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This is a poor question because your rest mass does not increase when you climb 30m. However I can see how the examiner expects you to answer. If your mass is m then your energy when static at the bottom of the building is $mc^2$. To climb a distance h you have to hav work $mgh$ done on you, so your energy is now $mc^2 + mgh$. So the percentage change in ...


5

I believe John's answer is sufficient to guide you through the question. My answer will try to pinpoint your mistake in your working. Your working is mostly correct except the ratio $\frac{m_{rel}}{m_{rest}}$. To get the correct value for $\frac{m_{rel}}{m_{rest}}$, use Taylor expansion: $\frac{1}{\sqrt{1-\frac{2gh}{c^2}}} = ...


4

You might be confusing some issues. In special relativity, space and time do not stretch or compress. It really comes down to measurements with clocks and rulers made by people that are moving uniformly with respect to each other. One option that is consistent with observations for SR is that there is one family whose clocks and rulers are right and ...


3

Deceleration is a "special case" of acceleration. More precisely, acceleration is given by the vector $\vec a$ which has both a magnitude and a direction. Sometimes the same vector $\vec a$ increases the velocity $\vec v$ – when they are oriented in "mostly the same direction" – and we speak about "real acceleration" in the sense of an increasing speed. And ...


2

You can find some information about that on John D. Norton's website. Einstein thought of this at the age of sixteen. Here's another article: "If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such ...


2

So Special Relativity states that for all non-accelerating objects of matter the laws of physics are the same. I think the point is just that the constants and the time and space derivatives that appear in a law of physics should not have to change the form of the equation if you measure the time and the space in two frames that move relative to each ...


2

General relativity is a theory that tells us the geometry of spacetime. However it predicts that in some situations the geometry of spacetime is undefined - this happens when we get a singularity. There is a singularity at the centre of a black hole, and the Big Bang was also a singularity. So we have the odd situation that the theory of general relativity ...


1

The axis of simultaneity, or in other words, the set of events which are simultaneous as measured in the rest frame of the ship, does indeed change suddenly when we turn back. This is because it depends on your reference frame. There isn't a single inertial frame that stays with the ship for the whole journey; you can either accept that the frame is ...


1

Perhaps it's more illuminating to look at the whole thing in a spacetime diagram. we have the earth frame with coordinates $(t,x)$, and its trajectory through spacetime is the blue line. The trajectory of the spaceship is the red one. Straight worldlines are inertial frames of reference, curved or non-straight worldlines are non-inertial frames of ...


1

Imagine a space ship ran put of fuel and a second is going to help. They will do a docking maneuver to hand out some fuel. Now, the second ship has to adjust its speed when it's near the first (because the first can't change its speed). A passenger on the second ship feels the acceleration. But does the ship accelerate or decelerate? If the first ship ...


1

I understand the main question to be "What is the physical intuition/geometric consideration that led one to relate periodicity in space to momentum?". Or, in other words, why do we identify the physical property "momentum" with the mathematical operator $-i\hbar \partial/\partial x$? (This is essentially the same question, because the eigenfunctions of ...


1

The expansion of the Universe has no effect on the local speed of light. Any local measurement of $c$ will yield $c$, and $c$ won't change. There is one thing that often causes confusion about the speed of light or faster-than-light travel. A photon moving in an expanding space-time appears to move at an average speed faster than $c$. Consider a ...


1

There is a much easier way to solve the problem. Quick derivation: if something is moving past you at speed $u = \alpha~c$ then in a reference frame travelling at the speed $\beta ~c$ in that direction, the Lorentz boost puts its trajectory as:$$\gamma\begin{bmatrix}1&-\beta\\-\beta&1\end{bmatrix}\begin{bmatrix}c t\\ut\end{bmatrix} = \gamma ...


1

Yes, the energy and the increase in energy all depend on your reference frame, but this is NOT special to relativity! The same thing happens in classical mechanics. I wrote a similar answer to the question, "Can you tell your absolute speed in space?" Consider the regular Newtonian mechanics equation, $\mathrm{Ke}=\frac{1}{2}mv^2$. If you weigh 50kg, are ...



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