Some comments on information theory

[PabloAngello]

Question to @ark @Cleopatre VII and others that are good in physics.
Considering Einstein's equation E = mc^2. Could we calculate what is time from this? C is speed of light so 300000km/1second.
So C = sqrt(E/m). But with further calculations to establish 1s = ... in results I have 1s on both sides of equation.
Another part of question: can we at all discuss about what is time, from such perspective(transforming this equation)? Is it correct in physical sense?

 

[John G]

Question to @ark @Cleopatre VII and others that are good in physics.
Considering Einstein's equation E = mc^2. Could we calculate what is time from this? C is speed of light so 300000km/1second.
So C = sqrt(E/m). But with further calculations to establish 1s = ... in results I have 1s on both sides of equation.
Another part of question: can we at all discuss about what is time, from such perspective(transforming this equation)? Is it correct in physical sense?

Well time in the Einstein sense could be different than time in the quantum transaction/propagator sense. One interesting related question could be if the speed of light doubled would we notice. I looked into this once but don't fully remember the answer or how sure of it I was. From time and length (Planck time/length) things you wouldn't notice but maybe mass (Planck mass) or EM things would require changes too to keep you from noticing. Perhaps as long as a few fundamental dimensionless ratios stay the same (the ones responsible for Planck units) then we wouldn't notice Planck units changing though I think Planck units for EM aren't as simple as for space, time and mass not that any of this is simple.

 

[dennis]

Can Planck unit be a point at which a phase transition occurs? Light becomes matter? Maybe there is another phase transition point where the process is reversed or changed again.

This video is interesting, its about 20 minutes long.

 

[PabloAngello]

@dennis From my limited knowledge, light interacts with matter, not becoming matter. Light == electromagnetic waves, not only those with our visible range, hitting other particles that are part of some objects, causing an effect on them. Planck unit describes what is the smallest value that has physical sense due to our current knowledge and mathematics, describing physic world, it doesn't mean that plack length is the smallest, it means that it is smallest that we can calculate and get some results that have sense that fits what we as humans can understand.

 

[Cleopatre VII]

Considering Einstein's equation E = mc^2. Could we calculate what is time from this?

We can look at this equation and use it to deliberate on the nature of time, but we do not get explicitly time as a parameter in physics.

I would like to add that in this equation we are dealing with the so-called relativistic mass. Relativistic mass is a relative quantity - its value depends on the frame of reference. Therefore, it is not a relativistic invariant. A relativistic mass can change without any change in the physical object itself, only by changing the frame of reference.

It is therefore a quantity different from the rest mass, which is an invariant quantity.

 

[Cleopatre VII]

@dennis From my limited knowledge, light interacts with matter, not becoming matter. Light == electromagnetic waves, not only those with our visible range, hitting other particles that are part of some objects, causing an effect on them.

In the standard model that currently functions in physics, photons are excitation of quantum electromagnetic fields and we often describe them as particles. These particles have no mass, they only have energy and momentum. In the collision of two high-energy photons, a pair of massive particles, such as an electron and a positron, can be formed. In general, we do not classify photons as particles of matter, although matter particles (quarks, leptons, neutrinos) are also excitations of certain quantum fields.

On the other hand, in physics there is really no one and only universally accepted definition of matter. On the one hand, we can say that fermions are building blocks of matter, and bosons (including photons) are the carriers of interactions. At the same time, we also have a wave-particle dualism.

Is light matter? I would not be able to answer this question unequivocally. This is not just a mathematical question, but largely a philosophical one.

 

[Bluegazer]

Is light matter?

What if it were a state of matter? Plasma, for example, is thought to be the fourth state of matter. What if light were the fifth state? The fifth element?

 

[PabloAngello]

We can look at this equation and use it to deliberate on the nature of time, but we do not get explicitly time as a parameter in physics.

I would like to add that in this equation we are dealing with the so-called relativistic mass. Relativistic mass is a relative quantity - its value depends on the frame of reference. Therefore, it is not a relativistic invariant. A relativistic mass can change without any change in the physical object itself, only by changing the frame of reference.

It is therefore a quantity different from the rest mass, which is an invariant quantity.

So do we have any equation for Time that combines mass or energy? We of course know that Time = distance/velocity (classical sense). Just for thought experiment, what would be result (equation) for time considering Einstein's famous equation?

 

[PabloAngello]

What if it were a state of matter? Plasma, for example, is thought to be the fourth state of matter. What if light were the fifth state? The fifth element?

I have great suspicions that it is the first 'state' not the fifth ;)

 

[John G]

So do we have any equation for Time that combines mass or energy? We of course know that Time = distance/velocity (classical sense). Just for thought experiment, what would be result (equation) for time considering Einstein's famous equation?

The dimensionless equations with Planck units kind of do in that the speed of light one relates Planck distance and Planck time and the Newton law of universal gravitation one relates Planck distance and Planck mass.

 

[Cleopatre VII]

What if it were a state of matter? Plasma, for example, is thought to be the fourth state of matter. What if light were the fifth state? The fifth element?

I don't think there are any particular contraindications to adopting such a definition, although, on the other hand, these considerations are quite fluid.

The point is that physics is exact when it comes to strictly mathematical terminology, but if we reflect on the nature of reality or individual beings, physical considerations turn into philosophical ones.

 

[Esote]

Given that mass (m = E/C2) is factually the measurement of the total quantity of interaction energy contained in a body, from quarks to galaxies, it seems that Time may be understood (partly at least) as the act of measurement itself, of conscious observation...

 

[Cleopatre VII]

So do we have any equation for Time that combines mass or energy?

The first mathematical formula to link time and energy that comes to my mind is [T, H] = iI,
where
T - time operator,
H - hamiltonian (energy operator),
i - imaginary unit,
I - identity matrix,
[T, H] = TH - HT and this operation is called a commutator.

The above formula is related to the famous Heisenberg uncertainty principle for time and energy. It more or less says that time and energy cannot be measured simultaneously with any accuracy. However, it is not about simultaneity in time, but about the fact that the more accurately one of these quantities has been measured, the less accurately we can measure the latter.

Probably this pattern came to my mind because yesterday, together with Ark, we sent a paper on the time operator for publication. Our article can be found here: [2202.10393] Time of arrival operator in the momentum space

What exactly is this time operator? In classical mechanics, we simply have physical quantities. If the conditions of the experiment do not change, we will obtain the same result. In quantum mechanics, so-called observables (linear operators with strictly defined properties) correspond to physical quantities. If the conditions of the experiment do not change, we will not necessarily obtain the same results, but the probability distributions of these results will be the same. Despite the existence of observables in quantum mechanics, time is usually considered a parameter anyway. In our paper, we show the conditions under which a time operator can exist.

 

[luc]

Another issue is possible arguments concerning the non-empirical nature of theology, manifested, for example, by the fact that revelation is regarded as a kind of axiom. It ought to be noted, however, that also in mathematics there are objects called primitive notions. They are, for example, sets or their features (elements).

Primitive notions play the role of universally accepted, undeniable obviousness, but for the person experiencing the revelation it becomes the undeniable obviousness. Primitive notions in mathematics were built on the basis of our intuition.

Of course the proof is based on axioms, and these can be replaced by other axioms. And we can also take the very existence of God as an axiom in some other system. The point is that while there are infinitely many different possible systems of axioms, some of them are rich in consequences and "useful", while other may be of no use at all. And what does it mean "useful"? Useful for whom and how?
That is an important but altogether different question.

Indeed, and as Collingwood pointed out (and it is my hunch as well), what he calls in his Essay on Metaphysics "absolute presuppositions" in a certain sense have no truth value. So in a way, our fundamental axioms have a relative or somewhat arbitrary nature to them. It is a difficult thing to accept because after all, we are seeking truth, and often we are very identified with out fundamental assumptions; indeed, we often cannot help but look at the world through the lens of certain assumptions. Good philosophy can help us "play around" with them and try to look at the world differently. I think it IS possible, and as Collingwood pointed out, Kant's categories for example were more or less an explicit statement of the presuppositions physicists of his time worked with, so they are not set in stone. They seem to develop. And of course mathematics and physics play a crucial role in this development - new formalisms can force us to change our presuppositions, or rather set in motion a process of change. Abstract formalism might also help to overcome our barriers, because it is a "safe space" where math can do its thing without us having to form a clear picture in our minds yet of the ontological and epistemological implications. But then again, there can be different ontological interpretations of physical formalism...

The way I look at it is that each set of fundamental axioms, or absolute presuppositions, is useful in different ways - they are like keys giving one access to different chunks of reality so to speak. Some might be more misleading or more problematic than others, some might have "bad consequences" etc., but they are all perspectives that open up certain aspects of reality...? Just some current thoughts.

BTW, I recently came across Whitehead's alternative rendering (or interpretation) of relativity theory - has anybody looked into this?

 

[John G]

Probably this pattern came to my mind because yesterday, together with Ark, we sent a paper on the time operator for publication. Our article can be found here: [2202.10393] Time of arrival operator in the momentum space

What exactly is this time operator? In classical mechanics, we simply have physical quantities. If the conditions of the experiment do not change, we will obtain the same result. In quantum mechanics, so-called observables (linear operators with strictly defined properties) correspond to physical quantities. If the conditions of the experiment do not change, we will not necessarily obtain the same results, but the probability distributions of these results will be the same. Despite the existence of observables in quantum mechanics, time is usually considered a parameter anyway. In our paper, we show the conditions under which a time operator can exist.

I wish I could understand this a bit better. You seem to have the external unitary time evolution operator (propagator) and some internal time operator via going from configuration space to momentum space (tautological solder form-like). It would be nice if the two times were very related. Relates to your teleparallelism interest too I think.