Assume for this thought experiment that there exists a material which has negligible rest mass density and arbitrarily high stiffness.  We build a tower out of this material, on the equator. The tip of this tower will spin faster as the tower is made taller.  When this tower reaches a hight of about $4\times10^{12}m$, the tip will be moving at the speed of light (circumference of 1 light-day). The mass density is negligible, so the angular velocity of the earth-tower is hardly changed during construction.  Without considering relativity, if we build the tower a bit higher, the tip will exceed $c$.  So, considering relativity, what's stopping us using this hypothetical material to build such a tower?
358
Imagine a bar   spinning like a helicopter propeller,  At $\omega$ rad/s because the extremes of the bar goes at speed  $$V = \omega * r$$  then we can reach near $c$ (speed of light) applying some finite amount of energy just doing   $$\omega = V / r$$  The bar should be long, low density, strong to minimize the amount of energy needed  For example a $2000\,\mathrm{m}$ bar  $$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$  (a dental drill can commonly rotate at $400000\,\mathrm{rpm}$)  $V$ (with dental drill) = 14% of speed of light.  Then I say this experiment can be really made and bar extremes could approach $c$.  What do you say?   EDIT:  Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB.  I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$  What do you think?
93292
Edit : Added a picture for better understanding of my querry. All the texts I have studied has used an non-inertial frame to explain the phenomenon. But every time I see something explained with pseudo forces, I try to realize in real forces.   But in this case I tried to explain it in a frame which is centered in Earth's center and not rotating. But I couldn't explain what happens to the tangential component (to the point on Earth's surface where $g$ to be measured) of centripetal acceleration in this scenario. It doesn't cancel out.   But then I thought the tangential component is so low that practically it would have no effect.  Is my explanation wrong?
53153
I am currently stuck on the following question.   A stone is dropped from a stationary helicopter 500m above the ground, at the equator. How far from the point vertically below the helicopter does it land and in what direction? Solve this problem by conserving angular momentum.   My current interpretation is that when the stone falls in order to converse angular momentum the angular velocity must increase. This leads to the stone travelling to the east.   I equated the angular momentum at the start       L0=*(re+h)mVo  where re is radius of earth, h is the height above that, m is mass and Vo is inital velocity. To the angular momentum at any time  L=(re+h-1/2gt^2)m(Ve+Vo)  where the 1/2at^2 term comes from gravitational acceleration and Ve is the additional velocity.   I rearranged to find Ve and then integrated over the time it takes to fall the 500m in order to work out the extra distance the stone traveled. However, my answer is 1/2 what the answer should be. I have checked the maths and it seems to be fine. So I believe my set up is wrong. Any help would be appreciated.
91372
I just want to first say that I'm aware I am asking a question due to my own confusion and ignorance and not because of anything to do with special relativity. I hope that's alright.   What I'm confused about is whether two beams of light moving in opposite directions away from eachother, have a relative speed of $c$, or $2c$.   The thing is, we can always say it's $c$, but then when we look at the relative distance travelled for the time elapsed, the result is $2c$.   Can anyone explain what is going on?   Response to Alfred Centauri 22/08/2016   I question your reasoning for two reasons. Firstly to photons moving in opposite directions was one of Einstein's examples of the counter-intuitive implications. So what you're saying wasn't around then, and Einstein himself was misconceived. In fact you can find instances opposite direction light beam as recently as 10 years ago. Phillip Green in his popular science book uses that very example in his introduction. So the question is whether this is a formal adjustment to SR, backed by a publication and a reasonable consensus. Is it?   The second reason is to do with your reasoning. You say it is not a legitimate measurement because there is no inertial frame in which one or the other photon is at rest.  That at-rest criteria as you define the constraints, is equally applicable to two beams coming toward eachother. In fact almost every problem setup has no way to assume that one of the two frames is stationary. The way it's handled, I believe, is mathematically by the simple addition of the equal and opposite motion. This is also implicit in the Laplace transforms, I think.  The reason this can be done, I think, is because all inertial frames are assumed to be equilvant....they are part of a global reference frame.   A further matter derives from the fact the relative motion of two frames can be represented as tangential and radial components. If what you are saying is correct, then one of the two components cannot be measured in almost all cases.   I definitely want to make clear I am a novice in the theory, and you probably are not. It's possible this is all misconception, except for the historic part of my response which can easily be confirmed. Please do let me know if you can as I am trying to learn and need my mistakes corrected, especially the long running ones.
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I was reading Landau &amp; Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct".   For example, if you consider a rigid rod and apply a torque at one end, by definition of being rigid, the whole body must start rotating at the same instant. But the information about the force being applied cannot travel faster than the speed of light.   The book hasn't mentioned how to resolve this paradox, and after thinking about it for a while, I'm wondering if one can even define a rigid body in a relativistically correct manner.  To summarize: How does one define a rigid body in special relativity?
68035
Assume we have a ball with diameter 1 meter and mass 1 kg rotating at 99,5% speed of light (Suppose I'm an observer placed above the ball, I see under me a disk wich external  speed is 99,5% the speed of light)  Then we accelerate such ball to 99.5% of speed of light, to make clear from wich position we look at the ball when it's moving so fast I did a picture (there's a black ring around the ball, as you se the rotational axis is vertical to our observer)    I'm interested in a full explanation of what we observe (measured rotation speed, color etc.) and why that happens, as far as I know we should not measure something moving faster than light but I'm not sure how relativity constraints would alter the "measured state" of the ball as long as we accelerate it.  What we see change while the ball accelerates?  EDIT:  A precisation, I assume the ball is spherical when I start rotating it before even moving, this is because commenters made me to note that shape may change.
92324
The Michelson-Morley experiment proved there was no aether, nothing that light moves through in space. Yet in GR, mass bends spacetime so that light travels in arcs around large masses. How can spacetime be bent, if there is nothing there to bend?  This question is not related to the factors that bend spacetime, which I noticed many physicists try to shuck it off to, to avoid giving a coherent answer, but the structure of spacetime itself.
90871
I've recently been contemplating things like artificial gravity in a rotating space ship (for example, the ) and learning about the Coralis effect and other interesting fictitious forces that appear in rotating reference frames.  It occurred to me that, if you were living on a space station spun for artificial gravity, it might be possible to become weightless in such an environment by travelling fast enough against the spin of the ship. My friend, who I was discussing this with, thinks otherwise, that you would actually be under more g's as you tried to gain the speed to lift off from the inner edge of the ship.  In terms of concrete numbers, say the ship is 4 kilometers in radius (as an O'Neill Cylinder would). At this size, the rate of rotation to generate 1g in centrifugal force (the artificial gravity) is under 0.5 rpm. If a vehicle travels on the inside of the cylinder against the spin fast enough, eventually the vehicle would cease moving when looked at from a static reference frame. I would think at this point, the vehicle could simply push off from the edge of the cylinder and float towards the center of the station. Is this correct?  Furthermore, would this method of "getting into air", as it were, be easier than it would be to counteract real gravity on Earth (with things like planes that generate lift with their wings)?
93613
Imagine, if you will, there exists somewhere out there a supermassive planet. For some reason, this planet is only a shell of its former existence and all that is left is a crust of substantial size to keep it from collapsing in on itself (let's imagine it is stable at 5000' thick). Now, this planet was HUGE! How large, you ask? Large enough that the remaining shell is still able to maintain a gravity well strong enough to keep you anchored to the surface.  Pretty neat, huh?  Well, since this is a sight to be seen by everyone, you stroll along and, not looking where you are going, you tumble into a chasm and straight down into a hole that permeates the thickness of the shell. As you are falling down and down and down, you think:  "At what point do I stop falling down and I start falling up? And would I be able to retain the velocity, since gravity is a conservative force, and fall back through another hole on the surface on the opposite side? Where would the center of gravity even exist? I mean, aaaaahhhhhhh!"  What say you, browsers and scientists? A stretch of the imagination, sure, but is it physically possible? Could there exists a configuration similar to this where gravity could be concentrated to a point but still allow free travel up to the focus?
17541
I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
76615
I am by no means an expert in this field, however something puzzles me about the speed of light and the relativity of time and space (space-time).  Is is universally acknowledged that the speed of light (299,792,458 m/s) is the universal speed limit, and that nothing can travel faster than light? That is a measurement based on a man-made interpretation of time (hours, minutes and seconds etc. are man made...there is nothing natural dictating how long a second should be).   For instance, according to Einstein, time and space bend around the physical matter of the universe, so for example, time near or on the surface of a "super massive black hole" should be drastically slower, relative to that of earth. Lets say for example that for every second that passes on the black hole, 10 seconds pass on earth, so essentially time on the surface of the black hole is 10 times slower than the time on earth.  Given the example above, is the speed of light at the surface of the black hole still 299,792,458 m/s, or is it 299,792,458,0 m/s?
108663
Is there an upper limit for  jerk in physics? What about higher derivatives?   A consequence of  special relativity is that no material body can reach or exceed the speed of light in vacuum (due to the relativistic mass increase, or the Lorentz contraction).    I am not interested in obtaining these upper limits  based on postulates (and following mathematical implications), like the postulate  of the constancy of speed of light in special relativity.    I would like to know whether there are experiments that would lead to these upper limits, as a matter of consistency with empirical evidence. For the speed of light in vacuum we have Maxwell's equations. As far as I know, it was established experimentally that the constant that appears in Maxwell's equations is the speed of light in vacuum.  For acceleration,  there is a previous question on StackExchange, , where in an answer it is discussed Caianiello's maximum acceleration (the result is linked to Heisenberg's uncertainty principle, that's the type of answer that I am interested in, as an example).   So for speed and acceleration,  I understand that there is  experimental evidence that tells us that in order to have consistency (with the empirical evidence),  then we must accept that there is a maximum speed and acceleration in physics.  I am not interested in arguments involving the Planck system of units, since these arguments would be sensitive to the choice of normalization.   What about jerk in physics, and higher order derivatives. Is there any experimental data that would force us to accept upper limits for these quantities? Would it be useful to imagine experimental scenarios that would force us to accept these upper limits?  I will reformulate the question,  for clarity. I will not focus on the chronological emergence of the mathematical models that explain the experimental data.  In physics, maximum speed can be linked to Maxwell's equations. Maximum acceleration can be linked to Heisenberg's uncertainty principle. Does this trend continue,  for jerk and higher derivatives? Because  intuition tells me that in physics there must be upper limits/bounds for all of them, and there is a countable infinity of these quantities.
104656
So, according to Einstein's theory of general relativity, gravity is not a force instead it is a consequence of objects with mass deforming spacetime, right? And so, according to him, there is no difference between standing on a platform accelerating upwards at 9.81 m/s^2 and standing on Earth, right? But, there is a difference. At least, I think it's a valid difference. If you drop two apples from a high altitude on Earth, not only will they accelerate downwards at 9.81m/s^2 but they will also slightly move towards each other because the Earth is a sphere and gravity acts radially inwards pulling the two apples closer to each other. But if you drop the apples from the same height above the accelerating platform, the apples will only appear to accelerate downwards at 9.81 m/s^2 but will not move towards each other like they would on Earth. Why is this true? Is this even a valid difference? If it isn't, why isn't it?
41357
It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?
56110
One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't believe that they provide as much insight as a mechanical explanation would.  The  Cedric provided looks similar to a diagram that I saw in my physics textbook. This diagram illustrates precession nicely, but doesn't explain why the top doesn't fall. Since the angular acceleration is always tangential, I would expect that the top should spiral outwards until it falls to the ground. However, the diagram seems to indicate that the top should be precessing in a circle, not a spiral. Another reason I am not satisfied with this explanation is that the calculation is apparently limited to situations where: "the spin angular velocity $\omega$ is much greater than the precession angular velocity $\omega_P$". The calculation gives no explanation of why this is not the case.
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Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of , but let’s consider . My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.  So do I pull Earth with the same force it pulls me? If yes, how?
57936
I found this interesting problem in :     Given a point $P$ in space, and given a piece of malleable material of constant density, how should you shape and place the material in order to create the largest possible gravitational field at $P$?   Any ideas?