A Proposed Measure of Motion

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Reference: The Quantum Phenomenon

The physical phenomena encountered in this universe are extremely varied. But there is a single aspect that characterizes all of them. That aspect is motion. Motion seems to underlie all physical phenomena. It is important to come up with a measure for motion that is consistent across the boards.

At cosmic levels, speed has served well as a measure of motion. It is a very basic notion of Classical mechanics. Even the theory of Relativity starts with the speed of light as a postulate. However, an interesting switch takes place at this point.

Speed is a notion derived from classical mechanics that assumes space and time to be absolute. The theory of relativity then demonstrates that neither space nor time is absolute. When one is traveling along a beam of light, the sense of space and time is very different. The units of space and time are no longer the “standard” units assumed when one is traveling along earth. We lose consistency in the measure of motion when we think about speed.

As long as one is viewing from a frame of reference that is “matter-centric” there is consistency in using speed as a measure of motion. But the moment one views from a frame of reference that is “light-centric” one loses that consistency. The inconsistency also shows up when viewing motion at atomic levels as studied in quantum mechanics.

The consistency of using speed as a measure of motion is limited to the classical “matter-centric” frame of reference.

Einstein leaned on Newton when he based his theory of relativity on a speed of light that was taken to be constant in all frames of reference. This postulate is exact enough when all the frames of reference being considered are matter-centric. There is a lot of validity to the theory of relativity as long as we make our observations in a matter-centric frame of reference.

The theory of relativity, however, leads to the conclusion that space and time are not absolute. Therefore, it cannot assume that the speed of light is absolute and independent of frames of references that are not matter-centric. Einstein’s postulate is also subject to the classical assumptions underlying the Maxwell’s equations. Quantum mechanics is now examining those assumptions as it tries to explain the wave-particle duality. One needs to reformulate Einstein’s postulate about speed of light for all frames of references.

However, this does not decrease, in any sense, the genius of Newton and Einstein. Their theories are extremely workable in their respective domains. And it is the understanding derived from those theories, which is now guiding us to properly address the inconsistencies noticed between the cosmic and atomic scale observations.

We can use Einstein’s equation to show that the frequency of a photon may act as a source of inertia (resistance to change in motion) just as the mass of an electron does.  This inertia may impart the property of discreteness as well.

From energy relationships,

E = hf = mc2
Or, f = [c2/h] m = [constant] m

In other words, frequency comes out proportional to mass equivalence, and it may play the same role as mass, within the electromagnetic spectrum. We may assume frequency to be a source of inertia where a wave is concerned, the same way that mass is a source of inertia for a particle.

Inertia is resistance to change in motion. Thus, as the frequency of electromagnetic radiation increases, it may act to slow its speed. However, from a matter-centric frame of reference, it may be difficult to detect the slowing down of the electromagnetic radiation.  But a difference might be detectable between the speeds of gamma rays and radio waves because there is a large difference between their frequencies. The following news item seems to suggest that this may be the case.

High Energy Gamma Rays Go Slower than the Speed of Light?

The article on Markarian 501 from Wikipedia states,

“The gamma rays from Mrk 501 are extremely variable, undergoing violent outbursts. The gamma ray spectrum of Mrk 501 shows two humps. One is below 1 keV and can be considered to be X rays and the other is above 1 Tev. During flares and outbursts the peaks increase in power and frequency. Flares lasting 20 minutes long with rise times of 1 minute have been measured by MAGIC. In these flares the higher energy gamma rays (of 1.2 Tev) were delayed 4 minutes over the 0.25 TeV gamma rays.”

When we carefully look at this situation, we see that frequency could be used as a more exact measure of motion than speed. Frequency is a repeating change that is observable with consistency despite the relativistic nature of space and time. Frequency may also suffer less than speed from a matter-centric bias.

The frequency of electromagnetic radiation could prove to be a better measure of motion than its speed.

Frequency as a measure of motion seems to open new avenues of investigation. For example, the de Broglie frequency of electron is in the same ballpark as the frequency of gamma rays. Therefore, a transition of inertia from frequency to mass seems to occur in gamma ray/electron region.

Of course, this is simply a hunch at this stage.
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The Quantum Phenomenon (old)

Here are the notes for the above lecture:

Click to access notes_quantum_7.pdf

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The phenomena being examined by quantum mechanics is that the motion of particles is not random at atomic levels.

Individual particles, when viewed together over a period of time, appear to be distributed in space as if they are parts of a wave pattern.

They somehow seem to “sense each other” not only when separated in space, much like a flock of birds, but also when separated in time.

Questions that spring up are:

  • Are these particles really discrete?
  • Do they really exist independent of each other in space and time?
  • What is the true nature of a particle?
  • What is the true nature of space and time?

We have created mathematical models that use the concept of probability to explain a pattern emerging from apparent randomness. But they do not really explain the underlying nature of matter, energy, space and time.

The above questions remain to be answered by science.

 

Wave-Particle Duality (Old)

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Reference: The Foundations of Mathematics

QM seems to be 5% experimental knowledge and 95% interpretation. We even call it Copenhagen interpretation.

It is not difficult to start out from the real experimental knowledge and then explore outwards from there keeping in mind that mathematics is just a tool. If we put too much faith in mathematics without checking against reality now and then, then it can be akin to being brainwashed by mathematics.

EXPERIMENTAL OBSERVATION: We cannot idealize a quantum object as a particle that has a precise location.

It is more like a wave packet (snake) of finite bounds. So, it doesen’t make sense to compute the probability of some “particle” as to its location and call it a wave function of the particle. That would be like computing the probability of “part of a snake” at a certain location. Why not compute the location of the whole snake (wave packet)?

The situation is that we cannot fit the whole “snake” in a precise point location as was done for a particle. We have to think in terms of location of the whole wave packet, and the probability of that is always going to be 1. However that location is not going to be a point.

So problem gets to be the fixed idea of thinking in terms of precise “point” locations only.

That is what mathematical integration from minus infinity to plus infinity is doing. I believe that integration no longer works at quantum levels. We need new mathematical tools for better understanding.

Maybe it is time to look at Georg Cantor’s ideas related to infinity and infinite sets, because it seems that the composition of wave packet belongs to a different infinite set then the infinite set in which it is moving.

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2014 in review

The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.

Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 25,000 times in 2014. If it were a concert at Sydney Opera House, it would take about 9 sold-out performances for that many people to see it.

Click here to see the complete report.

What Einstein might have Missed

Einstein

Apparently Einstein died wishing he knew more math. Actually he should have investigated the very foundations of mathematics.

Mathematics is a subject that is extremely consistent. One is not going to find any inconsistency in math. But Einstein should have been curious about the ideas on which mathematics is based. 

The Foundations of Mathematics

Einstein struggled to understand Quantum Mechanics all his life. He felt a fundamental disagreement with its basis but he could not put his finger on it.

Experimentations at quantum level have shown that there is wave-particle duality. This means that there is no such thing as a “point-particle.” Yet the quantum theory still looks for a point-particle in terms of probability through a wave function.

Maybe it is not a point-particle that is being assumed. Maybe it is a “point-location” and a “point-time” that is being taken for granted. This is possible because mathematics itself is founded on the ideas of “point” and “unit.” The truth is that our very thinking is constructed upon the ideas of “point” and “unit.” Mathematics is simply a refinement of logic.

Quantum Mechanics shows us that the classical thinking is no longer valid. The mass of a particle cannot be reduced to a precise center of mass . Nor is there an ideal disturbance with no center of mass. Infinite sine and cosine wave representations of disturbance are mathematical constructs only. The truth is somewhere in between. the center of mass gets increasingly diffused as we investigate the quantum levels.

The inconsistency seems to be that space and time are still being perceived as independent of the disturbance (wave) and the mass (particle). It is being believed that there is a “point-location” and a “point-time” even when there is no “point-particle.” Looks like reality is being confused with mathematical thinking.

Can the very space and time be “diffused” like the quantum “particle”?

Maybe space and time are not independent of disturbance and mass. Maybe space and time are as diffused at quantum levels as are the observations of waves and particles.

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