The Tritium Puzzle: Unravelling Mass-Energy Equivalence

[Stephen Bulking]

TL;DR

How can 1 amu = 931,5 MeV and 1.66e-27 kg at the same time? They have different units

I was finding the energy required to separate tritium into it's component parts, the binding energy when it hit me that how could 1amu= 931.2 MeV and 1.66e-27 kg at the same time?

 

[LCSphysicist]

E = mc²

 

[Isaac0427]

Summary:: How can 1 amu = 931,5 MeV and 1.66e-27 kg at the same time? They have different units

I was finding the energy required to separate tritium into it's component parts, the binding energy when it hit me that how could 1amu= 931.2 MeV and 1.66e-27 kg at the same time?

The answer is laziness. The actual unit is MeV/c^2 where c is the speed of light. But when you’re talking about mass, sometimes you’ll just say MeV (which is a unit of energy) and the /c^2 is implied.

 

[Stephen Bulking]

The answer is laziness. The actual unit is MeV/c^2 where c is the speed of light. But when you’re talking about mass, sometimes you’ll just say MeV (which is a unit of energy) and the /c^2 is implied.

Hah it's as simple as that, thanks man.

 

[sophiecentaur]

The answer is laziness.

That could be a bit harsh. When you are amongst workers who are all doing the same thing, a choice of 'different' unit is quite acceptable. A measuring instrument may present its answers in a certain unit. Alternatively, you could be dealing with photons (Hz?) and massive particles (kg?) at the same time (nuclear reactions). The Energy would be a suitable common currency.

Another current thread mentioned the use of mpg, still, in the UK when we have bought motor fuel in litres for decades. Same thing.

 

[Isaac0427]

The Energy would be a suitable common currency.

Right, and I agree there is a conversion factor. To me, measuring mass in eV is like measuring mass in pounds. The conversion is implied, but it’s technically incorrect and can confuse students.

 

[Ibix]

Right, and I agree there is a conversion factor. To me, measuring mass in eV is like measuring mass in pounds. The conversion is implied, but it’s technically incorrect and can confuse students.

A very common convention is to use units where $c=1$, and then measure time in units of length, or length in units of time (that's what a light second is - we just drop the "light" prefix). This is actually quite natural in relativistic physics because time is another direction in spacetime and it's odd to use different units for different directions. In such a system, mass and energy have the same unit because $E=mc^2$ simplifies to $E=m$. Note that this isn't the same as your mass and weight confusion example, since weight is an interaction while mass is a property of a body.

Some people describe $c=1$ as an error on philosophical grounds, even if there are no practical consequences beyond some confusion. As I understand it they argue that there is a distinction between time and distance and so $E=mc^2$ remains $E=mc^2$ even if your units are such that the numerical value of $c$ is one. I seem to recall Terry Tao is one such. Others argue that if the only consequence of an error is confused students, well, it doesn't take long to learn and then it's consequence-free. The physics of the distinction between time and space is encoded in the metric tensor anyway, so why add extra factors in your equations for no practical reason?

I lean towards the latter view, as you can probably tell. Certainly it's a standard convention to suppress $c$ wherever possible. You can always mentally read a mass of 100 MeV as 100 MeV/c² if you prefer. I bet you'll get bored of the extra effort fairly quickly.

 

[Isaac0427]

Some people describe c=1 as an error on philosophical grounds, even if there are no practical consequences beyond some confusion. As I understand it they argue that there is a distinction between time and distance and so E=mc2 remains E=mc2 even if your units are such that the numerical value of c is one

That's more or less where I am. I don't dislike setting c to 1, as long as there is an understanding that there is a factor of c there. Personally, though I may not always use it in my work, when I report results I always stick the c's back in, to cause minimal confusion. The OP seemed (and for a good reason) troubled by the missing /c², and I believe the best answer to that is that physicists understandably like to get rid of factors of c and just set them to 1, and they are implied in the units, though not explicitly mentioned.

The "lazy" characterization isn't aimed at any particular physicists, I say it more about how physics treats the unit in general, if that makes sense.

 

[Nugatory]

Perhaps "efficient" would be a better choice of word than "lazy"?

 

[Vanadium 50]

I say it more about how physics treats the unit in general, if that makes sense.

One might consider if a high school experience is sufficient to pass judgement on the entire field. Just sayin'.

 

[jbriggs444]

like measuring mass in pounds

Since the pound (mass) is a unit of mass, measuring mass in pounds is entirely appropriate.