Recent content by Matternot

https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates#Del_formula

In this case, it seems clear that they expect you to assume that locally, coordinates are Cartesian and hence, a bearing is probably what they expect. i.e. North is y axis, East is x axis.

It's important to remember that not only with other students be out of practice, but additionally many international students will not have studied many of the topics that you studied at A-level. As a result, the mathematics courses in first year of undergraduate are often self contained. i.e...

Locally, it is possible to express coordinates on the surface of a sphere with Cartesian coordinates and work with those, but it seems unnecessary. There is an easier solution. Perhaps try drawing a diagram. Also, the angles in a triangle on the surface of a sphere don't add up to 180°...

If you draw a graph of y=sin(x), where x is the phase in radians, think about when this function repeats itself.

Vitro is correct The problem of whether she measures the clock run faster or slower depends on how she is measuring. When writing the original problem statement, the subtleties between the words see/view and measure were not immediately apparent to me. Typically when considering the time...

Whether The muons are traveling towards the Earth at a speed very close to the speed of light, in the same way the planet is moving towards alice at very close to the speed of light. The lifetime of the muons are extended according to people on earth. But I am certain where the confusion is and...

The wave function need not be a pure sinusoid, but instead a solution to Schrodinger equation for the system in question which may be exponentials e.g. a free particle with energy higher than a constant potential or sinusoids (a free particle with energy lower than a constant potential) or a...

The first thing would be to ask yourself what the phase of a wave means. from your equation for the phase difference you've shown how you might calculate the phase of a oscillation, but what does it mean? Drawing a graph of position against time for an oscillation might come in handy when...

I think I understand the disagreement. I think the disagreement occurs when thinking about measurement vs 'observation' and how she records time. I mostly think about an array of clocks in space that are synchronised by setting the time to a distance d/c from a reference clock and emitting a...

There is plenty of doubt about the theory here. So let's ignore theory for a moment and instead think of example. Muons form in the upper atmosphere and travel toward the Earth. They typically have a lifetime of about 30ns at rest ⇒ they should never reach the surface of the Earth... yet they...

Perok's point is not that it's difficult to use movement of photons, but that by imagining the movement of photons instead on differences in the time observers measure, you can distract yourself from the fundamental nature of time. If Alice focused on the planet she would see the clock on the...

If you draw the spacetime diagram from the perspective of Alice, the result becomes more apparent. The frequency of photon release would be lower for her. She takes into account the distance the light had to travel to reach her in order to calculate when the photon was released. It is obvious if...

But despite Bob and Alice's clock both reading 0 at the instant she passes Earth, Bob sees this as simultaneous with the clock on the planet reading 0. Alice does not. Same time, but different point, (There is relativity of simultaneity). Since the event of Alice passing Earth and the planet...

Of course! How foolish of me! This makes plenty of sense! I mostly used that to align co-ordinates. But when considering the time Alice reads on the planet at τ=0 at the time she thinks she passes Earth, it isn't zero. I have questioned my instinct that the clock will run slow after considering...