/sci/ - Science & Math

Something turns into a black hole if its radius is smaller than the Schwarzschild radius, right?

The radius of a proton is 1.2x10^-15 meters, correct?

>>3746037
>>3746034
Samefag.

>>3746037
>>3746034
>!!BJiYgff8zf
>!!BJiYgff8zf

Pic related

where:
Rs is the Schwarzschild radius;
G is the gravitational constant;
m is the mass of the gravitating object;
c is the speed of light in vacuum.

So far so good?

>relativistic mass

Saged, reported, called the cops.

>>3746034
>>3746037
>MFW didn't remove trip

>>3746039
Nice catch.

Epic fail, OP.

>>3746037

No.

The schwarzschild radius is just the event horizon. Its not a constant, as it varies with the mass of the black hole.

>!!BJiYgff8zf2
>!!BJiYgff8zf2

>>3746034
>>3746037
I think he's just making multiple posts, you idiots.

>>3746037
>>3746034
Obvious samefag is obvious...

>>3746052
>samefags
>tries to backpedal
>calls others an idiot

>>3746037
>The radius of a proton is 1.2x10^-15 meters, correct?

At least get the right number, you demented moron.

>>3746052
>He... he... maybe they'll believe this excuse

No. Fuck off.

>>3746052

Yeah I know.

I think maybe its a samefag for the people accusing OP for samefagging.

God damnit, OP is a legitimate fellow. Havent you ever made a post, and then realized you forgot a detail and commented on your own post immediately?

>>3746037
>>3746034

At least remove your fucking trip before samefagging.

>>3746034
>>3746037
>>3746052
>>3746060

I smell a samefag.

Wow, /sci/ is fucking retar-
>!!BJiYgff8zf2
Never mind, continue.

>>3746060
>Implying you aren't OP

G = 6.67300 × 10^-11
c = 299792458

We want Rs = 1.2x10^-15

Therefore: 1.2*10^-15 = 13.346 * 10^-11 * m / 9 * 10 ^ 16

1.2*10^-15 = 1.48288889 * 10^-27 * m

m = 8.0923123 × 10^11

>>3746062
>>3746068

Fuck you Im not OP, you cynical assholes.

>ITT: oh wow I'm op and im a faggot oh no i died from and heart attack. In heaven : oh hi its god and god said "fuck off OP" but op said no and got sent to hell and satan called him a samefag and then op had a heart attack and went to double hell to suck engineer dick

>>3746071
You're persistent OP.

>>3746071
>cynical

And this is the NICEST board. If you can't handle the heat then get off The Chan.

The mass of a proton is 1.67262158 * 10^-27

We want it to increase to 8.0923123 * 10^11

So we need to increase the mass of a proton by 4.8381011 * 10^38 times

Someone isn't even allowed to ask a question, and provide a partial answer to get the discussion going.
Also, I don't even care if you call me OP.

>>3746034
Relativity doesn't work that way. "Relativistic mass" is a model and way of thinking that is so two decades ago.

We know that the rest energy of a proton is 0.938 GeV

Since mass is directly proportional to energy all we have to do is to increase the energy of a proton by 4.8381011 * 10^38 times

Giving us 4.53813883 × 10^38 GeV

Converting this to joules, we get 7.27089921 × 10^28 Joules

>>3746095
It doesn't?
So how does speed relative?

>>3746095

Please explain further

>>3746095
>>3746101
>>3746102
The general idea of general relativity is that the rules are the same for each observer. It makes no sense for a proton to become a black hole by going fast enough, because it'd be at rest according to another observer.

>>3746102
Relativistic 'mass' is not mass, but energy.

>>3746107

But evidence from particle accelerators suggest that particles do gain mass as they become faster.

Isn't there a universal frame of reference in General Relativity?

>>3746113

Energy is equivalent to mass

>>3746116
They don't. They gain kinetic energy, which can be converted into mass, via mass-energy equivalence.

>>3746107
Right. Makes sense.
Could it be that the mass does increase, but the (universal) gravitational constant decreases? (Such that the total gravity of the moving body remains constant.)

>>3746117
False. I bet you believe E = mc² is always true. You are so hilariously stupid.

>>3746117
Energy can be converted into mass, and vice-versa.

>>3746118

Energy is equivalent to mass, so it doesn't matter

>>3746121

Gravity is coupled to energy

>>3746107
So if mass doesn't increase when you're going faster, then why is it so hard to accelarate to near light speed velocity?

>>3746128
Because the laws of physics act differently at high energy.

Everyone thinking that OP was samefagging (as opposed to just posting twice) clearly don't understand relativity. He was asking about SPEED, then made a post about what he already knows - the Schwarzschild radius.

>>3746131

That sounds like a load of bullshit. It's not a physical law if it doesn't apply to everything everywhere at all times

>>3746119
No. The rules are the same for all observers who are not accelerating. There is no preferred reference frame.

>>3746134
F = ma
is simply false. That's only an approximation.

>>3746134
>guys whats an approximation

Continuing the calculations:

We need the proton to have an energy of 7.27089921 * 10^28 Joules

We know that k.e is 0.5*m*v^2

7.27089921 * 10^28 = 0.5* (1.67262158 * 10^-27) * v^2

v^2 = (7.27089921 * 10^28) / (0.5* (1.67262158 * 10^-27)) = 8.69401579 * 10^55

v = 9.32417063 × 10^27

Wait, that's wrong because nothing can travel faster than the speed of light. So we need to use the other equation.

>>3746131
Doesn't make sense yet. If the laws of physics change at near lightspeed velocity, then relativity of speed is violated.

>>3746152
No, it's not. You obviously have no idea what is being talked about.

Go ahead, write out the correct relativistic relationship between energy and speed.

>>3746152
What I mean is, just do an experiment on a rocket traveling through space. If F=m*a, then you're going slow, if F!=m*a, then you're going fast.
Clearly, it doesn't work that way.

>>3746156
I am interested in how it does work. I didn't major in physics, so I have no clue, all I know is HS physics + pop sci.

>>3746039
>>3746040
>>3746044
>>3746047
>>etc

Jesus fuck, /sci/, this guy clearly wasn't even trying to samefag.. I didn't realise quite how many of us were totally retarded.

(not even samefagging)

This thread:

>First year undergrads
>first year undergrads everywhere

>>3746162
Well, then know that E = mc² is only true in the frame of reference where the particle is at rest.

F = ma is always wrong, but if you are moving slowly it's a bit less wrong.

>>3746175
But doesn't general relativity forbid you to refer to a situation 'at rest'?
Or do you mean 'at rest relative to the observer'?

>>3746180
Oh, god, so many misconceptions. This is why I hate popsci.

You can always choose a frame of reference where the object you are studying is at rest, as long as said object is not moving at the speed of light. When Einstein wrote E = mc² he meant it to be true only in the rest frame of a system. In any other frame E² = (mc²)² + (cp)². Notice how that's different from E = mc² + cp.

>>3746034
>relativistic mass to increase enough for the proton to turn into a black hole

Nope. This can not happen. It leads to too many nonsensical fucked up contradictions. The bigest being that you could have "black holes" in one reference frame and not in another. WTF?

>>3746190
>implying your mothers vagina isn't a black hole which sucks in all dicks which get within 20m of it

>>3746187
I understand frames of reference. So with 'at rest' you meant, 'at rest relative to the frame of reference'. Then it makes sense.
But still, my question isn't answered. What specifically keeps us from exceeding light speed? Is it just time dilation?

>>3746199
>What specifically keeps us from exceeding light speed?
Causality. It appears to be a fundamental aspect of the universe.
Exceed lightspeed = break causality.

>>3746199
>So with 'at rest' you meant, 'at rest relative to the frame of reference'.

Well that's just so obvious it shouldn't need stating

>>3746190
>frame dependent blackholes

>>3746199
>What specifically keeps us from exceeding light speed?

Nothing. Things exceed the speed of light all the time in general relativity. It really all depends on frames and shit. For non-inertial frames THERE IS NO LIGHTSPEED LIMIT.

>>3746201
You are wrong good sir!

>>3746190
>frame dependent black-holes

>>3746204
Implying high schoolers (=90% of this board, sadly), don't literally mean at rest, relative to a universal frame of reference.

>>3746211
>Things exceed the speed of light all the time in general relativity.
Such as?
I'm fairly convinced that general relativity is built upon the assumption that all frames see light speed as being the same velocity. If an object exceeds light speed according to some other frame of reference, then there is a contradiction.

>>3746211
>Things exceed the speed of light all the time in general relativity.
They really don't.

http://www.physicsforums com/showthread.php?t=111307
please stop acting stupid, /sci/.
sage.

>>3746211
It is sad how many physicist/scienists who don't ever take GR never realize this.

Remember SR and all it's shit (lightspeed limit, Lorentz invariance, basic time dilations, basic length contractions, etc) only apply to inertial reference frames. In non-inertial reference frames it gets alot more complicated, and most of the same rules don't apply.

>>3746219
>implying they shouldn't be banned if they do

>>3746232
The lightspeed limit always applies, I'm afraid. Even in GR.

>>3746224
>>3746223
1) In any reference frame (vaccume assumed form this point on), the "local" light speed limit is c.

2) If there exists a poincare transform from reference frame "a" to "b", then "a" and "b" each see eacthothers light speed limit as c.

3) If there does not exist a poincare transform between "a" and "b" because of gravitational psuedo-forces, then "a" and "b" have different light speed limits relative to each other.

While "a" (or "b") will always see its local light speed limit at c, it will see the light speed limit of "b" (or "a") either higher or lower then c (dependent on the orientaion of the gravitaionl potential between the two frames).

Paraphrased from
'On the Influence of Gravitation on the Propagation of Light', Annalen der Physik, 35, 1911. - Albert Einstein

You can find an English translation of this paper in the Dover book 'The Principle of Relativity' beginning on page 99; you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential.

Anyother questions?

Pic related, it's the final solution.

>>3746250

>>3746250
>1911
>general relativity
full retard, etc.
Not to mention your little excerpt proves the exact opposite of what you're claiming.

>>3746252

In plaintext:

Speed of the proton: 299792457.999999999999999999999999999999999999999999999999999999999999999999999359 m/s

>>3746250

>>3746257

Well, I answered my own question, after almost 2 hours of calculation.

>>3746262
You're still wrong though, as we've explained.

>>3746262
How does it feel to have wasted two hours of your life on something that has been pointed out to be wrong minutes after you posted?

>>3746254
What are you bitching about?
You want more recent texts that give the deriavtion for the varible speed of light in GR?

1) The Meaning of Relativity, A. Einstein, Princeton University Press (1955).
See pages 92-93, eqn (107)

2) Relativity, Gravitation, and Cosmology', T. Cheng, Oxford University Press (2005). see pages 48-49, eqn (3.39)

I dare you to find one GR book that says "c" is the light-speed limit for non-inertial frames. (Hint: There are none)

>>3746257

Which is 099.999999999999999999999999999999999999999999999999999999999999999999999999999786185% of the speed of light

>>3746267
You're confusing the fact that light travels along geodesics in curved spacetime as it having a variable velocity.

>>3746263
>>3746265

You never explained it. As far as I'm concerned, the theory is right

>>3746270
The theory is right, it's your understanding of it that's flawed.
Relativistic mass is rest mass (gravitational mass) plus a kinetic energy factor. The kinetic energy factor does not add gravitational mass.

>>3746273
>The kinetic energy factor does not add gravitational mass

Why not?

>>3746274
Because energy has no mass. Relativistic mass is not an accurate term, and we need to stop using it.

>>3746277

http://www.physlink.com/Education/AskExperts/ae305.cfm

There's no difference between inertial mass and gravitational mass according to this link

>>3746278
Indeed. You seem to think that inertial mass increases as you near c. It doesn't. It may look like it does, but it does not. That is simply a result of trying to apply F=m*a when it doesn't.

>>3746280

As energy is equivalent to mass, when energy increases it's the same thing as mass increasing.

Here's a nice link on relativistic mass:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

>Another place where the idea of relativistic mass surfaces is when describing the cyclotron, a device that accelerates charged particles in circles within a constant magnetic field. The cyclotron works by applying a varying electric field to the particles, and the frequency of this variation must be tuned to the natural orbital frequency that the particles acquire as they move in the magnetic field. But in practice we find that as the particles accelerate, they begin to get out of step with the applied electric field and can no longer be accelerated further. This can be described as a consequence of their masses increasing, which changes their orbital frequency in the magnetic field.

More evidence in support of relativistic mass

>>3746282
>As energy is equivalent to mass, when energy increases it's the same thing as mass increasing.
No. This is simply untrue. Please go through mass-energy equivalence again.

A commonly heard argument against the use of relativistic mass runs as follows: "The equation E = mc2 says that a body's relativistic mass is proportional to its total energy, so why should we use two terms for what is essentially the same quantity? We should just stay with energy, and use the word 'mass' to refer only to rest mass." The first difficulty with this line of reasoning is that it is quite selective; after all, it should surely rule out the use of rest mass as well, since within special relativity, rest mass is proportional to a body's rest energy. On that note, a second difficulty of the line of reasoning is more technical: equating energy and relativistic mass cannot be done more generally. In general relativity, it's natural to consider quantities that are conserved for a system moving on a geodesic. However, γ m is not generally conserved along geodesics. (Actually, γ m is called pt in the language of general relativity. It turns out that a closely related quantity, pt, will be conserved along a geodesic if the metric is time independent.) Note, though, that while relativistic mass γ m is not a body's total energy in general relativity, it's also not simply the source of gravity within the same theory. Finally, a third difficulty with the above commonly heard argument is that, in the interests of consistency, it should surely be applied to rule out either the "momentum density" or the "energy flux density" of light, since these also are simply related by a factor of c2. Yet, and quite rightly, these last two terms co-exist in modern literature; no one ever suggests that either of these terms should be dropped in favour of the other, because they both have their uses and are fundamentally different quantities: a spatial density and an areal density.

>>3746286
Please, stop replying to this. There is no point in feeding an obvious troll.

>>3746269
I am just stating the facts. I have given numerous resouces that support such facts.

Are you saying the resources are incorrect? That the physicist who wrote them didn't understand general relativity?

Are you saying that Einstien was wrong in his 1955 book? That he didn't understand his own theory? You saying that Einstiens book, "THE MEANING OF RELATIVITY", where he clearly defines that light speed is vaible in GR, is wrong? WTF?

If you got a problem take it up with Einstein...not me...dipshit. Or better yet, take it up with your GR teacher who fucked you ober. I learned GR in my GR class, apparently you did't.

>>3746286

How about you tell me where I'm wrong? So far you've provided nothing to back up your claims whilst I've provided plenty.

>>3746291
I'm not saying Einstein is wrong, I'm saying your understanding of what Einstein (or GR in general) says is wrong.

>>3746292
Mass can be converted into energy, and vice-versa. This is not the same as saying mass IS energy.

Everyone agrees that a moving train's rest mass is a fixed property inherent to it, just as its rest length is a fixed property inherent to it. And yet, strangely, many of the same physicists who insist that a moving train's mass does not scale by γ are quite happy to say that its length does scale by γ. There is no argument in the literature about the uses of rest length versus moving length, so why should there be any argument about the uses of rest mass versus moving mass?

An optimistic view would hold that it's a measure of the richness of physics that focussing on different aspects of concepts like mass produces different insights: intuition in the case of relativistic mass in special relativity, and the also-intuitive notion of invariance and geometrical quantities in the case of rest mass within the tensor language of special and general relativity. The two aspects do not contradict each other, and there is room enough in the world of physics to accommodate them both.

Abandoning the use of relativistic mass is sometimes validated by quoting select physicists who are or were against the term, or by exhaustively tabulating which textbooks use the term. But real science isn't done this way. In the final analysis, the history of relativity, with its quotations from those in favour of relativistic mass and those against, has no real bearing on whether the idea itself has value. The question to ask is not whether relativistic mass is fashionable or not, or who likes the idea and who doesn't; rather, as in any area of physics notation and language, we should always ask "Is it useful?" And relativistic mass is certainly a useful concept.

>>3746297

They are equivalent

>>3746298
I know relativistic mass is a concept used a lot. What you don't seem to understand is that your understanding of the concept is just wrong.

The concept of relativistic mass is neatly encapsulated in the expression F = d(mv)/dt, where m is relativistic mass. This says that an impulse F dt causes an infinitesimal increase in a body's relativistic momentum mv.

Besides this definition and use of relativistic mass, we wish here to write down the relativistic version of Newton's second law, F = ma. In Newton's mechanics, this equation relates vectors F and a via the mass m of the object being accelerated, which is invariant in Newton's theory. Because m is just a number, in Newton's theory the force on an object is always parallel to the resulting acceleration.

The corresponding equation in special relativity is a little more complicated. It turns out that the force F is not always parallel to the acceleration a. We can express this fact using matrix notation. Let m be the rest mass, and v be the velocity as a column vector, whose entries are expressed as fractions of c and whose magnitude v is the speed as a fraction of c. Let vt be the velocity as a row vector, and let 1 be the 3 × 3 identity matrix. As usual, set γ = (1 – v2) –1/2. The relativistic version of F = ma turns out to be
F = (1 + γ2 v vt) γ m a

and

a = (1 – v vt) F
——————————
γ m

>>3746299
Fine, let's try this some other way.
The m in E=mc^2 is the rest mass, not the relativistic mass.
Does that help?

So defining mass via force and acceleration isn't as simple as it was for Newton (although it is simple, in principle, to define the mass as relating impulse and momentum increase, as mentioned a few lines up). Nevertheless, the three components of the two expressions above share a factor of γ m, and the rest mass m only ever appears in both expressions accompanied by γ. The acceleration is not necessarily parallel to the force that produced it, and it's not hard to see from the above equations that it's easier to accelerate a mass sideways to its motion than it is to accelerate it in the direction of its motion. This is how relativity reproduces Lorentz's original concepts of longitudinal and transverse masses; they are actually contained in these equations. The directional dependence that the newtonian meaning of mass has now taken on is neatly contained in the matrices 1 + γ2 v vt and 1 – v vt, and the remaining factor γ m is the relativistic mass. Taking our cue from the equations like this, to isolate quantities that might prove useful, is a powerful tool in mathematical physics.

References:
(Links are provided here, but the articles cannot be downloaded for free.)

[1] The Concept of Mass, Physics Today, 42 June 1989, pg 31

[2] Putting to Rest Mass Misconceptions, Physics Today 43, May 1990, pgs 13 and 115

[3] In Defense of Relativistic Mass, Am. J. Phys. 59, November 1991, pg 1032

Some historical details can be found in Concepts of Mass by Max Jammer and Einstein's Revolution by Elie Zahar.

>>3746303

E=mc^2 is a simplified equation of the one we're using.

The relativistic mass is the momentum divided by velocity.

>>3746294
I gave the reference and even the equation that EINSTIEN defines as the "varible speed of light".

How am I understanding that wrong? It is an equation that gives the speed of light as a function of gravtaional potential.

Are you saying EINSTEINS WORDING IS WRONG?
Please, exactly what do you think Einstein means by the "varible speed of light"? What is the equation representing?

>ITT: retards clinging to ancient concepts both in SR and GR

PROTIP: both the formalism and the understanding of these has changed massively in the last decade or two, using anything published before that is retarded

>>3746306
Now you're confusing your equations.

OP here, I just found the answer.

If you go too fast, do you become a black hole?

When an object approaches the speed of light, its mass increases without limit, and its length contracts towards zero. Thus its density increases without limit. Sometimes people think that this implies it should form a black hole; and yet, they reason, since its mass and volume haven't changed in its rest frame, it should not form a black hole in that frame—and therefore not in any other frame either. So does a black hole form or not?

The answer is that a black hole does not form. The idea that "if enough mass is squeezed into a sufficiently small space it will form a black hole" is rather vague. Crudely speaking, we might say that if an amount of mass, M, is contained within a sphere of radius 2GM/c2 (the Schwarzschild radius), then it must be a black hole. But this is based on a particular static solution to the Einstein field equations of general relativity, and ignores momentum and angular momentum as well as the dynamics of spacetime itself. In general relativity, gravity does not only couple to mass as it does in the newtonian theory of gravity. Gravity also couples to momentum and momentum flow; the gravitational field is even coupled to itself. It is actually quite difficult to determine the correct conditions for a black hole to form. Hawking and Penrose proved a number of useful singularity theorems about the formation of black holes. But even these theorems do assume certain conditions which we cannot be sure are true "out there".

>>3746306
>>3746034
An overwhelimg majority (99.999%) of particle physicst do not use the concept of "relativitic mass" anymore. Even Einstien grew to dislike this concept. It leads to many problems with the way we define the modern notion of "mass" and "objects".

In particle physics we use mass as a "constant property" to define a type of particle. This is the easiest way of book-keeping we have. We then define "motion" of the particle in terms of momentum, in analogy to the rest of physics. The information encoded in the mass, and momentum is plently.

We don't need the concept of "relativistic mass" because we already have the same information encoded in the momentum and mass. Hence, using relativitic mass is just redundnant, and add unneccary varibles. Why would we want to add redundant varibles?

You can use this concept if you wish, but ALL OF PHYSICS CAN BE DONE WITHOUT IT. In fact most of special relativity and general relativity is neater and easier without such a flawed concept.

>>3746344

Yes it just seemed like a useful concept at the time

>>3746340
OP is a troll or retarded.

\thread

>>3746344
I, for one, am convinced by now.
So, correct me if I'm wrong, but momentum can continue growing without bounds (even though mass is constant, and velocity limited)?

>>3746344

Hey wait a second.

How comes it becomes harder and harder to accelerate a particle the faster it becomes, if this is not as a result of increase in mass?

>>3746344

See this post >>3746285

It says as a particle gets faster its orbital frequency changes.

How do you explain this if the mass did not increase?

>>3746360
Jesus fuck dude, why are you talking about special relativity if you haven't even take an introductory course on it?

>>3746362
Do you know what a 4-vector is?

>>3746364

A vector with 4 dimensions?

>>3746369
You're trolling, right? Please tell me you're trolling.
Though I suppose you're technically correct.
Do you know what a 4-vector in GR is?

>>3746360

http://www.wolframalpha.com/input/?i=%28%28m*%283*10^8%29%C2%B2%29%C2%B2%2B%28%28m*3*10^8*x%29%2F%28
1-%28x%2F%283*10^8%29%29%C2%B2%29^%281%2F2%29%29%C2%B2%29^%281%2F2%29

>relativistic mass
>laughing girls

>>3746352
Yes, Mass is constant.
Momentum approches infinity at v=c.

>>3746360
Because of the momentum, mometum is does not follow a simple linear relationship with speed. The relationship is all fucked up, such that momentum "BLOWS THE FUCK UP".

Hence the more momentum I have, the more energy it takes to increase my mometum.

Make sense? What part is confusing you?

>>3746370
Look, if he doesn't know what a 4-vector is you may as well give up since you're not going to get anywhere with him

>>3746412
Seems to me like a 4-vector is a vector with 4 values. Mathematically speaking, that is a 4-dimensional vector.

>okay.jpg