NeonBlack

Obelix, welcome to SFN. I didn't realize that falling into the magic potion when you were a baby also made you smart. Do not be suprised or upset if few people find your post enlightening. It's probably a bit too advanced for this thread. I think a more hand-waving or "cartoon" description would be more appropriate.

This is more like the weird advice thread. I don't think anyone has mentioned the essential: Don't cook bacon while not wearing pants. Don't spit into the wind. And as for Sequence's advice about the refrigerator, I guess the same applies to cleaning the house. A couple of years ago, I read that a surprising number of men are hospitalized for things getting stuck in the vacuum cleaner hose. Nearly all of them claimed that they had been cleaning the house nude. Riiight...

Hey, some people have flat faces... Anyway, a couple of nights ago, I think either on the history or national geographic channel there was a program on the history of the shroud. Apparently, when the C14 testing was done, most of it was taped except for one small segment. After they cut off a little corner of the shroud, one person brought it into the back room, put it in a box and then brought it back out. Why didn't the cameras catch this most crucial moment? They said it was to prevent experimental bias, but a lot of people came up with their own reasons and a few people even claimed that it was the church that switched the samples.

Off the top of my head. I'm not even going to check first. edit: damn http://en.wikipedia.org/wiki/Uranium

No, plug in the numbers, 5kg time 299792458 SQUARED, and you will get the amount of energy stored in the mass of 5kg at rest. This energy could be released potentially by something like annihilation of ANTIMATTER. edit: missed 2 posts while typing this time! I need to dig out Mavis Beacon. AM, just think of c squared as a conversion factor between mass and energy, kind of like how boltzmann's constant is a conversion between temperature and energy. If you want to know WHY c squared is the factor, it involves a bit of math(s). I don't know your level of mathematics, but there is a fairly recent thread with a brief derivation that I'll be willing to dig up if you're advanced enough.

Markus, I made that comment with a bit of subtle irony that both you and darkshade seemed to have missed. This is excusable since english is probably not your first language.

Ignorance is bliss.

I would say that showing the measured data points with a fit line connecting them would be most appropriate. The only times I really see bar graphs is in experiments where you're counting something and where you have what we call "binning" of data, where data is grouped into relatively large discrete steps. Unfortunately some teachers are never wrong. I really wonder how they can teach when they aren't even willing to learn.

And what's so hard about calculating time dilation? If you're not willing to let go of the idea of "relativistic mass," consider this: There are actually 2 relativistic masses, which depend on direction (yes, you read that right!) The "longitudinal mass," in the direction of motion is [math]m_l=\frac{m_0}{1-\beta^2}[/math] And the "transverse mass," perpendicular to the direction of motion is [math]m_t=\frac{m_0}{\sqrt{1-\beta^2}}[/math] This is crazy. However, none of this becomes neccessary if you just accept that mass is an invariant. Not only is this confusing, but it is just wrong. If you derive the equations in SR, you will see that all the factors of gamma come from time dilation and have nothing to do with changing mass.

"Reaper"- You are correct that only the length in the direction of motion changes, but mass does not change as a function of speed.

Nevermind. I will add something helpful later.

Depends. Some areas of biology will require no more than high school level math(s), but some areas which are getting more advances are starting to rival chemistry as far as the level of math required goes. I'd say biology is a pretty common route for students who like science but hate math.

Of course they will fall towards each other. As I said before, gravity and inertia scale exactly proportionally and an apple is just like a small earth. They would only orbit if their velocities were not exactly in the radial direction. So say they begin at rest some finite distance from each other, they will be pulled together.

Slinkey, when you say a theory breaks down at a singularity, you are simply stating the definition of the word. And since relativity is singular at v=c, (for massive objects anyway) this is doubly redundant. I am only saying this because so many people don't understand what a "singularity" is. Klaynos, speaking of which, do you know what happened to Ben "the man"?

Incredible measurements have been made (1 part in 100 billion) which show that gravitational mass is exactly the same as inertial mass. That means as you increase mass, gravity increases in exactly the same way. You probably know that all objects on earth have the same freefall acceleration. Say you have a 1 pound object and a 2 pound object. The force pulling the 2 pound object is twice as great. So why doesn't it fall twice as fast? Because it has twice as much inertia resisting the pull. I hope this answers your question.

(I think this is my first thread in speculations) This probably doesn't even count as a speculation - just something I noticed when I was helping out a friend with some intro QM. Most people know special relativity's formula for momentum, [math]p=\frac{mv}{\sqrt{1-v^2/c^2}}[/math] and that if you put in a velocity greater than c, you will get an imaginary momentum. This is usually discarded as unphysical. Physicists believe that alpha decay occurs when an alpha particle "quantum tunnels" out of a nucleus. I have included the typical simplified cartoon picture of what this looks like (yes, I drew it in paint). The dashed line in the energy of the alpha and the solid line is the potential. The alpha is held inside the nucleus's potential well by the strong force and outside the nucleus, there is a very strong Electro-static repulsion. Obviously, it does not have enough energy to escape classically, but according to QM, it has a very small chance of moving through the potential and out of the nucleus. When the alpha particle is inside the classically forbidden region, it has an exponential wave function kind of like [math]\Psi \propto e^{-x/a} [/math] where a is a real constant with dimension of length. Now nobody really knows what the particle is doing while it is tunneling. If we try to apply the momentum operator, [math]\hat P = -i \hbar [/math] we get an imaginary eigenvalue (imaginary momentum). This is also regarded as unphysical, but what if it were a physical situation where the particle was traveling faster than c? Maybe someone will volunteer to do some numbers and get an estimate of what superluminal speed would be required for this to be consistent. I apologize if this is completely incoherent. The change to daylight saving time has wrecked my sleep schedule.

200 year old idea??? iNow, haven't you ever heard of the Great Wall?

Lockheed, I think it's time for you to reveal the correct answer.

Lance's last statement is very true; the smarter a biologist becomes, the more she becomes a chemist. Of course, there is a similar relationship between chemists and physicists. PhDs in all 3 sciences? No. That would be terrible. General broad knowledge is necessary, but doing a PhD in all 3 would be an abomination.

Swans, I don't know how many people doing serious physics have used relativistic mass in the past few decades, but I'm sure it must be in the vast minority. Most textbooks today will either make no mention it or only mention it to discourage its use. Not only is it pointless and confusing, but it is wrong. The factor of gamma that somehow gets attached to mass actually comes from time dilation (See the thread about Why c in E=mc2?). As a compromise, I am willing to say rest mass, as long as nobody says relativistic mass or implies that mass can be a function of speed.

I know what your intent was, but you arrived at your conclusion by the wrong means. And stop saying "rest mass." It's just mass.

Great post Martin (#9). I was going to post something to a similar effect, but I think you said it better than I could have. I die a little bit each time someone says something like "The big bang was a singularity" because I suspect that most people who talk about things like that have no idea what the word means. I have been thinking that it would be good to be more careful with our language. Instead of saying "a black hole is a singularity," we should say something like "GR is singular in a black hole." I think this would retard the misconception that singularities are something that exist in nature. And don't forget about Klaynos. He'll never stop nagging you.

Darkshade, forget you ever saw this equation. There is no "relativistic mass." The factor of gamma that you see is due to time dilation, not an increase in mass.

Your problem is in assuming that p=mv. I don't know if this is homework or not. If it is, you should have paid attention in class. The relativistic momentum is: [math]p=\frac{mv}{\sqrt{1-v^2/c^2}}[/math]

The fact that you can't go faster than c is the result of, not the reason for E=mc2. You do not have to assume that nothing can go faster than c, only that all physics (including the speed of light) is the same in all inertial frames. This is what (in my opinion) makes special relativity so beautiful. I only briefly skimmed the link Lockheed posted is nice that it's based on a physical situation, but I believe this mathematical derivation is much more straight-forward. It can get a little messy, but it's not very long at all. Anyone with university calculus should be able to handle it. If you're learning about relativity, you probably know [math]\gamma=\frac{1}{\sqrt{1-v^2/c^2}}[/math] The relativistic momentum is [math]p=mv\gamma[/math] (If you're not satisfied beginning here, you can derive the expression for momentum with the velocity addition and by assuming that momentum must be conserved). Newton's 2nd law says: [math]F=\frac{dp}{dt}=m\frac{dv}{dt}\gamma^3[/math] The regular old definition of work: [math]W=\int F dx[/math] Now here we do a little chain-rule trick to rewrite this as [math]W=m \int \gamma^3 \frac{dx}{dt} dv[/math] And since [math]\frac{dx}{dt}=v[/math] [math]W=\int \gamma^3 v dv = mc^2 \gamma[/math] Now just let v=0 and bam [math]E=mc^2[/math]