Experimental evidence for effective mass increasing with speed

[Bastion]

What is the best recent experimental evidence for effective mass increase (momentum/velocity) with speed, with experimental details? Searching the web all I find is either very old ones (early 1900s). Or vague generalized statements like (Wikipedia) "Many additional experiments concerning the relativistic energy–momentum relation have been conducted, including measurements of the deflection of electrons, all of them confirming special relativity to high precision." Thanks.

I am new to this forum and in line with its rules I am trying not to repeat a question already asked. I find that Jeremyfiennes original question I.e

Experimental evidence for effective mass increasing with speed”

is the question I want to ask but I am not satisfied with the answers given so far.

I note the Bertozzi experiment and accept it is a cogent demonstration that bodies cannot be made to accelerate to the speed of light and beyond, but what interests me the most is why. In the past, textbooks have suggested that as the kinetic energy of a body increases so does its mass( mass as Newton would think of it) and there reaches a threshold where the increase in mass cancels out the energy input as it approaches c.

However, I also note that in recent years the concept of relativistic mass has become rather unfashionable. Many physicists dispute that a body’s mass increases as its kinectic energy gets greater. So who’s right? Surely using a particle accelerator to make a particle travel at, for example,1/2c( easily doable) one could tell experimentally from the way that particle interacts with other particles whether its rest mass has increased or not.

Perhaps by analyzing the conservation of momentum or by how much damage the interaction between particles causes.( A freight train traveling at the same speed as a fly will have a greater impact because it is more massive).

I hope I am making clear what I am looking for. Surely there is an experimental way to determine whether a body traveling at relativistic speeds does have significantly more mass than a body at rest. If such experiments were carried out what were their results

 

[Drakkith]

However, I also note that in recent years the concept of relativistic mass has become rather unfashionable. Many physicists dispute that a body’s mass increases as its kinectic energy gets greater. So who’s right?

Both are right, because both are saying the same thing just using different words. Relativistic mass means something very specific in the context in which it is used and is not the same as a bodies invariant mass that gives it the gravitation and inertia that is measured in the same frame as the body.

The only thing that has changed is scientists stopped using relativistic mass for the most part. The underlying reasons why a moving body can't be accelerated beyond the speed of light has never changed, which is that the speed of light is a fundamental maximum speed limit and accelerating an object requires an ever increasing amount of energy as velocity increases. The required energy increases in such a way that there simply isn't a finite amount of energy that can be expended to accelerate an object to or above the speed of light.

Edit: Removed a paragraph that was based on a misreading of the OP's post.

 

[Dale]

So who’s right?

They both are, but the few relativistic mass people are using the word “mass” differently than the many invariant mass people. So that engenders confusion.

one could tell experimentally from the way that particle interacts with other particles whether its rest mass has increased or not

Yes, that is experimentally measurable and it is clear that the rest mass does not increase. The “relativistic mass” people do not claim that rest mass increases.

Surely there is an experimental way to determine whether a body traveling at relativistic speeds does have significantly more mass than a body at rest.

Not without defining the word mass. The problem is a disagreement on the definition of the word mass. Nature doesn’t provide definitions for words.

 

[PeterDonis]

Many physicists dispute that a body’s mass increases as its kinectic energy gets greater.

No, they're not "disputing", they're adopting a better and more useful usage of the term "mass", to mean rest mass (or, a better term, invariant mass), not relativistic mass.

So who’s right?

Both the statement that relativistic mass increases with speed relative to a given inertial frame, and the statement that rest mass is invariant and does not change with speed, are right.

Surely using a particle accelerator to make a particle travel at, for example,1/2c( easily doable) one could tell experimentally from the way that particle interacts with other particles whether its rest mass has increased or not.

Yes, and the experimental data shows that rest mass does not increase.

 

[PeterDonis]

No need to look for an experiment, you are living in/on one. The Earth itself is a prime example of the fact that a moving object does not experience an increase in its rest (invariant) mass. A cosmic ray or a particle in a particle collider is traveling at a significant fraction of the speed of light. That means that, from the frame of one of these particles, the Earth is traveling that same speed. If rest mass changed then we'd all be flattened to pancakes due to our extreme velocity relative to objects traveling at high relativistic speeds relative to us.

I don't understand your reasoning here.

 

[Ibix]

Surely there is an experimental way to determine whether a body traveling at relativistic speeds does have significantly more mass than a body at rest.

No, because the problem is two different definitions of mass. If you define "mass" to mean "invariant mass" (modern meaning) then any experiment measuring mass will show that it is invariant. If you define "mass" to mean "relativistic mass" (old meaning) then any experiment measuring mass will show that it varies. There's no experiment that can decide whether "mass" should mean "invariant mass" or "relativistic mass".

We just found that using "relativistic mass" at all leads to more confusion than it solves.

 

[DrGreg]

I note the Bertozzi experiment and accept it is a cogent demonstration that bodies cannot be made to accelerate to the speed of light and beyond, but what interests me the most is why. In the past, textbooks have suggested that as the kinetic energy of a body increases so does its mass( mass as Newton would think of it) and there reaches a threshold where the increase in mass cancels out the energy input as it approaches c.

"Relativistic mass" is just another name for "total energy divided by $c^2$" (which is why we might as well just talk about "energy" instead of "relativistic mass"). Total energy includes kinetic energy. So in fact the increase in relativistic mass always exactly equals the energy input at all speeds, assuming none of the input energy gets lost in heat or other forms of energy. Increase in relativistic mass doesn't just appear from nowhere, we have to supply it as energy. We observe experimentally that no matter how much energy a particle accelerator supplies to a particle, the particle never reaches the speed of light, which helps verify the theory that the energy of a particle (and therefore its relativistic mass) diverges to infinity as its speed approaches $c$.

By the way, the formula for total energy of a particle of rest mass $m$ is
$$E = \frac{mc^2} {\sqrt{ 1 - v^2/c^2} }$$
and it is possible to show that, for small $v$, this approximates to
$$E \approx mc^2 + \tfrac12 mv^2 + \text{terms smaller than }v^4/c^2$$
Also momentum is given by
$$\textbf{p} = \frac{m\textbf{v}} {\sqrt{ 1 - v^2/c^2} }$$
and that's the reason some people thought we should call $M = m / \sqrt{ 1 - v^2/c^2}$ "relativistic mass", as we could continue to use the Newtonian formula $\textbf{p} = M\textbf{v}$. But the modern view is that it should be the other way round, $\textbf{p} = m\textbf{V}$, where $\textbf{V} = \textbf{v} / \sqrt{ 1 - v^2/c^2}$ (which turns out to be the spatial component of a 4D vector).

 

[PeterDonis]

In the past, textbooks have suggested that as the kinetic energy of a body increases so does its mass( mass as Newton would think of it) and there reaches a threshold where the increase in mass cancels out the energy input as it approaches c.

No, nothing "cancels out" anywhere. The kinetic energy of the body continues to increase without bound as its speed increases, asymptotically approaching $c$ but never reaching it.

 

[PeterDonis]

the modern view is that it should be the other way round, $p = mV$, where $V = v / \sqrt{ 1 - v^2/c^2}$ (which turns out to be the spatial component of a 4D vector).

More precisely, in the modern view, $E = m \gamma$ and $\vec{p} = m \gamma \vec{v}$, so $(E, \vec{p}) = m (\gamma, \gamma \vec{v})$ are the time and space parts of a 4-vector, whose invariant norm is $m$.

 

[Drakkith]

I don't understand your reasoning here.

Whoops. I saw 'body at rest' and my brain then converted 'mass' to 'rest mass'. I'll remove that part of my post.

 

[hutchphd]

Whoops. I saw 'body at rest' and my brain then converted 'mass' to 'rest mass'. I'll remove that part of my post.

But as an ironic statement it illustrates nicely why the concept should be consigned to the Historical Dustbin. It is fraught...

 

[vanhees71]

Both are right, because both are saying the same thing just using different words. Relativistic mass means something very specific in the context in which it is used and is not the same as a bodies invariant mass that gives it the gravitation and inertia that is measured in the same frame as the body.

The modern way (i.e., Einstein from at latest 1907 on ;-)) is much more clear than all kinds of "relativsitic mass" which was introduced by Einstein in the very beginning, before the relativistic point-particle mechanics was completely understood. I think this has been achieved with a paper by Planck in 1906 for the first time. If you'd take the relativistic-mass paradigm seriously, you'd have to introduce a direction-dependent mass too, and that's very cumbersome.

The modern way is to formulate point-particle mechanics manifestly covariant with the invariant mass as a scalar parameter. As an intrinsic property of a particle it's defined as a property of that particle in its momentary inertial rest frame and thus by definition a scalar.

The relativistic energy and momentum are defined by the four-velocity of the particle,
$$u^{\mu}=\mathrm{d}_{\tau} x^{\mu},$$
where $\tau$ is the proper time, which is also a scalar, which makes $u^{\mu}$ a four-vector. The relation to coordinate time in an inertial frame of reference is
$$\mathrm{d} \tau = \mathrm{d} t \sqrt{1-\vec{v}^2},$$
where $\vec{v}=\mathrm{d}_t \vec{x}$ is the "coordinate velocity", which is not a covariant quantity.

The energy-momentum four-vector is then defined by
$$p^{\mu} = m u^{\mu}=m \gamma \begin{pmatrix}1 \\ vec{v} \end{pmatrix}, \quad \gamma=\frac{1}{\sqrt{1-\vec{v}^2/c^2}}.$$
where $m=\text{const}$ is the invariant mass of the particle. The time component is $p^0=E/c$, and the relation between energy and momentum is given by the covariant law
$$p_{\mu} p^{\mu}=m^2 c^2.$$
This translates to
$$E=p^0 c=c \sqrt{m^2 c^2 +\vec{p}^2}.$$
The covariant equation of motion is
$$\mathrm{d}_{\tau} p^{\mu} = K^{\mu},$$
where $K^{\mu}$ is the Minkowski four-force. Since $p_{\mu} p^{\mu}=\text{const}$ you have $p_{\mu} \mathrm{d}_{\tau} p^{\mu}=0$, and thus the four-force must fulfill the constraint
$$p_{\mu} K^{\mu}=0.$$
Splitting the equation in temporal and spatial components wrt. a given inertial frame of reference you see that "inertia" in relativistic physics is quantified by energy, not mass.

For more on relativistic mechanics, see the first sections of

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf

To understand the gravitational interaction you have to extend special relativivity to general relativity, as was realized by Einstein already in 1907, but it took him 8 more years to find the final form of general relativity. The result is that not mass is the source of gravitational fields but all forms of energy, momentum, and stress.