Uncertainty Principle Hypothetical question

[NetMage]

Ok hey forum. I thought it might be a neat idea to contemplate this idea, and perhaps regurgitate some thoughts back on to this thread. So, as the Heisenberg uncertainty principle states, one can not know both the velocity and position of a particle or electron. I was curious to hear thoughts as to what the implications would be if hypothetically we could know both with great precision. Would this perhaps be a large step into quantum teleportation and other areas of research in particle physics. Post your thoughts :) I was thinking about this quite a bit today, and am interested to hear further responses!

 

[DaveC426913]

I was curious to hear thoughts as to what the implications would be if hypothetically we could know both with great precision.

Q: What would the implications be if the laws of physics as we know them were not the laws of physics as we know them.

A: Faeries and unicorns.


The moral here is that nothing useful comes from just supposing something might be, without any reason to suspect it might be so.

 

[K^2]

You can improve the precision of the measuring device, but it's not going to improve precision of the measurement. The value itself is undetermined. You can get a super-precise result, but it will be just a random number within the uncertainty interval. That's not very useful.

Edit: Alternative to Dave's answer, if you could make such simultaneous measurements, forcing the particles into these states, and while keeping all of the other physics intact, what you'd do is reduce the value of Plank's Constant to zero, at which point all matter would gravitationally collapse into black holes. But that's really just a least-assumption version of Faeries and Unicorns hypothesis.

 

[ZapperZ]

Ok hey forum. I thought it might be a neat idea to contemplate this idea, and perhaps regurgitate some thoughts back on to this thread. So, as the Heisenberg uncertainty principle states, one can not know both the velocity and position of a particle or electron. I was curious to hear thoughts as to what the implications would be if hypothetically we could know both with great precision. Would this perhaps be a large step into quantum teleportation and other areas of research in particle physics. Post your thoughts :) I was thinking about this quite a bit today, and am interested to hear further responses!

Your understanding of the HUP is faulty.

I make a particle pass through a very tiny slit at a position x with a width that is $\Delta x$). My uncertainty in its position is $\Delta x$. I then let it hit a detector behind the slit. The off-axis distance where it hits the detector gives me its momentum $p_x$.

There! I've measured both the position and its momentum. Did I just violated the HUP?

Before you wonder about the "implication" of anything, you must first establish your accurate understanding of that thing. This, you have not done.

Zz.

 

[haael]

The uncertainity is the very root of the mathematical formalism of QM, so if we ever discovered that there is no uncertainity, this would be bad news. I personally find the uncertainity very elegant idea.

 

[ZapperZ]

The uncertainity is the very root of the mathematical formalism of QM, so if we ever discovered that there is no uncertainity, this would be bad news. I personally find the uncertainity very elegant idea.

I don't think it is the "very root of the mathematical formalism of QM". In fact, the HUP is merely a consequence of how QM defines operators/observables. It is of no coincidence that the commutation relations [A,B] is some time called First Quantization. One derives nothing much out of the HUP. Instead, we can start with First Principles and derive a bunch of other things, including the HUP.

The HUP is merely a "sexy poster" for many who are barely discovering QM.

Zz.

 

[DevilsAvocado]

Q: What would the implications be if the laws of physics as we know them were not the laws of physics as we know them.

A: Faeries and unicorns.

It could be worse... It could be Mama Grizzlies and Unicorns, if all went real bad...

 

[DevilsAvocado]

I was curious to hear thoughts as to what the implications would be if hypothetically we could know both with great precision.

I don’t know much about "mathematical formalism" or "sexy posters", but I do know that your question is not related to the physical reality:

https://www.youtube.com/watch?v=<object width="640" height="505">
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[haael]

One derives nothing much out of the HUP. Instead, we can start with First Principles and derive a bunch of other things, including the HUP.

I see it differently. HUP is the First Principle.

In classical physics we believe that there is space(-time) filled with point-like particles that have position and independent momentum, what sets their configuration space.

QM revealed that the real picture is different. Particles are not points, but waves. There's no distinct "position" and "momentum", instead there is one single entity, that can appear as classical position or momentum when viewed at from some angles, but never both at the same time. Position is a specific form of momentum, momentum is a form of position. Or, speaking more strictly, position and momentum are particular forms of something else, namely the quantum configuration space.

This is the core of QM for me. When asking questions like "what is reality", this would be the answer: momentum and position are not separate concepts, but one single thing. The rest of QM can be easily derived :).

 

[DaveC426913]

I agree with haael. HUP is a fundamental. To grasp it is to grasp that particles are not well-defined hard balls, they are waves, to which labels like position just don't make sense without heavy qualifiers. It is a paradigm shift in thinking about physicality.

I'll bet anyone who doesn't understand HUP is also surely stuck thinking of particles (whether bosons or fermions) and as well-defined points.

 

[yoda jedi]

Ok hey forum. I thought it might be a neat idea to contemplate this idea, and perhaps regurgitate some thoughts back on to this thread. So, as the Heisenberg uncertainty principle states, one can not know both the velocity and position of a particle or electron. I was curious to hear thoughts as to what the implications would be if hypothetically we could know both with great precision. Would this perhaps be a large step into quantum teleportation and other areas of research in particle physics. Post your thoughts :) I was thinking about this quite a bit today, and am interested to hear further responses!

maybe on non hilbert space.

 

[ZapperZ]

I see it differently. HUP is the First Principle.

Then derive QM out of it.

Zz.

 

[haael]

Then derive QM out of it.

I just did.

 

[ZapperZ]

I just did.

Then show it.

Zz.

 

[unusualname]

Dirac, Born, Jordan, Heisenberg and Schrödinger formulated the foundations of QM by end of 1926. Uncertainty Principle was published by Heisenberg in 1927. It is a consequence of the foundations of QM, it is not a first principle.

 

[DaveC426913]

Dirac, Born, Jordan, Heisenberg and Schrödinger formulated the foundations of QM by end of 1926. Uncertainty Principle was published by Heisenberg in 1927. It is a consequence of the foundations of QM, it is not a first principle.

I dunno. Observation precedes model. It's not like particles only began behaving according to the HUP after 1927.

True, HUP may not have been formalized until later, but it seems to me our QM model could change a hundred times as we develop it. HUP is simply a description of empirical evidence.

 

[haael]

Dirac, Born, Jordan, Heisenberg and Schrödinger formulated the foundations of QM by end of 1926. Uncertainty Principle was published by Heisenberg in 1927. It is a consequence of the foundations of QM, it is not a first principle.

But modern formulations of QM start with the uncertainity. The canonical quantization begins from it.

The early formulations did have HUP included, but this was not obvious then. Nevertheless, look at the early matrix theory and wave theory. They are equivalent, aren't they? What makes these theories equivalent is the HUP: matrices can be noncommuting; the "x" and "∂" oparators applied to waves are noncommuting too, so the HUP can be expressed.

Today we can say, that the ability to write down HUP is the "meat" of any mathematical apparatus that aims to describe QM. We can use any representation: matrices, waves and their differentials, operators on Hilbert space and so on. The particular representation is irrelevant; if we can write some QM law in one of them, then we can do it in any other. The existence of noncommuting objects is the point.

For intellectual entertainment, one could take any mathematical theory that contains nubers and some noncommutativity, be it topology or quaternions, and make identifications from objects of this theory to some physical concepts. This kind of theory will always be able to express QM; only if the HUP can be written, this will allways do.

 

[unusualname]

But modern formulations of QM start with the uncertainity. The canonical quantization begins from it.

The early formulations did have HUP included, but this was not obvious then. Nevertheless, look at the early matrix theory and wave theory. They are equivalent, aren't they? What makes these theories equivalent is the HUP: matrices can be noncommuting; the "x" and "∂" oparators applied to waves are noncommuting too, so the HUP can be expressed.

Today we can say, that the ability to write down HUP is the "meat" of any mathematical apparatus that aims to describe QM. We can use any representation: matrices, waves and their differentials, operators on Hilbert space and so on. The particular representation is irrelevant; if we can write some QM law in one of them, then we can do it in any other. The existence of noncommuting objects is the point.

For intellectual entertainment, one could take any mathematical theory that contains nubers and some noncommutativity, be it topology or quaternions, and make identifications from objects of this theory to some physical concepts. This kind of theory will always be able to express QM; only if the HUP can be written, this will allways do.

The "meat" of QM is discreteness and probability. Then you have Schroedinger Evolution or equivalent Heisenberg picture, and from either of those you get non-commutativity and the Uncertainty Principle for conjugate observables.

Quantum Gravity may modify the uncertainty principle but it won't modify Planck's constant or probabilistic nature of QM

 

[haael]

The "meat" of QM is discreteness and probability.

Discretness is just a consequence of wave interference over closed paths. And in QM itself there is no probability at all, it's just an iterpretation, falling off nowadays, BTW.

 

[unusualname]

Discretness is just a consequence of wave interference over closed paths. And in QM itself there is no probability at all, it's just an iterpretation, falling off nowadays, BTW.

Very funny.

I believe Planck discovered dicreteness of nature at the end of the 19th Century.

I don't know where you get the idea that probabilistic interpretation of QM is "falling off nowadays" , but I don't think that's true amongst the rational science community, maybe in the world of the deluded.