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August 6

Equivalence principle

I am no physicist, so I apologise in advance for incorrectly used terms.

I was reading the article about general relativity and got confused by it declaring free fall and inertial motion indistinguishable. So I read more on the subject and thought about it.

One of the common examples is a free-falling accelerometer, which would fail to measure acceleration from gravity. This is because all its parts receive the same acceleration. We can generalize this into a concept of "uniformly distributed" acceleration: the acceleration of any part of the system (no matter how small) received from external sources is equal to the acceleration of the system as a whole. And indeed, a system under "uniformly distributed" acceleration would appear indistinguishable from inertial motion.

But here arises the problem with gravity: usually (if not always) gravity fields are curved and thus "uniformly distributed" acceleration is possible only along lines that are perpendicular to the gravity field. Imagine an experiment: any two objects that are not on the same "gravity line" are freely falling. With sufficiently precise measurement of these two objects we can deduce the curvature of the gravity field and from it - mass of the gravity-causing body. The equivalence principle does not hold.

The question is: why does it not hold? Is the principle not applicable here? If so, then why? Is the system of such two objects (no matter how close they are) not considered "local"? Or do we, in our precise measurement, pass the margin of error allowed by the principle?

Also on an unrelated topic: are there gravity fields that are not curved?

178.94.238.17 (talk) 09:07, 6 August 2016 (UTC)[reply]

As it happens, exactly the same question occurred to me back in 1976 when I was reading Honours Astronomy at the University of St Andrews. The answer I received from a physics lecturer was that, as you suspected, detecting the curvature of a field would require measurements at two (or more) points with some separation perpendicular to the field/direction of motion, and this is not considered "local" within the terms of the equivalence principle. {The poster formerly known as 87.81.230.195} 2.123.26.60 (talk) 12:31, 6 August 2016 (UTC)[reply]

"Are there gravity fields that are not curved?"

Well, a uniform field is quite enough for some applications. Said otherwise, the Earth is flat as a first approximation. Now, of course, there is no infinite homogeneous plane of matter in the universe, so all gravity fields are curved to some extent. Tigraan^{Click here to contact me} 15:29, 6 August 2016 (UTC)[reply]

Inside a hollow sphere, Newton's Shell theorem shows there should be a zero gravity field arising from the sphere itself (given ideal circumstances), so that would not be curved. Might it be possible to construct a large object in space shaped in such a way as to produce a flat field in a limited volume? {The poster formerly known as 87.81.2301.85} 2.123.26.60 (talk) 09:51, 7 August 2016 (UTC)[reply]

See [1] Robert L. Forward How to flatten spacetime. A ring of mass about an object with the ring's axis intersecting the gravitational source can flatten space. Popularized in the novel Dragon's Egg. Jim1138 (talk) 10:02, 7 August 2016 (UTC)[reply]

D'oh! And I've read it, too, though admittedly 36 years ago when it was first published. {The poster formerly known as 87.81.230.195} 2.123.26.60 (talk) 21:02, 7 August 2016 (UTC)[reply]

Insect identification

Can anyone identify this little friend? Someone suggested to me that it might be some sort of longhorn beetle, which looks plausible, but that seems to be a large taxon so maybe someone can be more precise. It was seen yesterday in northwestern Montana, at about 4400 feet elevation. --Trovatore (talk) 20:17, 6 August 2016 (UTC)[reply]

Cosmosalia chrysocoma from the look of it [2]. Mikenorton (talk) 21:04, 6 August 2016 (UTC)[reply]

Thanks, that may well be it. --Trovatore (talk) 21:12, 6 August 2016 (UTC)[reply]

If we both started in the Devonian, would arthropods or humans have created more faeces if we counted them at present day?

So, let's suppose that all of humanity and extant arthropodity have been deposited on earth 419.2 million years ago. Both groups have turned immortal. Humans are all perfectly healthy and so produce the healthy amount of poo every day. We eat some magical substance that makes our digestive systems work perfectly. Arthropods have a normal production rate too (do arthropods get constipation? That would be interesting to know!) and if some groups don't create faeces, then any waste product created is counted as poop. All of them are also fed on this magical substance too. Neither of the groups can reproduce so populations stay the same. Our faeces don't disintegrate in any way and they are stored in a gigantic warehouse (another question, how big would this warehouse have to be to contain all our poop?).

Once we reach present times, we compare the sizes of the of the two piles of poop. Which is larger? I know this is a huge question but it is something I'd like to know. Thank you for reading, Megaraptor12345 (talk) 22:59, 6 August 2016 (UTC)[reply]

Perhaps I'm missing something: the ratio seems to be the same if you count only what humans and arthropods produce in one (recent) year, so why the Devonian? —Tamfang (talk) 05:28, 7 August 2016 (UTC)[reply]

If we began in the Devonian, and after 419.2 million years we compared the sizes of the piles, which would be larger? That's basically what I'm asking. I made so far back because I wanted to find out how big the warehouse would have to be. Megaraptor12345 (talk) 15:31, 7 August 2016 (UTC)[reply]

I would have to say arthropods considering that, as mentioned in Arthropod, "[t]hey have over a million described species, making up more than 80% of all described living animal species, some of which, unlike most animals, are very successful in dry environments." Factoring out poop size difference between humans and arthropods, I wager they have us beat on numbers alone. RegistryKey^(RegEdit) 16:03, 7 August 2016 (UTC)[reply]

Biomass matters more than numbers, but the total mass of krill on Earth comes to around 10 times the biomass of humans, so even on that scale arthropods are likely to generate a lot more. Looie496 (talk) 16:33, 7 August 2016 (UTC)[reply]

@Looie496; So, with my original question answered, how big does the warehouse have to be then? Megaraptor12345 (talk) 17:14, 7 August 2016 (UTC)[reply]

Megaraptor12345 That's a bit of an unknown because of the factor of humanity existing since the time period you gave, as opposed to as long as we have now. That said, for comparison I did some basic math. Assuming world population of about 7.5 billion, each person pooping twice a day, each stool being 8 inches long, gives us 12 million feet if placed end-to-end, and that's just over the course of one day! Assuming the Denovian period started 419 million years ago and that static 7.5 billion human population, we now have 1,529,350,000,000,000,000,000 feet of human waste we need to find a home for, or about 48,274 light-years. RegistryKey^(RegEdit) 19:17, 7 August 2016 (UTC)[reply]

@RegistryKey Thank you!!! That's amazing. How are we gonna contain all that poop if we live for another 419 million years (which I presume we will)?! Anyway, there's one last tiny question unanswered: do arthropods get constipation? Thanks again, Megaraptor12345 (talk) 21:16, 7 August 2016 (UTC)[reply]

We are not going to 'contain' that poop, User:RegistryKey, it is biodegradable and so it is going to be used by plants to feed on, and then we will eat the plants, or eat the animals who have eaten the plants. It cycles. --Lgriot (talk) 12:25, 9 August 2016 (UTC)[reply]