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Comment by abakker | Hacker News Reader

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?

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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.)

> 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

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.

> 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.

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

It basically means round-trip tests where the source of light and the detector are the same, and the light reflects back from a mirror. One-way would be having the source send the light to the detector directly, but the problem with testing that way comes down to synchronizing the clocks of the source and detector.

I don't know anything about this, I just found a Wikipedia page [1]

1: https://en.m.wikipedia.org/wiki/One-way_speed_of_light

Oh, ok.

Yeah, the one thing we tested again and again is that if there is any difference on the speed of light going and coming back, it must average to the same thing in every direction (actually in every circuit, with any number or directional changes).

There are some experiments that measure one-way speed even on the link you posted. The first measurement of the speed of light was one-way. Those are just low precision ones.

The two way speed are the same along the y axis versus the x axis. We have no ways to measure the one way speed.

we can’t falsify it. According to some HN-er, this must be unscientific

> we can’t falsify it. According to some HN-er, this must be unscientific

Apparently more than merely "can't falsify it": the maths is such that if it was different, there would never be any observation that could distinguish between them.

That extra step — that it genuinely makes no difference — would, I think, cause it to be unscientific.

At least, unscientific within relativity; given relativity can't be the whole picture (singularities popping out of maths that presumes spacetime is differentiable), we may well find another better model that would allow us to make the test, which in turn allows us to ask the question scientifically.

That said, after watching the Veritasium video ages ago, I was immediately asking myself: what about the CMB? Surely that would have a stonking big anisotropy if the speed of light wasn't close to the same in all directions? (It does have one which is assumed to be because of our motion relative to it, and I don't know enough to guess what to expect of a different-way-speed-of-light-anisotropy other than its existence, and therefore cannot compare and contrast with the observed one).

> I was immediately asking myself: what about the CMB? Surely that would have a stonking big anisotropy if the speed of light wasn't close to the same in all directions?

No, you can always cancel it out by making the whole rest of physics suitably anisotropic too. Which would, of course, be ridiculous.

changes in the speed of light would change spectroscopy, it really isn't observed in our cosmic neighborhood (maybe in the very early universe at very high redshift).

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.

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.

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

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-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!

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).

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.

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.

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.

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

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