A question about particle mass

[Kazz]

If you were to rearrange the equation E=mc^2 into m=E/c^2 and for E you used reduced Planck's constant (joules) would it be a mass of some unknown/known particle?

 

[jtbell]

If by "reduced Planck's constant" you mean $\hbar$, its units are joule-seconds, not joules.

 

[Kazz]

I know, but I'm assuming 1 sec

 

[K^2]

I know, but I'm assuming 1 sec

That's an absolutely arbitrary amount of time. Why not an hour? Or a day? There is nothing special about 1 second.

 

[Kazz]

Why are people like this on the forums.

 

[haruspex]

Why are people like this on the forums.

I read your remark as implying that K^2's replies have been unhelpful. In fact, they provide a sound basis for answering your question. Is it likely that 1 second is a such a special duration of time that there is a particle of energy ℏ/(1 second) joules?

 

[Kazz]

I just wanted the *base* energy. And so one times that equals well... H-bar

 

[K^2]

Why are people like this on the forums.

Physics Forums. If you were looking for science fiction forums, that's two doors down.

In physics, the question is just as meaningful as an answer. If you are going to ask a question that makes no sense, people are going to call you on that, and it's not our fault. Now, I am always happy to explain why a particular question is meaningless. Whether I can explain it in a way you would understand, I don't know. And that's as much limitation of my abilities as yours.

If something still isn't clear and you want a more detailed explanation, ask away. Try to be specific. If you simply want to pretend that every question you make up has meaning and must be answered as such, then you are in the wrong place.

And so one times that equals well... H-bar

Yes. One times h-bar is h-bar. One times anything is same anything. But h-bar doesn't have units of energy. Multiplying by 1 doesn't change that. You need to multiply by a quantity that has units of inverse time. For example, \hbar \omega is energy of a photon with angular frequency ω. But that frequency has to come from somewhere. You can't just grab an arbitrary number.

 

[K^2]

You cannot answer a bad question. A false assumption can be used to derive absolutely anything. The only good answer to a bad question is explanation why it's a bad question. Any other ideas you have on the topic are objectively wrong.

 

[Kazz]

Not 1... 1 second.

 

[haruspex]

Not 1... 1 second.

Exactly. 1 x some quantity of energy is still a quantity of energy. 1 second x some quantity of energy is a quantity of action. But 1 second is an arbitrary period. Why not one year?

 

[K^2]

Not 1... 1 second.

Unlike number 1, quantity 1 second is not a true unit. 1 second is also 1000 miliseconds. It is also 1/60th of a minute. It only has the number 1 in its description because of the choice of duration of a second. The moment I change the duration of a second, that number is no longer 1. So why in the world would multiplying by one second ever give you any significant value?

Worse yet, h-bar times one second doesn't give you joules either. The units of h-bar are joules-seconds, not joules/second. You have to multiply by something with units of inverse time.

 

[Kazz]

If you were to divide h-bar by one second wouldn't the seconds cancel out?

 

[mfb]

It would, but it does not have any special physical meaning. It is an arbitrary energy which depends on the length of a day on Earth (as this was originally used to define "1 second").

 

[haruspex]

If you were to divide h-bar by one second wouldn't the seconds cancel out?

Planck's constant, like any universal constant (such as velocity of light in vacuo), is independent of the units it's expressed in. In joule-seconds it's about 6.626×10−34. In electron-volt-years it would be 1.31 x 10-22. By your logic, you would divide that by one year and obtain 4.136×10−15 eV as some special quantity of energy. Or do the same with fortnights, millennia, ... and generate all sorts of magical numbers.
What is legitimate is to take a collection of universal constants and combine them: h-bar/c² will give you something apparently interesting in units of mass*time.

 

[Kazz]

I really wish I could post stuff here without being bashed for mistakes and explained POLITELY why it's wrong and not with sarcasm and rudeness.

 

[K^2]

There is no sarcasm. You were told several times by several different people that there is nothing special about 1 second as a unit of time. That's all there is. Why do you insist to divide by 1 second and not by 1 day? Can you explain that? If there is nothing special about it, then why should there be anything special about associated energy?

 

[haruspex]

I really wish I could post stuff here without being bashed for mistakes and explained POLITELY why it's wrong and not with sarcasm and rudeness.

I was not being sarcastic. The most effective way to point out a flaw in an argument is often to demonstrate its most absurd consequences. Reductio, as they say, ad absurdum. Nothing else was working.

 

[FeynmanIsCool]

The problem with rearranging it that way is that its slightly miss-using the equation. The m in E=mc2 is "rest mass", not relativistic mass.

 

[FeynmanIsCool]

Leonard Susskind talked about this in one of his Relativity Lectures

 

[K^2]

The m in E=mc2 is "rest mass", not relativistic mass.

Other way around. For rest mass, the equation is E²=p²c²+(mc²)². Though, convention is to reserve the symbol 'm' for rest mass. In which case, the first equation should be written as E=γmc².

 

[DrewD]

The number is \approx7.37\times10^{-51}kg. I doubt that there is an elementary particle with that mass for a number of reasons.

First, there is no reason to expect that there would be. That doesn't mean that there isn't, but the chance of there being one is about the same as any other number.

Second, and more importantly, this is about 20 orders of magnitude less than the any other known elementary particles. Perhaps there are smaller particles that we don't know about, but that would be 100% speculation.


P.S.
Don't take people's comments personally. The internet can make things sound mean when there was no intention of that. If you are interested in physics you should
A) learn to be told you're wrong (this will happen more often than anything else)
B) try to figure it out on your own. If you plug the numbers in and check on Wikipedia (more less all that I did) you'll see that numbers don't work out to be anything meaningful. If they did... you could ask why and you would get the answer "by chance"

 

[FeynmanIsCool]

Other way around. For rest mass, the equation is E²=p²c²+(mc²)². Though, convention is to reserve the symbol 'm' for rest mass. In which case, the first equation should be written as E=γmc².

Your right, I should clarify next time.

 

[Kazz]

I still got the same mass after I did c times Plancks length squared over gravitational constant (from GM/d^2)

 

[K^2]

No you didn't. Plank's length is meters. Squared is m². c is m/s, so you have m³/s. Gravitational constant is N(m/kg)². So your final result is m³kg²/(m²N*s) = m*kg²/(N*s) = m*kg²/(kg*m/s) = kg*s. Your answer isn't even in kilograms, so whatever you got, it isn't mass.