Uncovering the Truth: Laws of Time and Space in Relation to Motion

[InvariantBrian]

The laws of motion are not independent of time and place. Time and space are values that can be different depending on one’s frame of reference. Moving clocks run slower than stationary clocks and moving rulers are shorter than stationary rulers. This means that two people can get different results when measuring the time and distance of moving objects and they both can be right. Hence, the type of invariance that physicists anticipate is not that the laws of motion will be independent of time and place, but the principles governing temporal and spatial variation will remain unchanged.

Is this true?

 

[HallsofIvy]

You seem to be making a distinction between "laws of motion" and "principles governing temporal and spatial variation". What exactly do you mean by "principles governing temporal and spatial variation"?

The fundamental laws of motion must be independent of the frame of reference- that's one reason laws of motion in relativity theory are written as tensor equations- any tensor equation that is true in one frame of reference is true in all.

 

[chroot]

No, it's not really accurate. "Moving clocks run slow" is essentially a bastardization of the theory of relativity.

- Warren

 

[InvariantBrian]

Ok maybe I should state it this way:

The time and distance of objects in motion can be measured differently depending on one’s frame of reference. This means that two people can get different results when measuring the time and distance of moving objects and they both can be right. The type of invariance that physicists anticipate is not that the measurements of objects in motion will always be the same for all observers, but the principles governing temporal and spatial variation will be the same for all observers.

 

[chroot]

InvariantBrian,

That sounds about right. Time and distance appear differently to different observers, but there is only one set of physical laws, which apply equally to all observers.

- Warren

 

[Kirk Gregory Czuhai]

' . "Moving clocks run slow" is essentially a bastardization of the theory of relativity.
' !
gee whiz !
well, I NEVER !
T = [ t *(1/[1-r]) r=(v^2/c^2)
why would this be a "bastardization?"
at least "locallly" the equations of Physics are Lorentz invariant,
at least "classically they seem to obey Einstein's General Relativity Theory,
except at quantum distances,
why would this be a "bastardization?"
LOL!
peace and love,
and,
love and peace,
(kirk) kirk gregory czuhai
http://www.altelco.net/~lovekgc/kirksresume.htm

 

[DaveC426913]

Ok maybe I should state it this way:

The time and distance of objects in motion can be measured differently depending on one’s frame of reference. This means that two people can get different results when measuring the time and distance of moving objects and they both can be right. The type of invariance that physicists anticipate is not that the measurements of objects in motion will always be the same for all observers, but the principles governing temporal and spatial variation will be the same for all observers.

I think it can be boiled down to: "The application of 'invariance' in the universe is not in *what* we measure, but in *how* we measure."

And yes, that is true.

In Greene's 'Fabric o/t Cosmos', he explains how a highjumper in New York can expect that when he goes to the Lunar Olympics, he can expect gravity to behave the same way. It does not mean he *gets the same numbers*, but he can expect that, taking the laws of gravity as we know them, the gravity on the Moon will *behave as it should*.

 

[jdavel]

Kirk,

"...T = [ t *(1/[1-r]) r=(v^2/c^2) why would this be a 'bastardization?'..."

There's nothing wrong with the equation, but it's not equivalent to the statement "moving clocks run slow".

If two clocks are in relative motion, which one will "run slow"?

 

[chroot]

why would this be a "bastardization?"

"Moving clocks run slow" is a misconception. The proper way to express time dilation is "clocks appear to run slowly to observers with high relative velocities." The two statements are, in fact, very different.

- Warren

 

[InvariantBrian]

I'm confused..I thought time moves differently for objects moving at different velocities. Do a clock appear to run more slowly or does it 'really' run more slowly?

 

[chroot]

InvariantBrian:

Your wristwatch will always appear to tick at the same rate to you, no matter how fast you're moving with respect to other objects in the universe. To other observers, however, it might appear to tick slowly.

The debate over what's "real" and what's "perception" is a philosophical one, but most physicists are local realists: what you can measure is what's real.

- Warren

 

[Doc Al]

Do a clock appear to run more slowly or does it 'really' run more slowly?

The key is to realize that different observers will measure the same clock to tick at different rates. It's no illusion; according to all measurements made in a given frame, a moving clock runs slower than a stationary clock. But whether a clock is "moving" or not depends on what frame is observing the clock. Time measurements are frame dependent.

(Saying that moving clocks "appear" to run slow may lead some to think that time dilation is an illusion, not a real physical effect. But just saying "moving clocks run slow" is even more misleading without some elaboration.)

 

[InvariantBrian]

The key is to realize that different observers will measure the same clock to tick at different rates. It's no illusion; according to all measurements made in a given frame, a moving clock runs slower than a stationary clock. But whether a clock is "moving" or not depends on what frame is observing the clock. Time measurements are frame dependent.

(Saying that moving clocks "appear" to run slow may lead some to think that time dilation is an illusion, not a real physical effect. But just saying "moving clocks run slow" is even more misleading without some elaboration.)

Why will they measure the same clock tick at different rates? The difference in measurement is due to time dilation is it not?

Is it true to say that time flows differently for observers moving at different speeds? For example, if some one is going 100 mph and another is going 1000 mph. Doesn't time move more slowly for the one moving more quick?

 

[HallsofIvy]

Yes, IF you remember to say from which frame they are being observed.

If person A observes person B moving at, say 0.9 c relative to himself, he will observe B's clocks, B's heartbeat, B's aging, much slower than his own.

Of course, person B will observe A moving at 0.9 c relative to HIMSELF (in the opposite direction but time constraction is independent of the direction) and will observe B's clocks, B's heartbeat, etc as much slower than his own.

What do you MEAN by "really running slow" as opposed to "appear to run slow"?

 

[InvariantBrian]

Yes, IF you remember to say from which frame they are being observed.

If person A observes person B moving at, say 0.9 c relative to himself, he will observe B's clocks, B's heartbeat, B's aging, much slower than his own.

Of course, person B will observe A moving at 0.9 c relative to HIMSELF (in the opposite direction but time constraction is independent of the direction) and will observe B's clocks, B's heartbeat, etc as much slower than his own.

What do you MEAN by "really running slow" as opposed to "appear to run slow"?

I see the point of your queston. It's relative. fine. but what about the case where one twin ends up older than the other. In that case, time objectively moved more slowly for one of the twins. But I guess that's not really an inertal frame.

I think i get the first part though..
In inertial frames, the movenment of time is relative to ones frame of reference.

 

[chroot]

I see the point of your queston. It's relative. fine. but what about the case where one twin ends up older than the other. In that case, time objectively moved more slowly for one of the twins. But I guess that's not really an inertal frame.

That's correct. You can't compare the clock readings unless the clocks are brought back together again, and you can't bring the clocks back together unless one of the twins turns around. Turning around necessarily involves acceleration, and acceleration means the frame is no longer inertial.

- Warren

 

[InvariantBrian]

That's correct. You can't compare the clock readings unless the clocks are brought back together again, and you can't bring the clocks back together unless one of the twins turns around. Turning around necessarily involves acceleration, and acceleration means the frame is no longer inertial.

- Warren

But in the case of intertial frames, is the time dilation effect relative?

 

[cepheid]

I'm sorry that this question has nothing to do with physics, but can someone explain to me why everyone seems to be saying clocks "run slow"? Specifically those two words put next to each other. It doesn't really make sense to me when I hear it. Slow is an adjective right? So you can say that something is slow, such as the rate* at which the clock of a passenger on a moving train ticked, as measured by an observer on the rail embankment.

*in this case, the rate is the thing being described as slow

But if you are to describe the action itself (the act of running, or ticking), wouldn't you have to say, moving clocks run slowly? (adverb)

It's bothering me, because I have even seen the phrase "moving clocks run slow" (horror of horrors!) in print, which is making me second guess all this ^.

InvariantBrian: If by "is the time dilation effect relative", you mean that if two observers are in relative motion, and each one is moving at a constant velocity relative to the other, will each one measure the other's clock to be ticking more slowly than his own?, then I guess the answer is yes.

 

[chroot]

cepheid,

This isn't a grammar forum, but you're right, it should be "moving clocks run slowly." That's still misleading physically, but at least it's grammatical, eh?

- Warren

 

[cepheid]

Yeah, I see how it neatly sweeps away the whole essence of the special theory of relativity because it never specifies -- they run slowly as perceived by whom?! I suppose you could claim that it is implicit in the statement that the clock is moving relative to the observer, otherwise he wouldn't be describing it as a "moving" clock now would he? But I think it's a *bad* idea to state anything implicitly,assuming it will be interpreted the same way by everyone. Special relativity is difficult enough (for me, anyway) without additional ambiguities. The whole idea, as I understand it, is that no statement of time (e.g. a time interval, the duration of an event, whatever) has absolute significance. It is meaningful only when given with reference to the inertial frame of the observer who measured it. This statement about moving clocks just doesn't capture that. In case anyone's interested, I saw "moving clocks run slow" in Griffiths Electrodynamics, and he had put it in bold, inside a box, as if to imply that it nicely summarized the entire paragraph above it. :yuck:

 

[chroot]

cepheid,

See post #9.

- Warren

 

[InvariantBrian]

I have a question. if two interital observers measure each others clocks to be moving more slowly, it seems that the time dilation effect is just a question of measurement...in other words, time only APPEARS to be moving slowly for either one, but its not like they really age more slowly.

But in the case of the twin paradox. One twin is older and thus one can say that time objectively moved more slowly for one of the twin.

 

[chroot]

The twin paradox necessarily invovles acceleration (one twin has to turn around), and thus one of the two observers is not in a single inertial frame for the entire trip.

- Warren

 

[InvariantBrian]

The twin paradox necessarily invovles acceleration (one twin has to turn around), and thus one of the two observers is not in a single inertial frame for the entire trip.

- Warren

yes but even if both observers are an a single inertial frame right now, one of them at least had to start moving by accelerating.

 

[chroot]

yes but even if both observers are an a single inertial frame right now, one of them at least had to start moving by accelerating.

Not for the sake of the thought experiment.

The simplest arrangement possible is that one observer is always on the earth. The other observer is already in his spacecraft , and is already barreling down on the Earth at a significant fraction of the speed of light. When the spacecraft reaches its closest approach to the earth, the two people each start their clocks. Later, the one in the spaceship slows down, turns around, and comes back. There does not need to be an initial acceleration.

- Warren

 

[curvedlogic]

I had always assumed that, while testing relativity, clocks flown round the world actually had a physical final sum of the divided prime frequency when returned to base. I.e., there was a permanent reduction in the final count. Is this not true?

 

[Doc Al]

flying clocks

I had always assumed that, while testing relativity, clocks flown round the world actually had a physical final sum of the divided prime frequency when returned to base. I.e., there was a permanent reduction in the final count. Is this not true?

The Hafele and Keating experiment done in 1971 (where they flew atomic clocks around the world in commercial jets) did show absolute changes in the "moving" clock's time compared to the reference clocks fixed to the Earth as predicted by relativity. But realize that both sets of clocks (those being flown and those on earth) are in non-inertial frames. A simplified analysis of that experiment is given here: http://www.physics.gatech.edu/academics/Classes/spring2005/2213/b/lecture/AroundTheWorld.pdf

 

[curvedlogic]

Thanks for the link. Navigation on a 707 in those days was a bit primitive, I wonder how it affected the data!