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For clarificatiion: The stress energy tensor has a coefficient with specific dimensions. In order for the equation to be consistent, T, R and g must have dimensions to make the equation consistent. My understanding of the metric and curvature tensors is that they are geometrical and either have...

Thanks for your response. Newtons^-1 is the dimension of the coefficient of T. If the Ricci tensor has dimension of distance^2, would it not follow that T has dimension N(distance^2)?

The coefficient of the stress energy tesor in the GR equation reduces to 8π/Ν, where N = {"(Kg)m/s^2.} Is it correct to conclude that all the elements of the stress energy tensor must have the dimension of N = (Kg)m/s^2 since the curvature and metric tensors on the other side of the equation are...

According to the wikipedia article on virtual particles: . and: Yet, Hawking radiation is caused by the spontaneous creation of virtual particles -- as a consequence of the uncertainty principle -- that are separated by the event horizon and -- I guess -- become "real." Am I missing something?

What distiguishes real and virtual particles? Virtual photons, virtual gluons and virtual W particles are often referred to in discussing the interactions they determine. Why and when are they virtual? Why and when are they real?

This is great, thanks. Ignore the previous post.

OK, with Δx = Δy = Δz = 0, then τ = cΔt, which is a length. What does that mean?

Proper length is given by $$ L = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2 - c^2\Delta t^2 }$$ So, when $$ \Delta x = \Delta y = \Delta z = 0 $$ there is no motion and $$ L = ic\Delta t $$ What does that mean, if anything?

Thanks for all the comments. It is quite amazing that the Lagrangian is so fruitful in ways that Lagrange could never have imagined. For example, I was just reviewing its application to quantum field theory. I am continually awed by the mathematical nature of the universe.

Thanks for your response. I see that the observed forces in the Casimir effect are consistent with the quantum theory of the harmonic oscillator. However, is there any experiment that demonstrates that the ground state of the energy for a particle cannot be zero? I understand that a zero ground...

I hope this is a coherent question: Solving the Schrödinger equation for energy eigenvalues for a harmonic oscillator leads to the ground state of the energy for a particle being ω/2. What is the experimental evidence that this is, in fact, the lowest achievable energy and that zero energy is...

Thanks for all the helpful comments.

Thanks, that's very helpful.

Yes, I am describing a PROTON, which is at rest at A, travels to B at .999c and is again at rest at B.

Intelligent protons are also skeptical. When at rest at A, it says to itself, hey, I'm 10 LY from B. Then after I accelerate it, it says, wow, now I'm only about .3 LY away from B so I'll get there in .3 years. After it gets to B and stops, it confirms that it traveled 10 LY, but it believes it...

Suppose we have two points A and B, separated by ten light years. Now I shoot off a proton at .999c from A to B. From the perspective of the proton the distance between A and B is now about .3 light years. Would it get from A to B in less than four months in the time frame of the proton? If not...

Why is the position operator of a particle on the x-axis defined by x multiplied by the wave function? Is there an intuitive basis for this or is it merely something that simply works in QM?

Thanks for your response. Is there some intuitive way to understand the mechanism of the weak force interaction? Does it act counter to the strong force to allow for radioactive decay in the sense that it's repulsive action might overcome the attractive action of ther strong force? Is the strong...

Is the weak force really a "force"? I have seen that gravity, electromagnetism and the strong force are described by physicists in detail in the sense that specific things can be said about what is attracted and/or repulsed and under what circumstances these forces are manifested. All we ever...

Thanks for your response. I am familiar with some of the applications of the Lagrangian that you describe, but I have no experience with the quantum mechanical applications. It's quite remarkable that there is no explanation for it's usefulness and meaning in classical physics. In light of that...

Since it is based on the kinetic energy less the potential energy, what does the Lagrangian actually represent? Is there some intuitive way to understand why it is defined so and why it is such a fruitful concept using the principle of least action?

Thank you. That's very helpful.

Do the GR tensor equations have specific solutions that post-dict the big bang? I have seen references to GR providing a theoretical basis for the big bang. Exactly what is the nature of this theoretical basis? If the mathematics for this is too complex for posting on this forum, I would...

I'm struggling with trying to visualize the vector potential as in the identity: B = ∇⨯A For starters, how does A relate to, say, a uniform magnetic field, which is quite easy to visualize. Then, how about the magnetic field around a bar magnet -- where is A? Any help would be appreciated.

That's very helpful, thank you.

How would one determine a geodesic in Rindler space? Why would geodesics not be simply the same as those of Minkowsky space? Is it not analogous to using polar vs. Cartesian coordinates in euclidean space, where a straight line is the same in either case?

Both pressure and stress are defined in terms of force per unit area. Beyond that simple relationship, what might constitute a good intuitive way to distinguish these two concepts?

Is the requirement that \nabla_\mu T^{\mu\nu} = 0. due to energy and momentum conservation?

In the Einstein tensor equation for general relativity, why are there two terms for curvature: specifically the curvature tensor and the curvature scalar multiplied by the metric tensor?

When one considers (proper time) ΔΤ2 = Δt2 - Δx2 - Δy2 - Δz2, with c = 1, if t is in seconds, are the units of x,y and z necessarily 3x108 meters?