4 ms·

I recommend looking into LIGO and other similar experiments. They use laser interferometry to accurately measure the distance between two points, to an extreme

I recommend looking into LIGO and other similar experiments. They use laser interferometry to accurately measure the distance between two points, to an extreme degree. From LIGO's website: Gravitational waves cause space itself to stretch in one direction and simultaneously compress in a perpendicular direction. In LIGO, this causes one arm of the interferometer to get longer while the other gets shorter, then vice versa, back and forth as long as the wave is passing. The technical term for this motion is "Differential Arm" motion, or differential displacement, since the arms are simultaneously changing lengths in opposing ways. As described above, as the lengths of the arms change, so too does the distance traveled by each laser beam. A beam in a shorter arm will return to the beam splitter before a beam in a longer arm--as the wave passes, each arm oscillates between being the shorter arm and the longer arm. When they arrive back at the beamsplitter (where they re-merge), the light waves no longer meet up nicely; they are out of phase. Instead, they shift in and out of alignment for as long as the wave is passing. https://www.ligo.caltech.edu/page/what-is-interferometer https://www.ligo.caltech.edu/page/what-is-interferometer https://en.wikipedia.org/wiki/LIGO https://en.wikipedia.org/wiki/LIGO

samstave 3y ago
>*Gravitational waves cause space itself to stretch* Please ELI5 specifically and empiracally what "Space Itself" actually is. Would it be possible to build a 'galactic clock & Compass' - a "clock" to the regular pulses of a pulsar and the galactic direction the pulsar is in relation to the terrestrial compass (magnetic) on earth...? What is the pulsar with the most reliable timings?
- pantulis 3y ago
  Space itself means the metric of spacetime: how you measure distances. Locally, if there was no gravity, you could think of space as a plain reticule where distances would be calculated through eucledian geometry: that means cartesian distances, parallel lines would be parallel and the angles of a triangle would sum 180, and the shortest path between two points is the straight line. General Relativity successfully establishes that the presence of mass distorts this, so it defines a mathematical object (the Einstein tensor) that reacts to the distribution of mass and energy and precisely describes the changes to the metric. For example it can model how the mass of the sun distorts the space so that light from distant stars appear to follow a curved path because very close to the sun a curved path is now the shortest path. The Einstein tensor defines how distances --and time-- are measured and it's the best mathematical model that we have about what "space itself" is. Future theoretical advances could take us forward and demonstrate that space itself emerges from other more fundamental elements, but this needs bridging quantum mechanics and gravity. We don't really know what space is made of, but scientists have precisely modelled how it reacts to mass (and energy) with utmost precision. NB: At cosmic scales the exercise becomes more difficult, as there is an expansion of the metric of spacetime that is not due to the presence of mass, in fact it is caused by the _absence_ of mass as it seems to be due the energy of empty space: the phenomenon called Dark Energy. Hope this helps!
  - samstave 3y ago
    Super helps! thanks - while I knew a bunch of pieces and tidbits, you cemented it for me - thank you. - TensorFlow >*General Relativity successfully establishes that the presence of mass distorts this, so it defines a mathematical object (the Einstein tensor) that reacts to the distribution of mass and energy and precisely describes the changes to the metric.* This leads me to think that TensorFlow was attempting to map the 'weight' among topics of intersecting interests, sciences, etc... and seeing who the "tensor warping" was most strong with and adding higher eval weights to things that "gravitated" to one another based on the informational difference in distance? (I dont know the nomenclature, but is that were using 'tensors' in AI/ML/whatever 'weights' come from?
    - pantulis 3y ago
      A tensor is a mathematical object that has a lot of uses beyond general relativity, of course. It's a little tricky to visualize (I think there are good YouTube videos) but tensors can be thought of as multidimensional arrays, and also the whole tensor algebra can be done in terms of multidimensional array operations. So reasoning about a neural network weights and operations in terms of tensors makes sense and I guess that's what the name Tensorflow comes from.
      - samstave 3y ago
        Yes, but your explaination helped me to better understand the other types of tensors in a way I can 'grok' it - as opposed to trying to be at the level of some google quant or whatever with ML understandings of weights. It helped my put my own internal visualizations to the understanding. and I had a weird peripheral memory on this from a thought I had whilst driving in 1999 where I was thinking of tensors in this way, but I didnt know what I was just daydreaming about... but apparently, it was einsteins tensors coupled with information theory - and while to me it was a pedestrians take on the premise - it turns out that that day dream was correct! And it all ties back to when I was ten years old and meditating on the Mind of God -- It all tied into one another - and you gave me some cord to pull these experiences together with understanding which I havent had in 40 years... so that was nice. Thanks. Anyone else recall daydreams from their past where their later understanding was confurmed, even though you were just "daydreaming at the time"?
- sidlls 3y ago
  Take a sheet of elastic material, like a balloon, but square. Suspend the corners in clamps on posts so that it’s “perfectly” flat. Draw a line that is the shortest distance between two points on the material: it will be a “straight” line like what you learnt in geometry class. Now place a marble in the center of the sheet and let it stretch the sheet. Now draw the shortest possible line connecting these two points: it will curve (and unless you chose by coincidence) it will likely not overlap with the first line: the “shortest distance” between the points has changed. There’s another aspect to this: the expansion coefficient. One such model is that the coefficient depends only on time: as time passes, distances increase. To model this, draw the same line on the flat sheet of material, then expand it uniformly in all directions. The distance is still a straight line, but the line is longer after the expansion.

samstave 3y ago

>*Gravitational waves cause space itself to stretch* Please ELI5 specifically and empiracally what "Space Itself" actually is. Would it be possible to build a 'galactic clock & Compass' - a "clock" to the regular pulses of a pulsar and the galactic direction the pulsar is in relation to the terrestrial compass (magnetic) on earth...? What is the pulsar with the most reliable timings?

pantulis 3y ago
Space itself means the metric of spacetime: how you measure distances. Locally, if there was no gravity, you could think of space as a plain reticule where distances would be calculated through eucledian geometry: that means cartesian distances, parallel lines would be parallel and the angles of a triangle would sum 180, and the shortest path between two points is the straight line. General Relativity successfully establishes that the presence of mass distorts this, so it defines a mathematical object (the Einstein tensor) that reacts to the distribution of mass and energy and precisely describes the changes to the metric. For example it can model how the mass of the sun distorts the space so that light from distant stars appear to follow a curved path because very close to the sun a curved path is now the shortest path. The Einstein tensor defines how distances --and time-- are measured and it's the best mathematical model that we have about what "space itself" is. Future theoretical advances could take us forward and demonstrate that space itself emerges from other more fundamental elements, but this needs bridging quantum mechanics and gravity. We don't really know what space is made of, but scientists have precisely modelled how it reacts to mass (and energy) with utmost precision. NB: At cosmic scales the exercise becomes more difficult, as there is an expansion of the metric of spacetime that is not due to the presence of mass, in fact it is caused by the _absence_ of mass as it seems to be due the energy of empty space: the phenomenon called Dark Energy. Hope this helps!
- samstave 3y ago
  Super helps! thanks - while I knew a bunch of pieces and tidbits, you cemented it for me - thank you. - TensorFlow >*General Relativity successfully establishes that the presence of mass distorts this, so it defines a mathematical object (the Einstein tensor) that reacts to the distribution of mass and energy and precisely describes the changes to the metric.* This leads me to think that TensorFlow was attempting to map the 'weight' among topics of intersecting interests, sciences, etc... and seeing who the "tensor warping" was most strong with and adding higher eval weights to things that "gravitated" to one another based on the informational difference in distance? (I dont know the nomenclature, but is that were using 'tensors' in AI/ML/whatever 'weights' come from?
  - pantulis 3y ago
    A tensor is a mathematical object that has a lot of uses beyond general relativity, of course. It's a little tricky to visualize (I think there are good YouTube videos) but tensors can be thought of as multidimensional arrays, and also the whole tensor algebra can be done in terms of multidimensional array operations. So reasoning about a neural network weights and operations in terms of tensors makes sense and I guess that's what the name Tensorflow comes from.
    - samstave 3y ago
      Yes, but your explaination helped me to better understand the other types of tensors in a way I can 'grok' it - as opposed to trying to be at the level of some google quant or whatever with ML understandings of weights. It helped my put my own internal visualizations to the understanding. and I had a weird peripheral memory on this from a thought I had whilst driving in 1999 where I was thinking of tensors in this way, but I didnt know what I was just daydreaming about... but apparently, it was einsteins tensors coupled with information theory - and while to me it was a pedestrians take on the premise - it turns out that that day dream was correct! And it all ties back to when I was ten years old and meditating on the Mind of God -- It all tied into one another - and you gave me some cord to pull these experiences together with understanding which I havent had in 40 years... so that was nice. Thanks. Anyone else recall daydreams from their past where their later understanding was confurmed, even though you were just "daydreaming at the time"?
sidlls 3y ago
Take a sheet of elastic material, like a balloon, but square. Suspend the corners in clamps on posts so that it’s “perfectly” flat. Draw a line that is the shortest distance between two points on the material: it will be a “straight” line like what you learnt in geometry class. Now place a marble in the center of the sheet and let it stretch the sheet. Now draw the shortest possible line connecting these two points: it will curve (and unless you chose by coincidence) it will likely not overlap with the first line: the “shortest distance” between the points has changed. There’s another aspect to this: the expansion coefficient. One such model is that the coefficient depends only on time: as time passes, distances increase. To model this, draw the same line on the flat sheet of material, then expand it uniformly in all directions. The distance is still a straight line, but the line is longer after the expansion.