Science Quiz #2: Is E=mc² right or wrong?

E=mc² is one of the most famous equations ever, but is it the right equation?

Of course there are relativity deniers and fringe scientists who question all sorts of things about mainstream science, but that's not the topic of this thread. This source is a video by mainstream scientists who at 1:55 in the video say "It's not even the right equation":

E=mc² is wrong? - Sixty Symbols

www.youtube.com...

Then they proceed to give the right equation which is essentially the same for the rest mass term (though both sides are squared), and it has an extra term for momentum, as follows (screen capture from around 2 minutes in the video):



This momentum term can be significant, for example in determining the energy of protons in particle accelerators like the Large Hadron Collider.

To answer the question about whether it's right or wrong, I wouldn't say it's wrong unless you try to apply it to cases where it's inadequate like the energy of protons in the LHC. It's probably better to say it's incomplete, meaning it's missing a term which can be eliminated in special cases (where the momentum is zero).

I think "incomplete" is a more appropriate term than "incorrect". But that's just my opinion as a non-expert.

An interesting thing to bring up. Thanks. But I would question anyone at ATS who would judge this one way or another. Judging the truth of Einstein seems a rather precarious, if not hubris-fueled, endeavor.

originally posted by: AfterInfinity
I think "incomplete" is a more appropriate term than "incorrect". But that's just my opinion as a non-expert.

I'm no expert myself but it seems to me it can only be seen as incorrect. If it translates to negative mass for nothing, it's not just incomplete.

originally posted by: Antipathy17

originally posted by: AfterInfinity
I think "incomplete" is a more appropriate term than "incorrect". But that's just my opinion as a non-expert.

I'm no expert myself but it seems to me it can only be seen as incorrect. If it translates to negative mass for nothing, it's not just incomplete.

It's a Youtube video. Given that it could be full of crap and I wouldn't know, I'll take it with a fistful of salt.

originally posted by: schuyler
An interesting thing to bring up. Thanks. But I would question anyone at ATS who would judge this one way or another. Judging the truth of Einstein seems a rather precarious, if not hubris-fueled, endeavor.

Yes, Even Einstein may have underestimated himself when he said the cosmological constant was the biggest mistake he ever made. In 1998 when we discovered dark energy, we're now saying maybe "Einstein's biggest mistake" wasn't a mistake after all, as it might explain dark energy related observations.

The problem isn't so much agreeing or disagreeing with Einstein, it's getting taught over-simplified or distorted versions of what Einstein said that aren't quite right. For example, Einstein cautioned against the concept of "relativistic mass" yet that concept is taught in some schools. So my criticism in that case isn't with Einstein, but with what the school is teaching.

In the case of this thread's topic, it's a matter of a simplified equation with a term missing.

originally posted by: Antipathy17
I'm no expert myself but it seems to me it can only be seen as incorrect. If it translates to negative mass for nothing, it's not just incomplete.

I'm not sure I follow your logic about negative mass.

One of the problems with proposed "warp drive" technology is that it requires negative mass and we don't know how to do negative mass.

originally posted by: AfterInfinity
It's a Youtube video. Given that it could be full of crap and I wouldn't know, I'll take it with a fistful of salt.

The video interviews a number of physics professors from the University of Nottingham, so chances are if they're wrong, so is a lot of mainstream science. One professor did say something wrong in one of the videos, and when you watched the video, it had a corrected text subtitle superimposed on the video pointing out it was wrong and what the corrected version was, so apparently these videos are somehow reviewed to some extent for accuracy, if that's any indication.

Well, definately not wrong. I wouldn't even say incomplete. There are a lot of formulas where negligible factors are dropped. For instance, the formula for Force: F=ma omits the factor Cosine(theta) when the force and the acceleration are in the same direction, because the Cos(0)=1.

Now, we know that an object's mass increases as it approaches the speed of light. All the video is saying is that for speeds well below the speed of light, E=mc^2 is fine: but as you approach the speed of light you need to take into account the extra mass caused by the high speed.

Think back on how many physics problems you had on tests where you were told to assume friction was negligible.

a reply to: Antipathy17

He actually said:

The correct equation - even if the momentum is zero - is E²=m²c^4. And if you take the square root of that you can get negative energy.

So, he is talking about the correct equation producing the negative energy.

originally posted by: VictorVonDoom
Think back on how many physics problems you had on tests where you were told to assume friction was negligible.

Exactly, and then I graduated and had to solve real world problems and found out that it is rarely negligible, like maybe half the gasoline I burn when driving around could be be lost to friction.

originally posted by: lemmin
So, he is talking about the correct equation producing the negative energy.

You're right. That's not negative mass. Near the end of the video they talk about Dirac recognizing that the negative values might imply things like an anti-electron, known as a "positron", and the other anti-matter particles, which were eventually discovered.

originally posted by: Arbitrageur
[Exactly, and then I graduated and had to solve real world problems and found out that it is rarely negligible, like maybe half the gasoline I burn when driving around could be be lost to friction.

But, of course, without friction, the car wouldn't go anywhere.

I guess the surest way to prove it would be for light to be used to create matter.

Prolly would take a huge amount of energy, a huge sum of $ to make that energy, and net out nearly an immeasurable difference.

Derek

originally posted by: VictorVonDoom
But, of course, without friction, the car wouldn't go anywhere.

It's gone into the ditch more than once on a nearly frictionless ice-covered road before the salt trucks made their rounds. It's quite an experience when stomping on the brakes doesn't seem to slow down your car.

Both of those equations are correct. The first, Einstein's equation involves relativistic mass and the second, which includes momentum component involves rest mass.

I haven't looked at the videos, but from my university physics courses, E=mc^2 is correct only if momentum is zero. (or ignored if it is almost zero) It's like how people say force is mass times acceleration, but this isn't strictly true, as there is a 1/sqrt(1 - c^2/v^2) term in there (lorentz factor), but unless you're going close to light speed, it's irrelevant; in practical applications, it's generally ignored unless you're working with radar or a space shuttle or orbiting satellites or something where stuff is moving fast enough to make a difference. Same thing with the E=mc^2 vs E^2 = m^2c^4 + p^2c^4

Basically, E=mc^2 is correct in certain specific situations; otherwise, you need the full equation.

originally posted by: eManym
Both of those equations are correct. The first, Einstein's equation involves relativistic mass and the second, which includes momentum component involves rest mass.

Yes you may have been taught that, but it wasn't Einstein's intention that you would see it that way, and as the video points out, in line with the following quote, a subscript of 0 or "naught" is implied in the first meaning it does NOT consider relativistic mass, but due to some sloppiness and not following Einstein's advice, the implied subscript is rarely written (the OP video is an exception which explains that).

Rest mass versus relativistic mass

Einstein's equation E0=mc^2 became known in its famous but misleading form E=mc^2. One of the most unfortunate consequences is the concept that the mass of a relativistic body increases with its velocity. This velocity dependent mass is known as “relativistic mass.” Another consequence is the term “rest mass” and the corresponding symbol m0. These confusing concepts and notations prevail in such classic texts as the ones by Born and Feynman. Moreover, in these texts the dependence of mass on velocity is presented as an experimental fact predicted by relativity theory and proving its correctness.

To substantiate the formula m=E/c^2 some authors use the connection between momentum and velocity in Newtonian mechanics, p=mv, forgetting that this relation is valid only when v (is significantly less than) c and that it contradicts the basic equation m^2=(E/c^2)^2−(p/c)^2. Einstein's tolerance of E=mc^2 is related to the fact that he never used in his writings the basic equation of relativity theory. However, in 1948 he forcefully warned against the concept of mass increasing with velocity. Unfortunately this warning was ignored.

As one of the previous comments suggested, you should be careful about arguing against Einstein, which your interpretation (perhaps unintentionally) does. Here is the actual quote from Einstein:

Mass in special relativity


The professors at the University of Nottingham in the video are trying to teach the concepts as recommended by Einstein, and for this I commend them. Not all students have been so fortunate and it appears you've been subject to some contrary teaching. There is some debate about this topic and some scientists intentionally teach their students something like what you said, against what Einstein recommended. Personally, I don't see why Einstein's advice should be ignored like this.

a reply to: DragonsDemesne
Good assessment!

originally posted by: Arbitrageur

originally posted by: schuyler
An interesting thing to bring up. Thanks. But I would question anyone at ATS who would judge this one way or another. Judging the truth of Einstein seems a rather precarious, if not hubris-fueled, endeavor.

Yes, Even Einstein may have underestimated himself when he said the cosmological constant was the biggest mistake he ever made. In 1998 when we discovered dark energy, we're now saying maybe "Einstein's biggest mistake" wasn't a mistake after all, as it might explain dark energy related observations.

I'm not so sure. The cosmological constant is an ad-hoc "effective' term. When the underlying physics of dark energy is finally discovered it will likely be put back into the Einstein equations in its own physical way---which in some limiting case will look like a cosmological constant.

In any case, Einstein hacked in a constant which kept things quasi static (unlike dark energy); after Hubble expansion was discovered observationally Einstein recognized there was no reason to think that there is a fundamental term in there.

a reply to: mbkennel
Yes that's what happened exactly, he was trying to make a static universe, so the expanding universe some now guess may be expressed in such a way is not what Einstein expected at all, but nobody I know of expected to find the expansion of the universe was accelerating. It seems to have come as pretty much a complete surprise to everybody.

Good thread. I think that the "New Equation" is also limited and is not yet "Complete". Dark Matter / Dark Energy may be a possibility to be added to the equation but it needs to be studied / proved and the Constance's determined / proved before this could be actively inserted in to the New or Old equation.