3 ms·

I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which m

I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which means that anything that has energy associated with it (i.e., everything we've ever observed) affects the gravitational field. Examples: A compressed spring weighs more than the same spring in an uncompressed state. A box of light (e.g., a box with perfectly reflective mirrored walls) weighs more than the same box without light, despite the fact that photons have zero rest mass. The bulk of a proton's "effective mass" is due to the kinetic energy of the quarks that comprise it. The joint earth + moon system weighs less than if you added up each component weighed in isolation. The other interesting fact is that the Heisenberg Uncertainty Principle is commonly misunderstood to mean that you can't simultaneously measure the position and momentum of a particle. In fact, you can indeed obtain partial information on both properties at the same time, and there's quite a few papers out there describing how to perform joint measurements of incompatible observables. What HUP more accurately entails is that, for a quantum state corresponding to a specific system, you cannot obtain complete information about the two properties — no matter what you do. This is because performing a position measurement destroys your ability to perform a subsequent momentum measurement (on the same system) and vice versa. One of the postulates of quantum mechanics is that measuring a system collapses it into an eigenstate of the observable corresponding to the type of measurement that was performed. Since the position and momentum operators don't commute, it's not possible to put the two into a joint eigenbasis (they can't be simultaneously diagonalized).

sls 8y ago
Since you obviously like this sort of thing, let me point out that quantum uncertainty isn't simply a factor of measurement/observer effects[1][2]. (The only part of what you said that I am addressing by this is the "this is because" section.) [1] https://www.nature.com/news/quantum-uncertainty-not-all-in-the-measurement-1.11394 https://www.nature.com/news/quantum-uncertainty-not-all-in-t... [2] https://en.wikipedia.org/wiki/Uncertainty_principle https://en.wikipedia.org/wiki/Uncertainty_principle
- Xcelerate 8y ago
  Yeah, you may also find interaction free measurements interesting (https://en.wikipedia.org/wiki/Interaction-free_measurement https://en.wikipedia.org/wiki/Interaction-free_measurement).
noobermin 8y ago
I'll temper your statement about uncertainty. You can measure whatever you want, but if your observables are incompatible, you can't say it's still in the eigenstate you measured it in afterward each measurement. Then again, people have to explain what it means when they say "measure at the same time" means. If it means "system A is in eigenstate |1> and eigenstate |a>" where |1> and |a> are eigenstates of different (non compatible) operators the answer is no.
russdill 8y ago
Isn't the system collapsing a part of the Copenhagen interpretation, not an actual postulate?
voidmain 8y ago
> I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which means that anything that has energy associated with it (i.e., everything we've ever observed) affects the gravitational field. And not just energy, but tension. And tension is a signed quantity! Imagine that you go out into deep (flat) space and build a large disk out of unobtanium, an extremely strong and rigid material. The ratio of the circumference to the disk to the radius is exactly pi. Now imagine trying to bring the disk to Earth's surface. Here space is curved by gravity, so the radius of a disk is just a bit longer relative to its circumference. So the disk has to flex! If it is rigid enough, it will want to spring back into flat space to minimize energy. You could imagine adding some gearing that would let you control this (anti-)gravity effect at will. Calculating the material strength needed to make this effect usefully strong is left as an exercise to the reader. (Disclaimer: this makes sense to me, but I am not a licensed antigravity engineer)

sls 8y ago

Since you obviously like this sort of thing, let me point out that quantum uncertainty isn't simply a factor of measurement/observer effects[1][2]. (The only part of what you said that I am addressing by this is the "this is because" section.) [1] https://www.nature.com/news/quantum-uncertainty-not-all-in-the-measurement-1.11394 https://www.nature.com/news/quantum-uncertainty-not-all-in-t... [2] https://en.wikipedia.org/wiki/Uncertainty_principle https://en.wikipedia.org/wiki/Uncertainty_principle

Xcelerate 8y ago
Yeah, you may also find interaction free measurements interesting (https://en.wikipedia.org/wiki/Interaction-free_measurement https://en.wikipedia.org/wiki/Interaction-free_measurement).

noobermin 8y ago

I'll temper your statement about uncertainty. You can measure whatever you want, but if your observables are incompatible, you can't say it's still in the eigenstate you measured it in afterward each measurement. Then again, people have to explain what it means when they say "measure at the same time" means. If it means "system A is in eigenstate |1> and eigenstate |a>" where |1> and |a> are eigenstates of different (non compatible) operators the answer is no.

russdill 8y ago

Isn't the system collapsing a part of the Copenhagen interpretation, not an actual postulate?

voidmain 8y ago

> I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which means that anything that has energy associated with it (i.e., everything we've ever observed) affects the gravitational field. And not just energy, but tension. And tension is a signed quantity! Imagine that you go out into deep (flat) space and build a large disk out of unobtanium, an extremely strong and rigid material. The ratio of the circumference to the disk to the radius is exactly pi. Now imagine trying to bring the disk to Earth's surface. Here space is curved by gravity, so the radius of a disk is just a bit longer relative to its circumference. So the disk has to flex! If it is rigid enough, it will want to spring back into flat space to minimize energy. You could imagine adding some gearing that would let you control this (anti-)gravity effect at will. Calculating the material strength needed to make this effect usefully strong is left as an exercise to the reader. (Disclaimer: this makes sense to me, but I am not a licensed antigravity engineer)