Recent content by Mikeal

The above derivation confirms the result I came up with a while ago and explains the steps involved. Thanks.

A few years ago I was studying special relativity and came across a thought experiment that explored a faster-than-light causality-flip. It consisted of an observer on the track-side firing a bullet at a speeding train, with the bullet entering the back of a carriage and exiting the front. There...

This is what I'm having a problem with. The guy was a gifted and well respected scientist and we're supposed to believe that he floundered around until he had a epiphany (i.e. discrete energy values) which even he admitted, had no scientific basis at that time. That's not the way that scientists...

I've read several articles discussing how Max Planck decided to assume that the energy radiated by oscillators in a black-body came only in discrete increments of En = nhf, where n is an integer. Using this concept, he determined that the average energy of an oscillator was given by...

The solutions to the Friedmann-Lemaitre equations have curvature values of K = -1 (open universe), 0 (flat universe), +1 (closed universe). The corresponding critical density values at the current time are: ρc(k = -1), ρc(k = 0) and ρc(k = +1) If (k = 0) and the current density is less than...

Events (0,-5) and (0,5) reside -5 and +5 space units to the left and right of Event (0,0), but zero time from it. In other words they are simultaneous with Event (0,0). My understanding is that they cannot have a causal relationship with Event (0,0), or each other, due to the finite speed of light.

I decided to re-visit special relativity and spacetime. All went well until I reached the subject of time-like and space-like events and their relation to causality. Time-like Events The residual spacetime value between two time-like events is defined as: ∆S = √(c∆t)^ - ∆x^2, where c∆t > ∆x...

Thanks. The interesting thing is that Wien used a similar approach and came very close. His formula fit experimental results at wavelengths shorter than 10E06 meters and deviated only slightly at longer wavelengths. Down to 10E2 meters, you need a log-intensity scale to see it. I'm still not...

According to the documents I have read, Plank made two changes to Rayleigh-Jeans approach in order to produce an equation that matched the black-body radiation, experimental curves: 1) As a mathematical convenience he assumed that the oscillators in the walls of black-body cavity could only have...

I understand photon absorption/emission by electrons in atoms, that transition them between energy levels, producing sharp spectral lines. However, I am having difficulty understanding photon absorption/emission by the vibrational and rotational modes of molecules, with respect to black body...

Thanks. I am beginning to get there by considering particular solutions to the time-dependent version of the Schroedinger equation. I also checked the references and that helped.

I have read a number of books on quantum mechanics and I am now at peace with the idea that the wave-function of an electron instantaneously populates the universe with finite probabilities that the electron will be detected at a given point, if a measurement is conducted at that point. However...

Good. Thankyou for taking the time to help me with this issue.

And so taking it to its logical conclusion, the proper distance between two space-like events is equal the the spacetime distance between them. This is true even when the spacetime distance is measured by an observer in a frame that doesn't determine the events to be simultaneous?

I agree with the invariance part as that is the point of computing spacetime distances as opposed to t,x coordinates. I also agree that for a given spacetime distance of a space-like event pair there is a frame in which t will be determined to be zero (events simultaneous). But there will also...