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I apologize if this has been answered before -- The answer may be out there, but I may just not have the proper terminology to find it.

I was messing around with Universe Sandbox, and noticed that if I flung two objects at one another at the speed of light, they would pass through one another. Obviously, this is a limitation of the game engine and the speed at which it's being simulated, but it did prompt a question for me:

I know that as you approach the speed of light, the length of objects appears shorter. I recall that if you approached earth close to the speed of light, Earth would appear to only be a few miles thick. So, given quantum tunneling, with a velocity close to the speed of light, would it be possible for two macroscopic objects to "quantum tunnel" past one another without any interaction?

Qmechanic
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Ashten
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    Does this answer your question? Macroscopic quantum phenomena and tunneling – BioPhysicist Apr 29 '21 at 05:34
  • Hmmm... Not quite. I am aware that with macroscopic objects, quantum tunneling becomes astronomically unheard of, but I'm asking more along the lines of: With enough velocity, could you potentially "shorten" an object small enough that the interactions between the objects essentially start acting according to quantum mechanics. – Ashten Apr 29 '21 at 05:44
  • I suggest editing your question to make that clear then. It seems like many parts of your question distracts from the actual question of "at what size of objects do quantum effects become important?". I don't think you need to bring in length contraction at all, as traveling near light speed brings in a bunch of other things you probably didn't want to consider. – BioPhysicist Apr 29 '21 at 08:27

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First, most commonly when people try to apply the tunneling idea to macroscopic objects they provide a rudimentary form of calculation which may be quite wrong. The difficulty is in allowing correctly for things like the Pauli exclusion principle. You can't just treat the wall merely as providing a potential function, because the wall is itself made of matter.

But anyway, even if we treat a simplified model, your idea won't work. It is easiest to see this by treating it in the rest frame of the wall. In this case a fast-moving oncoming entity has lots of energy, which means we don't need to consider tunneling because in any case the oncoming object already has more energy than the height of whatever potential hill the wall can provide. So it will go through the wall not because of some quantum effect, but simply because the wall was not able to exert a force strong enough to reflect it. Basically it will break the wall.

Andrew Steane
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  • I wish that I could select two answers as the correct ones. Both you and Anna answered the question in slightly different ways, which helped me to better understand the answer! – Ashten Apr 30 '21 at 05:20
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True, massive objects approaching each other close to the speed of light, appear distorted to each other due to length contraction in the direction of approach, BUT there exists the famous $E=mc^2$ effect , where $m$ is the relativistic mass

$$m=\frac{m_0}{\sqrt{1-\frac{v^2}{v^2}}}=\gamma m_0\qquad\quad m_0=\text{"rest mass"}$$

increasing the inertial mass of the moving object. The dimensions of the object in the direction perpendicular to the motion do not change. The mass will be composed of the same number of tiny quantum mechanical entities ( atoms and molecules) distorted by length contraction only in one direction. So the probability of tunneling through anything is still very very small, as in the referenced answer, it would still need a coherent wave function for the whole object.

anna v
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In a somewhat different setting this is referred to as Klein paradox, where a (relativistic) electron tunnels through a barrier without reflection. The phenomenon has attracted a lot of attention about a decade ago when it became possible to realize it in graphene sheets, where electrons are described by relativistic-like equations.

Roger V.
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