# Blackhole formula explanation

#### philipishin

Blackhole formula Root(c^2)=c=Root(E/m) from (1+1=2) means energy is same with mass. So when we measure energy with mass, there is no number.
(1=1. When we put 2 into equation, 1:2=1:2. It means it is changed 1=1 into 2=2. This means number is changed.) It is black hole. So physics formula as v=at(speed) means true as basic from its origin. (E=m*c^2)

#### benit13

Blackhole formula
$$\displaystyle E = mc^2$$ is not the "black hole formula". It's Einstein's famous equation for the book-keeping associated with conversions between mass and energy. What makes it special is the fact that if 1 Joule of energy is converted to mass, we can find out precisely how much mass is converted.

Root(c^2)=c=Root(E/m) from (1+1=2) means energy is same with mass.
If you take the following equation

$$\displaystyle E = mc^2$$

and square root both sides

$$\displaystyle \sqrt{E} = \sqrt{m}c$$

then divide both sides by $$\displaystyle \sqrt{m}$$, then you obtain

$$\displaystyle c = \sqrt{\frac{E}{m}}$$

but this is just algebra to make c the subject of the equation. It doesn't show or prove anything.

Mass and energy are, in fact, not the same; the formula is a simplification of

$$\displaystyle E^2 = m^2 c^4 + p^2 c^2$$

in the case of zero momentum (p=0). It is a formula that describes the energy associated with an object travelling at the speed of light that has both mass and momentum. This is required because in some nuclear reactions and particle collisions, the momentum is an important contributor, such as in photo-absorption and photo-disintegration.

So when we measure energy with mass, there is no number.
Firstly, 1 + 1 = 2 is just 'counting' in mathematics. In physics, there's no additional meaning beyond what it states, which is how to get to the next number in a counting sequence.

Secondly, we can measure the mass of an object to be 10 kg and the kinetic energy of that same object to be 20 J, or 30 J, or whatever. They're physical quantities just like any other. All physical quantities have an amount (a number) and a unit (like J or kg).

(1=1. When we put 2 into equation, 1:2=1:2. It means it is changed 1=1 into 2=2. This means number is changed.)
The energy of objects changes all the time, the mass less so.

It is black hole.
A black hole is an object whose mass is so high that no force can compete with with the gravitational force that pulls everything inside. Therefore, it collapses to an object that has a very tiny volume (some believe it to be zero; a singularity) but a finite mass. This corresponds to an enormous density (possibly infinite if the volume is zero). Black holes are very strange objects indeed and they are under intense study.

So physics formula as v=at(speed) means true as basic from its origin. (E=m*c^2)
No, the formula

$$\displaystyle v = at$$

is actually derivative of the definition of acceleration, which is

$$\displaystyle a = \frac{dv}{dt}$$

When the change in velocity is constant over some time interval we have

$$\displaystyle a = \frac{\Delta v}{\Delta t}$$

Multiply by $$\displaystyle \Delta t$$ to both sides yields

$$\displaystyle \Delta v = a \Delta t$$

By definition

$$\displaystyle v_2 - v_1 = a (t_2 - t_1)$$

Finally, if the start velocity is $$\displaystyle v_1 = 0$$ m/s and the start time $$\displaystyle t_1 = 0$$ s, then

$$\displaystyle v_2 = a t_2$$

or, for convenience, we can drop the index, giving

$$\displaystyle v = at$$

The typical nomenclature is to keep $$\displaystyle v_1$$ as an unknown (usually denoted as the symbol $$\displaystyle u$$) but to set a reference time, $$\displaystyle t_1 = 0$$, for every problem. Therefore we instead have

$$\displaystyle v = u + at$$

which is one of the famous SUVAT equations for the motion of objects at constant acceleration.

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#### Pmb

PHF Hall of Fame
What makes it special is the fact that if 1 Joule of energy is converted to mass, we can find out precisely how much mass is converted.
Mass cannot be converted to energy. When such a statement is made it implies that one increases while another decreases. but both mass and energy of a closed system remain constant. Only the form of the energy changes.

A black hole is an object whose mass is so high that no force can compete with with the gravitational force that pulls everything inside.
That is incorrect. A black hole is an object which is confined to a region of space within the Schwarzschild radius. Hawking showed that micro black holes can exist which have a mass less than the Sun,

Regarding the equations you posted. The E = mc^2 one assumes that m is proper mass. As such E is proper energy and has the symbol $$\displaystyle E_0$$. But not all physicists use mass to mean proper mass. Many use it to mean inertial mass, aka relativitic mass. Also rest mass and proper mass are different things

Its important to now that if m is relativistic mass of a particle and that particle is in a gravitational field then its E is not equal to mc^2. Its a bit more complicated. 4-momentum is defined as P[/b ] = (mc, p) where m = relativistic mass and p is 3-momentum. Energy is then proportional to the time component of the corresponding 4-form.

It can be problematic. For example; people often make the mistake of thinking that if the mass of light (a directed beam) is zero then it has no gravitational field and it also cannot be deflected by a gravitational field. Both are wrong.

Since light has energy it has an effective mass. Watch this video for details
http://www.newenglandphysics.org/common_misconceptions/Alan_Guth_01.mp4

A very similar argument is given by Feynman in his lectures.

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#### benit13

Mass cannot be converted to energy. When such a statement is made it implies that one increases while another decreases. but both mass and energy of a closed system remain constant. Only the form of the energy changes.
Yes, but in certain systems, mass and energy aren't conserved independently; only their sum. In nuclear fusion reactions, for example, the total mass decreases and the total energy increases after the reaction, but nothing leaves the system because the additional energy manifests as kinetic energy of the products.

That is incorrect. A black hole is an object which is confined to a region of space within the Schwarzschild radius. Hawking showed that micro black holes can exist which have a mass less than the Sun,
Yes, agreed, but I want to point out that such objects haven't been observed yet; in fact, even our understanding of stellar mass black holes are a bit shaky because there's not many observations of them (except for Cygnus-X and the recent gravitational wave studies). Almost all black holes we know about are super-massive black holes.

#### Pmb

PHF Hall of Fame
Yes, but in certain systems, mass and energy aren't conserved independently; only their sum. In nuclear fusion reactions, for example, the total mass decreases and the total energy increases after the reaction, but nothing leaves the system because the additional energy manifests as kinetic energy of the products.
That's incorrect. Didn't you read the article? You're referring to the sum of rest masses and that's not the total mass. Recall that mass has two meanings

1) proper mass - Magnitude of 4-momentum = invariant mass
2) relativistic mass

You use #1. That means (using units in which c= 1) that m = sqrt(E^2 + P^2) where E = total energy and P = total momentum. That means that m is conserved when E and P is conserved.

For general situations that's not so. In that case I recommend readers see: Invariant Mass

I use #2: in that case the relativistic mass is conserved when energy is conserved.

Do you have Spacetime Physics - 2nd Ed? Do you know how to get the AJP article? Anyway, I explain it all in my own paper which I posted a URL to before.

You mentioned nuclear fission. Way ahead of you my friend. See

SR Template

The fact that mass isn't converted into energy in atoms bombs was pointed out as early as a year after Hiroshima as I recall. The author of the paper explained why. That article is

A Relativistic Misconception by C. Roland Eddy, Science, September 27, 1946.

I uploaded it for your convenience. I'm a cool dude in a loose mood.

Yes, agreed, but I want to point out that such objects haven't been observed yet; in fact, even our understanding of stellar mass black holes are a bit shaky because there's not many observations of them (except for Cygnus-X and the recent gravitational wave studies). Almost all black holes we know about are super-massive black holes.
That's irrelevant to the subject of black holes. The term "black hole" was coined by John Wheeler in the 60's as a star which collapsed so that all of its mass fell into the Schwarzschild radius, i.e. as an object from which light cannot escape. That doesn't require it to have a particular mass. And telling people that its defined as you did misleads them into thinking that the real black holes as they are actually defined is wrong. That's just bad cricket.

After all, the OP didn't ask what the mass of the black holes that we've detected so far. It also misleads them to think that stellar mass black holes can't exist and that's wrong. And it also implies that a star cannot collapse to become a black hole and then that's "your bad."

He's speaking of black holes and that's all. We need to make c100% certain that when we explain something they don't walk away with misconceptions which are our fault. If this case you actually provided the wrong definition of them. That's really bad tutoring if you did that intentionally. Please tell me you didn't??

Are you familiar with the text Exploring Black Holes- Introduction to General Relativity by Taylor and Wheeler? If you have a copy then turn to the glossary and look up the term black hole which is on page GL-3
black hole In this book, any structure with a horizon and surrounded at a great distance by flat spacetime.
Hmmmmm ....... Of course the person who wrote the glossary might not know the definition of a black hole. Then again one of the authors is the guy who coined the term "black hoie"

Then again the glossary wasn't written by either of the authors. It was written by some schmuck named "Peter M Brown" ...... the name sounds familiar but I can't place the face. Anyway, what does he know. He's probably an idiot. I'd like to request that you don't intentionally post definitions which are contrary to how they're defined in mainstream physics.

In this case the term is described and defined in Gravitation and Inertia by Ciufol and Wheeler on page 61.

I'll scan that in and upload it later today.

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#### benit13

Thanks for this... it looks like I've got some reading to do!

EDIT: no I didn't do it intentionally. I have a (bad) habit of giving loose definitions when describing things for lay-persons.

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#### Pmb

PHF Hall of Fame
Thanks for this... it looks like I've got some reading to do!

EDIT: no I didn't do it intentionally. I have a (bad) habit of giving loose definitions when describing things for lay-persons.
I perfectly understand. perfectly. In fact its part of the reason I created the New England Physics website, i.e. to have a place to hold things like this for easy reference. And because I love the name itself. Its been very difficult for me to do this too. There are certain terms which are defined/used differently by different physicists. "Total mass" is one of them. The one I used here is the one used significantly more than the other.

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