# The Wavelength of Earth

1. Aug 11, 2012

### student34

I got this from my grade 12 physics notes. It says that Earth, having a mass of 6.0x10^25kg and a speed of 3.0x10^4 m/s, when plugged into the wavelength equation λ=h/(mu) (where u is speed), has a wavelength of 4x10^-63 m. Then, does this mean it has a frequency of 7.5x10^70 Hz? If so, then it also means that the Earth's wave's energy is 4.97x10^37 J.

My main confusion is that I always hear scientists say that quantum mechanics has practically no effect on the macroscopic world (except for some things like bucky balls and superconductors). I would think that a wave with the energy of 4.97x10^37 J would have to have an enormous effect on something or even the Earth in an interference pattern using the Sun and other planets as its own really large double slit experiment.

2. Aug 12, 2012

### Staff: Mentor

Do not expect that quantum-mechanical formulas give meaningful results for macroscopic objects. Sometimes they do, in most of the cases they do not. This frequency would be an oscillation of a wave-function of a particle with the mass of earth, and the energy would be the kinetic (?) energy of the particle. Here, it should be the kinetic energy of earth. Sure, that is relevant, independent of quantum mechanics.

For a double-slit experiment, you would need slits with a size of ~10^(-63)m. Good luck building them. And good luck shooting earth through.

Edit: I checked the numbers, the kinetic energy (with respect to sun) is 2.6*10^33 J and the total (relativistic) energy is 5.4*10^41 J. No idea where your number comes from.

3. Aug 12, 2012

### ZapperZ

Staff Emeritus
You need to understand that just because you can calculate something, and get a number, does not mean that the result is physically meaningful. For example, when we solve the electrostatic problem of a charge in front of an infinite conducting plane using the image method, I can also calculate the field inside the conductor. Now, is there really such a field inside that conductor? No. But the result certain allows me to find such a thing inside the conductor! That part of the result is purely unphysical!

In your exercise, it should come with a bunch of caveat as assumptions: you assume that the whole earth is one, quantum entity (which it isn't). Consequently, you assume that every part of the earth is in coherence with each other.

In the observation of macroscopic manifestation of QM, you will notice that the "macroscopic object" is in complete coherence with all parts of itself. The buckyball experiments that showed the double-slit effects had to be done at extremely low temperature, so that every part of the buckyball are in coherence with each other. The experiments involving a superconductor is patently obvious - a supercurrent is, by definition, a single entity. All the charges that make up the supercurrent are in a single, coherent state!

Producing a "large", coherent object is the single, biggest obstacle to observing QM effect at the macroscopic scale. It isn't easy, as anyone can see by reading all of the relevant experiments. The earth is not even close to being such a thing.

Zz.

4. Aug 12, 2012

### sophiecentaur

@ student34
Be kind to your Teacher when you hit him with this (I can see you, in my mind's eye, printing off the above passage in preparation for a game-set-match, next lesson!) He wasn't seriously suggesting an experiment to demonstrate the de Broglie wavelength of Earth!

5. Aug 12, 2012

### ZapperZ

Staff Emeritus
Also note that sophiecentaur was not being literal about hitting your Teacher. You should not physically hit anyone with this. :)

BTW, I would use, and HAD used, this very same argument when people asked (on numerous occasions) on whether humans or a tennis ball can tunnel through a wall.

Zz.

6. Aug 12, 2012

### sophiecentaur

Do NOT wrap it round an iron bar!

7. Aug 12, 2012

### mikeph

I'm not sure I understand what it means for each part of a system to not be coherent with one another. Does that mean the Earth doesn't have a wavefunction, or that the wavefunction is lacking some special property?

I've heard people utilise the idea of a de Broglie wavelength for a non-rigorous description of a neutron star. Is that a coherent object?

8. Aug 12, 2012

### Staff: Mentor

This depends on the interpretation.

Yes. It lacks coherence.

Are you sure the concept is used for the whole neutron star? I would expect it as description of the neutrons inside.

The teacher? The tennis ball? The wall? :D

9. Aug 12, 2012

### mikeph

That must have been it. The explanation was that the wavelength of a neutron is equivalent to the size of the star itself, so.... that allowed us to deduce something else. Hand-wavy arguments never seem to stick in my brain.

10. Aug 12, 2012

### student34

With or without one's interpretation, what physically happens if we replaced a particle with Earth in the double slit experiment? Will Earth interfere with its own wavelength of 4x10^-63m or not? How powerful is this wavelength? What would it do to the Earth?

11. Aug 12, 2012

### Staff: Mentor

Well, it is not as hand-wavy as it might look like. Neutrons in a neutron star have an effective potential which depends on gravity only - the surface region (where the strong interaction depends on the position) is small compared to the whole volume. Therefore, you can treat them as fermi gas, and calculate how many neutrons fit within a specific volume (for a "cold" neutron star). If I remember correctly, you get some useful results based on this calculation.

@student34: If you could magically shield earth from any interaction with the environment (this includes single photons and even gravitational interaction with any nearby object), and emit an extremely slow earth to get some reasonable wave length (at least comparable with the size of earth), and wait for some 10^30 years or whatever (as the earth is really slow), you could in theory perform a double-slit experiment. However, it is impossible to shield earth as good as the experiment would require.

12. Aug 12, 2012

Staff Emeritus
You really need to read some of the replies.

How do you get a 8000 mile earth through a slit that small?

13. Aug 12, 2012

### student34

I did, but no one has replied to any of my questions in the OP.

14. Aug 13, 2012

### ZapperZ

Staff Emeritus
It has been answered, several times. Calculations were done to show you just how SMALL the slits should be and how they would NOT fit the earth. I have shown you why your question on what the effect would look like is similar to asking "When did you stop beating your wife?", and why such an effect would not happen to such a macroscopic object.

But obviously, these all fell on deaf ears and were a waste of time.

Zz.

15. Aug 13, 2012

### Staff: Mentor

That was the point in "And good luck shooting earth through."

If you do not understand the answers, tell us which part troubles you. But do not assume that we all posted irrelevant stuff, please.

16. Aug 13, 2012

### student34

Can't any wave interfere with itself outside of an exact double slit experiment?

17. Aug 13, 2012

### Staff: Mentor

The wave has to have some region in phase space where it overlaps. If your earth is in completely different regions of phase space (because it interacted with the environment somehow), you will not see interference.

18. Aug 13, 2012

### sophiecentaur

The two slits experiment is just the most simple example of interference.

Everything you see is the result of waves interfering with each other (diffraction) and producing a pattern*. Most of the optics you see are designed (usually by being big enough) to produce an image of an object but when the apertures are small compared with the wavelength, and you magnify the image enough you can see fringes around it.
*And I mean EVERYTHING. Lenses, mirrors, eyes, radio antennae. You name it.

19. Aug 13, 2012

### student34

But wouldn't it be unlikely that it would never overlap given the Sun, Moon and other planets?

20. Aug 14, 2012

Staff Emeritus
How far away is the sun in units of 10-64 meters?

21. Aug 14, 2012

### Darwin123

Composite particles, also called corporate bodies, only satisfy the de Broglie relations if the particles that they are comprised of are entangled. In order for the composite particle to have a characteristic wavelength or a characteristic frequency, the waves of the individual particles that comprise the corporate body have to be in phase.
When scientists do diffraction experiments on composite particles, they usually try to prepare the composite particle so that it is in its ground state. The ground state of a corporate particle is automatically an entangled state of its individual components.
The earth is not an entangled state of atoms. The de Broglie waves of the atoms that comprise the earth are out of phase. Thus, there is no characteristic wavelength or characteristic frequency.
If one were to bounce the earth off a very large diffraction grating with very fine lines, each atom would diffract in a different direction. The earth as a solid body would be destroyed.
Furthermore, the de Broglie wavelength of the entire earth is much shorter than the distance between separate atoms of the earth. If the wavelength of the entire earth were longer than the bond lengths, then maybe the atoms of the earth would diffract together. However, this is not possible at the high temperatures of the earth.
Maybe if one cooled the earth to absolute zero temperature, so that it is in its ground state, the atoms of the earth would be in an entangled state. Then the atoms would diffract in the same direction, and the earth would act as one particle. So in principle, one could
Even should we cool the earth to absolute zero, there would be problems measuring the de Broglie wavelength. In order to diffract the earth, one would have to move its center of mass at a finite speed relative to the grating. At any measurable speed, the wavelength would be smaller than the diameter of a proton. The appropriate line spacing for such an experiment would be very difficult to manufacture. One would have to move the earth extremely slowly with any reasonable line spacing.
Diffraction experiments with composite particles have been achieved. Diffraction has been performed with atoms, molecules, and Bose Einstein condensates. However, the deBroglie wavelength of the composite particle has to be longer than the spacing between the component particles. If not, the particles will diffract separately. So this adds complexity to the experiment. The experiment regarding the entire earth would be more complex, still.

http://arxiv.org/ftp/arxiv/papers/1107/1107.5794.pdf
“In contrast, confined quantum waves and their composites (such as nucleons and atoms) move collectively as particles following a classical Hamiltonian trajectory, as derived from the coherent phases of the component quantum waves. However, transitions between such quasi-classical trajectories are still subject to quantum transition rules of energy and momentum quantization (both linear and angular). Furthermore, there is no quantum decoherence, and no entanglement of multi-particle states. This provides a clear foundation for classical behavior, and avoids paradoxes of quantum measurement such as Schrödinger cat states.”

http://etheses.dur.ac.uk/3196/1/Thesis.pdf
“The first and principle reason is that the quantum nature of particles begins at the 1 mK mark. At ultra-cold temperatures the de Broglie wavelength of a particle becomes much longer than a typical bond lengths and degeneracy exceeds the average separation between atoms in a gas.”