[PmbPhy (OP)]

I came across a special relativity text which says A particle does not become heavier with increasing speed. Do you believe the author is correct? What would you expect would happen to the magnitude of the gravitational field if the source of the field was moving?

Authors who don't use and don't like the concept of relativistic mass make arguments such as the following which are from Appendix F in the text Special Relativity by T.M. Helliwell page 259. I'm going to paraphrase a bit to save myself some typing but the essence of what I'm quoting will not be changed. The author uses the symbol m_R to represent relativistic mass.

(i) By hiding √{1 - v²} in the mass, we may forget it is there. ...

(ii) One may get the mistaken impression that to go from classical to relativistic mechanics its only necessary to replay all masses by m_R. This certainly works for the momentum p = m_Rv, but it does not work, for example, for kinetic energy: The relativistic kinetic energy is not (1/2)m_Rv². And it works in Newton's second law F = ma only in the very special case where the force exerted on a particle is perpendicular to its velocity. In all other cases F != ma.

(iii) Relativity fundamentally serves to correct our notions about time and space. That is, it is really the dynamical equations dealing with motion, like energy and momentum, that ought to be changed, and not the properties of individual particles, like mass.

(iii) When relativity is cast in four-dimensional spacetime form, ...., the idea of relativistic mass is out of place and clumsy.

Of course I have my own opinions about each item but first I'm curious as to what others think about these arguments, so therefore please let me know what you think of each one.

I'd like to thank all of you for giving me your opinion on this.

[jeffreyH]

I came across a special relativity text which says A particle does not become heavier with increasing speed. Do you believe the author is correct? What would you expect would happen to the magnitude of the gravitational field if the source of the field was moving?

This is a very interesting post. Define heavier. Does an object become heavier simply because it crashes into another object at speed? How is relativistic mass interpreted? Is it an increase only in internal kinetic energy or some orther form?

Authors who don't use and don't like the concept of relativistic mass make arguments such as the following which are from Appendix F in the text Special Relativity by T.M. Helliwell page 259. I'm going to paraphrase a bit to save myself some typing but the essence of what I'm quoting will not be changed. The author uses the symbol m_R to represent relativistic mass.

(i) By hiding √{1 - v²} in the mass, we may forget it is there. ...

(ii) One may get the mistaken impression that to go from classical to relativistic mechanics its only necessary to replay all masses by m_R. This certainly works for the momentum p = m_Rv, but it does not work, for example, for kinetic energy: The relativistic kinetic energy is not (1/2)m_Rv². And it works in Newton's second law F = ma only in the very special case where the force exerted on a particle is perpendicular to its velocity. In all other cases F != ma.

(iii) Relativity fundamentally serves to correct our notions about time and space. That is, it is really the dynamical equations dealing with motion, like energy and momentum, that ought to be changed, and not the properties of individual particles, like mass.

(iii) When relativity is cast in four-dimensional spacetime form, ...., the idea of relativistic mass is out of place and clumsy.

Of course I have my own opinions about each item but first I'm curious as to what others think about these arguments, so therefore please let me know what you think of each one.

I'd like to thank all of you for giving me your opinion on this.

I am still thinking about the 3 points above.

[Bill S]

Define heavier.

My understanding is that heavier = having more weight, and that weight is the result of gravitational attraction between one massive (=mass/energy) object and another.

Does the author actually mean “heavier” or “more massive”?

I too an thinking about the three points, but it may take a while. 

[PmbPhy (OP)]

This is a very interesting post. Define heavier.

A good definition of the term weight for purposes such as this is best defined in the article
The equivalence principle and the question of weight by Kenneth Nordtvedt, Jr., Am. J. Phys., 43(3), Mar. (1975)
You can download this article from the following URL: http://booksc.org/book/20829048

The weight of a body is meant to be the force (e.g., the compression of a spring scale) required to either support the body in a gravitational field (gravitational weight) or to accelerate the body relative to an inertial space (inertial weight).

That definition means that the term heavier means that a greater force is required to support the body than that required when the body is at rest.

Does an object become heavier simply because it crashes into another object at speed?

Absolutely not.

How is relativistic mass interpreted? Is it an increase only in internal kinetic energy or some orther form?

I don't know what you're asking when you write How is relativistic mass interpreted? I'm not even sure that its meaningful to ask how any physical quantity is interpreted. To interpret means to explain the meaning. I really don't know what you're asking for here Jeff.

The relativistic mass, aka inertial mass, M, of a body of proper mass, m, is defined as M = m/√(1 - v²/c²). This expression is determined by requiring that the quantity p = Mv is conserved in completely elastic collisions. The derivation is on my website at: http://www.newenglandphysics.org/physics_world/sr/inertial_mass.htm

[lightarrow]

I came across a special relativity text which says A particle does not become heavier with increasing speed. Do you believe the author is correct?

I think it's wrong, on the particle there should be a greater force, proportional to the gamma factor. But maybe the author intended to refer to its mass and not to its weight (which kind of book is it? Is it a universitary text?)

What would you expect would happen to the magnitude of the gravitational field if the source of the field was moving?

Don't know, but is it really the same question as the particle's weight?

Authors who don't use and don't like the concept of relativistic mass make arguments such as the following which are from Appendix F in the text Special Relativity by T.M. Helliwell page 259. I'm going to paraphrase a bit to save myself some typing but the essence of what I'm quoting will not be changed. The author uses the symbol m_R to represent relativistic mass.

(i) By hiding √{1 - v²} in the mass, we may forget it is there. ...

(ii) One may get the mistaken impression that to go from classical to relativistic mechanics its only necessary to replay all masses by m_R. This certainly works for the momentum p = m_Rv, but it does not work, for example, for kinetic energy: The relativistic kinetic energy is not (1/2)m_Rv². And it works in Newton's second law F = ma only in the very special case where the force exerted on a particle is perpendicular to its velocity. In all other cases F != ma.

(iii) Relativity fundamentally serves to correct our notions about time and space. That is, it is really the dynamical equations dealing with motion, like energy and momentum, that ought to be changed, and not the properties of individual particles, like mass.

(iii) When relativity is cast in four-dimensional spacetime form, ...., the idea of relativistic mass is out of place and clumsy.

I agree with these three points and I would even add others, but I've already discussed about them in many other threads. All of this in SR only, however, even because I don't know anything of GR.

--
lightarrow

[syhprum]

Is there a definite answer, when two particles are moving on parallel tracks at a velocity near c is there a greater gravitational attraction between them than when they are moving at a more modest velocity.
My own humble opinion is that there is not.

[puppypower]

Kinetic energy; 1/2MV2, cannot reach or exceed 1/2MC2, since rest mass cannot move at the speed of light. If we tried to induce a mass to approach the speed of light, we would need to add infinite energy, yet kinetic energy is only able to reach the low finite limit of 1/2MC2. Relativistic mass accounts for the energy difference; E=MrC2, so energy conservation applies.
.


 

[PmbPhy (OP)]

I think it's wrong, on the particle there should be a greater force, proportional to the gamma factor. But maybe the author intended to refer to its mass and not to its weight (which kind of book is it? Is it a universitary text?)

No. He really meant weight. No physicist would ever make that kind off mistake. The text is a textbook on relativity. Although its as mathematically sophisticated as any text used in a university course, I doubt that this text would ever be used in a course on relativity

Don't know, but is it really the same question as the particle's weight?

No, of course not. This is an entirely different question.

I agree with these three points and I would even add others, but I've already discussed about them in many other threads.

Let's take each point at a time:
(i) (i) By hiding √{1 - v²} in the mass, we may forget it is there.

You mean to tell me that just because γ is not explicitly written down you'd forget that it was there? If you wouldn't forget its there then who is it that you think would? If you have in mind a student then all that means is that the student doesn't know the physics that well and needs to study it more. I can think of no actual equation or scenario in which someone would forget that it's there. When making a calculation its always clear what's being calculated so that nobody could reasonably emit it. E.g. please provide a reasonable scenario in which someone could forget γ.

(ii) One may get the mistaken impression that to go from classical to relativistic mechanics its only necessary to replay all masses by m_R.

Not something that could reasonably happen. After all, who do you think makes such calculations? Only someone who knows special relativity. After all, only a very poor student would attempt to write down an equation and use it when they've never learned how to calculate kinetic energy. No relativist could ever make such a mistake.

(iii) Relativity fundamentally serves to correct our notions about time and space. That is, it is really the dynamical equations dealing with motion, like energy and momentum, that ought to be changed, and not the properties of individual particles, like mass.

Also not a reasonable argument. Such an argument would also have to apply to everything else in relativity including time and length. A proper time interval Δτ is the magnitude of a time-like displacement 4-vector while a coordinate time interval Δt is the time component of the same displacement 4-vector. Proper distance Δλ is the magnitude of a space-like displacement 4-vector while distance ΔL is the magnitude of Δr which is the distance between two points in space represented by a space-like displacement 4-vector.

[PmbPhy (OP)]

Kinetic energy; 1/2MV2, cannot reach or exceed 1/2MC2, since rest mass cannot move at the speed of light.

What is the "M" that you used in that expression? Is it relativistic mass or proper mass? In either case that's not the expression for kinetic energy. Kinetic energy, K, is given by (letting m = proper mass aka rest mass)

K = (γ - 1)mc²

If we tried to induce a mass to approach the speed of light, we would need to add infinite energy, yet kinetic energy is only able to reach the low finite limit of 1/2MC2.

That's not true at all. Kinetic energy can have any value whatsoever. I.e. it can get as large as one would like. The value of K is the work done on the particle and you can do as much work as you'd like on a particle.

Relativistic mass accounts for the energy difference; E=MrC2, so energy conservation applies.

That expression is wrong. The energy associated with relativistic mass, M, is the energy E = Mc². It's equal to the sum of the particles kinetic energy and rest energy, i.e. E = Mc² = K + E₀ = K + mc²

[jeffreyH]

Is there a definite answer, when two particles are moving on parallel tracks at a velocity near c is there a greater gravitational attraction between them than when they are moving at a more modest velocity.
My own humble opinion is that there is not.

Firstly your post should be given particular attention since it raises a very important point which should be discussed further. In reply to a post of Pete's above I agree that weight would have to depend upon speed. So then what syhprum says is of particular significance. I haven't had time to think about other aspects. The internal kinetic energy remarks with respect to relativistic mass I may write up later. It is to do with an actual theory I am working on. Yes I  actually have a theory!

[Frazier]

No particle's inertial mass or gravitational mass does not increase with speed. The issue is when someone applies an absolute frame of reference of speed assuming that the force necessary to accelerate it 1mph faster gets harder and harder to do the closer you are to the speed of light. Velocity isn't absolute, it approaches light speed and the momentum approaches infinity. The issue is that F=ma considers acceleration with absolute frame of reference. The idea of relativistic mass is only necessary in order to make sense of relativity in absolute Newtonian terms. It does not exist as an actual phenomenon. The issue is the Newtonian conception of inertia breaks down.

[jeffreyH]

No particle's inertial mass or gravitational mass does not increase with speed. The issue is when someone applies an absolute frame of reference of speed assuming that the force necessary to accelerate it 1mph faster gets harder and harder to do the closer you are to the speed of light. Velocity isn't absolute, it approaches light speed and the momentum approaches infinity. The issue is that F=ma considers acceleration with absolute frame of reference. The idea of relativistic mass is only necessary in order to make sense of relativity in absolute Newtonian terms. It does not exist as an actual phenomenon. The issue is the Newtonian conception of inertia breaks down.

What you appearing to be talking about is a coordinate value for inertia. So that it only appears to change with a change in reference frame. Correct me if I am wrong. I think input from a particle accelerator engineer would be useful.

[PmbPhy (OP)]

No particle's inertial mass or gravitational mass does not increase with speed.

That's incorrect. It's a well known fact that inertial mass increases with speed. Engineers have to take this fact into account when designing particle accelerators. The educational material at CERN explains this. See:
http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/lhc-machine-outreach-faq.htm

Basically the relativistic mass of a particle increases with velocity and tends to infinity as the velocity approaches the speed of light. 

where the term relativistic mass is just another name for inertial mass. Gravitational mass also increases with speed.

See also: https://cerntruth.wordpress.com/

In the fall of 2015 CERN will begin colliding groups of 70 million lead hadrons at 287 tev, unpacking millions of quarks in each collision. Those quarks will be first accelerated at light speed, acquiring relativistic mass, becoming heavier strange quarks, the substance of a strange quark-gluon soup called a ‘strangelet‘. The strange liquid has the potential to become stable and start an ‘ice-9′ big-bang reaction. If that happens that effectively transforms the Earth into a pulsar.

The issue is when someone applies an absolute frame of reference of speed assuming that the force necessary to accelerate it 1mpfaster gets harder and harder to do the closer you are to the speed of light.

There's no such thing as an absolute frame of reference so what exactly are you claiming here?

Velocity isn't absolute, it approaches light speed and the momentum approaches infinity. The issue is that F=ma considers acceleration with absolute frame of reference.

Force isn't defined as F =ma. It's defined as F = dp/dt.

The idea of relativistic mass is only necessary in order to make sense of relativity in absolute Newtonian terms. It does not exist as an actual phenomenon. The issue is the Newtonian conception of inertia breaks down.

You're quite wrong. Mass is defined as the m in p = mv. Your assertion about Newtonian terms is incorrect. Your mistake is based on the erroneous assumption that there is a difference in the laws of mechanics between Newtonian mechanics and relativity. There isn't and there never have been. In fact Newton defined force as the time rate of change of momentum. It was Euler who wrote force as F = ma, not Newton. In both Newtonian mechanics and relativity force is given by F = dp/dt. Newton's three laws also hold in relativity where the only difference being that in Newtonian mechanics Galilean transformations are used where in relativity Lorentz transformations are used to transform between inertial frames. Newton's third law applies only between objects in contact.

[PmbPhy (OP)]

What you appearing to be talking about is a coordinate value for inertia. So that it only appears to change with a change in reference frame. Correct me if I am wrong. I think input from a particle accelerator engineer would be useful.

Increase in inertial mass is a fact that can be found in any text on accelerator physics. It's in the new text I bought recently.

[jeffreyH]

What you appearing to be talking about is a coordinate value for inertia. So that it only appears to change with a change in reference frame. Correct me if I am wrong. I think input from a particle accelerator engineer would be useful.

Increase in inertial mass is a fact that can be found in any text on accelerator physics. It's in the new text I bought recently.

Frazier seems to have an alternate view.

[saspinski]

Is there a definite answer, when two particles are moving on parallel tracks at a velocity near c is there a greater gravitational attraction between them than when they are moving at a more modest velocity.
My own humble opinion is that there is not.

For a measurement made in the particles referential, the gravitational atraction is the same. Nothing should change.

For a measurement made from the referential from which they have such a high speed, I'm not sure.
If they are really heavier, the aceleration due to the bigger gravitational field should make them colide in a shorter time. 

But I'm not sure if relativistic mass can be used straightforwardly for a=GM/r˛.

It is not valid for F=ma, (we could naively suppose it was), because dp/dt produces another 1/(1-v˛/c˛) term (when the force has the same direction of velocity).

[jeffreyH]

The gamma function includes a value for velocity that relates to the frame of the particle under consideration. Not a value as measured from a remote frame. In which case the particle has to become heavier in its own frame of reference. This will be undetectable in that frame since all objects will become heavier in propotion to anything under observation. Including measuring equipment. So that the laws of physics are the same as in a rest frame. As long as the velocity is constant and no external forces are applied to the frame. This is an important consideration. The question is then as syhprum stated above. Will gravitation draw particles together when they are both moving at relativistic speed and on parallel paths. Since both are becoming heavier then the inertia of both particles is increasing in direct proportion. This cannot have any effect to counter the increased attraction since acceleration due to gavity is independent of mass. All objects fall at the same rate. So we have a conundrum.

[PmbPhy (OP)]

What you appearing to be talking about is a coordinate value for inertia. So that it only appears to change with a change in reference frame. Correct me if I am wrong. I think input from a particle accelerator engineer would be useful.

Increase in inertial mass is a fact that can be found in any text on accelerator physics. It's in the new text I bought recently.

Frazier seems to have an alternate view.

I guess I should have made my question clearer. Obviously, anybody who knows me knows very well that I know everything that there is to know about relativistic mass, rest mass, proper mass, the energy-momentum tensor, four-momentum, all aspects of the debate regarding relativistic mass vs rest mass, etc. I don't need Frazier to repeat what I know so well. In all likelihood I know more about this subject than most physicists do.

But let me make something very clear: I do not wish to debate relativistic mass or debate whether mass should be defined in a particular way and whether it's better to do so. I already know this issues and have a stance on it. In fact I wrote an article on the subject located at: http://arxiv.org/abs/0709.0687

The purpose of this thread is for me to understand who it is that people think are making such terrible mistakes that I quoted in the three points in the OP. I also wanted to know whether people assume that weight depends on speed or not. By the way, the weight as measured in the rest frame of the body is a function of the velocity of the source. Here's two examples for those who can understand the math:
http://www.newenglandphysics.org/physics_world/gr/grav_field_sheet.htm
http://www.newenglandphysics.org/physics_world/gr/grav_field_rod.htm

As far as syphrums question goes; I'd have to actually sit down and calculate it. But it should be simple just to think about it. In the rest frame of one of the bodies the other body is also at rest. So you can easily calculate the force between the two bodies; believe it or not it has the same value as in Newtonian gravity. Now just transform your observations to a moving frame and calculate the quantities that you want to.

See also: Measuring the active gravitational mass of a moving object by D.W. Olson and R.C. Guarino, Am. J. Phys., 53(7), Jul. (1985). You can download it from here: http://booksc.org/book/20873864
The abstract reads as follows.

From: http://scitation.aip.org/content/aapt/journal/ajp/53/7/10.1119/1.14280

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

That's why I'm all for relativistic mass. In all aspects, relativistic mass behaves as we expect mass should behave. I suspect that's why Misner, Thorne and Wheeler use it in their text Gravitation. Where the say that Mass is the source of gravity. they're referring to the energy-momentum tensor, which really should be called the mass tensor since it fully explains/describes mass.

[PmbPhy (OP)]

What you appearing to be talking about is a coordinate value for inertia. So that it only appears to change with a change in reference frame. Correct me if I am wrong. I think input from a particle accelerator engineer would be useful.

I don't know any particle accelerator engineers but I do have the book Was Einstein Right by Clifford M. Will. Will is a renown experimental physicist. His area of expertise is relativity.

All that I'm doing in this post is responding to Jeff's remark about input from an engineer. I'm assuming that he's okay with an experimental physicist in relativity. But I'm not doing this to start a debate on relativistic mass. We've beat that horse silly in this forum and other forums and I'd have an anxiety attack if I had to see people repeating those same old arguments in this thread. That would be off-topic. It was my intention when I created this thread that we discuss relativistic mass and weight and who those people are that make those mistakes. That's all.

On page 262 Clifford Will writes

The U.S. National Budget. On 1983, particle physicists proposed that the United States build a gigantic 85 kilometer circumference particle accelerator called the superconducting super collider, costing over 6 billion dollars. One reason for the enormous size and cost is the special relativistic increase in the inertia of a particle moving near the speed of light that makes it harder and harder to accelerate it to higher speeds.

On page 273 Will says just about the same thing, i.e.

The principle of relativity can also be applied  to more complicated situations, such as the collision between two bodies, or the motion of a charged body in an electric field. In order for the outcomes of experiments like these to be independent of the inertial frame, the effective mass, or inertia, of a moving particle must increase. The relativistic increase of inertia is what prevents particles from being accelerated up to and beyond the speed of light, because the inertia of the particle increases without bound as it approaches c. This has been observed countless times in particle accelerators, and must be figured into all the engineering specifications and cost estimates for more powerful accelerators.

Think how difficult it would have been to explain that without invoking an increase in inertia.

[UltimateTheory]

If you accelerate proton to really really high velocity,
and hit it with other stationary proton,
there will be created proton-antiproton pair:

p+ + p+ -> p+ + p+ + p+ + p-
Input two particles are creating four particles on output.

Proton has rest-mass 938.272 MeV/c^2
Anti-proton (also) have rest-mass 938.272 MeV/c^2

So basically from kinetic energy of incoming particles there are created two new particles (proton and antiproton)..

Baryon Number conservation:
prior event: +1 +1
after event: +1 +1 +1 -1
+1+1=+1+1+1-1

BTW, kinetic energy in Special Relativity is not E.K.=1/2*m*v^2 but
E.K.=m0*c^2*gamma-m0*c^2
where gamma=1/sqrt(1-v^2/c^2)
Basically, subtract relativistic-mass from rest-mass, and multiply by c^2.