3 ms·

I wonder what the cut off speed is for relativistic speeds. If you think about it, it's not only a matter of speed but also how much precision you want in your

I wonder what the cut off speed is for relativistic speeds. If you think about it, it's not only a matter of speed but also how much precision you want in your calculations. Even if something was moving very slowly, you need to account for relatively if you want very accurate calculations.

quchen 4y ago
A rule of thumb in classical mechanics is that 0.1c is when you should start taking (special) relativity into account, I think it’s 0.5% contribution then. For general relativity I don’t know such a cutoff rule of thumb. Astronomy-wise, Mercury is the only planet that is obviously general-relativistic (its orbit is not an ellipse because it’s so close to the sun). On Earth, we don’t have strong/inhomogeneous enough gravity, so unless you’re synchronizing satellites or atomic clocks, GR is not something to worry about.
- thfuran 4y ago
  Some of the most precise clocks can actually measure precisely enough that a few feet of elevation change makes a measurable difference, which I expect also means that what you've placed under the table it's on also could.
  - deleted 4y ago
    [deleted]
- vkou 4y ago
  Mercury's orbit is absolutely an ellipse. It is incredibly elliptical, with an apogee of 69.8 million km, and a perigee of 46 million km. The relativistic effects on Mercury concern its precession - the way that elliptical orbit rotates [1] around the sun. And it's not caused by Mercury's speed (Which is only ~59 km/s at its maximum, compared to the Earth's 30 km/s). It's caused by spacetime being curved by the immense gravitational field of the sun. If Mercury had a circular orbit, it would have no precession. [1] Precession is akin to spinning a hula hoop around your body - with the hula hoop representing an orbit. https://en.wikipedia.org/wiki/Apsidal_precession https://en.wikipedia.org/wiki/Apsidal_precession
- joe__f 4y ago
  I think a good rule of thumb is 'check what accuracy you need your answer to, and then include all effects relevant to that precision'. If you needed an answer accurate to four significant figures, then you'd include relativistic effects for v < 0.1 c
  - bawolff 4y ago
    I don't think that fits the definition of rule of thumb.
    - asah 4y ago
      As a rule of thumb, I like to define my definitions first. /s
thfuran 4y ago
Even if something isn't moving at all (relative to your reference frame of choice), you might still need to care about local gravity's effect on time.
shagie 4y ago
You also get some relativity with some elements. Gold is the one that I recall most readily. Relativistic Effects and the Chemistry of Gold - https://link.springer.com/content/pdf/10.1007/BF03215471.pdf https://link.springer.com/content/pdf/10.1007/BF03215471.pdf > In atoms of high nuclear charge (Z), as a consequence of a relativistic effect, the s electrons of an atom become more bound and their orbitals smaller than if this effect were absent. Simultaneously, the d (and f) electrons are less bound because of this effect, which scales roughly as Z2. Gold exhibits a large relativistic effect. This accounts for gold being more resistant to oxidation than silver. It also accounts for higher oxidation states being more accessible in gold than in silver. These effects are illustrated by some fluorine chemistry of gold and silver. https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry > Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of gold: due to relativistic effects, it is not silvery like most other metals.

quchen 4y ago

A rule of thumb in classical mechanics is that 0.1c is when you should start taking (special) relativity into account, I think it’s 0.5% contribution then. For general relativity I don’t know such a cutoff rule of thumb. Astronomy-wise, Mercury is the only planet that is obviously general-relativistic (its orbit is not an ellipse because it’s so close to the sun). On Earth, we don’t have strong/inhomogeneous enough gravity, so unless you’re synchronizing satellites or atomic clocks, GR is not something to worry about.

thfuran 4y ago
Some of the most precise clocks can actually measure precisely enough that a few feet of elevation change makes a measurable difference, which I expect also means that what you've placed under the table it's on also could.
- deleted 4y ago
  [deleted]
vkou 4y ago
Mercury's orbit is absolutely an ellipse. It is incredibly elliptical, with an apogee of 69.8 million km, and a perigee of 46 million km. The relativistic effects on Mercury concern its precession - the way that elliptical orbit rotates [1] around the sun. And it's not caused by Mercury's speed (Which is only ~59 km/s at its maximum, compared to the Earth's 30 km/s). It's caused by spacetime being curved by the immense gravitational field of the sun. If Mercury had a circular orbit, it would have no precession. [1] Precession is akin to spinning a hula hoop around your body - with the hula hoop representing an orbit. https://en.wikipedia.org/wiki/Apsidal_precession https://en.wikipedia.org/wiki/Apsidal_precession
joe__f 4y ago
I think a good rule of thumb is 'check what accuracy you need your answer to, and then include all effects relevant to that precision'. If you needed an answer accurate to four significant figures, then you'd include relativistic effects for v < 0.1 c
- bawolff 4y ago
  I don't think that fits the definition of rule of thumb.
  - asah 4y ago
    As a rule of thumb, I like to define my definitions first. /s

thfuran 4y ago

Even if something isn't moving at all (relative to your reference frame of choice), you might still need to care about local gravity's effect on time.

shagie 4y ago

You also get some relativity with some elements. Gold is the one that I recall most readily. Relativistic Effects and the Chemistry of Gold - https://link.springer.com/content/pdf/10.1007/BF03215471.pdf https://link.springer.com/content/pdf/10.1007/BF03215471.pdf > In atoms of high nuclear charge (Z), as a consequence of a relativistic effect, the s electrons of an atom become more bound and their orbitals smaller than if this effect were absent. Simultaneously, the d (and f) electrons are less bound because of this effect, which scales roughly as Z2. Gold exhibits a large relativistic effect. This accounts for gold being more resistant to oxidation than silver. It also accounts for higher oxidation states being more accessible in gold than in silver. These effects are illustrated by some fluorine chemistry of gold and silver. https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry > Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of gold: due to relativistic effects, it is not silvery like most other metals.