De Broglie Wavelength at rest: λ = h/p = h/0 when v=0?

De Broglie Wavelength is λ = h / p.

So at rest, v=0, and p=mv, so p=0. This means that λ = h/p = h/0 so we run into a divide by 0 issue, or infinite wavelengths for objects at rest.

Is this line of reasoning flawed?

Or can we consider v=1 for rest masses?

Time Dilation is related to v. The faster something moves the slower its internal clock. Lets say at v = c an object experiences no internal time. So its clock we can say it goes to 0.

If v=c, t=1
if v=1, t=c

So we are just using scales from 1->c rather than 0 and infinity. Because time dilates with respect to v, the equation of time and v is of the form t=c/v or vt=c. If v or t become 0 then c would be 0. Hence v and t can only range between 1 and c.

For rest masses we dont see infinite time, if v=0, then time=c/0 = infinite, which is not the case for observed time, so v cannot be 0 at rest.

If c=vt is a constant then time would slow as velocity increases. This is what we observe with time dilation. But forces also cause time dilation, like Gravity. Gravity is a Force, therefore, perhaps Time and Velocity are Forces.

Hence for an object experiencing minimal external Force (Gravity, Movement) it can experience greater rate of Time. We can call this time c, which is the rate of time experienced at the energy level of quantum field fluctuations.

This total rate of Force is c, if the object moves or is under Gravity, the rate of local time decreases accordingly. Reaching a level of no time at velocity c, or for gravity at some threshold, perhaps the event horizon.

The value of v has to be 1 at rest for this to work though. For an object at rest to have velocity =0 would mean its De Broglie wavelength is infinitely long and its time infinitely fast which wouldnt make sense.

Kavi said:

So at rest, v=0, and p=mv, so p=0. This means that λ = h/p = h/0 so we run into a divide by 0 issue, or infinite wavelengths for objects at rest.

That's not a problem. It's only like the wavelength of DC EM waves. Remember, the momentum is zero so your 'particle' can't collide with things.

Kavi said:

c=vt is a constant then time would slow as velocity increases.

You are mixing relativistic and non-relativistic equations and concepts. This will not work.

If you want to use relativistic concepts at all, then I would recommend using the relativistic version of the de Broglie relation, which is exceptionally simple: $$P^\mu = \hbar K^\mu$$ where ##P## is the four-momentum ##P^\mu = (E/c,\vec p)## , and ##K## is the four-wavevector ##K^\mu = (\omega/c,\vec k)##.

In a reference frame where a massive particle is at rest then ##\vec p=0## so ##\vec k = 0## which is a perfectly valid wavevector, and there is no division by zero in the de Broglie relation itself.

Additionally, I think you need to put some numbers in. For example:

Given a baseball with a wavelength 1/1000 the radius of the ball, what is its momentum? Its velocity? At that rate, how many microns will it travel in a million years?