F=ma

[Semon]

true or false?

 

[AndersHermansson]

It's true by definition. In classical mechanics, a force acting on a particle is defined by F=dp/dt, where p is the momentum of the particle.

Since p=mv, we have F=d(mv)/dt=(dm/dt)*v + m*(dv/dt)={if mass is constant}=ma

 

[Neddy Bate]

I am sure that many on this forum would prefer that I do not turn this into another thread on relativity. I will try mny best to restrain myself. That said, one must wonder about the following:

f=ma
a=f/m

Acceleration approaches infinity as mass approaches zero. Where does an infinite acceleration take a zero-mass particle? To an infinite velocity, instantaneously. Does this accurately reflect what light does, for example? One can see why the formula might need some tweaking with respect to c in vacuo.

 

[cato]

AndersHermansson's answer works in "normal" conditions; things often get hairy when we get quantities approaching either infinity or 1/infinity

 

[PhysMachine]

True, F=ma requires that we are not accounting for relativistic effects. If we were, we would have to deploy General Relativity on our accelerating reference frame, and that's a whole new can of worms.

 

[martillo]

I am sure that many on this forum would prefer that I do not turn this into another thread on relativity.

It's inevitable! The only theory that neglects the formula F=ma is Relativity!

The question is wether the mass m really varies with velocity or not.

I propose to take a deep look in Davisson-Germer experiment. Remember? The experiment that relates the De Broglie wave-lenght to the velocity of electrons. It's amazing to note that in this experiment the classic formula for the kinetic energy is used: K=mv2/2 (this is only true if we assume the formula of this thread: F=ma), not the relativistic one: K=(m-m0)c2.

Of course it can be argued that the velocities are too small for relativistic effects appear but the electrons were accelerated only by 50 volts! It would be very easy to accelerate them more and verify what happens with the mass! It's an excellent experiment for both the relativity defenders and who are against.

I'm against Relativity and have studied The Davisson-Germer experiment with a look of some new theories I'm proposing in Physics. Unfortunately it will not be so easy because unexpected results are predicted by them. For example in the original experiment is measured the accelerating voltage and the velocity is deduced by the equation of energies: mv2/2=qV. In the new theories is shown that the voltage V measured by a voltmeter cannot be applied!
I suggest then that a modified version of the experiment should be made: a velocity selector with crossed electric and magnetic fields disposed after the accelerating stage will determine the velocity directly. With this modification the real behavior of mass with velocity can be perfectly determined!
I don't have the resources to construct the apparatus. Does somebody knows who can made it?
It's crucial. It can definitely demonstrate the truth!!!

The new theories I'm proposing are completely available at: A New Light In Physics
I must warn: Not only Einstein was wrong!
To understand them you must have your mind very open and admit that many things we have learned at school may be wrong...

 

[PhysMachine]

To be precise, Newton's Second Law isn't exactly preserved in quantum mechanics; however an analogy called Ehrenfest's Theorem appears in non-relativistic quantum mechanics.

 

[Tom2]

true or false?

The response by Anders is correct. F=dp/dt by definition. If the mass of the system is constant, then F=ma follows.

Acceleration approaches infinity as mass approaches zero. Where does an infinite acceleration take a zero-mass particle? To an infinite velocity, instantaneously.

Not necessarily. Acceleration is the rate of change of velocity with respect to time. An infinite rate of change of a function does not imply that the value of the function is infinite. Look at the unit step function U(t). On the interval (-infinity,0^-) the function is zero, and on (0⁺, +infinity) the function is 1. The derivative of U(t) blows up to infinity at t=0, but the function itself does not blow up to infinity.

Does this accurately reflect what light does, for example?

Of course not. Newton's second law was never meant to apply to light.

One can see why the formula might need some tweaking with respect to c in vacuo.

It doesn't need tweaking at all. One does not describe light with Newton, one describes light with Maxwell.

True, F=ma requires that we are not accounting for relativistic effects.

Not if the 4-vectors F and a are used. And if the mass of the system is not constant, then we can still use F=dp/dT in relativity provided that F and p are 4-vectors and T is the proper time.

If we were, we would have to deploy General Relativity on our accelerating reference frame, and that's a whole new can of worms.

That is not true. Special Relativity is perfectly capable of dealing with forces and accelerations. It's just that in SR accelerated frames are treated on a different footing than inertial frames, whereas in GR all frames are treated on equal footing.

It's inevitable! The only theory that neglects the formula F=ma is Relativity!

That's wrong on 2 counts.

First, it's wrong because F=ma does appear in relativistic dynamics. And second, it's wrong because there are other theories that do not acknowledge F=ma, such as QM and QFT.

The question is wether the mass m really varies with velocity or not.

No, that's not the question. The question is whether the quantities that are really conserved in nature are the 3-momentum and energy or the 4-momentum. Variation of mass with velocity is a matter of interpretation only. Whether one accepts it or rejects it has no bearing on relativistic dynamics.

I propose to take a deep look in Davisson-Germer experiment. Remember? The experiment that relates the De Broglie wave-lenght to the velocity of electrons. It's amazing to note that in this experiment the classic formula for the kinetic energy is used: K=mv2/2 (this is only true if we assume the formula of this thread: F=ma), not the relativistic one: K=(m-m0)c2.

It's not amazing at all, and you cite the reason why yourself. The electrons are decidedly nonrelativistic. Using the nonrelativistic expression for kinetic energy is no more "amazing" than an atomic theorist who uses nonrelativistic quantum mechanics.

Of course it can be argued that the velocities are too small for relativistic effects appear but the electrons were accelerated only by 50 volts! It would be very easy to accelerate them more and verify what happens with the mass! It's an excellent experiment for both the relativity defenders and who are against.

Ask anyone who works at any medium or high energy facility and they will tell you: You have to use relativistic formulae to match observations at relativistic velocities. It's a matter of daily routine for such people.

 

[Neddy Bate]

Not necessarily. Acceleration is the rate of change of velocity with respect to time. An infinite rate of change of a function does not imply that the value of the function is infinite. Look at the unit step function U(t). On the interval (-infinity,0^-) the function is zero, and on (0⁺, +infinity) the function is 1. The derivative of U(t) blows up to infinity at t=0, but the function itself does not blow up to infinity.

That is true, and it has made me realize that, as long as relativistic mass is used, F=ma holds true. Otherwise, all accelerations (both large and small) would eventually converge on an infinite velocity if given enough time. It is the changing relativistic mass that forces the function to be recalculated constantly in order to be accurate.

 

[martillo]

Tom2,

I think I know you from another forum and with another nickname, you say the same things...

Ask anyone who works at any medium or high energy facility and they will tell you: You have to use relativistic formulae to match observations at relativistic velocities. It's a matter of daily routine for such people.

I have another interpretation for the observations you are mentioning.

But I'm talking about Davisson-Germer experiment now. In it electrons are not being accelerated enough although it is easy: with only 50 volts velocities about 1% of C are reached!

The question is why the experiment is not done for more velocities and my answer, as I already said is that unexpected results are obtained.

I insist on the modified version of the experiment I have talked about, is not so complicated to do.

We don't need to discuss, the results of it will be definitive!

Somebody will do it.

 

[Tom2]

I think I know you from another forum and with another nickname, you say the same things...

Yes, you are right.

The question is why the experiment is not done for more velocities and my answer, as I already said is that unexpected results are obtained.

No, "the question" in this thread is "Is F=ma true or false?".

Your question, on the other hand, was first definitively answered by an experiment done by W. Bertozzi, Am. J. Phys. 32, 551 (1964). Kinetic energies and speeds were measured for electrons over an energy range from 0.5 MeV to 15 MeV. Bertozzi found a speed limit of c, and he verified the relativistic kinetic energy relation. Today this is no longer in dispute by anyone who works with accelerators.

 

[martillo]

Tom2,

Your question, on the other hand, was first definitively answered by an experiment done by W. Bertozzi, Am. J. Phys. 32, 551 (1964). Kinetic energies and speeds were measured for electrons over an energy range from 0.5 MeV to 15 MeV. Bertozzi found a speed limit of c, and he verified the relativistic kinetic energy relation. Today this is no longer in dispute by anyone who works with accelerators.

It could be under dispute now because I can question now the value of the energy Bertozzi used. He measured the Kinetic Energy of the electrons through the voltage of the accelerating stage: E=qV.
I argue that this cannot be done for high velocity electrons. I argue that a voltmeter actually cannot measure the electric potential over high energy electrons.

In the new theories I'm proposing the C velocity limit is present but not because of an increase of mass but a decrease of the electric field with velocity by the same factor.

Of course we are not going to discuss my theories here. I only want to say that a new experiment is needed because the old ones can be questioned or can have another interpretation.

 

[Tom2]

It could be under dispute now because I can question now the value of the energy Bertozzi used. He measured the Kinetic Energy of the electrons through the voltage of the accelerating stage: E=qV.
I argue that this cannot be done for high velocity electrons. I argue that a voltmeter actually cannot measure the electric potential over high energy electrons.

On what grounds? The accelerating voltage can be seen to be constant throughout the entire process.

In the new theories I'm proposing the C velocity limit is present but not because of an increase of mass but a decrease of the electric field with velocity by the same factor.

"Mass varying with velocity" is not the explanation for the phenomenon. The explanation is rooted in the postulates of relativity, which lead to the relativistic kinetic energy relation. As I said on the other forum, one is entierly free to accept or reject the idea that mass varies with velocity, and most if not all particle physicists reject it.

 

[martillo]

Tom2,

As I said on the other forum, one is entierly free to accept or reject the idea that mass varies with velocity, and most if not all particle physicists reject it.

We are not free to do that!
The variation (or not variation) of the mass with velocity is an intrinsic property of it. Only one possibility can be true.

Then the modified version of Davisson-Germer I proposed is urgently needed!


You wrote:

On what grounds? The accelerating voltage can be seen to be constant throughout the entire process.

Just only on the possibility that the Electric and Magnetic fields could vary with velocity. In this case the Electric Potential, that mathematically results of the integration of the Electric Field on the path will depend on the velocity of the electrons. The Classic Electric Potential will not apply for high energy electrons and the Potential is not that measured by a voltmeter anymore.

Is just a new possibility to be considered but I strongly reccomend to be taken into account. Nobody has presened this possibility before but I strongly believe in it.

I know I'm nobody and is unprobable that somebody will hear me, even more unprobable to take the propositions seriously enough and have the intention to make such experiment. But who knows? May be somebody in this forum can think about and with enough resources could do it...

 

[Tom2]

We are not free to do that!

Yes, we are. I've explained why at length in the thread at the other forum.

http://www.thescienceforum.com/viewtopic.php?t=196&postdays=0&postorder=asc&start=0

In case anyone else is interested, I'm quantumdude over there and I've explained over and over again how "mass as a function of velocity" is not deducible from the postulates of SR.

Just only on the possibility that the Electric and Magnetic fields could vary with velocity.

The fields vary with velocity in SR as well. Have you compared your expressions with those of SR?

 

[martillo]

Tom2,

The fields vary with velocity in SR as well. Have you compared your expressions with those of SR?

As I say in my text (A New Light In Physics ) the new theories proposes new definitions of the fields that give the same kinematic results as Relativity predictions. Even the equation e=mc2 is valid. The difference is that in my theories there are no Lorentz Transforms, time is absolute (doesn't depend on the referential choosed), The euclidian space is valid, etc.

Everyone can ask then now: "Is it possible all this without any relativistic assumption?" The answer is yes!!!

In case anyone else is interested, I'm quantumdude over there and I've explained over and over again how "mass as a function of velocity" is not deducible from the postulates of SR.

Einstein did it and you say it can't be done?

Then you are proposing a theory different from that of Einstein Relativity Theory!

 

[Tom2]

As I say in my text (A New Light In Physics ) the new theories proposes new definitions of the fields that give the same kinematic results as Relativity predictions. Even the equation e=mc2 is valid. The difference is that in my theories there are no Lorentz Transforms, time is absolute (doesn't depend on the referential choosed), The euclidian space is valid, etc.

Everyone can ask then now: "Is it possible all this without any relativistic assumption?" The answer is yes!!!

The trouble is, without the Lorentz transformation you either have to rewrite Maxwell's equations or affirm that they are different in every inertial frame. There is no reason to do either one of those things.

Einstein did it and you say it can't be done?

Einstein did not deduce the velocity dependence of mass from the postulates of SR, nor did he do it from the Lorentz transformation. What he did was show that such a thing is consistent with relativity, and he explicitly noted that with a different definition of force we would have a different definition of mass. I quoted the relevant part from On the Electrodynamics of Moving Bodies, but it seems that you either don't understand it or you are deliberately twisting the words around.

Then you are proposing a theory different from that of Einstein Relativity Theory!

No, I am not. The trouble here is that you do not understand:

1. Relativity.
2. The difference between logical implication, and logical consistency.

 

[James R]

Short answer to the original question:

f=ma is true in Newtonian mechanics, by definition, where f and a are expressed in three dimensional space.

In relativity (special or general) the equation must be modified. The equation F=mA is true in special relativity provided F is the 4-force, A is the 4-acceleration and m is the rest mass. If we want to extract the usual 3-force (corresponding to Newton) from the 4-force, we get a somewhat complicated expression for f. The 3-force is velocity dependent, as is the 3-acceleration.

 

[geistkiesel]

I am sure that many on this forum would prefer that I do not turn this into another thread on relativity. I will try mny best to restrain myself. That said, one must wonder about the following:

f=ma
a=f/m

Acceleration approaches infinity as mass approaches zero. Where does an infinite acceleration take a zero-mass particle? To an infinite velocity, instantaneously. Does this accurately reflect what light does, for example? One can see why the formula might need some tweaking with respect to c in vacuo.

Neddy Bate,
Actually this term is used in a similar fashion in the engineering world as "specificimpulse" and is a measure of the effeiciency of priopulsion systems, the given force f for the mass flow rate (not indicated here). But yiou can see that f/(dm/dt) where it is understoof that the dm/dt is mass flow rate. How much force is produced by a given mass flow rate tells us to accelrate the vacuum for best results.The units are in seconds, naturally.

Hiwever, Neddy, your question brought out a very interesting sghoertcoming to the Newtonian dp/dt \ mdv/dt +_ v dm/dt. Without the secont term a = f/m makes no sense. Force divided by mass is accelration? The a = f/m statement is ambiguous.
Geistkiesel​

 

[geistkiesel]

It's true by definition. In classical mechanics, a force acting on a particle is defined by F=dp/dt, where p is the momentum of the particle.

Since p=mv, we have F=d(mv)/dt=(dm/dt)*v + m*(dv/dt)={if mass is constant}=ma

The dm/dt term does not imply an increase (or decrease) in mass, it does unambiguously define a mass flow rate.
Geistkiesel​