Relativistic Mass vs. Rest Mass

Paul T

03-21-04, 02:32 AM

the box with the moving particles inside is at rest. it has a larger rest mass.

I agree that the box is at rest relative to the observer (us), but the gas molecules are not. Assuming that we have one mole of hydrogen gas in the box and therefore we know the number of melecules in the box. Rest mass of hydrogen molecule (or you may wish to call it simply mass) is the same according to any observer, but its energy (energy associated to its rest mass plus its kinetic energy) are not observer-independent. We agree that the box with moving particles inside has larger mass. If this mass is "rest mass", then dividing total mass with Avogadro number would give us the mass of molecule that is larger than normal. Do you think having this situation is better than accepting that the mass in question is not rest mass (but rest mass plus mass associated to the particles kinetic energy)?

for me, mass always means rest mass. like a lot of physicists, i refuse to talk about something you want to call "relativistic mass".

I can understand your standing. The rest mass is the constant part of mass, while the "relativistic mass" is simply energy. If this is your standing, I have no objection. However, the the strength of gravitational source or weight of object is proportional to the object energy, not the rest mass.

Newton said that gravity couples to rest mass. Einstein said that gravity couples to the stress tensor. for nonrelativistic physics, go with Newton. for relativistic physics, go with Einstein. It is incorrect to use Newton's equation for ultrarelativistic systems.

I don't think Newton did say that gravity must couple to rest mass. To the best of my knowledge, he wasn't aware of any other mass than rest mass or that mass has anything to do with energy. At this time, we are fortunate to know both Newton's law and Einstein's relativity. It was not my intention to say that applying Newton's gravitational law for photon is perfectly okay. My earlier approximate computation for deflection of light near the sun was made just for showing that the gravitational field works on photon energy (non-zero relativistic mass) and not its zero rest mass.

zanket

03-21-04, 05:12 AM

Imagine I have a thermodynamically impossible perfectly insulated and incredibly strong box.

Inside that box is a ball, bouncing around very very fast. All collisions between the ball and the box wall are perfectly elastic.

The ball and the box both have rest mass m.

Relative to the box, the ball has a speed of 0.866 c, giving it a relativistic mass of 2m.

Does the box + ball system have rest mass of 3m?

Is it possible to differentiate this box from a box containing two stationary balls (or substance of equivalent mass distributed evenly through the box) without opening the box?

the box with the moving particles will weigh more.

I'm mainly curious about whether or not photons produce their own gravitational fields because of their relativistic mass. If two photons were sent out on parallel courses, would they attract each other and gradually move closer together?

yes, photons produce their own gravitational fields. anything with a nonzero stress tensor does. so they will attract each other.

Lethe’s answers here contradict mine above, so I gave this more thought. There is an intuitive way to see that lethe is correct without knowing anything about stress tensors. (I’m assuming that lethe’s first answer is equivalent to “a box with moving particles weighs more than if the particles are stationary,” especially since Pete made no mention of a box with multiple moving particles.)

Let perfectly sealed box A contain 2 moving balls, and box B contain 2 stationary balls. Presumably lethe would say that A weighs more than B. Yet if A’s moving balls collided to become stationary, then the box could not change in weight because no mass or energy enters or leaves the sealed box. At first glance this seems to contradict lethe, because after the collision the boxes seem equivalent. But the boxes are not equivalent because the collision released heat, which remains in A. After the collision A contains 2 stationary balls + heat, whereas B contains only 2 stationary balls. But how do we know that heat has weight?

Take another perfectly sealed box containing burning coal. As the coal burns it loses mass. But the box is sealed so it must weigh the same throughout the burning. Therefore the coal’s lost mass must be transferred into what the burning adds to the box, which is heat. So heat has mass, therefore weight, as does any other form of energy. Some of the heat could be used to boil water to spin a generator to charge a battery, all within the box. Then some of the coal’s lost mass would be transferred to the battery, increasing its weight. A charged battery weighs more than a spent battery.

Having mass, any form of energy including photons produce their own gravitational fields.

From Does light have mass? (http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html)

The energy and momentum of light also generates curvature of space-time so according to theory it can attract objects gravitationally. This effect is far too weak to have been measured.

Going back to the boxes containing the balls, how is it that box A weighs more than box B, yet the moving balls do not become black holes at higher speeds close enough to c? This is because the extra mass in A is represented purely by the momentum and energy of motion of the balls therein. The motion is relative and not intrinsic to the balls, which of course are stationary in their own frame of reference. A relative thing affects only the observer.

A grain of sand that grazes Sun sufficiently close to c could wreak major damage to Sun, given the grain’s extra mass (hence gravitational attraction) inherent in its energy of motion. To help intuit how this could happen without the grain being anything like a black hole intrinsically, remember that from our perspective the grain is contracted along its axis of motion such that it’s, say, one-zillionth of its rest length. While the grain is the size of a grain of sand within its own frame of reference, from our perspective the grain is contained within one-zillionth of that volume.

lethe

03-21-04, 11:17 AM

I agree that the box is at rest relative to the observer (us), but the gas molecules are not. Assuming that we have one mole of hydrogen gas in the box and therefore we know the number of melecules in the box.
how would you establish this? the easiest way to figure the number of molecules is to weigh the box. but if we wanted to consider relativistic molecules, this would not work unless we also knew the speeds of all the molecules, including how many molecules there are, which is what we set out to measure in the first place.

Rest mass of hydrogen molecule (or you may wish to call it simply mass) is the same according to any observer
right, but we don't have access to a single hydrogen molecule in this Gedanken experiment, we only have a box full of hydrogen. i like to imagine that the box has no windows, no way to see inside whatsoever, and that we don't even know whether it is hydrogen inside.
but its energy (energy associated to its rest mass plus its kinetic energy) are not observer-independent.
if the observers could see inside the box, then they wouldn't agree as to the internal energy of the box in their rest frames. but all observers will agree on the rest mass of the box, which is a figure that includes the internal energy of the box (kinetic energy of its constituent atoms, etc), in its rest frame.

We agree that the box with moving particles inside has larger mass. If this mass is "rest mass", then dividing total mass with Avogadro number would give us the mass of molecule that is larger than normal. Do you think having this situation is better than accepting that the mass in question is not rest mass (but rest mass plus mass associated to the particles kinetic energy)?
but if we don't know the number of particles in the box, or their speed, then we can't do this calculation anyway.

and look at it this way, even if all the atoms were motionless, the electrons orbiting the atoms wouldn't be. or if we somehow got all the electrons to stop, we would still have the quarks moving quite fast inside each nucleon.

the point is, the mass that you see on the periodic table for a hydrogen atom includes some percentage that comes from the internal motions. this is part of the rest mass of a hydrogen atom.

you seem to think it would be more useful to know the mass of an object in terms of only rest masses of its components, but actually, this would be a nightmare. everytime you wanted to weigh something, you would have to break it up into its constituent atoms, and slow each atom so that it was at rest, before weighing it.

if you use my definition of rest mass, which includes the internal kinetic energy, then when you want to weigh something, you just toss it on the scale. of course, with my definition, i can't divide by the number of particles to find the mass per particle, and with your definition, you can, this is true.

I can understand your standing. The rest mass is the constant part of mass, while the "relativistic mass" is simply energy. If this is your standing, I have no objection.
yeah, good. i recommend you get in the same habit. no one ever talks about relativistic mass. it is not a useful concept. if you mean energy, then say energy.

However, the the strength of gravitational source or weight of object is proportional to the object energy, not the rest mass.
more or less, yeah. in the static limit, the dominant contribution is from T00 which is energy density, not rest mass density.

I don't think Newton did say that gravity must couple to rest mass. To the best of my knowledge, he wasn't aware of any other mass than rest mass or that mass has anything to do with energy.
OK, fair enough.
At this time, we are fortunate to know both Newton's law and Einstein's relativity. It was not my intention to say that applying Newton's gravitational law for photon is perfectly okay. My earlier approximate computation for deflection of light near the sun was made just for showing that the gravitational field works on photon energy (non-zero relativistic mass) and not its zero rest mass.
yeah, except that the calculation you showed us gave you the wrong answer!

lethe

03-21-04, 11:35 AM

Let perfectly sealed box A contain 2 moving balls, and box B contain 2 stationary balls.
i like that the boxes are perfectly sealed. this means that, a. no momentum or energy can escape the boxes, and b. we can perform no measurements about what is inside the boxes, which means that, in principle, due to quantum mechanical effects, we cannot even be sure about how many particles are in the box.

Presumably lethe would say that A weighs more than B. Yet if A’s moving balls collided to become stationary
this would violate conservation of energy-momentum. cannot happen. if the box is perfectly sealed, then the particles in the box must remain in motion.

then the box could not change in weight because no mass or energy enters or leaves the sealed box.
right, the box cannot change its weight, because no energy enters or leaves, and therefore, to change weight requires a violation of conservation of energy-momentum.

At first glance this seems to contradict lethe, because after the collision the boxes seem equivalent. But the boxes are not equivalent because the collision released heat, which remains in A.
oh, i see. you want there to be a collision which transfers energy-momentum from 2 large particles to a bunch of smaller particles. but now you see that there are more than 2 particles in the box. and of course, those smaller particles are in motion too.

After the collision A contains 2 stationary balls + heat, whereas B contains only 2 stationary balls. But how do we know that heat has weight?
heat is energy. therefore it adds to the total energy content of the box. the rest mass of the box is the rest mass of all components (for whatever choice of smallest component you want to make), plus all internal energy, including potential energy, kinetic energy, heat energy, chemical energy, whatever.

Take another perfectly sealed box containing burning coal. As the coal burns it loses mass. But the box is sealed so it must weigh the same throughout the burning. Therefore the coal’s lost mass must be transferred into what the burning adds to the box, which is heat. So heat has mass, therefore weight, as does any other form of energy. Some of the heat could be used to boil water to spin a generator to charge a battery, all within the box. Then some of the coal’s lost mass would be transferred to the battery, increasing its weight. A charged battery weighs more than a spent battery.
yeah, that is it.

Having mass, any form of energy including photons produce their own gravitational fields.
precisely

Going back to the boxes containing the balls, how is it that box A weighs more than box B, yet the moving balls do not become black holes at higher speeds close enough to c?
well actually, if you add enough energy to the box, without increasing the size, it will become a black hole

This is because the extra mass in A is represented purely by the momentum and energy of motion of the balls therein. The motion is relative and not intrinsic to the balls, which of course are stationary in their own frame of reference. A relative thing affects only the observer.
you can, of course, analyze the box from outside. i think it is clearer here. there is energy inside the box. whether it is kinetic energy/linear momentum, potential energy, rest mass of constituent parts, heat, etc. you cannot tell, because the box is sealed.

all you can tell is that there is a lot of mass there. and i do mean rest mass. so this is something all observers will agree upon. and if there is enough rest mass in that box, it will turn into a black hole.

A grain of sand that grazes Sun sufficiently close to c could wreak major damage to Sun, given the grain’s extra mass (hence gravitational attraction) inherent in its energy of motion.
the grain of sand, no matter how fast you see it going, has a small rest mass. its gravitational field will never look significant to the sun. it will never become a black hole.

To help intuit how this could happen without the grain being anything like a black hole intrinsically, remember that from our perspective the grain is contracted along its axis of motion such that it’s, say, one-zillionth of its rest length. While the grain is the size of a grain of sand within its own frame of reference, from our perspective the grain is contained within one-zillionth of that volume.
not only does it not look like a black hole in its rest frame, it doesn't look (even slightly) like a black hole in our rest frame, where it has γ=1 zillion (is a zillion even a real number?)

MacM

03-21-04, 12:29 PM

lethe

03-21-04, 01:07 PM

Lethe,

In theory could not if you knew the weight of the box empty and then use temperature and pressure determine internal energy and work backwards to statistically determine the number of hydrogen atoms?
you could if you knew the exact chemical make-up of the stuff in the box, and knew the velocity distribution and energy distribution (this is different for different state equations). but knowing those distributions actually amounts to knowing the number of atoms already.

so what i end up with is the following: i can know the number of atoms if i already know the number of atoms.

this situation is dramatically improved if you make some simplifying assumptions like: all the atoms have the same energy, or they follow some simple statistical distribution.

this latter is often done in statistical mechanics in the thermodynamic limit.

MacM

03-21-04, 03:43 PM

Lethe,

this situation is dramatically improved if you make some simplifying assumptions like: all the atoms have the same energy, or they follow some simple statistical distribution.

That was my assumption. With sufficient atoms (molecules) in the box to generate pressure and temperature they should have a reasonably stable average. That is there would not be one zinger at 99.9%c and the others ambient.

ryans

03-21-04, 07:52 PM

Posted by Mac

The above statement appears to me to be a very narrowily crafted statement as an attempt to undo an otherwise completely false statement. It seems more a play on words than physics and reality.

Mac, here is the deal. I am a condensed matter physicist. I calculate properties for systems containing Hundreds, even thousands of particles. Now, when calculating the Density of state for some titanium alloy, do you really think that I am going to take gravity into account? Do you know the effect this would have on my calculations? Thus when I calculate the dispersive interaction energies of my system, it is rightly assumed that photon modes do not couple. They do not scatter or attract each other, only with massive media.

Show me where in the Landau theory of critical phenomena, where photon coupling due to the presence of gravitional fields is included. I have no problem admitting that I am incorrect Mac, however in the above discourse, I was not incorrect in my understanding that photons do not couple in free space. My understanding of photon coupling in gravitational fields is limited however, as I also said above.

MacM

03-21-04, 09:14 PM

Ryans,

Well I am assuming that in regions of space where the local curvature is zero, the coupling between photons would tend to zero.

I see you think you can fair better by picking an arguement with me than Lethe. My comments were directed only at your above statement which is a double edged sword.

To have "0" curvature would mean to have "0" gravity. It therefore seems intuitively obvious that photons (or anythingelse) would not gravitate in absence of a gravity field or potential. It simply seemed to be a carefully phrased escape goat qualifier for your prior statements.

Beyond that you can debate with Lethe.

Rappaccini

03-21-04, 09:50 PM

I really don't think ryans was "picking" an argument with you, lethe, or anybody.
He was just explaining himself, man.
Obviously, his field of study doesn't require that he pay close attention to typically weak, minuscule effects like gravitation.

His references to perfect Euclidean space, free of a stress tensor... or anything at all really... are pretty much understandable, considering.

Pete

03-21-04, 09:55 PM

Very large but light perfectly sealed box. One relativistic particle inside.
Time between collisions with the box walls is measurable, momentum change in box at each collision is detectable.

What does the gravity of this system look like? Is it constant? Are there gravity waves produced at each collision?

MacM

03-21-04, 10:37 PM

Rappaccini,

Not meaning to attack his area of expertise. Just commenting on the duality of his statement. "No curvature" would seem to mean "No gravity" and from there it would be duplicitus to then claim a special status for photons.

Am I reading something into his statement that isn't there?

Rappaccini

03-21-04, 11:26 PM

No, you're right.

My horribly limited erudition in this area leads me to think that a space with zero curvature would, as in accordance with GR, at least, have to be totally empty.

So, yeah... the mere presence of photons, bearing a mass-energy stress, would imply that we are NOT dealing with such a weird, weird place.

It's just... you should be readier to excuse ryans than you seem to be. Be more forgiving; he wasn't trying to be duplicitous, I don't believe.

Paul T

03-21-04, 11:29 PM

how would you establish this? the easiest way to figure the number of molecules is to weigh the box. but if we wanted to consider relativistic molecules, this would not work unless we also knew the speeds of all the molecules, including how many molecules there are, which is what we set out to measure in the first place.

Since we have already fixed the condition that the gas in the box is one mole, we know that the number of molecules is equal to the Avogradro number. I thought this is a very clear cut situation. We don't have to know the exact number of the molecules to accuracy such as plus-minus 10 or something like that. My interest is not on the detail but on its principle. Once we know the number of molecules, we could raise the box temperature which would increase the molecules kinetic energy. In principle, this action does not modify the number of molecules in the box (just assume it really doesn't). The average speed of molecules could be determined using kinetic theory of gas or any other theory.

We have no problem on weighing the box to measure its mass. My point is the measured mass, although from the macroscopic point of view could be perceived as rest mass, however, since we know that there are certain number of molecules in the box that move at certain average speed (determined theoretically based on its temperature) we should realize that this mass is not the cummulative of molecules rest mass (I think we have already agreed, it includes molecules kinetic energy).

My thinking is this. The measured box mass (M1) is not cumulative rest mass (M2) of all protons and electrons composing the molecules. We know that M1 > M2 as M1 = M2 + S molecule kinetic energy.

right, but we don't have access to a single hydrogen molecule in this Gedanken experiment, we only have a box full of hydrogen. i like to imagine that the box has no windows, no way to see inside whatsoever, and that we don't even know whether it is hydrogen inside.

I think you concern about the detail set up of experiment. We are not trying to establish something new. We just want to answer the original question of this thread about whether gravity couple with the object rest mass or total energy. Your answer was total energy and I agree with that.

I believe you said that since photon has zero rest mass, Newton's gravitational law is totally not applicable for photon. Although I agree that Newton's law does not give the correct answer for the deflection of light, I do not agree that Newton's law is totally invalid in this regard. We agreed that in original Newton's law, gravity couple with mass only. However, since we now know that mass and energy are the same, it should be okay to extend Newton's law (just a "patching up" solution though) to include total energy as the source of gravitational force. Just for fun. :D

if you use my definition of rest mass, which includes the internal kinetic energy, then when you want to weigh something, you just toss it on the scale. of course, with my definition, i can't divide by the number of particles to find the mass per particle, and with your definition, you can, this is true.

I agree on the difficulty involve if we really want to draw a solid line what is rest mass and what is not. There isn't any solid line can be drawn in practice. Well, guess that's all I wanted to say about this matter.

ryans

03-22-04, 12:17 AM

Don't worry Rappaccini, Mac doesn't know what he is talking about. If he had half a physics brain, he would have understood my position.

1) I disagreed with Lethe from superfluous arguement. In fact I still disagree with him, in the sense that I disagreed with Dirac, Heisenberg and Scrodinger about QM until I studied it myself. That's the way I do things Mac. However I don't go around telling people I know things I do not. Just like in the limit that h approaches zero gives Hamiltons principle i.e. minimisation of action gives the classical trajectory, In the limit of zero curvature, photons do not interact.

I could just as well disregard your theory on the grounds that it doesn't not include corrections do to quantum mechanics, but that would be missing the point wouldn't it, because clearly your theory is not applied in that regime.

MacM

03-22-04, 02:11 AM

Typical ryans.

I could just as well disregard your theory on the grounds that it doesn't not include corrections do to quantum mechanics, but that would be missing the point wouldn't it, because clearly your theory is not applied in that regime.

Talks through his ass, casts uninformed innuendo, slander, bitches about my theory being posted but then brings it up at every chance. Funny you lost again in James R's thread and now you want to move the goal post again.

No my theory hasn't been applied to QM yet but then that wasn't the issue where you were shown to be all wet was it.

Seems Rappaccini above understood my objection to your statement.

i.e. minimisation of action gives the classical trajectory, In the limit of zero curvature, photons do not interact.

Nor would anythingelse it would seem.

BTW does your QM explain the reason local gravity is inverse square, MOND or the accelerating expansion of the universe as a function of gravity. I think not so your QM also has a limited regime.

You need to learn to swallow without gagging.

zanket

03-22-04, 02:19 AM

lethe – Gotta make this quick. Forget about perfectly sealed box then, let’s just say it’s sealed to the point where it doesn’t allow mass or energy to enter or leave the box (although I suppose that is still perfectly sealed, as no photons are escaping, so let's say it's sealed to the point where the energy of the photons that escape to allow us to see what's going on within the box is negligible). Just trying to show that the box with the moving balls must contain more energy from the observer’s perspective than does the box with stationary balls. When the balls collide they don’t have to break up into smaller moving particles; I said that the 2 balls collide to become stationary. Consider them to be balls of clay if need be, forming one stationary lump in a head-on collision of equal velocities.

I find my argument about heat having mass to be unsatisfactory. Yes, coal loses mass when burned, but how do physicists know for sure that the lost mass is not in all the byproducts of the burning except the heat? Like in the ash, carbon monoxide, etc.? Is there a better intuitive argument?

I didn’t say the grain of sand becomes a black hole, but that it doesn’t. I don’t see how the grain’s gravitational field will never look significant to Sun given that the grain’s gravitational field from our perspective approaches infinity with ever higher speeds past Sun. Perhaps you can explain. Zillion? You knew what I meant, right? Yeah I slaughter physics terminology. I’m a layman, that’s what we do.

zanket

03-22-04, 02:48 AM

well actually, if you add enough energy to the box, without increasing the size, it will become a black hole

Here the energy I was talking about is the energy of motion of the balls within the box. So you seem to be saying that if the balls go fast enough within the box, then the box becomes a black hole, even though no black hole exists from the perspective of the balls. That’s in contradiction to the basic logic given here:

From If you go too fast do you become a black hole? (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html)

If it is not a black hole in one reference frame, then it cannot be a black hole in any other reference frame.

Am I missing something?

ryans

03-22-04, 06:55 AM

Nor would anythingelse it would seem.

HA. What, you don't know what a curvature tensor is. What! Photons are the carriers of the electromagnetic force! What, electrons interact with photons! What, you don't know what a Lagrangian is!

I will stop replying to you out of respect of others. You have lost the plot man!

MacM

03-22-04, 08:27 AM

Rappaccini,

Posted by Ryans:HA. What, you don't know what a curvature tensor is. What! Photons are the carriers of the electromagnetic force! What, electrons interact with photons! What, you don't know what a Lagrangian is!

I will stop replying to you out of respect of others. You have lost the plot man!

See how he makes my point. He jumps from the physics issue he bombed at "gravity" to "electromagnetic forces", makes slanderous comments.

Who above has made any reference to electrons and electromagnetic interaction?

AND you said he wasn't looking for an arguement. :bugeye:

Ryans,

We have been discussing gravity and relavistic mass. Twit.

Pete

03-22-04, 05:59 PM

Hi zanket,
Apparently this stress-energy tensor thing is not a simple analog to total energy.
An energetic particle confined to a box appears to have a different stress-energy tensor to an unconfined particle.

I don't know how... I don't know what this stress-energy tensor is... But I'm curious.

Hence my post at the top of this page - is it the collisions that are important? Are gravity waves involved?

lethe

03-22-04, 09:22 PM

I agree on the difficulty involve if we really want to draw a solid line what is rest mass and what is not. There isn't any solid line can be drawn in practice. Well, guess that's all I wanted to say about this matter.
i am not entirely sure, Paul, but perhaps we are actually in agreement

lethe

03-22-04, 09:31 PM

I find my argument about heat having mass to be unsatisfactory. Yes, coal loses mass when burned, but how do physicists know for sure that the lost mass is not in all the byproducts of the burning except the heat? Like in the ash, carbon monoxide, etc.? Is there a better intuitive argument?
well, burning coal is a chemical reaction, so the change in mass due to energy loss is probably not measurable. so all the mass is in the ash.

I didn’t say the grain of sand becomes a black hole, but that it doesn’t. I don’t see how the grain’s gravitational field will never look significant to Sun given that the grain’s gravitational field from our perspective approaches infinity with ever higher speeds past Sun.
ahh.... but the gravitational field doesn't approach infinity as the grain of sand gets faster and faster. the gravitational field changes shape, and gets sharper and sharper around the direction of motion, and there is a stronger "magnetic" field that acts at right angles

Perhaps you can explain. Zillion? You knew what I meant, right? Yeah I slaughter physics terminology. I’m a layman, that’s what we do.
if you put fast enough moving grains of sand in the box, and then get them to stay in the box, by binding them somehow (this binding force will also contribute to the gravitational field), then you will get a black hole. the grain of sand alone is not enough

MacM

03-22-04, 11:43 PM

Lethe,

[/ahh.... but the gravitational field doesn't approach infinity as the grain of sand gets faster and faster. the gravitational field changes shape, and gets sharper and sharper around the direction of motion, and there is a stronger "magnetic" field that acts at right angles

Question? By your statement above are you saying that not all input energy into relavistic motion goes into mass perse? That some of the energy input is being focused into the EM field orthogonal to the vector of motion?

Pete

03-22-04, 11:45 PM

if you put fast enough moving grains of sand in the box, and then get them to stay in the box, by binding them somehow (this binding force will also contribute to the gravitational field), then you will get a black hole. the grain of sand alone is not enough

What about a single grain of sand bouncing around in a box?
How is this different to a boxless grain?
Are the collisions between grain and box significant (gravity waves??), since a grain in transit between the walls of the box doesn't seem different to the grain out of the box?

I really think I'm on to something... feel free to bust my bubble :)

Pete

03-22-04, 11:50 PM

...and there is a stronger "magnetic" field that acts at right angles

Que?
Is this a real magnetic field? For an uncharged grain of sand?
Or is this some gravitational analog (which would explain the quotes)?

lethe

03-23-04, 12:49 AM

Que?
Is this a real magnetic field? For an uncharged grain of sand?
Or is this some gravitational analog (which would explain the quotes)?
gravitational analogue. sometimes called the gravitomagnetic force

Pete

03-23-04, 12:54 AM

Just to confirm - this force is unrelated to electromagnetism (expect perhaps in some similarities of the formalism)?

lethe

03-23-04, 01:10 AM

Just to confirm - this force is unrelated to electromagnetism (expect perhaps in some similarities of the formalism)?
right. this effect is purely gravitational. it is present even if all my masses are electrically neutral. it is a purely relativistic effect (but so is normal magnetism)

Pete

03-23-04, 08:21 AM

lethe, are you able to address my question on whether the collisions between particle and box walls are significant in determining the gravity field of the box?

MacM

03-23-04, 09:14 AM

Lethe,

Interesting! A Google of the term "magnetogravational force" only returned (2) pages of available information. All basically oriented around T. Beardon and Searl. The only exception was the American Physics Review for which I was unable to read their presentation because it is only available to members.

Can you direct us to some mainstream sources of information or are you into T Beardon's physics?

BTW there are some very interesting claims being made by some regarding experiments and mathematics in the area which refute relativity. I am not saying they are valid but only that I found the absence of mainstream science in the search unusual.

Until I searched the term I had thought you were talking about the EM wave front associated with velocity and Lorentz Contraction.

lethe

03-23-04, 09:28 AM

Lethe,

Interesting! A Google of the term "magnetogravational force" only returned (2) pages of available information. All basically oriented around T. Beardon and Searl. The only exception was the American Physics Review for which I was unable to read their presentation because it is only available to members.
oops, that's my fault. the name of the force is gravitomagnetic, not magnetogravity. sorry.

Can you direct us to some mainstream sources of information
yeah, see gr-qc/0207065 (http://arxiv.org/abs/gr-qc/0207065) for a nice review of gravitomagnetism.

or are you into T Beardon's physics?
certainly not

MacM

03-23-04, 09:32 AM

Lethe,

oops, that's my fault. the name of the force is gravitomagnetic, not magnetogravity. sorry.

Quote:
Can you direct us to some mainstream sources of information

yeah, see gr-qc/0207065 for a nice review of gravitomagnetism.

Quote:
or are you into T Beardon's physics?

certainly not

Wheeew. I thought you had capsized. :D

Thanks for the link.

zanket

03-23-04, 07:25 PM

well, burning coal is a chemical reaction, so the change in mass due to energy loss is probably not measurable. so all the mass is in the ash.

As I understand, it’s too small to be measurable in any application. Is there an intuitive argument that you know of, that shows that heat (or a battery’s charge) must have mass? A book of mine uses the example of a nuclear reactor charging a battery. Since the reactor’s fuel loses mass, the lost mass must be in the battery, it says. But fission has other byproducts, and all the lost mass could be within them. I’d like to know a tighter intuitive argument, especially since heat’s mass has never been measured.

ahh.... but the gravitational field doesn't approach infinity as the grain of sand gets faster and faster. the gravitational field changes shape, and gets sharper and sharper around the direction of motion, and there is a stronger "magnetic" field that acts at right angles

That seems to contradict what you said above about the moving ball. The box with the moving ball weighs more than the one with the stationary ball, you said. Presumably regardless of the shape of the gravitational field, since the weigh scale couldn’t differentiate. Presumably the weight increases to approach infinity with ever-higher speeds approaching c. I assume that the strength of the gravitational field goes hand-in-hand with the weight. What am I missing?

MacM

03-23-04, 07:40 PM

Zanket,

But fission has other byproducts, and all the lost mass could be within them.

Not really. The fission/fusion process is substantially detailed. That is the mass of the fission by products including alpha, gamma and beta, etc is well known. The missing mass (mass defect) is measured in terms of amu (Atomic Mass Units) and shows up as kenetic energy of the fission fragments and radiation.

It is interesting in fact that the question regarding mass of temperature (velocity of particles - kenetic energy) isn't included as mass in nuclear calculations.

zanket

03-23-04, 07:46 PM

That's good to know, but I'm looking for an intuitive argument where one must logically accept that some of the missing mass is in the battery's charge, or in the heat or other energy byproduct. Just knowing that physics says it's there isn't good enough. I'll keep looking around myself.

MacM

03-23-04, 10:36 PM

Zanket,

The problem you have is that 1 amu = 1.66E-24 gram (3.66E-27 lb) = 0.00149 erg energy.

Coal typically has 13,000 BTU/lb = 1/3 Billionths lb.

1 lb mass = 38.7 trillion BTU

1 BTU raises 1 lb of water 1 degree F = 2.584E-14 lb mass. (258.4/1,000,000,000,000 trillionths of a lb.)

MacM

03-23-04, 10:41 PM

Lethe,

Curious. You are a proponent of Relativity. Yet in the paper you cited, the affect you refer to as relates to 2 Brane is is absolute disagreement with Relativity.

Which do you believe is correct.? See attachment.

lethe

03-24-04, 12:18 AM

Lethe,

Curious. You are a proponent of Relativity.
no, in fact, on the contrary, i believe that GR is wrong.

Yet in the paper you cited, the affect you refer to as relates to 2 Brane is is absolute disagreement with Relativity.

Which do you believe is correct.? See attachment.
Randall-Sundrum predicts measurable deviations from GR. it is a large extra dimension theory. actually, my roommate is currently crunching numbers to test Randall-Sundrum deviations from GR based on cosmological data. currently, i don't believe that they will measure a deviation, but as a scientist, i must admit the possibility. i don't find that work too interesting, but i would of course like to know what results my roommate measures.

MacM

03-24-04, 12:33 AM

Lethe,

no, in fact, on the contrary, i believe that GR is wrong.

You mean we actually agree on something? :D

Interesting work however. Results should be a bomb shell.

zanket

03-24-04, 02:41 AM

Coal typically has 13,000 BTU/lb = 1/3 Billionths lb.

I don't know what you're getting at here. I'm looking for an inutitive argument that shows heat has mass, like a thought experiment where the result can hardly be denied. Not just raw data.

lethe

03-24-04, 06:59 AM

Lethe,

You mean we actually agree on something? :D

does this mean you believe in string theory, Mac?

lethe

03-24-04, 07:19 AM

lethe, are you able to address my question on whether the collisions between particle and box walls are significant in determining the gravity field of the box?
ok, lemme see. you had a couple...

Very large but light perfectly sealed box. One relativistic particle inside.
Time between collisions with the box walls is measurable, momentum change in box at each collision is detectable.

What does the gravity of this system look like? Is it constant? Are there gravity waves produced at each collision?
when you put it that way, i have to admit that the position of the particle inside the box is detectible by its gravitational field. in principle, this would work for any number of particles, not just for one. so i think when i said before that i want to pretend that we can't know what's inside the box, i was off the track.

in the case of one particle, the gravity won't be constant, but will track the oscillations of the particle back and forth. and yeah, i expect that there will be gravitational waves at each collision

Hi zanket,
Apparently this stress-energy tensor thing is not a simple analog to total energy.
An energetic particle confined to a box appears to have a different stress-energy tensor to an unconfined particle.
yeah, that is what i was saying to zanket before, why you can fill the box with particles and it becomes a black hole, whereas the particles alone never will.

i think you have to take into account the energy of the walls of the box that holds the particles together. that is what distinguishes this system from a bunch of free particles. if the walls are perfectly rigid, then this energy would be infinite, but of course, that is not physical.

I don't know how... I don't know what this stress-energy tensor is... But I'm curious.
the stress tensor is a 4x4 matrix of energy densities, momentum densities, pressures and stresses. the 00th component is just plain old energy per unit volume. the 0ith component is energy density flux in the ith direction, i think. the ijth component is momentum density in the ith direction flux in the jth direction, also known as stress if i!=j. if i=j, this is also known as pressure. if you have particles in a box, then the walls of the box exert a pressure, and this has to be taken into account.

Hence my post at the top of this page - is it the collisions that are important? Are gravity waves involved?
the box itself must have a high stress tensor if it is going to keep these very energetic particles confined. i don't think gravity waves have anything to do with this issue.

What about a single grain of sand bouncing around in a box?
How is this different to a boxless grain?
Are the collisions between grain and box significant (gravity waves??), since a grain in transit between the walls of the box doesn't seem different to the grain out of the box?

I really think I'm on to something... feel free to bust my bubble :)
ok, i hope i addressed this question sufficiently above. so what are you on to?

lethe

03-24-04, 07:27 AM

As I understand, it’s too small to be measurable in any application. Is there an intuitive argument that you know of, that shows that heat (or a battery’s charge) must have mass? A book of mine uses the example of a nuclear reactor charging a battery. Since the reactor’s fuel loses mass, the lost mass must be in the battery, it says. But fission has other byproducts, and all the lost mass could be within them. I’d like to know a tighter intuitive argument, especially since heat’s mass has never been measured.
well, heat energy is just kinetic energy thermally distributed to the atoms of a system. you know that particles in motion have higher transverse inertia. when the kinetic energy is thermally distributed, on average, the same number will be in transverse motion to any axis you choose, so the rest mass of system with all these particles increases with heat.

ahh.... but the gravitational field doesn't approach infinity as the grain of sand gets faster and faster. the gravitational field changes shape, and gets sharper and sharper around the direction of motion, and there is a stronger "magnetic" field that acts at right angles
That seems to contradict what you said above about the moving ball. The box with the moving ball weighs more than the one with the stationary ball, you said. Presumably regardless of the shape of the gravitational field, since the weigh scale couldn’t differentiate. Presumably the weight increases to approach infinity with ever-higher speeds approaching c. I assume that the strength of the gravitational field goes hand-in-hand with the weight. What am I missing?
as i said in another post, the box with the moving ball has more going on than just a ball and a box. if you had a fast moving ball outside the box, then the box would not turn into a black hole, no matter how fast the ball is going. but if you want to keep the ball confined to the box, you have to add a bunch of energy to the system. this, together with the kinetic energy/momentum of the ball (which you might like to average over many bounces), contributes to the weight of the box.

in the case of the free ball, you only have the kinetic energy/momentum of the ball, and you can't average it over many bounces, since it is not in a box

lethe

03-24-04, 08:07 AM

i think maybe we should stop talking about the box, and instead consider a particle bound by a spring. in this case, it much clearer what the difference between the bound particle and the free particle is: in the bound case, there is also potential energy stored in the spring, as well as kinetic energy in the particle.

MacM

03-24-04, 08:30 AM

Lethe,

does this mean you believe in string theory, Mac?

To use your phrase "certainly not". :D

MacM

03-24-04, 08:35 AM

Zanket,

Originally Posted by MacM
Coal typically has 13,000 BTU/lb = 1/3 Billionths lb.

Posted by Zanket: I don't know what you're getting at here. I'm looking for an inutitive argument that shows heat has mass, like a thought experiment where the result can hardly be denied. Not just raw data.

What I'm getting at is that either in reality or thought your scenario must account for a virtually imperceptable, immeasurable quantity.

lethe

03-24-04, 09:07 AM

Lethe,

To use your phrase "certainly not". :D
right, that's what i thought. but the "interesting" (to use your own word) model that you noticed in that paper is a result from string theory. if you think GR is a silly mathematical complication on Newtonian gravity, then surely you would think that string theory is even sillier, plus it has the added distraction that it has never been measured

MacM

03-24-04, 09:12 AM

Lethe,

right, that's what i thought. but the "interesting" (to use your own word) model that you noticed in that paper is a result from string theory. if you think GR is a silly mathematical complication on Newtonian gravity, then surely you would think that string theory is even sillier, plus it has the added distraction that it has never been measured

Once again, I find we are in complete agreement. :D

My point however being that while they may be useful tools mathematically they are useless descriptors of reality. I have nothing to back this up but I tend to see the 11 dimensions of string theory as fuzz on a tennis ball. Still part of our 3D space but a form of greater degrees of freedom - Not true dimensions.

lethe

03-24-04, 09:32 AM

Lethe,

Once again, I find we are in complete agreement. :D

My point however being that while they may be useful tools mathematically they are useless descriptors of reality. I have nothing to back this up but I tend to see the 11 dimensions of string theory as fuzz on a tennis ball. Still part of our 3D space but a form of greater degrees of freedom - Not true dimensions.
well... whatever... i guess you can think of those extra dimensions however you want, since you don't think string theory is valid anyway. but let me assure you, "fuzz on a tennis ball" doesn't sound like a very good description to me.

so just so we are clear here: i think that GR is correct to a first approximation, but that it must have quantum corrections. but to say that "GR is exactly correct" is false. on the other hand, you think that GR is unnecessary mathematical masturbation that was never necessary to even achieve the level of a first order approximation that i think it is. and so in the end, you also believe that "GR is exactly correct" is a false statement, but we arrived there at routes that couldn't be more different.

is this an accurate assessment of your views?

MacM

03-24-04, 09:44 AM

Lethe,

is this an accurate assessment of your views?

No, not really. For example I see GR as being generally valid but for the wrong reasons as presented. That is the issue of "Curved Space" to me is absolutely valid but is better shown as a function of the origin of gravitational force (energy flow and attenutation) and space being a function of energy density, naturally causes distance to be variable as a function of the masses of the observer and observed.

The result are the same but one has cause and greter implications for the universe and reality, the other doesn't.

http://www.sciforums.com/attachment.php?attachmentid=2696

http://www.sciforums.com/attachment.php?attachmentid=2697

"Move your mouse to the speck in the upper left corner until the enlarge button appears then click it."

Note how I have avoided the terriable "U" word. :D

lethe

03-24-04, 09:49 AM

Lethe,
No, not really. For example I see GR as being generally valid but for the wrong reasons as presented.
GR is usually presented as the logical result of the equivalence principle. do you think the equivalence principle is wrong?

That is the issue of "Curved Space" to me is absolutely valid but is better shown as a function of the origin of gravitational force (energy flow and attenutation) and space being a function of energy density, naturally causes distance to be variable as a function of the masses of the observer and observed.
OK, great, so you like curved space. me too.

The result are the same but one has cause and greter implications for the universe and reality, the other doesn't.
i am fearful to ask what you think the implications of these two alternate views for the universe are.

MacM

03-24-04, 09:55 AM

Lethe,

GR is usually presented as the logical result of the equivalence principle. do you think the equivalence principle is wrong?

Not at all. I see why there is an equivelence principle.

OK, great, so you like curved space. me too.

Absolutely, but have you ever realized what that actually means? That is that distance is not the same between objects for different observers at rest?

i am fearful to ask what you think the implications of these two alternate views for the universe are.

For purposes of this string I'll let the above comment stand as the answer here - although there is much more.

If you don't follow the variable distance arguement then read the segment in the two links about the issue.:D

lethe

03-24-04, 10:03 AM

Lethe,

"Move your mouse to the speck in the upper left corner until the enlarge button appears then click it."
enlarge button? i have no idea what you are talking about. probably i have a different sort of computer than you, and it doesn't have an enlarge button. and i see nothing in those diagrams.

lethe

03-24-04, 10:07 AM

Lethe,
Not at all. I see why there is an equivelence principle.
OK, so then what is wrong about the reasons in GR as it is usually presented? bear in mind that GR is usually presented as the logical conclusion of the equivalence principle.

Absolutely, but have you ever realized what that actually means? That is that distance is not the same between objects for different observers at rest?
well... this is already true in special relativity. what happens in curved space is that, for example, the sum of the angles of a triangle is not 180 degrees.

MacM

03-24-04, 10:13 AM

lethe,

enlarge button? i have no idea what you are talking about. probably i have a different sort of computer than you, and it doesn't have an enlarge button. and i see nothing in those diagrams.

If you see nothing then look very carefully to the upper left corner. You should see a speck. Even if you can't see it move your mouse about x,y = 1 inch from the upper left corner. You should see an oragne square appear at the lower area of your screen. click on it.

Gotta go cut some trees. Back later.

ryans

03-24-04, 05:50 PM

well... this is already true in special relativity. what happens in curved space is that, for example, the sum of the angles of a triangle is not 180 degrees.

And the ratio of the circumference of a circle to the diameter is not pi.!!

MacM

03-24-04, 06:02 PM

Lethe,

OK, so then what is wrong about the reasons in GR as it is usually presented? bear in mind that GR is usually presented as the logical conclusion of the equivalence principle.

I would have to say the inertia of mass and gravity equivelence principle are indeed a function of the same physics. I'm not convienced that GR mathematics is the proper description of those functions.

well... this is already true in special relativity. what happens in curved space is that, for example, the sum of the angles of a triangle is not 180 degrees.

Not talking about angles of a triangle. I'm asking if you ever had thought that if a Bowling Ball and a Golf Ball were setting side by side and a Ping Pong Ball is some distance away on a line perpenticular and in the center of the line between those balls centers, forming an Isosceles triangle between centers of the three balls, that GR would mean that the length of the two sides of the isosceles triangle are not the same.!

I know that defies the description of an isosceles triangle but that is another matter because it is only an illusion from our perspective that those sides would be equal. In reality it is not an isosceles triangle.

MacM

03-24-04, 06:12 PM

ryans,

And the ratio of the circumference of a circle to the diameter is not pi.!!

HeHeHe. :p Back for more I see. I would think you would rather leave that subject alone. Your statement is valid only for properly defined conditions, which you were all wet on and I was correct where that issue was debated.

ryans

03-24-04, 08:04 PM

If you can accept that the internal angles of a triangle do not sum to 180 degrees in curved space, then surely you can use the same model to see that the relevant ration does not equal Pi?

P.S.
Let's be civilised shall we, so that means no name calling or superlfuous internet references.

MacM

03-24-04, 09:17 PM

Ryans,

If you can accept that the internal angles of a triangle do not sum to 180 degrees in curved space, then surely you can use the same model to see that the relevant ration does not equal Pi?

As I said the Pi ratio is only applicable under properly defined circumstances. I have never said relavistically the ratio doesn't change.

Let's be civilised shall we, so that means no name calling or superlfuous internet references.

You'll find I hold no grudge and will be as civilized as those that interact with me. I do question your description of a Physicist's reply as being superfluous however.

pmb

03-26-04, 08:47 AM

Does an object's gravitational pull increase when its relativistic mass increases? Or is it dependant only on rest mess?

I'm surprised that you had so many problems getting an answer. The answer to your question is Yes. If a body is moving then the gravitational field generated by the moving body is stronger.

The source of gravitational field, within the framework of GR, is not the mass, but the so called energy-momentum tensor.

Recall what Einstein stated in his 1916 paper The Foundation of the General Theory of Relativity

The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in a symmetrical tensor of second rank, the energy-tensor.

The tensor he speaks of is the stress-energy-momentum tensor T^uv. The T^00 component is defined as T^00 = c^2(mass density). For this reason it is said that mass is the source of gravity. For more on this see

Cosmological Principles, John A. Peacock, Cambridge University Press, (1999) page 17-18
http://assets.cambridge.org/0521422701/sample/0521422701WS.pdf

The complete description of mass is a tensor. This tensor you could call the mass-momentum tensor. But whatever name you give it its just proportional to T^uv. There is no real reason to say that one tensor is the source while the other tensor is not. I.e. I can defined M^uv as

M^uv = T^uv/c^2

where

M^00 = mass density

Einstein's field equations could then expressed as

H = (4*pi/c^2)M

where H = (c^2/2)G where G is the Einstein tensor. Which one used is a matter of taste.

Regarding mass as the source of gravity. Well if I were to quote "Gravitation," by Misner, Thorne and Wheeler - "Mass is the source of gravityt."

This is similar to saying that charge is the source of the elecctromagnetic field. The complete description of charge is the 4-current J^u where J^0 = c*(charge density). The difference being that mass is a function of speed where as charged is not.

If you had a box of particles, e.g. a gas, then if the kinetic energy of the particles is large enough, i.e. you keep pumping in more and more energy making the particles move faster and faster and the kinetic energy becoming higher and higher, then eventually the box would turn into a black hole (assuming the walls of the box didn't collapse). This, however, does not mean that a baseball in one frame turns into a black hole in another frame. One requires only that the energy of the gas with a finite space have a certain value. I could have just as well taken the same amount of mass and placed it in a small enough space and it would be a black hole. An object is not a black hole because it has a certain amount of mass. It's a black hole because its mass is confined to a certain region of space. I.e. all its mass is confined within a sphere whose radius is the Scwarzschild radius.

What about photons, which have only relativistic mass? Would a photon produce a gravitational field equivalent to an object with a mass of hv/c^2?

Yes. Photons generate a gravitational field. They have momentum and anything with momentum has (relativistic) mass.

Note: A moving particle weighs more than the same particle at rest.

I'm mainly curious about whether or not photons produce their own gravitational fields because of their relativistic mass. If two photons were sent out on parallel courses, would they attract each other and gradually move closer together?

Yes - photons produce their own gravitational field. I do not believe that photons moving parallel to not attract each other. I do believe that if they're traveling antiparallel that they do attract each other.

Note - Some people like to use the term "mass" to refer only to proper mass because they hold that the term "relativistic mass" leads to errors. That is 100% incorrect. A person may make errors but that is only due to a misunderstanding they have with relativity. Trying to avoid this by speaking only in terms or rest masss servers only to trade one set of errors for another set of errors. E.g. Some people make the mistake of thinking that a moving object will become a black hole if if its moving fast enough. For reasons like this some people say "Don't think of mass as relativistic mass. Think only in terms or rest mass." Then what happens is that some people then say "Oh! So mass is rest mass. Then since the rest mass of light is zero it follows that a directed beam of light has no gravitational field!" - What has happened is that one set of misunderstandings has been traded for another set of misunderstandings.

The most reasonable thing that can carry the name mass is relativistic mass.

Peter2003

03-26-04, 10:03 AM

What relativity says about the appearance of life and mind.
I don't see why one should take so seriously incomplete
description of reality.

photons should have some subtance and therefore mass.
it is a matter of math description how we shell treat their
small mass.

MacM

03-26-04, 01:29 PM

pmb,

I'm surprised that you had so many problems getting an answer. The answer to your question is Yes. If a body is moving then the gravitational field generated by the moving body is stronger.

Interesting. Your profile doesn't show your qualifications, so we'll have to read between the lines. You have made an absolute statement and seem to make light that not everyone seems to hold your view.

Recall what Einstein stated in his 1916 paper The Foundation of the General Theory of Relativity

Yes, he specifically warned about not considering relavistic mass but momentum. However, it is somwhat difficult to visualize how infinite momentum can occur in absence of infinite velocity or infinite mass. It seems a bit more of sweep it under the rug than a clear answer.

The tensor he speaks of is the stress-energy-momentum tensor T^uv. The T^00 component is defined as T^00 = c^2(mass density). For this reason it is said that mass is the source of gravity. For more on this see

Cosmological Principles, John A. Peacock, Cambridge University Press, (1999) page 17-18
http://assets.cambridge.org/0521422...521422701WS.pdf

The complete description of mass is a tensor. This tensor you could call the mass-momentum tensor. But whatever name you give it its just proportional to T^uv. There is no real reason to say that one tensor is the source while the other tensor is not. I.e. I can defined M^uv as

M^uv = T^uv/c^2

where

M^00 = mass density

Einstein's field equations could then expressed as

H = (4*pi/c^2)M

where H = (c^2/2)G where G is the Einstein tensor. Which one used is a matter of taste.

Regarding mass as the source of gravity. Well if I were to quote "Gravitation," by Misner, Thorne and Wheeler - "Mass is the source of gravityt."

This is similar to saying that charge is the source of the elecctromagnetic field. The complete description of charge is the 4-current J^u where J^0 = c*(charge density). The difference being that mass is a function of speed where as charged is not.

If you had a box of particles, e.g. a gas, then if the kinetic energy of the particles is large enough, i.e. you keep pumping in more and more energy making the particles move faster and faster and the kinetic energy becoming higher and higher, then eventually the box would turn into a black hole (assuming the walls of the box didn't collapse). This, however, does not mean that a baseball in one frame turns into a black hole in another frame. One requires only that the energy of the gas with a finite space have a certain value. I could have just as well taken the same amount of mass and placed it in a small enough space and it would be a black hole. An object is not a black hole because it has a certain amount of mass. It's a black hole because its mass is confined to a certain region of space. I.e. all its mass is confined within a sphere whose radius is the Scwarzschild radius.

True it isn't mass but mass density that creates a Black Hole. There are infact known to be microscopic Black Holes. Infact many labs are experimenting at trying to make such Black Holes. But your response seems to indicate you are aware that there are other views than the one your advanced as being the only correct view. What is your basis to claim your view is correct and the others aren't.

Yes. Photons generate a gravitational field. They have momentum and anything with momentum has (relativistic) mass.

OK, I'll accept that noting that this infers that mass/gravity causes light to bend passing near the sun and not curved space.

Note: A moving particle weighs more than the same particle at rest.

OK, so you are saying relavistic mass is real. Einstein said don't consider that.

Yes - photons produce their own gravitational field. I do not believe that photons moving parallel to not attract each other. I do believe that if they're traveling antiparallel that they do attract each other.

Interesting idea but it seems a bit confusing to think that a photon can have different gravity (hence move differently) to different observers. Can you qualify this a bit?

Note - Some people like to use the term "mass" to refer only to proper mass because they hold that the term "relativistic mass" leads to errors. That is 100% incorrect. A person may make errors but that is only due to a misunderstanding they have with relativity. Trying to avoid this by speaking only in terms or rest masss servers only to trade one set of errors for another set of errors. E.g. Some people make the mistake of thinking that a moving object will become a black hole if if its moving fast enough. For reasons like this some people say "Don't think of mass as relativistic mass. Think only in terms or rest mass." Then what happens is that some people then say "Oh! So mass is rest mass. Then since the rest mass of light is zero it follows that a directed beam of light has no gravitational field!" - What has happened is that one set of misunderstandings has been traded for another set of misunderstandings

The most reasonable thing that can carry the name mass is relativistic mass.

Interesting how you taut Einstein in one area and then oppose him in another. Eistein said do not consider relavistic mass.

pmb

03-26-04, 03:57 PM

pmb,

Interesting. Your profile doesn't show your qualifications, so we'll have to read between the lines. You have made an absolute statement and seem to make light that not everyone seems to hold your view.

I don't see that I made light of anything. To me its simply a matter of opinion.

Regarding qualifications - I'll give them to anyone whom I wish to work for. But on forums I'm just interesting in discussing physics I don't see where that matters. If one wishes me to back up a statement then I'll do so. If someone wants me to derive something which I stated/claimed I'll be glad to do so. If someone is really that interested in what my qualifications are then I'll be happy to tell them - in e-mail of course (see e-mail address below).

But I'll give you a few hints - I'm the "Peter M. Brown" in the following

http://www.whoi.edu/science/PO/people/jprice/class/aCt.pdf
http://www.eftaylor.com/pub/front_matter.pdf
http://cosmo.fis.fc.ul.pt/~Fisica2002/TaylorEvora.pdf
http://arxiv.org/pdf/physics/0204044
http://arxiv.org/pdf/physics/0308039

Regarding "absolute statement". If you mean the fact that the strength of the gravitational field is frame dependant then that is certainly not a matter of opinion. That is a matter of fact. As an example see the article

"Measuring the active gravitational mass of a moving object," D. W. Olson and R. C. Guarino, Am. J. Phys., Am. J. Phys. 53, 661 (1985). The abstract reads

If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic increase in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that Mrel = gamma*(1+beta2)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not M but is approximately 2M.

I can e-mail this to anyone who wishes to read it. There are other examples too. I've worked out another one on my web page.

http://www.geocities.com/physics_world/gr/grav_moving_rod.htm

I'm working on another one but the physics is the same. The only difference being the gravitaitonal potential is a different function.

Yes, he specifically warned about not considering relavistic mass but momentum. However, it is somwhat difficult to visualize how infinite momentum can occur in absence of infinite velocity or infinite mass. It seems a bit more of sweep it under the rug than a clear answer.

Actually that is not quite true. Einstein never really warned about relativistic mass per se. Einstein said that it is not good to introduce

m = gamma*m_o*v

Relativistic mass is defined as the m in p = mv. This is the spatial component of a particle's 4-momentum P. For a tardyon (I.e. v < c and thus m_o > 0) its given by

P^k = p^k = mv^k

where m = m_o*dt/dT where T is proper time. E.g. If the metric is time orthogonal (i.e. g_0k = 0) then

dt/dT = 1/sqrt[1 + 2*Phi/c^2 - beta^2]

where

Phi = (g_oo - 1)c^2/2

For v << c

dt/dT ~ 1/sqrt[1 + 2*Phi/c^2]

M ~ m_o/sqrt[1 + 2*Phi/c^2]

Thus for a slowly moving particle the mass is still dependant on the gravitational potential - At least, that is, according to Einstein. But I do agree with him on this point. When it came to radiation Einstein did state that electromagnetic energy has a mass densit rho which was related to its energy density u by rho = u/c^2. This still is used today by many cosmologists, e.g. Peacock, etc.

Consider how Alan Guth explains all this in his class notes from his "Early Universe" course at MIT
http://www.geocities.com/physics_world/guth.gif

True it isn't mass but mass density that creates a Black Hole. There are infact known to be microscopic Black Holes. Infact many labs are experimenting at trying to make such Black Holes. But your response seems to indicate you are aware that there are other views than the one your advanced as being the only correct view. What is your basis to claim your view is correct and the others aren't.

I'm afraid you misread. Nowhere did I state that this was the only correct view. I made two points

(1) When you try to switch from relativistic mass to rest mass for because you think relativistic mass is the source of a few errors made by students just learning relativity then all you're doing is giving them a definition which has lead to other misunderstandings.

(2) I believe that mass = relativistic mass is the most reasonable way to define the term "mass" since it has all the properties associated with mass and it fits more naturally into relativity.

I do not believe that the notion of proper mass is not useful.

Consider the two types of "time" and distance that is used in relativity. There is "time" and there is "proper time." E.g. Consider the timelike spacetime displacement dX where

dX = (cdt, dr)

dt = time interval, dr = spatial displacement. Then the proper time interval, dT, is given by

c^2*dT^2 = |dX|^2

Likewise there is "distance" L and there is "proper distance" q. Consider the spacelike spacetime interval dX = (cdt, dr). Then

dq^ = -|dX|^2

In a similar fashion there is "mass" m and "proper mass", m_o where. Consider the 4-momentum P = (cm, p)

c^2*(m_o)^2 = |P|^2

There is a nice pattern here. Think of proper mass as you would all other proper quantities and think of mass as one of the components of the 4-vector of which proper mass is the magnitude of. The idea of proper mass cannot be extended to something more general in relativity. For example: In SR one cannot, in general, define a proper mass for an arbitrary system of particles. This is only possible for a closed system of particles.

To be detailed in this would take up far too much room here. In fact when I tried to write it up to be complete and precise it took 84 pages. However if anyone wishes to read it then feel free to e-mail me at peter.brown46@verizon.net

OK, so you are saying relavistic mass is real. Einstein said don't consider that.

Not really. He refered to a specific case. And he seemed only to be refering to special relativity. He made such a comment in a letter to Lincoln Barnett in 1948. There was an article about all this in Physics Today back in 1989 by Lev Okun. I assume that's what you're refering to. If so then Okun was unaware of something else in Einstein's book that he was quoting. He took one part of his book (as well as a letter to Linbcoln Barnettr) as proof of his idea that Einstein didn't like relativistic mass but he ignored the GR section of Einstein's text where Einstein actually used it. In his relativity text "The Meaning of Relativity" where he addresses both SR and GR he didn't follow that rule when it came to mass in GR. In fact Einstein himself stated that inertial mass of a body depends on the gravitational potential of the body. And the last revision he made to that text was in the mid 50's (1954). Had he changed his mind and wanted to use the term "mass" to only refer to proper mass then his idea of Mach's Principle wouhld have been meaningless. He also said indicated that light has mass in his text "The Evolution of Physics" (I'm too lazy to look it up right now - will upon request)

Interesting idea but it seems a bit confusing to think that a photon can have different gravity (hence move differently) to different observers. Can you qualify this a bit?

A problem was worked out regarding this way back in 1931 in the paper

"On The Gravitational Field Produced by Light," Tolman, Ehrenfest and Podolsky, Physical Review, Vol(37), March 1, 1931, pg 602-615

Tolman works this out in his text
"Relativity, Thermodynamics and Cosmology," Richard C. Tolman, Dover Pub, Sections 112-115 cover more aspects of the gravitational field generated by light than is presented here.

See - http://www.geocities.com/physics_world/grav_light.htm

Interesting how you taut Einstein in one area and then oppose him in another. Eistein said do not consider relavistic mass.[/QUOTE]

It would be weird for me to agree with every single view point by any single individual. But in this case I believe I'm justified since it appears to me that Einstein had a different definition of mass for different applications. that doesn't seem like a reasonable thing to do. But I only disagree with his notion about the velocity depedance regarding the mass of a tardyon. In other aapplications where Einstein used the idea I agree with him.

Pete

MacM

03-26-04, 11:05 PM

pmb,

I don't see that I made light of anything. To me its simply a matter of opinion.

Perhaps I misread your tone but it seemed the comment about "I don't see why it took so long......(and then gave your answer as though yours might be the only correct view.

Regarding qualifications - I'll give them to anyone whom I wish to work for. But on forums I'm just interesting in discussing physics I don't see where that matters.

It is not necessary to give qualifications but it would certainly help others determine how much weight to give your views.

Regarding "absolute statement". If you mean the fact that the strength of the gravitational field is frame dependant then that is certainly not a matter of opinion. That is a matter of fact.

OK, suppose I agree that it is a matter of fact, then we should be able to answer this simple fact. If I assume the earth orbits the sun or the moon orbits the earth in a balance between gravity per Fg = m1*m2/r^2 and centrifugal force Fc = m*v^2/r, I find I have a unique situation.

If I assume I am in a rocket with a relative velocity to the earth and moon and I fly over the orbital plane and inbetween the earth and moon at 86.6% c, then I should see m1 and m2 double. Fg therefore becomes 2 * 2 = 4 times the gravity. But the counter balancing centrifugal force of the moon Fc = 2. You have quadroupled the gravity but only doubled the centrifugal force. So why doesn't the moon spiral down to earth when we fly by?

If that isn't bad enough, if you have two bowling balls moving (initially parallel) in space they will gradually be drawn together by the Fg calculation above. Depending on the seperation there is a given amount of time before they collide. Yet there can be an umlimited number of observers flying around out there watching the experiment, all at different velocities, and each observer would find that the bowling balls aren't obeying the laws of physics since they can only close at their rest mass rate for gravity.

Otherwise there would have to be numerous different times before collision. Show us how your view resolves these issues.

Actually that is not quite true. Einstein never really warned about relativistic mass per se. Einstein said that it is not good to introduce

m = gamma*m_o*v

Actually Einstein's point of view is described in the following quote:

"It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

Go to: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html#relcon

Then Click on "Relavistic Mass"
Then Click on "Problems with Relavistic Mass" at the bottom of that block.

zanket

03-27-04, 12:25 AM

well, heat energy is just kinetic energy thermally distributed to the atoms of a system. you know that particles in motion have higher transverse inertia. when the kinetic energy is thermally distributed, on average, the same number will be in transverse motion to any axis you choose, so the rest mass of system with all these particles increases with heat.

Thanks for this explanation. How do you know that the rest mass increases with higher transverse inertia?

but if you want to keep the ball confined to the box, you have to add a bunch of energy to the system.

I understand this. I still don't understand why the moving ball (or grain of sand) outside of the box does not have a stronger gravitational attraction than a stationary ball or grain. (It seems that pmb says that it should.) If the grain of sand hits the sun at sufficiently close to c the sun will be destroyed as we know it, due to the grain's energy of momentum, which can approach infinity. Why wouldn't that energy be reflected by a stronger gravitational field such that the grain, if it grazed the sun, could damage the sun?

Pete

03-27-04, 05:38 AM

but if you want to keep the ball confined to the box, you have to add a bunch of energy to the system.
Why? Note that in the spring analogy, the total energy is the same... just alternating between spring potential energy and particle kinetic energy.

In the spring analogy, there is obviously real energy in the system when the spring is stretched... but what about when the spring is relaxed? How is that different to an unconfined particle at that instant?

Why wouldn't that energy be reflected by a stronger gravitational field such that the grain, if it grazed the sun, could damage the sun?
The difficulty is that gravity is not frame-dependant, but relativistic mass is. I don't know how pmb accounts for this.

Consider things from the grain of sand's reference frame. In the grain's reference frame, the grain is stationary, and the Sun is moving very very fast. The Sun's relativistic mass is enormous... So much that it should collapse into a Black Hole.

It doesn't, of course. Relativistic mass obviously does not directly produce a gravitational field.

I have a potentially crackpot idea that while kinetic energy does not produce a gravitational field, a change in momentum does produce a gravity wave. For the confined particle, it is changing momentum with every collision with the box walls... and the cumulative gravity waves look like a gravitational field that matches the particle's kinetic energy. I don't think this has far-reaching implications... it's just interesting.

pmb

03-27-04, 05:59 AM

pmb,

Perhaps I misread your tone but it seemed the comment about "I don't see why it took so long......(and then gave your answer as though yours might be the only correct view.

I wrote that because I looked through the posts and I didn't see a direct response to the question asked. That was all I meant. However there were a ton of responses so I didn't read them all and there probably was an answer.

Regarding "view" - I don't believe that I posted anything which constitutes a different view beyong a difference of opinion on how a term should be defined. How a term should be defined as merely a matter of opinion and I see no way in which any claim that a definition is wrong can be correct.

It is not necessary to give qualifications but it would certainly help others determine how much weight to give your views.

I agree that this is a valid point. I'm a physicist. I've spent about 15 years learning SR beyond college and 5 years studying GR.

[b]OK, suppose I agree that it is a matter of fact, then we should be able to answer this simple fact. If I assume the earth orbits the sun or the moon orbits the earth in a balance between gravity per Fg = m1*m2/r^2 and centrifugal force Fc = m*v^2/r, I find I have a unique situation.

If I assume I am in a rocket with a relative velocity to the earth and moon and I fly over the orbital plane and inbetween the earth and moon at 86.6% c, then I should see m1 and m2 double. Fg therefore becomes 2 * 2 = 4 times the gravity. But the counter balancing centrifugal force of the moon Fc = 2. You have quadroupled the gravity but only doubled the centrifugal force. So why doesn't the moon spiral down to earth when we fly by?

Ahh! Excellent question. This is why I love these discussion forums. I'll take a crack at an answer: A question may sound easy and yet may be difficult to provide a precise answer. Perhaps an answer by analogy. You're ignoring gravitational radiation. So let's consider the similar situation in EM and ignore EM radiation. If I ignore EM radiation then we can have a stable orbit of a negative charge orbiting a positive charge. Then the centifugal force is counter balanced by the electric force. Assume the mass of the positive charge is so massive that we can basically consider it to be at rest (i.e. we ignore its acceleration). Let S be the rest frame of the positive charge. Change frames from S to S' where S is in standard configuration with S'. In the new frame there is a magnetic field. The electric field has also changed. The component of the E field parallel to the velocity of S relative to S' will remain unchanged. The component of the field perpendicular to the field will increase by a factor of gamma. However in this new frame there is also a magnetic field which has a transverse component equal to (v/c)xE where E is the electric field and v is the velocity of the frame. In relativity all forces are velocity dependant and this is no different in GR since the gravitational force is also velocity dependant. In GR there is a paradigm in called "gravitomagnetism". This paradigm views the the equations of motion etc. in the weak field approximation in terms of equations which are nearly identical to Maxewell's equations. Regarding the gravitational case that you mention - In the new frame S there is an increased gravitomelectric field but now there a gravitomagnetic field. If you can understand why the negative charge can orbit the positive charge in each frame then you should now be able to understand why the moon can orbit the Earth in the new frame. I can go ahead and try to do a calculation in the EM case and find where each component is increasing and decreasing and where each component is comming into play in the EM case etc. But I imagine you're able to do that yourself. We can go over this if you'd like?

If that isn't bad enough, if you have two bowling balls moving (initially parallel) in space they will gradually be drawn together by the Fg calculation above. Depending on the seperation there is a given amount of time before they collide. Yet there can be an umlimited number of observers flying around out there watching the experiment, all at different velocities, and each observer would find that the bowling balls aren't obeying the laws of physics since they can only close at their rest mass rate for gravity.

I disagree. The rate at which they approach each other is frame dependant due to time dilation. Consider the same question with a positive and negative charge and how fast they approach each other.

[b]Actually Einstein's point of view is described in the following quote:

[color=blue]"It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

Go to: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html#relcon

Thanks. I'm intimately familiar with Einstein's thoughts on this matter. In fact his comment is why I chose to study the concept of mass in detail. In fact I have a copy of Einstein's letter. I even had to send away to Isael to get it.

Yes. As I agreed earlier Einstein said that a mass should not be given which is veclocity dependant. But he did not say that relativistic mass was a bad idea. It may seem that he did because many people actually define M(v) = m/sqrt[1-v^2/c^2] as the definition of relativistic mass. However that is quite untrue. That is a result of the choice of defining mass as relativistic mass. Another result is that light has mass and Eisntein agreed that light has mass. Einstein never really disagreed with the definition of relativistic mass as it is defined today, i.e. as the ratio of momentum to velocity. Since light momentum it has energy. One can also say that since light has energy it has mass. This is why I say that Einstein never disagreed with the defintion of relativistic mass.

Taken in a vacuum that comment of Einstein's seems to support the claim that Einstein held that relativistic mass was a bad idea. As such it seems almost a matter of fact that Einstein would say that light does not have mass or that a body's mass can't change when placed in a gravitational field. However the contrary is true. Einstein also wrote that light has mass since it has energy. In his and Infeld’s book The Evolution of Physics dated 1938, Einstein comments on the observation made by an observer inside an accelerating elevator. The elevator observer claims that light is ‘weightless’. Einstein then explains on page 31

But there is, fortunately, a grave fault in the reasoning of the inside observer, which saves our previous conclusion. He said: “A beam of light is weightless and, therefore, it will not be affected by the gravitational field.” This cannot be right! A beam of light carries energy and energy has mass.

Now consider what Einstein states in his GR book, the last edition of which was dated after his comment in that letter. Note that this was Einstein's most rigorous book on relativity

The inertia of a body must increase when ponderable masses are piled up in its neighborhood.

You mention a page which claims there are problems with relativistic mass. There are no problems other than students have a difficult understanding relativity. Note what that page argues

(1) You can use relativsitic mass to explain particle motion in accelerators
(2) Einstein seemed to say that he didn't like it
(3) You don't need it.

Regarding point 2 - It only seemed that Eintein didn't like relativsitic mass. In actuality he was inconsistent with his use of the term mass. Sometimes he used the concept and at other times he didn't.

Regarding point 3 - That's not a meaningful statement. It pretends that relativitic mass doesn't exist when in fact you're just not naming it. For example: The Lorentz force is given by

d(gamma*m*v)/dt = q(E + vxB)

where m = proper mass. Notice how the letter "p" doesn't appear in that equation? Notice how the letter "f" doesn't appear in that equation? Does this mean that I don't need or use the concept of force or momentum?