Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

True statements you made:

1.) Mass resists speeding up or slowing down (by its inertia)

2.) The gamma factor in special relativity is the mathematical device that enforces the universal speed limit .

Incorrect statements you made:

1.) Einstein (i.e., special relativity) says that acceleration creates more mass by the gamma factor.

2.) An accelerating frame slows time

3.) Mass resists changes in the time metric.

Faults in your reasoning include:

1.) When you refer to the "increase in mass" due to the increase in the gamma factor, you are no doubt referring to 3-dimensional momentum in special relativity.  At ordinary speeds, the 3D momentum is .  At relativistic speeds, the 3D momentum is .  The gamma factor is a number that is nearly equal to 1 at ordinary speeds and increases to a vertical asymptote at as the speed of the particle is increased.  Thus it looks like the mass has increased by a factor of , and calling the "effective mass" of the particle makes some sense in this context.  But it is not a true increase in the mass; the mass of all fundamental particles is invariant in all inertial frames.  In a relativistic sense, the mass can be defined to simply be the rest energy: .  Since it is defined based on the frame in which the particle is at rest, the mass, like proper time, is invariant in all inertial frames.  It is true that it takes more and more energy to accelerate a massive particle the closer its speed gets to , but this again does not mean its mass is increasing.  This is because Newton's second law does not hold in relativity.  It is only valid at nonrelativistic speeds.  Relativistic mechanics is described not by Newton's laws but by the relativistic Lagrangian formalism.

2.) Relativistic effects, such as time dilation and length contraction, do not require the frame to be accelerating, but only to be moving.  Accelerating frames are by definition noninertial frames, and physics in noninertial frames is quite different from physics in inertial frames.  You will get transformations on both the space and time coordinates in an accelerating frame, but the behavior will be far more complicated than that of ordinary inertial frames.

3.) Time dilation is not a change in the time metric; it is simply an effect of the ordinary, static metric.  To see how the metric changes with time as mass (or, more generally, energy density) moves around, you must solve Einstein's field equations.  This is done in general relativity; in special relativity,  the effects of mass/energy density on the curvature of the metric is neglected.

These may be your beliefs, but they are not the predictions of special and general relativity.  You're welcome to your own beliefs, but they do not describe how the physical world works.  Special and general relativity make specific predictions about how the world should behave that correctly predict the results of experiments.  That's why relativity is right and you are wrong in the only sense that matters - the sense of predicting the results of experiments.  If your theory can precisely explain an experiment that relativity cannot, then you have improved upon relativity.  If not, then you're not doing physics, you're doing mysticism.

Chris wrote:

Mass increases during acceleration.

In a previous post, I suggested that you read Taylor's and Wheeler's "Exploring Black Holes." There is a great section that discusses the misconception that mass increases with increased speed. Mass is invariant.

I thought you were a big fan of Wheeler. Why won't you read one of his books?

Mass increases in a nongravitational accelerating frame by Gamma.

You are talking rest mass not relativistic mass due to motion as described by Einstein.


Mass and steady motion are undectable after acceleration. Mass is undectable until a force is applied. F=MA

Mitch Raemsch

Last edited by Nicholas (2008-05-15 02:16:18)

Nicholas wrote:

You are talking rest mass not relativistic mass due to motion as described by Einstein.

If you're talking about the theory of special relativity due to Einstein, then cite your sources so that we can have a transparent discussion.  If you're talking about a mystical theory of your own, then you are not bound by the confines of rationality or consistency.

Nicholas wrote:

Have you not read Albert Einstein say that the train gets heavier during acceleration by Gamma.

No, I haven't.  Have you read it anywhere?  If so, where?

Nicholas wrote:

I cannot help you if you do not know that motion is a form of energy. Let's be clear about that.

Motion is most definitely a form of energy.  The difference is that Newton and Einstein disagree on how much energy:

Nicholas wrote:

Show me where I am wrong.

Chris has already given you one reference by Wheeler.  I'll give you another one from a standard textbook.  I quote the following from Taylor, Zafiratos, and Dubson, Modern Physics for Scientists and Engineers, 2nd Ed., 2004, Prentice Hall, Upper Saddle River, NJ, p.51:

Taylor wrote:

Some physicists like to think of the relativistic momentum as the product of and , which they write as

               (2.7)

(Note that these vectors are 4-vectors.)

where

      (2.8)

The quantity is called the variable mass since, unlike the rest mass , it varies with the body's speed .  The form (2.7) has the advantage of making the relativistic momentum look more like its nonrelativistic counterpart .  On the other hand, it is not always a good idea to give two ideas the appearance of similarity when they are in truth different.  Further, the introduction of the variable mass does not achieve a complete parallel with classical mechanics.  For example, we will see that the quantity is not the correct expression for the relativistic kinetic energy and that the equation is not the correct relativistic form of Newton's second law.  For these reasons, we will not use the notion of variable mass in this book.

As I said before, Newton's second law F=ma does not hold in relativistic mechanics.  So you're wrong because you're taking an oversimplified statement ("you can in some ways think of as a variable mass") to unjustified conclusions based on applying classical mechanics (F=ma) to relativity.  At best, the variable mass does not mean what you think it means.

Nicholas wrote:

Chris why do you argue that acceleration doesn't create more mass?

Matt and I have presented two sources that say mass is invariant. There are many more.

If you'd like, you can think in terms of a relativistic "variable mass", but by doing so you are re-defining the concept of mass. Many modern physics texts do this; unfortunately, because it leads to exactly this type of misconception.  But -- and this is a BIG but -- you CANNOT simply plug this variable mass back into Newtonian equations. If you do, then you will get results that contradict the special theory.

The fact is, the special theory of relativity does not claim mass increases with increasing velocity. I'm still waiting to hear your source for claiming otherwise, because I assure you that you will not find it in Einstein's writings.

For example, let's assume that the mass changes. I am riding on a baseball moving close to the speed of light relative to some other inertial frame that you sit inside. In my frame, the baseball is not moving. In your frame, the baseball and myself are moving close to the speed of light. In my frame, the mass would be the rest mass. In your frame, the total mass would be significantly larger. In my frame, I would experience a small gravitational attraction to the ball. In your frame, the gravitational attraction would be immense! How can the gravitational force be both small and large at the same time and not contradict the general theory?

What I will grant you, though, is that this is a common misconception. So I cannot fault you too much for making this claim.

Nicholas wrote:

I am sorry but mass increase is absolute by the math of the universe (or Gamma for velocity.)

That may be your belief, but it is not the prediction of special relativity, the theory proposed by your much-touted Einstein.  You can say whatever you want, but Einstein says that the effect you're talking about is only an apparent increase in mass and not a true one.  Again, you're welcome to believe whatever you want.  But this is the theory that correctly predicts the behavior of relativistic effects.  If you disbelieve its tenets, then you must find alternate explanations for a great deal of physical phenomena.

M@Man wrote:

Nicholas wrote:

I am sorry but mass increase is absolute by the math of the universe (or Gamma for velocity.)

That may be your belief, but it is not the prediction of special relativity, the theory proposed by your much-touted Einstein.  You can say whatever you want, but Einstein says that the effect you're talking about is only an apparent increase in mass and not a true one.  Again, you're welcome to believe whatever you want.  But this is the theory that correctly predicts the behavior of relativistic effects.  If you disbelieve its tenets, then you must find alternate explanations for a great deal of physical phenomena.

Motion has energy and the increase in mass is a true one.

Nicholas wrote:

Energy of motion and therefore mass goes up.

You can believe this and repeat it all you want, but the behavior of the physical world - which is what physicists care about - didn't ask for your opinion.  Observations of the behavior of physical systems lead us directly to the theories of special and general relativity as described by Einstein.  Alternative theories put forward by you do not correctly predict the behavior of physical systems and are logically inconsistent. 

You must always differentiate between things you believe to be true and things that are experimentally shown to be true.  The point is not to help you build a mystical philosophy about the world that makes you feel clever, but to ultimately compile a list of rules that the universe is experimentally shown to obey.

Nicholas wrote:

There is no more argument on your point.

You've never offered an argument on the point.  You've merely restated a wrong conclusion, drawn from vacuous sources, offered without justification.

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