Interpretation of De Broglie's wavelength ( matter wave ) for macro objects?

[anumah]

The De Broglie's wavelength is given by λ = h / mv
h = 6.626 x 10^(-34) Js

Now, if a macro-object of 6.626 kg is moving at a speed of 10^(-34) m/s then its De Broglie's wavelength comes out to be 1 meter (metre). What does it mean to have 1 meter wavelength for that object? If another object of same mass is moving with double the velocity then its wavelength comes out to be half meter. How an object with 1 meter wavelength is different from an object of 1/2 meter wavelength?

 

[xts]

It doesn't mean anything - it makes no sense to speak about objects traveling at a speed of 10^-34m/s.
Such body would need 20 times more than age of Universe to travel as far as proton diameter.
De Broglie's laws (as the rest of QM) have some accepted range of applicability - it is inappropriate to extrapolate them 20 orders of magnitude beyond.

It is much more inappropriate than metaphores used in pop-science programs, like my favourite (Discovery Channel) showing a snail climbing a grass, with comment: "it would take 10,000 years for this snail to climb to the Moon" - here the extrapolation went only 7 orders of magnitude too far.

Physically real snails do not climb to the Moon, and physical objects do not travel at 10^-34m/s.

 

[anumah]

But if the object was originally at a high speed but is now decelerating then before coming to rest, wouldn't there be a moment when its speed will actually be 10^(-34) m/s ?

(If speed is Not quantized)

 

[xts]

No. There won't be such moment. Your body at this speed would have kinetic energy of 3.313 10^-68J, which leads to time uncertainity of 3 10³³s = 10,000,000,000,000,000 times more than age of Universe - pretty loooong moment.

Any object existing for a shorter time than that must have higher energy. There are no quantum objects "in rest". They must move - otherwise their position and time would be infinitely uncertain. For all real objects we always may limit uncertainity of their position and time to a lab size and detection timescale, and even in thought experiments they must be limited to an age of Universe and Hubble's horizon.

It makes no sense to consider so low speeds - other sense than to illustrate absurdical implications of extrapolation of some rules 20 orders of magnitude beyond their applicability.

Attempt to use De Broglie waves to macroscopic objects always leads to beyond-Universe scale: either in time, distance, energy, or to incredible densities of matter (beyond black hole densities). In both cases we know that Quantum Mechanics is not applicable - in such areas it must be extended by more general theory of Quantum Gravity.

 

[anumah]

Thanks for your reply. It's my first time on this website and I am having a nice experience here. Please give me some more of your precious time:

Let the object be originally moving with velocity 'u'. Its constant deceleration be 'a'. Then for final velocity 'v' = 10^-34m/s, we can calculate time 't' by (v-u)/a=t. This time calculated should be the moment when v=10^-34m/s, but then why it isn't so? If Not 10^-34m/s, then what will be the actual velocity at the time we've calculated?

 

[xts]

Your calculation is based on Newtonian physics: mass, bodies traveling through continuos Cartesian space and time, having always defined their positions, momenta, energies, etc. with absolute precision (or if with limited precision: that was only tue to imperfection of our tools, but in deep view they always had real positions and momenta).

Such approach is not valid under QM view and (for small particles) is contrary to experimental results. Heisenberg's principle and experiments like Young's double slit shows, that we cannot speak about well defined positions and momenta. Of course - for macroscopic objects we can measure frequently (billion times per second) their positions (with a nanometer accuracy) such, that thoise measurements do not disturb significantly next measurements.
But you cannot extrapolate such view ab infinitum: you may speak about bodies traveling at 1 micrometer per second, but not about 10^-34m/s.

You may speak about measuring speed at some moment of time only in sense, that you measure the speed with some finite accuracy, and measurement must last for a while. You may measure a speed of a cannonball in a microsecond osing optical devices. But if your measurement is supposed to last for 10^-30s, you'd have to use really energetic photons - and those photons bouncing from your body would transfer to it more momentum than it had previously.

There is no possible way to measure the speed of 10^-34m/s. This is not a technical problem of our tools - it is fundamentally impossible: such measurement would have to last many orders of magnitude longer than age of Universe. Your decelerating body having such speed at some moment of time is only a mathematical idealisation of reality, made under Newtonian assumptions - which perfectly well describe snooker balls traveling at 1m/s, but are not valid at that scale.

There won't be any speed at that moment! In QM speed is something you may measure (and QM predicts probability density distribution of the measurement outcome), but is not a property you may attribute to a particle regardless of the measurement.

 

[anumah]

Thank you so much!