Relativity

Suppose that at the top of Mt. Everest precision clock has been installed, and the same second clock was installed at the bottom of the mountain, 8 km below the summit. Before installing, clocks were carefully synchronized. The question is: what difference of time these clocks will show per day (24h), according to the theory of relativity?

What have been the major contributions to our understanding of the Universe made by the study of GR from 10 years after its formulation to this day?

I think this causes the e/m bubbles at the edge of our solar system and exists around all large gravitaional systems: As light curves around a large body of gravitation, a small percentage of that light should wind up scattered as a field, or "photon cloud". This field should extend from the straight line of an observers position, to the edge of the curve. The lite light density, scattered over a large distances, probably form huge e/magnetic "Bubbles" on the edge of large mass objects like solar systems and galaxies. I guess the scattered photons would meet their curved partner photons at the same time and place, on the otherside, thus defining the very edge of the t…

Has anyone wondered how it looked to the theory of relativity, in the world of bats? Assume that in this world there is no light, and the bats know nothing about it. The only medium to measure the speed and distance, are the waves of sound of their maximum speed of 340 m / s. Do according to their theory of relativity, the speed limit for the particles, therefore, was to 340 m / s? Do as it approaches of their vehicle to the speed of sound, would have also changed their time and mass in the same way as in SR? Please do not use in considerations the speed of light, because for the bats it does not exist.

?Hi,Has ther ever been an experimental verification of length contraction? Thank You

Suppose that somewhere in the universe is the civilization that exist exclusively in the underwater world, in which the speed of light is 230 km/s. The question concerns whether their imaginary underwater rockets can therefore overtake the light in their world?

Scientists at CERN discovered that 15000 neutrinos were found to travel faster than light. A webcast is planned today about the findings: http://webcast.cern.ch/ Woo hoo!

Relativity has always been a stumbling block for me. No matter how much I read about and try to understand it, I find myself with more questions than when I started. Here are a few that have been picking my brain recently: It's my understanding that as any mass approaches the speed of light, its mass approaches infinity--or do you just say that its energy approaches infinity? I get confused with the mass energy relationship when something is accelerated to near light speeds. If mass and/or energy approach infinity with increasing velocity then shouldn't subatomic particles, such as neutrinos, possess infinite mass? Do they travel just shy of the speed of light? …

Here's what I think I undertstand: Newton's bucket: a bucket of water is made to spin. The water rises up at the edge of the bucket. Looking at it per general relativity (GR) from two frames of reference: (1) Ground reference frame - Bucket spins and makes water form concave surfrace. (2) Bucket reference frame - From bucket's point-of-view, it is stationary and rest of universe is spinning. But if bucket at rest, what makes the water surface concave? General relativity says: the rotation of the rest of the universe causes the water to become concave in case 2. This is due to frame dragging. Imagine a massive rotating object, a huge hollow sphere (a s…

Could you use reflectors, anchored to the moon, for long-base-line Gravity Wave detectors? What about satellites, or systems thereof, in Geo-Synchronous Orbit? (Or, given the success of detecting earth's precession, with Relativistic accuracy, w/ gyro-scopes, could 3 mutually-perpendicular gyro-scopes detect GWs -- i.e., would GWs affect transverse vs. longitudinal rotations differently??)

Are there any hard evidence that the relativistic mass of the rocket (or particles) increases with its speed ?

If, by applying the Correspondence Principle, to the Classical Relativistic 4-vector equation [math]\vec{p} \circ \vec{p} = m^2[/math] yields the Klein-Gordon equation [math]\left( \partial_t^2 - \partial_x^2 \right) \Psi = m^2 \Psi[/math]; then, why not simply extend the 4-dot product, from Minkowskian flat space [math]\vec{p} \circ \vec{p} \equiv p^{\mu} p^{\nu} \eta_{\mu \nu}[/math], to curved space, via the GR metric [math]\eta_{\mu \nu} \rightarrow g_{\mu \nu}[/math], i.e., [math]\vec{p} \circ \vec{p} \equiv p^{\mu} p^{\nu} g_{\mu \nu}[/math] ? Likewise, for purposes of computing the metric tensor, from the wave-functions, via the Stress-Energy Tensor, one could sim…

Here is my understanding (or lack thereof) in dealing with time. From what I understand time is directly related to gravity. The higher the gravity, the slower the time. But it is relative. Just because time is moving slower does not mean you will sense everything in slow motion. So, if you were to be on the outside of a black hole, watching someone fall into the black hole, they would appear to be falling slower and slower, until they stopped moving indefinitely, but to them, it would be a constant motion (except for spaghettification, so there would be a difference in different parts of …

Can anyone explain for me the following case, please: A rocket is moving at speed 0.5 c, from planet A to planet C, which are distant from each other by 4 light-days. During the flight the rocket passes the planet B, located exactly halfway between planets A and C. At the time of passing the planet B, from the rocket and from the planet B are simultaneously sent SMS messages to the planets A and C. SMS sent from the planet B reaches the planets A and C at the same time, in two days. Question, when the SMS sent from the rocket, will be received on the planet A and the planet C, respectively. Thanks. This is not a homework.

Suppose a traveller has slowly approached a 3-solar mass non-rotating black hole, & is now hovering near it at 3 times the Schwarzchild radius. He now commits suicide by switching his engines back on so that he begins to slowly drift towards the black hole. How many minutes of his time pass before he hits the singularity? How many kilometres in his reference frame will he have travelled? Or are black holes infinitely many kilometres deep?

The speed of light is 299,792,458 metres per second, Let's assume the distance between Point A and Point B is 299,792,458 meters away. Let's assume two scenarios happen. One: Light leaving Point A travels in a straight line WITHOUT encountering a massive object. It should arrive at Point B in 1 second correct? Two: Light leaving Point A travels in a straight line BUT encounters a massive object. It should arrive at Point B in >1 second correct? My question is this. Did scenario two slow down? Let me offer this theory. Light that bends warps spacetime. I believe both scenarios would arrive at Point B at the exact same time. Why? Because when light bends i…

It seems that GR claims to know that space and time exist. Not only that it claims to know the nature of space with out providing any proof that space exists in the first place. My reasoning goes something like this, if we ask the questions does space exist? we might answer it by saying that it does and we might give our description of what we think space is. classical physics will call it a volume. But let's say we remove all the matter in the universe are we still left with space? Some (I think Mach) have said that, no if matter is missing there is no space. Even if this is un true, whatever our concept of space is, does it not fall on GR to give us a working definition…

Hypothesis: If gravity is not instantaneous then any two masses travelling parallel to one another will not only converge, as one would expect, but they will also decelerate against the axis of their mutual forward motion, violating the law of conservation of momentum. (Their CM frame will slow down, even though there are no external forces on the objects in that frame). Hypothetical reason: Both objects will be "experiencing the arrival of" some gravity from the other object, but it will have been "time-lagged" (i.e. delayed in it's arrival by the constraint that gravity is not instantaneously acting at a distance--that it, for instance, propagates a the speed of…

Several things I don't get: 1. Can we say that every event in the universe is causally connected to the big bang? 2. Can inflation cause 2 time-like events to become space-like? In a flat universe, inflation could cause 2 locations to not be in any single light cone*, right? And thus there is no single event that could be causally related to both. So does that mean that inflation prevents various locations in the universe from having a common causal source (and thus the answer to question 1 would be "no")? Or does it mean that inflation allows 2 events that are not in any single light cone, to have a common causal source? I think what I'm asking is "Does in…

Suppose we're considering the velocity of a point P relative to an observer O. P's velocity can be expressed as a change in the distance to P as measured by O, divided by the change in time as measured by O. It can also be expressed as a change in the distance measured by P, divided by the change in time of P. These two velocities are the same value; the speed that O measures P approaching is the same speed that P measures O approaching. If we're talking about everything from O's perspective, do these 2 velocities have different names? That is "change in locally defined distance over local time" vs "change in remotely defined distance over remotely defined time"…

Question about gravitational time dialation Could one say that: as a light ray bends around a large body of mass that, the distance (space) between the photons stretches and/or bends towars the gravitationally massive object?

So if one person travels at 99.99 percent the speed of light near Earth for one second, then people on Earth would measure one second and observe that the person traveled nearly 99.99% of 186,822 miles but the only problem would happen is that the person traveling 99.99% the speed of light would be a few seconds younger than everyone else? Also, if two people traveling at 99,99% the speed of light are right next to each other, will they not see each other's time slowing down because they are not traveling 99.99% the speed of light faster than each other relative to each other?

Where and when (in schwarzschild coordinates) is the white hole which appears in the eternal singularity model? Or if we want to avoid the mis-behavior of Schwarzschild coords, where and when is a region of comparatively low curvature outside of the white hole? Hmm, this is harder to word than I thought. I guess what I'm trying to ask is, were there to exist an eternal black hole like those dealt with in Schwarzschild geometry, where would I -- a roughly inertial observer in a very weak field -- look to try and find it? In watching this Kruskal diagram: It looks like it's at [math]t=-\infty[/math] and in the same place as the black hole. Or would it only be at […

If you did hypothetically travel at the speed of light, for some reason people think time would stop, but if time stopped, wouldn't you not be traveling distance over time and therefore not be traveling at the speed of light? In fact, wouldn't you be traveling distance in 0 time making your speed actually instantaneous?

In case you can't read my handwriting, this is what it says. "Satellite orbiting sun at a distance of 10,000 AU. Satellite completes one circuit every 365.25636 days, travelling at 99.35 percent the speed of light, but maintains a constant distance from the earth. Not counting time dilation incurred during transit to this distance, or acceleration to this speed, and reckoning only from the moment the satellite receives a confirming signal from the earth... would the satellite's clocks experience time dilation (relative to the earth)?" NOTE – I'm aware that the satellite couldn't actually be orbiting at that speed and at that distance; Kepler's laws demand that the…