studiot

Water has very strong Van Der Waals forces. Hydrophobic particles are not influenced by these. That leaves momentum/KE exchange for the buffeting.

On a slightly different tack here is an interesting modern pdf about this issue, from a fractal invariant maths and a neuroscience point of view, from Oxford university.

Basically I agree with pretty well all you have said here. I would just stress that there are many types of invariants (see my answer to StringJunky below) invariants are not functions, there is no' invariant function', as there is a 'constant function' in maths. Invariants are a property of certain types of functions or transformations. Yes Invariants are a property of certain types of functions or transformations. As such they are the foundation of the modern way that relativity is viewed. But not all invariants work the same way. For instance the fractal invariant or the scale invariant is an invariant of geometry that does not related to a coordinate frame like relativity. There is an interesting modern view of fractal invariants in Neural Nets and the Brain from Oxford University (in pdf) that I am about to post in that long runningargument over artificial consciousness. https://academic.oup.com/cercor/article/33/8/4574/6713293

I checked an my memory of long ago was correct. I thought brownian motion was where I had first heard of lycopodium powder.

I didn't say it was and I agree that one of the main uses of the term invariant is the comparison of something between different coordinate systems or frames. I tried to avoid some of the more esoteric uses and offer a solid physical one. The physics of tha lamp oscillation is form invariant between the frames. But that form include a coefficient which is constant, but that constant has a different value is different in every frame, so the constant itself is not invariant. I was also trying not to point the finger at individuals but since you are commenting on Markus, I think he was to enthusiastic when he wrote this. all circumstance ? No any more than the spring constant has the same value under all circunstances. It too is constant under a ( more limited) specific set of circumnstances in that it is constant over a range of extensions of the spring. Anyway if you don't like that example try analysing the oft quoted 'constant AC voltage'. Or perhaps the example I gave before, which has nothing to do with coordinate systems or frames. My freezer keeps a constant temperature, but this temperature is not invariant as I am at liberty to turn the temperature maintained up or down. Or a final one Most of physics can be described by differential equations. We obtain 'solutions' to these DEs by integrating them. But integration includes an arbitrary constant of intgration, which is not therefore invariant. Of course we can eliminate the constant if we work by difference as in the definite integral or in the case of relativity coordinate differences. These words have a lot of work to do.

https://www.facebook.com/watch/?v=323855678960326

I'm sorry I don't follow. As the lamp is osscillating up and down its travel distance lies at right angles to its motion as part of the train so it is unaffected by relativity. But as part of the train its receeding motion affects the observer's perception of the period of the oscillation in accordance with relativity. So its period will appear to increase (as Markus says). But its period depends on the spring constant Since the period increases k must decrease. So it is a different spring constant.

Another good comment and viewpoint. I think that the fact that it will decay to a proton etc and not a raspberry pie is determined, but that when it will happen is not.

So with all that latitude we should all be more careful how we use the word in technical discussions.

The only way I would use that would be to mean to establish a base temperature to measure from. Otherwise knows as 'benchmarking' in modern parlance. There is no cause and effect relationship in play. Keep the questions coming because they are showing good things and just how deceptively complex the subject whicha t first sight seems to simple and clear cut, really is.

Here is a counter example to (1) Lycopodium powder. This was once used to demonstrate brownian motion, where the hydrophobic powder particles definitely do not clump together.

So it is not constant in all cases ? Nor is it an invariant of the system.

Both good thoughts, hopefully my response will add some clarification. There is a cause and effect connection to determinism so if we can consider the very last cause before the effect Joigus comment of how far back can we go along the chain of cause and effect is pertinent. Does determinism require the whole chain, just part of it, or just the immediate precedent ? When I said that humanity has never known enough to determine everything, I wasn't thinking of (only) data and the idea that if we knew the state variables of every particle at some time we could calculate the evolution or future history of the universe. I was thinking rather of our knowledge of the laws we would use to calculate this. And my counter example from the cuurent time would be dark matter and dark energy, not quantum theory (though obviously qm is not discounted) Isn't fixed another word for determined ?

There is more than one meaning to 'determined' ?

My answer to the first one is not necessarily, but you need to tell us your answer and why you think that since this looks like homework to me.

Is 'free will' not a form of determinism ? Once we have made our choice and enacted it the result is determined. Chocolate or Vanilla ? Once I walk away scoffing my chocolate ice cream the result was determined by my free will.

Yet there seem to still be some who promote it in threads here. Some of these threads have been have been very long and it is now even difficult to determine (pun intended) what their position actually is.

There have been several threads recently where some dubious statements about the distinction between constant and invariant have been made. I am therefore posting this thread to examine this issue by discussion. I am kicking off with a question An observer is watching the rear end of a train which is receeding a high speed , but not accelerating. Hanging on the back of the train by a long coil spring is a lamp which is oscillating up and down. What is the relativistic effect on the spring constant, ie what is the difference, if any, between the spring constant according to the train guard and the observer ?

With the recent debates about determinism v some other explanation of everything is a belief in determinism unwise ? I ask this because throughout the entire history of mankind there has never been a time when there was not something known that was unexplained. Even the God-did-it squad can only say GDI, they cannot say why or how he did it so cannot in all honesty say it was or was not determined. Likewise those philosophers and scientists who cleave towards the mechanistic 'clockwork universe' have to admit that they cannot definitely conclude that everything, because if their their best explanation is ' we believe there is an explanation, we just don't know what that is' this is not conclusive.

You are definitely moving forward. +1

My freezer is kept at a constant temperature of -20oC, but this is not invariant as I can turn the control knob up or down.

Since you clearly think you know better than anyone else and are not interested in what they have to say I wish you goodnight and pleasant dreams.

Perhaps I should add related words 'steady' and 'uniform' to the list of oft misapplied words.

Do you mean this ? Just what is a disturbance of spacetime ? If you don't understand something ask don't guess. Of course I don't call them time varyiing. Why would I ? Is there any evidence of gravitational field varying with time ? A gravitational field is however a good example to make my point. When viewed as a field (it can be viewed or described in other ways) the quantity of interest is called the gravitational potential. This potential has a definite, measurable value at every point in the gravitational field. It is an example of a potential field, with some special properties, one being that it is a conservative field. Other fields may also be assigned to the region of space occupied by the gravitational field. One such is the field of gravitational force acting on a material body. Another is an example of a direction field as force is a vector and as such has a direction at every point in the field. So you see, fields can be pretty complicated things, and so far we have just opened the book at static fields. The answer to my question 'what is waving' is the quantity of interest. This quantity may be a field quantity (ie part of a field) or it may not. It may be a material quantity such as water or it may be non material such as displacement or amplitude.

People used to imagine the atom as a plum pudding before Rutherford. I asked you what was waving., but received no answer. My question was not a joke but a subtle hint as to the proper definition of a Field. A Field is a region of 1, 2, or 3 dimensional space where some quantity can be defined and assigned a definite value. Most primary fields are static which means that these values do not vary. If the values are functions of another parameter such as time they are called time (or whatever) varying fields.