4 ms·

but e=mc^2 is just an approximation e: nice, downvoted for knowing special relativity

by whimsicalism 2y ago

amluto 2y ago
Can you elaborate? How is E=mc^2 an approximation, in special relativity or otherwise? What is it an approximation of?
- whimsicalism 2y ago
  E^2 = m^2 + p^2 where p is momentum and i’ve dropped unit adjustment factors like c this allows light to have energy even if its massless
- ac29 2y ago
  e=mc^2 is only correct for objects at rest. The full equation takes into account velocity, but for "low" speeds where v<<c, the term is close enough to zero than E=mc^2 is still a good approximation.
- ijustlovemath 2y ago
  E^2 = (mc^2)^2 + (pc)^2, where p is momentum. When an object is traveling at relativistic speeds, the momentum forms a more significant portion of its energy
gus_massa 2y ago
I didn't downvote it, but short comments are a very big risk. People may misinterpret it, or think it's crackpot theory or a joke and then downvote. When in doubt, add more info, like: But the complete equation is E=sqrt(m^2c^4+p^2) that is reduced to E=mc^2 when the momentum p is 0. More info in https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Extension_for_systems_in_motion https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalenc...
- tame3902 2y ago
  What I learnt is that there is a rest mass and a relativistic mass. The m in your formula is the rest mass. But when you use the relativistic mass E=mc² still holds. And for the rest mass I always used m_0 to make clear what it is.
  - whimsicalism 2y ago
    sounds like you had a chemistry education. relativistic mass is IMO very much not a useful way of thinking about this and it is sort of tautologically true that E = m_relativistic because “relativistic mass” is just taking the concept of energy and renaming it “mass”
    - amluto 2y ago
      This is all sort of silly IMO. The equation, like basically all equations, needs context. What’s E? What’s m? If E is the total energy of the system and m is the mass (inertial or gravitational? how far past 1905 do you want to go?), then there isn’t a correction. If m is rest mass and E is total energy, then I would call it flat-out wrong, not merely approximate. After all, a decent theory really ought to reproduce Newtonian mechanics under some conditions beyond completely at rest. IMO, when people get excited about E=mc^2, it’s in contexts like noticing that atoms have rest masses that are generally somewhat below the mass of a proton or neutron times the number of protons and neutrons in the atom, and that the mass difference is the binding energy of the nucleus, and you can do nuclear reactions and convert between mass and energy! And then E=mc^2 is apparently exactly true, or at least true to an excellent degree, even though the energies involved are extremely large and Newtonian mechanics can’t even come close to accounting for what’s going on.
      - whimsicalism 2y ago
        inertial mass, rest mass, gravitational mass - these are essentially all the same thing. “relativistic mass” is an additional concept where we rewrite energy as mass and is considered archaic
        deleted 2y ago
- ackfoobar 2y ago
  The next section of the wikipedia link discusses the low speed approximation, where sqrt(m^2c^4+(pc)^2) ≈ mc^2 + 1/2 mv^2. Calling E=mc^2 an "approximation" is technically correct. It's the 0th order approximation. That's just pointlessly confusing. A better word choice would be "a special case".
  - whimsicalism 2y ago
    i think we are venturing into pedantic territory - the point of my comment is that the full derivation is a little harder than just E=mc^2 dimensional analysis
- mcnamaratw 2y ago
  Kind of agree. But pervasive downvoting by folks who don’t understand the subject is a form of forum rot. The risk is only that we expose the rot. Not such a terrible risk, because either the owners notice and fix the problem, or the forum continues to rot. In the latter case karma points wont be desirable in the long run.
- bcoates 2y ago
  This is why RLHF causes those overly verbose answers to simple questions, it's a fundamentally busted evaluation function so you wind up optimizing for the wrong thing
  - gus_massa 2y ago
    [Sorry for the dealy.] In one extreme there are wall of text and in the other extreme very short answers that only the initiated understand (like inside jokes). Somewhere in between there is a sweet spot that helps everyone else to follow the discusion and gain a litle of knowdledge. (I don't claim I get the best lenght in my comments, but I hope it's good enough.)
make3 2y ago
it's a special case, not an approximation
- whimsicalism 2y ago
  its not an either/or, it is both. regardless, my point is that you cannot simply dimensional analysis your way to special relativity or the energy-momentum relation
mitthrowaway2 2y ago
This thread has come up before(1), but I'll continue to argue that relativistic mass is a perfectly valid concept as much as any other, and if you disagree, you'll need arguments more substantial than it just being unpopular these days. Especially if you're trying to argue people out of using a concept that they personally find useful to aid their own understanding, just because it doesn't fit your own mathematical or aesthetic preferences. 1: https://news.ycombinator.com/item?id=38425252 https://news.ycombinator.com/item?id=38425252
- whimsicalism 2y ago
  sure but i think it 1. is not very intuitive/useful to have mass that varies on the direction (which is what this implies) 2. is somewhat tautological to define a new mass m_rel = E/c^2 and say that it satisfies the equation when this is not what most people understand mass to be. most people understand photons to be massless particles. at minimum, relativistic mass should always be specified as m_rel to distinguish from what is typically referred to as mass. but i don’t think relativistic mass is a wrong concept any more than any other mathematical convenience like virtual particles. the main question is how useful is it and should it be described using the word “mass” or is this confusing. there is value in having shared language, even if you can construct an alternate system of symbols and rules that can yield the same answer to every question. to the extent to which intent of the author matters at all (probably doesn’t), Einstein agreed that relativistic mass was not a useful concept. i'll concede that the arguments in the thread you linked are not good
  - amluto 2y ago
    > most people understand photons to be massless particles. I suspect that most people have no opinion at all and are generally unaware of the properties of light. That being said, a (perfectly reflective or otherwise steady state, e.g. black body at equilibrium) box of photons has mass due to those photons. You can stick it on a scale or a pendulum and measure it. It attracts other nearby objects according to GR or, in the appropriate limit, Newtonian gravity, in accordance with the relativistic mass of those photons.

but e=mc^2 is just an approximation e: nice, downvoted for knowing special relativity

amluto 2y ago

Can you elaborate? How is E=mc^2 an approximation, in special relativity or otherwise? What is it an approximation of?

whimsicalism 2y ago
E^2 = m^2 + p^2 where p is momentum and i’ve dropped unit adjustment factors like c this allows light to have energy even if its massless
ac29 2y ago
e=mc^2 is only correct for objects at rest. The full equation takes into account velocity, but for "low" speeds where v<<c, the term is close enough to zero than E=mc^2 is still a good approximation.
ijustlovemath 2y ago
E^2 = (mc^2)^2 + (pc)^2, where p is momentum. When an object is traveling at relativistic speeds, the momentum forms a more significant portion of its energy

gus_massa 2y ago

I didn't downvote it, but short comments are a very big risk. People may misinterpret it, or think it's crackpot theory or a joke and then downvote. When in doubt, add more info, like: But the complete equation is E=sqrt(m^2c^4+p^2) that is reduced to E=mc^2 when the momentum p is 0. More info in https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Extension_for_systems_in_motion https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalenc...

tame3902 2y ago
What I learnt is that there is a rest mass and a relativistic mass. The m in your formula is the rest mass. But when you use the relativistic mass E=mc² still holds. And for the rest mass I always used m_0 to make clear what it is.
- whimsicalism 2y ago
  sounds like you had a chemistry education. relativistic mass is IMO very much not a useful way of thinking about this and it is sort of tautologically true that E = m_relativistic because “relativistic mass” is just taking the concept of energy and renaming it “mass”
  - amluto 2y ago
    This is all sort of silly IMO. The equation, like basically all equations, needs context. What’s E? What’s m? If E is the total energy of the system and m is the mass (inertial or gravitational? how far past 1905 do you want to go?), then there isn’t a correction. If m is rest mass and E is total energy, then I would call it flat-out wrong, not merely approximate. After all, a decent theory really ought to reproduce Newtonian mechanics under some conditions beyond completely at rest. IMO, when people get excited about E=mc^2, it’s in contexts like noticing that atoms have rest masses that are generally somewhat below the mass of a proton or neutron times the number of protons and neutrons in the atom, and that the mass difference is the binding energy of the nucleus, and you can do nuclear reactions and convert between mass and energy! And then E=mc^2 is apparently exactly true, or at least true to an excellent degree, even though the energies involved are extremely large and Newtonian mechanics can’t even come close to accounting for what’s going on.
    - whimsicalism 2y ago
      inertial mass, rest mass, gravitational mass - these are essentially all the same thing. “relativistic mass” is an additional concept where we rewrite energy as mass and is considered archaic
      - deleted 2y ago
ackfoobar 2y ago
The next section of the wikipedia link discusses the low speed approximation, where sqrt(m^2c^4+(pc)^2) ≈ mc^2 + 1/2 mv^2. Calling E=mc^2 an "approximation" is technically correct. It's the 0th order approximation. That's just pointlessly confusing. A better word choice would be "a special case".
- whimsicalism 2y ago
  i think we are venturing into pedantic territory - the point of my comment is that the full derivation is a little harder than just E=mc^2 dimensional analysis
mcnamaratw 2y ago
Kind of agree. But pervasive downvoting by folks who don’t understand the subject is a form of forum rot. The risk is only that we expose the rot. Not such a terrible risk, because either the owners notice and fix the problem, or the forum continues to rot. In the latter case karma points wont be desirable in the long run.
bcoates 2y ago
This is why RLHF causes those overly verbose answers to simple questions, it's a fundamentally busted evaluation function so you wind up optimizing for the wrong thing
- gus_massa 2y ago
  [Sorry for the dealy.] In one extreme there are wall of text and in the other extreme very short answers that only the initiated understand (like inside jokes). Somewhere in between there is a sweet spot that helps everyone else to follow the discusion and gain a litle of knowdledge. (I don't claim I get the best lenght in my comments, but I hope it's good enough.)

make3 2y ago

it's a special case, not an approximation

whimsicalism 2y ago
its not an either/or, it is both. regardless, my point is that you cannot simply dimensional analysis your way to special relativity or the energy-momentum relation

mitthrowaway2 2y ago

This thread has come up before(1), but I'll continue to argue that relativistic mass is a perfectly valid concept as much as any other, and if you disagree, you'll need arguments more substantial than it just being unpopular these days. Especially if you're trying to argue people out of using a concept that they personally find useful to aid their own understanding, just because it doesn't fit your own mathematical or aesthetic preferences. 1: https://news.ycombinator.com/item?id=38425252 https://news.ycombinator.com/item?id=38425252

whimsicalism 2y ago
sure but i think it 1. is not very intuitive/useful to have mass that varies on the direction (which is what this implies) 2. is somewhat tautological to define a new mass m_rel = E/c^2 and say that it satisfies the equation when this is not what most people understand mass to be. most people understand photons to be massless particles. at minimum, relativistic mass should always be specified as m_rel to distinguish from what is typically referred to as mass. but i don’t think relativistic mass is a wrong concept any more than any other mathematical convenience like virtual particles. the main question is how useful is it and should it be described using the word “mass” or is this confusing. there is value in having shared language, even if you can construct an alternate system of symbols and rules that can yield the same answer to every question. to the extent to which intent of the author matters at all (probably doesn’t), Einstein agreed that relativistic mass was not a useful concept. i'll concede that the arguments in the thread you linked are not good
- amluto 2y ago
  > most people understand photons to be massless particles. I suspect that most people have no opinion at all and are generally unaware of the properties of light. That being said, a (perfectly reflective or otherwise steady state, e.g. black body at equilibrium) box of photons has mass due to those photons. You can stick it on a scale or a pendulum and measure it. It attracts other nearby objects according to GR or, in the appropriate limit, Newtonian gravity, in accordance with the relativistic mass of those photons.