Let's not talk about the Big Bang

[Polymath257]

No reliable reference provided for any proposal of a continuous space time in the Quantum smallest scale. Just word salad referring to books.

A quote from Peskin&Schroder on page xx of the introduction:
"We will often work with the Schrodinger wavefunctions of single quantum-
mechanical particles. We represent the energy and momentum operators
acting on such wavefunctions following the usual conventions:"

Here, I cannot quote the mathematical equations, but the first identifies
the energy operator as i times the partial derivative with respect to time.

To do a partial derivative already shows an assumption of continuous time.

The second equation identifies the momentum operator in a similar way
using partial derivatives with respect to spatial coordinates. And, again, that already
assumes space is continuous (or else the partial derivatives make no sense).

So, right from the beginning, a standard text on quantum field theory (the
quantum theory of particles at the smallest scale we can probe) assumes
continuous space and time.

Once again, this is clear to anyone reading the material. At no point is the continuity
assumption specifically mentioned because it is *standard* in almost all of physics.

You seem to think that the denial of the classical world (Newtonian) in favor of
quantum mechanics also implies that space and time are discontinuous. And that is simply
not the case.

NOBODY here is arguing that quantum mechanics is wrong. What we are pointing out
is that YOUR understanding of it is wrong.

I would also point out that you are now arguing against *three* people who have actually
studied quantum mechanics in actual physics or chemistry courses. And you are presenting
popular articles that simply don't support your viewpoint.

It isn't a good look.

 

[shunyadragon]

On the basis of your logic, you can claim quantum theory relies on egg sandwiches. After all, neither I nor @Polymath257 can give you a citation explicitly denying it.

Reliable Sources and a coherent response concerning continuous time/space and gravity at the Quantum scale. instead of egg salad word games.

 

[shunyadragon]

And precisely why is the book by Peskin&Schroder not reliable?

Reliability of any text is not the question , IT IS THE FAILURE of you to cite and quote a specific trliable reference that describes continuous time/space and gravity at the Quantum smallest scale.

You could probably cite Valakovsky to support your argument

 

[shunyadragon]

A quote from Peskin&Schroder on page xx of the introduction:
"We will often work with the Schrodinger wavefunctions of single quantum-
mechanical particles. We represent the energy and momentum operators
acting on such wavefunctions following the usual conventions:"

Here, I cannot quote the mathematical equations, but the first identifies
the energy operator as i times the partial derivative with respect to time.

To do a partial derivative already shows an assumption of continuous time.

The second equation identifies the momentum operator in a similar way
using partial derivatives with respect to spatial coordinates. And, again, that already
assumes space is continuous (or else the partial derivatives make no sense).

So, right from the beginning, a standard text on quantum field theory (the
quantum theory of particles at the smallest scale we can probe) assumes
continuous space and time.

Once again, this is clear to anyone reading the material. At no point is the continuity
assumption specifically mentioned because it is *standard* in almost all of physics.

You seem to think that the denial of the classical world (Newtonian) in favor of
quantum mechanics also implies that space and time are discontinuous. And that is simply
not the case.

NOBODY here is arguing that quantum mechanics is wrong. What we are pointing out
is that YOUR understanding of it is wrong.

I would also point out that you are now arguing against *three* people who have actually
studied quantum mechanics in actual physics or chemistry courses. And you are presenting
popular articles that simply don't support your viewpoint.

It isn't a good look.

This describes wave function behavior at the Quantum smallest scale of individual particles and NOT continuous time/space and gravity at the Quantum scale.

Still waiting . . .

 

[ratiocinator]

This describes wave function behavior at the Quantum smallest scale...

The point seems to have sailed way over your head. You can't do a partial derivative with respect to time and space coordinates unless they are continuous.

 

[exchemist]

Reliable Sources and a coherent response concerning continuous time/space and gravity at the Quantum scale. instead of egg salad word games.

What is, in your view, the "quantum scale"?

 

[viole]

Well @viole knows that I am drunk and knows that over the Internet, so stay out of that one.
So if she can use negative projections on me, I will just taunt her.

What is negative about being drunk?

ciao

- viole

 

[Polymath257]

This describes wave function behavior at the Quantum smallest scale of individual particles and NOT continuous time/space and gravity at the Quantum scale.

Still waiting . . .

yes, it does describe continuous spacetime. Otherwise, there would not be partial derivatives (do you know what those are?).

 

[shunyadragon]

This is getting comical. "Stonewalling out of ignorance" seems to sum up your entire attitude here. I asked a very specific question: what part of the article specifically do you think supports your idea? You ignored it.

I was giving you the benefit of the doubt. I thought you actually did know something of the subject and had just got a bit confused between speculation and current, accepted theory, but after you posted that article supposedly in support of your ideas when it didn't say anything remotely relevant, has led me to believe that you really don't understand it at all.


That's exactly what quantum mechanics deals with in terms of scale. You get quantised energy levels because the wavelengths of the wavefunctions are significant at the scale of atoms. You start with a 'particle in a box' because its easy to visualise and the mathematics is relatively simple, but the principle is the same in an atom, it's just you have to use spherical harmonics, instead of a simple picture like this:

Particle in a box - Wikipedia

en.wikipedia.org

If you're talking about smaller scales, down to the Planck length, for example, you simply run out of theories. It all becomes speculation.

Yes, this represents the Quantum behavior of particles at the Quantum scale, but it fails to demonstrate continuous time/space and gravity at the Quantum scale.

I made an attempt to give a reference defining the issues and present view of the nature of the relationship between the large scale and the small scale, but alas it has been consistently ignored The only references you and others provided demonstrated observed Quantum behavior in the large scale, and the behavior of Quantum particles.

An important principle I defined for you and others to understand the basics.

Quantum decoherence - Wikipedia

en.wikipedia.org

Quantum decoherence is the loss of quantum coherence, the process in which a system's behaviour changes from that which can be explained by quantum mechanics to that which can be explained by classical mechanics. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.

If a quantum system were perfectly isolated, it would maintain coherence indefinitely, but it would be impossible to manipulate or investigate it. If it is not perfectly isolated, for example during a measurement, coherence is shared with the environment and appears to be lost with time; a process called quantum decoherence. As a result of this process, quantum behavior is apparently lost, just as energy appears to be lost by friction in classical mechanics.

Decoherence was first introduced in 1970 by the German physicist H. Dieter Zeh[1] and has been a subject of active research since the 1980s.[2] Decoherence has been developed into a complete framework, but there is controversy as to whether it solves the measurement problem, as the founders of decoherence theory admit in their seminal papers.[3]

Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath),[4] since every system is loosely coupled with the energetic state of its surroundings. Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion).[5] Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the system and environment. These have the effect of sharing quantum information with—or transferring it to—the surroundings.

Decoherence has been used to understand the possibility of the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse. It only provides a framework for apparent wave-function collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wave function are decoupled from a coherent system and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.

With respect to the measurement problem, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, observation indicates that this mixture looks like a proper quantum ensemble in a measurement situation, as the measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put, they require that the coherence of states be preserved and that decoherence be managed, in order to actually perform quantum computation. The preservation of coherence, and mitigation of decoherence effects, are thus related to the concept of quantum error correction.

 

[shunyadragon]

yes, it does describe continuous spacetime. Otherwise, there would not be partial derivatives (do you know what those are?).

No it DOES NOT you failed to understand the very basic concept of decoherence.

There is absolutely no reference to continuous time/space and gravity at the Quantum scale. in any of your references.

As previously cited one of the major directions of current research is explain the emergence of continuous rime space/time and gravity from the Quantum smallest scale fully acknowledging in the concept of decoherence. that continuous time/space and gravity are emergent ptopertrirs from the Quantum particles. Yes, there is a lot of research on Quantum behavior in the larger scale, and this research is part of the goal of understanding the emergent properties of continuous time/space from Quantum Mechanics in the larger scale.


Still waiting . . .

 

[Polymath257]

No it DOES NOT you failed to understand decoherence.

Actually, I bet I do a LOT more than you. Have you ever read a research paper about it? Do you know how it is relevant to quantum computing?

There is absolutely no reference to continuous time/space and gravity at the Quantum scale. in any of your references.

That you don't understand how my references say that is not my problem.

As previously cited one of the major directions of current research is explain the emergence of continuous rime space/time and gravity from the Quantum smallest scale fully acknowledging in the concept of decoherence.

Your article in Ars Technica did not deal with the 'smallest quantum scale'. And decoherence has NOTHING to do with the 'emergence of a continuous spacetime and gravity from the Quantum smallest scale.

That you think it does is also very revealing.

that continuous time/space and gravity are emergent ptopertrirs from the Quantum particles. Yrd, there is a lot of research on Quantum behavior in the larger scale, and this research is part of the goa, of understanding the emergent properties of Quantum Mechanics in the larger scale.

Show where this is part of *accepted* quantum mechanics. I think you misunderstand a great deal of what you are reading about QM.

Still waiting . . .

So are we all.

 

[ratiocinator]

Yes, this represents the Quantum behavior of particles at the Quantum scale, but it fails to demonstrate continuous time/space and gravity at the Quantum scale.

Just look at the mathematics on the page I linked to. What do you see? From the statement of the Schrödinger equation (in a form relevant to the problem):

onwards, we have operators that only make sense if applied to continuous variables. So, in the above equation, we have two partial derivatives, a first order with respect to time and a second order with respect to position. Partial derivatives don't make sense unless the variable (time and position in this case) is continuous. Lower down you've got integrals, which also make no sense unless the relevant variable is continuous.

Do you actually understand calculus and what partial derivatives are?

An important principle I defined for you and others to understand the basics.

Quantum decoherence - Wikipedia

en.wikipedia.org

Quantum decoherence...

We know what decoherance is. It has nothing to do with quantised space-time. Nothing.

 

[Polymath257]

Yes, this represents the Quantum behavior of particles at the Quantum scale, but it fails to demonstrate continuous time/space and gravity at the Quantum scale.

I made an attempt to give a reference defining the issues and present view of the nature of the relationship between the large scale and the small scale, but alas it has been consistently ignored The only references you and others provided demonstrated observed Quantum behavior in the large scale, and the behavior of Quantum particles.

An important principle I defined for you and others to understand the basics.

Quantum decoherence - Wikipedia

en.wikipedia.org

Quantum decoherence is the loss of quantum coherence, the process in which a system's behaviour changes from that which can be explained by quantum mechanics to that which can be explained by classical mechanics. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.

If a quantum system were perfectly isolated, it would maintain coherence indefinitely, but it would be impossible to manipulate or investigate it. If it is not perfectly isolated, for example during a measurement, coherence is shared with the environment and appears to be lost with time; a process called quantum decoherence. As a result of this process, quantum behavior is apparently lost, just as energy appears to be lost by friction in classical mechanics.

Decoherence was first introduced in 1970 by the German physicist H. Dieter Zeh[1] and has been a subject of active research since the 1980s.[2] Decoherence has been developed into a complete framework, but there is controversy as to whether it solves the measurement problem, as the founders of decoherence theory admit in their seminal papers.[3]

Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath),[4] since every system is loosely coupled with the energetic state of its surroundings. Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion).[5] Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the system and environment. These have the effect of sharing quantum information with—or transferring it to—the surroundings.

Decoherence has been used to understand the possibility of the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse. It only provides a framework for apparent wave-function collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wave function are decoupled from a coherent system and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.

With respect to the measurement problem, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, observation indicates that this mixture looks like a proper quantum ensemble in a measurement situation, as the measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put, they require that the coherence of states be preserved and that decoherence be managed, in order to actually perform quantum computation. The preservation of coherence, and mitigation of decoherence effects, are thus related to the concept of quantum error correction.

Very good. You made some quotes that describe decoherence. Nobody here is disputing this.

Now, at what point does it state anything like your position? Where does it say anything about a discontinuous space or time?

 

[exchemist]

Yes, this represents the Quantum behavior of particles at the Quantum scale, but it fails to demonstrate continuous time/space and gravity at the Quantum scale.

I made an attempt to give a reference defining the issues and present view of the nature of the relationship between the large scale and the small scale, but alas it has been consistently ignored The only references you and others provided demonstrated observed Quantum behavior in the large scale, and the behavior of Quantum particles.

An important principle I defined for you and others to understand the basics.

Quantum decoherence - Wikipedia

en.wikipedia.org

Quantum decoherence is the loss of quantum coherence, the process in which a system's behaviour changes from that which can be explained by quantum mechanics to that which can be explained by classical mechanics. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.

If a quantum system were perfectly isolated, it would maintain coherence indefinitely, but it would be impossible to manipulate or investigate it. If it is not perfectly isolated, for example during a measurement, coherence is shared with the environment and appears to be lost with time; a process called quantum decoherence. As a result of this process, quantum behavior is apparently lost, just as energy appears to be lost by friction in classical mechanics.

Decoherence was first introduced in 1970 by the German physicist H. Dieter Zeh[1] and has been a subject of active research since the 1980s.[2] Decoherence has been developed into a complete framework, but there is controversy as to whether it solves the measurement problem, as the founders of decoherence theory admit in their seminal papers.[3]

Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath),[4] since every system is loosely coupled with the energetic state of its surroundings. Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion).[5] Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the system and environment. These have the effect of sharing quantum information with—or transferring it to—the surroundings.

Decoherence has been used to understand the possibility of the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse. It only provides a framework for apparent wave-function collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wave function are decoupled from a coherent system and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.

With respect to the measurement problem, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, observation indicates that this mixture looks like a proper quantum ensemble in a measurement situation, as the measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put, they require that the coherence of states be preserved and that decoherence be managed, in order to actually perform quantum computation. The preservation of coherence, and mitigation of decoherence effects, are thus related to the concept of quantum error correction.

None of this makes any reference to space and/or time being granular rather than continuous. What is its relevance to your contention?

(Just realised this asks almost the same question as @Polymath257 's post, so no need to reply separately.)

 

[shunyadragon]

The point seems to have sailed way over your head. You can't do a partial derivative with respect to time and space coordinates unless they are continuous.

Nothing of substance here, again . . .

The Particle in a Box you cited is the nature of an individual in a limited movement within a theoretical limiting box not continuous time as in the large scale. The particle would have to get out of the box in continuous time in space for your clinging to this reference to be repotely valid.

Particle in a box - Wikipedia

en.wikipedia.org

In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.

The particle in a box model is one of the very few problems in quantum mechanics which can be solved analytically, without approximations. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It serves as a simple illustration of how energy quantizations (energy levels), which are found in more complicated quantum systems such as atoms and molecules, come about. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.

 

[exchemist]

Nothing of substance here, again . . .

The Particle in a Box you cited is the nature of an individual in a limited movement within a theoretical limiting box not continuous time as in the large scale. The particle would have to get out of the box in continuous time in space for your clinging to this reference to be repotely valid.

Particle in a box - Wikipedia

en.wikipedia.org

In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.

The particle in a box model is one of the very few problems in quantum mechanics which can be solved analytically, without approximations. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It serves as a simple illustration of how energy quantizations (energy levels), which are found in more complicated quantum systems such as atoms and molecules, come about. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.

No you are once more refusing to see the point. The particle in the box was chosen as it is about the simplest example of applying Quantum Theory to a physical system. And to do it you need a differential equation, i.e. calculus, which only works on variables that have continuous values. We could equally well choose the hydrogen atom, but the maths would be excessively complicated to write out on a forum not designed for that. Are you going to claim the hydrogen atom is a bad example because the electron in the 1s orbital doesn't have enough energy to get out of the atom?

Whether you like it or not, the modern model of the hydrogen atom is a Quantum Mechanical model which, because it employs differentials of functions with respect to time and spatial coordinates, must assume continuous values for these coordinates. That is part of the maths of calculus. ( @Polymath257 would be the best person to explain why, seeing as he is actually a professor of maths at an American university and teaches this sort of thing for a living. I could have a go, in a handwavy sort of way, but I might get it a bit wrong, as I'm just a chemist who uses maths from time to time.)

 

[shunyadragon]

No you are once more refusing to see the point. The particle in the box was chosen as it is about the simplest example of applying Quantum Theory to a physical system. And to do it you need a differential equation, i.e. calculus, which only works on variables that have continuous values. We could equally well choose the hydrogen atom, but the maths would be excessively complicated to write out on a forum not designed for that. Are you going to claim the hydrogen atom is a bad example because the electron in the 1s orbital doesn't have enough energy to get out of the atom?

Whether you like it or not, the modern model of the hydrogen atom is a Quantum Mechanical model which, because it employs differentials of functions with respect to time and spatial coordinates, must assume continuous values for these coordinates. That is part of the maths of calculus. ( @Polymath257 would be the best person to explain why, seeing as he is actually a professor of maths at an American university and teaches this sort of thing for a living. I could have a go, in a handwavy sort of way, but I might get it a bit wrong, as I'm just a chemist who uses maths from time to time.)

Actually the above I agree sort of, but you are dancing around and not addressing the main issue. Still nothing here that demonstrates continuous time/space and gravity at the Quantum scale.

A Quantum particle dancing around in a box is continuous time/.space at the large scale.

Still waiting . . .

 

[Polymath257]

Actually the above I agree sort of, but you are dancing around and not addressing the main issue. Still nothing here that demonstrates continuous time/space and gravity at the Quantum scale.

A Quantum particle dancing around in a box is continuous time/.space at the large scale.

Still waiting . . .

Still waiting for any article claiming that discrete time/space are accepted science.

No, the particle in a box is a standard quantum mechanical exercise that applies to *any* particle. It isn't a matter of size.

It isn't at all clear what you are wanting.

Are you wanting a discussion of quantum gravity? If so, there is no accepted theory of such. Anything said about it will be pure speculation.

Now, it is YOUR turn. Give any article showing that discrete, quantized space and time is accepted science. AT this point, none of the articles you have given are relevant to that claim.

 

[gnostic]

Yes, this represents the Quantum behavior of particles at the Quantum scale, but it fails to demonstrate continuous time/space and gravity at the Quantum scale.

As far as I know, gravity operate at macro & massive scales. Massive body or massive object affect spacetime itself, causing curvature of spacetime.

Quantum Gravity is still at very “theoretical” hypothesis stage, yet to be tested, and definitely not an accepted “scientific theory”.

There are some theoretical physicists advocating and proposing gravity at quantum scale, but none of them have found accepted empirical solution(s) to QG...yet.

 

[shunyadragon]

Still waiting for any article claiming that discrete time/space are accepted science.

No, the particle in a box is a standard quantum mechanical exercise that applies to *any* particle. It isn't a matter of size.

It isn't at all clear what you are wanting.

Are you wanting a discussion of quantum gravity? If so, there is no accepted theory of such. Anything said about it will be pure speculation.

Now, it is YOUR turn. Give any article showing that discrete, quantized space and time is accepted science. AT this point, none of the articles you have given are relevant to that claim.

You have not presented anything from your view os accepted theory from any source that
Actually the above I agree sort of, but you are dancing around and not addressing the main issue. Still nothing here that demonstrates continuous time/space and gravity at the Quantum scale.

A Quantum particle dancing around in a box is continuous time/.space at the large scale.

Actually the above I agree sort of, but you are dancing around and not addressing the main issue. Still nothing here that demonstrates continuous time/space and gravity at the Quantum scale.

A Quantum particle dancing around in a box is continuous time/.space at the large scale.

Those books must be getting heavy.