Johnny5

http://en.wikipedia.org/wiki/Quantum_field_theory[/url'] is quite good... try learning a few of the basics and then asking a more precise question, so rather than 'tell me everything' try 'why does the ____ theory work?' or 'how does the ___ equation work?'... not that I will be able to answer questions on QFT, just that that way you'd get somewhere and I could learn from it too!

That article is well written, thank you. Well from memory the Schrodinger equation is:

[math] \frac{-\hbar}{2M} \nabla^2 \Psi + U \Psi = i \hbar \frac{\partial \Psi}{\partial t} [/math]

The reason I start here, is because I have used the equation above to derive the spherical harmonics for the hydrogen atom before. I used separation of variables. In the solution, M was the reduced mass. I still have all the mathematical work which went into the solution.

The wikipedia article starts out with the Schrodinger equation in a different form, it uses the 'bra' 'ket' notation, due to Dirac, which came years after Shrodinger formulated his equation. I think schrodinger wanted psi to represent energy density if I am not mistaken, and it was Born's idea to interpret psi times the complex conjugate of psi as related to the probability of the particles being in some region of space.

You asked for me to ask a question. I guess the intelligent first question to ask is, what mass does the letter m denote, in the first equation at the wikipedia site?

First of all I am already uncomfortable using the first equation at the wikipedia site, because it is not the one I derived the spherical harmonics of a hydrogen atom with. I don't immediately see the equivalence of it to the equation I have. (Perhaps demonstrating equivalence would be a good place to start)

I can see that the first term of the operator there represents "kinetic energy" the second term of the operator represents the potentially kinetic energy, and the operator operates on [math] | \Psi (t) > [/math], you would have to be blind not to notice that.

I see a whole lot of differences between the equation I am familiar with, and the starting point there. I can make a small adjustment to the original Schrodinger equation as follows:

[math] [\frac{-\hbar}{2M} \nabla^2 + U ]\Psi = i \hbar \frac{\partial \Psi}{\partial t} [/math]

That starts off demonstrating equivalence, but of course the wikipedia site is already using the 'bra' 'ket' notation, which is highly abstract, not to mention anachronistic.

Regards

The e represented in [math]e = hf[/math] and the e in [math]e^2 = (pc)^2 + (m_0 c^2 )^2[/math] represent different types of energy.

 

Reason:

if it was the same type of energy' date=' which i thought it was then:

[math']e^2 = (pc)^2 + (m_0 c^2 )^2 = (hf)^2[/math]

and if m=0 then

[math]e^2 = (pc)^2 = (hf)^2[/math]

[math]e = pc = hf[/math]

but how can pc = hf when f is a variant depending on the photon's frequency and pc is a constant? The answer is that pc doesn't equal hf because they're referring to different types of energy... maybe that was obvious, i just realised it though!

 

=========

 

moving onto the photons don't have rest frames thing... if you are going to disagree with relativety then fine, but in the universe as we know it photons do not have rest frames.

What on earth are you trying to show me? It would help me follow you, if you actually derived the formula we are talking about from your starting point.

Regards

Johnny' date='

 

What you are asking is too tall an order for anyone to reasonably fill, unless they have already set aside the time to do it. Your best bet is to go to http://www.superstringtheory.com, where they regularly offer free online courses in QM and QFT. If you can't find the next starting date at that site, the you should go to http://www.physicsforums.com and send a PM to the member named vanesch. He is the one who led the last QFT course from Peskin and Schroeder.[/quote']

 

Thank you, I don't think I will end up doing all that though. It would have been easier for me to learn it here. But I guess you're right.

 

Regards

Another force besides the attraction between the two particles would be needed to accelarate one particle in a direction tangent to an ellipse around the other particle. Then theoretically, if the velocity of the orbiting object is the correct magnitude and direction in relation to the distance between the two objects at a given point, they should start orbiting another.

Yeah I thought so, so let me ask you this. Suppose I am a source which is going to "push" the thing in the direction which is tangent to the elliptical orbit this thing finally takes on. I would have to "push" perfectly to get the orbit to be elliptical. Not enough push would mean the things spiral together, and too much would mean they sail away from each other. So how is it that nature managed to get things perfect? Do you know?

Regards

There isn't any reason mathematically why the differential of time couldnt be negative just like the differential of any other variable in a function. There is no definition in mathematics that I know of that states that the variable "time" is any different from any other variable. However when you apply mathematics like this to physics you also have to take into account the properties of what you are applying the math to, not just the math itself. In the case of time, it is unidirectional, and therefore obtaining a differential of time that was negative in a physics problem would be nonsensical.

Oh this answer is excellent, because I see you clearly understand the question. I think in fact there is a reason, and it goes back to the finite discrete difference calculus, which the differential calculus is based upon. Let me explain.

Consider the difference operator:

[math] \Delta Q = Q2-Q1 [/math]

Here we see that the idea of change in the difference calculus is based upon subtraction, where Q denotes some quantity of physics. In order to have delta Q be nonzero, time has to increment or decrement. Now, if we stipulate that Q2 is measured after Q1 is measured, or even better yet stipulate that Q2 is the value of Q after Q1 is the value of Q, then we have inserted the unidirectionality of time into our mathematics haven't we? I mean this is my whole question. The moment Q takes on its value Q2 and the moment Q takes on its value Q1 aren't the same moment in time. Necessarily, one moment must come before the other. By convention Q2 is the value of Q later in time. So doesn't this convention "stipulate" that time flows unidirectionally? Recall that the definition of the derivative is based upon the difference operator.

OK. You didn't say you were starting here - it sounded like you wanted to derive it from first principles.

Have you ever seen the kind of derivation I am asking about?

Regards

Why does the amount of energy need to be finite? Can you measure it? No you can't - you can measure the energy density but that is not the same thing. In fact, if space-time is infinite (and measurements seem to indicate that it is) then it is unresonable for the energy content not to be infinite too.

The number of bodies is finite, the inertial mass per body is finite, hence the total inertial mass of the universe is finite, hence the total energy is finite.

Regards

I don't think that's a valid representation of the Big Bang.

Why on earth not? It makes total intuitive sense, it's practically obvious to me now. I guess you could say that in my model, vacuum cannot be created, hence was always there. Using that model of vacuum, it makes sense to say that somewhere in the universe is the center of mass of the universe.

Regards

You might like this then.[url']http://www.space.com/businesstechnology/blacklight_power_000522.html[/url]

I don't like the hydrino idea, the originator of it has no understanding of physics, he was a doctor, not a physicist. Night and day. I've seen the blacklight thing before, I pay no attention to it, I don't waste my time with it. I am positive that if i were to ask him simple questions, he would get them wrong.

But thank you for showing me the link. I don't really see how any of this gets to the heart of the matter though, which is does the universe have a center of inertia or not. Why doesn't anyone seem to 'know' the answer?

Regards

The link doesn't work.

It did yesterday, I will try to find another.

Regards

[url']http://www.amazon.co.uk/exec/obidos/ASIN/0201503972/qid%3D1109770995/026-2811211-6333217[/url]

Thanks, but I wanted someone who already knows it to explain it.

Regards

You go to a bookstore or library and get books on the topic. A bulletin board is really not the place to learn a topic from the ground up.

That all depends on who frequents the board. It's one of several things I am currently interested in. Also it's a good way to find people with similar interests. I could read a book on it, but its more enjoyable to interact with a person who already has the knowledge you seek.

Regards

Yes - if you use relativistic or inertial mass, instead of rest mass.

Well exactly how have you reached the conclusion that the formula for relativistic mass is true?

Regards

my chemistry teacher said it is impossible to calculate the entire energy of a particle but i disagree. it may sound stupid but i'm still in highschool.

The energy of a photon (which is a particle of light) is given by the following formula, in the rest frame of a laser:

[math] E = hf [/math]

The symbol h denotes Planck's temporal constant of nature. That means that its difference taken over any two consecutive moments in time must be zero, i.e.

[math] \Delta h = 0 [/math]

The symbol f denotes the frequency of the photon, and this varies from photon to photon. The point is, since photons are particles, and their energy is given by the quantum mechanical relation above, it certainly is possible to calculuate the energy of a particle.

Regards

No they don't. Light speed © is a constant in all frames. It doesn't matter which frame you sit in' date=' light always travels at c and is therefore not at rest. Thus there can be no rest frame for light. (Assuming they don't have mass.)

 

I suggest you read my post before commenting on it.[/quote']

 

Severian, you are making a mistake. Photons do have rest frames, and their speed in their own rest frame is of course zero. The rest frame of a particle is a three dimensional rectangular coordinate system, with the particle situated at the origin, in which the particle is permanently at rest regardless of whether or not that particle is being subjected to any external forces. In other words, in the rest frame of a particle, the speed of the particle is always zero, no matter where the particle goes. The frame is permanently "attached" to the particle.

 

And the fundamental postulate of the special theory of relativity is not that the speed of light is c in all frames, but that its speed is c in any reference frames in which Maxwell's equations are true. <--- that much is of course correct, because it is a tautology. The question is are there any reference frames in which Maxwell's equations are true. Special theory says, "yes there are reference frames in which Maxwell's equations are true, and those frames are the inertial frames.

 

Regards

The second postulate of special relativity is that c is the same for all inertial observers. I can't prove it. But if you can disprove it, you disprove all of relativity. I'm pretty confident that relativity is correct.

Being pretty confident, isn't being certain. The simplest way to prove that the second postulate leads to a contradiction, is to prove that simultaneity is absolute not relative. The barn and ladder problem does this perfectly.

Regards

Suppose that a spaceship is initially at rest with respect to me. Then, the spaceship accelerates off in some direction trying to reach the speed of light. As I understand it, the time dilation formula tells me that the accelerated ship will experience time dilation interior to it. According to the formula, that means that time will slow down inside the ship. That means that things will appear to move in slow motion, until (at the speed of light) all motion inside the ship would stop. Isn't this the condition for the ship to be at a temperature absolute zero degrees? Time and temperature aren't related in this manner are they?

And one more thought... if the time dilation effect is relative, then when his ship reaches the speed of light, is my temperature absolute zero degrees?

Regards

What is the fastest proof of the Pythagorean theorem in the world?

Thank you

J5

I am interested in learning quantum field theory as fast as possible. Is there anyone here who can help me learn it quickly? Assume that I already know classical electrodynamics.

Thank you

In case anyone here hasn't noticed' date=' there have been a lot of debates on this online between people on other forums, some with a good grasp of mathematics and some without. The debate is over whether 0.99[u']9[/u] does or does not equal 1.

 

There are many different proofs to prove that it does, but because some people understand some proofs better than others, and some not at all the debates still go on. I've personally been involved in these sort of debates and I can think up at least five different proofs, all based on different sorts of logic, that show that they are equal. The more forms we can find, the better the chances are that someone will understand it.

Well I would enjoy seeing just one of your five proofs, because they aren't equal. In fact, 1 is a number, and .99999... isn't a number, so your proof is guaranteed to contain an error, you will equate apples to oranges, which is similiar to adding apples and oranges, but not identical. I'm not playing semantical games either. In this particular problem, semantics happens to matter.

Regards

Suppose that I have two particles in vacuum, and there is only one interaction force between them, and that force is a central force.

Assume that at the beginning of time, the particles are a distance R apart, but are being pulled together by this one superforce S. How can I get the particles to orbit one another. Won't they just head right for the center of mass of the universe, collide, and then reflect or something in linear motion rather than circular motion?

Put another way, exactly how does a central force end up making things orbit the center of mass.

Regards

Suppose that I wanted to model the universe as a collection of an integral number of bodies, and then intelligently discuss changes in the state of the universe. Suppose I choose to represent the state of the universe by the symbol [math] \Psi [/math].

Now I want to focus on a single change of the state of the universe, which I will represent using:

[math] \Delta \Psi [/math]

Here is my question.

Why would it be wrong to say that the state of the universe has changed if and only if the center of inertia of at least one object moved relative to the center of inertia of another?

Regards

However' date=' in more reasonable scientific convention, no the universe has no centre. The Big Bang happened everywhere at once.[/quote']

 

I regard this as patently absurd, without any argument for my position whatsoever. I am willing to construct one ad hoc though.

 

Space is infinite. The big bang had a finite amount of energy, and so represented a finite amount of mass. You cannot spread out a finite amount of mass over an infinite amount of space, can't be done.

 

J5

 

If what you said is true, then the density of the universe would be equal to a finite number, divided by an infinite number, which (though it isnt even really a number) would be equal to zero.

It's just wrong. That is not the definition of mass. You are trying to generalise the rest frame energy mass relation to something it isn't applicable for' date=' because the photon has no rest frame.

 

Let me put it this way, for a massive particle you are saying that E=mc^2, therefore why not regard this as the definition of mass and thus the mass of the photon is E/c^2. Right?

 

But this is not the correct expression - you should really write [math']E^2=m^2c^4 +p^2c^2[/math]. Then we have

 

[math]m=\sqrt{E^2/c^4 - p^2/c^2}[/math]

 

Now, it is OK to use this as a definition of mass, but then you will find for the photon that E=pc and m=0. The photon has no mass.

Severian, photons do have rest frames. I suggest you try to derive the equation for total energy yourself. See the other thread.

Regards

Thank you Pangloss, but my question really wasn't answered.

I just want to know whether or not the universe has a center. It exploded into pure vacuum, so I think there is one, but how would you go about proving that it has one experimentally. <-- That's the question I want answered.

Thank you