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14

Have a look at the article by Phil Gibbs on the relativistic rocket. This describes the motion of a rocket that is accelerating with a constant acceleration. In this context constant acceleration means the crew of the rocket feel a constant acceleration. Technically the rocket has a constant four-acceleration. Anyhow, the velocity of the rocket as observed ...


13

We do. The LHC accelerates two protons, each with 3.5 TeV of energy, giving a total of 7 TeV in the CoM frame (The energies are from the previous LHC run which discovered the Higgs. The energies are doubling now for Run II). The main reason for this is as you mentioned, the energy involved. In any frame, we have the following invariant quantity, $s = (p_1 + ...


6

Is there some other formula ... which ... does not allow the speed ... to surpass the speed of light? That would be the equations of special relativity mentioned by sahin in a comment. Image from Loodog? Another factor you have to take into account with classical mechanics is to work out how a constant force can be applied to your object over 11 ...


5

Many modern particle accelerators do accelerate both particles towards each other. LEP accelerated electrons and positrons in opposite directions in the same chamber, and the Tevatron did the same for protons and antiprotons. The LHC is a proton-proton collider, and so it has two stacked rings that accelerate protons in different directions. For the BaBar ...


3

Relativists tend to use the proper time, $d\tau$, and the proper distance, $ds$, interchangably. If you're working with proper time you'd expect the equation for it to look like: $$ d\tau^2 = dt^2 + \text{other terms} $$ while if you're working with proper distance you expect: $$ ds^2 = dx^2 + dy^2 + dz^2 + \text{other terms} $$ The sign problem comes ...


2

Let us take a uranium nucleus being hit by a neutron .At the rest mass system of the two bodies there is an invariant mass m described by E=m*c^2. The CM system, seen as an excited U236 in the diagram below, is not moving in three dimensions nor in any other dimensions, velocity needs a dx/dt. An induced fission reaction. A neutron is absorbed by a ...


2

From the reference frame of the space ship, your body is stationary. When you swing your arm back and forth, it has a non-zero speed in this frame, and thus its mass, or rather momentum, increases. The space ship's velocity of $v_\mathrm{ship} = 0.866c$ doesn't add to this. That means that the increase in momentum is exactly the same as if you swing your arm ...


2

We conclude that the lenght perceived by the observer in S is bigger than the lenght perceived by the observer in S. No, that would be an error. Why? The short answer is that the coordinate difference $(x_2 - x_1)$ is not a length in S. A length is the (spatial) coordinate difference at the same coordinate time. To be clear, there are two events - ...


1

Yes, I do believe there is and that is the approach I outline in my answer to the Physics SE equation "What's so special about the speed of light" as well as my answer here. I like to think of SR as simply Galileo's basic idea but with the assumption of absolute time relaxed (not to devalue Einstein's bold step in making this relaxation). One begins with ...


1

Complex mass means gravitational mass + i.lambda.higgs mass. The weak coupling constants are all proportional to (higgs) mass with Higgs vacuum value (=246 GeV) as the proportionality constant. Thus mass necessarily becomes a complex number. The real part produces attractive gravity forces and the imaginary part produces repulsive "weak" forces. The factor ...


1

I'll give this a shot. I think I follow what you're asking. I'm thinking of the to-be-fissioned-away material as a mass traveling at the speed of light in some sense, In a sense that's true, but it's probobly good to keep in mind that time isn't a dimension quite like the other 3 and traveling through time isn't exactly moving, so in a sense it's ...


1

Pressure is a single component of the rank-2 stress-energy tensor; it isn't a Lorentz scalar and observers will disagree about the pressure of a gas in a box. You say that the box might explode (perhaps the walls of the box break) if the pressure exceeds a critical value. Perhaps, then, observers disagree about whether an explosion occurs? I don't think ...


1

$g$ denotes the metric. For Euclidean space the metric is just the unit matrix $I$. For Minkowksi space, which is of interest when talking about the Lorentz group it's the Minkowski metric $\eta_{\mu \nu}$. The lower right matrix inside the Minkowski metric is the 3-dimensional unit matrix and therefore for the space-like components of the Minkowski metric ...


1

Look at sparknotes.com/physics/specialrelativity/dynamics/…, you can see $dE/dx=F$ - if your force is constant, it is the energy that increases constantly. $E=\gamma(v)m_0c^2$, you can deduce the $v$. Beacause of laziness I used mathomatic, and it gives me something like this: $v=c\sqrt{1-\frac{m_0 c^2}{(F\cdot x + m_0 c^2)^2}}$ If you check it for x=0 and ...



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