A couple of questions on mass increase

[alba]

I found these [experimental data](https://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum#Bertozzi_experiment) on mass increase.
> Data of the Bertozzi experiment show close agreement with special
> relativity. Kinetic energy of five electron runs: 0.5, 1, 1.5, 4.5, 15
> MeV (or 1, 2, 3, 9, 30 in mc²). Speed: 0.752, 0.828, 0.922, 0.974, 1.0
> in c (or 0.867, 0.910, 0.960, 0.987, 1 in c²).

- Do you know of any link where I can find more precise experimental data (say accurate to five digits) for mass increase?
For example, in the above table, is 0.5 MeV a rounded figure for 0.511 MeV , the rest mass of an electron? supposing the latter, what is the exact mass increase, is it exacly one mass (+ the usual rest mass), so the total mass is 2.00000 $m_e$?
And, if we give energy equal to 30 m(e) speed is surely not 1, what is the exact value?
- At what speed/energy there is minimum agreement with the SR formula? according to the picture it is about 5-6 MeV, is this correct?

- Can you also specify if "increased mass" means that the body exerts an increased (and exactly proportional) gravitational force? Does it mean that an electron with 1 GeV Ke exerts a pull equal to a proton?

 

[Orodruin]

You really should stop using "relativistic mass" as most physicists have abandoned the concept as redundant. You will still find it in popular science and older textbooks, but it really adds nothing to the discussion and tends to confuse more than it helps - one of the more common misconceptions being that the gravity of the object changes according to the relativistic mass (it does change, just not in accordance to relativistic mass).

Please see https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[alba]

I only mentioned mass increase, is that wrong? did I miss something in your link, does it answer my questions?

 

[Orodruin]

"Mass increase" only occurs if you use the concept of relativistic mass. An object's invariant mass (generally just called "mass" because we no longer use relativistic mass) is an invariant and the same regardless of the state of motion.

 

[alba]

"Mass increase" only occurs if you use the concept of relativistic mass. An object's invariant mass (generally just called "mass" because we no longer use relativistic mass) is an invariant and the same regardless of the state of motion.

Could you re-frame my question in current appropriate terms, and reply to it? My main question is:

what happens if an electron gets 0.511 MeV of energy (or twice or 30 times as much), what is its speed and what is its mass (if it increases, doesn't it?) ,according to recent experiments, and how much they differ from the SR formula.

Thanks

 

[Orodruin]

You can easily compute the speed according to the relativistic relation between speed and total energy. All results are compatible with SR within experimental errors.

 

[alba]

You can easily compute the speed according to the relativistic relation between speed and total energy. All results are compatible with SR within experimental errors.

I know results are compatible with theory, what I am asking is to know the exact difference between theory and experiment in the range between 1 an 20-30 M(e) and where the disagreement is greatest. Do you know or can you direct me to a link?

 

[Orodruin]

where the disagreement is greatest

There is no disagreement. Did you not read what I just wrote?

 

[alba]

There is no disagreement. Did you not read what I just wrote?

Is it possible to have some up-to-date figures or a chart like the one in the wiki article I quoted? can you give me at least one single figure, say,at 5 mc^2, please?

 

[Orodruin]

I do not understand what you are after. The agreement with special relativity is exceptional and modern particle accelerators would not function if this was not the case (not older ones either btw - old fashioned TVs needed to take relativistic effects into account).

 

[alba]

I do not understand what you are after. The agreement with special relativity is exceptional and modern particle accelerators would not function if this was not the case (not older ones either btw - old fashioned TVs needed to take relativistic effects into account).

You keep talking as if I am denying the agreement.

It is so hard to understand I am just asking for a list of figures more recent and accurate than Bertozzi's. (the one I quoted)? What is so strange about it?

Can I ask for the most precise figure avalaible of the speed of an electron with Ke of 9*0.511 Mev? is it exactly 0.974 c? THAT is what I am after!

 

[jtbell]

High-energy particle accelerators like the LHC are designed, and the experiments using them are analyzed, under the assumption that energy and momentum vary with speed in the way that relativity predicts. If the relativistic energy and momentum equations didn't work for proton energies up to 6.5 TeV at least, particle physicists would have noticed it by now.

 

[Orodruin]

You may rest asured that the agreement is good to a large number of significant digits. I do not know where you would find recent data, because this agreement is so good that things we have built would simply not work if it was not.

 

[alba]

High-energy particle accelerators like the LHC are designed, and the experiments using them are analyzed, under the assumption that energy and momentum vary with speed in the way that relativity predicts. If the relativistic energy and momentum equations didn't work for proton energies up to 6.5 TeV at least, particle physicists would have noticed it by now.

Can you tell me what is the greatest energy and highest speed ever reache in such facilitty? Is there a list of data of such experiments there?

 

[jtbell]

Can you tell me what is the greatest energy and highest speed ever reache in such facilitty?

The Large Hadron Collider at CERN has been accelerating protons to 6.5 TeV (6.5 x 10⁶ MeV) since last year. That is the current record.

Can you also specify if "increased mass" means that the body exerts an increased (and exactly proportional) gravitational force?

We had a thread about this a few days ago in our relativity forum:

https://www.physicsforums.com/threads/velocity-of-an-object-and-its-gravitational-pull.861305/

 

[alba]

You may rest asured that the agreement is good to a large number of significant digits. I do not know where you would find recent data, because this agreement is so good that things we have built would simply not work if it was not.

Why do you keep reassuring me, sir? haven't I made myself clear yet?
The chart I cited shows that agreement does vary at different energies, is that Bertozzi wrong? Has that experiment been disproved? Can you provide more recent or accurate data? If you can't , just say so. You haven't tried to answer one single question in my posts

 

[alba]

The Large Hadron Collider at CERN has been accelerating protons to 6.5 TeV (6.5 x 10⁶ MeV) since last year. That is the current record.
/

Thanks, Do you have info regarding electrons, please? If you can't direct me to a link, please tell me the highest energy recorded and the exact speed corresponding to that, please

Thanks for your help

 

[jtbell]

The record for electrons is held by the accelerator that previously occupied the tunnel that is now occupied by the LHC: the Large Electron-Positron Collider (LEP).

https://en.wikipedia.org/wiki/Large_Electron–Positron_Collider

 

[Orodruin]

Why do you keep reassuring me, sir? haven't I made myself clear yet?
The chart I cited shows that agreement does vary at different energies, is that Bertozzi wrong? Has that experiment been disproved? Can you provide more recent or accurate data? If you can't , just say so. You haven't tried to answer one single question in my posts

No, you misinterpret the result. In actuality, the Bertozzi experiment shows good agreement with SR within experimental uncertainty (you cannot expect more than that) and rules out the Newtonian description. That should be your takeaway message.

 

[DrGreg]

See What is the experimental basis of Special Relativity? -- Tests of Relativistic Kinematics and in particular the subsection "Electron Relativistic Mass Variations".

 

[alba]

See What is the experimental basis of Special Relativity? -- Tests of Relativistic Kinematics and in particular the subsection "Electron Relativistic Mass Variations".

Thanks for your link, but I found no data there, just a list of references Icannot access (including bertozzi):

Electron Relativistic Mass Variations
In the early 20th century there was an alternative theory by Abraham that is now little known, because these experiments rejected it in favor of SR. A critical review of the experimental evidence concerning the Lorentz model compared to the Abraham model was given in: Farago and Jannossy, Il Nuovo Cim. Vol5, No 6, pg 1411 (1957).
W. Kaufmann, Nachr. K. Ges. Wiss. Goettingen 2, pg 143 (1901) W. Kaufmann, Nachr. K. Ges. Wiss. Goettingen 3, pg 291 (1902); W. Kaufmann “Die elektromagnetische Masse des Elektrons”, Phys. Zeitschr. 4, pg 54 (1902) W. Kaufmann, Nachr. K. Ges. Wiss. Goettingen 4, pg 90 (1903) W. Kaufmann, “Uber die Konstitution des Elektrons”, Ann. Physik 19 ,495 (1906) and Nachtrag 20, 639–640 (1906); W. Kaufmann, “Uber die Konstitution des Elektrons”, Sitzungsberichte der preussichen Akademie der Wissenschaften, 1905, Part 2. W. Kaufmann, “Uber die Konstitution des Elektrons” Ann. Physik 19 ,495 (1906); W. Kaufmann, “Uber die Konstitution des Elektrons”, Sitzungsberichte der preussichen Akademie der Wissenschaften, 1915, Part A.H. Bucherer, Phyz. Zeitschr. 9 (1908), pg 755; Ber. d. deutschen Phys. Ges. 6 (1908), pg 688. A. Bucherer, “Die experimentelle Bestatigung des Relativitatsprinzips”, Annalen der Physik, 28, 1909E. Hupka, Ann. Phys. 31 (1910), pg 169 Cl. Schaefer and G. Neumann, Phys. Zeitschr. 14 (1913), pg 1117. G. Neumann, “Die träge Masse schnell bewegter Elektronen”, Ann. Phys. 45, pg 529 (1914) Ch.E. Guye and Ch. Lavanchy, Comptes rendus 161 (1915), pg 52Zahn and Spees, Phys. Rev. 53 (1938), pg 511Rogers et al., Physical Review 57 (1940), pg 37 Measurement of m/e and v for three beta-particles (electrons) from Radium. Supports the Lorentz model over the Abraham model by > 10 σ

• W. Bertozzi, Am. J. Phys. 32, 551 (1964).
  Measurements of speed vs. energy for 0.5–15 MeV electrons.
  

 

[Dale]

Are you looking for something like a plot of v as a function of E with error bars?

 

[Mister T]

Can I ask for the most precise figure avalaible of the speed of an electron with Ke of 9*0.511 Mev? is it exactly 0.974 c? THAT is what I am after!

No. It is much closer to 0.995 c.

You cannot have an exact value. There is always an uncertainty associated with every measurement. The rest energy of an electron is not exactly 0.511 MeV.

But, ignoring that for now, let's answer a different question that is as close to the one you're asking as I can come up with, and that has an exact answer. What is the speed of an electron whose kinetic energy is 9 times its rest energy? That electron would have a total energy that is 10 times its rest energy, because total energy equals kinetic energy plus rest energy, so $\gamma$ equals 10.

(Using the antiquated notion of relativistic mass, you would say that such an electron is 10 times heavier than when at rest, but instead it is a more modern usage to say that the total energy is 10 times the rest energy, where rest energy is equivalent to mass. And by mass I mean the ordinary mass, what you might call the rest mass to distinguish it from the relativistic mass.)

Anyway, since $\gamma=(1-\frac{v^2}{c^2})^{-1/2}$ the speed $v$ would be exactly $\sqrt{0.99}c$, or about 0.995$c$.

Modern particle accelerators achieve such high particle energies that it doesn't even make sense to look at the speed, because it's so close to $c$. Or equivalently, the kinetic energy is such a large fraction of the total energy that the rest energy is negligible. The distinctions made in the references you cited have all been been put to bed by modern experiments that impart energies that are orders of magnitude greater.

 

[alba]

Are you looking for something like a plot of v as a function of E with error bars?

Yes, that is exactly what I am looking for
,https://en.wikipedia.org/wiki/File:BertozziExp.svg
something like the old one from 1964 I quoted, (bartozzi) with more precise and up to date figures. Surely those data can't be accurate since they were taken on such a short distance. I remarked above that such plot clearly indicate differnt agreements at different energies

Recent experiments am modern colliders, moreover, test energies much greater than 15 MeV, right?
See my next post, please

 

[alba]

No. It is much closer to 0.995 c.
You cannot have an exact value. .

I am not asking for an exact value, but for an appproximation of 5 digits and surely an experiment at LHC or the like produces such approximation.

- The predicted value for an increase of 9 rest masses is v = 0.994 987 437 (2) with the accuracy of 9 digits or, if we take all 10 digits, we get the value od 10.000 000 09 masses)
- At LHC or at any other sinchrotron, you know the exact energy provided, the magnetic field and the radius r of the collider

I suppose the can get a result with a five-digit accuracy, am I wrong?

 

[Orodruin]

I remarked above that such plot clearly indicate differnt agreements at different energies

And as I have indicated above, this is a misconception and expected only from measurement errors.

Perhaps it would be clearer why you keep beating a dead horse if you told us what you want this data for.

 

[Mister T]

I am not asking for an exact value, but for an appproximation of 5 digits and surely [...]

But you did, and you do again ...

- At LHC or at any other sinchrotron, you know the exact energy provided, the magnetic field and the radius r of the collider

 

[alba]

But you did, and you do again ...

When I say exact I mean accurate to five digits. The assumed value I gave is exact to 9 digits. Do you have any experimental data exact to five digits? If you have, please provide them, if you do not have them, why deny they can possibly exist? Also, until you or anybody provides those experimental data and compares them to the predicted values, how can one state that there is excellent agreement? This attitude is not scientific at all.

 

[Dale]

Yes, that is exactly what I am looking for

I don't have exactly that (plot of E vs v). But I do have a plot of E vs p. Since E, v, and p are so closely related often you get different combinations. This is considered an undergraduate laboratory, so the precision is not >5 digits.

http://arxiv.org/abs/1108.5977

 

[alba]

I don't have exactly that (plot of E vs v). But I do have a plot of E vs p. Since E, v, and p are so closely related often you get different combinations. This is considered an undergraduate laboratory, so the precision is not >5 digits.

Thanks a lot, Dale, a useful response at last. If you find something better, please remember to post it anytime.

I'd appreciate, as long as you are at it, if you cared to explain (with your usula clarity) what is the big deal in abjuring mass increase? It escapes me the point of referring to it with a verbal trick, calling it momentum. If you increase energy from 9 to 99 MeV, velocity increase is negligible, it is always roughly 3*10^10 cm/s, right? the increase of momentum is just an increase of mass, so what is the improvent ? It seems completely unnecessary, since bounf energy is always considered a mass increase in all other contexts, be it heat or glueing energy etc., so why discriminate kinetic energy? Increasing KE the mass of a body increases proportionally, what is the problem?

Thanks

 

[Dale]

I'd appreciate, as long as you are at it, if you cared to explain (with your usula clarity) what is the big deal in abjuring mass increase?

In relativity usually we use units where c=1, so things that differ only by factors of c are considered to be the same thing. This means that relativistic mass is just another name for energy.

On the other hand, the invariant mass is a fundamentally different quantity ($m^2=E^2-p^2$ in units where c=1). This quantity turns out to be very useful.

Thus we have three useful quantities (m, E, p) and three relevant words (mass, energy, momentum). So it makes more sense to assign one word to each quantity than it would make to assign two words to E and none to m.

 

[Nugatory]

what is the big deal in abjuring mass increase?

Over the past century, the way we think about relativistic mechanics has evolved in ways that make the concept of relativistic mass positively harmful less useful. This is somewhat to be expected, as Einstein was working his way through unknown territory - the mathematical formalism of modern relativity was developed after the fact. It's not surprising that with 20/20 hindsight and the benefit of knowing the answer ahead of time, Einstein's 1905-vintage formulation can be improved upon.

Einstein proposed the notion of relativistic mass increase in 1905, perhaps because he was reluctant to sacrifice the three-dimensional $F=\frac{dp}{dt}$, an understandable position in historical context (even if the different behavior of transverse and parallel forces is seriously disconcerting). Only several years after that did Minkowski publish the four-vector mathematical formulation of Einstein's discovery that we use today - and in that formalism relativistic mass is somewhere between unnecessary and downright confusing. It was a full decade after that that Einstein discovered general relativity - and one of the prerequisites for learning GR is unlearning relativistic mass and learning Minkowski's formalism.

Another historical factor is that during the first few decades of the 20th century, some of the most practical laboratory tests of relativistic kinematics involved measuring the acceleration of a moving body when subjected to a transverse force - and this is one of the very few problems that is simplified by the concept of relativistic mass. Nowadays, modern particle accelerators provide far more compelling support for special relativity, so experiments of this sort are no longer an area of active investigation. You'll have noticed that the paper Dale pointed to is about how to do an undergraduate-level demonstration, not about developing any new understanding (and it's been that way for decades - when I did a similar experiment as an undergraduate in the 1970s the proposition being tested was not "Are the predictions of SR supported by experiment?", it was "Is nugatory competent to set up and run an experiment?").

So the answer to your question "what is the big deal in abjuring mass increase?" is, in no particular order:
- It gets in the way of understanding the modern mathematical formalism of SR.
- If you learn it you have to unlearn it before you can progress beyond SR.
- The only problems that it makes easier are no longer especially interesting.
as well as the issues that others have already touched on in this thread.

 

[vanhees71]

Energy is energy and mass is invariant mass and invariant mass only. It is easy to calculate an electrons velocity with a given kinetic energy. First you calculate the total energy, including its rest energy $E_0=mc^2$ ($m$ invariant (!) mass)
$$E=E_0+E_{\text{kin}}.$$
Then the momentum is given by
$$\vec{p}^2 =\frac{E^2}{c^2}-m^2 c^2,$$
and finally it's three-velocity is
$$v=\frac{|\vec{p}| c^2}{E}.$$

 

[vanhees71]

I am not asking for an exact value, but for an appproximation of 5 digits and surely an experiment at LHC or the like produces such approximation.

- The predicted value for an increase of 9 rest masses is v = 0.994 987 437 (2) with the accuracy of 9 digits or, if we take all 10 digits, we get the value od 10.000 000 09 masses)
- At LHC or at any other sinchrotron, you know the exact energy provided, the magnetic field and the radius r of the collider

I suppose the can get a result with a five-digit accuracy, am I wrong?

Now I use natural units $c=\hbar=1$. Then for $E_{\text{kin}}=9m$ you get $E=10m$ and thus $\vec{p}^2=E^2-m^2=99 m^2$ or $|\vec{p}|=\sqrt{99}m$ and $v=|\vec{p}|/E=\sqrt{99}/10 \simeq 0.994987$.