# Lets try this again

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Here is a question I've posted on here and other forums before. I'll keep asking until I get one of the answers enough that I feel I can trust it.

Ok, you accelerate a massive body to a high percentage of c. Its relativistic mass grows accordingly. Does this added mass/energy exert an extra gravitational influence on other bodies?

All I'm looking for is a yes or no here. I've recieved both answers in the past, and have had both explained to me. If you know of an authoritative source that specifically states the answer, that would be useful too.

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Would you consider the electromagnetic field of a moving charge and a charge at rest (only electric field, then) as different? If "yes", then the gravitational field of a moving body probably differs from that of the same body at rest. If "no, it´s the same field seen from different frames of reference" then a moving body and the body at rest should have the same gravitational field.

Although I´m aware that I´m not being very popular with these kind of questions, I can´t resist asking the following question: What´s a gravitational field? And to give a little explanation why I´m asking this: I think it´s something you should ask and try to answer for yourself (mathematically, ideally), not for me.

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Well my physics teacher gave an answer along these lines:

Because we're dealing with relativistic mass we cannot apply classical/Newtonian physics to it (that's kinda obvious). However we are using relativity. So if your relativistic mass increases then the amount you bend spacetime should increase too (ie. increased gravitational field).

This is a theroetical view point though, the maths would give you the answer, although it is a bit more complicated!

[Tycho?] can you tell me the explanations for both the yes and the no answers which you have heard already?

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I asked a similar question and I came to the idea that mass dosn't really increase, but it's the density of matter that increases, which just gives the impression that it is mass increasing instead.

Because at speeds relative to c, matter is constricted into becoming 2 dimensional at exactly c (like a singularity, except as a 'sheet' and not a 'point') - and to contract 3 dimensional matter into a 2 dimensional existence would require infinite energy. Motion and speed is nothing more than an observed side-effect of this contracting.

Admittedly it's just an idea to explain the concept of infinite energy for matter to travel at c and probably can't really be classed as a true scientific hypothesis... but I like it.

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A standard argument against is that an object can't collapse into a black hole because of your relative motion, and only in some frames but not others.

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Clever argument Swansont!

Is there a standard argument for it? More to the point isn't a real answer which we could get using the mathematics?

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Clever argument Swansont!

Is there a standard argument for it? More to the point isn't a real answer which we could get using the mathematics?

I don´t even know what Swansont commented on, but in case your "get a real answer using the mathematics" refered to the original question: It seems you didn´t notice, my answer was a mathematical one.

In Relativity, the structure of spacetime is entirely described by the metric tensor. Being a tensor, it´s an invariant object where "invariant" means it remains the same under arbitrary coordinate transformations e.g. the frame where the object is moving.

This invariance, which physicists usually call "covariance", has a slight catch, however. While the objects remain unchanged under coordinate transformations, their representations can change. That´s what my comparison with the EM field was about. The EM field can be described by the EM field strength tensor. The electromagnetic field strength tensor is ... right: A tensor, and therefore invariant under coordiante transformations (charge at rest <-> moving charge). If one writes down this tensor in a suitable representation (it´s a 2nd order tensor so a matrix is suitable) one can identify 6 independent entries of this matrix. Three of them can be combined to form the electric field, the three others form the magnetic field. And as we all know, the magnetic field of a moving charge and a charge at rest differ.

So to sum it up and to repeat what I already said in my first post: The question whether the gravitational field of a moving object differs from that of the same object at rest depends on what your preferred understanding of "differ" is (tensor level or representation level).

In the case of this thread however, there is an additional problem: I simply don´t know what a "gravitational field" is supposed to be in GR. Gravitiy is an effect completely determined by the spacetime structure. So I´d see little point in introducing a gravtiational field at all.

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Gravity in GR is described by a riemann manifold, beyond this I don't know enough mathh to talk much more, however the only part of the equation that mentions any property related to the inertia of the object mentioned energy, so I would venture to guess that a faster object would exert more gravity.

The article on wikipedia has a good description of the mathmatics if anyone here is qualified to understand them.

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Gravity in GR is described by a riemann manifold [...]

I could agree with this statement. But I still wanted to comment on it:

1) One might take GR (and especially the equivalence principle) to a point where one sais that gravity doesn´t exist in GR. To some extend, the whole stuff with curved spaces is about getting rid of gravity and making it a fictional force appearing due to the use of "improper" coordiante systems.

2) That manifold is called "spacetime". I was assuming that the term was commonly known so I didn´t explain anything on it. That manifold is described by its metric (-tensor). That´s the point where my previous post started.

3) Minor technical correction: It´s a Lorentz Manifold. A Riemann Manifold does (at least to my sources) have a positive definite metric.

The only part of the equation that mentions any property related to the inertia of the object mentioned energy

Of course I don´t know which equation you are talking about but the equation describing the relation between spacetime structure and energy content is the "Einstein Equations". All of the appearing objects are tensors which ultimately brings us back to the difficulties about defining "differ" raised in my previous post.

The article on wikipedia has a good description of the mathmatics if anyone here is qualified to understand them.

Perhaps you should also post the link or at least specify "the article".

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A standard argument against is that an object can't collapse into a black hole because of your relative motion, and only in some frames but not others.

Logically,if mass is relative,then all the properties asoosiated with it should be relative.So,an object should be a black hole for one observer and not for other. Though I am digressing a bit,but,what will be the properties of such a black hole ,and what will be the outcome of this phenomenan?

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Logically,if mass is relative,then all the properties asoosiated with it should be relative.

You'll note that [imath]m_0 = \left((\frac{E}{c^2})^2 - (\frac{p}{c})^2\right)^\frac{1}{2}[/imath] is invariant.

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I was reffering to the einstein field equations, sorry for not puralizing, I thought it could be assumed those were the ones I was talking about because this discussion is on GR.

I was reffering to the article "general Relativity" on wikipedia, since this discussion was on general relativity I thought I could assume that others would recognize what article I was refffering to.

however here is the article I was referring to

http://en.wikipedia.org/wiki/General_theory_of_relativity

it does seem that the article has split into a number of seperate branches as well, so here is a more mathmatical article

http://en.wikipedia.org/wiki/Mathematics_of_general_relativity

the original article "general relativity" contains a number of stubs on different sections of general relativity and links to larger articles on each of these stubs.

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A standard argument against is that an object can't collapse into a black hole because of your relative motion, and only in some frames but not others.

Either I thought this argument up on my own or I just read it somewhere and forgot where I read it. But yes, this is my main argument for the "no" answer. However, just because something does not seem to make logical sense does not mean that its not true, particularly in the strange world of relativity. Perhaps an object can actually appear to be a black hole in one frame but not in others.

So, yet again I am not getting much in the way of deffinative answers. We have an object moving very close to c. Would its gravitational pull on other objects be greater than it was while it was at rest, would it be the same, or some other answer?

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You'll note that [imath]m_0 = \left((\frac{E}{c^2})^2 - (\frac{p}{c})^2\right)^\frac{1}{2}[/imath'] is invariant.

Just to clear up any confusion this guy said $m_0$ which is the rest mass, in this thread we are talking about the relativistic mass, different thing.

[Tycho?] you seem to have run into a question which we can't answer for certain, it sure is an interesting one and I think I'm heading towards saying no, but I'm not really sure.

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Just to clear up any confusion this guy said $m_0$ which is the rest mass' date=' in this thread we are talking about the relativistic mass, different thing.

[Tycho?'] you seem to have run into a question which we can't answer for certain, it sure is an interesting one and I think I'm heading towards saying no, but I'm not really sure.

Its interesting how much trouble this question gives people. To me it seems pretty darn fundamental, regardless of whether the answer is a yes or a no. But oh well, I'll continue to search, I'll get the answer eventually.

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']Here is a question I've posted on here and other forums before. I'll keep asking until I get one of the answers enough that I feel I can trust it.

Ok' date=' you accelerate a massive body to a high percentage of c. Its relativistic mass grows accordingly. Does this added mass/energy exert an extra gravitational influence on other bodies?

All I'm looking for is a yes or no here. I've recieved both answers in the past, and have had both explained to me. If you know of an authoritative source that [i']specifically[/i] states the answer, that would be useful too.

I don't know but I would argue yes.

Compare two identical planets orbiting a sun. Identical except one is hotter than the other. The energy of the heat, which is really just the additional kinetic energy of the constituent parts, adds inertia to the hotter planet and must therefore increase the gravitational force as well. If not the equivalence principle would not hold exactly. I think this low speed example should hold in principle even though as the constituent particles increased in their velocities the planet would fly apart well below light speed.

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A standard argument against is that an object can't collapse into a black hole because of your relative motion, and only in some frames but not others.

If I accelerate to increase my velocity relative to you, I see your time flow slow down and some distances change. I cannot picture how I would expect you to gravitationally implode, but if that was the case would I not expect it to take/approach an infinite time to do so?

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No... because if I'm travelling at c-1 relative to you then my time goes pretty slowly (from your point of view) however no matter how slowly my time seems to be flowing I'm still a black hole.

It doesn't take me an infinite amount of time to reach c-1 and my relavistic mass is always up to date so if it does not take me an infinite amount of time to reach c-1 then it doesn't take me an infinite amount of time to become a black hole.

Does that make sense?

(This is all assuming I would become a black hole at high speeds)

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No... because if I'm travelling at c-1 relative to you then my time goes pretty slowly (from your point of view) however no matter how slowly my time seems to be flowing I'm still a black hole.

It doesn't take me an infinite amount of time to reach c-1 and my relavistic mass is always up to date so if it does not take me an infinite amount of time to reach c-1 then it doesn't take me an infinite amount of time to become a black hole.

Does that make sense?

(This is all assuming I would become a black hole at high speeds)

I think we are assuming you will not. The idea being you could get there by me accelerating to high speed off in the distance where I cannot affect you- you would be near light speed in my reference frame but how could that possibly make you into a blackhole because of your relativistic mass in my reference frame. If this was true we would all implode upon constructing and using particle accelerators. I think that was Swansont's point. All frames might not agree but they must "agree to disagree" in a way consistent with relativity.

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Yeah yeah, agreed... I didn't agree with the infinitely long to become a black hole thing, but sure the whole 'in which reference frame are you a black hole?' thing makes it seem logical that your gravitational field doesn't vary with relativistic mass.

=====

And just a question, in a universe in which there was only me and you, we are moving relative to each other... Am I right in saying that to you I have a relativistic mass, whereas to me you have a relatvistic mass?

If that's true then relativistic mass has nothing to do with energy gain, because afterall I could be absolutely still and yet you would still see me as having relativistic mass... in which case what type of mass is it that increases when your energy increases?

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Yeah yeah' date=' agreed... I didn't agree with the infinitely long to become a black hole thing, but sure the whole 'in which reference frame are you a black hole?' thing makes it seem logical that your gravitational field doesn't vary with relativistic mass.

=====

And just a question, in a universe in which there was only me and you, we are moving relative to each other... [b']Am I right in saying that to you I have a relativistic mass, whereas to me you have a relatvistic mass[/b]?

If that's true then relativistic mass has nothing to do with energy gain, because afterall I could be absolutely still and yet you would still see me as having relativistic mass... in which case what type of mass is it that increases when your energy increases?

Yes, and I think there must be an associated additional gravitational force between objects that are not at rest wrt each other.

As for the last bit: you cannot claim you are absolutely at rest, but if you add energy to a body, say heat, then the rest mass of the body increases whereas the rest mass of it's constiuent particles/molecules do not increase but they have a corresponding increase in relativistic mass via their KE. Because it is random it would be considered an increase in the rest mass of the body and not an increase in the relativistic mass or KE of the body as a hole. (I think I have the concept right but as per usual I may be using the terms incorrectly. There may be some increase in rest mass of the particles/molecules, but it will all add up to energy attracting energy gravitationally)

In this way I think there must be an increase in gravitational pull with increased relative velocities. Since you don't increase your "velocities of your respective parts" wrt each other when I go off on my near speed of light trip you should feel no need to implode on youself or become a Black hole.

So what I am saying is if two particles fly past near light speed on parallel courses, say a meter apart, there will be a greater gravitational force between them if they are going in opposite directions (though obviously not for long)

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I know you can't be absolutely still in reality... that is specifically why I stated it (it's a thought experiment!) and why I said it's a universe with only us in it... prove that I'm not at absolute rest , nah you know what I mean, I said it for the sake of simplifying the model.

If you heat something up it's rest mass increases??? Are you sure? I thought rest mass aka invariant mass never changed.

If you heat something up then you're increasing the KE of the particles which is an increase in what mass?

Rest doesn't change, and relativistic, well it depends on your frame of reference.

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I know you can't be absolutely still in reality... that is specifically why I stated it (it's a thought experiment!) and why I said it's a universe with only us in it... prove that I'm not at absolute rest ' date=' nah you know what I mean, I said it for the sake of simplifying the model.

If you heat something up it's rest mass increases??? Are you sure? I thought rest mass aka invariant mass never changed.

If you heat something up then you're increasing the KE of the particles which is an increase in what mass?

Rest doesn't change, and relativistic, well it depends on your frame of reference.[/quote']

Well the idea is by heating an object, hence you are giving it energy, and if gravitational pull depends on energy density then you have a higher gravitational pull.

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If you heat something up it's rest mass increases??? Are you sure? I thought rest mass aka invariant mass never changed.

The fundamental particles for which rest mass is usually used cannot be "heated up" as such, since temperature implies an ensemble of atoms in thermal equilibrium, not an individual particle.

I don't think the mass of such an ensemble could be considered the rest mass, since it is true that the mass would depend on the total energy it has in its rest frame. Imagine you took a snapshot of the system, so you measured all pertinent values at some time: the constituent particle would each have some KE, which would have to transform into some other reference frame, and while total energy is conserved, the value of that energy does not remain the same in different frames. I don't know off the top of my head how the average energy would end up - observers in two frames might not agree on the mass of the system. So it's not an invariant mass; the constituent particles are all in different reference frames. I don't know how much of thermodynamics has been treated relativistically.

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hmm, mass just went to the next level!

So when we say rest mass we would generally be referring to a single particle, not a group or body (many particles).

Whereas when we say relativistic mass we are talking about a body.

So if I said that I have a mass of x then is that rest mass? No. Relativistic mass? No... so what is it???

When talking about a whole body (many particles) what is the name of the mass that doesn't vary (if it isn't rest mass as swansont said) and what is the name of the mass that does vary with energy? (I know that relativistic mass varies according to reference frame)

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