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Author Topic: How does mass increase at higher speeds?  (Read 46019 times)

Offline Bill S

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Re: How does mass increase at higher speeds?
« Reply #25 on: 12/12/2012 23:39:21 »
[quote = JP] If you understand mass as a measure of the "resistance" of something to being pushed faster, then it does increase as the speed increases. [/quote]

Assuming that the Higgs particle has really been found, this would seem to herald a new era in physics.  How will it influence our understanding of mass?
 

Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #26 on: 12/12/2012 23:44:50 »
It all depends on how you think of it Chery. Physicists like to find the smallest common nominator for things, and when we (they) talk about mass then that should be 'mass-energy'. Just exchange matter for mass-energy and it will make more sense. Physically at least. So it's not 'more particles' in the matter weighting more after being heated, but there is definitely more 'energy' inside it, as heat.
 

Offline bizerl

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Re: How does mass increase at higher speeds?
« Reply #27 on: 12/12/2012 23:52:34 »
At the risk of departing on an entirely new tangent, does the theoretical "Higgs Boson" come in to consideration? I was led to believe that this is what actually gives something "mass" (whatever that is, now there appears to be different types  :o). Does more energy "create" more Higgs Bosons?

Is the increase in mass phenomenon the same as the length contraction phenomenon, and dependent on how it is measured (or indeed, defined)?

What type of mass does the "m" represent in the good old E=mc2?
 

Offline Phractality

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Re: How does mass increase at higher speeds?
« Reply #28 on: 13/12/2012 00:07:24 »

Do you remember when I showed that a system of 2 photons with opposite velocities has non zero invariant mass?

If the two photons are somehow bound together, the pair would act like a particle. Since we're in the mainstream forum I'll refrain from speculating on what force or field could conceivable bind a pair of photons together. A change in relative velocity, dv, of the center of the pair (whether they're bound or not) is equivalent to looking at the pair from a different reference frame, having velocity dv relative to the center of the pair. SR gives the ratio of the pair's energy and momentum in the two reference frames. At non-relativistic speeds, the momentum ratio for a given velocity difference is the mass of the pair. That's what inertial mass is ...  M = dp/dv.

I don't accept the claim that a photon has no mass. A bound pair of photons (if there is such a thing) would have a rest mass. The radiant energy of the photons would become the rest mass of the pair (or particle).

In the reference frame centered on the pair, the mass would be M = E/c2. In a different reference fame it would be greater by the SR factor, gamma. Mathematically, you would get the same result if the photons are not bound together, but considered as the sum of the two free photons.

If you consider only one photon, it also has different momenta in different reference frames. A change of reference frame gives a change of momentum. If dv is in the direction of v, then dp/dv is the inertial mass of the photon. So a photon has mass. If dv is not parallel to the path of the photon, you have to apply the relativistic form of M = dp/dv. At relativistic speeds, M varies; dp = Mdv +vdM, which, I believe, turns M into a hyperbolic function of v. (Above my pay grade.) Perhaps the mass of an individual photon is different in different directions; I lack the math skill to settle that question.
 

Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #29 on: 13/12/2012 05:52:24 »
mo= rest mass (SR)
m= can be relativistic mass, or rest mass depending, as far as I've seen.

Einstein is said to not have used that formula. It's a abbreviation made later, by others.
Take a look here for one side of the discussion :) Rest Mass Versus Relativistic Mass.

I find the idea of a rest mass simpler, as I don't have to consider accelerations relative different uniform motions, because even though you could, if considering a Higgs field, assume that a acceleration then results in more 'energy' locally expressed, what about the changed uniform motion after the acceleration? Gaining a different (although still 'relative') speed, but not a different energy, locally? All as I interpret relativity naturally.
 

Offline Spacetectonics

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Re: How does mass increase at higher speeds?
« Reply #30 on: 13/12/2012 08:11:35 »
Good question !
Particle gets mass when interacting with higgs field(H.F),higgs field is through out the universe and it is an energy field.
particles considered as wave"behavior" in QM >
wave/Pare. interacting with H.F creating mass >
Nature always wants to be in its lowest state and that is why H.F born>
In QM Wave Interacting with the lowest known state of energy in universe creating mass>
mass is a quantitative measure of an object's resistance to acceleration>
If acceleration reaches C mass will be Infinite.
!!Based on this apparently, argument will be "Resistance"!!
Quantitative measurements are those which involve the collection of numbers.I put this in a post
And yet I  don't know the answer ,as everyone comes up with different solutions!

Cheers
 

Offline JP

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Re: How does mass increase at higher speeds?
« Reply #31 on: 13/12/2012 15:05:26 »
[quote = JP] If you understand mass as a measure of the "resistance" of something to being pushed faster, then it does increase as the speed increases.

Assuming that the Higgs particle has really been found, this would seem to herald a new era in physics.  How will it influence our understanding of mass?
[/quote]

I'm not a Higgs expert, but from what I understand it won't be too revolutionary to have found the standard Higgs.  This is because it's been part of the Standard Model for a while (since the 1960s, I think) and people have spent a lot of time thinking about its implications.  If we find the standard Higgs particle, it validates the model, but doesn't introduce new physics. 

Now, if we find a Higgs that isn't exactly as the model predicts, find more than one Higgs-like particle or don't find it at all, we'd need to retool our theories. It would, however, save people time in looking for alternatives to the Higgs mechanism.

There are other reasons why the Higgs won't completely revolutionize our idea of mass.  As Yor_on mentioned earlier it explains the inertial mass, or resistance to pushing, of simple particles.  But most matter is due to particles bound together with forces, and the energy of these bonds also creates mass which the Higgs doesn't explain (as far as I understand it, at least). 

Another reason is that the Higgs provides a mechanism for inertial mass--the Higgs field makes particles resist changes in velocity.  However the magnitude of a particle's mass is determined by how strongly it interacts with the Higgs field.  There's no theoretical reason why an electron couples to the field with one strength and a muon with another.  We determine the strengths experimentally.  Presumably, if the Higgs is discovered (and even now that there's very strong evidence for it), physicists will start working on theories to explain the interaction strength.
 

Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #32 on: 13/12/2012 15:27:49 »

Do you remember when I showed that a system of 2 photons with opposite velocities has non zero invariant mass?

If the two photons are somehow bound together, the pair would act like a particle.
There is no need of binding and, anyway, two photons don't bind together, but I see what you want to say.
Quote
Since we're in the mainstream forum I'll refrain from speculating on what force or field could conceivable bind a pair of photons together.
Good choice  :)
Quote
A change in relative velocity, dv, of the center of the pair
How do you define the centre in a system of two photons?
Quote
(whether they're bound or not) is equivalent to looking at the pair from a different reference frame, having velocity dv relative to the center of the pair. SR gives the ratio of the pair's energy and momentum in the two reference frames. At non-relativistic speeds, the momentum ratio for a given velocity difference is the mass of the pair. That's what inertial mass is ...  M = dp/dv.
I don't accept the claim that a photon has no mass.
It's not a claim: if it had (invariant) mass, it would have infinite energy.
Quote
A bound pair of photons (if there is such a thing) would have a rest mass.
But even unbound, the system has invariant mass, what do you want more?  :)  If two photons escape one from the other, or if staied close each other as in a sort of atomic system, it wouldn't make difference: the system has/would have invariant mass for the same reason.
« Last Edit: 13/12/2012 15:32:07 by lightarrow »
 

Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #33 on: 13/12/2012 15:30:01 »
What type of mass does the "m" represent in the good old E=mc2?
Invariant mass (the one sometimes also called "rest" mass or "proper" mass).
 

Offline Phractality

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Re: How does mass increase at higher speeds?
« Reply #34 on: 14/12/2012 00:35:27 »
How do you define the centre in a system of two photons?

Tough question! ::) I'll have to ponder this for a while. Let's not even think about the effect of the expansion of space; just confine the discussion to short distances and times where space does not expand appreciably.

For openers, let's consider only inertial reference frames whose relative motion is restricted to the x direction, which is the direction of relative motion of the two photons, which are moving in opposite directions parallel to the x-axis. (Later we may try to generalize to other reference frames.) Let's define the origins of all these reference frames as the point in space-time where the two photons pass closest to one another, at x = 0, t = 0. In all such reference frames, the center of the two-photon system is the origin, but the origins of different reference frames only coincide at the instant when the photons pass one another.

I guess you have to start with a reference frame in which both photons have equal energy and equal and opposite momenta. In that reference frame, the energy of each photon is E, and  the momentum of each photon is p = E/c. Since the momenta are equal and opposite, the momentum of the system is zero.

Next, consider a reference frame moving in the +x direction at .866 c relative to the first reference frame. Gamma = 2; so in this reference frame, the photon moving in the +x direction has energy E'1= E/2, and the other photon has energy E'2 = 2E. Do I have that correct? My brain is about to trip a circuit breaker, here. Someone, please let me know if I got the photons' energy right before I proceed to dig myself into a deeper hole.

My postulate is that, at low velocities, the two photon system has inertial mass M = dp/dv = E/c2. At higher velocities, I suspect that formula turns into a hyperbolic function. Rats! I hate hyperbolic functions!   [xx(]

Thinking ahead: In any one reference frame, the center of the two-photon system is fixed, so a two-photon system can't have a non-zero velocity in an inertial reference frame. However, when you change to another reference frame, you move that center. (This gets into a gray area between SR and GR. I'm not sure I'll be able to handle the math.) A gradual change from one reference frame to another by small increments, dv, will gradually move the center of the system. So the rate of change of reference frame's velocity relative to the first reference frame (dv/dt) imparts motion to the system's center. I don't know yet whether the systems center has acceleration or uniform velocity while the reference frame's velocity is changing at a constant rate. If the momentum of the system changes at the rate dp/dv, that is the inertial mass of the system.
« Last Edit: 14/12/2012 00:41:29 by Phractality »
 

Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #35 on: 14/12/2012 10:25:57 »
How do you define the centre in a system of two photons?

Tough question! ::)
Next, consider a reference frame moving in the +x direction at .866 c relative to the first reference frame. Gamma = 2; so in this reference frame, the photon moving in the +x direction has energy E'1= E/2, and the other photon has energy E'2 = 2E. Do I have that correct?
No. In the first case:

E' = E*sqrt[(1-beta)/(1+beta)] = E*sqrt[(1-sqrt(3)/2)/(1+sqrt(3)/2)] = [2 - sqrt(3)]E ~ 0.268E;

in the second case:

E' = E*sqrt[(1+beta)/(1-beta)] = E*sqrt[(1+sqrt(3)/2)/(1-sqrt(3)/2)] = [2 + sqrt(3)]E ~ 3.73E.
« Last Edit: 24/01/2013 09:10:37 by lightarrow »
 

Offline Phractality

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Re: How does mass increase at higher speeds?
« Reply #36 on: 15/12/2012 04:46:09 »
How do you define the centre in a system of two photons?

Tough question! ::)
Next, consider a reference frame moving in the +x direction at .866 c relative to the first reference frame. Gamma = 2; so in this reference frame, the photon moving in the +x direction has energy E'1= E/2, and the other photon has energy E'2 = 2E. Do I have that correct?
No. In the first case:

E' = sqrt[(1-beta)/(1+beta)] = sqrt[(1-sqrt(3)/2)/(1+sqrt(3)/2)] = 2 - sqrt(3) ~ 0.268E;

in the second case:

E' = sqrt[(1+beta)/(1-beta)] = sqrt[(1+sqrt(3)/2)/(1-sqrt(3)/2)] = 2 + sqrt(3) ~ 3.73E.
Thanks for the correction. I had a feeling I got it wrong. I know how to do the math, but the math corner of my brain was in full revolt.

I'm wondering, now, if I should consider the center of the two-photons to be the center of energy; equivalent to center of mass. Applying inverse square law to the energy of each photon to get a ratio of each photon's distance from the center. My brain hurts; maybe I'll just play solitaire, instead.  :-\
 

Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #37 on: 15/12/2012 15:12:26 »
Thanks for the correction. I had a feeling I got it wrong. I know how to do the math, but the math corner of my brain was in full revolt.

I'm wondering, now, if I should consider the center of the two-photons to be the center of energy; equivalent to center of mass. Applying inverse square law to the energy of each photon to get a ratio of each photon's distance from the center. My brain hurts; maybe I'll just play solitaire, instead.  :-\
You can't localize a photon, so you can't do that.
 

Offline Phractality

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Re: How does mass increase at higher speeds?
« Reply #38 on: 15/12/2012 22:49:01 »
You can't localize a photon, so you can't do that.
Suppose you know that a pair of equal photons were emitted in opposite directions from a certain point in space-time (as determined by detected particles left behind). Define the origin of an inertial frame at that point, with the photons on the x-axis. Then you can assume they exist at points x = ct and x = -ct.

It gets more interesting and challenging when you try to describe those same photons in a different inertial frame at relativistic speed relative to the first frame. If you reflect the two photons off of perfect mirrors to make their paths parallel but not collinear, it gets a bit more challenging. I don't even want to think about accelerating reference frames, but I'm afraid they are necessary to describe the inertia of the two-photon system, which is given by dp/dv (for small values of dv). Accelerating an observer relative to the two photon system is equivalent to accelerating the center (of perhaps center of mass/energy) of the system in the observer's frame. But acceleration takes us out of the realm of SR, and the math gets way to hairy for my puny brain to handle.   :-\
 

Offline Bill S

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Re: How does mass increase at higher speeds?
« Reply #39 on: 19/12/2012 19:13:57 »
Quote from: JP
I'm not a Higgs expert, but from what I understand it won't be too revolutionary to have found the standard Higgs.  This is because it's been part of the Standard Model for a while (since the 1960s, I think) and people have spent a lot of time thinking about its implications.  If we find the standard Higgs particle, it validates the model, but doesn't introduce new physics. 

Point taken, but if we have found the standard Higgs particle, then, presumably, we have found the Higgs field.

If we have found the Higgs field, must we not have co-ordinates for an "absolute space". 

I could be wide of the mark, but the thinking goes something like this:  If we are saying that a particle's mass arises from its motion through the Higgs field, the Higgs field must be stationary, in an absolute sense, or the masses of particles would vary, depending on their direction of movement through the Higgs field.
 

Offline JP

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Re: How does mass increase at higher speeds?
« Reply #40 on: 19/12/2012 20:21:55 »
Bill, the inertial mass of a particle does depend on its motion.  The important bit is that the way the interaction is measured is observer dependent, so that what matters is the relative velocities between observer and observee, which keeps the whole thing in line with special relativity.
 

Offline jopie64

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Re: How does mass increase at higher speeds?
« Reply #41 on: 19/12/2012 23:56:43 »
Yor_on, here's the same question, but in a slightly more extreme form:  If you have a box made of perfect mirrors and you inject some light into it, the box's energy has now increased.  If it's sitting still next to you, its mass increases (by E=mc2, which holds for stationary objects).  So clearly its mass, measured at rest, went up.  Since invariant mass is supposed to not change with reference frame, and the rest frame is a reference frame, its invariant mass also went up.  Additionally, if you try to push it, you'll find its inertial mass went up. 

But photons individually have no mass?  How did it gain mass?

To what I've learned from physics, photons dont have mass, but they do have impulse. Photons can 'push' things when something absorbs or reflects it. The mirrors reflect the photons. So when you push the box and accelerate it a bit, photons push harder against the side you push. So you feel resistance. Even so photons are following the spacetime curve of gravity, so they tend to move more down then up in the box. So more photons reflect to the bottom then to the top of the box. This way the box feels heavier.

My question is, does this increased mass you feel, because of the 'impulse pressure' (or whatever you call it), also generate gravity?
 

Offline bizerl

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Re: How does mass increase at higher speeds?
« Reply #42 on: 20/12/2012 00:42:17 »
To what I've learned from physics, photons dont have mass, but they do have impulse. Photons can 'push' things when something absorbs or reflects it. The mirrors reflect the photons. So when you push the box and accelerate it a bit, photons push harder against the side you push. So you feel resistance. Even so photons are following the spacetime curve of gravity, so they tend to move more down then up in the box. So more photons reflect to the bottom then to the top of the box. This way the box feels heavier.

My question is, does this increased mass you feel, because of the 'impulse pressure' (or whatever you call it), also generate gravity?
I like this idea, however it would only increase the weight of the box if it was already in a gravitational field, but not necessarily the mass.

It seems like one of those ideas that depend on how "mass" is defined and measured.
 

Offline JP

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Re: How does mass increase at higher speeds?
« Reply #43 on: 20/12/2012 02:00:37 »
Yes!  The box is a source of gravity, whether you call it "mass" or not, it certainly contains energy and energy is a source of gravity.
 

Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #44 on: 20/12/2012 05:00:11 »
Quote from: a_dark_knight
But mass creates a gravitational field. Whereas inertia doesn't, in my opinion.
By definition, the quantity which generates a gravitational field is an objects active gravitational mass. Since the active gravitational field of a body increases with the speed of a body it follows that an objects active gravitational mass also increases. Since the active gravitational mass of a body equals the body’s inertial mass it follows that the body’s inertial mass also increases with speed.

Quote from: a_dark_knight
That's the distinction I'm referring to.
You weren’t the person that post was responding to.

Quote from: a_dark_knight
Mass also implies the amount of "stuff" …
The term “matter” does is not well defined and is only be used in a vague sense. Inertia really refers to the idea that Newton referred to when he spoke of “quantity of motion” which refers to the quantity m in the relation p = mv where p is defined as in F = force = dp/dt.

Quote from: a_dark_knight
So does that mean that things moving near the speed of light have a larger gravitational field than they would otherwise?
The faster a body moves the stronger its gravitational field
 

Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #45 on: 20/12/2012 19:46:45 »
But that doesn't count for uniformly moving bodies Pete, right?

Or do you mean that it is strictly observer dependent, and so needs two bodies in relative motion versus each other? But that way 'gravity' would 'fluctuate' with what observer we have in relative motion, relative what body's gravitational field he measures. My thought has been, and still is, that uniform motion no matter its speed, as measured relative something else, has no effect on the gravitational field surrounding it?

Assuming that we have a buildup of gravity depending on uniform motion wreaks havoc to relativity as I think, because to me it implies a 'global speed definition' in where you locally do have a 'absolute definition' of what a speed is, not relative.
 

Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #46 on: 22/12/2012 00:53:32 »
Quote from: yor_on
But that doesn't count for uniformly moving bodies Pete, right?
Sure it does. Why wouldn't it?

Quote from: yor_on
Or do you mean that it is strictly observer dependent, and so needs two bodies in relative motion versus each other?
That question is not clear. Please rephrase. Why d you need two bodies? What function do these bodies serve?

Do you do you think that, for some reason, something that is observer dependant requies two bodies in relative motion?

Quote from: yor_on
But that way 'gravity' would 'fluctuate' with what observer we have in relative motion, relative what body's gravitational field he measures.
I don't understand what you're talking about wqen you speak of "gravity would fluctuate". Do mean that the gravitational field changes with the speed of the source? Its an odd thing but the fact that the strength of a gravitational source depends on the velocity of the source is a fundamental fact in GR but its such a little known fact on these internet forums. I suppose its because so many people who use the concept of mass being independant of its motion in SR also assume that they should also imploy that same definition in the mass of a gravitational source in GR. Just look at how much confuses it causes??? :(

Quote
My thought has been, and still is, that uniform motion no matter its speed, as measured relative something else, has no effect on the gravitational field surrounding it?
Why? What led you to that conclusion? It certainly isn't one that arrives at through calculation, that's for sure.

Consider quantities which define the strength of the gravitational field such as the Christofell symbols or the components of the metric tensor. Since these quantities become velocity dependant when one invokes a coordinate transformation from one inertial frame to another then the new field strengths will become velocity dependant.

Here is a few examples of gravitational fields for which the gravitational field in the "rest frame" is given as well as in a frame moving relative ti the object


 object whose gravitational field is velocity dependant.
http://home.comcast.net/~peter.m.brown/gr/grav_moving_rod.htm
http://home.comcast.net/~peter.m.brown/gr/grav_moving_sheet.htm
http://home.comcast.net/~peter.m.brown/gr/grav_moving_sheet.htm

 

Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #47 on: 22/12/2012 00:59:41 »
Physicists like to find the smallest common nominator for things, and when we (they) talk about mass then that should be 'mass-energy'.
This phrase makes no sense to me at all!  In what sense are you saying that “Physicists like to find the smallest common nominator for things” and what does that have to do with mass-energy? By the way, when one is speaking of mass-energy one is speaking about the kinetic energy of a body that is moving. E.g. If T is the stress-energy-momentum tensor of, say, a gas then T^00 (the energy density) is also referred to as the mass-energy density. T^00 includes kinetic energy and not just rest energy.
 

Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #48 on: 22/12/2012 01:18:39 »
Quote from: jopie64
But photons individually have no mass?  How did it gain mass?
If you keep thinking like this you’re going to keep confusing yourself. I fail to understand why you folks like to make life hard for yourself with this bizarre definition of mass?

Two ways of looking at this; 1) photons have mass m according to E = mc^2. This is the relativistic mass of the photon. The mass of a system of photons is then the sum of the relativistic masses of all the photons.

(2) mass = invariant mass of photons – I.e. for a box of photons the box itself allows there to be a frame of reference in which all the photons are confined. The total energy in the box is the sum of all the energies of all the photons in the box. In the rest frame of the box the total momentum of all the photons is zero. That means that the energy in the box is the rest energy. The mass of the photons in the box is therefore defined through E = mc^2
 

Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #49 on: 22/12/2012 01:20:47 »
What type of mass does the "m" represent in the good old E=mc2?
Invariant mass (the one sometimes also called "rest" mass or "proper" mass).

The term “invariant mass” typically refers to a system of particles and not to a single particle. In anycase the concept of invariant mass can only be used in flat spacetime
 

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Re: How does mass increase at higher speeds?
« Reply #49 on: 22/12/2012 01:20:47 »

 

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