I don't consider this worthy of discussion, but nevertheless I'd like other peoples opinion and also, a concrete consensus of what Relativity says on the issue.

OK - the subject is mass. The question is: Is mass a form of energy, distinct from other forms of energy or is mass a measure of an objects total energy?

I got this quote off of wikipedia:

The mass of an object, as we have defined it, is a quantity intrinsic to the object, and independent of our current frame of reference. The energy E, on the other hand, varies with the frame of reference; if the frame is moving at a high velocity relative to the object, E will be very large, simply because the object has a lot of kinetic energy in that frame

It was referring to the statement that mass and energy are equivalent.

OK - I only asked for opinions and what Relativity says. Are you claiming wikipedia is the final say as to what Relativity says?

Fine I agree with wikipedia in this case. Someone else might not.

Einstein said we should not introduce the concept of variable mass since there is no clear definition of such a concept. Instead we should speak of proper mass and energy and momentum.

Mass and energy are two forms of the substance of the universe. E = mc² relates the forms.

My opinion is that this is what relativity says.

From this website (http://pop.obscure.org/physics-faq/Relativity/SR/mass.html):
The first record of the relationship of mass and energy explicitly in the form E = mc2 was written by Einstein in a review of relativity in 1907. If this formula is taken to include kinetic energy, then it is only valid for relativistic mass, but it can also be taken as valid in the rest frame for invariant mass. [...] an examination of his papers and books on relativity shows that he almost never used relativistic mass himself. Whenever the symbol m for mass appears in his equations it is always invariant mass. He did not introduce the notion that the mass of a body increases with velocity--just that it increases with energy content. The equation E = mc2 was only meant to be applied in the rest frame of the particle.

The sentence in red specifically, as well as the entire paragraph in general, implies mass is a measure of the total energy content and not that mass is a form of energy. This leads to contradiction, because thermal energy is considered internal energy of a system, but in actuality it is just a measure of the kinetic energy of internal atoms.

So, if we aren't going to include kinetic energy as a part of an object's mass, then thermal energy shouldn't be included either.

So my question still stands, does Relativity say that mass is a measure of an object's total energy or is mass just another form of energy?

An electron has rest energy of E = mc². If it meets a positron it will be converted into mc² worth of energy.

If the electron is moving (wrt a positron wall) it will also contribute it's kinetic energy.

The total available energy of a particle in its rest frame is therefore mc².

The total available energy of a particle viewed from a different frame is γmc².

If the electron is moving (wrt a positron wall) it will also contribute it's kinetic energy. Is the positron wall moving or is the electron moving? :bugeye:

I think this goes back to two particles colliding and forming a new particle. The kinetic energy of each is said to contribute to the mass of the new particle. But in fact, we should know that no particles are going to collide in this manner to form a new particle - the kinetic energy will be converted to thermal energy. It is only the view that this thermal energy contributes to the objects rest mass that one can claim the kinetic energy of the two particles contribute to the mass of the new particle. I've already shared my opinion on thermal energy though.

If one is going to say that thermal energy contributes to an objects rest mass, then after considering that thermal energy is a measure of the internal kinetic energy - One should also accept that a particle can accelerate itself to a velocity such that it's relativistic mass from the frame it began it's acceleration, would see the particle as a black hole because it's mass is so huge. :bugeye:

This has already been rejected by physicists.

Therefore it is my personal opinion that mass is another form of energy regardless of what Relativity says or anyone else.

I think mass is defined by the equations of motion and gravity.

Inertial mass is a measure of an object's resistance to a change of velocity as indicated by the following equation.Force = Mass * Acceleration

Gravitational mass is a measure of an object's reaction to and contribution to a gravitational field as indicated by the following equation.Force = Gconstant * MassOne * MassTwo / Distance²I think it might be more precise to view the first of the above equations as relating to change in momentum rather than acceleration resulting in a change in velocity. At any rate, Einstein considered momentum to be a fundamental quantity, while he viewed mass as an abstraction used by our thought processes. In his early development of relativity, he assumed conservation of momentum, which led to non-conservation of mass. When asked if he ever thought about mass conservation which would have led to failure of momentum conservation and a flawed theory, he said no (due to his view of momentum as more fundamental than mass).

BTW: Perhaps the anti-relativity posters at this forum might want to investigate the conclusions resulting from a mass conservation assumption instead of a momentum conservation assumption. Perhaps Albert was wrong and this line of thought might uncover a flaw in his theories (snicker, snicker).

The above equations ignore relativity, but are surely very good approximations to the relativistic point of view.

In the absence of experimental evidence, there is no reason to assume that inertial mass and gravitational mass are equivalent. Experiments show that they are proportional and they can be made equivalent by choosing certain units of measure. Einstein viewed this equivalence as either a cosmic coincidence or the consequence of some then unknown theory. Thinking about the equivalence led him to General Relativity.

Perhaps viewing the above equivalence as merely a coincidence might lead to a refutation of GR (some more snickering at the anti-relativity posters).

Is the positron wall moving or is the electron moving?

Read my post. I said "wrt a positron wall". The next person that asks is a or b moving gets kicked in the shins. From the POV of the wall the electron has γmc².

From the POV of the electron the wall has γmc².

From the POV of the electron the electron has mc².

Right? So you say mass is a different form of energy? I say mass can be converted to energy. So what? Semantics.

I think mass is defined by the equations of motion and gravity.

Inertial mass is a measure of an object's resistance to a change of velocity as indicated by the following equation.Force = Mass * Acceleration

Gravitational mass is a measure of an object's reaction to and contribution to a gravitational field as indicated by the following equation.Force = Gconstant * MassOne * MassTwo / Distance²

OK - first of all, very good analysis.

Are you sure this is how mass is defined? Correct me if I am wrong, but I thought mass was defined interms of energy, m=E/c².

At any rate, if you define mass from F=ma, you'll get that the relativistic mass to satisfy this equation in relativity is m_r=γ³m. and even this mass has to be defined as a vector (read: directional mass).


I think it might be more precise to view the first of the above equations as relating to change in momentum rather than acceleration resulting in a change in velocity. Yes this is correct. But for most cases, the mass is constant or approximately so.


At any rate, Einstein considered momentum to be a fundamental quantity, while he viewed mass as an abstraction used by our thought processes. In his early development of relativity, he assumed conservation of momentum, which led to non-conservation of mass. When asked if he ever thought about mass conservation which would have led to failure of momentum conservation and a flawed theory, he said no (due to his view of momentum as more fundamental than mass). The only objection I would raise concerning conservation of momentum over conservation of mass is: what is momentum on the quantum level and what is mass on the quantum level? Which of the two is more fundamental?

So you say mass is a different form of energy? I say mass can be converted to energy. So what? Semantics.

OK - my question then is: Does thermal energy contribute to an objects mass? This has nothing to do with energy being converted to mass or vice versa. We are only talking about an object with thermal energy. If you need an example, then let's use you. What is your mass at 98.6 F and what is your mass at 10,000 F?

Aer,

On what you took from a web site:
...an examination of his papers and books on relativity shows that he almost never used relativistic mass himself. ...

This is false!

I'm reading Einstein's book translated to spanish and in his own words Einstein says (section 15):

"Cabe, por tanto, decir: si un cuerpo absorbe la energía E, su masa inercial crece en E/c2; la masa inercial de un cuerpo no es una constante, sino variable según la variación de la energía."

What can be translated to:

"It can be said then: if a body absorbs the energy E, its inertial mass augments in E/c2; the inertial mass of a body is not a constant but variable with the variation of the energy."

You are trying to invent a modified version of the Relativity Theory...

Aer,

On what you took from a web site:


This is false!


Perhaps you don't have a meaning for almost in Spanish, here is the quote again:

.an examination of his papers and books on relativity shows that he almost never used relativistic mass himself

While he almost never used relativistic mass, he did talk about such a concept.

You are trying to invent a modified version of the Relativity Theory...
I will be the first to tell you that such a modification wouldn't be a bad thing.

Aer:

OK - my question then is: Does thermal energy contribute to an objects mass? This has nothing to do with energy being converted to mass or vice versa. We are only talking about an object with thermal energy. If you need an example, then let's use you. What is your mass at 98.6 F and what is your mass at 10,000 F?

I would say higher as measured in my rest frame. Energy is energy whether kinetic or whatever. So if your particles are moving wrt your body as a whole, each particle will have a greater effective mass.

Maybe.

Maybe.
Maybe at best :D and I believe that is the answer you'll find most places elsewhere if you bother to look it up. I have no problem with disagreeing with it however.

Because just like it would be theoretically possible to accelerate a particle to have a relativistic mass of a black hole, it is also possible to heat you up to have a mass of a black hole :eek:

This is why using relativistic mass is misleading I think. Your proper mass never changes. So you would never collapse into a black hole.

This is why using relativistic mass is misleading I think. Your proper mass never changes. So you would never collapse into a black hole.
Well, claiming thermal energy adds to your mass is the same as having a box with a particle inside bouncing all about at a velocity such that it's relativistic mass wrt the rest frame of the box is that of a black hole. Do you see the analogy?

Well, claiming thermal energy adds to your mass is the same as having a box with a particle inside bouncing all about at a velocity such that it's relativistic mass wrt the rest frame of the box is that of a black hole. Do you see the analogy?I see the analogy, but think SL is correct when he states:

"Your proper mass never changes. So you would never collapse into a black hole."

but perhaps he shoul have said that the proper mass of each of the particles that make up "you" never changes and consequently none can become a black hole.

The mass the box measures could exceed that of a black hole. lets consider what "mass" to the box means with the aid of a cyclotron and an already relativistic charged particle, perhaps a proton, traveling essentially at c, around in a perfectly circular path of constant radius. (The frequency of the cyclotron is essentially constant so that each time the particle crosses the two gaps of the cyclotron's "Ds," it gain the same energy and increases its mass.)This means the strength of the magnetic filed that is bending (accelerating) the particle to keep the circular radius constant is increasing. The magnetic force, F, is vBe, and B is increasing but v = c and e certainly is also remaining constant.

F=ma as definition of mass is OK and a is approaching zero, not changing much. Thus m and force are increasing essentially in direct proportion. It is getting harder and harder to bend the flying particle into the same circle as its mass is growing as the cyclotron "see" it. In a frame of the flying particle, it still has its rest mass and is in no danger of becomng a black hole in either frame.

I see the analogy, but think SL is correct when he states:

"Your proper mass never changes. So you would never collapse into a black hole." I agree with this statement. It is essentially a statement that relativistic mass is not "mass". "mass" creates a gravitational field. How might you propose that something with "relativistic mass" produces a gravitational field that expands in strength in another relative inertial frame?

Now let's look at some definitions of gravitation field from google:

(1) The volume over which an object exerts a gravitational pull.

(2) Field created by any object with mass, extending outward in all directions, which determines the influence of that object on all others. The strength of the gravitational field decreases as the square of the distance.

(3) the area of interaction between two masses

(4) The area surrounding an object which is under the influence of its gravitational pull. A more massive object will have a larger and stronger gravitational field.


Personally, I don't think any of these are very good definitions. They all indicate that gravity is a force, which is the Newtonian way of looking at gravity. In General Relativity, what we know as gravity is caused by the curvature of spacetime. It is not a force per say, but as the equivalence principle states - there is no experiment one could conduct to differentiate between a gravitational field and an equivalent uniform acceleration. Now to obtain this equivalent uniform acceleration in flat spacetime, we would have to use a force. But notice that the equivalence principle does not equate a gravitational field to a force; it is merely caused by the curvature of spacetime.

Anyway, the point is, gravity is curvature of space and is caused by mass by definition. So how does this incorporate relativistic mass or thermal energy - which is fundamentally just kinetic energy on a much smaller scale.

Aer: I think Einstein viewed momentum as fundamental because neither velocity nor mass exist independently of each other. At least not in classical mechanics. Note that both Special and General Relativity are extensions of classical physics, unlike Quantum Theory.

I am not sure what is fundamental at the quantum level, but I would guess that Albert had the right idea and go with momentum as being more fundamental than mass..

Einstein also seemed to view space-time as real, with time and space each being as abstraction used by our mind to understand the more fundamental concept of space-time. He once said something like the following.Thinking about space without time is geometry. Thinking of time without space is philosophy. Physics deals with space-time.That is why he used the mathematics developed by (I think) Minkowski and the concept of an event occurring at (x, y, z, t) as being a fundamental concept.

I think Einstein viewed momentum as fundamental because neither velocity nor mass exist independently of each other. By definition of momentum, velocity and mass do not exist independently, not by any empirical evidence of which I am aware.

At least not in classical mechanics. Ahh yes, by definition in Relativity :)

Note that both Special and General Relativity are extensions of classical physics, unlike Quantum Theory. You mean Special Relativity collapses into the classical Newton equations when c approaches infinity. General Relativity deals with spacetime distortion in gravitational fields - that is the curvature of spacetime. This is fundamentally different from classical gravity.

I am not sure what is fundamental at the quantum level, but I would guess that Albert had the right idea and go with momentum as being more fundamental than mass.. A guess on your part as it was a guess on Einstein's part. My guess is that Relativity as is will never be compatible with quantum physics. That is my guess of course. Maybe Einstein saw this because of the momentum/mass issue we are discussing here and is the reason he dismissed quantum physics without consideration.

Einstein also seemed to view space-time as real, with time and space each being as abstraction used by our mind to understand the more fundamental concept of space-time. Yes, most people here think of spacetime as real because of the evidence for time dilation. However, we have no direct evidence for length contraction or the relativity of simultaneity which are also results of spacetime. Time dilation can be explained within the "local ether" theory proposed by others. I'm not claiming to know either one is more right than the other - I have no evidence for either claim.

He once said something like the following.Thinking about space without time is geometry. Thinking of time without space is philosophy. Physics deals with space-time.That is why he used the mathematics developed by (I think) Minkowski and the concept of an event occurring at (x, y, z, t) as being a fundamental concept. Doesn't seem like a very good reason to me - I think he initially had a much better reason than that and that is just something he babbled later :)

Aer: Both SR & GR are classical-like theories. Both deal with continuous variables and deterministic laws. Classical physics provides excellent approximations to both SR & GR for most every day conditions. Quantum Theory is really fundamentally different with probabilistic laws, an apparent breakdown of causality, and discrete variables.

The claim that GR will never explain quantum phenomena is a tautology. It is similar to claiming that the laws of mechanics will never explain electromagnetic phenomena. I wonder if quantum theory will ever explain gravitation. The real question is whether there will ever be a single theory which encompasses both GR and quantum phenomena. It might not be doable, just as classical physics never encompassed mechanics and electromagnetics in a single theory. .

Einstein did not dismiss quantum theory. In spite of the general belief in Planck as the originator of quantum theory, it was Einstein who first recognized the significance of Planck’s paper on black body radiation, while Planck did not understand the implications of his own work. They called Einstein a nut when he claimed that energy was quantized. Einstein argued against later conclusions of quantum theory, mainly that probabilistic laws were applicable. He expected deterministic laws to be discovered. It is my belief that he would not have objected if the time and effort expended on GR was spent working in the further development of Quantum Theory. When physicists accepted his views on quantized energy and his interpretation of black body radiation, he did not pay much attention to quantum theory. His famous arguments with Bohr occurred in the 1920's, after most of GR had been developed and more than 15 years after his paper on the photoelectric effect and his other work on quantum phenomena.

Many of his remarks which seemed whimsical were more profound that they seemed at first glance. His remarks about space & geometry, time and philosophy, spacetime & physics were intended to be taken seriously. Another of his whimsical remarks to a committee responsible for granting research funds.If I knew the outcome, I would be writing a paper instead of calling it research and applying for a grant.

Both SR & GR are classical-like theories. Both deal with continuous variables and deterministic laws. Classical physics provides excellent approximations to both SR & GR for most every day conditions. This is where the problem lies - classical physics is perfect for everyday use. SR & GR try to predict things that are not everyday. GR is by no means perfect as any true physicist must admit, particularly the theory breaks down near black holes. SR is just GR in flat spacetime so any modification to GR will possibly modify SR.

Quantum Theory is really fundamentally different with probabilistic laws, an apparent breakdown of causality, and discrete variables. No one claims quantum theory is completely accurate. But the principle is to analyze the universe at such a level to explain everything as a whole. This is very hard to do as we don't have the technology to observe things at such a level and may never be able to "observe" things as we classically think of observing.

The claim that GR will never explain quantum phenomena is a tautology. I never said GR would explain quantum phenomena. I said that my guess is GR as is will not be compatible with any quantum theory now or in the future - but like I said, that is my opinion at the present. And we cannot have two incompatible but completely accurate theories. That is pure logic.

The real question is whether there will ever be a single theory which encompasses both GR and quantum phenomena. Now see, you are assuming GR and quantum phenomena are compatible - I guessed that they won't be. Of course my guess could be wrong - which is why it is a guess.


It might not be doable, just as classical physics never encompassed mechanics and electromagnetics in a single theory. . I don't think the comparison here is fair. Classical physics doesn't even explain our macroscopic universe completely accurately, how could even come close to doing so for the microscopic universe?

Einstein did not dismiss quantum theory. In spite of the general belief in Planck as the originator of quantum theory, it was Einstein who first recognized the significance of Planck’s paper on black body radiation, while Planck did not understand the implications of his own work. They called Einstein a nut when he claimed that energy was quantized. Einstein argued against later conclusions of quantum theory, mainly that probabilistic laws were applicable. He expected deterministic laws to be discovered. It is my belief that he would not have objected if the time and effort expended on GR was spent working in the further development of Quantum Theory. When physicists accepted his views on quantized energy and his interpretation of black body radiation, he did not pay much attention to quantum theory. His famous arguments with Bohr occurred in the 1920's, after most of GR had been developed and more than 15 years after his paper on the photoelectric effect and his other work on quantum phenomena. Perhaps, but he did spend much of his later life trying to merge theories into one single theory without much attention to quantum physics.

Is mass a form of energy, distinct from other forms of energy or is mass a measure of an objects total energy?

It depends how you define mass.

If you define "mass" as "rest mass", then it is a property inherent in an object. However, it will necessarily include contributions from certain types of energy (such as binding energy between and within atoms). The rest mass has the advantage of being invariant when we change reference frames, though, which is why it is popular in relativity. It always satisfies E=mc^2 in the rest frame.

If you want a wider definition of mass, you might try something like "mass is a measure of the resistance of a body to acceleration", which is the spirit of Newton's definition in the equation F=ma. In the relativistic context, this equation remains true, but only if m is taken to be the rest mass, and F and a are taken to be the 4-force and 4-acceleration. Taking the spatial components only of the 4-vector equation, we get an equation in three dimensions which does not look like Newton's F=ma.

Some people define mass as relativistic mass (equal to the Lorentz factor times the rest mass). However, this turns out not to be very useful. For a start, it still doesn't make the 3-dimensional version of F=ma look any more like Newton's 2nd law. And the other major problem is that things like kinetic energy become a part of the mass, which is not in accord with traditional definitions.

I never said GR would explain quantum phenomena. I said that my guess is GR as is will not be compatible with any quantum theory now or in the future - but like I said, that is my opinion at the present.

As far as I know, quantum field theory is relativistic but without gravity.

So you're saying that you believe string- (and M-) theory to be a lost cause? Quantum Loop Gravity, too? In fact, that there's no way to describe gravity quantum mechanically at all?

It depends how you define mass.

If you define "mass" as "rest mass", then it is a property inherent in an object. However, it will necessarily include contributions from certain types of energy (such as binding energy between and within atoms). The rest mass has the advantage of being invariant when we change reference frames, though, which is why it is popular in relativity. It always satisfies E=mc^2 in the rest frame. Does rest mass increase with thermal energy? I am not considering energy on the quantum level here - that energy is very well understood to be apart of the "rest mass". Thermal energy is not a quantum level energy, but nevertheless would exist as part of an objects "rest energy".


If you want a wider definition of mass, you might try something like "mass is a measure of the resistance of a body to acceleration" What if we try "mass is a measure of the gravitational field a body creates".

As far as I know, quantum field theory is relativistic but without gravity.

So you're saying that you believe string- (and M-) theory to be a lost cause? Quantum Loop Gravity, too? In fact, that there's no way to describe gravity quantum mechanically at all?
No no no... First of all, I cannot possibly know how GR will merge with quantum physics as nobody does at this point. I am just saying that GR might have to be altered slightly to be compatible with any quantum theory of gravity.

Edited nonsense wording :D

James R, I was hoping for your input on this:

Does rest mass increase with thermal energy? I am not considering energy on the quantum level here - that energy is very well understood to be apart of the "rest mass". Thermal energy is not a quantum level energy, but nevertheless would exist as part of an objects "rest energy".


What if we try "mass is a measure of the gravitational field a body creates".

first of all, Hi everyone, im new here so I hope its ok to butt in... Its such an interesting topic...

First of all my position with regards to GR / SR ... They are good solid theories, they have stood the test of time as far as describing the nature of matter above a quantum level. If there is anything the theories have missed, I am sure someone will experiment find evidence and propose an extension to them...

What dragged me into this topic is mass in relation to temperature... As far as I can tell temperature is energy, an object at a higher temperature has more energy - but it still contains the same amount of matter (if its not combusting or whatever), so I can't clearly see how temperature would affect mass...

Have there been experiments where a cup of water has been put on a scale and then frozen, or something, to determine if there is a change?

Also I can't see how thermal energy doesn't count at the quantum level - aren't atoms etc made up entirely of quantum "particles"... so wouldn't anything you do to an atom directly affect the quantum particles from which its made?

Have there been experiments where a cup of water has been put on a scale and then frozen, or something, to determine if there is a change?

The short answer: no. The long answer: The change in mass would be too small to be able to measure any difference in mass, it is not until we heat superluminal up to 10,000 F that we might be able to notice a difference.

Also I can't see how thermal energy doesn't count at the quantum level Thermal energy is a measure of the kinetic energy of atoms. It has nothing to do with quantum physics.

aren't atoms etc made up entirely of quantum "particles" Nope. No such thing as particles on the quantum level, quoted or unquoted.

so wouldn't anything you do to an atom directly affect the quantum particles from which its made? No quantum particles... An electron is more correctly visualized as a cloud of energy than a spherical particle. I imagine the same applies to protons, etc.

Ok definition aside, say we're talking waveforms, rather than particles... When you increase the kinetic energy of an atom, what is the energy actually doing? If the atom itself is just a collection of energy / waveforms / fields, then heating an atom involves putting more energy into the collective of waveforms... doesn't it? I wish I had my trusty particle collider here so I could get some idea of what in fact is happening at that scale - but I uh... left it at home.

Ok definition aside, say we're talking waveforms, rather than particles... When you increase the kinetic energy of an atom, what is the energy actually doing? If the atom itself is just a collection of energy / waveforms / fields, then heating an atom involves putting more energy into the collective of waveforms... doesn't it? I wish I had my trusty particle collider here so I could get some idea of what in fact is happening at that scale - but I uh... left it at home.
I don't believe you can mix quantum level energies and macro-scale energies in that way. Kinetic energy and Thermal energy are both macro-scale energies so to speak.

Ok... so the question of thermal energy relating to mass is kinda still out there at the moment.

Is it possible quantum level energies and macro scale energies are related at all - isn't the macro universe essentially made up of quantum energies??? Quantum physics is not my field however so if theres some good site that acts as a reference for the topic it might be easier to direct me there.

I've already had people definately say that thermal energy contributes to an objects rest mass. But they proved themselves to be idiots so I cannot trust the account they gave me. I was seeking input from the knowledgable James R :eek: :bugeye: ;)

I've already had people definately say that thermal energy contributes to an objects rest mass. But they proved themselves to be idiots so I cannot trust the account they gave me. I was seeking input from the knowledgable James R :eek: :bugeye: ;)About a page back, I tried to explain that: Yes, thermal energy does increase the mass, so I presume I am in the group you think are "idiots." Let me try again, this time not worring about what is mass or giving cycolotron information/ example to discuss "what is mass."

Even though the velocities associated with "thermal energy" are typically so much lower than the speed of light, there is a small increase in the mass as a particle speeds up.

Temperature is directly proportional to the square of the particle speed in this normal thermal range. Thus, the mass of a hot collection of n particles is slightly greater than the mass of those same n particles when they have cooled down a little.

About a page back, I tried to explain that: Yes, thermal energy does increase the mass, so I presume I am in the group you think are "idiots."

No. I do not think anyone is an idiot for thinking a certain way. I only said they are idiots because when they tried to back it up they couldn't even differentiate between the "equivalence principle" and "weak equivalence principle" even after I explained the difference, nor could they correctly give an account of General Relativity - even after I explained it in detail. Furthermore they tried to tell me that things on the quantum level could be analyzed as if they were on the macro-level. Where they got this from - I don't know, because all the evidence I've seen points to the contrary. Thus, I was left with no choice but to question their intellect.


Let me try again, this time not worring about what is mass or giving cycolotron information/ example to discuss "what is mass."

"What is mass" is very important! The arbitrary nature in which mass has been treated is the root of the problem here.


Even though the velocities associated with "thermal energy" are typically so much lower than the speed of light, there is a small increase in the mass as a particle speeds up.

Yep, this is well established. That is why it takes a lot (way more than you think is a lot) of thermal energy to notice any difference.


Temperature is directly proportional to the square of the particle speed in this normal thermal range. Thus, the mass of a hot collection of n particles is slightly greater than the mass of those same n particles when they have cooled down a little.

You seem to be attributing some significance to "relativistic mass", am I correct? Again, this goes back to "what mass is". Normally, we think of gravitational potentials around massive bodies, correct? Then as a body speeds up relative to a certain reference frame, it's mass increases (relativistic mass). So, should the gravitational potential also increase? It must if you want to attribute relativistic mass to the same level as rest mass. However, that makes no sense if you spend a little time thinking about it.

...Yep, this is well established. That is why it takes a lot (way more than you think is a lot) of thermal energy to notice any difference.Your "yep..." is agreeing with my statement that mass does increase with the increase in speed that is associated with temperature (and that was the original concern/ question). This is true for any reasonable definition of mass, so I don't see your concern about which mass definition is selected to answer the question: Does mass increase with temperature? I think we agree it does.

I note you have no way to know what I think is "a lot" and I never said the mass increase was "a lot", so your second sentence contains an unwarrented assumption, (and a false one I might add). I have not done any calculation, but bet the increase in mass of even the highest melting point solid is so small that there does not exist any measurement technology that could even detect the change, much less measure it. - That is why I said your unfounded assumption about what I think is false. Please don't correct thoughts you only assume for me.


You seem to be attributing some significance to "relativistic mass", am I correct? Again, this goes back to "what mass is". Normally, we think of gravitational potentials around massive bodies, correct? Then as a body speeds up relative to a certain reference frame, it's mass increases (relativistic mass). So, should the gravitational potential also increase? It must if you want to attribute relativistic mass to the same level as rest mass. However, that makes no sense if you spend a little time thinking about it.
In my view mass is mass and all mass has/ produces a gravity field or distortion of space time if you want to take a GR point of view. I really don't care about, or undestand, your first question. "relativistic mass" is just a common way to refer to the mass excess of a moving particle over its "rest mass" and does not signify the existence of two different types of mass, one with gravity and one with out as your last sentence implies you think. Neither does mass divide into different "levels." I suggest you need to follow your own final recomendation. Mass is mass, period.

I don't know how to please you. In my first post, I used a cyclotron to help you understand what is mass. I the recent post, I avoided this as I understood you did not want to discuse what is mass but the original question about the effect of increasing temperature on mass.

Briefly again: A very relativistic particle traveling around a constant radius circle in a cyclotron gains a little mass (and energy) each time it crosses he "D" electrodes gap. The magnetic field,B, and magnetic force, F = VBE (velocity times B field times charge) must increase a little with each gap crossing to keep the circle radius constant. That is, more centripidal force is required to keep the circle radius constant for a particle with V essentially equal to c, the constant speed of light, and constant charge E. the reason for this required increase in B (and F) is the fact that the mass of the particle is increasing. It is much like swinging a bucket around your head at constant RPM. The more water in the bucket, the more force required in the rope. In both cases, it is the force required is proportional to what we call "mass" and you cna take this as both a definitionand explanation of what mass is. For more details read my first post.

Your "yep..." is agreeing with my statement that mass does increase with the increase in speed that is associated with temperature NO! My "yep" was agreeing that thermal energy is just a form of kinetic energy! I know, because I was the one who said it!

I claim relative velocity does not add to an objects mass. Relatavistic mass is a misnomer and has no fundamental application. Take F=ma for example. For this equation to hold true from a relative frame, the relativistic mass must be γ³m. And then you must get into the concept of directional mass because it changes depending on what direction you apply the force! People claim photons have "relativistic mass" which is why they are effected by gravity. This wrong, photons just follow the same curvature of spacetime as every other object. Note that gravity makes all objects regardless of mass follow the same path.





(and that was the original concern/ question). This is true for any reasonable definition of mass, so I don't see your concern about which mass definition is selected to answer the question: Does mass increase with temperature? I think we agree it does. Who is we? I don't agree! What is a reasonable definition of mass? I've never seen anyone give a reasonable and unambiguous definition.



I note you have no way to know what I think is "a lot" and I never said the mass increase was "a lot", so your second sentence contains an unwarrented assumption, (and a false one I might add). I have not done any calculation, but bet the increase in mass of even the highest melting point solid is so small that there does not exist any measurement technology that could even detect the change, much less measure it. Very good observation!


- That is why I said your unfounded assumption about what I think is false. Please don't correct thoughts you only assume for me. Oh please, I was just expressing that temperature increase would have to be very significant for any significant increase in energy over the rest energy at room temperature.



In my view mass is mass and all mass has/ produces a gravity field or distortion of space time if you want to take a GR point of view. Mass is mass - thanks for your insight. Let's take a hydrogen atom moving at .99(repeat 9 100 times)c in the Earth's atmosphere. What is the mass of the hydrogen atom from the Earth's frame? What gravitational field does the hydrogen atom create?


I really don't care about, or undestand, your first question. Then why are you responding to my post? I've heard your point of view before - it doesn't hold water. Did you even think it through?


"relativistic mass" is just a common way to refer to the mass excess of a moving particle over its "rest mass" and does not signify the existence of two different types of mass, one with gravity and one with out as your last sentence implies you think. I'm telling you flat out that I do not think "relativistic mass" has anything to do with mass. PERIOD. It is a flawed concept and a lot of physicists don't even bother with the concept of "relativistic mass". My physics professor certainly never used the term or idea of "relativistic mass". It is also not in any of my physics textbooks. However, it is abundant on the internet and in most every instance, misused.


Neither does mass divide into different "levels." I suggest you need to follow your own final recomendation. Mass is mass, period.[/QUOTE[ That is the worst definition I've ever seen.

[QUOTE=Billy T]
I don't know how to please you. In my first post, I used a cyclotron to help you understand what is mass. I don't believe you understand what is mass. At the very least, we have a different opinion of what is mass. Most of my knowledge on this subject comes from college level physics and almost none from the internet. Where does you knowledge come from on this subject?



I the recent post, I avoided this as I understood you did not want to discuse what is mass but the original question about the effect of increasing temperature on mass. Actually, I was only asking James R. I pretty much know what answer to expect from everyone else.

To Aer: I am not really responding to you, but there are several errors in your post that should be corrected for others. (I understand you want James to respond, but I am begining to understand why he has not.) :) ....I claim relative velocity does not add to an objects mass.Your claim is wrong. Your are disputing Special Relativity, which is widely accepted (at least 99% of all physics Ph.D.s.) To answer one of your later questions: very little of my knowledge of physics comes from the net. I earned my Physics Ph.D. at Johns Hopkins after graduating from Cornell in an experimental 5 year program (called Enginering Physics) which satisified all the requirements of both the art school's physics major and the Engineering college. (It was discontinued as too demanding after about a 10 year test.) I continued to learn while serving as a university professor. I have been student and teacher of physics for almost 50 years now - my only profesional activity. I am now retired. I hesitated to tell this as I place little faith in "appeal to authority" defenses of ideas, but you did ask.
...Relatavistic mass is a misnomer and has no fundamental application. Take F=ma for example. ....And then you must get into the concept of directional mass because it changes depending on what direction you apply the force!
"no fundamental application" indeed! - Tell that to anyone who works with or designs particle accelerators.
"Relatavistic mass" seems like a good name to me as it refers to the mass increase predicted by Relativity theory and observed in every particle accelerator. How do you think these particles continue to gain energy (perhaps gaining many times their rest mass energy) after they can no longer gain even 1% more in speed because of the speed of light limit?

Your comments about "directional mass" are nonsense. True F =ma is a vector equation, (F & a being the vectors) , but mass is a scalar, no more a vector that the number 5 is. In view of your obvious ignorance about this, people would be well advised to pay little attention to your claims.

People claim photons have "relativistic mass" which is why they are effected by gravity. This wrong, photons just follow the same curvature of spacetime as every other object. Note that gravity makes all objects regardless of mass follow the same path. They are not wrong, only expressing a truth that can also be descrided as you do in terms of the curvature of space time. Your last sentence is too general. "all objects" indeed! - Cows are subject to gravity yet they walk different paths. What I think you are trying to say is that inertial mass appears to be identical to gravitational mass (and I believe it is, but have no idea as to why it is). They are now known to be the same to very high precision by experiments, but need not be the same by theory.

...What is a reasonable definition of mass? I've never seen anyone give a reasonable and unambiguous definition.
Newton gave one of the first in terms of modern views, but before recorded history, mass was defined in many cultures by various standard objects, including even a set number of grain seeds. For years, more recently, it was legally defined by a piece of metal sitting in Paris. etc. You just are ill informed. If there is any problem, it is that too many definitions exist.

Even today, some people describe the quanity of gold as so many "grains." I am so old that I still call what most people call a refrigerator an "icebox". Language is very conservative (slow to change).

... I'm telling you flat out that I do not think "relativistic mass" has anything to do with mass. PERIOD. It is a flawed concept and a lot of physicists don't even bother with the concept of "relativistic mass". My physics professor certainly never used the term or idea of "relativistic mass". It is also not in any of my physics textbooks. Get a new professor (and some more advanced books).
I take your "flat out" claim as equally well suported by the facts as your claim that mass is a vector ("directional" as you put it.)


... Mass is mass, period.
That is the worst definition I've ever seen.
That was not a definition, but a statement that tried to express the idea that all parts of the total mass of a particle are mass with exactly the same properties. You wrongly believe that the fractional increase in particle mass produced in an accelerator is a different type of mass, with no gravity etc. (I am giving you credit here for not being in the position of denying that accelerators do increase particle mass, but perhaps I am being overly generous as at times you seem to be denying the experimental facts.- Recall my cyclotron example: greater force required to keep a particle in constant radius circle as it gains energy. This is due to the increase in mass because that force is F = VBE = ma and E is strictly constant, V is not able to increase even 1% with c as upper limit, which also means that the RPM around the circle is essentially constant. A constant RPM and constant radius makes acceleration "a" constant, so only mass "m" is left to account for the great increase in B {or F} required to bend/ confine the ever more massive particle in the same circle.)

I might note in passing that mass can produce energy (sun as example) and energy can produce mass (accelerator as example).

Perhaps if I give a name to the top third of a cake (I'll call it "top cake") you will also believe that the top cake now has different properties from "cake." "Relativistic mass" is only a name given to that fraction of the total mass (part more than the rest mass) which was, for example, produced by a particle accelerator. Relativistic mass, being only a name for part of the total mass, does not get any different properties from "mass" or "rest mass" by having been given a name. Neither does "top cake" get any new properties different from "cake" by virture of having being given a name.

In rereading the various posts to this thread, I noticed the following.It can be said then: if a body absorbs the energy E, its inertial mass augments in E/c2; the inertial mass of a body is not a constant but variable with the variation of the energy.The above is alleged to be from a text on Relativity. Since it refers to inertial mass, there is an implication that it does not apply to gravitational mass, but perhaps it was from a text on SR which does not address gravitational mass.

I remember all sorts of articles and course content relating to the increase in inertial mass due to increased velocity, but do not remember any reference to a corresponding change in relativistic mass. I do not think the articles and course content specifically referred to inertial mass, but inertial mass would be implied by the context.

Does gravitational mass as well as inertial mass increase with velocity? Are there conditions requiring gravitational computations to make relativistic adjustments to the mass of the various objects interacting with each other?

A distant observer moving at relativistic speed with respect to our solar system would view the sun and planets as being more massive. Would he see motions as distorted from our point of view? I am guessing that either gravitational mass is not effected by relativistic motion or that applying Lorentz transformations to time and distance along with the mass transformations would make it all come out looking the same to both observers. My guess is merely a WAG, not even a SWAG, so maybe the distant observer would see crazy motions (from our point of view) of the planets and satellites in our solar system.

I hope the above does not provide ammunition for the relativity bashers who post at this forum. Perhaps I should hope it does provide ammunition. Their attempts to knock Albert and his theories are often amusing rather than annoying.

Some off the topic remarks follow.

Relativity uses the mathematics of differential geometry to model the laws of physics. The model is very convenient and provides an excellent description of gravitation. It should be remembered that it is a model, not a reality. Statements like the following are not really valid.In General Relativity, what we know as gravity is caused by the curvature of spacetime. It is not a force . . .When dealing with forces causing an object to deviate from its geodesic path in a gravitational field, it is more convenient to use a model employing force rather than the geometric model. A force/field model of gravity could be used for GR, and the geometric model can be translated to a force/field model. The geometric model is merely more convenient for many purposes.

A trivial issue which has arisen in this and many other threads. Posters mention opinions expressed by physics professors and/or physics text books. It is my guess that at least 90% of physics courses deal with classical physics (probably 100% of high school courses). Even a professor familiar with SR, GR, & QT might never mention them to students in a course relating to classical physics, and the text books for such courses never (at least hardly ever) mention the concepts of modern physics.

Statements like the following are not really valid.In General Relativity, what we know as gravity is caused by the curvature of spacetime. It is not a force . . .When dealing with forces causing an object to deviate from its geodesic path in a gravitational field, it is more convenient to use a model employing force rather than the geometric model. A force/field model of gravity could be used for GR, and the geometric model can be translated to a force/field model. The geometric model is merely more convenient for many purposes.

Actually the Newtonian force/filed model could not explain 43 arc seconds out of total 2 degrees advance of Mercury's perihelion every century. GR could explain this with great precision with its treatment of gravity as curvature of space-time caused by mass rather than a force.

Everneo: You are correct: The Newtonian or classical force/field description of gravity could not explain the advance of mercury's perihelion nor could it explain many other phenomena described by General relativity.

However, there is no reason why a modernized force/field description could not be devised to explain such phenomena. I repeat: curved space time is a mathematical model, not a reality.

Neither could it (a force/field model) explain instantaneous action at a distance, only curvature can.
To insist that physical laws are a model of reality is kinda splitting hairs, like saying language is a model of reality. It is, but it's all we have to describe it.

To Aer: I am not really responding to you, but there are several errors in your post that should be corrected for others. (I understand you want James to respond, but I am begining to understand why he has not.) :) Your claim is wrong. You are claiming relativistic mass then which as I understand, was a concept from a long time ago that modern physicists have abandoned (At least the physicists at the University I graduated from have abandoned the concept). So your claim that I am wrong is unwarranted.


To answer one of your later questions: very little of my knowledge of physics comes from the net. I earned my Physics Ph.D. at Johns Hopkins after graduating from Cornell in an experimental 5 year program (called Enginering Physics) which satisified all the requirements of both the art school's physics major and the Engineering college. (It was discontinued as too demanding after about a 10 year test.) I continued to learn while serving as a university professor. I have been student and teacher of physics for almost 50 years now - my only profesional activity. I am now retired. I hesitated to tell this as I place little faith in "appeal to authority" defenses of ideas, but you did ask.

As I said above, many modern physicists have abandoned "relativistic mass". You appear to not be a modern physicists as you are retired. My claim still stands because it is essentially not mine, but that of my physics professors.


"no fundamental application" indeed! - Tell that to anyone who works with or designs particle accelerators.
"Relatavistic mass" seems like a good name to me as it refers to the mass increase predicted by Relativity theory and observed in every particle accelerator. How do you think these particles continue to gain energy (perhaps gaining many times their rest mass energy) after they can no longer gain even 1% more in speed because of the speed of light limit?
You are refering to the kinetic energy they gain. The total energy is given by:

E=γmc²

where mc² is the rest energy and ( 1-γ )mc² is the kinetic energy. No matter how much energy you've expended to accelerate the particles, in the particles own rest frame, the velocity of light is c so it would still take an infinite amount of energy to reach c.


Your comments about "directional mass" are nonsense.
Of course it is nonsense, but that is where relativistic mass takes you. If you apply a force to an object perpendicular to the motion of travel the object, then you cannot use the same "relativistic mass" for the calculation.


True F =ma is a vector equation, (F & a being the vectors) , but mass is a scalar, no more a vector that the number 5 is. In view of your obvious ignorance about this, people would be well advised to pay little attention to your claims. These are not my claims, the claim of "directional mass" is that of those on physicsforums! Remember, I call them idiots, apparently you agree?


They are not wrong, only expressing a truth that can also be descrided as you do in terms of the curvature of space time. I asked James R about this before, he agrees with me and not you.



They claim a photon has relativistic mass which causes it to be effected by the gravitational field... I suppose that is one way to look at it - although, I am not sure it is fundamentally correct. James R, thoughts?

It's better to look at photons as following geodesics in curved spacetime, rather than as having some kind of mass.



Your last sentence is too general. "all objects" indeed! - Cows are subject to gravity yet they walk different paths. What are you talking about? I am talking about objects following the same path due to gravity and no other effect. This does not include the surface of the Earth which would be a resistance.


What I think you are trying to say is that inertial mass appears to be identical to gravitational mass

NO! - that is the "weak equivalence principle" and has nothing to do with General Relativity and curved spacetime and has everything to do with Newton's concept of gravity as a force.



Get a new professor (and some more advanced books).
I take your "flat out" claim as equally well suported by the facts as your claim that mass is a vector ("directional" as you put it.)
Actually, I think my professors did quite a good job and were very knowledgable. Just to make sure that my University wasn't on the fringe edge of science, I did a quick check at wikipedia to see what they had to say about relativiistic mass:
In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity.

Precisely as I have stated.

The part in red has to make you smile, especially when you told me to get more advanced books!


I'll assume the rest of your post is much of the same uninformed blather.

It is my guess that at least 90% of physics courses deal with classical physics (probably 100% of high school courses). Even a professor familiar with SR, GR, & QT might never mention them to students in a course relating to classical physics, When referring to professors, I am talking about those professors that taught courses directly related to relativity, not classical physics. Now come on... you surely didn't think that I figured "relativistic mass" had no relevance because it wasn't mentioned in my introductory physics course dealing with Newtonian mechanics, DO YOU? :looks at world in disgust:

...Does gravitational mass as well as inertial mass increase with velocity? Are there conditions requiring gravitational computations to make relativistic adjustments to the mass of the various objects interacting with each other?..on your first question:
I believe that gravitational mass and inertial mass are the the same, so I would answer "Yes". The primary reason for believing that the "m" in F=ma is the same as the "m" in F = GMm/(r^2) is the high precision of the experiments which have not been able to discover any difference. I don't think anyone can show by logical argument that they must be the same.

For practical purposes one can assume they are the same. I also note that even if a particle in an accelerator has mass several times greater than its rest mass, the mass that is observalble is the inertial, not the gravitational, mass. I.e. as stated in my prior posts discussing the cyclotron, the increasing force required to keep a very relativistic particle in a constant radius circle in a cylotron as it gains energy (and mass) is the mass in equation F= ma. Recall that the particle velocity is essentially c and thus with constnant radius circle the RPMs of the particle are essentially constant, which implies that acceleration "a" is essentially constant. Because "a" is essentiallyconstant in this case, only the "m" in F=ma is growing significantly as the energy (and total mass) increases in the very relativistic region.

on your second question:

Yes - When a distant star's photon passes near a massive object (such as the sun) it appears to have originated from a different point in the sky. (This assumes that you want to talk about mass and gravity as a force, instead of use the GR view of "warped space/time.)

Yes, again - When a photon "climbs" out of a "gravity well" which is deeper than the one our sun creates, it is red shifted for us on Earth. This is most easily seen if it comes from a near by massive star (Less of the observed red shift is due to the expansion of the universe.) and is creadted by an atomic transition between two well known energy levels. (For this photon's initial frequence to be well known, it should come from colder, low density gas near the star rather than the star itself. Obviously if the gas is too distant from the star, the star would need to be very massive (or near a black hole, or part of a compact star cluster) to have the emitting atom in a strong gravity field. Thus, in pratice, this gravitational red shift is best observed in the radiation of gas approaching a black hole, but before it is heated too much and thus Doppler broadened to extent it is hard to be sure of the initial frequency)

I believe that gravitational mass and inertial mass are the the same, so I would answer "Yes". The primary reason for believing that the "m" in F=ma is the same as the "m" in F = GMm/(r^2) is the high precision of the experiments which have not been able to discover any difference. I don't think anyone can show by logical argument that they must be the same.

OK - let's talk about these experiments that measure "m". Any discussion on this matter should have an a prior list of experiments to discuss. So can you provide links to the menitoned experiments above?

....If you apply a force to an object perpendicular to the motion of travel the object, then you cannot use the same "relativistic mass" for the calculation..... I asked James R about this before, he agrees with me and not you. .... The force applied magnetically to a charge particle in a constant radius orbit in a cylotron is precisely perpendicular to the particle's velocity and the relativistic mass increase is what is used to calculate how the B field must be increased to keep the radius constant. Your statement is contray to facts and common pratice in cylotron accelerators. Relativistic mass is also what larger accelerators use in their calculations, but "strong static magnetic focusing" is also used to keep them in their constant radius circle, so things are more complex than in my cylotron example.

On your comments about James R's views/opinions, I think you are also wrong. Lets wait for a direct comment from James.

Your assert, without any proof or logical argument, that the mass added to a partricle by an acclerator has no gravity (causes no increase in the particle's gravity field). I assert the contray, based on experimental fact that inertial mass is not experimentally different (to high precision) from gravitational mass. I.e. that there is only one form of mass, not two different forms, one with gravity and one without as you assert.

What do you say James if you are reading? Does all mass, reguardless of its nature (rest or relativistic) produce gravity (my view) or only rest mass produces gravity (Aer's view)?

I do not currently know Aer's view, but if he is consistent, I think he must also thinks that there is no gravity field produced by photons as none of their mass is rest mass. All of their mass is due to their energy and given by m = E/ (c^2). Since photons have none of the type of mass Aer thinks produces gravity (rest mass), I assume Aer thinks photons produce zero gravity field.

Aer: please comment - Do you think photons (and other energetic, but zero rest mass objects) produce gravity field or not?

Again, it is not MY CLAIM that you have to use directional mass. That is what the idiots at physicsforums said. I took their word for it since they seem to use relativistic mass a lot and probably used this so called "directional mass" in a thought experiment of their own.

And what you are refering to is the centripital force in your example above. Centripital force is given by:

F = m v²/r.

Are you sure relativistic mass is used? because if you want to increase the speed and keep the radius the same, then the force must be increased with the square of the velocity increase.

On your comments about James R's views/opinions, I think you are also wrong. Lets wait for a direct comment from James. I did not skew James R's words in anyway, I only provided a direct quote.

Your assert, without any proof or logical argument, that the mass added to a partricle by an acclerator has no gravity (causes no increase in the particle's gravity field). I assert the contray, based on experimental fact that inertial mass is not experimentally different (to high precision) from gravitational mass. I.e. that there is only one form of mass, not two different forms, one with gravity and one without as you assert. Very well - we'll both choose to assert. Your assertion is based on the misconception that gravity is a force as described by Newton. My assertion is based on General Relativity's version of curved spacetime to describe gravity.


I do not currently know Aer's view, but if he is consistent, I think he must also thinks that there is no gravity field produced by photons as none of their mass is rest mass. All of their mass is due to their energy and given by m = E/ (c^2). Since photons have none of the type of mass Aer thinks produces gravity (rest mass), I assume Aer thinks photons produce zero gravity field.
Yes, it would stand to reason that a photon does not create curvature in spacetime (i.e. a gravitational field).

Aer: please comment - Do you think photons (and other energetic, but zero rest mass objects) produce gravity field or not? I already did.

Now it is your turn, please comment on this view by the collective knowledge of contributors to wikipedia:


In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity.

OK - let's talk about these experiments that measure "m". Any discussion on this matter should have an a prior list of experiments to discuss. So can you provide links to the menitoned experiments above?I don't plan to spend time in discussion of these experiments and rarely use the internet for physics information, but since you asked for a list of experiments I found in Wikipedia under "weak equivalence priniciple":

Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. These experiments demonstrate that all objects fall at the same rate when the effect of air resistance is either eliminated or negligible. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum, and see if they hit the ground at the same time. More sophisticated tests use a torsion balance of a type invented by Roland Eötvös.
Researcher Year Method Result
Galileo Galilei ~1610 Dropping metal balls of different mass from the Tower of Pisa no detectable difference
Isaac Newton ~1680 measure the period of pendulums of different mass but identical length no measurable difference
Friedrich Wilhelm Bessel 1832 measure the period of pendulums of different mass but identical length no measurable difference
Roland Eötvös 1908 measure the torsion on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotation of the Earth difference is less than 1 part in a billion
Roll, Krotkov and Dicke 1964 Torsion balance experiment, dropping aluminum and gold test masses difference is less than one part in one hundred billion
David Scott 1971 Dropped an eagle feather and a hammer at the same time on the Moon no detectable difference (Not a very good experiment, but it was the first lunar one.)
Branginsky and Panov 1971 Torsion balance, aluminum and platinum test masses, measuring acceleration towards the sun difference is less than 1 part in a trillion (most accurate to date)
Eöt-Wash 1987– Torsion balance, measuring acceleration of different masses towards the earth, sun and galactic center, using several different kinds of masses difference is less than a few parts in a trillion

END of LIST
At the originaly wikipedia site you can click to learn more. It certainly justifies my statement that the two types of mass are equal to "high percision" To be honest, I did not think I did not realize it was parts in a trilion, but thought it only parts in a billion.

As I said, this is the "weak equivalence principle" and deals with the Newtonian concept of gravity as a force. You cannot take these same results over to General Relativity in which gravity is not treated as a force. The fact that inertial mass = gravitational mass is not in dispute - only the relevence to relativistic mass is in dispute. The concept of relativistic mass does not exist with Newtonian mechanics. It is only in General Relatvity that you will find relativistic mass.

I already did. Now it is your turn, please comment on this view by the collective knowledge of contributors to wikipedia:

Originally Posted by Wikipedia
"In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity."

I have no reason to doubt your quoted two paragraphs above. I agree with it, but admit to not knowing much about how GR is being used in quantum field theory. At the level of understanding commonly found in this forum and because it is simplier, the use of "relativistic mass" is very appropriate and I will continue to use this term, despite some times meaning only the mass added to the rest mass to make the total mass greater than the rest mass and at other times meaning the total mass, when it is significantly different from the rest mass. I also sometimes use the term "mass/energy" and think it mainly a mater of style, not physics, how one refers to the particle's energy or mass - they are even idential in value in the system of units commonly used by high energy physicists and most theoretical physicists. (In this system the speed of light is 1, so m = E.) I have also noted that the spreading understand (at a very superficial level) of GR is promoting the wider use of "space/time distortion" type concepts instead of "gravity force" concepts, but again it is a question more of style, not physics; however, some observations can only be understood in terms of the GR view, so one can argue that only that view is "correct".

If you have ever tried to read some of the papers in Phys Rev. Section B, you will understand why the "gravity as force" view will be arround for a long time. I certainly do not have the ability to be creative in the GR field and doubt if there are more than several hundred people in the world who do. It has been so long since I worked with these tensor equations that I can barely read them with understanding now. That notation is very compact - for example, it would take at least a long paragraph in English to explain what the repeat of a subscript means.

Changing subject: I am disapointed that you only say "I already have." in responce to my question asking if you believe photons have/cause a gravity field. Why not answer the question with a simple "yes or no" instead of a vague claim that it is answered by you already in some undisclosed post? (If I had read that post I would not need to ask the question.) Are you afraid to give a direct simple answer?

Again I ask: Do you believe photons have/cause a gravity field?

Originally Posted by Wikipedia
"In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity."

I have no reason to doubt your quoted two paragraphs above. I agree with it, How can you agree with it and still use relativistic mass?

it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether


but admit to not knowing much about how GR is being used in quantum field theory. At the level of understanding commonly found in this forum and because it is simplier, the use of "relativistic mass" is very appropriate and I will continue to use this term, despite some times meaning only the mass added to the rest mass to make the total mass greater than the rest mass and at other times meaning the total mass, when it is significantly different from the rest mass. I also sometimes use the term "mass/energy" and think it mainly a mater of style, not physics, how one refers to the particle's energy or mass - they are even idential in value in the system of units commonly used by high energy physicists and most theoretical physicists. (In this system the speed of light is 1, so m = E.) I have also noted that the spreading understand (at a very superficial level) of GR is promoting the wider use of "space/time distortion" type concepts instead of "gravity force" concepts, but again it is a question more of style, not physics; however, some observations can only be understood in terms of the GR view, so one can argue that only that view is "correct".

If you have ever tried to read some of the papers in Phys Rev. Section B, you will understand why the "gravity as force" view will be arround for a long time. I certainly do not have the ability to be creative in the GR field and doubt if there are more than several hundred people in the world who do. It has been so long since I worked with these tensor equations that I can barely read them with understanding now. That notation is very compact - for example, it would take at least a long paragraph in English to explain what the repeat of a subscript means.

Changing subject: I am disapointed that you only say "I already have." in responce to my question asking if you believe photons have/cause a gravity field. Why not answer the question with a simple "yes or no" instead of a vague claim that it is answered by you already in some undisclosed post? (If I had read that post I would not need to ask the question.) Are you afraid to give a direct simple answer?

Again I ask: Do you believe photons have/cause a gravity field?

Apparently you missed where I answered your question:

I do not currently know Aer's view, but if he is consistent, I think he must also thinks that there is no gravity field produced by photons as none of their mass is rest mass. All of their mass is due to their energy and given by m = E/ (c^2). Since photons have none of the type of mass Aer thinks produces gravity (rest mass), I assume Aer thinks photons produce zero gravity field.
Yes, it would stand to reason that a photon does not create curvature in spacetime (i.e. a gravitational field).

What exactly about yes do you not understand as an answer to your yes/no question "do photons produce a zero gravity field"?

How can you agree with it and still use relativistic mass? Now it is my turn to state "I have aready explained" but I will repeat explanation by pasting it in again here:

I said: "At the level of understanding commonly found in this forum and because it is simplier, the use of "relativistic mass" is very appropriate and I will continue to use this term, ... I also sometimes use the term "mass/energy" and think it mainly a mater of style, not physics, how one refers to the particle's energy or mass - they are even idential in value in the system of units commonly used by high energy physicists and most theoretical physicists. (In this system, the speed of light is 1, so m = E.)"

Thank you for clearly confirming my assumption that you believe all zero rest mass particles ("objects" if you prefer to speak of photons etc. as waves) do not produce any gravity field.

Now we can see who is supported by James R on this if he is reading. I ask him same question (Do energetic objects with zero rest mass produce any gravity field?) Aer says "no" and I say "yes," but of course it is small in most cases, but not zero.

("Small" when compared to the gravity field of a particle with rest mass.)

I do, however, note that there is no upper limit on the energy of a gamma ray in theory, so the gravity field of a conceptually possible, very energetic, gamma ray could be as large as that from a resting electron. (This is why I said "in most cases.")

PS by edit: I was too quick to post paragraph immediatley above. - Many gamma rays, if not most, have greater gravity fields than a resting electron. The rest mass of an electron is only 0.511 Mev if memory serves me correctly. A gamma ray with energy of 0.512Mev produces slightly more gravity than the electron at rest. (I forget the minimum energy a photon must have to be considered a "gamma ray" but certaily some that have been observed make 1000 times more gravity than a resting electron.) I also forget the most energetic gamma ray yet observed, perhaps it had more than a 1000 times the gravity field of a proton.

I do not think anyone here has addressed the question I raised in a previous post.Does gravitational mass as well as inertial mass increase with velocity? Are there conditions requiring gravitational computations to make relativistic adjustments to the mass of the various objects interacting with each other?

A distant observer moving at relativistic speed with respect to our solar system would view the sun and planets as being more massive. Would he see orbital motions as distorted from our point of view? I am guessing that either gravitational mass is not effected by relativistic motion or that applying Lorentz transformations to time and distance along with the mass transformations would make it all come out looking the same to both observers. My guess is merely a WAG, not worthy to be called a SWAG, so maybe the distant observer would see crazy motions (from our point of view) of the planets and satellites in our solar system.My formal study of Relativity is so far in the past, that I cannot answer the above question by applying first principles, and I do not remember ever seeing it addressed in any text, class, or article.

All the experiments showing inertial mass and gravitational mass to be equivalent are essentially classical experiments. I have never read about similar experiments involving relativistic velocities.

Aside from experimental evidence, I do not believe there is any logical analysis leading to the conclusion that they are equal. The experimentally determined equivalence was the starting point for Albert’s development of General Relativity, but I do not remember if that theory assumes the equivalence to be valid in situations including relativistic velocities.

At the quantum level and in particle accelerator experiments, gravity is so weak that its effect cannot be measured (at least I do not think it can be measured). Therefore discussion of the effect of velocity on mass/energy in accelerators does not address the question of increase of gravitational mass due to velocity.

The controversy over the term relativistic mass is a trivial issue. It is a matter of style. The more modern approach is to use the term mass to refer to rest or proper mass, and express total mass or mass/energy as a function of mass and velocity. This approach avoids misunderstandings, but does not make the term relativistic mass absurd or meaningless.

Aer: Give me a break!! Sorry I did not explicitly exclude you and a few others as not being guilty of nonsense citations when I posted the following.It is my guess that at least 90% of physics courses deal with classical physics (probably 100% of high school courses). Even a professor familiar with SR, GR, & QT might never mention them to students in a course relating to classical physics.BTW: Do any of you dislike the size and style resulting from quote . . . /quote? I have been using list & /list instead.

Now it is my turn to state "I have aready explained" but I will repeat explanation by pasting it in again here: I understand your explanation.

IT IS WRONG


I said: "At the level of understanding commonly found in this forum You need not dumb things down for me. :rolleyes:


and because it is simplier, the use of "relativistic mass" is very appropriate and I will continue to use this term, Spoken with complete arrogance.


... I also sometimes use the term "mass/energy" and think it mainly a mater of style, not physics, how one refers to the particle's energy or mass Here is where you are wrong. You claim it is a matter of style when in fact we have no concrete definition of mass because of this fuzzy "matter of style" argument you just used. If the curvature an object creates is a function of it's mass, then kinetic energy of any kind cannot cannot CANNOT CANNOT be included as a part of an object's mass. This is the point that is lost on you because you claim that a photon will create curvature in spacetime.

Let's take a look at the fundamentals (I borrowed from a site at UCLA (http://www.astro.ucla.edu/~wright/relatvty.htm)):
Thus the fundamentals of relativity that are important for cosmology are:

* The speed of light is a constant independent of the velocity of the source or the observer.
* Events that are simultaneous as seen by one observer are generally not simultaneous as seen by other observers, so there can be no absolute time.
* Each observer can define his own proper time -- the time measured by a good clock moving along his worldline.
* Observers can assign times and positions to events not on their worldlines using radar observations.
* Every observer will see his clock running faster than other clocks which are moving with respect to him, and this is a mathematically consistent pattern required by the properties of radar observations.
* As a result, the unaccelerated worldline between two events will have the longest proper time of all worldlines connecting these events.
* In the presence of gravity, the worldlines of objects accelerated only by gravity have the longest proper times.
* Gravity requires that spacetime have a non-Euclidean geometry, and this curvature of spacetime must be created by matter.

The one in red is the most important and only one relevant to our discussion here. Gravity is created by matter. Are you saying that a photon is matter? I googled "photon is matter" and could not find one legitimate site that makes this claim. I do not think a photon is matter, do you?

To settle this, I think a defintion of matter is in order:

matter: Anything that has mass and can be detected and measured. All matter is made up of atoms. Matter usually exists as a solid, a liquid or a gas.

Now let's take another look at what I said.

If the curvature an object creates is a function of it's mass, then kinetic energy of any kind CANNOT be included as a part of an object's mass.

Suppose for a moment that the kinetic energy of an object did increase the curvature of spacetime that it created. From which frame of reference are you going to measure this kinetic energy? In the rest frame of the object, the kinetic energy is always zero. So I'll ask again - what is the all important, preferred if you will, reference frame from which kinetic energy should be measured so that we know how much curvature an object should impose on spacetime?



- they are even idential in value in the system of units commonly used by high energy physicists and most theoretical physicists. (In this system, the speed of light is 1, so m = E.)" That is about the stupidest argument I've ever heard. even if m = E, the units of m and units of E are still different. So what if c=1? I can make c=.00001 too, or c=32478943289432789, depending on my units.



Thank you for clearly confirming my assumption that you believe all zero rest mass particles ("objects" if you prefer to speak of photons etc. as waves) do not produce any gravity field.

Now we can see who is supported by James R on this if he is reading. I ask him same question (Do energetic objects with zero rest mass produce any gravity field?) Aer says "no" and I say "yes," but of course it is small in most cases, but not zero. Good luck with your claim that a zero rest mass particle/wave creates curvature of spacetime. :D



("Small" when compared to the gravity field of a particle with rest mass.)
You do realize that something can have a greater relativistic mass than it's own rest mass, do you not? A hydrogen atom traveling at .99(repeat 9 100 times)c would have a relativistic mass of a black hole. Do you claim that it would become a black hole?



I do, however, note that there is no upper limit on the energy of a gamma ray in theory, so the gravity field of a conceptually possible, very energetic, gamma ray could be as large as that from a resting electron. (This is why I said "in most cases.")

PS by edit: I was too quick to post paragraph immediatley above. - Many gamma rays, if not most, have greater gravity fields than a resting electron. The rest mass of an electron is only 0.511 Mev if memory serves me correctly. A gamma ray with energy of 0.512Mev produces slightly more gravity than the electron at rest. (I forget the minimum energy a photon must have to be considered a "gamma ray" but certaily some that have been observed make 1000 times more gravity than a resting electron.) I also forget the most energetic gamma ray yet observed, perhaps it had more than a 1000 times the gravity field of a proton.

Right, waves create gravity fields :rolleyes:

BTW: Do any of you dislike the size and style resulting from quote . . . /quote? I have been using list & /list instead.
You can use quote] size=3] ... /size] /quote] If you really want the quoted text to be larger. Most people don't want to reread a quote - it is just there so you know what the response is to.

You claim it is a matter of style when in fact we have no concrete definition of mass because of this fuzzy "matter of style" argument you just used. You call it fuzzy, I would simply say that you can have m = E/c² or E = mc². Mass and energy in this context are interchangeable, so, yes, it is a matter of style.If the curvature an object creates is a function of it's mass, then kinetic energy of any kind cannot cannot CANNOT CANNOT be included as a part of an object's mass. No, this is wrong. Spacetime curvature is a function of the total mass-energy content of the source. Note the total in there - you can call the "energy" part kinetic if you want, but on this scale most of us wouldn't

Gravity is created by matter. Are you saying that a photon is matter? So what is "matter" according to you? "Stuff", "oh, you know...things"? But of course, you are hopelessly wrong. "Gravity is created", in your erudite language, by mass-energy. Have you any idea what the field source in the gravitational field equations represents?I googled "photon is matter" and could not find one legitimate site that makes this claim. Yay! Here is the guy who claims (by implication only, it's true) to have a degree in physics. Truth via Google!To settle this, I think a definition of matter is in order:Which is entirely beside the point.



Suppose for a moment that the kinetic energy of an object did increase the curvature of spacetime that it created. From which frame of reference are you going to measure this kinetic energy? Huh?? Frames of reference in relation to gravitational field theory? That's crazy. Good luck with your claim that a zero rest mass particle/wave creates curvature of spacetime. Oh, you heard about wave/particle duality somewhere and thought you'd throw it in to sound knowledgeable.

Look, my final word ever to you: In this and other threads, you have shown youself to be a deeply unpleasant individual. I particularly deplore your attitude toward BillyT, which was highly offensive, even to an onlooker.

You call it fuzzy, I would simply say that you can have m = E/c² or E = mc². Mass and energy in this context are interchangeable, so, yes, it is a matter of style. The equation you used is REST ENERGY. The total energy, with kinetic energy included is:

E=γmc².


No, this is wrong. Spacetime curvature is a function of the total mass-energy content of the source. Note the total in there - you can call the "energy" part kinetic if you want, but on this scale most of us wouldn't
You are wrong, I provided a source that says otherwise!



So what is "matter" according to you? "Stuff", "oh, you know...things"?
You must have missed the defintion of matter:

matter: Anything that has mass and can be detected and measured. All matter is made up of atoms. Matter usually exists as a solid, a liquid or a gas.

But this doesn't suit your argument, so of course you ignored it.



But of course, you are hopelessly wrong. "Gravity is created", in your erudite language, by mass-energy. Have you any idea what the field source in the gravitational field equations represents?Yay! Here is the guy who claims (by implication only, it's true) to have a degree in physics. Truth via Google!Which is entirely beside the point. Again you must have missed one of the fundamentals I supplied for people just like you:

Gravity requires that spacetime have a non-Euclidean geometry, and this curvature of spacetime must be created by matter.

So yes, curvature of spacetime is CREATED by matter, where matter is an object with rest mass. You are hopelessly stupid.



Huh?? Frames of reference in relation to gravitational field theory? That's crazy. How the fuck are you going to have kinetic energy (relativistic mass you would say) without a different frame of reference? OOOOOH, you say. :D



Oh, you heard about wave/particle duality somewhere and thought you'd throw it in to sound knowledgeable.
You just sound stupid. I've know what wave/particle duality was since high school physics - it's not a new concept.



Look, my final word ever to you: In this and other threads, you have shown youself to be a deeply unpleasant individual. I am only unpleasant to dipshits such as yourself.


I particularly deplore your attitude toward BillyT, which was highly offensive, even to an onlooker. I started out with a cordially conversation with Billy T, but he appears to have the attitude that he is smarter than anyone he is talking to. I'll reply likewise everytime.

And one last thing Quarkhead - I have no problem with talking down to you because you've shown yourself to be stupid without any help.