Dear Sydney Ernest Grimm

I initiated this discussion to find out about different opinions and approaches to the issue. Please go ahead.

I should add that, if we accept energy-time pair for uncertainty principle, every state including position of a particle is conjugate with time due to wavy nature of its movement.

What I cannot understand is that the concept of uncertainty is manipulated according to any unreasonable demand from any difficult subject. Sometimes we say “a quantum state that exists for only a short time cannot have a definite energy” and sometimes “Quantum mechanics allows, and indeed requires, temporary violations of conservation of energy, so one particle can become a pair of heavier particles (the so-called virtual particles), which quickly re-join into the original particle as if they had never been there.”, Gordon Kane 2006.

That is uncertainty has become a panacea for any problem in QM.

Dear Ziaedin Shafiei ,

Please take a look into the book : "Introduction to Quantum Mechanics" by David J. Griffiths, in section "3.4.3 The Energy-Time Uncertainty Principle", this important sentence:

In the energy-time uncertainty principle is not the standard deviation of a collection of time measurements; roughly speaking it is the time it takes the system to change substantially.

With best regards.

Dear Mazen Khoder

In the same book, Griffiths claims that “the uncertainty principle is extraordinarily robust: It can be misused without leading to seriously incorrect results, and as a consequence physicists are in the habit of applying it rather carelessly.” But we know that what he rejected forcefully a few sentences earlier is the most misused concept of uncertainty principle.

“It is often said that the uncertainty principle means that energy is not strictly conserved in QM – that you are allowed to borrow energy ΔE, as long as you pay it back in a time Δt ≈ ℏ ⁄2ΔE; the greater the violation, the briefer the period over which it can occur. There are many legitimate readings of the energy-time uncertainty principle, but this is not one of them. Nowhere does QM license violation of energy conservation, and certainly no such authorisation entered into the derivation of Eq 3.151 (ΔE Δt≥ℏ/2)”

Dear Sydney Ernest Grimm

“Thus a certain amount of energy has caused a change of position of the conditions in I to point II.”

Case A

Suppose a particle travels at open space with constant speed. Its position changes continuously but its momentum and energy are constant. Here no further energy is required for any change of position.

Case B

Now suppose some energy is spent to increase the momentum and energy of the particle between the two points (I) and (II).

Can momentum and energy in points (I) and (II) be measured instantaneously or with delay in the two above cases?

Dear Mazen Khoder

"In the energy-time uncertainty principle is not the standard deviation of a collection of time measurements; roughly speaking it is the time it takes the system to change substantially."

This quotation from Griffiths can apply to any variable such mometum or position. If so, which is my main question, why it has been considered for energy only? Is not it because there was a need for it as stated by Gordon Kane, please see his statement in my previous comment.

I also wanted to repeat that what Griffiths rejected was happily accepted and popularized as leading science such as Hawking radiation.

Hi Ziaedin Shafiei ,

The uncertainty principle shall not be that intimidating. I can provide a much simplified physical perspective to this "principle".

Starting from two basic relations:

(1) Planck-Einstein E=hf for photon where E is energy, h is the Planck constant and f is the frequency of a photon. Because f=1/T where T is the period of the photon's oscillation, so E*T=h.

(2) The de Broglie wave length momentum relation λ=h/p where λ is the matter wavelength, h is the Planck constant and p is the momentum. So p*λ=h.

Now you know E*T=p*λ =h from (1) and (2). The so-called uncertainty comes in when E, T, p and λ are not completely well known or well measured. They each have their standard deviations around the expected values. If one varies around a fixed value, in order to make (1) and (2) hold, the other must also varies around a fixed value. The uncertainty principle just points out the fact that E and T are co-varying, p and λ are co-varying. If you do a mathematical deduction, you will arrive at the uncertainty principles that were established by the pioneers of quantum physics.

To be specific, energy and time are a pair of quantities whose product of variations must vary around h (or other more accurate number), momentum and position are a pair of quantities whose products of variations must vary around h (or other more accurate number).

There are just so many ways to interpret uncertainty principles that involve possibly other physics observable quantities. But first of all, these observable quantities must be related, such as E*T=h or p*λ=h, otherwise they are not related to the uncertainty principles in (1) nad (2). For example, if two physics quantities A and B has the following relation A*B=1000h, then their uncertainty principle will be sqrt()*sqrt() on the order of 1000h.

Time is a very interesting observable quantity, of course it can be physically observed - or in other words, compared with a time standard. It relate the duration from beginning to the end of a physical process to the number of oscillations of a standard atomic clock. But how to meaningfully define the beginning and the end of a physical process is another important decision point in order to apply the uncertainty principle properly.

In my opinion, the uncertainty principle has been well misunderstood or misused. For example, the energy level of a hydrogen atom is very strictly fixed and conserved if it experiences no change of states. It doesn't depends on the time it stays at this energy level. The amount of energy cannot be more, cannot be less, unless something changes. It should have nothing to do with how long the atom has acquired the energy. So the energy won't vary with time, it is conserved.

The uncertainty should be applied to statistical variations among multiple measurements of the same quantities, and the variation of time it takes to realize the measurements, not what it takes for the atom being held at that fixed amount of energy.

Here's my analogy of the Uncertainty Principle:

Represent velocity through Time and Space as two sine waves 90 degrees out of phase and on perpendicular planes (Timerate, Velocity) The distance between the curves is always =1 (speed of light)

During each tick of the clock (each Time cycle), the Space curve passes through all of its possible positions consistent with the Timerate (as does the Time curve relative to the velocity). Therefore, the clock resolution prohibits finer resolution of the Space curve.

It's also analogous to phase transitions in materials. The solid/liquid state is the quantum step, but the enthalpy, i.e. the potential energy stored in the stretching of bonds before they break, satisfies the Conservation of Energy. A thermometer detects no change even though the energy continues to increase from the external source.

Dear Hong Du

When energy-time is concerned the formula (E*T=h) is only applicable for massless photon, which cannot be extended to other particles. Moreover, T, is not time but the period of the photon's oscillation. In that case constant T can be precisely measured for a specific electromagnetic radiation and with that knowledge energy can be precisely measured too. Therefore, both variables are precisely and concurrently known.

Hi Ziaedin Shafiei ,

Thank you for thinking deeper on the suggested thought, and it helps theoretical developments to raise questions about any thought.

(1) As we all agree, E*T=h works for massless photon. But it doesn't prevent massive objects from following the same rule. Physics should be simple, and a lot of things work the same way, massless or massive. Extension of principles from one physics process to another is a good way of physics development. If there is a difference, just figure out the difference and work on it.

As mentioned previously, suppose A*B=1000h works for some massive objects, then the uncertainty rule will be around 1000h approximately. If the uncertainties proposed by quantum pioneers are correctly varying around h, then it indicates that these physics process do have rules similar to E*T=h.

(2) The application of uncertainty principle is very tricky, and sometimes just full of issues. As you mentioned, T can be precisely measured, then dT=0. If energy is precisely measured, then dE=0. Now the problem becomes bigger because the uncertainty principle is strictly broken in that dT*dE cannot be greater than h/4/pi any more. So there must be something missing in the thought process.

In reality, there is no measurements can give exactly the same results, all measured quantities have uncertainties from various sources. Some of them, including the time and energy, are just varying up and down no matter how accurate they are.