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A related question to stump a physicist is what does a polarised photon look like

You're right, he has to accelerate to take off too, that's true. Thank you, I didn't even think of that.

> The paradox itself was not that the twin's experiences are different, rather than the one who traveled more, aged less.

No, sorry. The paradox is the fact that depending on which twin you take as a reference frame, each twin would age more than the other.

The Wikipedia article on this is quite good. If you want some intuition for this, you have encountered things that work kind of like this in your daily life: cups of water.

1. Take two different cups of water, cup A and B. As long as they are kept separate you can kind of label them by the cup they are in.
2. Pour them into the same container. Now you know that you have two cups of water, but it does not make sense to ask which is which.
3. Pour the water out into the two cups again. You can not say whether the current cup A is the same as the first cup A.

That particles act like this has huge consequences for any physics that depend on how many different states are available to the system. Consider two distinguishable particles: 1 and 2, that each can be in one of two states: up or down. There are four possible states:

1. 1 up, 2 up
2. 1 up, 2 down
3. 1 down, 2 up
4. 1 down, 2 down

If they are indistinguishable there are only three states:

1. Two particles are up
2. One is up and one is down
3. Two are down

This is a pretty big thing, and has macroscopic consequences! Distinguishable particles follow Maxwell-Boltzman statistics while indistinguishable particles follow either Fermi-Dirac or Bose-Einstein statistics. Identical particles of the first group are called fermions and the second bosons. Fermions have the property that two fermions can not be in exactly the same quantum state, and since protons, neutrons and electrons are fermions this is partly what gives matter "solidity". Bosons can all be in the same state, allowing for things like laser light and Bose-Einstein condensates.

Thank you, that is a really usefull answer.

> So the two twins' elapsed times will depend on how fast they are moving with respect to this preferred frame.

In any case (any choosen frame), the one travelling would move faster, right?

So are there really different photons or are all photons the same photon that we just perceiving as different photons ?

I've always taken the explanation that "light is a propagation of a wave in the electromagnetic field, and it propagates slower through a medium than a vacuum." So from my viewpoint, its not that the photon is slowing or being absorbed and re-emitted, its simply that the speed of light in a medium is less than a vacuum. Is there a reason this interpretation would be wrong, or just yet another way to think about it?

And finding out that Legionella was the main cause was also very lucky as the Hotel had started to clean the ventilation shafts before a proper investigation of them had started.

What I think most the posts right now are missing that condensation itself isn’t enough to sustain life. Moisture is only one part. There is a lot of dust in the air that gets sucked into the vents. Usually hvac systems blend a mix of inside and outside air. Indoor air has a lot of things like skin cells, fibers from clothing and carpets. Outdoor air has dust air pollution pollen and other stuff.

Commercial hvac systems in theory have filters, but they aren’t perfect filters, and roof mounted systems are notorious for having old dirty filters, missing or not properly placed so they intake a lot of unfiltered air.

All that stuff settles in the vents, add moisture and it’s a perfect combination for bacteria to grow. Especially in poorly maintained systems they might have other mechanical issues, such as condenser coils that don’t run a defrost cycle long enough or often enough to prevent the formation of ice or excess condensation build up. Burnt out uv lamps in some commercial hvac systems.

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https://en.wikipedia.org/wiki/Legionnaires%27_disease#Epidemiology

Elderly men, possibly with a large proportion of smokers or ex-smokers. It had been thought the outbreak was a form of pneumonia.

They inhaled atomized water droplets from the cooling towers that carried the bacteria.

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About the fungible particles thing - an interesting tidbit is that physicists had hints about this way before QM was formally developed. If you look up the derivation of the sackur-tetrode equation, they had to reduce by a factor which removed the states which could be accounted for by swapping particles (e.g. because of their uniqueness via a label). This correction turned out to be absolutely correct in deriving the entropy of an ideal gas (and more importantly, validating the extensiveness of entropy). Gibbs new about this a long time before it was formally resolved - see Gibbs' Paradox. Fascinating if you ask me

Edit: and this was roughly late 1800s, for context

You've got titanium nitride coated drillbits sitting on what looks like a velvet-like cloth. Titanium nitride is triboelectric. You're generating a shittonne of static electricity just by moving it around on the cloth from the triboelectric effect, every time you touch the two together it's discharging, producing a broadband source of RF.

I'm betting if you attached a ground wire to both drillbits and got rid of the cloth you'd see nothing or next to nothing.

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I saw an explanation which said since light is an EM wave it moves electrons when it passes. The wave of the electrons moving is a slower wave which when combined with light makes it slower.

Or something similar to that

As I said, so long as it's the same type of liquid you absolutely can. The weighted average for equal portions simply would be the average

But if you have different liquids that doesn't work because different liquids can store different amounts of heat

>their wave functions overlap

But their wave functions always overlap?

My, understanding was that the "event" that they spontaneously switch, placesis quite low, but always non-zero, and more importantly, indistinguishable from staying still.

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I think the point you are missing is that the universe is (statistically) the same everywhere. This means that there will always be light reaching you from some distance -- and hence some time -- and the objects that you see at that distance/time have similar statistics to what happened in our own past.

Did the bacteria enter the hotel's ventilation system? Aren't they sealed off from each other? I'm picturing my home cooling unit and an invasive element would have to penetrate the metal coil to get into the house, and repeat that to access the air.

There is exchange energy for bosons and it is attractive: https://en.m.wikipedia.org/wiki/Exchange_interaction

Exchange interaction exists for bosons and it is attractive: https://en.m.wikipedia.org/wiki/Exchange_interaction

Explains the superfluidity of helium-4, for example

Thank you a lot once again, you explained it clearly for me and i hope i understood it right, but i have a question still if you can, shouldn't allele dominance solve the issue? As in, we have an allele of each gene encoded in each X chromosome, if each gene has a dominant allele that is expressed and a regressive one which is not, wouldn't that mean that the total expressed wouldn't surpass the genes of one X chromosome? Or is co-dominance going to create enough duplicates for it to be troublesome, i know allele dominance is way more complex than that but I'm wondering where I'm being wrong.