What Determines the Direction of an Object's Motion Expressed as Energy?

[Matt777]

Hello everyone, I've recently run into a thought experiment that is persistent and seems to have no intention to leave my mind alone ^^ I was hoping someone who is more experienced in this topic could leave some input.

This is the setup for my thought experiment: Consider an object which is traveling in space with no exterior forces and therefore with constant speed in a certain direction. Now let's freeze time (that is, stop the world in which our thought experiment takes place) such that our object appears to be at rest. Certainly, the object still has kinetic energy, making it have a distinct property which an identical object without velocity does not have. This explains why our object will continue moving when we unfreeze our world.

Well, now to my question: How does it 'know' in which direction it should go? Certainly, the object would have exactly the same kinetic energy if it were to go in a different direction, yet it does not. Or a more precise question would probably be, what is it that determines what direction a certain objects kinetic energy forces it to travel in?

 

[arildno]

Why has it lost its velocity??

 

[Razzor7]

Kinetic energy alone doesn't fully describe the motion of the object at t=0. Basically what you're saying is that you don't necessarily know the direction something with a given kinetic energy is traveling. That's just an observation about the definition of kinetic energy, I believe.

 

[thomasxc]

momentum that it had already going in that direction.

 

[luckis11]

The definition of "instantateous" velocity, does not happen in Δt=0, but in Δt->0. Also, it is named that the space that moves "has" its velocity, but in reality velocity is composed of a Δx and a Δt, which are two spaces which are not contained into the space that "has" this velocity. Therefore it is also logically necessary that the definitions of kinetic energy, momentum, etc. are not contained in the space that moves and "has" them, because the spaces which compose each such definition are not contained in the space that moves.

 

[thomasxc]

Kinetic energy alone doesn't fully describe the motion of the object at t=0. Basically what you're saying is that you don't necessarily know the direction something with a given kinetic energy is traveling. That's just an observation about the definition of kinetic energy, I believe.

is kinetic energy a scalar quantity?

 

[bp_psy]

Well, now to my question: How does it 'know' in which direction it should go? Certainly, the object would have exactly the same kinetic energy if it were to go in a different direction, yet it does not. Or a more precise question would probably be, what is it that determines what direction a certain objects kinetic energy forces it to travel in?

Nothing about the kinetic energy makes the particle move in a certain direction.The thing that does that is the momentum $$\vec{p}$$ which is conserved if no external force acts on the particle. Then again I do not think that any real prediction could be made about a system in which you stopped time.Why should anything be conserved?

 

[Matt777]

Nothing about the kinetic energy makes the particle move in a certain direction.The thing that does that is the momentum $$\vec{p}$$ which is conserved if no external force acts on the particle. Then again I do not think that any real prediction could be made about a system in which you stopped time.Why should anything be conserved?

Yes I guess that is a more formally correct way to put it, the momentum keeps it going of course. Kinetic energy is, I guess, more of a side effect which simply gives the information that the object is moving and that it is doing so at a certain speed.

In any case, I think you (and others) have misunderstood my question. Yes, it has momentum, forcing it to keep following its path. What I was wondering is if there is any sort of parallell to kinetic energy, but that instead of describing movement at a certain speed describes in which way the object is traveling? We know it has momentum, which is a vector, but that is merely our way of representing the fact that the object is moving in a given direction which we know through observation beforehand. Kinetic energy on the other hand is something measurable, something that states "yes, there is movement!". Perhaps it is too intuitive - that an object should simply move in the apparent direction that we push it - to even consider my question.

Furthermore, I'm beginning to get the feeling that what I'm actually contemplating is more philosophical in nature than I had first thought. It feels more and more like a question of "why" rather than "what" or "how". I apologize for that, most likely I'm looking into something which has no good logical answer.

If anyone is still interested in what I mean, I simply would like to know if there is something associated with a moving object that stores the information about the direction of movement. Considering my thought experiment, I must clarify that the "freezing of time" has no effect on the world in which the thought experiment is performed. I used it mainly because there is an obvious distinction between two identical objects, where one object has a velocity and the other has none. One can measure the kinetic energy of both of the objects and come to a conclusion about which one will continue to move once the world is unfrozen. Let's say that you have not seen in which way the object was moving before freezing though, then I presume that you will not be able to tell where the object with kinetic energy will go until you actually unfreeze the situation.

My initial question was indeed, what determines the direction of movement, given that its non-zero kinetic energy determines the fact that it shall move at least somewhere. I must also apologize for ranting but it was much needed for myself to realize that what I'm asking is perhaps rather foolish. I'm posting it all anyway in case someone else will find it useful.

 

[luckis11]

You are not expressing with precision what you mean, thus I am forced to half-guess what you mean. However I am answering to you according to my quess.

You did not pay attention to my previous answer. The space that moves is not moving if you ignore its previous positions. It is its previous positions that compose its movement, and if you try to give yourself a definition of movement, you will realize this fact. And thus if you ignore its previous positions, then it has no velocity, no kinetic energy and no momentum.

 

[protonchain]

is kinetic energy a scalar quantity?

K = 1/2 mv^2.

m = mass which is a scalar (you can't have negative mass)

v = velocity, which is a vector, but since it's squared, it loses it's direction here and becomes a scalar.

So yes. Kinetic energy is a scalar.

 

[Matt777]

You are not expressing with precision what you mean, thus I am forced to half-guess what you mean. However I am answering to you according to my quess.

You did not pay attention to my previous answer. The space that moves is not moving if you ignore its previous positions. It is its previous positions that compose its movement, and if you try to give yourself a definition of movement, you will realize this fact. And thus if you ignore its previous positions, then it has no velocity, no kinetic energy and no momentum. Therefore all these definitions cannot be contained in the last position of the space, position which happens in Δt=0.

So what you say is that an objects path of movement is in some ways emergent, depending on where it has been? I see what you mean, and of course, had it not had previous positions that all were different from each other, it wouldn't have moved and thus would not continue to move. Well, that's an insightful way to look at it I guess. It certainly gave me something to think about, and I like the way in which this states that the objects sense of direction cannot be contained within a single moment of existence. But what consequence would this statement have for, for example, the energy levels of electrons? Certainly, they have no prior momentum (other than tangential) before doing what appears to be an almost instantaneous movement when it becomes excited or the opposite. I guess it is easily explained if this is not considered motion.

It certainly makes sense in other ways than that I guess, since what it actually says is that motion can never be zero (if it could, then it would forever remain zero which goes against current theories), which is very consistent with the fact that temperature cannot be zero either.

I thank you for your input luckis11, it was obviously very enlightening for me once I looked into it with more of an open mind.

Also, I excuse myself for not being clear, I am not very resourceful when it comes to expressing thoughts in text. English isn't my primary language either, which is probably apparent and half the reason for my inability to convey my thoughts.

 

[luckis11]

The problem of the definitions is not so easy. For example, I have a question too: The vector of the definition of force happens in Δt=0?

If the theory of relativity says that mass is energy, then the most recent position of the mass cannot happen in Δt=0. But any definition of motion requires that the space that moves itself, takes place in Δt=0. So how can mass move?

And if you also consider the theory of uncertainty as you implied, things get even more messed up.

It took me years of thinking on such questions, but it requires a book to explain my conclusions.

 

[dE_logics]

such that our object appears to be at rest.

Considering time has stopped, the observer will too lose ability to observe change in distances over time.

Certainly, the object still has kinetic energy

No, K.E is a function of velocity, velocity is a function of time, if time stops...every thing will be 0.

making it have a distinct property which an identical object without velocity does not have

Its the same thing.

The 2 object will be identical since information about velocity/time etc...is invalid/lost.

BTW velocity is a slope of a t vs d graph, and a point cannot have a slope (yeah, we compute the slope of a point using calculus, but that's in infinitely small interval and not a 'point' in time).

 

[bp_psy]

Yes I guess that is a more formally correct way to put it, the momentum keeps it going of course. Kinetic energy is, I guess, more of a side effect which simply gives the information that the object is moving and that it is doing so at a certain speed.

Kinetic energy gives the information about how much work an object can do in a specific inertial reference frame do to its velocity relative to that specific inertial frame.

I used it mainly because there is an obvious distinction between two identical objects, where one object has a velocity and the other has none.

This is not entirely true.There isn't any fundamental distinction between the 2 objects.There is no such thing as a absolute reference frame. Therefore the motion and the kinetic energy of your two particles is due to your choice of inertial reference frame.I can chose a frame in which both are moving and have KE and we would both be right.

We know it has momentum, which is a vector, but that is merely our way of representing the fact that the object is moving in a given direction which we know through observation beforehand. Kinetic energy on the other hand is something measurable, something that states "yes, there is movement!"

.How exactly would you measure the kinetic energy of the particle in "frozen time".There are two ways to measure the KE. The first method consists in measuring its mass and velocity(the same information you need for momentum).The second is by letting the object do work and measuring it.None of these can be done if you have just a "photo"

Let's say that you have not seen in which way the object was moving before freezing though.I presume that you will not be able to tell where the object with kinetic energy will go until you actually unfreeze the situation.

There no way to tell there is an object with KE. For example I play Pong and I pause it. You never saw that game in your life and you don't know the rules.If you see the just a still image could you actually say anything about the motion of the dot.The dot could move in any direction or just stay there.In order to make any predictions about a system you must have a minimum of information (boundary conditions) about it. In this case it is the present position $$\vec{r}$$ and the velocty as a function of time $$\vec{v}(t)$$.Knowing this you know where the particle was and will be next. You can't do the same knowing just $$\vec{r}$$ and $$\vec{a}(t)$$ or any other information.

 

[Matt777]

There no way to tell there is an object with KE. For example I play Pong and I pause it. You never saw that game in your life and you don't know the rules.If you see the just a still image could you actually say anything about the motion of the dot.The dot could move in any direction or just stay there.In order to make any predictions about a system you must have a minimum of information (boundary conditions) about it. In this case it is the present position $$\vec{r}$$ and the velocty as a function of time $$\vec{v}(t)$$.Knowing this you know where the particle was and will be next. You can't do the same knowing just $$\vec{r}$$ and $$\vec{a}(t)$$ or any other information.

I wasn't aware of this actually, that KE is not attached to the object so to speak. I've always thought that an object actually increase in weight because of its kinetic energy, thus making it distinct from an object that travels at a slower pace. Is it not so that all energy is measurable? Is it not so that a neutron star, or even more extreme, a black hole can reach such enormous gravitational fields partly due to their rotational kinetic energy? Perhaps I'm completely off the hook, or maybe I should say "probably" rather than "perhaps". I'd just like to understand all such fundamental definitions as well as is possible. I apologize for my lack of experience and I hope my questions aren't too much of a burden, or that they are contagious with foolishness ^^ thank you all for participating, it certainly is helpful to me and I appreciate any further input!

 

[diazona]

Well, according to relativity, an object with more kinetic energy will weigh more (note that this isn't what gives black holes and neutron stars their immense gravity - that's just a high density of stellar mass). But you can only measure weight by putting the object in a known gravitational field and seeing how it reacts. If time is stopped, you can't do that.

Basically, the point to take away from all the replies you've been getting is that, given only a "snapshot" of the universe (a single instant in time), you can't make any measurement which will tell you how much energy something has. So it's kind of meaningless to ask about the energy, velocity, etc. of an object at a single moment in isolation.

 

[Dale]

KE and momentum are frame variant quantities, not inherent properties of the object itself.

 

[dE_logics]

Well, according to relativity, an object with more kinetic energy will weigh more

According to relativity, the velocity is not a factor?...actually there should be a square relation to v, it's just that the velocity won't change as expected.

But you can only measure weight by putting the object in a known gravitational field and seeing how it reacts.

Weigh is by virtue of g.

Did you mean mass?

 

[bp_psy]

I wasn't aware of this actually, that KE is not attached to the object so to speak. I've always thought that an object actually increase in weight because of its kinetic energy, thus making it distinct from an object that travels at a slower pace.

I have just a very basic understanding of special relativity so some of the things I will write may not be very accurate . First if we accept the concept of relativistic mass 2 objects the same rest mass with different velocities with respect to a frame will have different relativistic masses with respect to that frame.If we chose 2 other frames one for each object so that each object is at rest with respect to their respective frame they will have the same mass as in the initial rest mass. The fact that they move at a speed close to c with respect to the first frame does not matter in these 2 new frames. Now if we chose yet another reference frame to which the first frame moves at a velocity close to c we measure different relativistic masses on the objects. According to the postulates of relativity all of the measurements are valid . We will hoverer agree that the objects do not reach c in any of the frames and c will be the same. However the concept of relativistic mass is somewhat controversial. This article shows some of the problems with the concept.http://arxiv.org/PS_cache/physics/pdf/0504/0504110v2.pdf

Is it not so that all energy is measurable?

KE with respect to something can be measured but there isn't anything like net energy with respect to everything. I have very small KE in the frame of my room and I have a very high KE due to my motion around the galaxy . i can't say anything about 'all" my KE with respect to the universe .

Is it not so that a neutron star, or even more extreme, a black hole can reach such enormous gravitational fields partly due to their rotational kinetic energy

I don't really know . There was a discussion about the effect of rotational KE on gravitation here https://www.physicsforums.com/showthread.php?t=224598
My suggestion though is to try to learn the basics before moving to more advanced stuff. I usually avoid physics to which I can't do the math. This way I don't have any misconceptions when I actually am capable of learning those concepts. Also try to isolate a concept you are learning. It is not very helpful to think about to the uncertainty principle. special and general relativity, black holes and neutron stars when you are trying to figure out the behavior of a 2 particle system.