Gravity and it's relationship with time.

[Little Bang]

I made this post in the thread, “What is Time?”, in the hope that someone else would see it’s significance.

 

“Time is relative to the observers frame of reference which we all know. A clock in another moving frame of reference slows with respect to our observer. This goes back to post #580. If we had a one kg block setting on a frictionless surface and apply a force of 1kg.m/sec^2 it will accelerate at 1m/sec^2. The only way to increase this acceleration is to increase the applied force OR slow the observer's clock. Isn't this exactly what happens in a gravity well?”

 

I hope the reader will agree that any particle can be considered it's own clock ( an observer ) and that a clock even one nanometer higher in a gravity well will run slightly faster than a clock one nanometer lower. Suppose we had a frictionless tube, one meter long, whose inside diameter is just large enough to allow a diatomic hydrogen molecule to move freely up and down in the tube. We fill the tube with diatomic hydrogen at STP and stand the tube up perpendicular to the surface of the Earth. Each molecule is moving up and down in the tube colliding with the molecule above and below. Let’s observe the path of a particular molecule which we call B. The molecule above we call A and the one below we call C. We start watching B as it moves down the tube toward C with velocity d/t. The molecule B (clock/observer) will calculate it's momentum, at the instant before the collision with C, using it's clock which is running slightly slower than when it collided with A. B will find it's momentum at C to be greater than the momentum of the collision with A. Doesn't this suggest that gravity is strictly a function of time dilation?

[Little Bang]

Inertial forces can be considered as the same process. Particles accelerated in free space exhibit the same time dilation which would explain why we can't tell the difference between inertial forces and gravitational forces.

[Johndude969]

Forces are the primary cause of time dialtion. However since force is a result of velocity (or gravity 9.8m/s) x mass. Therefore it is reasonable to say that mass is also key in the idea of temporal dilative effects.

[Little Bang]

I agree John. So how do we show that mass is also related to time? If we assume mass to be a wave then we can also show the relativity of mass gain through acceleration.If a mass is accelerated the wavelengths of all it's constituent particles will become shorter thereby increasing the mass.

[Little Bang]

This is not proof that mass is a wave but it is a pretty good indicator.

 

Electron

f = MC^2/h where M is the mass of the electron, h is Planck’s constant

f = (9.109 X 10^-31 Kg)(3 X 10^8 m/sec)^2/6.626 X 10^-34 J

f = 12.37 X 10^19 Hz

Lambda = C/f

Lambda = 3 X 10^8 m/sec/12.37 X 10^19Hz

Lambda = 2.42 X 10^-12 m

Proton

f = MC^2/h where M is the mass of the proton, h is Planck’s constant

f = (1.673 X 10^-27 Kg)(3 X 10^8m/sec)^2/6.626 X 10^-34 J

f = 2.27 X 10^23 Hz

Lambda = 3 X 10^8 m/sec/2.27 X 10^23 Hz

Lambda = 1.32 X 10^-15 m

 

It should be noted here that QM calls the electron a point particle (lacks spatial extension, being zero-dimensional) which eliminates any requirement for showing a relationship between the mass of the proton and electron. Since the proton is 1836 times as massive as the electron then one should be able to multiple the wave length of the proton by that number to get the wave length of the electron.

 

electron’s wavelength = (1.836 X 10^3)(1.32 X 10^-15 m) = 2.42 X 10^-12 m

[Little Bang]

I couldn't get the negative powers to work right using LaTeX. I'll work on that.

[UncleAl]

“Das ist nicht nur nicht richtig, es ist nicht einmal falsch." (re Wolfgang Pauli)

[Little Bang]

So muss bedeuten, dass es eine Chance gibt, es ist richtig.

[modest]

This is not proof that mass is a wave but it is a pretty good indicator.

 

Electron

f = MC^2/h where M is the mass of the electron, h is Planck’s constant

f = (9.109 X 10^-31 Kg)(3 X 10^8 m/sec)^2/6.626 X 10^-34 J

f = 12.37 X 10^19 Hz

 

I don't think you did that quite right.

 

The formula you start with:

[math]f=\frac{mc^2}{h}[/math]

comes from Planck's Hypothesis. The term [math]mc^2[/math] is energy. So, it would more properly look like:

[math]f=\frac{e}{h}[/math]

where the frequency of a photon is equal to the energy of the photon divided by Planck's constant. This is related to the DeBroglie wavelength (which is what I think you're intending to find), but it is not exactly the same. The DeBroglie hypothesis is:

[math]\lambda=\frac{h}{p}[/math]

where [math]\lambda[/math] is wavelength, h is Planck's constant, and p is momentum. If the particle under consideration has zero rest mass (if it is a photon) then the DeBroglie hypothesis becomes the formula you used (Planck's Hypothesis). This can be shown as follows. Starting with DeBroglie's Hypothesis:

[math]\lambda=\frac{h}{p}[/math]

the momentum of a zero rest mass particle is e/c. This can be found with Einstein's energy, mass, momentum formula: [math]e=\sqrt{p^2c^2+m_0^2c^4}[/math] where the term [math](m_0^2c^4)[/math] is zero. Substituting p=e/c into the DeBroglie Hypothesis above we get:

[math]\lambda=\frac{h}{e/c}[/math]

or, rearranged:

[math]\lambda=\frac{hc}{e}[/math]

Since you used the frequency form we need to use the relationship [math]\lambda=c/f[/math]. Subbing that into the wavelength expression above we get:

[math]\frac{c}{f}=\frac{hc}{e}[/math]

solving for f we get:

[math]f=\frac{ce}{ch}[/math]

canceling c,

[math]f=\frac{e}{h}[/math]

And, that is the expression you used. It is Planck's hypothesis. It is the DeBroglie wavelength for a particle with zero rest mass. The numbers you used essentially found the frequency and wavelength for a photon with the energy of 5.1 x 10⁵ electron volts (or 8.19 x 10^-14 Joules).

 

To find the wavelength of an electron you should use:

[math]\lambda=\frac{h}{p}[/math]

where p is the momentum of the electron. Where its velocity is not relativistic, momentum is mass times velocity:

[math]\lambda=\frac{h}{mv}[/math]

So, for example, an electron with a velocity of 1,000 m/s will have a wavelength of 727 nanometers, like so:

[math]\lambda=\frac{6.626 \times 10^{-34}}{(9.109 \times 10^{-31})(1000)} = 0.727 \times 10^{-6} \ m = 727 \ nm[/math]

 

Since the proton is 1836 times as massive as the electron then one should be able to multiple the wave length of the proton by that number to get the wave length of the electron.

 

I agree. Wavelength is inversely proportional to mass. So long as the velocity of the two particles is the same, what you say should hold. In the case of an electron and proton it can be shown like so:

[math]\lambda(1836)=\frac{h}{m(1836)v}[/math]

where you might consider [math]\lambda[/math] to be the wavelength of the proton and m to be the mass of the electron.

 

~modest

[Little Bang]

There is nothing wrong with your logic. My original equations are correct If fh = E = MC^2.

 

Something slightly off topic and this is not directed at any individual but is actually directed at all of us. This thread was started because I began wondering about the equation f = ma being a universal constant. The thought occurred to me that if it varies according to gravitational time dilation then it could explain gravity, inertia, the pioneer anomaly and the rotation curve of galaxies. Instead of questioning a premise that we hold to be a truth we would rather invent something new ( dark energy and dark matter ) to explain the anomalies. Einstein questioned the belief that time was a universal constant and look where that led but alas, I have neither the brains nor the skills to do anything with it.