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Yes, the effective mass of a photon is determined by E=mc^2 even though it has no mass, but it's sort of by definition because nothing with mass can reach the s

Yes, the effective mass of a photon is determined by E=mc^2 even though it has no mass, but it's sort of by definition because nothing with mass can reach the speed of light. Also anything moving at the speed of light doesn't perceive the passage of time, because from its perspective we're so time-dilated that the universe comes and goes in an instant as it crosses that expanse. So an argument could be made that only one photon exists, forming a frozen 4D crystal with the shape of every photon's path through the universe. A black hole's average density decreases by increasing radius. So theoretically a black hole could be formed from a gas like air, and in fact IRAS 20100-4156 with a mass of 3.8 billion suns and a diameter of about 10 billion km (according to the video below) has the same density as air: https://www.youtube.com/watch?v=71eUes30gwc https://www.youtube.com/watch?v=71eUes30gwc Also from the video, if we take the average density of the universe and consider it a uniformly distributed gas, we find that it fits within a black hole 10 times larger than the radius of the visible universe, which is 45 billion light years. So I believe that we're inside of a giant black hole and that the expansion of the universe is driven by Hawking radiation at the event horizon causing it to evaporate, which lowers the radius, which from our perspective looks like galaxies slipping away from us faster than the speed of light as they pass that velocity due to the Hubble constant multiplied by that distance. So technically a black hole could be created by just photons with a mass energy equivalence similar to air. It would be curious to see what the radius of a black hole filled with the cosmic background radiation would be, and how that correlates to the ~5 hydrogen atoms per cubic meter from the video. It wouldn't surprise me if they're equivalent or correlated so that the background radiation represents how much matter is inside the universe, not just its age since the Big Bang. In the first 4 minutes of this video, Neil deGrasse Tyson is worried about the end of the universe trillions of years from now, when the last galaxies have slipped outside the observable radius, so that future life will think that the Milky Way galaxy is the entire universe: https://www.youtube.com/watch?v=rFVdueuDD_o https://www.youtube.com/watch?v=rFVdueuDD_o But I think that the inward rush of the universe's event horizon will continue forever and that even our galaxy won't be spared, even though right now it looks gravitationally bound. Eventually everything will be pulled apart in a big pop as even the force between nucleons won't be enough to resist Hawking radiation within a small enough black hole. Also the universal black hole will catch up to the Sagittarius A* supermassive black hole at the center of our galaxy, pulling even it apart. So eventually everything pops back out into the surrounding universe. So probably the universe can be thought of as perhaps an infinitely wide nested swiss cheese of black holes. There may be one principle formula that states how that shape comes from quantum mechanics where the long tail of probabilities leads to energy and particles arising (I'm speculating since my studies didn't take me that far), or maybe the physics of the child black holes can vary from their parent universes because they're separated by an event horizon so that our universe evolved physics favorable for life to observe its own existence. Which takes us back to the Anthropic Principle which doesn't really tell us much. TMI I realize, but hey, it's Sunday. - Edit: I forgot to add why I was writing this. At large scales, the universe forms bubbles with matter along the surfaces where they meet, and large voids in between. Which suggests that something caused matter to be attracted to those boundaries. I wonder if this is similar to how something like dark matter causes galaxies to rotate faster than they should for how much mass is at their perimeters. It suggests that space is moving there without having an attractor. As if space itself can acquire momentum without mass. This is sort of how space looks to us as it flows into Earth, causing us to perceive an accelerating reference frame which we feel as gravity. If the ground disappeared and we began falling, then we would no longer perceive gravity or its associated time dilation (except from tidal forces as we approach the center). Which suggests that someone falling into a black hole would remain weightless and stay synchronized with our frame of reference, even as they passed the speed of light from our reference frame and appeared close to frozen to us. So it might be possible to travel from outer to inner black hole. Although the speed of expansion by Hawking is so large that probably the falling observer would become suspended at the equilibrium point where expansion matches inward acceleration. So in a very real way, the amount of space within a black hole could be much larger than its apparent radius from our frame of reference. Giving some credibility to the idea that child universes exist within black holes. Also I don't know if there is a gravitational lens effect on photons arriving to us as they cross the heavier space at the edge of galaxies: A) If there is, then the mass exists there in the form of dark matter, neutrinos, WIMPs, etc. B) If there isn't, then space appears to be moving without an attractor, meaning that something like a Hubble constant might be missing from our relativity equations or work something like MOND, or that sci fi stuff like warp drives might be possible. I like to think that our universe evolved the conditions for sci fi, and that stuff like dark matter is a wink to us so we can figure out how to do it through something like electrogravitics.

pixl97 2y ago
>Yes, the effective mass of a photon is determined by E=mc^2 even though it has no mass I think for the photon itself it's the more complete equation of E = (square root) m^2c^4 + p^2c^2 that shows how much relativistic energy is in that photon.
- zackmorris 2y ago
  Hey thanks you're absolutely right. Just to save people some time, here are some Google hits for that and its geometric representation: https://www.britannica.com/video/185388/equation-theory-energy-relativity-mc https://www.britannica.com/video/185388/equation-theory-ener... https://physics.stackexchange.com/questions/6202/does-e-mc2-apply-to-photons https://physics.stackexchange.com/questions/6202/does-e-mc2-... So for massless particles your E=sqrt(m^2c^4 + p^2c^2) formula becomes E=sqrt(p^2c^2) which simplifies to the formula for photon momentum p=E/c (aka light pressure). - HN wouldn't let me reply, but since it's Monday I might as well procrastinate: If we assume that the light is columnated like a laser, then a 1 watt light absorbed by a 1 kilogram object for 1 second imparts 1 joule so p=E/c so that's 1/c or 3.34e-9 newton seconds of momentum. Note that the momentum imparted is twice this if the light is reflected, to account for absorption and reemission. To see how much force is produced per watt it's: https://www.physicsforums.com/threads/radiation-pressure-causing-acceleration.450749/ https://www.physicsforums.com/threads/radiation-pressure-cau... Power is just energy per unit time. If you really want forces, then note that force is momentum per unit time... so for light, the relation between power and force of a light beam is the same as the relation between energy and momentum of a light pulse. P<->F relation has same form as E<->p p=E/c p/t=(E/t)/c F=P/c Acceleration of an object of a certain mass produceed by light of a certain power: F=ma=P/c a=P/mc Power of light required to accelerate an object of a certain mass: P=amc For example, the power needed to accelerate an object at Earth's gravity of 9.81 m/s^2 is P = 9.81 * m * c=m * 2.94e9 so that's about 3 GW per kg. A light jetpack for a 100 kg person to fly above Earth would take about 300 GW or about 150 Hoover dams or 250 DeLoreans from Back to the Future. The power required to accelerate a 1 million kilogram nuclear interstellar spacecraft continuously at 1 Earth's gravity is 3 PW, or about 1000 times the 3.3 TW of power produced by all countries on Earth currently. So aliens have probably figured out a more efficient means of propellantless space travel. - To procrastinate further: If we go back to your mass-energy equivalence formula E = (square root) m^2c^4 + p^2c^2: https://en.wikipedia.org/wiki/Mass–energy_equivalence https://en.wikipedia.org/wiki/Mass–energy_equivalence https://en.wikipedia.org/wiki/Equivalence_principle https://en.wikipedia.org/wiki/Equivalence_principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times. The extended form by Albert Einstein requires special relativity to also hold in free fall and requires the weak equivalence to be valid everywhere. This form was a critical input for the development of the theory of general relativity. The strong form requires Einstein's form to work for stellar objects. Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small. It's basically saying that gravitational and inertial acceleration are the same. As a thought experiment, imagine being in a large spacecraft, feeling artifical gravity about the same as Earth's, and trying to determine if it's sitting on the ground or accelerating through space. A way to do that is to measure the divergence of the acceleration with a (laser) tape measure and two plumb bobs. Hang the bobs on distant walls and measure the distance between the strings at floor and ceiling. In space, the strings will be parallel due to linear acceleration. But on Earth, the strings at floor will be slightly closer together due to the divergence of the gravitional field: https://www.mathscinotes.com/2017/01/effect-of-earths-curvature-on-suspension-bridge-dimensions/ https://www.mathscinotes.com/2017/01/effect-of-earths-curvat... In metric, that bridge is 1298 m long and 211 m tall with a 42.61 mm discrepancy. By similar triangles, a 1 km distance has h=211 * 1000/1298=163 m height and 42.61 * 1000/1298=32.83 mm discrepancy. So the discrepancy per meter of height is 0.03283/163=201.4 microns at 1 km. Plumb bobs hung from the ceiling by a 3 meter tall wall will be about 600 microns or 0.6 mm closer at the floor for a room 1 km on a side. - Where I'm going with this is that the divergence at the perimeter of galaxies is higher than it should be, because stars are orbiting faster there than can be accounted for by visible mass alone. Since there's not enough mass (no attractor) to account for the faster orbits, then something else is curving space, which we currently call dark matter. But it's possible that there's a missing term or dimension from your (Einstein's) E=sqrt(m^2c^4 + p^2c^2) formula, or that the Equivalence Principle doesn't always hold. Meaning that something else besides mass or energy might contribute to momentum, making objects appear to be moving faster than they should be, or that space is flowing around them to drag them along faster without an attractor. Which is similar to how a warp drive would work. If we could figure out what that something is, and perhaps modulate it with energy, then we could modulate space and build a reactionless rocket. That would make the divergence of space higher in front of the rocket to accelerate it forward. Unfortunately we can't detect dark matter, much less modulate it, so we either need a huge empirical discovery or new physics to build a warp drive.

pixl97 2y ago

>Yes, the effective mass of a photon is determined by E=mc^2 even though it has no mass I think for the photon itself it's the more complete equation of E = (square root) m^2c^4 + p^2c^2 that shows how much relativistic energy is in that photon.

zackmorris 2y ago
Hey thanks you're absolutely right. Just to save people some time, here are some Google hits for that and its geometric representation: https://www.britannica.com/video/185388/equation-theory-energy-relativity-mc https://www.britannica.com/video/185388/equation-theory-ener... https://physics.stackexchange.com/questions/6202/does-e-mc2-apply-to-photons https://physics.stackexchange.com/questions/6202/does-e-mc2-... So for massless particles your E=sqrt(m^2c^4 + p^2c^2) formula becomes E=sqrt(p^2c^2) which simplifies to the formula for photon momentum p=E/c (aka light pressure). - HN wouldn't let me reply, but since it's Monday I might as well procrastinate: If we assume that the light is columnated like a laser, then a 1 watt light absorbed by a 1 kilogram object for 1 second imparts 1 joule so p=E/c so that's 1/c or 3.34e-9 newton seconds of momentum. Note that the momentum imparted is twice this if the light is reflected, to account for absorption and reemission. To see how much force is produced per watt it's: https://www.physicsforums.com/threads/radiation-pressure-causing-acceleration.450749/ https://www.physicsforums.com/threads/radiation-pressure-cau... Power is just energy per unit time. If you really want forces, then note that force is momentum per unit time... so for light, the relation between power and force of a light beam is the same as the relation between energy and momentum of a light pulse. P<->F relation has same form as E<->p p=E/c p/t=(E/t)/c F=P/c Acceleration of an object of a certain mass produceed by light of a certain power: F=ma=P/c a=P/mc Power of light required to accelerate an object of a certain mass: P=amc For example, the power needed to accelerate an object at Earth's gravity of 9.81 m/s^2 is P = 9.81 * m * c=m * 2.94e9 so that's about 3 GW per kg. A light jetpack for a 100 kg person to fly above Earth would take about 300 GW or about 150 Hoover dams or 250 DeLoreans from Back to the Future. The power required to accelerate a 1 million kilogram nuclear interstellar spacecraft continuously at 1 Earth's gravity is 3 PW, or about 1000 times the 3.3 TW of power produced by all countries on Earth currently. So aliens have probably figured out a more efficient means of propellantless space travel. - To procrastinate further: If we go back to your mass-energy equivalence formula E = (square root) m^2c^4 + p^2c^2: https://en.wikipedia.org/wiki/Mass–energy_equivalence https://en.wikipedia.org/wiki/Mass–energy_equivalence https://en.wikipedia.org/wiki/Equivalence_principle https://en.wikipedia.org/wiki/Equivalence_principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times. The extended form by Albert Einstein requires special relativity to also hold in free fall and requires the weak equivalence to be valid everywhere. This form was a critical input for the development of the theory of general relativity. The strong form requires Einstein's form to work for stellar objects. Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small. It's basically saying that gravitational and inertial acceleration are the same. As a thought experiment, imagine being in a large spacecraft, feeling artifical gravity about the same as Earth's, and trying to determine if it's sitting on the ground or accelerating through space. A way to do that is to measure the divergence of the acceleration with a (laser) tape measure and two plumb bobs. Hang the bobs on distant walls and measure the distance between the strings at floor and ceiling. In space, the strings will be parallel due to linear acceleration. But on Earth, the strings at floor will be slightly closer together due to the divergence of the gravitional field: https://www.mathscinotes.com/2017/01/effect-of-earths-curvature-on-suspension-bridge-dimensions/ https://www.mathscinotes.com/2017/01/effect-of-earths-curvat... In metric, that bridge is 1298 m long and 211 m tall with a 42.61 mm discrepancy. By similar triangles, a 1 km distance has h=211 * 1000/1298=163 m height and 42.61 * 1000/1298=32.83 mm discrepancy. So the discrepancy per meter of height is 0.03283/163=201.4 microns at 1 km. Plumb bobs hung from the ceiling by a 3 meter tall wall will be about 600 microns or 0.6 mm closer at the floor for a room 1 km on a side. - Where I'm going with this is that the divergence at the perimeter of galaxies is higher than it should be, because stars are orbiting faster there than can be accounted for by visible mass alone. Since there's not enough mass (no attractor) to account for the faster orbits, then something else is curving space, which we currently call dark matter. But it's possible that there's a missing term or dimension from your (Einstein's) E=sqrt(m^2c^4 + p^2c^2) formula, or that the Equivalence Principle doesn't always hold. Meaning that something else besides mass or energy might contribute to momentum, making objects appear to be moving faster than they should be, or that space is flowing around them to drag them along faster without an attractor. Which is similar to how a warp drive would work. If we could figure out what that something is, and perhaps modulate it with energy, then we could modulate space and build a reactionless rocket. That would make the divergence of space higher in front of the rocket to accelerate it forward. Unfortunately we can't detect dark matter, much less modulate it, so we either need a huge empirical discovery or new physics to build a warp drive.