# Idea of increased mass at relativistic speeds

• mitchellmckain
In summary, this idea of mass increasing at relativistic velocities is an explanatory tool only that comes from the fact that in some equations, the factor gamma = 1/sqrt(1-v^2/c^2) multiplies the mass. However, I think it is a flawed explanatory tool and I never use it in explanations of special relativity. Not only is it completely unnecessary but I think it creates more confusion than understanding.
mitchellmckain
I would like to clarify that this idea that mass increases at relativistic speeds is an explanatory tool only (usually to explain why you cannot exceed the speed of light). It comes from the fact that in some equations, the factor gamma = 1/sqrt(1-v^2/c^2) multiplies the mass. However, I think it is a flawed explanatory tool and I never use it in explanations of special relativity. Not only is it completely unnecessary but I think it creates more confusion than understanding.

The idea of mass increasing at relativistic velocities leads to the unavoidable conclusion that mass is relative just like velocity, which I find absurd. Reading some of the other post I see that it also leads to the conclusion that mass is different in different directions, which is even more absurd. This idea of mass increasing has forced us, for the sake of clarity, to rename the sensible concept of mass as "rest mass" which is not relative and does not change. In short the absurdites and confusion promoted by this idea of increasing mass warrant giving the whole idea a decent burial.

The total energy of a mass m at a relative velocity v and thus lorentz contraction factor gamma is given by E = gamma m c^2.
Well what about kinetic energy? We can extract the classical kinetic energy from a binomial expansion of gamma.
gamma = 1 + .5(v/c)^2 + .375(v/c)^4 + ...
when you put this into the above equation you get
E = m c^2 + .5 m v^2 + .375 m v^4/c^2 + ...
The first term is the famous mass energy, and the second term is the classical kinetic energy.
To handle the relativistic correction, we typically write
E = m c^2 + (gamma-1) m c^2
and we say that the first term is the mass energy (or rest energy) and the second term here is the relativistic kinetic energy, KE = (gamma-1) m c^2

In this case we are obviously not thinking that the mass has increased by a factor of gamma at all, because the energy associated with mass has not changed. To say that the mass has increased by a factor of gamma would mean that all of the energy is a part of the mass and there is no energy of motion, and I don't think this helps in understanding special relativity at all.

I do not even like the idea as an explanation of why you cannot exceed the speed of light because it is too stuck in the thinking of motion as absolute. What I mean is that it puts too much emphasis on one particular relative velocity as if that were special. It is true that increasing the relative velocity with respect to something requires and increasing amount of energy for the same increase in that relative velocity, but I think this misses the point.

I guess the only way to make what I am saying clear is to look at an example. Suppose you accelerate a big ship to 1/2 the speed of light relative to the earth. If you have a medium ship inside the big ship then you can accelerate that medium ship to 1/2 the speed of light relative to the big ship. Then if you have a small ship inside the medium ship you can accelerate the small ship 1/2 the speed of light relative to the medium ship.

The energy requirements of all these acceleration depend on the rest masses of these ships (lets call them mbig, mmed, and msmall) in exactly the same way, using the KE shown above KE = (gamma-1) m c^2.
In each of the three cases gamma = 1/sqrt(1-.25) = 1.1547
First acceleration: energy required was KE = .1547 mbig c^2
Second acceleration: KE = .1547 mmed c^2
Third acceleration: KE = .1547 msmall c^2

If you want to talk about the resulting velocity with respect to the Earth then you need the velocity addition formula v3 = (v1+v2)/(1+ v1 v2/c^2).
So the velocity of the medium ship with respect to the Earth is (c/2+c/2)/(1+.25) = 0.8 c, and the velocity of the small ship with respect to the Earth is (.8 c + .5 c)/(1+ .8x.5) = .92857 c. If you look carefully at the velocity addition formula you will see that if both v1 and v2 are less than c then v3 will be less than c, but if either v1 or v2 is equall to c then v3 will also be c.

The point is there is no increase of mass in this explanation nor should there be. The idea of mass increase promotes a misconception that something changes as you accelerate making an increase of speed more difficult. Absolutely nothing changes. The only limit is on relative velocity at which you see objects receding behind you. It does not even limit how fast you can travel to a destination.

The speed of light is unreachable because it is like an infinite speed in the sense that if you chase after a light beam your accelertion never reduces the relative velocity between you and the light beam you are chasing, the light continues to speed away from you at 3x10^8 m/s. You cannot catch the light no matter how fast you go, just as if the light were traveling infinitely fast. In fact, we know from the relativity of simultaneity that any travel faster than light would be equivalent to arriving at your destination before you left, leading to the same paradoxes as in time travel. Also if you think of the infinite speed as the limiting case where you get to your destination in no time at all, the speed of light is exactly such a limiting case.

P.S. Check out my relativistic flight simulator at www.relspace.astahost.com[/URL]

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mitchellmckain said:
P.S. Check out my relativistic flight simulator at www.relspace.astahost.com[/URL][/QUOTE]

Is the demo free?

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Yes, and it is the same program, only a few features are disabled until you register it. What kind of operating system do you have? Did you find the relspace12-2.exe file and try to run it? What happened when you did?

mitchellmckain said:
I would like to clarify that this idea that mass increases at relativistic speeds is an explanatory tool only (usually to explain why you cannot exceed the speed of light). It comes from the fact that in some equations, the factor gamma = 1/sqrt(1-v^2/c^2) multiplies the mass. However, I think it is a flawed explanatory tool and I never use it in explanations of special relativity. Not only is it completely unnecessary but I think it creates more confusion than understanding.
It it is never completely unnecessary. That phrase has always been suspect to me. I distrust it because the writer always refuses to back himself up. All you have actually done is to regroup terms and given them different names.

Its not as easy as you make it out to be. Once mass is defined it follows whether it is or is not a function of speed. Since we humans have never directly perceived such effects we assumed there was none (way back when). However $m = \gamma m_0$ isn't even always correct. Its for that reason you can't claim that rel-mass and energy are the same thing.

Pete

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This is the clearest explanation that I have ever read about why relativistic mass can be a source of confusion.

The substantive point I gather from this is that mass (unlike, say, size) is an invariant quantity and cannot be thought as directional (unlike size, say again). What is more, mass is not energy (and neither is energy mass, or is it?).

As a non-physicist, the easiest way to rationalize this to myself is to think of the concept of mass as belonging to the pre-Einstein physics. Sorry if this sounds too philosophical or metaphysical, but I say it as I see it.

I don't get the point you're trying to make. What's wrong with relativistic mass? It works and it isn't at all confusing for me.

However, I think it is a flawed explanatory tool and I never use it in explanations of special relativity.

So are you a teacher? Just curious.

What I mean is that it puts too much emphasis on one particular relative velocity as if that were special.

Which velocity?

The idea of mass increase promotes a misconception that something changes as you accelerate making an increase of speed more difficult.

Something does change, it's called inertia.

Entropy said:
What I mean is that it puts too much emphasis on one particular relative velocity as if that were special.
Which velocity?
E.g. velocity relative to an observer, which can be one of many obervers traveling at different velocities, is the OP's point, I believe.

E.g. velocity relative to an observer, which can be one of many obervers traveling at different velocities, is the OP's point, I believe.

And how are we putting emphasis on one observed?

Entropy said:
What's wrong with relativistic mass? It works [...]

In fact, what most people know as the "relativistic mass", works only for a limited number of purposes. Even as inertia, that is, as a proportionality constant between force and acceleration, it works only if the force applied to an object is perpendicular to the direction of the object's motion. If the force is exerted parallel to the direction of the object's motion, the proportionalty is different. Some people have used the terms "transverse mass" and "longitudinal mass" in reference to this.

I don't get the point you're trying to make. What's wrong with relativistic mass? It works and it isn't at all confusing for me.

Relativistic mass is unnecessary, cumbersome and undesirable upon close examination.

How, physically, does increasing the velocity of an object increase its mass relative to you? Where does the mass confrom? To answer a question like that, we would need a better understanding of mass (i.e. speeding up increases the rate at which higgs bosons are involved some how). The point is, it is better to leave mass (which is ill-understood in some sense) as the mysterious concept that it already is ("rest mass", you would say), when we would be much better of just speaking of energy.

When we increase the velocity of an object relative to us, its (relativistic kinetic) energy increases. Energy, in special relativity, is unbounded (can be any real number greater then zero). Of course, velocities cannot exceed c. But for any increase in energy, the velocity increases slightly (there is no question of the form of the energy or where it goes, it is in the motion).

In addition to being kinematically desirable over relativistic mass, relativistic energy is an absolutely necessary part of special relativity (energy-momentum four vector).

How, physically, does increasing the velocity of an object increase its mass relative to you?

Well, when something increases it's speed it gains energy, and energy and mass are interchangeable. So therefore, as you gain speed you also gain mass. That's the simplification of my understanding.

to answer a question like that, we would need a better understanding of mass

Mass is the property of matter that resists changes in motion and is proportional to the gravitational field created by the object. The faster something is moving the more it "resists change in motion" but I'm unsure if any experiments that show objects' gravitational field is effected by it's kenetic energy but I have heard theories about it. Maybe someone else on the forums know more about it.

pmb_phy said:
Its not as easy as you make it out to be. Once mass is defined it follows whether it is or is not a function of speed. Since we humans have never directly perceived such effects we assumed there was none (way back when).
But I am saying that mass is not so defined, but that this idea of increasing mass was concocted as an explanatory tool, which I claim is a failure at explaining anything. It is not a matter of perception but of interpretation.

Entropy said:
I don't get the point you're trying to make. What's wrong with relativistic mass? It works and it isn't at all confusing for me.
Crosson response is good for me. Thanks Crosson.

Entropy said:
So are you a teacher? Just curious.
Yes. I have a masters in physics and I teach physics for ITT Tech.

Entropy said:
Which velocity?
EnumaElish said:
E.g. velocity relative to an observer, which can be one of many obervers traveling at different velocities, is the OP's point, I believe.
Yes, thanks for the help. In my example of the three ships I showed how you can change your reference point rather than keeping the same observer every time. This is natural because it is natural and easier to treat acceleration as relative to the frame you are in at the time.

Entropy said:
Something does change, it's called inertia.
But inertia is a nearly dead and usless concept. It is replaced by the superior concepts of kinetic energy and momentum. And when you say it is changed, for who has it changed? The ship or the observer? In relativity you cannot say which is really moving. Inertia is relative. Besides, it is a fundamental postulate of relativity that nothing important has changed when you go to a different inertial frame.

Entropy said:
Well, when something increases it's speed it gains energy, and energy and mass are interchangeable.
But it is not interchangeable and defining it to be so is not a useful thing to do. That is why we had to invent the term rest mass to recover the original meaning of mass from the confusion created by this flawed explanation. It is rest mass that is used in all the physics I have studied and this relativistic mass has no use at all.

Entropy said:
Mass is the property of matter that resists changes in motion and is proportional to the gravitational field created by the object. The faster something is moving the more it "resists change in motion" but I'm unsure if any experiments that show objects' gravitational field is effected by it's kenetic energy but I have heard theories about it. Maybe someone else on the forums know more about it.
Your first specification of mass as the property which resists changes in motion is undefined because you do not specify an inertial frame. It would be natural to specify the rest frame but then this would define the rest mass. You cannot define mass by interaction with gravity because the photon is massless and yet it is both affected by gravity and has a gravitational field of its own. I think you are caught in a web of oversimplifications. Of course kinetic energy is affected by gravity. Once you choose an inertial frame to work in, gravity interacts with the stress energy momentum tensor which includes kinetic energy and momentum of the object that would be calculated for that inertial frame.

mitchellmckain said:
But I am saying that mass is not so defined, but that this idea of increasing mass was concocted as an explanatory tool, which I claim is a failure at explaining anything. It is not a matter of perception but of interpretation.
Quite wrong, laddy. There are at least two ways to define "mass" and each has its merits. Defined as m = p/v = mass, can be found in many places. Sayang one is the correct one and the other incorrect is nonsense. And I don't really care if paticle physicist is bothered by it or not.

Please provide proof that was increasing mass was concocted as an explanatory tool,

Then prove that
which I claim is a failure at explaining anything. It is not a matter of perception but of interpretation.
Physicists Einstein included, never intentionaly fool someone or "concoct" something for a teaching tool.

I'll await proof for said claims.

Pete

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mitchellmckain said:
The idea of mass increasing at relativistic velocities leads to the unavoidable conclusion that mass is relative just like velocity, which I find absurd.
This is your basic assumption? You don't like it so it must be wrong huh?
Reading some of the other post I see that it also leads to the conclusion that mass is different in different directions, which is even more absurd.
People who make that claim don't know what they are talking about.

So. Did you read my entire paper? My website? Give it a whirl.

Pete

EnumaElish said:
This is the clearest explanation that I have ever read about why relativistic mass can be a source of confusion.

The substantive point I gather from this is that mass (unlike, say, size) is an invariant quantity and cannot be thought as directional (unlike size, say again). What is more, mass is not energy (and neither is energy mass, or is it?).

As a non-physicist, the easiest way to rationalize this to myself is to think of the concept of mass as belonging to the pre-Einstein physics. Sorry if this sounds too philosophical or metaphysical, but I say it as I see it.
In pre-Einstein physics rods don't contract, volumes don't change and there is non-similaneity is gone. Therefore do you wish to get rid of these thinhgs too?

Pete

pmb_phy said:
In pre-Einstein physics rods don't contract, volumes don't change and there is non-similaneity is gone. Therefore do you wish to get rid of these thinhgs too?
This is a question for the OP, I take it.

And when you say it is changed, for who has it changed? The ship or the observer?

You know which is which because atleast one of the objects has been accelerated in its past, in other words it has "felt" a force. This information tells you which object's mass has changed.

But it is not interchangeable and defining it to be so is not a useful thing to do.

$$E = m c^2$$

Your first specification of mass as the property which resists changes in motion is undefined because you do not specify an inertial frame.

It doesn't matter what inertial frame you're in, the mass of an object appears the same to all observers.

photon is massless

Only when at rest. Photons carry energy and therefore mass except when they are at rest.

Entropy said:
$$E = m c^2$$

It doesn't matter what inertial frame you're in, the mass of an object appears the same to all observers.

Invariant mass is the same for all observers. Relativistic mass depends on your frame (add: it's larger when you are moving then when you are standing still). Which mass were you talking about again?

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pervect said:
Invariant mass is the same for all observers. Relativistic mass depends on your frame (add: it's larger when you are moving then when you are standing still). Which mass were you talking about again?
Its amazing how this subject continues forever.

Folks. This has been done for prosperity and left at
http://www.geocities.com/pmb_phy/mass.pdf

I've referred to it many times and guess what? Nobody has read the whole thing I bet. It covers all of these little things in decent detail.

Pete

pmb_phy said:
Its amazing how this subject continues forever.

Yep.

Folks. This has been done for prosperity and left at
http://www.geocities.com/pmb_phy/mass.pdf

I've referred to it many times and guess what? Nobody has read the whole thing I bet. It covers all of these little things in decent detail.

Pete

I don't recall seeing this before, though I see from the date at the top that you wrote it last year.

So far I don't have any major arguments with the first dozen or so pages. (I haven't read the whole thing yet :-)).

There are a few things I do have to say:

Mass as it's usually definied in GR (which is usually taught using the 4-vector approach, not the 3+1 approach as you mention) is probably the most closely related to what you call "active gravitational mass". GR actually has multiple concepts of mass, all of which are closely related - the Bondi mass, the ADM mass, and what could be called the Noether mass (though I've never seen the last name used). The detailed discussion of these concepts of mass in GR really goes beyond the scope of the thread - it's probably useful for people to know that they exist, though.

So far I personally still lean towards teaching students the 4-vector view of relativity and not the 3+1 view, if they are only going to learn one view.

Relativistic mass depends on your frame (add: it's larger when you are moving then when you are standing still).

I mean your mass, relativistic or not, is the same for all observers. Meaning that your mass will appear the same to all observers no matter how fast they are going. Not that it doesn't change when you change velocity, all observers will see the same change in mass as your velocity changes.

Entropy said:
I mean your mass, relativistic or not, is the same for all observers. Meaning that your mass will appear the same to all observers no matter how fast they are going. Not that it doesn't change when you change velocity, all observers will see the same change in mass as your velocity changes.

The gamma in the equation

(relativistic mass) = gamma * (invariant mass)

depends only on relative velocity, gamma = 1/sqrt(1-(v/c)^2).

Thus if you have two observers observing the same mass, one which is stationary relative to some mass, and another which is moving relative to the same mass, the stationary observer will get a different value for "relativistic mass" than the moving obsever.

Sorry but the overwhelming number of responses means I am going to be more selective in responding. If you are addicted to the need to win an argument you may take my failures to respond as concession for your piece of mind, however the truth may be that I simply felt the point was already well explained and that repeating myself would be a waste of time, or even more likely I just did not have time to respond yet.

pmb-phy, I am going to restrict my responses to your posts to a response to the link you provided. The article is new to me and interesting for many reasons. The first is that it shows me that many other physicists have come to the conclusion which I came to independently. The second is that he implies that the academic consensus seems to swinging toward agreement with my conclusion. Peter Brown's first objection that the term is used in papers, is not important because there are other concept (like inertia, and centrifugal force) that have fallen by the wayside but they are still explained as a footnote for just this reason.

On the whole, Peter Brown's paper gives the impression that the exception proves the rule. The fact that the concept is used in general relativity (and only by a faction for that matter) hardly justifies the confusion it generates in teaching special relativity to the beginner. His formulation of the 3+1 view does not not prove anything. As he himself admits, there is a great flexibility in how physics can be presented. Most of the way that physics is presented is simply a result of tradition. But it is absurdly rigid to object to changes to that tradition which can improve the accessibility of physics and simplify the tasks of the educator. While I find his paper to be an interesting exploration of the role and use of mass in relativity I do not see any compelling arguments. I find his arguments to be exercises in rhetoric and not at all convincing. I think his viewpoint and paper is valuable and worth reading for more advanced students of relativity, but I think I must agree with the apparent consensus of the physics community on this topic.

Entropy said:
It doesn't matter what inertial frame you're in, the mass of an object appears the same to all observers.
Only when at rest.
Only if the mass we are talking about is the rest mass.
Entropy said:
Photons carry energy and therefore mass except when they are at rest.
Photons at rest is meaningless. The fact that it is massless means many things including the fact than you cannot use E= gamma m c^2 for the energy.

Ah well sorry, that is all that I have time for right now.

mitchellmckain said:
Photons at rest is meaningless. The fact that it is massless means many things including the fact than you cannot use E= gamma m c^2 for the energy.
That's a "wow." It's obvious when I think about it, yet... How does physics explain this? (I am sure the explanation is obvious to a physicist, too.)

I remember Einstein saying in his book, Relativity, that when an object acquires velocity relatively to some inertial frame of reference, the Lorentz transformations on the electric fields generated by its subatomic particles imply a sort of magnification of the electromagnetic energy in this frame and thus, it is this increase in the internal fields of matter that corresponds to an increase of mass.

I may be remembering INXS but I thought this reasoning seems to be ok.

EnumaElish said:
That's a "wow." It's obvious when I think about it, yet... How does physics explain this? (I am sure the explanation is obvious to a physicist, too.)
The photon's energy is given by E = hv, where h is Planks constant and v is the frequency. It has momentum too, you just cannot use mass to calculate it. Its momentum is given by p = h/wavelength.

The usual equation for mass m^2 = E^2/c^4 - p^2/c^2 is equal to zero in the case of the photon because the wavelength times the frequency equals the speed of light c.
Or in other words E = hv = hc/wavelength.
So the equation for mass becomes,
m^2 = (hc/wavelength)^2/c^4 - (h/wavelength)^2/c^2 = 0.

Here is an interesting link http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html
Which discusses the question of whether a photon has mass.

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Entropy said:
You know which is which because atleast one of the objects has been accelerated in its past, in other words it has "felt" a force. This information tells you which object's mass has changed.

What was the purpose of stating $$E = m c^2$$??

Pete

What was the purpose of stating [e=mc^2].

What? Stated it where?

Entropy said:
What? Stated it where?
In post #17

Pete

Entropy said:
You know which is which because atleast one of the objects has been accelerated in its past, in other words it has "felt" a force. This information tells you which object's mass has changed.

$$E = m c^2$$

It doesn't matter what inertial frame you're in, the mass of an object appears the same to all observers.

Only when at rest. Photons carry energy and therefore mass except when they are at rest.

Even if a particle is neither moving nor part of a bound system, it has an associated energy, simply because of its mass. This is called the particle's rest energy, and it is related to the particle's rest mass as

rest energy = (rest mass)· c2

This in Einstein theory. E=Mc^2 has many fargilities as I already said in another threads.

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In post #17

Then why did you quote something different from that post?

Does it help to consider relativistic mass equation as a tool with which one can explain the different perceptions regarding the momentum of a particle when observed from two different inertial frames?

By way of example consider two inertial frames one of which we label the "rest" frame. For convenience we can then just call the other frame the "inertial" frame which travels at a velocity of u, in relation to the the rest frame.

Observers in each of the frames are observing a particle which has a velocity of v according to the rest frame and v' according to the inertial frame. Therefore, the particle has momentum of p = mv according to the rest frame and p' = m'v' according to the inertial frame.

How does the observer in either frame explain how a single object can have a different momentum in another frame?

The terms I've used above give a clue - there are equations for translation of velocities between inertial frames so we can work out what v' is in terms of v and u (and c). We can then say that either there is "relativistic momentum" so that there is actually a real difference in the momentum (and hence energy) of a single particle when observed from two perspectives, or there is a difference in the mass as perceived from each of the frames and use the equations mentioned above to work out what that difference is - that is values of m and m' so that momentum is invariant.

The law of conservation of momentum is axiomatic, there is no reason to think that it is false and plenty to support it being true. It therefore also seems sensible to say that you can't change the momentum of a particle by just changing your perspective in respect to it - the implication is that something odd is happening with the mass, which is precisely what standard relativity tells us.

neopolitan

neopolitan said:
Does it help to consider relativistic mass equation as a tool with which one can explain the different perceptions regarding the momentum of a particle when observed from two different inertial frames?

By way of example consider two inertial frames one of which we label the "rest" frame. For convenience we can then just call the other frame the "inertial" frame which travels at a velocity of u, in relation to the the rest frame.

Observers in each of the frames are observing a particle which has a velocity of v according to the rest frame and v' according to the inertial frame. Therefore, the particle has momentum of p = mv according to the rest frame and p' = m'v' according to the inertial frame.

How does the observer in either frame explain how a single object can have a different momentum in another frame?

The terms I've used above give a clue - there are equations for translation of velocities between inertial frames so we can work out what v' is in terms of v and u (and c). We can then say that either there is "relativistic momentum" so that there is actually a real difference in the momentum (and hence energy) of a single particle when observed from two perspectives, or there is a difference in the mass as perceived from each of the frames and use the equations mentioned above to work out what that difference is - that is values of m and m' so that momentum is invariant.

The law of conservation of momentum is axiomatic, there is no reason to think that it is false and plenty to support it being true. It therefore also seems sensible to say that you can't change the momentum of a particle by just changing your perspective in respect to it - the implication is that something odd is happening with the mass, which is precisely what standard relativity tells us.

neopolitan

I'm not sure what exactly you're saying. The momentum is different from a different perspective... This is true pre-relativity and post-relativity.

Entropy said:
Then why did you quote something different from that post?
What does that have to do with my question? I was simply asking why you posted it in that post.

If you need to know why I didn't quote something else from there its because it was only that equation that I couldn't see why you made it where you did.

Pete

If you need to know why I didn't quote something else from there its because it was only that equation that I couldn't see why you made it where you did.

Because mass can be converted to energy.

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