4 ms·

> This is the consequence of all the forces of physics being gauge invariant: absolute values don't exist—only differences matter there's something about this

> This is the consequence of all the forces of physics being gauge invariant: absolute values don't exist—only differences matter there's something about this quote that i really like, going to have to use it out of context on people

4b11b4 2y ago
I've come back to this idea of "differences" from many angles... From images: information _is _ the differences between pixels From opinions: my opinion alone is worthless, but a difference of opinions? now we've got something From relationships, graphs, networks: edges are _differences_ between nodes. the edges are everything. nodes alone... are meaningless From music: this one is a little easier to take at face value, you can't have a sound without a change (difference) over time. the speaker cone can only wobble... Not sure about the absoluteness or correctness of this intuition, please criticize
- kortilla 2y ago
  For images, you need a reference pixel to get the color right. You can apply differences from there but you’re effectively working with absolutes because of that so it’s a meaningless distinction. Any time an absolute reference point is assumed, all downstream calculations are effectively absolutes
  - cgriswald 2y ago
    Is this strictly true? Suppose you have a reference pixel but don’t know its value. You don’t get the color right but there is plenty of other information there, right? Which pixel also probably limits the range of values since your highest and lowest values are probably within a certain range.
  - brianpan 2y ago
    I have a blue/black (or possibly white/gold) dress that says it's relative. You can also ask a UI designer about "absolute" colors. One color needs to be different depending on the context it's in order to LOOK the same (it's size/thickness, background, what it's next to).
    - kortilla 2y ago
      The blue black dress thing is how people perceive it, but the values for pixels are absolute. The pixel values aren’t changing from viewer to viewer. If OP had said “perceived color”, I would agree. But we’re talking at pixel level here.
- PaulDavisThe1st 2y ago
  "Information: any difference that makes a difference" - Gregory Bateson
- nartho 2y ago
  For music, a note is just a frequency. It is the difference between the notes that makes music, not the notes themselves
insonable 2y ago
sounds like Robert California
eggn00dles 2y ago
there most certainly are absolutes. theres an absolute maximum amount of distance a massive object can travel through spacetime. theres an absolute maximum amount of mass/energy that can exist within a volume of space before an event horizon forms. universal constants which have dimensions are more or less measurable absolutes. differences maybe more apparent but that doesnt mean absolutes dont exist.
- almostgotcaught 2y ago
  > theres an absolute maximum amount of distance a massive object can travel through spacetime Wut. No there's not? Specifically for spacetime it's obvious to see that's not correct because the time axis has no upper bound.
  - d1sxeyes 2y ago
    I agree OP misspoke, but are we sure the time axis has no upper bound? Or that it doesn’t loop back round on itself? Or that it even exists meaningfully as an axis?
  - pixl97 2y ago
    Heh, i wonder what the mean free space between blackholes is? Now, given that in quadrillions of quadrillions of years all black holes will evaporate and potentially even protons decay there could be a time in the universe where everything is mass less radiation.
- awesome_dude 2y ago
  An absolute on the upper bound of velocity that a massless object can travel through space at maybe? Although - I had it explained to me that the fabric of space was entering a black hole faster than light could travel, which is why light couldn't escape. Which made me wonder - is light (the massless object) travelling, or is it space travelling and carrying things at different velocities.
awesome_dude 2y ago
It's all relative!
xelxebar 2y ago
Or said another way, forces carry the structure of G-torsors! The terminology is way too pompous for such a simple concept, though. John Baez has a really clean writeup on them, accessible to anyone interested: https://math.ucr.edu/home/baez/torsors.html https://math.ucr.edu/home/baez/torsors.html. Heck, even differences are usually non-physical; it's their ratio that matters. I.e. choosing feet or meters doesn't change the physics; the same goes for energy. So we have two free parameters: choice of origin and choice of units. Baez only hints at this near the end of the above article, but we can actually fuse translations and scalings into a single group of elements that are combined translation + scale operations, an affine group. It turns out that this combined group is just a certain combination (semidirect product[0]) of the translation and scaling groups, as one would hope. And once we are thinking about affine groups, it's natural to consider more complicated ones. Most famous is probably the Poincaré group[1]. That is, points in space are physically described by G-torsors over the Poincaré group! [0]:https://ncatlab.org/nlab/show/semidirect+product+group https://ncatlab.org/nlab/show/semidirect+product+group [1]:https://en.wikipedia.org/wiki/Poincar%C3%A9_group https://en.wikipedia.org/wiki/Poincar%C3%A9_group
- Y_Y 2y ago
  Excellent comment. The only thing I can add is the obligatory "why stop there?", Poincaré true to form gives a beautiful description of the symmetries of flat spacetime, but we know that spacetime is only locally flat, the measurement symmetries at large scale are carried by the (unfortunately named) Killing fields[0]. [0] https://en.wikipedia.org/wiki/Killing_vector_field https://en.wikipedia.org/wiki/Killing_vector_field

4b11b4 2y ago

I've come back to this idea of "differences" from many angles... From images: information _is _ the differences between pixels From opinions: my opinion alone is worthless, but a difference of opinions? now we've got something From relationships, graphs, networks: edges are _differences_ between nodes. the edges are everything. nodes alone... are meaningless From music: this one is a little easier to take at face value, you can't have a sound without a change (difference) over time. the speaker cone can only wobble... Not sure about the absoluteness or correctness of this intuition, please criticize

kortilla 2y ago
For images, you need a reference pixel to get the color right. You can apply differences from there but you’re effectively working with absolutes because of that so it’s a meaningless distinction. Any time an absolute reference point is assumed, all downstream calculations are effectively absolutes
- cgriswald 2y ago
  Is this strictly true? Suppose you have a reference pixel but don’t know its value. You don’t get the color right but there is plenty of other information there, right? Which pixel also probably limits the range of values since your highest and lowest values are probably within a certain range.
- brianpan 2y ago
  I have a blue/black (or possibly white/gold) dress that says it's relative. You can also ask a UI designer about "absolute" colors. One color needs to be different depending on the context it's in order to LOOK the same (it's size/thickness, background, what it's next to).
  - kortilla 2y ago
    The blue black dress thing is how people perceive it, but the values for pixels are absolute. The pixel values aren’t changing from viewer to viewer. If OP had said “perceived color”, I would agree. But we’re talking at pixel level here.
PaulDavisThe1st 2y ago
"Information: any difference that makes a difference" - Gregory Bateson
nartho 2y ago
For music, a note is just a frequency. It is the difference between the notes that makes music, not the notes themselves

insonable 2y ago

sounds like Robert California

eggn00dles 2y ago

there most certainly are absolutes. theres an absolute maximum amount of distance a massive object can travel through spacetime. theres an absolute maximum amount of mass/energy that can exist within a volume of space before an event horizon forms. universal constants which have dimensions are more or less measurable absolutes. differences maybe more apparent but that doesnt mean absolutes dont exist.

almostgotcaught 2y ago
> theres an absolute maximum amount of distance a massive object can travel through spacetime Wut. No there's not? Specifically for spacetime it's obvious to see that's not correct because the time axis has no upper bound.
- d1sxeyes 2y ago
  I agree OP misspoke, but are we sure the time axis has no upper bound? Or that it doesn’t loop back round on itself? Or that it even exists meaningfully as an axis?
- pixl97 2y ago
  Heh, i wonder what the mean free space between blackholes is? Now, given that in quadrillions of quadrillions of years all black holes will evaporate and potentially even protons decay there could be a time in the universe where everything is mass less radiation.
awesome_dude 2y ago
An absolute on the upper bound of velocity that a massless object can travel through space at maybe? Although - I had it explained to me that the fabric of space was entering a black hole faster than light could travel, which is why light couldn't escape. Which made me wonder - is light (the massless object) travelling, or is it space travelling and carrying things at different velocities.

awesome_dude 2y ago

It's all relative!

xelxebar 2y ago

Or said another way, forces carry the structure of G-torsors! The terminology is way too pompous for such a simple concept, though. John Baez has a really clean writeup on them, accessible to anyone interested: https://math.ucr.edu/home/baez/torsors.html https://math.ucr.edu/home/baez/torsors.html. Heck, even differences are usually non-physical; it's their ratio that matters. I.e. choosing feet or meters doesn't change the physics; the same goes for energy. So we have two free parameters: choice of origin and choice of units. Baez only hints at this near the end of the above article, but we can actually fuse translations and scalings into a single group of elements that are combined translation + scale operations, an affine group. It turns out that this combined group is just a certain combination (semidirect product[0]) of the translation and scaling groups, as one would hope. And once we are thinking about affine groups, it's natural to consider more complicated ones. Most famous is probably the Poincaré group[1]. That is, points in space are physically described by G-torsors over the Poincaré group! [0]:https://ncatlab.org/nlab/show/semidirect+product+group https://ncatlab.org/nlab/show/semidirect+product+group [1]:https://en.wikipedia.org/wiki/Poincar%C3%A9_group https://en.wikipedia.org/wiki/Poincar%C3%A9_group

Y_Y 2y ago
Excellent comment. The only thing I can add is the obligatory "why stop there?", Poincaré true to form gives a beautiful description of the symmetries of flat spacetime, but we know that spacetime is only locally flat, the measurement symmetries at large scale are carried by the (unfortunately named) Killing fields[0]. [0] https://en.wikipedia.org/wiki/Killing_vector_field https://en.wikipedia.org/wiki/Killing_vector_field