Quantum Tunnelling and Spacetime

[εllipse]

Does relativistic quantum mechanics make use of 4 dimensional Minkowskian geometry? Or does it just use special relativity formulated in 3 space dimensions and 1 time dimension? And if quantum mechanics can apply to Minkowskian spacetime, then can something tunnel through time?

 

[WhiteWolf]

Hmm... I got a question. Doesn't quantum tunneling violate the conservation of energy? When a particle tunnels out of an atom, a phenonema that has been proven, it goes against the strong force and gains electromagnetic potential energy, without expending any energy to acquire that potential energy. So for a small instant, it seems like it violates one of the most fundamental laws of physics.

 

[ZapperZ]

Hmm... I got a question. Doesn't quantum tunneling violate the conservation of energy? When a particle tunnels out of an atom, a phenonema that has been proven, it goes against the strong force and gains electromagnetic potential energy, without expending any energy to acquire that potential energy. So for a small instant, it seems like it violates one of the most fundamental laws of physics.

No, because in an elastic tunneling (ballistic), the tunneling particle stays at the same energy state and tunnels into the vacuum state that is also at the same energy (in the form of its KE). That's the whole point of tunneling, it keeps the same energy that is lower than the barrier.

Zz.

 

[marlon]

Does relativistic quantum mechanics make use of 4 dimensional Minkowskian geometry? Or does it just use special relativity formulated in 3 space dimensions and 1 time dimension? And if quantum mechanics can apply to Minkowskian spacetime, then can something tunnel through time?

Tunneling is space time is very possible. you know that quantum tunneling lowers the groundstate energy of a system so for this reason it can happen. If something can happen in QM, then it will happen.

In QM tunneling is easy to understand, however in quantum field theory it is more difficult because of the involved topology. However in QFT you have particles called instantons that can tunnel from one gauge configuration to another at spatial infinity. In lower dimensions, hese instantons are called solitons (2 Dim).

regards
marlon

 

[WhiteWolf]

No, because in an elastic tunneling (ballistic), the tunneling particle stays at the same energy state and tunnels into the vacuum state that is also at the same energy (in the form of its KE). That's the whole point of tunneling, it keeps the same energy that is lower than the barrier.


Thanks. Didnt know that. So the Kinetic Energy of the particle is higher with the distance it tunneled also? Hmmm, so what if it tunnels at a much longer distance? If it tunnels past, say... a moles worth of atoms, then wouldn't it have enough energy to approach light speeds? I would imagine that it would acquire great speeds as it is to break the barrier of the strong force from a single atom. So it would eventually have a limit, wouldn't it?

(Sorry, my physics teacher can't answer anything...)

 

[ZapperZ]

Thanks. Didnt know that. So the Kinetic Energy of the particle is higher with the distance it tunneled also?

Er.. I didn't say that.

Remember that in the bound state, one can naively say that the KE of the particle is equivalent to E-V(r). When it tunnels out elastically, this is the same KE that it will have. That was what I was trying to say. There are no violation of conservation of energy in elastic/ballistic tunneling.

Zz.

 

[DaTario]

Mr. Zapperz,

There was a famous work by Nimtz, in which he attempted to send a simphony of Mozart along a channel, from the emiter to the recorder and then concluded that the velocity od transmission was 4,7 c. He used tunneling to do so. I guess his experiment was based on the property that tunneling time does not depend on the extension of the barrier. Do you know if his work was accepted by the physics community ?

 

[marlon]

There was a famous work by Nimtz, in which he attempted to send a simphony of Mozart along a channel, from the emiter to the recorder and then concluded that the velocity od transmission was 4,7 c. He used tunneling to do so. I guess his experiment was based on the property that tunneling time does not depend on the extension of the barrier. Do you know if his work was accepted by the physics community ?

I know of it and No it does not contradict with special relativity.
Check out MadSci :
http://www.madsci.org/posts/archives/mar98/889017260.Ph.r.html

Also check out his personal website at http://www.ph2.uni-koeln.de/Nimtz/
and scroll down to the link of his papers. There are some on superluminal signaling.

marlon

 

[ZapperZ]

Mr. Zapperz,

There was a famous work by Nimtz, in which he attempted to send a simphony of Mozart along a channel, from the emiter to the recorder and then concluded that the velocity od transmission was 4,7 c. He used tunneling to do so. I guess his experiment was based on the property that tunneling time does not depend on the extension of the barrier. Do you know if his work was accepted by the physics community ?

I would strongly advice you to read:

M. Büttiker and S. Washburn, Nature v.422, p.271 (2003).
M. Büttiker and S. Washburn, Nature v.424, p.638 (2003).

Zz.

 

[Orion1]

Photons can transverse barriers transluminously based upon their wave packets, however, what about particles?

Can a particles wave packet transverse a barrier transluminously?

 

[DaTario]

This superluminal effect is understood as an illusionbased on the folloying reasoning.

Supose you have a gaussian packet traveling in the x direction left-to-right.

Supose this packet will soon face a barrier.

When passing through the barrier the packet suffers an attenuation, such that its beginning ( the first non zero amplitude of the packet ) has traveled through the barrier with velocity c. The peak of the packet has come to a nearer point in relation to its begining.

Therefore, if you detector could click at the arrival of the first no zero amplitude of the packet, it would yield a c velocity transmission, but what happens in fact is that our detector are only able to click under a somewhat larger and finite amplitude, so that, due to the attenuation, it clicks a little bit earlier than it would, if no attenuation has taken place.

Consider this poor diagram:

the packet before the barrier:
->
00011122233344433322211100000000000000000000000000000000000

the barrier's amplitude:

00000000000000000000000000099999000000000000000000000000000

the packet after 1 second if no barrier exists:

00000000000000000000000000000000001112223334443332221110000

the packet after 1 second with the presence of the barrier:

00000000000000000000000000000000000000000000000000123210000

I hope it has helped...

 

[Orion1]

What theorem describes the transluminal velocity through the barrier?

 

[DaTario]

I guess this is still a matter of discussion, read my explanation of the objections to transluminal experimental evidence.

Rudolf Bonifacio is one who defends transluminal propagation of information.
Luiz Davidovich is one who attacks it.

Try a google search on this names.