# Time and Motion

1. Feb 16, 2010

My question here borders on philosophy, but I'm posting it here because I'd like to discuss it in a scientific context.
I was thinking about time and motion the other day, and how I cannot distinguish between a motionless universe and one without time. For example, if everything were to stop for a million years, and then start moving again exactly as it was, this would be indistinguishable from no time having elapsed at all.
In Einstein's equivalence principle, he notes that the effects of gravity are locally indistinguishable from the effects of inertial motion. From this he promotes the "coincidental" equivalence to a "law of nature".
So I was wondering if it would be possible to make a similar step with the equivalence of time and motion. For example, we might decide that if we transform to a frame where everything is motionless, then no time elapses in this frame. I know what I'm saying is a bit rough around the edges but I'm interested in how to take what seems like a philosophical concept and turn it into a testable theory.

2. Feb 16, 2010

### Staff: Mentor

I believe that a motionless muon will still decay, similarly with other unstable particles. So I think that it is incorrect to say that a motionless universe is indistinguishable from one without time.

3. Feb 16, 2010

### Mentz114

Jesse, does the muon decay not create motion and change? So even this would cease if there was no time.

The commonest definition of time is that 'time is change'. We can only percieve time by being aware of change. No change -> no time. No time -> no physics. Which makes the question philosophical not about physics.

4. Feb 16, 2010

### bcrowell

Staff Emeritus
This question arises in the context of classical mechanics. Say you consider conservation of energy to be more more fundamental than Newton's laws. Let U be the potential energy and K the kinetic energy. Given conservation of energy, we have for an object released in a uniform gravitational field
$$a=\frac{dv}{dt} = \frac{dv}{dK} \frac{dK}{dU} \frac{dU}{dy} \frac{dy}{dt} = \frac{1}{mv}(-1)(mg)v$$
There are two possibilities here: (1) v=0, and (2) $v \ne 0$ and a=-g. If v=0 you can't cancel the v's; this is simply the mathematical way of saying that the object can hover indefinitely while conserving energy.

In the context of general relativity, this has a very natural interpretation. GR has general covariance, so you can elastically stretch and contract the time coordinate, and the laws of physics are still obeyed.

5. Feb 17, 2010

### RasRemi

While this is a good point, decay implies motion by its very nature. An utterly motionless universe would have to be one without change; without decay or growth.

Last edited: Feb 17, 2010
6. Feb 17, 2010

### JesseM

Particle decay is different from our ordinary notions of decay, it just means one type of particle vanishes and some other particle or particles appear in its place. But for most type of particle decay I think the decay products include photons, which can't help but move at the speed of light even if the original particle was motionless in whatever frame we're using.

7. Feb 17, 2010

There are definitely complications. I might want to start off with a simplified GR type scenario where there are only classical particles moving under mutual gravity. Then there are certain gauges (e.g. transverse traceless) in which particles stay still and the coordinates move in order to compensate. I don't know if it would be possible to include light. I think it would be interesting to investigate the consequences of imposing an equivalence between time and motion, but I don't think I have enough genius to actually make such a theory.

8. Feb 17, 2010

### Dmitry67

If you have multiple particles at exactly the same distance for some time you imply:

1. The temperature of the 'gas' of such partciles = exactly 0, which is impossible because Unvirse started from the hot state and every act of cooling down decrase tempreature by some ratio, so you cant reach 0 in finite time;

2. In QM p=0 implies coordinate is *absolutely* unknown, or, if you define 'motionless' using the coordinate, then it also a nonsense because of HUP. In any case, the cosmological horizon sets the limit on how low the p and temperature can be.

9. Feb 17, 2010

### Staff: Mentor

No, it doesn't. A decay is a change, certainly, but not all change is motion. The OP was specific about motion, not other changes. I think it is incorrect.

10. Feb 17, 2010

### matheinste

To measure time we need a clock. An ideal clock can be looked at as a closed system with no external forces acting on it, which, from a given configuration, chages and returns to exactly the same configuration, and so will repeat this cycle continuously. One such cycle is its period or tick. This definition implies changes of state of the system within the cycle and I suppose these changes imply motion of some sort, maybe just at atomic level. So without some motion in the universe we cannot have a clock and so cannot measure time. In this case, is the concept of time meaningless, or is time just not measureable. If nothing ever happens then we would have no use of a clock or time anyway. Does that make any sense.

Matheinste.

11. Feb 17, 2010

### Mentz114

Yes. That's what I was saying. The only arguable thing is - can there be change without motion ?

12. Feb 17, 2010

If I have a universe consisting entirely of emtpy space and a clock, I can make a change of coordinates such that the hands of the clock stay still in the new frame. Do you argue that time is meaningless in this new frame?

13. Feb 17, 2010

### matheinste

Is such a change of coordinate system possible?

Matheinste.

14. Feb 17, 2010

Actually I'm not sure, but when studying gravitational waves the transverse traceless gauge is used, which is a coordinate system physically represented by taking test masses to mark the coordinates. Then free masses stay stationary in this frame even in the presence of a gravitational wave.

15. Feb 17, 2010

### matheinste

Too complicated for me.

Matheinste.

16. Feb 17, 2010

### I_am_learning

Motionless universe?! What kind of universe is that? Do Newtons laws follow there? If Yes then Planets can't suspend near the sun without revolving?? Or gravitational forces vanishes in Motionless universe??? If Motionless universe is to be considered as an snapshot of our universe, then there is no time in it. Its like saying,
Hey, look, 1000 years of motionless universe just passed just now and resumed and we didn't notice it!!!

17. Feb 17, 2010

### yuiop

If the universe everywhere were to stand still for a million years simultaneously for what appears to be one Planck time interval according to one set of observers in a common rest frame it might seem that this frozen state would be undetectable because no physical process could detect this passing of a million years locally. However, to a single observer, far away frozen events would happen later than nearby frozen events and he would notice the universe getting out of sync due to light travel times. If the frozen state events were synchronised in such a way that the information about the frozen events all arrived simultaneously at a single observer to hide the event, then any other observer spatially separated from the first observer or moving rleative to the first observer would notice the pause, due to diefferences in simulteity.

18. Feb 19, 2010

### phyti

How would you be aware of either?

19. Feb 20, 2010

### Frame Dragger

Am I the only person who thought, "why on earth is this guy asking about time & motion studies? What does workplace efficiency have to do with physics." Then I remembered why I shouldn't read the forums when I'm tired.

Anytime someone asks what would happen if time stopped, or accelerated... I just ask, "what is time?". If you follow that conversation to its conclusion, they usually answer their own questions by realizing the lack of a universal time, and maybe even a non-thermodynamic/psychological arrow of time.

Edit: At the risk of angering the Olympian lords of PF by talking about getting QM in your SR/GR... a truly MOTIONLESS universe, devoid of even the minor fluctuations dictated by Uncertainty is impossible (in this universe, during its known history). In a time-stopped universe, or one in which all motion ceased, particles would ALL have definite positions, velocities, etc.

I suppose you could say that a god would be a being able to view and interact with the universe in just such a fashion. That is fanciful of course, but then this is philosphical to begin with.

20. Feb 20, 2010