What is kinetic energy?

[Nowhere357]

Imagine an arrow in flight. We know there is kinetic energy associated with it - hence it's movement. My question is, can this energy be detected through the theoretical examination of the arrow alone? That is, if we examine only the arrow, can we detect that it has kinetic energy?

[Kat_Somm_Faen]

Heheh a bit of a loaded question really! How do you examine the arrow alone? You have to define its position but in reference to what? To examine is to define its frame of reference. It can simultaneously have Ek and not have Ek.

Kinetic energy Ek ( E sub k) = 1/2m*v^2

All you ned to know is the mass and velocity. Right. The reason why your question is "loaded' is how do we know velocity of a n arrow in some reference frame eh? Well its velocity is always a result of fidning out what velocity does the object move with respect to a reference frame.

Can you detect an obect static on you floor having energy? In all likelyhood not! We would say that your computer as not moving in your room. Yet the entire planet is moving and it velocity is actually quite a large quantity. So you computer in the reference frame of an observer outside of Solar system or static in relation the the Earth moving around the Sun would definitely consider as having no kinetic energy. It real depends on the reference frame. To me sitting by the end of the highway a cup of coffee some trucker is drinking has indeed kinetic energy. To the trucker it has none.

[Undercurrent]

At least in Newtonian mechanics, "energy" is the constant of integration in the first integration of the equations of motion for a point particle in a force field that depends only on spacial coordinates. Energy isn't a thing in the physical universe, just a formal quantity that happens to be constant over time solely as a consequence of the particle obeying Netwon's second law, which doesn't mention energy at all. The "kinetic energy" is just the term in this integral that contains the parameters related to the moving object.

You might as well take a dozen eggs, isolate one of them, and examine it to try to find the "twelve" in it.

[DigitalChicken]

Originally posted by Nowhere357
Imagine an arrow in flight. We know there is kinetic energy associated with it - hence it's movement. My question is, can this energy be detected through the theoretical examination of the arrow alone? That is, if we examine only the arrow, can we detect that it has kinetic energy?

You are thinking of energy as a "thing" when it is not really thought of that way. It is merely an abstract quantity for which relations can be discovered. Matter interacts and acts via these relations.

DC

[Nowhere357]

Good, thank you all, this agrees with what I was arguing elsewhere - that kinetic energy describes a relationship between objects, and is not something inherant in an object itself.

But then I got to thinking that if the arrow was accelerated to near light speeds, physical changes do occur, and it seems to me that if we could examine the arrow then, we could in theory detect those changes and determine the arrow is moving.

Then I get confused - moving compared to what? It looks like it's moving compared to itself? And I think that at regular speeds, the physical effects occur, just to a much less degree. If so, while these changes are not kinetic energy per se, it seems to me they would be a component of kinetic energy - there would be a relationship between the ke and the physical changes.

Is my error in thinking that the physical changes which occur at near light speeds could in theory be detected from an outside frame of reference? :confused:

[Silent Acorns]

Originally posted by Nowhere357
Is my error in thinking that the physical changes which occur at near light speeds could in theory be detected from an outside frame of reference? :confused:
I'm not sure what you mean by "physical changes" that occur at near light speeds. Are you talking about the decreasing length and increasing mass of the arrow?

If we're talking about simple special relativity, the the length of the arrow only decreases from the point of view of an observer. The same goes for the arrow's mass.

Suppose an arrow moving at 0.9 times the speed of light flew past you. If you knew what the arrow's mass and length were when it was at rest, the arrow would look "bunched up" and "heavy" (if you could measure the gravitational force between you and the arrow). If you then caught up and ran along side it, it would look completely normal to you.

These "physical changes" in the arrow are really just observational manifestations of the fact that the arrow is moving w.r.t. you. It's just all a part of what it means to "move".

[Nowhere357]

Silent Acorns
Are you talking about the decreasing length and increasing mass of the arrow?
Yes. As well as the slowing of time.

If we're talking about simple special relativity, the the length of the arrow only decreases from the point of view of an observer. The same goes for the arrow's mass.
I understand. To the arrow, it's the same length it always was.

These "physical changes" in the arrow are really just observational manifestations of the fact that the arrow is moving w.r.t. you. It's just all a part of what it means to "move".
That is my understanding.

Now consider the twin paradox. The ship leaves earth and approaches c, then returns. Less time has passed on the ship than on earth - from the earth frame. From the ship frame, it looks like more time has passed on earth - which amounts to less time has passed on the ship. Iow, whether from the earth, the ship, or even an outside frame, less time has passed on the ship than on the earth.

This tells me that the act of accelerating/moving causes actual physical changes on the ship - atomic and subatomic activity on the ship slowed down - relative to itself, as well as relative to the earth, and to the outside observer.

At one time I had thought I had a handle on this, but I think I've toasted the brain cells charged with holding the understanding. :(

[Silent Acorns]

Originally posted by Nowhere357
Now consider the twin paradox. The ship leaves earth and approaches c, then returns. Less time has passed on the ship than on earth - from the earth frame. From the ship frame, it looks like more time has passed on earth - which amounts to less time has passed on the ship. Iow, whether from the earth, the ship, or even an outside frame, less time has passed on the ship than on the earth.
Yes, this is my understanding as well.
This tells me that the act of accelerating/moving causes actual physical changes on the ship - atomic and subatomic activity on the ship slowed down - relative to itself,
I'm pretty sure this is wrong. Changes on the ship have slowed down realtive to an inertial observer, not realative to the ship itself. As far as the ship is concerned, all things continue normally.

[DeLurking]

[excuse the typos: english is not my native tonge]

If someone could explain us the twin´s paradox, I´d appreciate it very much.

What confounds me is that we could set the reference system on the ship. To the ship´s crew, it´s like all the universe moved at near c while they were still, and thus the time should pass slower for it. Or what´s the same, the nomad twin should return also older than the one sedentary one. :confused:

[Silent Acorns]

Originally posted by DeLurking
[excuse the typos: english is not my native tonge]

If someone could explain us the twin´s paradox, I´d appreciate it very much.

What confounds me is that we could set the reference system on the ship. To the ship´s crew, it´s like all the universe moved at near c while they were still, and thus the time should pass slower for it. Or what´s the same, the nomad twin should return also older than the one sedentary one. :confused:
Unfortunately, the proper answer to this involves the far more complicated and difficult General Relativity. Special Relativity deals with the special case of constant velocities, it's totally incapable of dealing with accelerations. It took Eistein many years to expand Special Realtivity to include the effects of acceleration to produce his truly great work: General Relativity.

The basic idea is that the twin on the ship goes through acceleration and decceleration, while the other doesn't. The twin on the ship can't detect his absolute velocity, but he can detect and measure his acceleration. The acceleration is the key to resolving the paradox. The twin on the ship ages slower because of this.

If you want more, you'll have to take a number of advanced physics courses from someone who knows a lot more about this than me.

[pmurray]

Energy is a numerical relation that is preserved whenever fundamental particles interact. The interesting thing about this relation is that there is an induction rule, which ultimately means tht energy is preserved for a macrosopic system of any size. Because this relation is preserved, it is natural to think of it as a "thing" that moves from place to place - like seeing a ripple in the water "move". But like the ripple, it is not thing in it's own right but an emergent property.

Kinetic energy is related to mass. Current thinking is that mass is something to do with a theoretical particle, the "Higgs boson". So KE would have something to do with interactions between particles with mass and the Higgs field.

[Jesse]

Silent Acorns:
Unfortunately, the proper answer to this involves the far more complicated and difficult General Relativity. Special Relativity deals with the special case of constant velocities, it's totally incapable of dealing with accelerations. It took Eistein many years to expand Special Realtivity to include the effects of acceleration to produce his truly great work: General Relativity.

The answer to the twin paradox does not require general relativity, you only need to know that acceleration is not relative, and that physics works the same in all inertial reference frames, but not in non-inertial ones. However, from within an inertial reference frame you can easily integrate over a curvy (accelerating) path to find the total time elapsed by an object moving along that path, so again, general relativity is not needed.

A longer explanation of how you can use do a path integral to find the proper time of the accelerating twin can be found in this section of the Usenet Relativity FAQ (http://www.weburbia.demon.co.uk/physics/relativity.html):

http://www.weburbia.demon.co.uk/physics/twin_spacetime.html

Of course, you could also solve the problem using general relativity, although this is more complicated, and not the way physicists would ordinarily approach things...from the same FAQ, here's a discussion of this approach:

http://www.weburbia.demon.co.uk/physics/twin_gr.html

[pmurray]

How do you measure the length of a moving object? By finding out where the start and end of it are at a given simultaneous instant of time. Right?

Imagine that you and I are in space, drifting relative to one another. Imagine I hold a spanner out in front of me and release it. It will just hang there is space, stationary. But from your POV, it's not stationary at all - it's drifting just like me.

Special relativity explains that just as relative motion means that we disagree about what "stationary" means, so too will we disagree on what "simultaneous" means. The motion distorts our frame of reference for both space and time.

Say you are in a 100m moving train that is relativistically shortened. To measure you, I make a chalk mark on the wall as your train passes - the nose and tail simultaneously. I measure the distnce between the two and it's 50m.

From your POV on the train, however, I did not make my chalk marks simultaneously at all. I marked the nose and then after an interval marked the tail. That's why I erroneously get the wrong length.

The converse would have happened if you on the train had marked the wall with chalk from the nose and tail of the train simultaneously. From my POV, you did the tail first, and then th nose. That's why your marks are further apart than they should be.

[Kat_Somm_Faen]

Pmurray!

I like your explanation!

Veru easy to undestand which usually mean that one persona talking about it undesrtands it :)

Straightforward...

TY!

[Nowhere357]

Consider that when the twin returns, there is a definite difference between them, beyond the types of differences that would have normally occured if they had both remained on earth.

I think the explanation from relativity theory reduces to a fact - time slowed down on the ship relative to the earth.

What can that statement mean, other than all physical activity on the ship slowed down? Then the molecules and atoms must have physically slowed down, relative to earth. And doesn't that mean actual physical changes occured on the ship?

If so, and these changes are due to acceleration, then perhaps the arrow's kinetic energy relative to earth has a physical component - a change in the molecules and atoms that is detectable only from an outside frame of reference. Because there is a physical difference between two atoms moving relative to each other - if one of the atoms had received acceleration?

Here (http://members.tripod.com/conduit9SR/SR0.html) are some good nickle lectures, But I haven't found the answer there yet. I don't see anything to contradict the idea.

[Friar Bellows]

There are (at least) two ways in which you could analyse the twin "paradox" using special relativity. Do the thing that Jesse described, where you infinitesimally chop up the (realistic) motion of the rocket into a series of momentarily comoving inertial reference frames and then integrate across the entire journey, or you could have just two inertial reference frames, one for the outgoing rocket, and one for the incoming rocket, and we could make the changeover between the two frames as brief as we like (or if you want something physically realistic, just have two rockets, one going in, one going out, crossing at the turnaround point). In the former case, you clearly aren't preserving the symmetry of the original twin "paradox" example, but then again, neither are you doing so for the latter case (*). And that's the point: the two situations can never be made symmetric, and the resolution of the "paradox" lies in this asymmetry.

Studying the twin paradox will really help you learn special relativity. I recommend Mermin's book, "Space and Time in Special Relativity".

By the way, the consequences of this time dilation can be pretty sobering for the budding interstellar space traveller. If he wants to visit the prettiest spots in the Galaxy within a human lifetime, then he'll have to travel at close to the speed of light. But when he returns to Earth from his Galactic voyage, thousands of years will have passed on his home planet. In what sense has he returned? For him as human being, it might not be in any meaningful sense at all. An interesting treatment of this can be found in Stanislaw Lem's novel, "Return from the Stars".

(*) For the latter case, the Earth can be represented by one inertial reference frame (ignoring gravity) for the entire round trip, while the rocket needs at least two.

[Shadowy Man]

Originally posted by Friar Bellows
or you could have just two inertial reference frames, one for the outgoing rocket, and one for the incoming rocket, and we could make the changeover between the two frames as brief as we like (or if you want something physically realistic, just have two rockets, one going in, one going out, crossing at the turnaround point).

This is the way that the resolution of the twin paradox was described to me in a class I took in college called "the philosophy of space and time."

Neither acceleration nor general relativity was needed.

[DeLurking]

Originally posted by Friar Bellows
An interesting treatment of this can be found in Stanislaw Lem's novel, "Return from the Stars".


Read that. I generally love Lem´s work, and I recommend them vehemently, specially the tales (like cyberiad, diaries from the stars and the pilot Pirx tales) are even better than the novels.

Back to the topic, so the rocket and the earth are not equivalent as systems of reference. Thanks; I´ll follow your advice and look for more.

[Friar Bellows]

Originally posted by pmurray
Kinetic energy is related to mass.

But, as I'm sure you know, massless particles still have kinetic energy. In special relativity the kinetic energy is defined as the total energy minus the rest mass energy (K = E - mc^2). So for a massless particle, like a photon (with m = 0), its kinetic energy is identical to its total energy (K = E).

[Kat_Somm_Faen]

Ummmm

E(photon)=E=hf

Plancks constant * frequency.

[Jesse]

Also, E^2 = m^2c^4 + p^2c^2

[Friar Bellows]

Originally posted by Kat_Somm_Faen
Ummmm

E(photon)=E=hf

Plancks constant * frequency.

Thanks, but I can't see the relevance of that to what I wrote about the kinetic energy of a photon being equal to it's total energy. Unless you simply wanted to remind us of how the energy of a photon relates to its frequency.

[DaveGE]

Originally posted by Nowhere357
What can that statement mean, other than all physical activity on the ship slowed down?

One thing it could mean is that the path of the ship in spacetime had a shorter proper time than the path of the Earth. No slowing happened; the ship just experienced less time, that's all.

[Nowhere357]

Originally posted by DaveGE
One thing it could mean is that the path of the ship in spacetime had a shorter proper time than the path of the Earth. No slowing happened; the ship just experienced less time, that's all.
But what does the phrase "experienced less time" mean? "Time" is the measurement of physical movement! Compared to earth, and whether viewed from the ship, earth, or outside observer, the ship experienced less time, which means it experienced less total atomic oscillations, for example.

There have been some interesting threads in the Philosophy forum, and I think the concensus is that time is a measurement based on observation of cyclic movement. Here, the ship experienced fewer such cycles then it would have it had remained on earth. What caused all movement on the (rapidly moving!) ship to experience fewer cycles? The acceleration is the only cause I can see.

So it looks to me like acceleration affects the physics of the matter being accelerated, relative to everything not so accelerated.

[pmurray]

Originally posted by Nowhere357
There have been some interesting threads in the Philosophy forum, and I think the concensus is that time is a measurement based on observation of cyclic movement. Here, the ship experienced fewer such cycles then it would have it had remained on earth. What caused all movement on the (rapidly moving!) ship to experience fewer cycles? The acceleration is the only cause I can see.

You are probably wasting your time if you expect to find empirical truth about this universe in the philosophy forum.

[Nowhere357]

Originally posted by pmurray
You are probably wasting your time if you expect to find empirical truth about this universe in the philosophy forum.
I disagree. Philosophy involves experience and observation. What do you think they are philosophizing about? :)

You apparently disagree with the definition of time as measurement of cyclical physical movement. Why? What is your definition?

[DaveGE]

Originally posted by Nowhere357
What caused all movement on the (rapidly moving!) ship to experience fewer cycles? The acceleration is the only cause I can see. The problem with that approach is that the slowing can happen on either leg of the trip, or both, or just during the acceleration, depending on which frame of reference you choose to analyze the problem in. So is the slowing caused by acceleration, or the speed? Or by moving away from the Earth? Or by moving towards the Earth? It's better to say just that the ship took a path through spacetime with a shorter length of time.

[Nowhere357]

DaveGE
The problem with that approach is that the slowing can happen on either leg of the trip, or both, or just during the acceleration, depending on which frame of reference you choose to analyze the problem in.
Well, given that we're looking at physical changes, I note that acceleration physically adds force or energy - if we accelerate an atom, we are adding energy from outside of the atom. Wouldn't this sort of compress the atom, ie physically change the atom?

So is the slowing caused by acceleration, or the speed?
Speed is entirely relative - there is no physical difference between objects moving at different speeds that I can see. Speed depends on frame of reference.

Or by moving away from the Earth? Or by moving towards the Earth?
I don't see any reason why this would be the case, unless Earth has some sort of specialness we don't know about yet.

I think acceleration is the more likely answer.

It's better to say just that the ship took a path through spacetime with a shorter length of time.
But my idea doesn't contradict this. Here you're talking about the mathematical representation, and I understand the value of this.

The sub-atomic decay associated with an atom happens statistically over time - the more time that passes, the greater the chance of decay. So the "age" of an atom can be considered the number of oscillations taken.
Consider two similar atoms at rest. They each oscillate at a given rate. If we accelerate one of the atoms (there and back again) it will be younger - it will have experienced fewer oscillations - then the unaccelerated one. It looks to me as if adding acceleration - energy - to the atom affects the sub-atomic activity, slowing the oscillations down, during acceleration. When the acceleration quits, whether at speed or at rest, the atom bounces back to normal. So to speak.

I think that an object taking a shorter path through spacetime is the same as an object taking fewer atomic oscillations. (Then it would have otherwise; or relative to an outside frame of reference.)

[DaveGE]

Originally posted by Nowhere357
Well, given that we're looking at physical changes, I note that acceleration physically adds force or energy - if we accelerate an atom, we are adding energy from outside of the atom. Wouldn't this sort of compress the atom, ie physically change the atom? Perhaps, but my point is that the apparent slowing can happen *before* the acceleration occurs; in fact, the apparent slowing can happen even if there is no acceleration.

But my idea doesn't contradict this. Here you're talking about the mathematical representation, and I understand the value of this. I am suggesting that the mathematical representation reflects the physical fact that the ship just experiences less time.

What causes it to experience less time is that it takes a "bent path" through spacetime. This is analogous to the fact that in Euclidean geometry a crooked path is longer than a straight one. I guess you could say that acceleration causes the slowing in the same sense that angles in a crooked line cause it to be longer than a straight line. But you seem to be suggesting that the slowing "really happens" when the acceleration happens. Since the acceleration period can be made arbitrarily small, and since in some reference frames the slowing happens *before* the acceleration, I don't think that is a reasonable view.

[RoddyM]

I think every kg of mass everywhere in the universe has the same kinetic energy, kind of summed up, relative to every thing else. In other words, no, you can't examine the structure or the measure the mass of the arrow to tell that it's moving.

I think that kinetic energy only has useful meaning as it's applied to ordinary Newtonian systems like engines or artillery.

[Nowhere357]

DaveGE
Perhaps, but my point is that the apparent slowing can happen *before* the acceleration occurs; in fact, the apparent slowing can happen even if there is no acceleration.
If the apparent slowing can happen even if there is no acceleration, that would shoot me down all right. I admit I can't think of a situation - do you have an example?

I am suggesting that the mathematical representation reflects the physical fact that the ship just experiences less time.
I agree with this, and it doesn't contradict my position. If you think it does, I need you to explain why.

What causes it to experience less time is that it takes a "bent path" through spacetime. This is analogous to the fact that in Euclidean geometry a crooked path is longer than a straight one.
This is from the mathematical representation, it is correct and I understand it.

But it is speaking loosely to say the mathematical representation causes the experience. For analogy we have a law of gravity because things fall down, not the other way around. It's not the case that things fall down because we have a law of gravity.

So from my pov the physical changes (less aging) in the accelerated object is still physically unaccounted for - hence my 'theory'. Iow, I'm translating the mathematical explanation of "it experienced less time" into a physical explanation of "the atomic activity slowed down". I claim this is necessary, because there is a physical change in the accelerated object.

Since the acceleration period can be made arbitrarily small, and since in some reference frames the slowing happens *before* the acceleration, I don't think that is a reasonable view.

Well, the acceleration to near light speed can be short in duration and large in magnitude, or long in duration and small in magnitude. I don't think that's a problem. The smaller the total acceleration, the smaller the effect.

And I think we can recognize relative acceleration (acceleration due to reference frame and not the influx of energy), since it won't exist from an outside frame? For example, from the rocket it looks like the earth accelerates away - is that what you mean? But the whole twin experiment shows that the object which did receive acceleration is fundamentally changed! NOT relatively changed, but actually changed. When the rocket returns to earth, it is always the rocket that has aged less. Something physical must have happened, and it always happens to the object that was accelerated.

[Nowhere357]

Originally posted by RoddyM
I think that kinetic energy only has useful meaning as it's applied to ordinary Newtonian systems like engines or artillery.
I think I agree.

I would like to change the title of the op to something like:

Does the slowdown of time for an object at relativistic speeds indicate or translate to physical changes in the object? If not, how do we explain the physical changes that are evident in the rocket/twin experiment?

[Mexicola]

Originally posted by Nowhere357
...But the whole twin experiment shows that the object which did receive acceleration is fundamentally changed! NOT relatively changed, but actually changed. When the rocket returns to earth, it is always the rocket that has aged less. Something physical must have happened, and it always happens to the object that was accelerated.

Just a quick question from someone who doesn't know much about this: From the perspective of the rocket-twin, would it not appear that the earth-twin had aged comparatively faster? Couldn't one then equally argue that it was the earth twin who had undergone physical change, as from the perspective of the rocket it's the earth which has accelerated, etc? Where are you judging the 'actual physical change' from?

Feel free to ignore this if it's completely off-track...

[DaveGE]

Originally posted by Nowhere357
If the apparent slowing can happen even if there is no acceleration, that would shoot me down all right. I admit I can't think of a situation - do you have an example? There's what you might call the simple paradox: the ship flies away from Earth and never comes back. Earth sees the ships' clocks as being slowed. There's the two-ship version: Ship A leave Earth for Alpha Centauri at the same time (in the rest frame of Earth) as ship B leaves Alpha Centauri for Earth. When A and B pass, B sets it's clock to agree with A. Then when B reaches Earth, its clock will show less time than the Earth clock.
Finally, you might consider the following situation. Let's remove the Earth so we don't have to worry about gravity, and imagine a rotating space station that uses centripetal acceleration to simulate a 1-g gravity. Let's suppose the ship flies in a giant circle, light-years in diameter, always accelerating at 1 g. Both parties experience the same magnitude of acceleration, but the ship still experiences less time.I agree with this, and it doesn't contradict my position. If you think it does, I need you to explain why.It seems to me that you *don't* really agree with this; you seem to be arguing that the ship experiences the same amount of time as the Earth but things happen slower on the ship. But it is speaking loosely to say the mathematical representation causes the experience. I don't say that; I say the mathematical representation is a correct description of the physical reality. If spacetime *physically* has the Minkowski geometry of relativity, then the ship *physically* experiences less time, because it takes a bent path. The bent path is caused by acceleration, but acceleration is not what causes spacetime to have Minkowski geometry. I don't know what causes that. Well, the acceleration to near light speed can be short in duration and large in magnitude, or long in duration and small in magnitude. I don't think that's a problem. The smaller the total acceleration, the smaller the effect. I'm not sure I understand your idea. If the slowing happens during the acceleration, then a fast acceleration wouldn't take enough time for any significant slowing. Something physical must have happened, and it always happens to the object that was accelerated. As I mentioned above, both objects can be accelerated, and still one will experience less time than the other.

[Nowhere357]

Originally posted by Mexicola
From the perspective of the rocket-twin, would it not appear that the earth-twin had aged comparatively faster?
Yes. Note however that in addition to the home-bound twin, the entire world also would be older! As would the solar system, and etc. I think Occam's razor says that view is less reasonable.

[Mexicola]

Originally posted by Nowhere357
Yes. Note however that in addition to the home-bound twin, the entire world also would be older! As would the solar system, and etc. I think Occam's razor says that view is less reasonable.

Ok, thanks. I'm glad I wasn't completely wrong then! :) Of course I accept that pragmatically we would prefer to say that the rocket-twin is the one who 'changes', but this doesn't mean that this is the 'actual' physical change. So your question as to why the the rocket-twin 'actually' changes is resolved then, surely? Because there is no 'actual' (objective, non-perspectival) change which we can pick out as 'the' change, even if we would pragmatically want to judge from 'our' perspective. From the perspective of the rocket-twin he hasn't undergone any change, and the earth-twin's claim that he has changed has no 'physical' priority over the rocket-twin's claim.

[Nowhere357]

DaveGE
There's what you might call the simple paradox: the ship flies away from Earth and never comes back. Earth sees the ships' clocks as being slowed. There's the two-ship version: Ship A leave Earth for Alpha Centauri at the same time (in the rest frame of Earth) as ship B leaves Alpha Centauri for Earth. When A and B pass, B sets it's clock to agree with A. Then when B reaches Earth, its clock will show less time than the Earth clock.
If we leave aside the twins, then I agree that these two examples do not imply the physical "slowing" that I've been talking about. There is no reason to look at these examples and come to the conclusion that the accelerated atoms slow down.

Finally, you might consider the following situation. Let's remove the Earth so we don't have to worry about gravity, and imagine a rotating space station that uses centripetal acceleration to simulate a 1-g gravity. Let's suppose the ship flies in a giant circle, light-years in diameter, always accelerating at 1 g. Both parties experience the same magnitude of acceleration, but the ship still experiences less time.
If I understand this situation correctly, then I see no problem. The rotating station experiences no actual acceleration - there is no constant influx of energy, as there is in the accelerating one. Centripedal force is a "psuedo" force.

It seems to me that you *don't* really agree with this; you seem to be arguing that the ship experiences the same amount of time as the Earth but things happen slower on the ship.
The ship experiences less time, I really do agree with that. I just see a difference between a mathematical description of an event, and the event itself.

You have said "What causes it to experience less time is that it takes a "bent path" through spacetime." I agreed with this, as a mathematical representation. If I assume it's a physical representation, I see problems. For example, imagine the rocket runs on a stationary track, like a monorail. We build the track heading off into space, and include a little turnaround loop at the end, perhaps. Now consider - the ship exactly and precisely follows the track. Where does the ship take a bent path, when we can see a one-to-one correspondance between the ship's path and the track, and the track does not take a bent path?

I don't say that; I say the mathematical representation is a correct description of the physical reality. If spacetime *physically* has the Minkowski geometry of relativity, then the ship *physically* experiences less time, because it takes a bent path. The bent path is caused by acceleration, but acceleration is not what causes spacetime to have Minkowski geometry. I don't know what causes that.
We both are aware of the difference between the map and the terrain, so that's not the problem. I would say no, spacetime does not *physically* have the Minkowski geometry of relativity; rather, the physical properties of spacetime are represented mathematically as Minkowski geometry. It sounds semantical, but from my pov the mathematical descriptions are not an explanation; they are descriptive only.

I'm not sure I understand your idea. If the slowing happens during the acceleration, then a fast acceleration wouldn't take enough time for any significant slowing.
I think the relationship is between the total influx of energy (acceleration) and the slowdown effect, and not between the time-length of the acceleration (and the effect). For analogy, the escape velocity from earth for an object is a constant - whether we boost slowly and continuously like a rocket, or rapidly all at once like a bullet, makes no difference. The total influx of energy remains the same.

As I mentioned above, both objects can be accelerated, and still one will experience less time than the other.
Remember, the rotating station does not actually accelerate. If my theory is right, then the total slowdown effect is directly related to the total acceleration delivered - the total influx of energy.

Delivering acceleration - kick a ball - distorts the object being accelerated. This is physical change to the object. It looks to me like relativity theory shows that accelerating an object physically distorts it in such a way that time passes slower, ie it experiences less time. If time is our measurement of physical movement, such as atomic oscillations, then "time passes slower" means that the oscillation slowed down.

It's not clear to me why this is controversial. But that does set off flags - I expect that I'm missing something.

[Nowhere357]

Mexicola
So your question as to why the the rocket-twin 'actually' changes is resolved then, surely? Because there is no 'actual' (objective, non-perspectival) change which we can pick out as 'the' change, even if we would pragmatically want to judge from 'our' perspective.
But there is an actual change, apparent from the perspective of the ship, OR the earth, OR the outside. The nature of the change is in doubt, but it's existence is not.

[Mexicola]

Originally posted by Nowhere357
But there is an actual change, apparent from the perspective of the ship, OR the earth, OR the outside. The nature of the change is in doubt, but it's existence is not. Yes, but it's not an intrinsic change; it's a relative change. Nothing peculiar physically happens to either twin as a result of the 'relativistic speeds'; all that changes is their relation to one another. Nothing peculiar even could happen to them as a result of the speed, as this too depends on the frame of reference. Doesn't it?

[DaveGE]

Ghod I *hate* the posting interface here! Who thought it would be a good idea to have an edit window 1/3 the width of the screen and 1/2 the height?

Originally posted by Nowhere357
If I understand this situation correctly, then I see no problem. The rotating station experiences no actual acceleration - there is no constant influx of energy, as there is in the accelerating one. Centripedal force is a "psuedo" force.
You definitely do not understand the situation correctly. It is flatly, unambiguously, incontrovertibly *wrong* to claim the rotating station experiences no actual acceleration. In any case, you could set up the same situation with two rocket ships, one traveling in a tight circle (say 1 km in radius) for several years, one traveling in a circle 1 light-year in radius for several years. Or you could set it up with two rotating stations; one normal sized and one a light-year or so in diameter; each would experience about 1 g of acceleration but the larger one would be slowed.For example, imagine the rocket runs on a stationary track, like a monorail. We build the track heading off into space, and include a little turnaround loop at the end, perhaps. Now consider - the ship exactly and precisely follows the track. Where does the ship take a bent path, when we can see a one-to-one correspondance between the ship's path and the track, and the track does not take a bent path? You are confusing the path in space with the path in spacetime. I would say no, spacetime does not *physically* have the Minkowski geometry of relativity; rather, the physical properties of spacetime are represented mathematically as Minkowski geometry. It sounds semantical, but from my pov the mathematical descriptions are not an explanation; they are descriptive only.This still looks to me like you think that space and time are actually Galilean, but that some physical effect of acceleration causes it to appear Minkowskian. (This is close to what Lorentz believed at one time, iirc; he suggested that length contraction and time dilation were caused by moving through the ether at high speeds.) It looks to me like relativity theory shows that accelerating an object physically distorts it in such a way that time passes slower, ie it experiences less time. But if the object experiences less time, there is no need for it to be distorted--it is no more surprising that the 'travelling' clock shows less time than a 'stationary' clock than it is that a clock today shows less time than a clock tomorrow.

[Nowhere357]

Originally posted by Mexicola
Yes, but it's not an intrinsic change; it's a relative change. Nothing peculiar physically happens to either twin as a result of the 'relativistic speeds'; all that changes is their relation to one another.
All change is relative, isn't it? To identify change always requires a comprison, a relation. That doesn't preclude that a change is real. A melted candle has changed relative to the unmelted candle, but the candle really did melt.

Nothing peculiar even could happen to them as a result of the speed, as this too depends on the frame of reference. Doesn't it?
Yes. Speed depends on frame of reference. Note that things kick along at speed with no energy being applied - no acceleration. It seems to me that acceleration implies or demands that energy be added to the system/object. In the case of the rocket, the energy source is carried internally, but only as potential energy - releasing the energy adds acceleration to the sytem, ie adds energy.

Accelerating an object definitely add energy to the object, I don't think that's in doubt. It seems like the current view is that this added energy increases speed without affecting the atoms of the object. But why should that be? Atoms aren't ideal and unchanging. Surely they individually react to getting kicked in the seat of the pants?

[Nowhere357]

DaveGE
Ghod I *hate* the posting interface here! Who thought it would be a good idea to have an edit window 1/3 the width of the screen and 1/2 the height?
I build the posts in wordpad, solving this problem and also protecting me when I get dropped. :)

You definitely do not understand the situation correctly. It is flatly, unambiguously, incontrovertibly *wrong* to claim the rotating station experiences no actual acceleration.
What I meant was, an object in motion tends to remain in motion, this works for both linear and rotational movement. The rotating station is just coasting, no energy is being input into the system.
But to the object experiencing the centripedal force, I think you are correct - it experiences acceleration. I was thinking of the station as a whole, so let me try again:

Finally, you might consider the following situation. Let's remove the Earth so we don't have to worry about gravity, and imagine a rotating space station that uses centripetal acceleration to simulate a 1-g gravity. Let's suppose the ship flies in a giant circle, light-years in diameter, always accelerating at 1 g. Both parties experience the same magnitude of acceleration, but the ship still experiences less time.
I would expect the twins to age the same, given the same total acceleration. But the station itself isn't accelerating, so would be older? I'm confused about that, because where is the energy being input to the twin coming from? Maybe you should pry at this spot some more.

In any case, you could set up the same situation with two rocket ships, one traveling in a tight circle (say 1 km in radius) for several years, one traveling in a circle 1 light-year in radius for several years.
If a twin was on each ship, and each ship is accelerating at the same rate, then I would expect the twins to have the same relative age when they meet at the end. (Ignoring any problems with high speed and tight radius of the first ship.)

Or you could set it up with two rotating stations; one normal sized and one a light-year or so in diameter; each would experience about 1 g of acceleration but the larger one would be slowed.
Actually, a person on the outer rim would experience said acceleration. (I assume the small station is rotating at a higher rate of speed then the large one, in order for both to provide 1 g on outer rim. Is this what you mean by "the larger one would be slowed"?).

I would expect the twins to have the same age here, also, since they experienced the same total acceleration.

You are confusing the path in space with the path in spacetime.
I really am not. The path in spacetime is a mathematical construct. I was trying to show that the mathematical construct is not space itself. Here it is again:

For example, imagine the rocket runs on a stationary track, like a monorail. We build the track heading off into space, and include a little turnaround loop at the end, perhaps. Now consider - the ship exactly and precisely follows the track. Where does the ship take a bent path, when we can see a one-to-one correspondance between the ship's path and the track, and the track does not take a bent path?

I think this shows that the bent path is a mathematical representation, nothing more (and nothing less).

This still looks to me like you think that space and time are actually Galilean, but that some physical effect of acceleration causes it to appear Minkowskian. (This is close to what Lorentz believed at one time, iirc; he suggested that length contraction and time dilation were caused by moving through the ether at high speeds.)
I understand the concern. But in fact I understand that space and time have no independant meaning - they each are defined in terms of the other. I understand there is no overall objective viewpoint - that we understand things only in relation to other things. I understand that for example gravity (acceleration!) can be seen as curving spacetime. From my pov, none of this contradicts my position.

But if the object experiences less time, there is no need for it to be distorted--it is no more surprising that the 'travelling' clock shows less time than a 'stationary' clock than it is that a clock today shows less time than a clock tomorrow.
Note that tomorrow's clock has experienced more oscillations! So today's clock has experienced fewer. We can tell the age from the number of oscillations. And the earthbound twin has experienced more oscillations, while the rocket twin has experienced fewer! The difference here, of course, is that the twins are existing side-by-side, with one of them having experienced fewer oscillations. One of them experienced something that made the oscillations slow down! This is not a relative difference, this is an actual quantifiable difference, from any frame of reference!

Anyway, I would say the object experiences less time, because it is distorted. It got kicked, and the harder the kick, the longer it takes to recover. Maybe the sub-atomic physics is slightly altered, so the oscillations slow down. All our macro-physics are built on that, and so slow down also. The object experiences less time. For example, electric signals depend on the reaction of atoms - if the atoms slow then the signals slow, so nerves slow. Chemical reaction depend on atomic reaction also - and so on.

[Mexicola]

Originally posted by Nowhere357
Note that tomorrow's clock has experienced more oscillations! So today's clock has experienced fewer. We can tell the age from the number of oscillations. And the earthbound twin has experienced more oscillations, while the rocket twin has experienced fewer! The difference here, of course, is that the twins are existing side-by-side, with one of them having experienced fewer oscillations. One of them experienced something that made the oscillations slow down! This is not a relative difference, this is an actual quantifiable difference, from any frame of reference!But from the point of view of the rocket-twin, the oscillations didn't slow down. The rocket-twin simply 'travelled through' less time than the earth-twin. The oscillations only slow down from the perspective of the earth-twin. The point of relativity is that time and space are treated similarly - they can both be 'bent' (by travelling through them at different 'speeds', so to speak), giving rise to the twin paradox, etc. You're still thinking as though both space and time remain the same in relativistic cases, in which case there must be some intrinsic change to explain the paradox. But they don't remains the same. They 'bend'. The rocket-twin can experience less time than the earth-twin in the 'same' (from the earth-twin's perspective) time, just by travelling at relativistic speeds. There's no single 'objective' time in which to judge that one twin has experienced oscillations faster than the other. How many oscillations the twin experiences in a sense defines how much time they've experienced; hence you can't judge that one set of oscillations has 'slowed down', except from another, equally relative, perspective.
The importance (as I understand it) of relativity is precisely that whereas previously we had a picture of an objective, universal time and space in which events happen, relativity gives us a picture in which both space and time are dependent on one's inertial frame. The difference observed between the earth-twin and the rocket-twin is not a result of one set of oscillations speeding up, or of the other one slowing down. It's a result of them taking different 'paths' through space-time, not just through space. The rocket-twin takes (as it were) a 'short-cut' through space-time; it (and its oscillations) 'experience less time' than the earth-twin, just as you and I might experience less (or more) distance in order to get to the same destination at the same time by taking different routes at different speeds.

[DaveGE]

Originally posted by Nowhere357
I build the posts in wordpad, solving this problem and also protecting me when I get dropped. :) Thanks for the tip. What I meant was, an object in motion tends to remain in motion, this works for both linear and rotational movement. The rotating station is just coasting, no energy is being input into the system.
But to the object experiencing the centripedal force, I think you are correct - it experiences acceleration. I was thinking of the station as a whole, so let me try again:


I would expect the twins to age the same, given the same total acceleration. But the station itself isn't accelerating, so would be older? I'm confused about that, because where is the energy being input to the twin coming from? Maybe you should pry at this spot some more. OK, let me take another stab at explaining this. Consider two rockets, A and B, traveling in circles with centripetal acceleration of 1 g (so the astronauts are comfortable). A travels in a small circle, say 1 kilometer in radius, while B travels in a very large one, say 1 light-year across. Let's suppose that A's little circle is just tangent to B's circle, and that the two astronauts synchronize clocks when B passes A's circle. According to Special Relativity, when B is done making a big circle, which will take several years, B's clock will show less time then A's. (I don't feel like typing in the derivation of this at the moment but it's fairly simple and if you want I suppose I can summon the energy.) The same thing will happen in the case of two rotating space stations, a small one (A) with a radius of 1 km and a big one (B) with a radius of one light-year. If each station is rotating to produce 1-g at the rim, then astronauts on the rim of the stations are in the same situation as the previous case with the rocket ship. A clock on the rim of B will show less time has passed in one revolution of B than the clock on the rim of A. The equations are exactly the same as for the rocket case, because the equations of Special Relativity don't know or care how acceleration is acquired or maintained--rockets or rotating space stations, it makes no nevermind.

[Nowhere357]

DaveGE
OK, let me take another stab at explaining this.
In the past few days I've explored about a half dozen sites which try to explain the time paradox. But I haven't found one that talks about the rotating reference frames - if you have a good one please share.

Anyway, it's beginning to look to me like velocity is the vector in question, and not mere acceleration.

[Nowhere357]

Originally posted by Mexicola
But from the point of view of the rocket-twin, the oscillations didn't slow down. [/B]
I feel I've answered your objections already.

First, from the pov of the rocket twin, of course they cannot detect any slowing or increaing because the clocks they use for measuring time have also slowed or increased! However, when they reach earth, from the pov of the rocket twin, they realize they have experienced fewer oscillations! The difference is real.

Second, the mathematical representation is just that. I've twice mentioned a simple experiment that shows the path through space is the same - the difference is in the moving object.

Third, afaics, everything you've said is correct. But it doesn't contradict my position!

[Abacus]

Originally posted by Nowhere357
I've twice mentioned a simple experiment that shows the path through space is the same - the difference is in the moving object.

But the path through space-time is very different.

[Nowhere357]

Originally posted by Abacus
But the path through space-time is very different.
Yes. The mathematical representation is not the thing represented. The map is not the terrain.

[Abacus]

Originally posted by Nowhere357
Yes. The mathematical representation is not the thing represented. The map is not the terrain.

But the mathematical representation is a very good model of the real thing.

I'm having a hard time understanding what your position is. Do you believe that the transformation of coordinates given by the Lorentz transformation is just an illusion?

[Nowhere357]

Originally posted by Abacus
I'm having a hard time understanding what your position is. Do you believe that the transformation of coordinates given by the Lorentz transformation is just an illusion?
No, I do not claim the mathematics are illusory.

I do claim that relativistic speeds lead to objective changes;
the twin experiment identifies the nature of this change;
the twin that experenced the high velocities experienced fewer atomic oscillations then it would have if it hadn't experienced the high velocities.

My conclusion is that the rocket twin experienced less time because of the slowing of atomic oscillations. High velocity slows atomic physics. I claim that this is the physical result. I expect that the mathematics can be interpreted to support this. Note that the time dilation formulas relate change in time to velocity.

From a look at time dilation (http://members.tripod.com/wmhxbigguy/Theory/time.html):

delta t = delta t0 / sqrt(1-v^2/c^2)

where t0 is the time interval in one reference frame and
t is the time interval measured by an observer in another reference frame. then
v is the relative velocity of the same reference frame, and
c is the speed of light.
Note that the denominator is always less than 1 (v < c), so t is always greater than t0.

Rocket time (delta t1) becomes smaller in relation to earth time (delta t) as v approaches c.

Iow high velocities experience less time. Which means fewer oscillations.

[Abacus]

Originally posted by Nowhere357
Iow high velocities experience less time. Which means fewer oscillations.

Velocity with respect to what?

Now let me pose a variation on the usual twin paradox scenario. Suppose one twin boards a rocket ship and blasts off from the earth with no intention of ever returnig. He very quickly accelerates up to some high speed, let's say 0.9c with respect to the earth, at which point his fuel runs out. Now he's stuck and will drift through the universe forever, or until he crashes into something by chance.

In this case, from the earth twin's perspective, his brother on the rocket ship will be aging slower than himself. On the other hand, from the rocket twin's perspective, the twin on the earth will be aging slower.

Now, how can you explain this?

[NialScorva]

Originally posted by Abacus
Now, how can you explain this? [/B]

They're moving apart. If it's traveling at .5c, 20 years later the ship will see the earth as it was 10 years prior, and vice versa. At 40 years there will be a 20 year speed of light, meaning that each appears to age at half the speed of the other.

If the ship was heading towards the earth, the reverse would happen.

[DaveGE]

Originally posted by NialScorva
If the ship was heading towards the earth, the reverse would happen. That turns out not to be the case. Each would appeared slowed in the other's rest frame, even after delays due to the finite speed of light are taken into account, and even if the two travellers are moving towards each other. This is possible because the two parties disagree about whether or not two events happen at the same time.

[Abacus]

Yes, what DaveGE says is correct. Even after taking the delays due to a finite light speed into account, earth time is still slower than rocket time in the rocket's frame. If, as Nowhere357 is suggesting, the Lorentz transformation is just an expression for how some actual physical change within the atoms is causing them to "slow down", then I'd like to know how it is that these changes are occuring on the earth?

[Nowhere357]

Abacus
Velocity with respect to what?
When the rocket returns to earth, why is it always the rocket twin who is younger? Because his velocity was acquired due to acceleration. The earth was not accelerated - the rocket was. Relative to it's original frame of reference.

Now let me pose a variation on the usual twin paradox scenario. Suppose one twin boards a rocket ship and blasts off from the earth with no intention of ever returnig. He very quickly accelerates up to some high speed, let's say 0.9c with respect to the earth, at which point his fuel runs out. Now he's stuck and will drift through the universe forever, or until he crashes into something by chance.
In this case, from the earth twin's perspective, his brother on the rocket ship will be aging slower than himself. On the other hand, from the rocket twin's perspective, the twin on the earth will be aging slower.
Now, how can you explain this?
It follows from the theory that the speed of light is constant in any reference frame. It does not indicate my theory - we've already talked about that. In the twin experiment, they return to the same frame of reference, and we can see the real difference.

Yes, what DaveGE says is correct. Even after taking the delays due to a finite light speed into account, earth time is still slower than rocket time in the rocket's frame.
I agree with Dave also. But as the ship returns to earth, the size of the disagreement reduces towards zero, and when the ship lands there is no disagreement. And the rocket twin is younger, having ACTUALLY experienced less time. Compared to the non-accelerated twin, in the original reference frame (whether the ship or the earth!).

If, as Nowhere357 is suggesting, the Lorentz transformation is just an expression for how some actual physical change within the atoms is causing them to "slow down", then I'd like to know how it is that these changes are occuring on the earth?
(I guess you mean in your example where the ship continues on.) They don't occur on earth - the returning twin shows that.

If it's not the velocity aquired through acceleration which is the difference between the rocket twin and the earth twin (as opposed to relative velocity due to pov), then what is the diffference?
And if it is the velocity aquired through acceleration which is the difference, and the difference is that the object which received the acceleration is younger than it would have been if it hadn't accelerated, then the object experienced less time. How could it do this, unless it's rate of time was slowed? And what is the rate of time for an object, other than the rate of atomic oscillations - the 'pace' of the subatomic physics?

[Shadowy Man]

Originally posted by Nowhere357
How could it do this, unless it's rate of time was slowed? And what is the rate of time for an object, other than the rate of atomic oscillations - the 'pace' of the subatomic physics?

It's not that anything slowed down, it's that the returning twin moved through a shorter space-time interval.

You keep thinking of it in the manner of some universal time to which both the twin and the Earth can have their "rates of time" compared. But there isn't a universal time.

So, it's not that some physical change is happening in a fixed reference frame, it's that the reference frames aren't identical and the actual amount of time available to the twin between his journey away and back to the Earth is different than the amount of time available to the Earth.

[Nowhere357]

Shadowy Man
It's not that anything slowed down, it's that the returning twin moved through a shorter space-time interval.
I find those concepts equivalent. The first is the physical observation, the second is the mathematical representation.

You keep thinking of it in the manner of some universal time to which both the twin and the Earth can have their "rates of time" compared. But there isn't a universal time.

I understand there is no universal time. In fact, the relativity of time does not indicate my position - it's not until the twins are together again that the physical difference is noted.

So, it's not that some physical change is happening in a fixed reference frame, it's that the reference frames aren't identical and the actual amount of time available to the twin between his journey away and back to the Earth is different than the amount of time available to the Earth.
The physical change is very real, whether viewed from the reference from of the travelling twin, or from the frame of the 'stationary' twin.
____________________________

Space is 3d. Time is measurement of cyclical physical (matter/energy) movement. Four dimensional space/time is a mathematical construct. Given this pov, I claim my conclusion follows.

I think there are two ways to debunk my theory:
1) Assume my pov above (the premise) and show my conclusion doesn't follow;
2) Show the premise to be unsound.

What is happening in this thread is people are trying to show my conclusion is unsound without assuming the premise, yet also without showing the premise to be false. I think we are talking past each other.

__________________________

What prompted the op in my mind is contemplating the difference between an arrow in flight and an arrow at rest. The arrow in flight is associated with kinetic energy - but that is relative and not inherant in the arrow. What then is inherant to the moving arrow such that it 'knows' to move forward? It seems to me that there is a functional, physical difference between the arrows, and not merely a relative difference. Regardless of reference frame, something happened to the moving arrow compared to the non-moving arrow - it received acceleration. It seems to me that the happening left it's mark on the arrow and can in theory be detected by an examination of the arrow alone.

If that is true, then acceleration delivers physical change to an object. This is verified by the twin experiment given the premise that time is measurement of cyclical physical movement.

Acceleration is relative - the twins each received the same relative acceleration - yet one twin reacted to the relative acceleration in a different fashion than the other. Thus there is 'true' acceleration, an acceleration to an object compared to itself! The rocket received it; the earth did not.

If the rocket twin accelerated out, then deccelerated to a relative stop; then the earth twin similarly accelerates out and comes to a stop next to the rocket, I predict that the twins would have the same relative age. Doesn't this conclusion follow from my position, and isn't it falsifiable?

[Jesse]

Originally posted by Nowhere357
Acceleration is relative - the twins each received the same relative acceleration - yet one twin reacted to the relative acceleration in a different fashion than the other. Thus there is 'true' acceleration, an acceleration to an object compared to itself! The rocket received it; the earth did not.

Yes, it's a feature of relativity that acceleration is not relative--only inertial reference frames are equivalent, but accelerated reference frames are not. If you're in a windowless rocket there's no way to determine if you're "really" standing still or moving at a constant velocity (relativity says there's no such thing as absolute velocity), but you can tell if you're accelerating, because you'll experience fictitious "G-forces" on board the ship (although the equivalence principle of general relativity says there's no way to tell the difference between fictitious G-forces due to acceleration and gravitational force due to sitting on the surface of a massive object).