What is time?

[freeztar]

I have said over and over that the latter (Earth periods) do not vary just because the former(time keepers) do. Clocks at different altitudes (velocities, etc) do indeed "keep time" differently, but one Earth orbit stays the same, as does its period of revolution, regardless of the variance in time keeping devices. There is nothing at all "internally inconsistent" about the above.

 

This only holds true for all observers in the same frame of reference.

 

If I took off on a spaceship traveling at near the spped of light and you stayed on Earth and we both had watches, I might signal to you after only ten of your minutes that I've witnessed one rotation of Earth. Of course, you would think this was silly because for you on Earth, your clock only shows the passage of ten minutes. The sun is nearly in the same place in the sky. Everyone on Earth would agree with you and everyone on the spaceship would disagree with you.

 

Modest was right in saying that your viewpoint is internally inconsistent. Since clocks measure duration, It is incorrect to say that duration stays the same while clocks change. It's both or neither. If a thermometer measures temperature, it's inconsistent to say that temperature can change while the thermometer reads the same, or vice versa.

[watcher]

This only holds true for all observers in the same frame of reference.

 

what makes frame of references different? and why observation of time differs in ever frame of reference. do you have an explanation?

 

i think these are the issues Michael should understand.

[freeztar]

what makes frame of references different? and why observation of time differs in ever frame of reference. do you have an explanation?

 

In short, gravity and velocity.

[watcher]

In short, gravity and velocity.

 

yes. let's take gravity first.

in every point in space, there are varying degrees of gravitational force field. so why is it that the same exact clock would record different time in those different points in space.?

[watcher]

michael,

 

consider the rule ...

no particle can exists at the same time in the same place.

a particle can only exist at different places at the same time or

at different times for the same space.

 

iow, all particles including you are separated from the rest of all other particles not only in space but also in time.

we are all separated by space and separated by time.

[modest]

yes. let's take gravity first.

in every point in space, there are varying degrees of gravitational force field. so why is it that the same exact clock would record different time in those different points in space.?

 

Because of the equivalence principle, you should ask why a clock in the nose of an accelerating rocket keeps different time from a clock in the rear of the accelerating rocket. Whatever the answer, it should apply via the equivalence principle to a gravitational field.

 

Both clocks feel the same force of acceleration throughout the trip, so that seems unlikely to be the cause of the difference in timekeeping. Since clocks are dilated that have different relative velocity, does the clock in the nose have a different velocity as the aft clock?

 

~modest

[lawcat]

why a clock in the nose of an accelerating rocket keeps different time from a clock in the rear of the accelerating rocket.

 

Only if the nose and the tail are accelerating at different rates should the clocks read differently. There should be either the path difference or the velocity difference between the nose and the tail. But if two are traversing the same path, as they are, and at the same velocity as they are, then the clocks should read the same. No?

[modest]

Only if the nose and the tail are accelerating at different rates should the clocks read differently.

 

Indeed they do run at different rates. The clock in the nose runs faster by [math]e^{gh/c^2}[/math].

 

The inside of the accelerating rocket can be described with rindler coordinates which corresponds terribly with our Euclidean intuition. There's a small part of Gravitational time dilation - Wikipedia, the free encyclopedia that supports:

 

In an accelerated box, the equation with respect to an arbitrary base observer is [math]T_d = e^{gh/c^2}[/math], where

• [math]T_d[/math] is the ''total'' time dilation at a distant position,
  
• [math]g[/math] is the acceleration of the box as measured by the base observer, and
  
• [math]h[/math] is the "vertical" distance between the observers.
  

 

Imagine an observer outside the rocket (not accelerating) watching it go by. In the rocket the clock in the nose emits 20 flashes of light per second regularly. The aft section receives those flashes. As judged by the person outside the rocket, does the nose emit the flashes of light at the same rate as the aft section receives them? Remember, the speed of light is constant and does not depend on motion of the source (even if it is accelerating).

 

~modest

[lawcat]

No, not at the same rate. But the reason is that the observer is no longer the nose. The observer is a stationary outside observer and the time dilation is between the observer and the tail of the rocket--the rates are different. The original question was about time dilation between the nose and the tail; not the observer and the tail. Now, as you pointed out, there are small differences in acceleration due to gravity perhaps, between the nose and the tail; which should account for some theoretical difference in clock reading but this is of no practical significance?

[modest]

No, not at the same rate. But the reason is that the observer is no longer the nose. The observer is a stationary outside observer and the time dilation is between the observer and the tail of the rocket--the rates are different. The original question was about time dilation between the nose and the tail; not the observer and the tail.

 

Yes, I'm not interested in the time dilation between the rocket and the stationary observer. The reason I introduced the stationary observer was to make the frequency change intuitive—the idea that the number of flashes per clock revolution is different between nose and aft. The stationary observer can look at the clock in the nose and see it advance one second and count 20 flashes. He can then look at the aft clock and observe it tick off one second and count the flashes it receives. He will notice, as you agree, that the aft clock receives more than 20 flashes.

 

This is intuitive because for the stationary observer the ship is moving relative to light. Their speed is steadily increasing so that they might go 20% of c, 30% of c, and so on. We can exaggerate and say that when the nose clock emits 20 flashes it is going 40% of the speed of light as judged by the stationary observer. It then takes time for the light to reach the back of the craft. By the time the 20 flashes hit the aft clock the ship is now going 41% of the speed of light. The aft clock has, in a sense, sped up toward the incoming flashes to catch them quicker than they were sent.

 

As an analogy, it might take one second to catch 20 raindrops for a person standing on earth's surface. But, if that person had velocity moving upward toward the cloud, then it would take less time to catch 20 raindrops.

 

This observation by the stationary observer is invariant in that it doesn't matter who makes it. If someone observes that a clock flashes 20 times while it advances one second then all other observers must agree—they would see the same thing.

 

In case I'm not explaining this well, here it is in different words:

 

The most well-known example of the power of the equivalence principle is the thought experiment that leads to gravitational time dilation. Consider an accelerating frame, which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons toward the floor. If the rocket accelerates upward at g, the floor acquires a speed v=gh/c in the time taken for a photon to travel from roof to floor. There will thus be a Blueshift in the frequency of received photons, given by dv/v = gh/c

²

, and it is easy to see that the rate of reception of photons will increase by the same factor.

 

Now, since the rocket can be kept accelerating for asa long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time dt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect.

Modern cosmology - Google Books

 

The question then,

yes. let's take gravity first.

in every point in space, there are varying degrees of gravitational force field. so why is it that the same exact clock would record different time in those different points in space.?

I don't know what 'causes' gravitational time dilation. Mass somehow turns ordinary inertial reference frames into accelerated reference frames. Perhaps the reason that time dilates in a gravitational field is the same as the reason it dilates in an accelerated reference frame. The question then would be: why does a clock in the nose of a rocket run fast? Why do two events (two flashes of light, let's say) take more time as judged by the nose of an accelerating rocket than they do as judged by the aft?

 

~modest

[watcher]

Because of the equivalence principle, you should ask why a clock in the nose of an accelerating rocket keeps different time from a clock in the rear of the accelerating rocket. Whatever the answer, it should apply via the equivalence principle to a gravitational field.

 

yes, i would like to ask what is it with accelerating body that affects the surrounding space and clock tick. what is the mechanisms involved?

[coldcreation]

I love

 

 

t--i---m-----e---------d-----------i------------l-------------a------------t---------i------o----n

 

 

 

 

CC

[coldcreation]

yes, i would like to ask what is it with accelerating body that affects the surrounding space and clock tick.

 

Curved spacetime.

 

 

what is the mechanisms involved?

 

The physical mechanism of gravity is not known.

[lawcat]

Modest,

 

Thanks for the explanation. Time dilation has to do with the clocking of observed motion; it is always the time of motion that we are measuring, not just simply time. So I presume, you are saying that the nose is emitting photons at the constant rate, and the clock appears on time to the nose. But to aft, due to acceleration, the motion of photons is shorter and shorter, and the clock appears to be accelerating?

 

In essence, time dilation is just a way of correcting our perception of time in another locality? The aft observer must acount for time dilation to understand the time at the nose.

[watcher]

Curved spacetime.

 

spacetime curvature is the effect . is it not? it is not the cause.

 

The physical mechanism of gravity is not known.

 

the lorentz transformation described the spacetime distortion when a charged particle accelerates. what has gravity got to do with it? as pointed out by modest, we only say its gravity because of the equivalence principle, but the real culprit is acceleration.

[coldcreation]

Time dilation has to do with the clocking of observed motion; it is always the time of motion that we are measuring, not just simply time. So I presume, you are saying that the nose is emitting photons at the constant rate, and the clock appears on time to the nose. But to aft, due to acceleration, the motion of photons is shorter and shorter, and the clock appears to be accelerating?

 

In essence, time dilation is just a way of correcting our perception of time in another locality? The aft observer must acount for time dilation to understand the time at the nose.

 

Actually it is a real effect, i.e., time dilation is not "a way of correcting our perception of time in another locality."

 

The time dilation in the example above is real, not just apparent (as you seem to imply).

 

Evidence is that time dilation also occurs when objects are not in motion, called gravitational time dilation. In this case the dilation occurs depending on the height within a gravitational field. Clocks run at different rates at different places in a gravitational field.

 

So time dilation occurs physically in at least three scenarios. Simply, with (1) motion, (2), location in a gravity field, (3) and the combination of both motion and location in the field.

 

See here: Velocity time dilation tests, Gravitational time dilation tests, Velocity and gravitational time dilation combined-effect tests.

 

CC

[coldcreation]

spacetime curvature is the effect . is it not? it is not the cause.

 

I understand you quandary, but there is an equivalence (in affect and in effect) between acceleration and curved spacetime. There is a displacement from linearity (curvature) in the field of an object in a state of acceleration, just as there is a displacement from linearity in a field (gravitational field) of an object 'at rest.'

 

So, the 'cause' above is the acceleration. That is what produces the curved field.

 

the lorentz transformation described the spacetime distortion when a charged particle accelerates. what has gravity got to do with it? as pointed out by modest, we only say its gravity because of the equivalence principle, but the real culprit is acceleration.

 

Again, I understand your quandary. This should help visualize what is happening. Remember Einstein's elevator thought experiment?

 

“From this correspondence [EEP] follows that it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether its motion is straight and uniform and the observed effects are due to a gravitational field” (Einstein 1940).

 

Take K and K'. Where K is a uniform gravitational field, and K' has no gravitational field but is uniformly accelerated such that objects in the two frames experience identical forces:

 

"We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course." (Einstein 1911)

 

This observation was the start of a process that culminated in general relativity. Einstein suggested that it should be elevated to the status of a general principle when constructing his theory of relativity:

 

"As long as we restrict ourselves to purely mechanical processes in the realm where Newton's mechanics holds sway, we are certain of the equivalence of the systems K and K'. But this view of ours will not have any deeper significance unless the systems K and K' are equivalent with respect to all physical processes, that is, unless the laws of nature with respect to K are in entire agreement with those with respect to K'. By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. For by theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes in a homogeneous gravitational field." (Einstein 1911)

 

 

CC