5 ms·

Maybe others can answer this naive question that I have: how do we know that e=mc^2 actually has the correct number of variables? E.g. what if either mass or li

Maybe others can answer this naive question that I have: how do we know that e=mc^2 actually has the correct number of variables? E.g. what if either mass or light speed were composites of some other variables? Say that light speed really had a directional component or a distance from the Big Bang component? Or mass was itself a composite of particles and the forces acting in the nucleus? Wouldn’t some additional term here be a plausible way of explaining discrepancies in the observable vs predicted universe?

tux3 3y ago
This doesn't really answer your question, but there is already an extra term! (only sometimes it is zero) E^2 = (mc^2)^2 + (lc)^2
- spanglasaur 3y ago
  I was going to comment this as well. Here is a thorough explanation of the missing term: https://physics.stackexchange.com/questions/143652/is-e2-mc22pc2-or-is-e-mc2-the-correct-one https://physics.stackexchange.com/questions/143652/is-e2-mc2... The thing that I love about this formulation of the equation is that it directly ties it to the Pythagorean theorem: c^2 = a^2 + b^2 . It really shows you just how pretty that equation really is!
- lamontcg 3y ago
  the m in that equation is the rest mass (m_0) which is a proper scalar. the m in E=mc^2 is the relativistic mass which depends on rest frame and therefore isn't a proper scalar quantity and that isn't a proper tensor equation. the (E, px, py, pz) energy-momentum 4-vector is a tensor that transforms to any reference frame with a lorentz transform. all observers will agree on the shape of that 4-vector object, although they'll measure the components differently. that equation is just the dot product (rearranged), where the rest mass is the length of the 4-momentum vector (and a proper scalar quantity that all observers agree on is exactly that value in all reference frames). the rearrangement introduces a negative sign which actually comes from the SR metric -- usually diag(-1, +1, +1, +1) but sometimes diag(+1, -1, -1, -1).
simonh 3y ago
Distance from the Big Bang? So zero then. But even if say energy or the speed of light are derived from other parameters, that doesn’t make the equation wrong, just incomplete. Anyway for all the phenomena we don’t have complete explanation for, none of them give any indication relativity is incorrect, and therefore there’s no reason to suppose tweaking it would help explain them.
FetusP 3y ago
Intro college Physics is reformatting formulas to solve for variables in other formulas, and inserting them into each other. So even if c = (w+x+y+z), e=mc^2 and e=m(w+x+y+z)^2 would still be equivalent.
layer8 3y ago
Your what ifs are theories that have been or are being explored. But so far the predictions they made either have been falsified, or they haven’t made any that would make them more plausible overall than the standard model. For any such ideas that come to mind, you can be pretty sure that many, many physicists have already gone through them.
- abakker 3y ago
  Oh, I was not trying to be original or second guess experts. It’s just hard to google a concept like this and get useful answers.
marcosdumay 3y ago
We don't know anything. If you want to know how we are sure of it, we aren't. But the information that light always move on the same speed, on any direction and for every observer has been tested again and again since the end of the 19th century. Nobody ever saw it fail. There is of course a huge number of variables nobody tested yet. And we can't know if those are important or not. But we are very logically biased into assuming they aren't until we have a real need for them to explain something. (Anyway, the thing you are trying to invent is a kind of modified Newtonian mechanics - even though it's not quite Newtonian, but people use that same name. There are other people trying to get a workable theory with similar parameters. Up to now, nobody got any.)
- V__ 3y ago
  > light always move on the same speed, on any direction and for every observer has been tested again and again I might be wrong or misunderstanding, but I think that hasn't actually been tested ever. Only two-way speed of light is known. [1] [1] https://www.youtube.com/watch?v=pTn6Ewhb27k https://www.youtube.com/watch?v=pTn6Ewhb27k
  - marcosdumay 3y ago
    I'm sorry, but I'm not watching a 19 minutes video to discover what you mean by "two-way speed". Can you explain it? But anyway, we've been comparing the speed of light over different directions since the 19th century. Modern relativity was created because of those measurements, and nowadays you can buy accelerometers and gyroscopes that work based on that constant speed.
    - ajuc 3y ago
      > Can you explain it? Can't measure one-way speed of light because you need to get the result back somehow (and that's also limited by speed of light). Usually we just send light and wait for it to bounce back.
    - j16sdiz 3y ago
      We can measure the speed from A to B back to A. We can’t measure the speed from A to B directly (without sending something from B back to A wrt speed of light). https://en.wikipedia.org/wiki/One-way_speed_of_light https://en.wikipedia.org/wiki/One-way_speed_of_light
tekla 3y ago
Everything you've proposed has already been tested non stop for a hundred years.
deleted 3y ago
[deleted]
johndunne 3y ago
It's a salient question. We don't know. There's still physics we don't fully understand (e.g. dark matter/energy) which could end up requiring adjusting or explaining further out understanding of the constants in e=mc^2 for example.

tux3 3y ago

This doesn't really answer your question, but there is already an extra term! (only sometimes it is zero) E^2 = (mc^2)^2 + (lc)^2

spanglasaur 3y ago
I was going to comment this as well. Here is a thorough explanation of the missing term: https://physics.stackexchange.com/questions/143652/is-e2-mc22pc2-or-is-e-mc2-the-correct-one https://physics.stackexchange.com/questions/143652/is-e2-mc2... The thing that I love about this formulation of the equation is that it directly ties it to the Pythagorean theorem: c^2 = a^2 + b^2 . It really shows you just how pretty that equation really is!
lamontcg 3y ago
the m in that equation is the rest mass (m_0) which is a proper scalar. the m in E=mc^2 is the relativistic mass which depends on rest frame and therefore isn't a proper scalar quantity and that isn't a proper tensor equation. the (E, px, py, pz) energy-momentum 4-vector is a tensor that transforms to any reference frame with a lorentz transform. all observers will agree on the shape of that 4-vector object, although they'll measure the components differently. that equation is just the dot product (rearranged), where the rest mass is the length of the 4-momentum vector (and a proper scalar quantity that all observers agree on is exactly that value in all reference frames). the rearrangement introduces a negative sign which actually comes from the SR metric -- usually diag(-1, +1, +1, +1) but sometimes diag(+1, -1, -1, -1).

simonh 3y ago

Distance from the Big Bang? So zero then. But even if say energy or the speed of light are derived from other parameters, that doesn’t make the equation wrong, just incomplete. Anyway for all the phenomena we don’t have complete explanation for, none of them give any indication relativity is incorrect, and therefore there’s no reason to suppose tweaking it would help explain them.

FetusP 3y ago

Intro college Physics is reformatting formulas to solve for variables in other formulas, and inserting them into each other. So even if c = (w+x+y+z), e=mc^2 and e=m(w+x+y+z)^2 would still be equivalent.

layer8 3y ago

Your what ifs are theories that have been or are being explored. But so far the predictions they made either have been falsified, or they haven’t made any that would make them more plausible overall than the standard model. For any such ideas that come to mind, you can be pretty sure that many, many physicists have already gone through them.

abakker 3y ago
Oh, I was not trying to be original or second guess experts. It’s just hard to google a concept like this and get useful answers.

marcosdumay 3y ago

We don't know anything. If you want to know how we are sure of it, we aren't. But the information that light always move on the same speed, on any direction and for every observer has been tested again and again since the end of the 19th century. Nobody ever saw it fail. There is of course a huge number of variables nobody tested yet. And we can't know if those are important or not. But we are very logically biased into assuming they aren't until we have a real need for them to explain something. (Anyway, the thing you are trying to invent is a kind of modified Newtonian mechanics - even though it's not quite Newtonian, but people use that same name. There are other people trying to get a workable theory with similar parameters. Up to now, nobody got any.)

V__ 3y ago
> light always move on the same speed, on any direction and for every observer has been tested again and again I might be wrong or misunderstanding, but I think that hasn't actually been tested ever. Only two-way speed of light is known. [1] [1] https://www.youtube.com/watch?v=pTn6Ewhb27k https://www.youtube.com/watch?v=pTn6Ewhb27k
- marcosdumay 3y ago
  I'm sorry, but I'm not watching a 19 minutes video to discover what you mean by "two-way speed". Can you explain it? But anyway, we've been comparing the speed of light over different directions since the 19th century. Modern relativity was created because of those measurements, and nowadays you can buy accelerometers and gyroscopes that work based on that constant speed.
  - ajuc 3y ago
    > Can you explain it? Can't measure one-way speed of light because you need to get the result back somehow (and that's also limited by speed of light). Usually we just send light and wait for it to bounce back.
  - j16sdiz 3y ago
    We can measure the speed from A to B back to A. We can’t measure the speed from A to B directly (without sending something from B back to A wrt speed of light). https://en.wikipedia.org/wiki/One-way_speed_of_light https://en.wikipedia.org/wiki/One-way_speed_of_light

tekla 3y ago

Everything you've proposed has already been tested non stop for a hundred years.

deleted 3y ago

[deleted]

johndunne 3y ago

It's a salient question. We don't know. There's still physics we don't fully understand (e.g. dark matter/energy) which could end up requiring adjusting or explaining further out understanding of the constants in e=mc^2 for example.