Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 17/02/2019 18:38:17
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I’ve lost track of recent threads, so, although this might fit into one of them; I’m starting a new one just to test my thoughts.
A and B are in relative non-accelerated motion. Each knows that one of them is moving, because their relative positions are changing, but neither can say which is moving, and which, if either is stationary. No experiment carried out in either RF will determine which is moving; other than that, each can say there is relative motion between the two.
A accelerates. An accelerometer in A’s RF will establish that A is accelerating. A knows that she is the one accelerating,and, therefore, moving.
B’s accelerometer does not register acceleration, so B also knows that it is A who is accelerating, and is therefore moving.
Observers in non-uniform motion can establish that they are moving; but motion must be motion relative to something; or does that apply only to uniform motion?
If A and B are the only objects in an empty universe, the motion of each/either must be motion relative to the other. Unlike the case of uniform motion, both can know which is in accelerated motion.
If B is removed from this imaginary universe, A has nothing relative to which she can measure non-accelerated motion. Uniform motion becomes meaningless; she has no way of knowing if she is moving, in any sense.
If A accelerates, she can measure this acceleration, thus, she knows she is moving; although there is nothing relative to which she can be said to be moving. This begins to look like “absolute” motion; but can have little, or no, real meaning.
Consider that, in this “empty universe” scenario, A starts with a possible velocity (v1), which is effectively meaningless; accelerates, then returns to uniform motion, (v2). By the above reasoning, v2 is also meaningless. However, A has accelerated, which implies a change of velocity; So v1 and v2 must differ from each other.
If that is right, what actual difference could there be?
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Good to hear from you Bill. Been thinking aboutcha.
I’ve lost track of recent threads, so, although this might fit into one of them; I’m starting a new one just to test my thoughts.
A and B are in relative non-accelerated motion. Each knows that one of them is moving, because their relative positions are changing, but neither can say which is moving, and which, if either is stationary. No experiment carried out in either RF will determine which is moving; other than that, each can say there is relative motion between the two.
Well, that's what motion is: relative to something. There is no meaning to just being in motion, without the relation. Even an absolutist must relate your motion to some posited absolute frame.
A accelerates. An accelerometer in A’s RF will establish that A is accelerating. A knows that she is the one accelerating,and, therefore, moving.
B’s accelerometer does not register acceleration, so B also knows that it is A who is accelerating, and is therefore moving.
Acceleration is absolute (in SR), so yes, this is detected in any frame. Both of them know who is doing the acceleration.
Observers in non-uniform motion can establish that they are moving; but motion must be motion relative to something; or does that apply only to uniform motion?
Observers in non-uniform motion can establish that they are accelerating: that their motion (velocity) is changing. That's all. Motion is relative to things, so that velocity relative to something presumably not accelerating is changing.
If A and B are the only objects in an empty universe, the motion of each/either must be motion relative to the other.
This is similarly true with any number of objects.
Unlike the case of uniform motion, both can know which is in accelerated motion.
It seems to be like the uniform case, where both know that there is zero acceleration.
If B is removed from this imaginary universe, A has nothing relative to which she can measure non-accelerated motion.
Nothing against which velocity has meaning I suppose, except perhaps the frame before the acceleration. The one observer can still detect acceleration with the weight scale. Accelerometers still work, but it would be hard to explain what it means to your passengers unless you leave a trail of litter behind you, violating the postulate of there being no object B. Velocity really has no meaning if there is one object, and so acceleration is not to a different velocity, it is just a meaningless measured pressure of sorts.
If A accelerates, she can measure this acceleration, thus, she knows she is moving;
For the reasons I state above, A as a sole existent gives no meaning to motion. There is just acceleration, whatever that means. It is detectable, but that's all.
This begins to look like “absolute” motion; but can have little, or no, real meaning.
Yes, exactly.
Consider that, in this “empty universe” scenario, A starts with a possible velocity (v1), which is effectively meaningless; accelerates, then returns to uniform motion, (v2). By the above reasoning, v2 is also meaningless. However, A has accelerated, which implies a change of velocity; So v1 and v2 must differ from each other.
There seems to be neither v1 nor v2 in this scenario, since both are meaningless. There is no change between two different meaningless things. There is just the fact of the acceleration, which is a local effect that makes one of the walls apply a force.
If that is right, what actual difference could there be?
I see none.
A good deal more than motion is relative. Distance is a simple example. Distance requires 3 objects to have meaning. In a universe with just 2 (dimensionless) objects, the distance between them is meaningless.
For that matter, acceleration of a dimensionless object is locally meaningless. For your object above to have a local accelerometer, it would need to have nonzero dimensions. So two dimensionless objects with only one of them accelerating would be indistinguishable from a scenario with only the other one accelerating, or both or neither.
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If A accelerates, she can measure this acceleration, thus, she knows she is moving; although there is nothing relative to which she can be said to be moving. This begins to look like “absolute” motion; but can have little, or no, real meaning.
You have put your finger on the nub of newtonian mechanics. Quite simply, motion is a change in position vector, but in the absence of an origin for that vector, there is no way that a body can "know" it is moving at a constant speed. Beware of getting philosophical and introducing terms like "real meaning" - it can poison your physics!
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Considering relative things and acceleration the two can be combined to find the relative time dilation of an accelerating object using T = T0/√(1 -[2as]/c2). Where a is acceleration and s is the distance traveled.
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If A and B are the only objects in an empty universe, the motion of each/either must be motion relative to the other. Unlike the case of uniform motion, both can know which is in accelerated motion.
That's not observable. It belongs to the realm of metaphysics, not physics.
All motion is relative.
When you used the term "object" you meant it as a system which has instruments within it and not just a dumb rock or something. How you ask questions about this concerns what you have for instruments.
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If an object is accelerating it must surely be a composite object. So there will always be relative motion between the components of the accelerated object.
Even if the original companion (against which relative motion was measured) has magically disappeared the acceleration will create new "companions" as elements of the now accelerating object.
Also the accelerating object (in the "empty" universe) will, I suppose be composed of elements whose relative momentums (correct term?) will add up to zero.
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If an object is accelerating it must surely be a composite object.
Not at all. It could be a particle such as an electron which is not a composite object but a point object.
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If an object is accelerating it must surely be a composite object.
Not at all. It could be a particle such as an electron which is not a composite object but a point object.
This is a confusing area for me. An electron would require an environment to "accelerate" though wouldn't it ?It could not accelerate under its own steam ,as it were.(unlike a composite object,perhaps)
I think Bill (in the OP) was proposing an object that was alone in the universe undergoing acceleration.
If there were only two electrons in the universe (shortly to become one ,if I understood correctly) would those two electrons repel one another? That would seem like acceleration to me...Would the acceleration be ongoing ?
Would the acceleration be inversely proportionate to separation and so taper off to zero eventually? (there would be no gravity presumably if there were no gravitons in the universe ;) )
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What is ship a using to accelerate itself with ? Fuel gravity, all ship a actually knows if its a rocket is that its accelerating away from its reaction, devoid of ship b. Thing is there that your empty universe has just become populated ?
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Thanks for the wealth of responses. I hope to get back to several points, but it will be "hit and miss"; so to any I might miss, I say: don't take it personally. :)
Each knows that one of them is moving, because their relative positions are changing,
There is no meaning to just being in motion, without the relation.
I was hoping someone would say that.
In a universe with just 2 (dimensionless) objects, the distance between them is meaningless.
Do they have to be dimensionless because if they have dimensions, parts can be differentiated, thus, they can be regarded as “multiple” objects?
…. A as a sole existent gives no meaning to motion….
As I have long suspected: the solipsist is trapped, motionless, by bis own belief.
It seems to be like the uniform case, where both know that there is zero acceleration.
I missed that one! Still pondering its implications.
There seems to be neither v1 nor v2 in this scenario, since both are meaningless. There is no change between two different meaningless things. There is just the fact of the acceleration, which is a local effect that makes one of the walls apply a force.
In a thought experiment, one of the walls would apply a force, but can we know that acceleration would have any effect in an “empty universe” scenario?
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In a universe with just 2 (dimensionless) objects, the distance between them is meaningless.
Do they have to be dimensionless because if they have dimensions, parts can be differentiated, thus, they can be regarded as “multiple” objects?
Perhaps. I was thinking more of one homogeneous object, but with a length since it is not a point, so it is meaningful to say the 2nd object is 12 of those lengths away. Only 2 objects needed then. Yes, a thing comprised of parts is already multiple objects.
In a thought experiment, one of the walls would apply a force, but can we know that acceleration would have any effect in an “empty universe” scenario?
I suppose so. 'Force' is pretty meaningless for one existent, and hence acceleration is also unmeasurable and equally meaningless. An accelerometer requires at least 2 parts that move in relation to each other, even if those two parts are just me and one of the walls.
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…..Quite simply, motion is a change in position vector, but in the absence of an origin for that vector, there is no way that a body can "know" it is moving at a constant speed.
Succinctly put. Am I right in thinking that a “position vector” differs from a “position” in that it relates the position of a point to a specified origin?
Beware of getting philosophical and introducing terms like "real meaning" - it can poison your physics!
“real meaning” was intended to signify “not in a thought experiment”. I have accusations of philosophy when talking about infinity. :)
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That's not observable. It belongs to the realm of metaphysics, not physics.
Would that not apply to thought experiments, in general?
When you used the term "object" you meant it as a system which has instruments within it and not just a dumb rock or something. How you ask questions about this concerns what you have for instruments.
Point taken; I hadn’t got that deeply into the details, yet.
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If an object is accelerating it must surely be a composite object.
Not at all. It could be a particle such as an electron which is not a composite object but a point object.
Is a “point object” the same as a “point particle”?
If so, how can an electron be a point object?
My understanding is that a point particle has no spatial extension; whereas, an electron, although it has no internal structure, is a particle, or wave-packet, which always occupies a nonzero volume.
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What is ship a using to accelerate itself with? Fuel gravity, all ship a actually knows if its a rocket is that its accelerating away from its reaction, devoid of ship b. Thing is there that your empty universe has just become populated?
It's only a thought experiment, which Terry Pratchett describes as “One that you can’t do, and which won’t work” :)
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If an object is accelerating it must surely be a composite object.
Not at all. It could be a particle such as an electron which is not a composite object but a point object.
Is a “point object” the same as a “point particle”?
If so, how can an electron be a point object?
My understanding is that a point particle has no spatial extension; whereas, an electron, although it has no internal structure, is a particle, or wave-packet, which always occupies a nonzero volume.
I don't use the term "object" to have a particular meaning which excludes it being a particle in some cases.
That's a misconception of quantum waves. A wave is merely a probability description of where a particle is. E.g. when an electron is detected it has no spatial extent. Any spatial extent is merely the probability of where it would be found had its position been measured. All particles are point particles with the exception of particles made up of quarks.
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Yep, you're right Bill.
That's logic.
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That's a misconception of quantum waves. A wave is merely a probability description of where a particle is. E.g. when an electron is detected it has no spatial extent. Any spatial extent is merely the probability of where it would be found had its position been measured. All particles are point particles with the exception of particles made up of quarks.
Pete, I have neither the qualifications nor the desire to challenge your assertion, but my professional background leads me to suspect that this has about it an air of propitious obfuscation.
That aside; does Any spatial extent is merely the probability of where it would be found had its position been measured
mean that a particle such as an electron does not exist, as a measurable entity, until it is measured?
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Yep, you're right Bill.
Thanks, but now I'm not sure what I'm right about! :(
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Locally defined
" There is just acceleration, whatever that means "
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What that tells me is that 'relative motion' isn't local.
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That's a misconception of quantum waves. A wave is merely a probability description of where a particle is. E.g. when an electron is detected it has no spatial extent. Any spatial extent is merely the probability of where it would be found had its position been measured. All particles are point particles with the exception of particles made up of quarks.
Can that be rephrased as that the electron has a spatial extent (before measuring or interacting) that may be any size but that it is most probably vanishingly small? (I am assuming that the probability graph of its position peaks at the centre of that undefined spatial extent area)
I am not sure if I have not written gobble-de-gook ;)
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As an electron has mass, it cannot be infinitesimal since that would imply infinte density - infinities are evenless palatable than infintesimals!
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As an electron has mass, it cannot be infinitesimal since that would imply infinte density - infinities are even less palatable than infintesimals!
Well they've never found a particle that occupied actual volume either.
Density seems to be a measure of how close a group of particles are, and with only one, it has no meaning, just like expressing how close the cars are parked to each other in a lot with only one car. That isn't infinite density, it's just not density.
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Well they've never found a particle that occupied actual volume either.
Interesting comment. Does it depend on what you mean by finding a particle?
Some more information about such things as where a particle might be if it doesn't occupy volume would be appreciated.
Does the concept of "where" even apply to particles?
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Well they've never found a particle that occupied actual volume either.
Interesting comment. Does it depend on what you mean by finding a particle?
They're easy enough to find. No denying an electron is there, having charge and all that. It even may have a location of sorts, even if only defined as where you're most likely to find it if you measure it.
But what is not listed in the chart of fundamental particles is their volume. Sure, a quark say might hold the next quark at bay at some more or less fixed 'radius', but that's because the nuclear strong force is repulsive below a certain distance. Black holes demonstrate that such forces can be overcome, so it isn't the volume of the thing getting in the way. If black holes achieved their density by squashing fundamental things like quarks into smaller sizes, then they're not things, but collections of things which can be pressed closer together. So the only models that seem to work are ones that give no volume to such particles. They're effectively mathematical points, except mathematical points have actual locations, not just probabilities of where you might find them if you check.
Some more information about such things as where a particle might be if it doesn't occupy volume would be appreciated.
Well, there is a definition location where mathematical lines x and y meet at some point, and that point has no area or volume. Should you expect it to have that? The intuitions are all about collections of points. It seems quite unintuitive that a fundamental thing would extend into more than one place.
Does the concept of "where" even apply to particles?
Only as a probability it seems. There is the principle of counterfactual definiteness that underlies the concept of objective reality. It says that there is an objective state of things even if not measured. There is also the principle of locality which says information cannot travel faster than light or back in time. Bell's theorem proved that only one of these two principles can be true, so there are valid QM interpretations that hold to one or the other (or neither), but not both of them. I find it far more offensive to violate locality, so I am force to discard objective reality, and part of that includes an objective location of a particle between measurements.
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I'm going to have to find time to do justice to the last two posts, unfortunately, that won't be now.
One point jumps out, though:
It seems quite unintuitive that a fundamental thing would extend into more than one place.
Does this say that a fundamental thing occupies a space?
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No denying an electron is there, having charge and all that. It even may have a location of sorts, even if only defined as where you're most likely to find it if you measure it.
No denying an electron is there
How do you define “there” if it is not a place?
It even may have a location of sorts, even if only defined as where you're most likely to find it if you measure it.
I’m not sure what a “location of sorts” might be, nor how you can measure something that doesn’t have a location until you measure it.
So the only models that seem to work are ones that give no volume to such particles. They're effectively mathematical points, except mathematical points have actual locations, not just probabilities of where you might find them if you check.
I’m confused, I thought mathematical points had no dimensions. If they have no dimensions, how can they have locations?
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The classical electron radius is 2.82 x 10-15 m
This is a calculated , not an observed, value. The problem is that the damn things don't stand still and can't be imaged. There's no point in quoting the entire Wikipedia article which is quite concise but essentially formalises the "noninfinite density" argument by equating the mass-energy equivalent of an electron to the energy required to assemble the electron charge in a sphere of any given radius - i.e. a noninfinite charge density.
Whilst re has some value in modelling electron-photon interaction cross-sections, it can be misleading in giving a visualisation of the Bohr atom, which is self-contradictory.
The known mass of an electron, at about 10-30kg divided by its volume (7 x 10-44 m3) gives it a classical density of 1.43 x 1014 kg/m3, significantly less than that of a proton and therefore entirely reasonable.
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I'm going to have to find time to do justice to the last two posts
You're going to do justice to the rock/paper/scissors thing? That's good because it needs it.
One point jumps out, though:
It seems quite unintuitive that a fundamental thing would extend into more than one place.
Does this say that a fundamental thing occupies a space?
Having a location is not the same thing as occupying space. The point where two mathematical lines cross has a location, but it occupies no space. As for reality, it doesn't even seem to go as far as having a location. There is just a location where it is measured to some degree of accuracy.
No denying an electron is there
How do you define “there” if it is not a place?
It can be measured/detected. The situation is distinct from one that lacks an electron. I can choose to measure its location at the expense of clues as to its trajectory.
I’m not sure what a “location of sorts” might be, nor how you can measure something that doesn’t have a location until you measure it.
It doesn't have a location until measured, or (depending on your interpretation of choice) it has a location, but that location is not known. Sort of like a photon in a double-slit experiment, fired from a source. It doesn't have a location until it hits the target and makes a dot somewhere, but we know we fired it (do we? or just know in hindsight when a dot appears?). Before then, it is unmeasured and hence doesn't factually go through one slit or the other.
These sorts of games are better illustrated with the quantum bomb detector where you sort light-sensitive bombs from duds without looking at them. https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester if you're interested.
I’m confused, I thought mathematical points had no dimensions. If they have no dimensions, how can they have locations?
How is the dimensionless point at x=3, y=4 not have a location? 3, 4 (relative to the origin) is its location.
The classical electron radius is 2.82 x 10-15 m
This is a calculated , not an observed, value. The problem is that the damn things don't stand still and can't be imaged. There's no point in quoting the entire Wikipedia article which is quite concise but essentially formalises the "noninfinite density" argument by equating the mass-energy equivalent of an electron to the energy required to assemble the electron charge in a sphere of any given radius - i.e. a noninfinite charge density.
Agree with all of this. It is a functional radius, which is oddly about thrice the accepted radius of a proton, despite the much smaller mass. The proton radius seems to be quite a puzzle for physicists and there seems to be quite a bit published on the subject.
From the classical electron radius wiki page:
According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Attempts to model the electron as a non-point particle have been described as ill-conceived and counter-pedagogic.[1] Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems.
This seems to agree with what both of us are saying.