Johnny5

No way. I told you I am a physics watcher. I am not a working relativist or quantum gravitist.

 

So then you don't understand tensor calculus, you are just a novice/fan of GR and QG?

But I do think that it will be quantized and replaced before very much more time has passed. the LQG papers I watch are getting very interesting

Tell me what it is that appears increasingly interesting... something experimental, or theoretical?

 

 

the expansion of space stretches light out when it travels for a long time it gets redshifted due to this stretching effect' date=' so over billions of years of travel light can lose quite a lot of energy, but it still goes the same speed

[/quote']

 

I have a serious problem with the underlined part. Can you isolate where in the mathematics of GR, this is for me?

 

 

Instead of expansion of space, can we just say that matter is moving away from the center of the universe?

 

In the meantime' date=' did you read the March 2005 SciAm article by Charlie Lineweaver and Tamara Davis?[/quote']

 

The long-distance thinker

 

Martin Bojowald is on a journey back in time to see what happened during the Big Bang. Quirin Schiermeier tags along for the ride.

 

 

Is that you? If it is, hello.

If not, no harm done.

 

Is that the march article you are talking about?

you should know about the units of the Einst. eqn.

 

curvature is measured as reciprocal area (one over distance squared)

 

 

multiply any curvature by a force and you get a pressure (force over area) and that is the same as an energy density (energy over volume)

 

This is easy enough to remember... (for my own edification)

1. 'Curvature' has units of 1/meter^2' date=' inverse area, inverse r squared... like a certain portion of the Newton gravity formula.

2. Pressure has units of force per unit area, so that Force times 'curvature' has units of pressure, which would be Newton/meter squared, also equivalent to Newton meter/meter^3 same as Joule/cubic meter.. which is units of "energy density"

 

so when you see einst. eqn.

 

G_ab = (1/F) T_ab

 

LHS is curvature, RHS is energy density (actually the stress energy tensor whose unit of measure is energy density) divided by a universal constant force F = c⁴/(8piG)

G_ab this is a tensor, is the whole tensor called 'curvature'? Can you explain tensors to me quickly, just enough so I can understand this one?

(of course an equation is just a tautology in the end, at any rate)...

So the curvature is equivalent to the RHS, there is a constant of proportionality (to be constant means I can differentiate this portion with respect to time and nothing happens right?) and that constant you are telling me is a force constant (but inverted)? Something with units of kilogram meter per seconds squared? (where did the factor of [math] 8 \pi [/math] arise?)

Why not lift it (the inverted force constant) to the other side, and divide the Maxwell stress tensor by the curvature?) ?

As for the stress energy tensor...

T_ab

After you explain the curvature tensor, can you explain the stress energy tensor briefly. Does it have something to do with stretching something? (And please don't say space) I will probably have a lot of questions about this tensor, if you do say space.

As for that 'force' constant, let me check out the units:

c⁴/(8\pi G)

c has units of meters/second, G is the Newtonian gravitational constant I presume... 6.672 x 10^-11 meter^3/kg s^2 so that, the force constant has units of...

(m^4/s^4)/ (m^3/kg s^2) = (m^4/s^4)(kg s^2/m^3) = (m/s^2)(kg ) = Newtons

ok at least that checks out, but where did the 8 pi come from, thin air?

 

so what you are likely to see if you look on google for Einst. eqn is

 

G_ab = ((8piG)/c⁴) T_ab

 

that is our main equation describing gravity! all we know is that it works!

 

How did we find out that it works?

 

the expansion of space stretches light out when it travels for a long time it gets redshifted due to this stretching effect' date=' so over billions of years of travel light can lose quite a lot of energy, but it still goes the same speed

[/quote']

 

I have a serious problem with the underlined part. Can you isolate where in the mathematics of GR, this is for me?

the perception that matter couples to geometry goes back to 1915 with the publication of einstein first Gen Rel paper

 

concentration of any type of energy (call it matter for want of better word) curves space...

 

so the shape of space and the density of energy are COUPLED

 

Ok, supposing that the "shape of space" (call it space for lack of a better word) is COUPLED (good word) to the density of MATTER (best word)"

does space have inertial mass? In other words, is it a resistive medium?

If (assuming GR to be correct under some interpretation) I throw a baseball in outer space, will it slowly come to rest?

Thank you

Ok, go slowly. You say that the temperature of a black hole is inversely proportional to the mass. As the mass increases, the temperature decreases.

According to the formula, what mass is required for a black hole to have a temperature of absolute zero? Infinite mass? I would think some quantum formula would sort of prevent that.

Martin, i have a question about something on page 2 http://arxiv.org/gr-qc/0503020

 

2. Variables

 

A spatially isotropic space-time has the metric

[math] ds^2 = -dt^2 + \frac{a(t)^2}{(1 - kr^2)^2} dr^2 + a(t)^2r^2d\Omega^2 [/math]

 

where k can be zero or ±1 and specifies the intrinsic curvature of space, while the scale factor a(t) describes the expansion or contraction of space in time. It is subject to the Friedmann equation

 

[math] 3( (da/dt)^2 + k)a = 8 \pi G H_{matter} [/math]

 

where G is the gravitational constant and Hmatter the matter Hamiltonian (assumed here to be given only by a scalar φ and its momentum p. The matter Hamiltonian depends on the matter fields, but also on the scale factor since matter couples to geometry.

What does he mean when he says that "matter couples to geometry"?

Thanks

I have a question. Is a black hole really hot, or really cold?

Thank you

Suppose that anything which historically was referred to as a particle, is really just a node in a traveling wave.

So this would hold for 'photons'.

Electrodynamics leads to the conclusion that what is vibrating, in the case of our "photon nodes" is electric/magnetic fields.

Photon's propagate in vacuum.

My question is coming up shortly.

I am thinking of a piece of thread which stretches from the earth to the moon. The thread is taught. It's vibrating, there are nodes in it, the nodes are moving in this frame close to the speed of light.

Here is my question:

What is the string? I don't see any string. There is no string. The notion of a universe interwoven with strings we cannot see, is strange.

Do we have to throw away the idea that particles are really nodes in waves?

If we do, then I suggest we throw away the E/B field treatment of EM waves. If not, what is the string?

It's true in R³. Basically' date=' your argument amounts to this:

 

[i']Time cannot be the 4th dimension because the universe is 3 dimensional.[/i]

 

Or more formally,

 

A

__________

Therefore A

That argument (at most three...) wasn't mine, it was an ancient one. Seems fine to me.

How about this one:

If I were situated someplace, a rotation through 2 pi radians brings me looking where I was looking before. I think this basically proves space is three dimensional, since it would be true in any plane which I start the rotation in.

To start with' date=' I'd say that general covariance and canonical quantization have to be ingredients of any candidate for a grand unification theory.

 

[/quote']

 

What does "general covariance" mean?

What does "canonical quantization" mean?

Does light of equal frequency interfere as originally thought or is it the individual photons primarily "interfering with themselves"?

 

Or do we know?

What do you mean "interfere as originally thought"?

Wave superposition

Ok well we have drifted off the topic. Originally, my question was, is the verbal formulation of Newton's second law (at the site I quoted) correct. Then eventually we progressed to the analysis of a rigid bar, where there was a force applied to one end of the bar, and I think I wanted to analyze the motion of the whole bar.

Then you said all of the force goes into translating the center of mass, and all of the force goes into rotating the object. I said that violates conservation of energy, and that some of the force goes into translating the center of mass, and some of the force goes into rotating the bar. I do not insist that I am right, I'm not sure.

So which is right?

Indeed' date=' neither of them can be because neither of them are identical to the GR model, which is known to be correct.

[/quote']

 

Which GR model are you talking about, and known by who to be correct exactly?

That's only the case if you stipulate that you are working in R^{3[/sup'] to begin with. So this argument against more than 3 spatial dimensions is circular, I'm afraid.}

^{The statement is true, so what's the difference?}

Another post has made me want to develop a better understanding of waves in general. Does anyone have an approach to remembering everything there is to know about waves? I need a referesher.

1. Transverse waves

2. Longitudinal waves

3. Compression waves (longitudinal synonym)

4. Shear waves (transverse synonym)

5. Standing waves

6. Traveling waves

7. Spherical waves

8. Plane waves

9. Beats

All waves have what in common exactly?

It's one thing to understand the sine function, or cosine function, its something totally different to understand a sine wave, or a cosine wave, in which you have the medium changing in time.

There are density changes, and also, in order to define wavespeed, you have to have some frame of reference, and there are all kinds of different frames of reference to choose from. All this has to be handled in a comprehensive theory of waves. Can anyone help, in the sense that they have a quick way to remember all there is to know about waves?

Thank you

No. Newton's third law dictates that the force you exert must equal the force exerted on you. You can't exert F and feel 2F back.

That's not what I am saying. I tried to make it clear. The net force on me is 2F, and the net force on him is also 2F.

My maximum punch can deliver F.

His maximum punch can deliver F.

All I am saying is that if we punch each other simultaneously, the net force upon either of us is given by F+F=2F.

If only one of us punches the other, then we each have an external force of magnitude F applied on us.

OK, let's get back to the point. Out in space if you push against me with F then I will push back with F and there will be no 2F resultant force on either one of us. If a bar is in between us and the bar does not move it works the same way. You push with F, I push back in the opposite direction with F and cancels it out for the bar [/b']. You are accelerated one way at F=ma and I am accelerated the opposite at F=ma.

Ok, I think I know what the source of confusion is.

Let us suppose that I am Ivan Drago, and you are Rocky Balboa.

There was this machine in Rocky III that could measure the strength of Ivan Drago's punch. We could discuss energy, force, power, let's deal with impulse. Instantaneous force. Let this be F1 for me, and F3 for you.

Suppose there is an inert brick wall somewhere. I can punch it, and it will barely accelerate, for all intent and purpose, the wall can be treated as infinitely massive.

Let us suppose I punch this wall. The moment my hand is fully extended, contact is made. There is a force F1 upon that wall.

However, I will also hurt my hand.

The force of the wall upon my hand is F2.

These forces have equal magnitude, opposite direction, so F1=F2 but:

[math] \vec F1 = - \vec F2 [/math]

Now suppose this takes place in space, replace the wall with you.

In the case where you do not simultaneously punch my fist with your fist, I will exert F1 upon you, and you will exert F2 upon me, and F2=F1.

But, if you also simultaneously punch, so that both our fists meet at a common point in space at the same time, when both our arms are fully extended, and the maximum force you can punch with is F3, then the magnitude of the net force upon me at the moment our fists contact each other is given by:

F3+F2

or F3+ F1

Since F1=F2, as was stated earlier.

Since you can punch just as hard as me... F3=F2=F1

The net force on me therefore is

F3+F2 = F2 + F2 = 2 F2 = 2F1

That's where the factor of two comes in. You said that we both push each other. Is this clear?

Isn't space 4 dimensional (time)?

 

What does 'k' stand for?

Time is not a spatial dimension. At most three mutally perpendicular infinite straight lines can meet at a point' date=' not four.

k is the wavenumber vector, I was trying to write this:

[math'] \vec P = \hbar \vec k [/math]

Here is a link which explains it:

Wavenumber vector

I'm busy looking for a better explanation, but in the meantime, here is an excellent site which seems devoted to waveform analysis:

Acoustic and vibration animations

Ok, I found what I want:

Wavenumber

Wavevector

Lets say you're standing still and your weight is 200 lb.

 

The floor is pushing you upwards with a force of 200 lb.

 

Now lets say you push back with a force of 200 lb.

 

Now is the force 400 lb or 200 lb?

Vector analysis will help.

The earth pulls me down' date=' and creates a reading on a scale which we will call W. If I slowly varied the mass of the earth, I could change the reading of the scale. For example, if I take my scale, and me to the moon, and stand upon it there, the reading on the scale will be less than what it read on the earth. So that W is affected by the mass of what is underneath the scale.

The earth pulls things towards its center of mass, via gravitational force.

Let the x axis be horizontal, and let the y axis be vertical. So j^ points into the sky, and -j^ points right at the center of mass of the earth.

The planet earth pulls my body down, and the harder it pulls, the greater the reading on the scale. This force is being denoted as W. Specifically we have:

[math'] \vec W = w_1 \hat i + w_2 \hat j + w_3 \hat k [/math]

The earth isn't pulling me horizontally in any direction in the tangent plane. Therefore w1=0 and w3 = 0. The only component of W points in the negative j hat direction. Hence we have:

[math] \vec W = -w_y \hat j [/math]

where [math] w_y [/math] is a positive number.

Ok so that covers my weight, which has been handled as a force. Now, the tangent plane is fixed to the earth. There is no acceleration in the -j hat direction, because the surface of the earth is there, and it is pushing me up in just the right amount, to cancel out my weight. Let us call this upwards force the normal force, and denote it by N. We have this now:

[math] \vec N = n_1 \hat i + n_2 \hat j + n_3 \hat k [/math]

And there are no components of N in the tangent plane. Therefore we have:

[math] \vec N = n_2 \hat j [/math]

And [math] n_2 [/math] is a positive number.

Assume these are the only forces on me. Therefore, the sum of all the forces upon me is W+N:

[math] \sum_{i=1}^{i=2} \vec F_i = \vec W + \vec N [/math]

And this vector sum is equal to ma, where m is my inertial mass, and a is my acceleration in this reference frame, which is attached to the earth.

I am not accelerating, I am at rest in this frame, therefore:

[math] \vec W + \vec N = 0 [/math]

That is:

[math] \vec W = -w_y \hat j [/math]

+

[math] \vec N = n_2 \hat j [/math]

is equal to zero, from which it follows that

[math] w_y = n_2 [/math]

You say that the floor is pushing me upwards with a force of 200lbs. Yes, that is the normal force, the floor is reacting to my weight.

My weight is 200 lbs.

The net force upon me is zero.

You ask if the force is 400 or 200, that isn't a perfectly clear question, but the force is not 400 lbs simply because I am not accelerating in the frame. The net force upon me is zero.

My weight is 200 lbs, but that isn't the only force upon me. The other force has the same magnitude, but opposite direction.

As for which of the two my sensory perception detects, that is a good question.

Lets say you're standing still and your weight is 200 lb.

 

The floor is pushing you upwards with a force of 200 lb.

 

Now lets say you push back with a force of 200 lb.

 

Now is the force 400 lb or 200 lb?

I am standing on my bathroom scale, it reads 200 lb. Ok.

My weight is W=Mg = 200 lb

where M is my inertial mass.

Free body diagram of the forces upon me:

There is my weight W down, and the Normal force of the earth upon me.

Let N denote the normal.

The sum of forces on me is N+W, and this must equal zero, since I am not accelerating.

I have to go. I will think about this later, and finish up tomorrow.

Thank you

Nope

Aren't you forgetting about Newton's third law?

2F? It's only F.

I push on you plus the bar with force F.

If you didnt push back, then there is a force on me of F.

But you also pushed me with force F, so its 2F.