# Kinetic Time Energy

1. Oct 26, 2005

### nemosum

Alright, I'm new at this, so I'll try to explain my question as best I can, and I hope it's not a stupid one. When you move through space 3-dimensionally you gain Kinetic energy, right? So wouldn't something moving through time, since it's just another dimension according to Einstein, gain kinetic energy for that too? And, if so, isn't it possible that on object's potential energy is just kinetic energy for moving through time? Especially since as time slows down for an object its potential energy becomes less. Which means that it's kinetic energy for poving through time is lessening. Do I make sense? Yeah, I was just wondering about that.

-nemosum

2. Oct 26, 2005

### metrictensor

very interesting question about traveling through time affecting KE. I'll have to think about it.

3. Oct 27, 2005

### JesseM

The problem is, what do you mean by "moving through time"? Kinetic energy is based on velocity, and velocity is (change in position)/(change in time), so it seems like kinetic energy already takes time into account as well as space. In relativity, the technical definition of kinetic energy is $$(\gamma - 1)mc^2$$, where m is the object's rest mass and $$\gamma$$ is the following function of velocity: $$1/\sqrt{1 - v^2/c^2}$$

Also, what do you mean when you say "as time slows down for an object its potential energy becomes less"? Where'd you hear that from?

4. Oct 27, 2005

### Staff: Mentor

Not when you're moving at constant speed.

5. Oct 27, 2005

### Pengwuino

Also add to this that time is not a spacial dimension so I would assume kinetic energy doesn't apply here. I mean exactly how would it come into play mathematically?

6. Oct 27, 2005

### nemosum

First of all, Something I should have stated before was that I'm only 16 and I just barely got accepted to a college and am just barely starting my major in Math and Physics, I haven' even taken Calculus yet, so my question was a truly innocent one.
Second, the only things I know about Relativity Theory came out of a 20 year-old book, that merely gave the theoretical part of the theory, and not the math. I don't know anything about the mathematics involved. So it was a truly innocent question indeed.
It was in that book I referred to before that it stated that as you get closer to a center of gravity that time slows down, AND on object's potential energy becomes less. It also said that as you get closer to the speed of light time slows down, AND an object's potential energy becomes less. I think there might have been a couple of other cases too, but the point is that I just thought it was a little interesting that every time time slows down on objects potential energy becomes less (or, at least that is what it seemed like to me).
And jtbell said that you don't gain KE when you're moving at a constant speed? But wouodn't you still have more KE than if you were just standing still right?

7. Oct 27, 2005

### Jimmy Snyder

When you consider time as a separate coordinate and space as three other separate coordinates, you are thinking in a frame dependent way. For instance when you speak of a particle that is at rest in space and moving in time, you are describing that particle as it would look to an observer in a particular frame.

Energy and momentum stand in a similar relation to each other as time and space. When considered individually, they are frame dependent concepts. In the particular frame described above, the energy is rest mass and the momentum is zero.

From that point of view, the energy of a particle that is moving through time alone is its rest mass.

Last edited: Oct 27, 2005
8. Oct 27, 2005

### El Hombre Invisible

Moving at constant speed and standing still are the same thing. That's the most basic concept of relativity you need to grasp. You may choose your x, y and z axes such that you are at rest, but I may choose mine such that you are moving at constant non-zero speed.

Also, your speed does not effect your potential energy - your potential energy function does, and that is a function of distance. It may well be that the author you refer to meant that because you are accelerated towards the speed of light, whatever your potential energy was (say, gravitational energy due to an initial orbit around the Earth), it will decrease because you will be moving away from it. However, it is not your speed that is causing the decrease in potential energy. Two objects orbiting the Earth at a height h with different speeds (one closer to c) will have the same gravitational potential energy.

The short answer to your original question is that things don't gain energy just because they are moving forward in time, just as they don't simply by moving forward (or backward) in any of the spatial dimensions. That would be a violation of the conservation of energy, since everything would be gaining energy.

Good to question all these things, though, and it's great you have a keen interest in pondering the nature of such things.

9. Oct 27, 2005

### El Hombre Invisible

Having said that, though, I guess you could argue a link between how fast time passes for a fast-moving body and how much kinetic energy it has. If you supply energy /\E to a body moving at, say, 0.8c, and you didn't know about relativity, you would expect its kinetic energy to increase by /\E and time to pass the same as before. In reality, time would seem to pass more slowly than before, and its kinetic energy would increase by considerably less than /\E.

But Jimmy's statement is more realistic. The energy you have by virtue of moving through time alone is your rest mass energy.

10. Oct 27, 2005

### El Hombre Invisible

11. Oct 27, 2005

### Jimmy Snyder

There is no frame in which they are at rest.

12. Oct 27, 2005

### nemosum

Sorry, you're right, I forgot that part.

13. Oct 27, 2005

### nemosum

I think that's what I meant. You have rest mass energy for moving throught time, even if you're standing motionless in reference to the up, down, left and right. So, is rest mass energy different than potential energy?

14. Oct 27, 2005

### Garth

Welcome to these Forums nemosum!!

Keep asking those questions, that is how we learn. If you keep an open questioning mind and learn to "stand on the shoulders of giants" you will become a great physicist! Keep working at it.

Garth

15. Oct 28, 2005

### El Hombre Invisible

Precisely, and yet they move through time. So the energy a particle has by which it moves through time alone cannot be it's rest mass energy, since not all particles that move through time have rest mass.

16. Oct 28, 2005

### El Hombre Invisible

Well, I don't think you can say a particle moves through time by virtue of its rest mass or vice versa for the reasons above.

Yes, rest mass is different from potential energy. You can describe a massive particle's total energy as the total of its mass energy, its kinetic energy and its potential energy.

For a massless particle, such as a photon, it's just 'energy'. Unless we describe gluons as having potential energy due interactions with quarks and other gluons? Anybody know? I've never heard of such a thing.

17. Oct 28, 2005

### Jimmy Snyder

For the photon, no time passes.

18. Oct 28, 2005

### El Hombre Invisible

True, but to us it does travel through time. So travelling through time cannot depend on rest mass (or vice versa) in normal frames. Relativistic mass, maybe.

19. Oct 28, 2005

### masudr

Energy is the time component of the energy momentum 4-vector.

20. Oct 28, 2005

### Jimmy Snyder

I'm sorry I wrote that, although I do think it is pertinent. I wrote it because I lost track of my own train of thought. When I wrote my explanation, I wrote the words "In that sense". I meant that the explanation was limited to the sense to which it refered, namely for particles in rest frames. When you asked about massless particles, I responded "There is no frame in which they are at rest." What I meant by that is that the case you are talking about is not covered under "In that sense". You can take that to mean that you're case is not a counter-example since it doesn't match the sense, or you can take it to mean that you are right, there are other senses.

21. Oct 28, 2005

### El Hombre Invisible

You are right - nemosum did explicitly end his question that you replied to with the case of a body at rest. However this is a special frame of reference, so I was extending it to all inertial frames. I stopped considering the rest frames when this opened up to photons. There were some thought progressions I kept to myself. My fault entirely. The thing is that when you take relativistic mass into account, the more you have the slower time passes for you, be it in someone else's rest frame (as in SR) or your own (as in GR, where the relativistic mass is also your rest mass).

Going back to the OP, I don't know GR. I cannot say whether or not the increase in relativistic mass in SR that corresponds to a decrease in the rate by which time passes for it compared to its rest frame looks much like the increase in the gravitational field in GR that corresponds also to a decrease in the rate by which time passes for it compared to negligible gravitational field.

But, yes, the similarities look interesting. Relativistic mass seems to be inertial in time as it is in space. This still has nothing to do with potential energy so far as I can fathom.

22. Oct 28, 2005

### masudr

Sorry I wrote more, but it seemed to have been swallowed up by my browser before I clicked submit.

What I meant to say was, that the energy-momentum 4-vector is defined as

$$p^\mu = m\frac{dx^\mu}{d\tau}$$

where $\tau$ is proper time and $x_\mu = (-ct, x, y, z)$ (I've written it as a row vector, hence the minus sign on the time component). This 4-vector captures everything to do with motion through spacetime, and kinetic energy is the 0th component, and the other 3 components are just the ordinary momenta.

23. Oct 28, 2005

### nemosum

K, assuming that rest mass energy is a result of moving through time. Then perhaps you could look at it like a kind of scale, where, on the one hand you have KE for moving 3-dimensionally, and on the other you have you rest mass energy for moving though time alone. If you accelerate, then the scales will tip, and you will have more KE and less rest mass energy as a result of moving more slowly through time. Hipothetically you could say that as soon as you get going fast enough (perhaps c) then time would stop, and the whole of you energy would be kinetic energy. Basically turning yourself into a big photon. This is just an idea I'm throwing out there.

And I didn't think photons and massless particles moved through time anyway. Am I wrong?

24. Oct 28, 2005

### El Hombre Invisible

When you say "proper time", do you mean time in the observer's rest frame? I assume, then, that t is dilated time.

I'm not entirely sure how that answers the question. Could you elaborate?

25. Oct 28, 2005

### El Hombre Invisible

If you choose a frame such that the body is at rest, it will have no KE. If you choose a frame such that it is moving through space, it does have KE. To travel through time in your own frame, you have to have mass. In any other frame, you have relativistic mass and travel through time more slowly, that is: you travel through less time than an observer in his frame.

No, I think you've gone astray somewhere. Acceleration does not lower your rest mass. If the acceleration is positive, it increases your relativistic mass when viewed from your original frame. Your rest mass is unchanging.

In normal frames, it takes some time between emission and absorption. To that extent, photons travel through time.