Recent content by Jehannum

I read that Euler used to write "it is obvious that ..." for stuff that took him months of labour.

While working on a probability problem I accidentally found this relationship: $$\frac a b = \frac a {(b-1)} - \frac a {{(b-1)}^2} + \frac a {{(b-1)}^3} - \frac a {{(b-1)}^4} + ~...$$ I have done a bit of work on it myself, and have tried to research similar series. It seems to lead to some...

In a proof of a theorem or in mathematical writing generally, if there is a statement of a sub-theorem, does a proof always need to be given if 'obvious' or if obtained by inspection? Is there a way of saying "I got this by trying some numbers in a calculator and the pattern was clear"? The...

Everybody's always so amazed that e to the i pi is -1. Huh! I've just discovered that i is actually equal to e. Try it yourself. Put -1 into a calculator and press the square root button.

It's desirable that propane and butane be interchangeable as fuels in gas-burning appliances. However, butane has a higher calorific value. If used at the same pressure as propane it would give a higher heat output. My guess was that the reason propane is set to a higher pressure is to offset...

The wave function is a mixture of all possibilities, at least one of which would contain conscious observers. Note: I was only kidding about this.

In a superposition of wave functions of the universe, one of them would contain a conscious observer that could cause collapse. Consciousness is therefore inevitable! Not that I think any of this is true, I hasten to add. It's just an intriguing idea I heard a long time ago.

Thanks. I think I would have to describe the measurement as "automated". The measuring device would have to stay in exactly the same place and not be touched until the end of the test (partly down to safety reasons - i.e. exclusion zone). As far as I understand it, a micrometer can't work this...

Ideally, the method should be accurate down to 0.01 millimetres or better. We're probably talking pipes of up to 150 mm (6") diameter. Accurately measuring the actual diameter of the pipe is of less importance - it's how much it expands that matters. My idea is wrapping something around the...

Is it suprising that something normally taken to be non physical (the wavefunction regarded as a probability amplitude) has a physical manifestation (electric / magnetic field oscillations)? What's the deeper reason behind this? Are there any other instances where classical and quantum are the...

Sorry for the delay in replying. I sometimes have "social issues", i.e. embarrassment at having asked a stupid question and it takes me a while to pluck up the courage to peek at the replies. The reference is a quiz question on Brilliant.org (quantum mechanics). Edit: I got the question wrong...

A SG device oriented along z-axis is used to prepare a stream of spin up particles from a randomised source. These are then passed through an x-axis SG device. If their spins were to be measured now they would be 50% left, 50% right. But instead, the two beams are recombined and passed through a...

The classical picture of the electromagnetic wave has electric and magnetic field oscillations which give the wavelength of the light. In the quantum picture, is the wavelength of the (de Broglie) wave function of the photon the same thing?

I was sure I put a question mark in the original title.

I went with this one. 55 pages in so far, and it's exactly what I was looking for.