Dear Azizul:

Working in meter rather then cm.

Units of planck constant h are J.s = N.m.s

Therefore mass m = h/(λv) = N.m.s / (m^2 / s) = N.s^2 / meter. = Kilogram = unit of mass. Therefore mass does not vary inversely proportional to L^2.

In expression E= (+/-) mc^2. The negative sign does not mean negative energy but negative momentum in my theory. Which means particle antiparticles are flying away in opposite directions.

Vikram,

Planck's constant does not vary when a particle is in motion. Only the wavelength and the velocity of a particle varies. This, in turn, makes mass vary inversely proportional to (length)^-2.

One should remember thst when a body moves or oscillates its frequency does not change .Further Planks constant does not change . Then you do your maths to understand the problems.

Prof Rath

Biswanath,

Make the same particle move with different velocities. Then the particle will have different wavelengths and the de Broglie relation will yield different masses for the same particle. This is the way you figure out that mass varies inversely proportional to length^2.

Remi,

Einstein's E=hv requires defining what is v(neu) for a photon particle. A photon can have different string lengths. That is, a photon may be 2 wavelengths long, 3 wavelengths long and so on. How can a photon with different wavelengths will have the same energy? Photon energy needs to be defined for unit wavelength to overcome this confusion which still persists in E=hv definition.

Azizul:

In relation m = h/(Lambda.v), if you associate Lambda with the length L, then the length corresponding to velocity v is certainly not L but some other value depending on relation V = c^2/v. where V is the velocity of the phase and it is this velocity which is associated with the wavelength Lambda and therefore L. Hence one cannot say that m is inversely proportional to L^2. This can be further explained as follows.

A clock travels from one end of the wavelength to another end with velocity equal to the phase velocity V. In the rest frame of a particle, its wavelength measures Lambda_o = V T_o, where clocks in the rest frame of the particle measures time required for the moving clock to reach the other end as T_0, which is the period of the wave. And the travel time measured in the rest frame of the moving clock is T, which gives the contracted wavelength Lambda = VT. From this we get the relation (Lambda / Lambda_o) = (VT / VT_o) = (hNu_o / hNu) = (E_o / E) = (m_oc^2 / mc^2) = (m_o / m ). This shows that m varies inversely as Lambda. Lorentz transformation equation does not work here.

Another point. In relation m = h/(Lambda v), if we put v = c^2/V and V = Lambda / T we get m = h / Tc^2 From previous derivation we have (Lambda / Lambda_o) = (T / T_o) . Therefore we get m = (hLambda_o) / (LambdaT_oc^2). This shows that m varies inversely as Lambda.

Vikram,

What I have done here is a simple dimension analysis of the de Broglie relation. This relation is very general and describes both phase and group velocities. This relation is derivable without using E=hv and E=mc^2. In your derivation, you have chosen E=hv=hc/lambda instead of hv/lambda. This has allowed to make mass inversely proportional to length. For a particle moving at a velocity less than light velocity, you should obtain:

lambda /lambda_0 = (velocity. m0 / vel0city0. m)

Haque

Rest mass does not change .Read recent work on variation of mass with distance.

Calculate the eigenvalues and compare with others .Then  you will realise , the content of your letter.

Prof Rath

Azizul,

Relations E=hv/lambda, and

lambda /lambda_0 = (velocity. m0 / vel0city0. m)

suggested by you are erroneous expressions. There is only one relative velocity between the coordinate sysytem of the wavelength measured and that of the moving clock. Therefore you cannot have two different values, velocity and velocity_o. Anyway, I stand by what I have said earlier and therefore I rest my arguments here.

Vikram,

Corrections:

E=h.nu=h. velocity / lambda.

Again,lambda1=h. velocity1 /E1

lambda2=h. velocity2 / E2; E1 and E2 are energies.

Remember that in a rest frame the de Broglie relation does not hold since no information about a particle can be obtained. Please think before you respond. Thank you.

Vikram,

Correction: "Remember that in a rest frame" should read "a rest particle". 

Biswanath,

I am talking about variations in mass with wavelength and velocity as prescribed by the de Broglie relation and not mass variation with distance. de Broglie relation suggests that mass varies inversely proportional to (length)^2 and not length for particles moving slower than light velocity. Can you disprove this?  

Azizul:

Your corrected equations says nothing about length contraction. They simply measure particle parameters from two different coordinate systems (cs1 and cs2). If I redo the whole thing in your terminology then it would go as follows:

In cs1 there is a clock1 and an observer and a moving particle in cs1 has a wavelength Lambda1 and period T1 measured by clock1. Another clock2 is in cs2 which is moving at velocity V (which is also the velocity of the phase of the particle in motion.) relative to cs1 in direction parallel to the particle motion. For clock2 to travel from one end of Lambda1 to another end, it takes time T2 measured by clock2. This gives us following identities.

Lambda1 = VT1, Lambda2 = VT2

It is to be noted that particle is neither stationary in cs1, nor in cs2 because particle velocity v is not same as the phase velocity V. This yields the same results which I mentioned earlier.

(Lambda2 / Lambda1) = (VT2 / VT1) = (hNu1/ hNu2) = (E1 / E2) = (m1c^2 / m2c^2) = (m1 / m 2).

Therefore mass is inversely proportional to length.

velocity (V)= frequency(nu). lambda

Thus, lambda=velocity / frequency = velocity. time (VT)

Again, Energy= h. nu = h. velocity (V) / Lambda

Thus, Lambda = h. velocity (V) / Energy (E)

Therefore, Lambda2 / lambda1 = VT2 / VT1

and,

Lambda2 / Lambda1 = (V2 E1 / E2 V1) = ((V2 hNu1) / (V1 hNu2)) and not (hNu1/ hNu2) that you have written.  You would be right if Lambda were = h. c / E. instead of = h. v / E. This is not the case for a particle moving with velocity less than light velocity (c). This is where we need to pay attention.  Thank you for being so sincere.. 

.

Azizul

I notice you have not  taken my suggestions in going through the literature on variation of mass with distance . I hope you will change your mind . With this I stop from my side .

Prof Rath

Azizul:

You are making the same mistake again. There is only one wavelength which is scrutinized for contraction and that is Lambda1 (earlier I designated it as Lambda_o). This same wavelength contracted is Lambda2 (earlier I designated it as Lambda). So we are dealing with only one velocity of the phase of the wave, which is V (or in your terminology V1). Therefore parameter V2 used in your equation is meaningless.

Lambda2 / Lambda1 = (V2 E1 / E2 V1) = ((V2 hNu1) / (V1 hNu2))

(Lambda1 - Lambda2) in your equation does not give length contraction. I think it is right time to drop this discussion.

The purpose of the Lorentz transformation is to relate the coordinates of your frame to a uniformly moving frame. It seems you apply this transformation outside its intended context. As remarked above, while a moving mass is higher,  its rest  mass (it's mass in its own frame) doesn't change. 

James 

You have correctly suggested the frames on rest mass .However one should remember

that material particles having mass are not photons -Hence correct form of Relativity relations involving energy ,de Brogile wave lenth and mass should be used .

Prof Rath

Was Azizul asking about photons? I didn't think so.

Vikram,

I have two questions for you.

1. How can one associate SR with a particle riding a wave. We know that waves have phase That is, the particle you are studying has accelerated motion when traverses a wavelength. We know that a periodic wave describes a circle (non-inertial frame). Again, as much I understand, time in your approach is varying satisfying SR. Would you please elaborate on this accelerated motion and different time ( T, T0) in different frames satisfying SR.

2. Why the phase velocity V has the same value in both frames?  I understand that Lorentz transformations (LT) are for a fixed velocity (as in (1- (v^2 / c^2)). For this reason, LT is not capable of describing mass variation with respect to velocity variation. My emphasis in this thread is: "how mass varies when both velocity and wavelength varies". Leaving out velocity variation creates a situation equivalent to mass = h / (Lambda v), where v is the velocity appearing in LT denominator ((1 - (v^2 / c^2)) and is a constant (since describes only one inertial frame). This is similar to the de Broglie relation: mass = h / (Lambda c), where c is the velocity of light and is a constant. In this situation, we are not studying mass variation with respect to velocity variation. Hence, mass is inversely proportional to length. However, in this discussion thread I am emphasizing on mass variation with respect to both length and velocity. If one does not vary velocity, then, obviously mass is inversely proportional to length. For this reason, your results reflect mass inversely proportional to length.

In this thread I am trying to draw attention to the fact that when both mass and velocity varies, we cannot obtain the energy expression E^2 = p^2 c^2 + m0^2 c^4, since  LT does not describe mass variation with respect to velocity variation of a particle. This is important because, this energy expression is attributed to the existence of negative energy particles (anti-particles) by Dirac.

To All Readers,

Through this posting I have tried to draw your attention to the fact that the mass of a particle varies with both velocity and wavelength. These are experimentally established facts. Davission & Germer experiments have demonstrated that an elementary particle possesses wave character and the wavelength of a particle varies with velocity. Again, from Einstein's extension of Lorentz transformation (LT) to the mass variation, we learn that the mass of a particle increases with increase in velocity. These two aspects of a particle are combined in the de Broglie's wave-particle duality relation where, velocity = h / (Lambda . mass). For this reason, mass variations relation, as proposed by LT, is incomplete in the sense that it does address changes in mass arising from changes in wavelength. In fact, isotropic compression of a particle increases its mass without relying on velocity increase. Velocity does this compression of a particle anisotropically, and thus, increases a particle's mass only in a given direction. Dependence on these two variables (velocity and wavelength), as demonstrated by the de Broglie's wave-particle duality relation, makes variation in mass inversely proportional to (length)^2 in contrast to (length)^-1 by LT for mass variation. This is my way of addressing the deficiency in LT for mass variation.

Why am I discussing this topic? Partly because, so much is riding on the LT for mass variations. This relation gives rise to E=mc^2 and negative energy particles (anti-particles). In fact, E^2 = p^2 c^2 + m0^2 c^4, is derived from the LT for mass variations. Again, this relativistic energy-mass relation is used by Dirac to merge special relativity with quantum mechanics and predict anti-particles. Notably, the rest mass of a quantum particle, in the relativistic mass-energy relation, is always unknown as imposed by the quantum measurement requirement.

Your feedback is welcome.

Azizul:

1. Waves having a phase does not imply accelerated motion. Wave having a phase imply velocity of phase V faster than the speed of light. Accelerated motion comes into picture when the particle velocity v is not constant. Normally in SR dealing with transformations between two coodinate systems moving relative to each other with constant velocity v, we use two constants Beta = B = v/c, and Gamma = G = 1/sqrt(1 - B^2). Then, when it comes to dealing with accelerated motions, physicists use the momentum approach and the Lotrentz Force. You will see particle velocity used in the Bohr atomic model, but subsequently Schrodinger formalism droped this parameter and it is based on momentum p. Lorentz force = dp/dt. This force is not equal to the classical force F = ma which is part of the classical physics in which a is the acceleration. This classical acceleration can also be written in terms of normal and tangential component and the curvature of the trajectory. But this classical picture of acceleration is consider inadequate in Quantum mechanics as well as in General relativity. And no body knew the relation between the Lorentz force and the classical force till I came up with the solution described in the

following article.

http://ptep-online.com/index_files/2015/PP-40-11.PDF

To derive these equations, I treated constants B and G of SR to be variables w.r.t. time. The solution is given in sec.2.1 of above article from eqn.(17) to eqn (27). And then I was able to get an expression for Lorentz invariant acceleration. In eqn.(23) you can see the relation between the Lorentz force and the classical force. In this eqn.23 you can see one additional term called deBroglie force which is completely ignored by physicists. Here particle frequency variation w.r.t. time contributes to the acceleration. This is the reason you don't see any text book literature on accelerated motion and different time ( T, T0) in different frames satisfying SR. While General Relativity uses Lorentz force in defining the four vectors, it has no choice but to ignore the deBroglie force while defining the principle of equivalence. But since the gravitational acceleration and the inertial acceleration get cancelled out in defining this principle, the end result comes close to correct but with one deficiency and that is GR treats gravitational mass equal to inertial mass m_o, but Lorentz invariance would require gravitational mass equal to relativistic mass m. This is why in my theory, gravitational mass is equal to relativistic mass.

2. Why the phase velocity V has the same value in both frames? -- This is the relative velocity between two coordinate systems cs1 and cs2, as well as the phase velocity of particle wave in cs1.

In order to consider mass variation with respect to velocity variation one has to jump from SR to GR (general relativity). Here the theory of Geodesics incoporates the velocity variation. Method described in point 1 is simpler method which I have utilized in my theory "Periodic Relativity." You should also note that De Broglie wavelength definition uses variable (relativistic) mass and variable velocity. So velocity in mass = h / (Lambda v) is definitely not a constant as you say. The reason you cannot obtain energy momentum invariant E^2 = p^2 c^2 + m0^2 c^4

from the Lorentz invariance is discussed in sec.4 of following article.

https://www.researchgate.net/publication/279330500_

Dirac's negative energy particles does not have more than historical significance at present time. Dirac did not use the energy momentum invariant in developing quantum mechanics but rather the linearized version of this equation which is E(psi) = H(psi).

Research Alternative explanation for orbital period decay of a pulsar

What's the point of trying to separate effects due to mass from that due to waves? In Bohmian mechanics both wave and particle motions are determined by the equations.

Javeri,

Thanks for your answer. As I have told Biswanath, make an elementary particle move at different velocities in the same inertial frame. This will produce a set of wavelengths and masses for a set of velocities. Next, assume that the de Broglie relation has its own independent existence and is not derived from E=mc^2 and E=h. nu. Again, we know that, compression of a particle changes its mass and thus, mass is not dependent on velocity. Velocity does the job of compressing a particle anisotropically.  Compression of a particle changes its wavelength as well. Under these circumstances doesn't de Broglie relation show that mass is inversely proportional to (length)^2. What do you think?

Azizul:

I don't have anything more to say on the subject.