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**New Theories / Re: Mathematics proven inconsistent an integer= a non-integer**

« **on:**23/01/2019 09:58:57 »

I don't know. ∞-∞ undetermined.

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I don't know. ∞-∞ undetermined.

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By multiplying by 10 you move the decimal point to the right, but in this case you get a number that is written the same way, 9.999...You assume 9.999... is 10x0.999... But you need to demonstrate it first.I don't think I need to show that you can multiply a number by 10 by moving the decimal point one place to the right.

And I understand your point, but perhaps you might go back and answer my earlier questions; especially this one

What is the difference between the number of nines after the decimal point in both cases?

What is the difference between the number of nines?

The difference is always 1 for any finite number of decimals, but I cannot tell for an infinite number. Does it vanish?

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0.999999...Yes, it may be but your explanation is flawed because of circular reference.

is the same as 1

it's just 2 ways of writing the same number

You assume 9.999... is 10x0.999... But you need to demonstrate it first.

9.99999x10=99.99990 not 9.99999 so what happens if we go on with bigger and bigger numbers? You will always have that 0 decimal, you can't get rid of it although the difference between the two numbers is smaller and smaller.

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To me.0.(9) seems ...To whom, and why?

...because, I thought that 0.999... never reaches 1. But you are right, 0.(9) doesn't clearly mean it belongs to (0,1) and not to (0,1].

Another thing, 1/3 is said to be 0.(3), but is it? What if it is again, belonging to (0,1/3) rather than to (0,1/3]?

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0.(9) seems to be a number within the interval (0,1) but not in (0,1]

whereas 1 can be found in (0,1] and not in (0,1)

Does it still mean 0.(9)=1 ?

whereas 1 can be found in (0,1] and not in (0,1)

Does it still mean 0.(9)=1 ?

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Spin example

While the position of a detected particle cannot be found with infinite precision although theoretically the detection appears at a single definite point when determining the spin, thing look more clear. For example we create a magnetic field between a magnet poles (C shape) and check the polarization of electrons. The magnetic field is assumed to be in a known direction. That's because the spin of the atoms interacts with the particles acordingly. However the spin of each atom in the magnets is unknown before any interaction but is a matter of probability. If you have for example much stronger magnetic filed and take each individual atom in the initial system of magnets, these atoms will align predominantly acording to the direction of the magnet they compose but each atom spin is not definite before measurement.

Now we know that if we prepare electrons in a magnetic field, their spin will become definite and known after they exit the magnetic field according to QM. However according this hypothesis most of the electrons will behave as having the expected spin. They will actually not have a definite spin, but a very high probability for the prepared spin.

While the position of a detected particle cannot be found with infinite precision although theoretically the detection appears at a single definite point when determining the spin, thing look more clear. For example we create a magnetic field between a magnet poles (C shape) and check the polarization of electrons. The magnetic field is assumed to be in a known direction. That's because the spin of the atoms interacts with the particles acordingly. However the spin of each atom in the magnets is unknown before any interaction but is a matter of probability. If you have for example much stronger magnetic filed and take each individual atom in the initial system of magnets, these atoms will align predominantly acording to the direction of the magnet they compose but each atom spin is not definite before measurement.

Now we know that if we prepare electrons in a magnetic field, their spin will become definite and known after they exit the magnetic field according to QM. However according this hypothesis most of the electrons will behave as having the expected spin. They will actually not have a definite spin, but a very high probability for the prepared spin.

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According to QM a system that has an associated wavefunction in a superposition of eigenstates of a position operator, collapses upon a measurement to a single eigenstate. Depending on the measurement precision in practice the result gives a linear combinations of close eigenstates. However, I don't think it is a measurement problem. The theoretical collapse to a single state doesn't seem to be a good idea.

Basically, when we do a measurement, it involves a designed system which can only be made of materials which are made of atomic structures. In any case, it involves an interaction between two particles that have never definite positions. For example we detect a transition of an electron to a different energy level. Therefore any collapse of a i.e. photon wavefunction is triggered by the interaction of the photon with a massive particle. But the interaction doesn't happen at a definite position. The photon energy quantum is absorbed by the electron but it doesn't happen at a point in space because the electron position is still in a superposition of eigenstates. In this case I would say, the photon wavefunction collapses and the position we get is the superposition of eigenstates of the electron that has absorbed the photon quantum, not a single point in space.

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If linear momentum is not quantized, it doesn't mean you can accelerate a particle continuously. The linear momentum can have any value, but you would reach that using various quanta.

Using gravity you can apparently accelerate smoothly but that's of course because the gravity quanta either don't exist or they are too small in energy. The same thing with using an electric or magnetic field, the quanta would be very low.

Using gravity you can apparently accelerate smoothly but that's of course because the gravity quanta either don't exist or they are too small in energy. The same thing with using an electric or magnetic field, the quanta would be very low.

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The idea starts from the equivalence principle where you can't distinguish between acceleration and gravity in certain theoretical conditions. If the principle holds you may expect gravity to be continuous and not quatised. However, when you accelerate something, as far as I know it doesn't happen smoothly. At a more fundamental level, there are force carriers, particles that make othet massive particles or systems like atoms and objects made of atoms accelerate. That means it can only happen in many small steps. These objects receive momentum quantum by quantum and you end up with a fairly constant acceleration on certain setups like for example a spacecraft using a constant power thruster. Therefore, if pefectly smooth acceleration wouldn't be possible, perhaps gravity happens the same way.

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But even a classical field, extends to infinity, the electric field around an electron extends to infinity. The strength of the fields vary and at some small distance from the peak, it becomes infinitesimal but not zero. So most of the energy is concentrated into a small place. That also explains particles "poping in and out of existence" from "nothing ".

Also there is no propagatin wave between entangled particles to carry information. Another thing, instead of thinking about particles in a superposition of being at certain positions according to the wavefunction, it is easier to think of a field and probabilities of an interaction of the field as a independent unit. QFT makes more sense in physics, QM uses a mathematical model that is quite weird because it tries to adapt the classical model of a particle as a corpuscle to quantum world which may not be a good idea.

Also there is no propagatin wave between entangled particles to carry information. Another thing, instead of thinking about particles in a superposition of being at certain positions according to the wavefunction, it is easier to think of a field and probabilities of an interaction of the field as a independent unit. QFT makes more sense in physics, QM uses a mathematical model that is quite weird because it tries to adapt the classical model of a particle as a corpuscle to quantum world which may not be a good idea.

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Yes, so what we call particles are fields that behave in a certain way, they interfere, interact, create waves and have an identity as a individual system. There is another thing I was wondering. They say the fields collapse to a single definite position and in QM for a particle when we apply the position operator we get a single position. In my opinion it is not quite like that. Here is some basic description. There is no way of designing some apparatus to determine an exact position. So I would say the fields simply interact with each other during a collapse, say a photon is absorbed by an electron. The photon field continues further as embeded into the electron field. This hapens at a moment of time an throughout all the space the fields occupied(which is the whole universe). Hence there is no definite position of interaction. When we detect something those positions are regions where the fields are stronger. And there is also the problem of time. How does it happen, at a single moment of time? This is another issue in my opinion.

Thanks

Thanks

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Here is my opinion on this:.

Can space

1) be considered a super fluid, by most theories,

2) exist without quantum fluctuations.

3) be multidimensional if non local effects can not be explained in any other way.

4) allow both real and virtual particles to exist in it.

5) expand due to dark energy( possibly caused by virtual particles/quantum fluctuations)

6) contract due mass and gravity( possibly due to the absorption of quantum fluctuations/gravitons)

1. It is more of a terminology matter. If you assume a superfluid, normally it can exist within a volume of space, but you can treat space so that it behaves similarly to a superfluid. In relativity there is no preferred reference frame, therefore this superfluid should be defined in such a way so that it can make the same predictions as relativity does. I'm not sure this could be a problem.

2. I don't think it can. I can only think of space extending to infinity or space could change far away from the known universe like when aproaching a black whole. So I don't think you can have space without any particle field in it with non zero field value. Space and time can't exist separately.

3. You should define what other dimensions you want, space, time, how many and how they work. But normally, because of energy conservation you should not need another dimension as it would allow energy to escape.

4. Don't see a problem

5. I don't know enough about dark energy,

6. You mean mass and energy. You will need to show how it works and if it makes the right predictions. To simulate gravity some scientists use air vacuum tubes and sound. But I've asked some physicist and they say it is not quite how spacetime works. Personally I don't see the problem. Whether you play a movie with time marks or show all the slides at once basically is the same thing.

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Thanks. About the link, yes it explains that there are no contradictions, but some physicist think there are, so it must be some confusion somewhere, I don't know enough of the details so I can't comment on it.Why relative motion is not necessary?I think you are forgetting gravitational effects. I know you know, because we’ve discussed before.Here is a different point of view, with more details:As it says in the link “None of this is really a contradiction between general relativity and quantum mechanics. ”

https://physics.stackexchange.com/questions/387/a-list-of-inconveniences-between-quantum-mechanics-and-general-relativity

Regarding gravitational effects I may have made a confusion. It was about what creates gravitational effects, or what makes spacetime to curve or if there is a medium what makes it react. And that should be I suppose the energy of the quantum field. A massive particle has rest energy in a form of mass and also if it has kinetic energy, then it should affect the spacetime. But can gravitational potential energy of a particle taken into account for evaluating how spacetime or presumably the medium is afected? It doesn't sound right.

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However, we know that a particle has higher energy when the associated wavelength is smaller. ......, therefore higher wavelength apear only if there is relative motion between the observer and the particle.Relative motion is not necessary.We are dealing now with effects on quantum fields, which GR cannot handle,I don’t understand what you are saying here. GR can handle quantum fields, but the 2 work at different scales. You wouldn’t use a micrometer to measure a football field.

Why relative motion is not necessary?

A massive particle has invariant mass and if in motion it gets additional energy. The faster it goes the shorter the wavelength. Do you mean we can also take into account a potential energy in some context?

Whether there are conflicts between GR and Quantum physics is debatable, but you may be right.

Here is a different point of view, with more details:

https://physics.stackexchange.com/questions/387/a-list-of-inconveniences-between-quantum-mechanics-and-general-relativity

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"Quantum spin isn't the same as light polarization though, so I don't see how this is a problem."

No it is not, you are right, but the way photons behave when passing through filters is related to quantum spin. By definition spin 1 corresponds to a left hand circularly polarized photon and -1 for right , (when h/2pi=1 ), and then you can write |H> and |V> using |L> and |R>. However you can also talk about photon polarization.

But if you use a linear filter and then send photons through the BBO, I don't think the two pairs will have same polarization between successive pairs.**So here must be the problem.**

Apparently a BBO produces SPDC of** two types **and you can have type I correlations where in fact the polarization will be the same for both photons and type II where they will have perpendicular polarization.

No it is not, you are right, but the way photons behave when passing through filters is related to quantum spin. By definition spin 1 corresponds to a left hand circularly polarized photon and -1 for right , (when h/2pi=1 ), and then you can write |H> and |V> using |L> and |R>. However you can also talk about photon polarization.

But if you use a linear filter and then send photons through the BBO, I don't think the two pairs will have same polarization between successive pairs.

Apparently a BBO produces SPDC of

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If you have set the experiment up so that both beams are definitely known to be vertically-polarized, I'm not sure why you think putting one of the beams through a filter would change that fact for either beam. It seems more likely that the filter would simply break the entanglement. You can't force entangled particles to be in one state or another.Yes, you are right. I thought that if you start with a polarized beam, let it go through the BBO crystal the entangled particles will have the initial polarization. But entangled particles always have opposite spin upon measurement. I don't see how this can work.

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As I understand it, quantum entanglement doesThis example is classical an of course it makes sense. However, this implies a single hidden variable...quantum mechanics doesn't. That's the difference.notinvolve instantaneous information transfer.

It is very hard to give examples that are both accurate to QM and relatable to our experiences, but the common comparison is this:

Two twin brothers want to share their birthday cake, but they are both on vacation in different places. Their mother cuts the cake with a single slice and sends each piece to one of her sons. Until opening the package, neither son knows whether the cut was made evenly, or if the other twin got a larger or smaller piece. It doesn't matter how far away the twins are, when one opens his package to see 60% of a cake, he instantly knows that his brother will be disappointed.

This example is representative of most QM entanglement sort of experiments in that an operation (cutting of the cake) is done that produces two complimentary things (slices of cake), which are then sent mailed) different ways such that information about them is unknown until the thing is actively inspected (package opened). The example falls short of QM reality because the outcome (who got how much cake) is determined by the mother (and she knows)--and even if some randomization is introduced, it still doesn't quite capture the nature of superposition... but it works well enough.

There is nothing magic about the instantaneity here. Each twin already has the knowledge that the cake slices will together add to one cake, and then presented with one slice, has all the information required to know the size of the other slice. This breaks down if their assumption is invalid (maybe mom ate a piece too). It is also important to remember that it still took time to send the cake to each of the twins, so the information sent from mom to son is constrained by the speed of light. That each son gains insight into both packages at the same time is only a matter of logic, not physics.

In the classical example, we have slice A and B. The kid can look and it test is wether it is A and make another test to see if it is B. Suppose it is A. The kid makes a test to see if it is B and yields negative. And if it tests fot A gets positive. So the hidden variables are Tested A + / tested B - and for the other pair the opposite signs. So the hidden variable can be a matrix that can have two options (+,-) or (-,+), which can be represented by 0 or 1, so a single boolean variable, for a classical particle you would need an infinity (in quantum you need none ). That's classical.

Now in quantum the state is not defined until a measurement is done. So it seems an instantaneous action at distance. Even with the detection of a single particle emmited by a source, the particle is everywhere until measured then it disappears from all positions and reveals itself on a single one. In other words a measurement here makes the particle appear here and vanish from all other superpositions. But at least what is clear is that there unlike particle travel as waves, the collapse of a quantum field does not involve waves or signals traveling. I don't get it. I think something is wrong either with relativity or QM, if not with both.

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I was thinking of a way to send instant signals using entanglement.

Introduction:

Some say the measurement changes the system state. For example I make a measurement on a photon which has an unknown spin, then subsequent measurements for the same axis will show the same spin. We would conclude the first measurement changed the quantum state of the particle. If you do that to entangled particles, you change the state of the whole system. A measurement on the system using this time the other pair, will give the expected result of oposite spin. The system is not in a definite state before measurement which was demonstrated by the absence of hidden variables. Therefore we are not revealing the state of the system, we are interacting with it, yet they say there is no instant cause and effect.

The experiment:

We setup a laser, and using lenses and a BBO crystal we send a pair of photons vertically polarized in opposite directions. The entangled photons will have half of the frequency of the original beam so we can distinguish between entangled photons and not entangled ones. They reach two locations preferably very far from each other ar different distance from the laser, location A will be closer and B farther. At each site we use a linearly polarized filter in front of each beam. If A places the filter at 90 degrees it blocks all the radiation and it should change the entangled system so that a following measurement at 0 degrees will result in no detection.

I wonder what happens at location B. Before we place the filter at A all photons are vertically polarized and will pass. Will the filter at A influence what happens at B? I guess not but what would be the answer given by QM. I expect it would give exactly the result we get from the experiment.

Introduction:

Some say the measurement changes the system state. For example I make a measurement on a photon which has an unknown spin, then subsequent measurements for the same axis will show the same spin. We would conclude the first measurement changed the quantum state of the particle. If you do that to entangled particles, you change the state of the whole system. A measurement on the system using this time the other pair, will give the expected result of oposite spin. The system is not in a definite state before measurement which was demonstrated by the absence of hidden variables. Therefore we are not revealing the state of the system, we are interacting with it, yet they say there is no instant cause and effect.

The experiment:

We setup a laser, and using lenses and a BBO crystal we send a pair of photons vertically polarized in opposite directions. The entangled photons will have half of the frequency of the original beam so we can distinguish between entangled photons and not entangled ones. They reach two locations preferably very far from each other ar different distance from the laser, location A will be closer and B farther. At each site we use a linearly polarized filter in front of each beam. If A places the filter at 90 degrees it blocks all the radiation and it should change the entangled system so that a following measurement at 0 degrees will result in no detection.

I wonder what happens at location B. Before we place the filter at A all photons are vertically polarized and will pass. Will the filter at A influence what happens at B? I guess not but what would be the answer given by QM. I expect it would give exactly the result we get from the experiment.

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Hi,

Regading the OP, I also think of this possibility that quantum fields should require a medium that excitates. Actually I don't see any other possibility.

From the start I'd like to clarify that space and a medium are different things. I think you either use some rules of spacetime or a medium in which the light and matter waves travel. Not sure if you can call what you have described space anymore. It still confuses me as the GR spacetime actually is like a medium.

In this case the medium can occupy a volume of space. This space can be euclidean or you can even use the Minkowsky spacetime but I suppose an euclidean spacetime would be the right option as it would be just for reference.

Wether this medium is static or like a fluid is another question that would need to be answered. If you want to be closer to GR, a dynamic medium would be preferable. In this case the medium would react to let's say the intensity of the field. However, we know that a particle has higher energy when the associated wavelength is smaller. But all particles have invariant rest mass, therefore higher wavelength apear only if there is relative motion between the observer and the particle. We need some math to see if this works, and it is quite complicated from my point of view. Anyway, gravity would be the effect on this fluid. We are dealing now with effects on quantum fields, which GR cannot handle, so it would be required completely new equations to work with these.

If on the other hand the medium is static, gravity could be mediated by quantum particles or just continuous effect between fields.

For now we have a good classical theory for gravity that we can't use because at a fundamental level there is quantum physics, and another problem is we don't have physical interpretation for Quantum physics either.

Regading the OP, I also think of this possibility that quantum fields should require a medium that excitates. Actually I don't see any other possibility.

From the start I'd like to clarify that space and a medium are different things. I think you either use some rules of spacetime or a medium in which the light and matter waves travel. Not sure if you can call what you have described space anymore. It still confuses me as the GR spacetime actually is like a medium.

In this case the medium can occupy a volume of space. This space can be euclidean or you can even use the Minkowsky spacetime but I suppose an euclidean spacetime would be the right option as it would be just for reference.

Wether this medium is static or like a fluid is another question that would need to be answered. If you want to be closer to GR, a dynamic medium would be preferable. In this case the medium would react to let's say the intensity of the field. However, we know that a particle has higher energy when the associated wavelength is smaller. But all particles have invariant rest mass, therefore higher wavelength apear only if there is relative motion between the observer and the particle. We need some math to see if this works, and it is quite complicated from my point of view. Anyway, gravity would be the effect on this fluid. We are dealing now with effects on quantum fields, which GR cannot handle, so it would be required completely new equations to work with these.

If on the other hand the medium is static, gravity could be mediated by quantum particles or just continuous effect between fields.

For now we have a good classical theory for gravity that we can't use because at a fundamental level there is quantum physics, and another problem is we don't have physical interpretation for Quantum physics either.

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What does quantum mechanics have to say about this aspect?

Matter usually differs by antimatter having opposite charge.

It is said that the Universe in the early stages should have created equal amounts of matter and antimatter.

The total charge is conserved no matter the interactions and if we go back in time indefinitely the universe has always been neutral. If in the early stages the universe was all EM radiation, the total charge had to be zero. This is also means a charge symmetry which feels a more natural course. But the can reason we don't have matter-antimatter symmetry have do with the randomness of nature. A classical universe would have evolves perfectly symmetrical. The whole Universe would've been a perfect sphere growing ( it doesn't matter how you model it, it remains classical). But in quantum terms, if we restarted the universe like 1000 times, would it go ~50% of times with more matter and ~50% times more antimatter? If this is the case it is extremely unlikely to be go equal parts. Can we apply this principle?

For example we flip a coin for like

Matter usually differs by antimatter having opposite charge.

It is said that the Universe in the early stages should have created equal amounts of matter and antimatter.

The total charge is conserved no matter the interactions and if we go back in time indefinitely the universe has always been neutral. If in the early stages the universe was all EM radiation, the total charge had to be zero. This is also means a charge symmetry which feels a more natural course. But the can reason we don't have matter-antimatter symmetry have do with the randomness of nature. A classical universe would have evolves perfectly symmetrical. The whole Universe would've been a perfect sphere growing ( it doesn't matter how you model it, it remains classical). But in quantum terms, if we restarted the universe like 1000 times, would it go ~50% of times with more matter and ~50% times more antimatter? If this is the case it is extremely unlikely to be go equal parts. Can we apply this principle?

For example we flip a coin for like

Code: [Select]

`10^{20}`

times. We will get a ~50/50 ratio. However, in absolute values we can have something like Code: [Select]

`5.000001•10^{19}`

tails and Code: [Select]

`4.999999•10^{19}`

heads. But Code: [Select]

`0.000001 • 10^{19}`

is very large and would be equivalent to the matter left in the Universe.