This is seriously cool stuff

[iantaylor2uk]

Thanks for that vlaiv. I thought the one I posted though was pretty good at explaining things, although a bit long at 40 mins

[iantaylor2uk]

I've been thinking a bit about these various videos, and the potential links to physics. 

I think a lot of problems arise when we think of infinity. 

I would suggest that infinity is a purely mathematical concept, and in fact never exists in real physical systems.

There are a lot of particles in the universe, but I don't believe there are an infinite number. There are space time theories out there (loop quantum gravity for example) where there is a minimum size for space-time - crucially it can't get infinitesimally small. Some people may like string theory, but as I understand string theory just assumes space-time is there so is no help in understanding space-time.

I know there are some cosmologists out there that think the universe is infinite - this is simply untestable, so you could argue it is not really a valid theory (since theories need to be testable, in my view).

It would be interesting, I think, to further explore what the implications are if we decide, in principle, that infinities never exist in real physical systems. 

[andrew s]

20 minutes ago, iantaylor2uk said:

I've been thinking a bit about these various videos, and the potential links to physics. 

I think a lot of problems arise when we think of infinity. 

I would suggest that infinity is a purely mathematical concept, and in fact never exists in real physical systems.

There are a lot of particles in the universe, but I don't believe there are an infinite number. There are space time theories out there (loop quantum gravity for example) where there is a minimum size for space-time - crucially it can't get infinitesimally small. Some people may like string theory, but as I understand string theory just assumes space-time is there so is no help in understanding space-time.

I know there are some cosmologists out there that think the universe is infinite - this is simply untestable, so you could argue it is not really a valid theory (since theories need to be testable, in my view).

It would be interesting, I think, to further explore what the implications are if we decide, in principle, that infinities never exist in real physical systems. 

Interesting, you dismiss the current standard cosmology as untestable as it includes an infinite flat space but not loop quantum gravity or string theory(ies) which don't have any testable predictions!

Personally I have no idea if reality includes infinities or not but that does not stop very good mathematical models of reality (our physical theories) including them!

Regards Andrew

Edited February 22 by andrew s

[iantaylor2uk]

I'm suggesting that if mathematical models of physical processes predict infinities then it is the model that is wrong, even if it may give a good description of the physics.

[Ratlet]

14 minutes ago, iantaylor2uk said:

I'm suggesting that if mathematical models of physical processes predict infinities then it is the model that is wrong, even if it may give a good description of the physics.

I agree.  I tend to take the opinion that an infinity is when maths has a blue screen moment.  Not Applicable.  Also think that maths isn't how the universe is, but rather how it behaves. 

[iantaylor2uk]

I think the main part of the problem is that mathematical models are based on calculus, differential equations etc, which usually assume nice continuous functions and that can things can be divided infinitely finely, whereas we have leant over the last 100 years or so that physics is essentially digital and not continuous at the smallest scales.

Edited February 22 by iantaylor2uk
typo

[andrew s]

59 minutes ago, iantaylor2uk said:

I'm suggesting that if mathematical models of physical processes predict infinities then it is the model that is wrong, even if it may give a good description of the physics.

A model in my view is right or wrong in how well it predicts the observation we can make, not one's  personal philosophical preferences. 

Virtuality all of our physical model rely on the continum. Space and time are continuous in SR, GR and QED not to mention all classical physics. 

1 minute ago, iantaylor2uk said:

when we have leant over the last 100 years or so that physics is essentially digital and not continuous at the smallest scales.

Can you give any examples? It's not true in quantum physics as many mistakenly think. Even spectral lines are broad to a greater or lesser degree.

Time of flight companions of light of different frequencies from distant events showed none of the expected differences expected from quantized space.

We can agree to differ 😉 

Regards Andrew 

[iantaylor2uk]

There are plenty of examples. 

The one that quicly comes to mind is: the whole of quantum mechanics effectively started because assuming that photons could have any continuous value of energy gave a result for the electromagnetic emissions from a blackbody which was plainly wrong. The only way the right result could be obtained was if photons could only have energies which came in discrete "chunks" whose value depended on the photon frequency. 

The assumption that a model is correct if it explains physical phenomena is, quite frankly, nonsense. Just look back in history, where Ptolemy's epicyclic model of the movement of planets, based on a sun centred solar system with lots of epicycles, gave excellent agreement with observations, but the model turned out to be completely wrong. 

When people do research, they ask "what if" questions. Einstein asked "what if the speed of light is constant" and worked out the consequences. 

It is perfectly reasonable, as a physicist, to ask the question "what if infinities do not exist in real physical processes" and work out the consequences from there. You are right that under such a scenario, space-time would be discrete so you would have to work out the consquences of this and whether there is experimental evidence of this being true.

The problem I have with a continuous space-time is that it does not explain what particles are - are they "in" space-time or do they somehow "sit on top of" space-time. 

With a discrete space-time model, you have the possibility that particles could be discrete patterns of space-time, which could be hundreds or thousands times larger than the Planck length, but which to us would, experimentally, still be point particles. Think of Conway's Game of Life. This shows that a 2-D lattice, with simple rules, can give rise to stable structures, some of which can propagate. If we had 3-D discrete space-time, again with fairly simple rules, you could imagine that certain structures could occur in space-time, which we effectively see as "particles", and the quantities we call charge etc. could be related to the topological properties of these structures.  

If no-one asks such questions, no research would get done, and no progress would be made, so whether you disagree with what people are suggesting, it is quite right that people are working on different things. 

[andrew s]

Firtly, no theory is ever "right" just more or less accurate at prediction. No one knows what reality is .

In quantum mechanics particles are localised excitations in quantum fields which are continuous.

While some measured values are indeed found to be discrete they in reality are not a single precise value but have a range. For example , spectral lines width depends on the life time of the states involved.

It maybe that a better set of theories of reality based on discrete components exist, but we don't have one yet.

Regards Andrew 

PS Several attempts have been made to create space time etc. from basic discrete elements but have not been successful.  

Edited February 22 by andrew s

[iantaylor2uk]

I don't think you have answered the key question of whether particles are "in" space-time or some how "sit on top of" space-time.

I've seen the explanation in terms of field before but this simply begs the question as to which is the more fundamental, space-time, or fields?

[andrew s]

40 minutes ago, iantaylor2uk said:

I don't think you have answered the key question of whether particles are "in" space-time or some how "sit on top of" space-time.

I've seen the explanation in terms of field before but this simply begs the question as to which is the more fundamental, space-time, or fields?

In QM space-time is the geometry on which the fields are described.  Particles are elements of our models that describe what we observe. What they are in reality or if they exist as in Plato's forms is anyone's guess. 

This is the paper on gamma rays mentioned. 

Regards Andrew 

[Zermelo]

6 hours ago, Ratlet said:

I agree.  I tend to take the opinion that an infinity is when maths has a blue screen moment.  Not Applicable.  Also think that maths isn't how the universe is, but rather how it behaves. 

I think quite a few physicists agree with this. For example, when GR predicts an infinite density for a black hole singularity, it's an indication that the theory has broken down, and not that there really is a point with infinite density.

In my mind I distinguish between, for example, (a) the universe may in principle have infinite extent, and (b) some physical quantity may take on an infinite value at a specific point. 

I'm comfortable with (a), but not (b). Perhaps in the same way that mathematicians (at least, before Cantor!) were careful to distinguish between the "potential" infinite and the "completed" infinite. The latter was considered beyond the pale: division by zero does not give "infinity" as an answer, it is undefined.

 

[andrew s]

In all these discussions it's important to remember that modern physical theories are just mathematical models. 

The best theories give valid predictions within their range of applicability. All theories have limits.

If you want more look to philosophy or religion. 

Regards Andrew 

Edited February 23 by andrew s

[vlaiv]

8 hours ago, andrew s said:

In all these discussions it's important to remember that modern physical theories are just mathematical models. 

The best theories give valid predictions within their range of applicability. All theories have limits.

If you want more look to philosophy or religion. 

Regards Andrew 

Problem is with the predictive power of the theories.

If it walks like a duck and quacks like a duck - it is easy to think that it is then accurate description of underlying physical reality

 

[iantaylor2uk]

Another issue is that it is well known that fractals appear almost everywhere in the natural world (see for example Mandelbrot's book). These usually arise due to scale invariance and simple rules. However, such curves are usually not differentiable, so standard methods of analysis (calculus) are not easily applied to them. If space-time is in fact fractal, then a lot of the maths being done may need to be revised.

See for example: https://arxiv.org/abs/0811.1396

This was published in Physical Review Letters in 2009 (this is the best physics journal that exists)

Edited February 23 by iantaylor2uk

[andrew s]

30 minutes ago, iantaylor2uk said:

Another issue is that it is well known that fractals appear almost everywhere in the natural world (see for example Mandelbrot's book). These usually arise due to scale invariance and simple rules. However, such curves are usually not differentiable, so standard methods of analysis (calculus) are not easily applied to them. If space-time is in fact fractal, then a lot of the maths being done may need to be revised.

The interplay between mathematics and theories physics is fascinating.  Sometimes mathematics has led other times physics. Several attempts at using new maths have been tried as by Penrose and Twistor Theory. 

Personally,  I don't think we are lacking in ideas and effort by theoretical physicists or in mathematics.  Rather, we don't have any new observations to motivate particular lines of enquiry. 

The LHC has failed to find convincing evidence for physics beyond the standard model.  Cosmology has dark energy  and matter but efforts to go further refining what they are other than numbers in LCDM lack motivation. 

I hope the JWST can find some new observations to light the way.

It seems we have reached a point where we have probed most of the scales and energy ranges experimentally available to us on Earth so we are left with looking up at the sky for guidance.

Regards Andrew 

Edited February 23 by andrew s