some 4 million times more massive than our Sun), but it quite small compared to the mass of the galaxy itself( 5.8 x 1011 times the mass of the sun or 145,000 times more massive than the SMBH at its center). So when it comes to the overall gravitational effect of the galaxy, it is quite a small player.
  3. Time to rethink the Earth's motion?

    For example, using the golf drive example, one can do a quick and dirty estimate of how much further the ball would travel when hit East vs West: Assume the ball leaves a tee located at the equator* at a 45° angle to the ground at a velocity of 42.4264... m/s ( I chose this value because it makes both the horizontal and vertical velocity component 30 m/s and would result in a ~200 yd drive over a level surface) Hitting the ball East would add 30 m/s to the 463 m/s due the Earth's rotation relative to its center, which would bring the centripetal acceleration up 0.0381 m/s2 This would be subtracted from the acceleration due to gravity of 9.8 m/s2 to give a net effect of 9.7618m/s2. Ignoring air friction, it would take this net downward acceleration 3.0732 sec to stop the upward rise of the ball, and it will take another 3.0732 sec for it to hit the ground. total flight time of 6.1464 sec, during which it is traveling horizontally at 30m/sec and will cover a distance of 184.39 m or 201.65 yd. Hitting the ball to the West subtracts 30 m/s from the balls speed relative to the Earth's center, though it will still be moving Eastward at 433 m/s . This cause the centripetal acceleration to be slightly less, at 0.29396m/s2 . Subtracting this from the acceleration due to gravity and you get a net of 9.7706m/s2. It takes this acceleration 3.0704 sec to stop the upward rise of the ball and results in a total flight time of 6.1409 sec, during which the ball has traveled 184.23 m or 201.47 yd This makes a difference in the length of the two drives of 0.18 yds or ~6 1/2 inches**. Show me a golfer who's stroke is so consistent that he can hit the ball 200 yd and maintain less than a 7 in difference in the distance from drive to drive, and I've have to wonder why he isn't playing in the PGA * Placing the tee at the equator gives the greatest difference in the length of the paths. Moving towards the poles reduces the centrifugal effect. **In reality the difference would be even smaller. To get a more accurate answer involves invoking orbital mechanics to determine the exact path of the balls relative to the Earth's surface. Doing so gives a answer that is under a 5 in. difference.
  4. Time to rethink the Earth's motion?

    Centripetal acceleration needed prevent a object moving in a circle from flying off on a tangent is equal to v2/r, where v is the velocity of the object and and r the radius of the circle. Tangential velocity at the Equator: 463 m/sec. Radius of the Earth 6378000 m This gives a centripetal acceleration of 0.0336 m/s2 compared to the 9.8m/s2 centripetal acceleration supplied by Earth's gravity. In other words, gravity is 291.6 times as strong asit would need to be in order to just to barely keep you from flying off into space. The rotational speed at the equator would have to be better than 7.9 km/sec in order to enough to toss you from the surface of the Earth ( And even then, you'd only be flung into an orbit around the Earth unless the velocity exceeded 11.2 km/sec) Your golf ball does travel further if hit to the East vs. the West assuming you hit the ball exactly the same both ways. However, for the speed at which you can hit a golf ball, this difference is going to be insignificant compared to other factors such as wind speed and even the variation in your stroke ( even on the driving range, when you are consistently hitting from the same spot and in the same direction, the length of your drive varies from swing to swing. But while the rotation of the Earth has a minimal effect on your golf game, it does have a significant effect on the accuracy of long range artillery, and when they aim the big guns this has to be taken into account if they want to hit the target.
  5. Moving at the speed of light

    The simple answer is that the universe works in such a way as to prevent your ever exceeding c relative to your starting point. You are essentially asking what prevents you from constantly accelerating at 1 m/s2 until you exceed the speed of light. If the Universe operated under the Rules of Newtonian physics, nothing. After 7 years, 21 days, 20 hrs, 47 min and 38 sec, you would be moving faster than light. However, we don't live in a universe that follows Newtonian rules, but follows Relativistic ones instead. And one of those differences in rules is in how velocities add together. Under Newton if you want to get the sum of two velocities, you simply add them together like this, w=u+v. Thus if you were moving at 1 m/s relative to some reference and then added 1m/s to your current speed, you would be moving at 1+1=2m/s relative to the initial reference. However, it turns out that this isn't correct. the right way to add the velocities is by w= (u+v)/(1+uv/c2) where c = the speed of light in a vacuum or 299,792,458 m/s Now when you add 1 m/s to 1m/s you get a resultant velocity of 1.9999999999999999777469988789276 m/s almost, but not quite 2 m/s At low speeds, this doesn't amount to much, but as the speed increase, the difference starts to mount up. If you were moving at 0.1c and increased your velocity by 0.1c, you would be moving at .198019802 c relative to the point you were initial moving at 0.1c relative to. If you boost you speed by another 0.1c, you will now be moving at .2922330097c relative to the initial frame. Do this 7 more times, and instead of moving at c relative to the initial frame like you would under Newton, you would be moving at 0.7629989373 c. Each time you add change your speed by 0.1 c relative to your current speed as measured by you, you add less than 0.1c total change in your velocity. And the closer you get to a total of c, the less change in total velocity you'll end up with, and no matter how you try and add up the velocities, the resultant velocity will always end up being less than c.
  6. The use of acceleration due to gravity here has nothing to do with relative motion, it is a more universal expression for comparing the force of gravity, since it does not rely on the mass of the object undergoing the acceleration. As far as your next post goes: The first part holds in that a gravitational potential does imply a gravitational force, however, this does not in turn imply that objects at different heights must experience different accelerations for there to be a difference in potential. The difference in potential is the integral of the force over a distance and does not require that the force differs over the distance. In this case, the space traveler would have to combine two separate calculations to determine how fast the Earth clock ticks relative to his own at any given instant. One that factors in his position relative to the Earth's gravitational field, and another to determine its relative position in the "acceleration field". The main difference being that the Earth's gravitational field strength decreases with distance from the Earth, and the strength of the "acceleration field does not. This would be in addition to any time dilation due to relative velocity differences. (if you choose the instant in which the ship has just stopped its velocity away from the Earth and is just going to start back to Earth, At that moment it will be at rest with to the Earth, and you will only need to use the first two calculations.)
  7. No, it isn't. To put numbers to my earlier example: Acceleration due to gravity is GM/r2 Gravitational potential is -GM/r For the Earth, the difference in acceleration at the surface and 1 earth radius above the surface is 7.35 m/s2 The difference in potential is 31255879.6 joules/kg For our 4x Earth mass planet, the difference in acceleration between surface and the same altitude above the surface is 5.45 m/s2 The difference is potential is 41674506.2 joules/kg This is 33% larger than that for the same altitude difference for the Earth, while the difference in acceleration is only 74% as much. You can even have a difference in potential without any difference in acceleration. In a uniform gravity field, the difference in gravitational potential would be found by gh, where g is the acceleration due to gravity throughout the whole field and h is the height difference between them. In this case, there is no difference in acceleration over the region being measured (gravitational potential over small height differences approach this ideal, as g changes insignificantly over the region considered.)
  8. To build on what swansont has already alluded to. The fact that our Earth observer and space traveler experience the same local acceleration is not the determining factor in terms of the time dilation each would measure in other clocks. As swansont said, gravitational time dilation is due to the difference in gravitational potential, or in other words, the total effect of the gravitational field between the position of the two clocks. One way to visualize this is to consider how fast would something dropped from the higher altitude be moving when it reached the lower altitude. That would be a measure of the difference in gravitational potential. So if we take an object and drop it from a altitude 1 earth radius above the surface, when it starts its fall it will experience 1/4 the acceleration it does at the surface and it will hit the ground moving at some speed. A clock placed at this altitude will run faster than one on the surface. Now if we put a clock on the surface of the world with 4 times the mass of the Earth and twice the radius, it will experience 1g just like a clock on the surface of the Earth. If we put an object 1 earth radius above the surface, it will experience 4/9 the acceleration as the surface. If we drop an object from this height, it will hit the surface moving faster than one dropped from an equal height on the Earth. In addition, a clock placed here will run faster than one on the surface by a greater factor than the difference in rate between the two clocks separated by the same altitude in the Earth scenario, even though the difference in acceleration experienced by the Earth clocks is larger than the difference for the second set of clocks. When applying this to our accelerating space traveler, to use the equivalence principle, we have to consider what the equivalent gravitational field to his acceleration would be like. In this case, it would be a uniform gravity field that extends to infinity along the line of acceleration that does not diminish in strength with distance. Clocks that are in the direction he is accelerating will run fast, and clocks in the opposite direction will run slow. The greater the distance between them and these clocks, the larger the difference in their tick rates. Thus for our space traveling observer, As he accelerates at 1 g away from the Earth, not only does his speed relative to the Earth increase causing him to measure a time dilation in the Earth clock, but the Earth is getting increasingly further away in the direction opposite to his acceleration vector. As a result, he would measure an additional increase in the slowing of the Earth clock tick rate. When he changes his acceleration in order to decrease his relative velocity and then accelerate back towards the Earth, the magnitude of the acceleration remains unchanged. However, the Earth's position relative to the acceleration vector does change. Now it is in the direction of the acceleration, and thus according to our traveler, the Earth clock runs fast. This is how the equivalence principle would be applied in this case. One thing to note is that this "equivalent gravity" due to acceleration is only measured by our accelerating observer. Our Earth observer would only measure time dilation due to the difference in relative velocities. (Both observers would also measure any difference due to relative positions in Earth's gravity field, but depending on the exact scenario, this can be insignificant. If you are using scenarios of high fractions of c over light year distances, this additional factor will likely be smaller than the rounding errors in your calculations. )
  9. Which way is up?

    Neutrinos were hypothesized before they were ever detected, but we had detected other particles such as electrons, protons and neutrons. This did not mean that neutrinos were likely to turn out to be one of these particles. The very reason they were hypothesized was the fact that none of these particle had the properties that the neutrino needed to have. In the same way, quantum fluctuations do not behave in a manner the is consistent with them fulfilling the role of the hypothesized gravtion.
  10. Which way is up?

    It is "specific energy" or energy per unit mass. In this case it would be joules/kg
  11. Which way is up?

    The fact that there is zero gravitational force at the center of the Earth does not mean that an object at the center of the Earth isn't at a lower gravitational potential than an object on the surface. A difference in gravitational potential is tied to the energy needed to make the entire trip between two points and not what happens at the start or finish of the trip. Using the standard reference which puts zero gravitational potential at an point an infinite distance from the gravity source, the gravitational potential from the surface of a sphere outward is found by -GM/r, where r is the distance from the center of the sphere. As r gets smaller the potential goes more negative and thus becomes lower. For a point inside a uniformly dense sphere, the potential is -GM [ (3R2-r2)/2R3] which reduces to -3GM/2R at the center. -3gm/2R is more negative than -GM/r, so the gravitational potential at the center is lower than at the surface. Here's a graph for the gravitational potential for the Earth (assuming a uniform density) starting at the center and moving out to some distance above the surface. the green line marks off the radial distance of the Earth's surface. The exact shape of the curve on the left of the green line will be different for the real Earth due to the variance of density with depth, but will still be lower at the center than any other point. Time dilation is related to the difference in gravitational potential and thus a clock at the center of the Earth, being at the lowest potential will run the slowest. Going back to what I said about the potential difference applying to the entire trip, If you take a clock and move it from the center of the Earth to that point an infinite distance from the Earth, it will start at zero g and end at zero g, but it will have raised its gravitational potential by a fair amount and will run faster at the far removed point than it did at the center of the Earth.
  12. As far as planets orbiting stars goes, the equation for an orbiting clock would give the time dilation for any given planet as measured by a distant observer. (As long as you are dealing with circular or nearly circular orbits, adjustments would have to be made to deal with highly elliptical ones. Of course for most normal stellar systems this going to be a very small effect (for the Earth it works out to be about a difference of 1/2 sec per year.) And since our detection of extra-solar planet are by indirect means (measuring it parent star's wobble or it's transit in front of the star) and not direct observation of light from the planet, this is not something we presently would measure.
  13. But now you have to invoke GR and gravitational time dilation. And this has nothing to do with what the clocks "experience" but with their relative positions in the gravitational fields. For example consider two satellites orbiting the same body at different altitudes. Both are in free fall and experience 0 g. If this is what determined the gravitational time dilation difference between them, then it should be zero, and the only time dilation would be from their orbital velocity difference, and if R is the radius of a clock's orbit then its time dilation factor should be found by. T = t0 sqrt{1-GM/Rc2} since orbital velocity is v = sqrt{GM/R} However the actual time dilation for an orbiting clock is T = t0 sqrt{1-3GM/Rc2} The difference being due to the fact that one of the orbiting clocks is higher in the gravitational field than the other. They are accelerating in the sense that they are changing velocity with respect to some observer at rest with respect to the gravitational field. They are not accelerating in the sense of being in an accelerated frame, as they would not measure clocks in the direction they are falling as running fast, but would instead measure their respective tick rate depending on their relative position in the gravitational field. Put another way, if you had a rocket gaining velocity towards a clock due to its firing of its own engines and far removed from any gravity field, it would measure that clock as running fast due to the rocket's acceleration as an additional factor along with the time dilation due to the difference in velocities. With a rocket falling towards the surface of a planet in free fall, the rocket would measure a clock on the ground as running slow due it's lower position in the gravity field in addition to the time dilation caused by the difference in velocities.
  14. Turning does break the reciprocal effect. This is because measurements made in an accelerated frame differ from those made in an non-accelerated (inertial) frame. If you are in an inertial frame all you need to know to determine the time dilation of another clock is its relative velocity to you. If you are in an accelerated frame, you additionally have to take into account three new factors: The magnitude of the acceleration, the direction of the other clock relative to the acceleration, and the distance to the clock along the line of acceleration. Both the acceleration magnitude and distance effect the degree of difference in tick rate you will measure. The direction determines whether it is a faster tick rate or a slower one. If the clock is in the direction of acceleration, you will measure it as ticking fast, if it is in the opposite direction, you will measure it as ticking slow. This measurement holds for clocks whether they share your accelerated frame or not. (This means that if you are in an accelerating rocket, a clock in the nose will run faster than one in the tail, even if they don't move relative to each other in the rocket frame.) With the twin paradox this means that when the traveling twin turns around, he is both a great distance from the Earth twin and accelerating towards him. This combination results in the Earth twin clock advancing very quickly during the turnaround period according to the traveling twin, which more than compensates for the fact that it ticks more slowly during the coasting periods of the both the outbound and return legs. The Earth twin, which remains in an inertial frame throughout only measures the traveling twin's clock run slow due to relative velocity.
  15. In the past you might have said that, but the term "relativistic mass" is no longer used. The energy increases asymptotically and energy has properties that used to be only associated with mass.
  16. I'm at a loss to how your first statement above relates to the section of my post you quoted. I was referring to relativistic effects only. In the early days of Relativity, they used the term "relativistic mass" to refer to the apparent mass increase of a moving object to distinguish it from the "rest mass" of the object or its mass as measured when at rest with respect to the observer. That term has fallen out of favor. Today, "mass" is used to mean only the "rest"mass. "Relativistic mass" is now just energy which has some "mass equivalent" properties. Its a matter of convention in terminology to avoid confusion. Thus Is not correct by modern usage of the term "mass" which refers to the "rest mass" which is invariant across reference frames. The length contraction part is correct because it is reciprocal.
  17. Actually, no. While it is common to see it said that mass increases with velocity in many popularizations of SR, modern physics tends to treat mass as an invariant property (this avoids the confusion caused by having to distinguish between rest mass and relativistic mass. What used to be called relativistic mass is now just included under the label of energy. (with the understanding that some of the properties expressed by mass alone under Newtonian physics are now also expressed by energy.) So as an object's velocity increases with respect to you its kinetic energy relative to you increases, but if you change your own velocity, your kinetic energy relative to yourself remains 0. This is no different than for Newtonian physics. If you collide with a bullet with a relative velocity of several 100's of meters/sec, it doesn't matter if you are at rest with respect to the ground and the bullet was traveling, or the bullet was suspended at rest with respect to the ground and you were traveling with respect to it. The impact between bullet and yourself will be the same, and you will suffer the same consequences. The difference Between Newton and Relativity is that for Newton the KE increases by the square of the relative velocity and thus approaches infinity only is the velocity approaches infinity, while in Relativity, the KE increases by an asymptotic function and approaches infinity as the relative velocity approaches c. Length contraction (and time dilation) result from the fact that observers in relative motion with respect to each other measure time and space along different axis in space-time.( an analogy is to map time as being in the front-back direction and space in the left-right direction. people facing in different directions measure left-right and front-back relative to themselves and differently from each other. In Relativity, we are dealing with 3 spacial and one time direction and it is relative motion that creates the difference in the space-time axis of the observers.
  18. Water has calories

    Reminds me of the "Scotch on the Rocks" diet. It was based on the idea that there were a smaller number of Calories in a scotch on the rocks than the calories your body expends bringing the consumed drink up to body temp. The trick was in that fact while perfectly true, a Calorie is actually a kilocalorie and equal to 1000 calories.
  19. How can you measure distances across space?

  20. Rotation - is it absolute?

    I'm not sure what you are getting at. But let's say that you have one frame that is rotating a 1 rad/sec relative to an inertial frame and you have another frame that is rotating at 2 rad/sec relative to an inertial frame that has a velocity of 10m/s to the first inertial frame. Then the second rotating frame is rotating at 2 rad per sec relative to the first inertial frame and the first rotating frame is rotating at 1 rad /sec relative to the second inertial frame and both rotating frames are absolute.
  21. graviton / space / dark matter / dark energy ?

    The graviton is a hypothetical particle that would have the same role in gravity as the photon does in electromagnetism. The photon is a stable, spin 1 boson. The graviton is a quantum of gravitational radiation in any theory of gravity that posits their existence, just like the photon is a quantum of electromagnetic radiation. And like in QED, where the electromagnetic force is mediated by virtual photons, in any quantum theory of gravity which uses gravitons, it would be virtual gravitons that mediate gravity.
  22. graviton / space / dark matter / dark energy ?

    No. While any gravitons near the Event horizon an on the right trajectory would fall into the Event horizon (with a non-rotating BH a graviton could just skim past just outside the Event horizon without falling in), this has nothing to do with gravitons falling into the BH causing space-time curvature or the gravitational field. Photons following the same trajectories would also fall into the black hole, but this would not be the cause of the BH having a electromagnetic field (and Black holes can carry an electric charge.) You can have a BH absorbing lots of photons without it carrying a charge, or you could have one with a charge and absorbing no photons. You can have a BH and its associated gravitational field /local space-time curvature without it absorbing gravitons. I know that I said this before, but. Electromagnetic fields are mediated by] virtual photons, and gravitational fields would be mediated by virtual gravitons. Virtual particles are not bound by all the rules that "real" particles are, and thus virtual photons and virtual gravitons can escape the event horizon in order to mediate their associated fields. Virtual particles are a construct of the Uncertainty Principle. Basically, they are allowed to pop into and out of existence as long as they do it in a short enough period as to slip under the radar, as it were. As a result, they can get away with all kinds of things short of violating causality. They are an actual physical example of the old saying "If you don't get caught, it's not cheating".
  23. The car was there to provide the test payload mass. It's not enough to just launch the rocket, you have to demonstrate that it is capable of carrying a payload. Typically, something like cement blocks would be used for this. Using the Tesla instead brought more media attention to the launch.
  24. It carries an ARCH, which is a high tech data storage unit which is supposed to be able to withstand the rigors of space. Stored on the ARCH is a copy of Issac Asimov's Foundation Trilogy. The words "Don't Panic" are also displayed on the dashboard.
  25. And centered around the fact that humans had been abducted from Earth in 1937. One of which was Amelia Earhart (who, for some reason was in cryostasis and still alive.) Oddly enough, that old pickup truck with its metal body would likely fare better than the Tesla with its carbon fiber body which is much more susceptible to degradation by cosmic radiation.