# Are there no discontinuities in Nature ?

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The following statement was offered in a recent thread as justification for a point.

As this was not really germane to the thread and I can't find it anyway since the forum upgrade, I thought it woudl make a good discussion subject.

Quote

There are no discontinuities in Nature

Well I take'Nature' to mean the real world, both theoretical and observable and I respond "Science sees Nature as rife with discontinuities. In fact so much so that many Sciences have coined specific (often quite colourful) words for their discontinuities."

So in Earth Sciences (Geology, Paleontology etc) we have

Unconformity
Fault (many sub types)
Extinction

In (Fluid) Mechanics we have

The Hydraulic jump

In Mathematics and Computer Science we have the terms

Concete Mathematics
Discrete Mathematics
Endpoint
Boundarypoint
and of course discontinuous.

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The statement seems both false and ambiguous at least when not put in a context.

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1 hour ago, studiot said:

The following statement was offered in a recent thread as justification for a point.

As this was not really germane to the thread and I can't find it anyway since the forum upgrade, I thought it woudl make a good discussion subject.

Well I take'Nature' to mean the real world, both theoretical and observable and I respond "Science sees Nature as rife with discontinuities. In fact so much so that many Sciences have coined specific (often quite colourful) words for their discontinuities."

So in Earth Sciences (Geology, Paleontology etc) we have

Unconformity
Fault (many sub types)
Extinction

In (Fluid) Mechanics we have

The Hydraulic jump

In Mathematics and Computer Science we have the terms

Concete Mathematics
Discrete Mathematics
Endpoint
Boundarypoint
and of course discontinuous.

Is "discontinuity" being used in the mathematical sense of non integrability? "Not smooth" ?

(any way to delete frames?)

Edited by geordief

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37 minutes ago, koti said:

The statement seems both false and ambiguous at least when not put in a context.

Which statement the inspirational one or mine?

15 minutes ago, geordief said:

Is "discontinuity" being used in the mathematical sense of non integrability? "Not smooth" ?

Some uses correspond to this but I was trying to emphasize usage that has meaning in many sciences and the wide range of such usage.

17 minutes ago, geordief said:

(any way to delete frames?)

Try placing the cursor at the top of your second quote frame and use the back arrow (by the += key).

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9 minutes ago, studiot said:

Which statement the inspirational one or mine?

I would say that the inspirational one seems false, though there may be some contexts where it might fit to varying degrees.

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12 minutes ago, studiot said:

Which statement the inspirational one or mine?

This one: „There are no discontinuities in Nature”

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18 minutes ago, studiot said:

Which statement the inspirational one or mine?

Yours .You seem to have answered this viz:

"Some uses correspond to this but I was trying to emphasize usage that has meaning in many sciences and the wide range of such usage."

Try placing the cursor at the top of your second quote frame and use the back arrow (by the += key).

thanks ,a long standing niggle solved(discontinued)

..

Edited by geordief

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8 minutes ago, geordief said:

thanks ,a long standing niggle solved(discontinued)

I have just encountered your difficulty, the quote button is misbehaving when you try to quote the full post.
Thus:

9 minutes ago, geordief said:

..

Which is all I get when I click on 'the Quote at the bottom of your post.

Selecting a aprt of the post and using the pop-up 'quotethis' still works correctly.

Also if you do get a blank frame you can remove it holding down the CTRL key and hitting the letter Z (shortcut for undo) but only immediately after.

12 minutes ago, geordief said:

Which statement the inspirational one or mine?

Yours .You seem to have answered this viz:

If you look back at my original this was a question to koti, not you, so no I did not answer it, but thanks koti for yours.

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Phase changes (esp. sublimation)

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35 minutes ago, studiot said:

I have just encountered your difficulty, the quote button is misbehaving when you try to quote the full post.
Thus:

Which is all I get when I click on 'the Quote at the bottom of your post.

That was my fault . I answered your post within the text of your own frame (adding format to differentiate authorship)  and added a couple of sneaky full stops in the area we are expected to post in.

That's because I haven't mastered multi quoting after all these years

Edited by geordief

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On 30/09/2017 at 11:55 AM, studiot said:

The following statement was offered in a recent thread as justification for a point.

As this was not really germane to the thread and I can't find it anyway since the forum upgrade, I thought it woudl make a good discussion subject.

Well I take'Nature' to mean the real world, both theoretical and observable and I respond "Science sees Nature as rife with discontinuities. In fact so much so that many Sciences have coined specific (often quite colourful) words for their discontinuities."

So in Earth Sciences (Geology, Paleontology etc) we have

Unconformity
Fault (many sub types)
Extinction

In (Fluid) Mechanics we have

The Hydraulic jump

In Mathematics and Computer Science we have the terms

Concete Mathematics
Discrete Mathematics
Endpoint
Boundarypoint
and of course discontinuous.

I won't even look at the response, however, if point particles are not actually pointlike, discontinuities of the electromagnetic field do occur. It has been speculated by other scientists, maybe the gravitational field may even take a discontinuity over the boundary of a non-zero radius particle. Other discontinuities exist in theoretical physics, such as the creation of virtual particles, but they tend to exist only for a short period of time (an energy in this case owed back to the vacuum). On the other hand, the theory of observable matter actually involves a concept of the ''longer lived virtual particle,'' that is, it is possible particles have arisen much similar to virtual particles and allowed to live in an irreversible process. So they will take on features, identical to those of observable particles. Renormalization processes may be hinted at but I would warn to search for other dynamics.

The whole point of gravity however taking such a discontinuity over the boundary was suggested to act like a Poincare stress.

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On 10/26/2017 at 5:22 PM, Dubbelosix said:

I won't even look at the response, however, if point particles are not actually pointlike, discontinuities of the electromagnetic field do occur. It has been speculated by other scientists, maybe the gravitational field may even take a discontinuity over the boundary of a non-zero radius particle. Other discontinuities exist in theoretical physics, such as the creation of virtual particles, but they tend to exist only for a short period of time (an energy in this case owed back to the vacuum). On the other hand, the theory of observable matter actually involves a concept of the ''longer lived virtual particle,'' that is, it is possible particles have arisen much similar to virtual particles and allowed to live in an irreversible process. So they will take on features, identical to those of observable particles. Renormalization processes may be hinted at but I would warn to search for other dynamics.

The whole point of gravity however taking such a discontinuity over the boundary was suggested to act like a Poincare stress.

I tend to think there are no discontinuities in reality besides 0 and above the speed of light. The reason for this discontinuity is not in the universe but rather the mathematics being used as Dubbelosix suggested the discontinuity from gravity was a lack of math to explain it or knowledge to explain it on the human side not universe side. Such discontinuities such as Tachyon condensation turned into the Higgs Mechanism when proper math was applied even GR was created due to discontinuities in SR and Maxwell's equations due to discontinuities in classical Electromagnetism. The idea of 0/0 being undefined and speed above C may be later defined as current math is just insufficient to explain the fine details of it.

Edited by Vmedvil

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I'm sorry, Dubbelosix and Vmedvil but my knowledge and enthusiasm for cosmology and particles physics waned with the closing of the 1960s so both your comments have rather passed me by.

Would either of you like to comment on the OP itself and/ or explain your own contributions?

Edited by studiot

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If I can find the relevant source for the discontinuities of the electromagnetic field I certainly will. I should know where the source is located so will be back later.

In a system that is static, only spatial derivatives contribute to the electromagnetic tensor

$\partial_0 T^{ij}_0 = -\partial_{0j}T^{ij}_0 = - \rho_0E^{i}_{0}$

The charge density is the same as the surface charge where in the rest frame is simply

$\sigma = \frac{e}{4 \pi R^2}$

which satifies

$\rho_0 = \sigma \delta(R - \tau_0)$

at the surface of the electron, there is a discontinuity at least in principle, in which the electric field is said to jump from $\frac{e}{4 \pi \epsilon_0R^2}$

$E^{i}_{0}$ is satisfied by

$r_0 < R: 0$ and $r_0 > R: \frac{e}{4 \pi \epsilon_0 R^2} \frac{x^i}{r_0}$

I have this written as a reference below my notes, no idea if it is related to the source of this information.

Edited by Dubbelosix

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Well, yes one of my contributions is to the bell paradox it is a relativity famous one in special relativity Bell Paradox Wiki which was a thought experiment back in 1959  which basically states that you have two space ships both start accelerating at the same-time in their own inertial reference frame which is called frame S and both having the same velocity and Lorentz contraction over Frame S, but these two ships have a string running between the two of them. It is suggested that the string would not break which seems to be incorrect despite logically seeming correct. For more on this you can read the Wiki which explains it pretty well, but the question was when will it break which required a different approach to solve.

Which basically was a long equation that said it will break when the Length contraction force of tension for a observer at rest on the string was above the tensile strength of the string which is equivalent to the electromagnetic bonds holding the string together at the weakest point if heterogeneous string or highest point of tension if homogeneous.

∇E(x,y,z) = (1/(1- (u2+a2t2)/C2)1/2)mc2

This can be used for a infinite amount of sources of acceleration but let's try just these two sources assuming that Acceleration is Homogeneous across (x,y,z) and not different for each point of (x,y,z) like in real life based on the location of the propulsion device on the ship and are in opposite directions upon L or X.

∇E(x,y,z)1 + ∇E(x,y,z)2 > σmax

So the string when break when relativistic energy goes above the Max Stress for the unit volume that the material can handle which assuming Y and Z have no pressure the Laplace operator can be dropped if all is upon X.

E(x)1 + E(x)2 σmax

Which the stress is equal to the max tensile strength for that unit volume for that material to break it at a point.

This tells when exactly from a observer frame when the string would break which is equivalent to the ship's masses at that point exceeding the tensile strength or strength of the electromagnetic bonds.

Edited by Vmedvil

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Thank you for replying, but I don't see a discontinuity.

Can you pinpoint it ?

The endpoint of a load extension graph is not a discontinuity since the graph does not go beyond that point.

Edited by studiot

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1 hour ago, studiot said:

Thank you for replying, but I don't see a discontinuity.

Can you pinpoint it ?

The endpoint of a load extension graph is not a discontinuity since the graph does not go beyond that point.

Well, the S or L frame was originally a discontinuity on whether the string would break or not until the proper math was used because each frame used here has a different synchronization scheme, the front rocket will not only appear to be a larger distance from the back rocket with respect to an instantaneous inertial frame, but also to have started at an earlier time. There is the discontinuity which was solved. Minkowski spacetime was discontinuous there.

Edited by Vmedvil

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Stating there

2 hours ago, Vmedvil said:

Well, the S or L frame was originally a discontinuity on whether the string would break or not until the proper math was used because each frame used here has a different synchronization scheme, the front rocket will not only appear to be a larger distance from the back rocket with respect to an instantaneous inertial frame, but also to have started at an earlier time. There is the discontinuity which was solved. Minkowski spacetime was discontinuous there.

Surely that is a contradiction, (hence Bell's paradox) not a discontinuity ?

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4 minutes ago, studiot said:

Stating there

Surely that is a contradiction, (hence Bell's paradox) not a discontinuity ?

Well, I guess that depends on how to define a discontinuity "Discontinuity in physics is something that means that a variable might be multi-valued at certain points."

There was some definite multiple values for the equation while in the original form for Frame S or L. It was solved for thus that discontinuity disappeared.

Edited by Vmedvil

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Here is an example from mathematics that is as clear cut as I can make it

The integer line is discontinuous

The real number line is continuous

But I don't see any multiple values in either.

Edited by studiot

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11 minutes ago, studiot said:

Here is an example from mathematics that is a clear cut as I can make it

The integer line is discontinuous

The real number line is continuous

But I don't see any multiple values in either.

Well, this is posted in the physics section of this forums, well then physics does not have discontinuities of that nature being uniform if an equation has any of those problems it does not make it to physics and dies on peer review being a inaccurate description of the universe always having continuity.

Edited by Vmedvil

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2 minutes ago, Vmedvil said:

Well, this is posted in the physics section of this forums, well then physics does not have discontinuities of that nature being uniform if an equation has any of those problems it does not make it to physics and dies on peer review.

So can you show this for the mathematics of the hydraulic jump since that was one of my OP examples?

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8 minutes ago, studiot said:

So can you show this for the mathematics of the hydraulic jump since that was one of my OP examples?

Ya, it was solved on the wiki by the Froude number as a super-critical flow like a superconductor's Tfor resistance-less flow Hydraulic Jump Wiki. It has a critical velocity where this phenomena happens based on matter density.

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I have been unsure as to your position on the topic, since your comments have all been rather cryptic.

But thinking about it, you are right that at many discontinuities some physical, measurable quantity has multiple values (the imperfection of our equipment aside).

The hydraulic jump is one such which has a discontinuity with duplicate values in the specific energy line.

Other examples would be the electrical output v time of a square wave generator or a staircase generator.

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26 minutes ago, studiot said:

I have been unsure as to your position on the topic, since your comments have all been rather cryptic.

But thinking about it, you are right that at many discontinuities some physical, measurable quantity has multiple values (the imperfection of our equipment aside).

The hydraulic jump is one such which has a discontinuity with duplicate values in the specific energy line.

Other examples would be the electrical output v time of a square wave generator or a staircase generator.

Okay, I will clear this, The discontinuities of nature are caused when the forces of nature fight each other and cause a strange effect that the original equation did not take account for, as you suggest there is a missing multi-variable element usually missing, the equation is not as simple as originally thought when that happen and was too simplistic originally to explain the motion involved. Ever wonder why Gravity and QFT cannot be merged that is due to missing variables in GR and QFT not due to the universe not having those effects at that level two different physicist made those equations based on them understanding the fine details of that subject or part, they did not all go into the same detail nor math methods to generate them, this causes the different parts to miss parts that the other parts explain well due to not being as versed on the subject in that area. They were human and in no way perfect, thus problems are created in the realms between the areas as they did not use the same methodology to create those parts being from different minds. You can explain the universe in a billion different ways mathematically as long as it relates to the phenomenon that same way using different math methods. This is all on the human understanding side of things. Max Born and Einstein had very different ideas on how to define things in this example in mathematics

Edited by Vmedvil