What are the physics of changes of timecounts of accelerated/decelerated clocks?

[Bob K]

The Fitzgeral-Lorentz transformation equations describe what is the time, e.g., the timecount, of a clock which has been accelerated or decelerated from an initial reference frame into a different reference frame.

If two identical clocks, C1 and C2, are in an initial reference frame, K, and C2 is accelerated into reference frame, K', there is a difference velocity v between K and K', then the time t in K ≠ the time t' in K' (t ≠ t'), e.g., the timecount of C1 ≠ the timecount of C2.

Mathematics describe physical changes, which are effects, but not necessarily the causes of the effects.

Q1: What is the cause of the effect of the changes of the timecounts of accelerated or decelerated clocks?
A1: _____ (?)

Q2: What is the cause of the effect wherein when C2 is accelerated or decelerated relative to C1 and t in of C1 in K ≠ t' of C2 in K'?
A2: _____ (?)

Perhaps another way to ask the same question may be thus:

When a clock is accelerated, its rate of ticking slows down, and when a clock is decelerated, its rate of ticking speeds up.

Q3: What is the physical cause of a decrease in a clock's rate of ticking when the clock is accelerated and what is the cause of an increase in a clock's rate of ticking when the clock is decelerated?
A3: ______ (?)

A change of a clock's rate of ticking is considered to be time dilation/contraction when the change is a decrease of the clock's rate of ticking or timecount when the clock is accelerated and the change is considered to be time expansion when the change is an increase of the clock's rate of ticking or timecount.

Q4: What is the physical cause of a clock's time dilation/contraction when the clock is accelerated or the clock's time expansion when the clock is decelerated?
A4: _____ (?)

 

[Al68]

The Fitzgeral-Lorentz transformation equations describe what is the time, e.g., the timecount, of a clock which has been accelerated or decelerated from an initial reference frame into a different reference frame.

If two identical clocks, C1 and C2, are in an initial reference frame, K, and C2 is accelerated into reference frame, K', there is a difference velocity v between K and K', then the time t in K ≠ the time t' in K' (t ≠ t'), e.g., the timecount of C1 ≠ the timecount of C2.

Mathematics describe physical changes, which are effects, but not necessarily the causes of the effects.

Q1: What is the cause of the effect of the changes of the timecounts of accelerated or decelerated clocks?
A1: _____ (?)

Q2: What is the cause of the effect wherein when C2 is accelerated or decelerated relative to C1 and t in of C1 in K ≠ t' of C2 in K'?
A2: _____ (?)

Perhaps another way to ask the same question may be thus:

When a clock is accelerated, its rate of ticking slows down, and when a clock is decelerated, its rate of ticking speeds up.

Q3: What is the physical cause of a decrease in a clock's rate of ticking when the clock is accelerated and what is the cause of an increase in a clock's rate of ticking when the clock is decelerated?
A3: ______ (?)

A change of a clock's rate of ticking is considered to be time dilation/contraction when the change is a decrease of the clock's rate of ticking or timecount when the clock is accelerated and the change is considered to be time expansion when the change is an increase of the clock's rate of ticking or timecount.

Q4: What is the physical cause of a clock's time dilation/contraction when the clock is accelerated or the clock's time expansion when the clock is decelerated?
A4: _____ (?)

None of those clocks run slower or faster in their own frame, or in an absolute sense. A clock in motion will run slow compared to a clock at rest in a specific frame. The cause is just a choice of frame.

As an analogy, the relative velocity of a car will be less relative to a truck it's passing than for a pedestrian. There is no physical "cause" for the car moving "slower", it just depends on the frame of reference.

Likewise, a clock doesn't tick slower just because it's viewed from a different frame, it's rate just depends on relative velocity, just like any other measurement.

Al

 

[Fredrik]

All questions of this sort are answered by the simple statement that what a clock measures is the integral of $\sqrt{dt^2-dx^2}$ along the curve in spacetime that represents the clock's motion. (I'm using units such that c=1).

 

[Al68]

All questions of this sort are answered by the simple statement that what a clock measures is the integral of $\sqrt{dt^2-dx^2}$ along the curve in spacetime that represents the clock's motion. (I'm using units such that c=1).

Hi Fredrik,

I don't think that does anything to answer the OP's questions. None of his questions were about how to calculate what any clock measures. He was asking what the physical causes were for differential clock rates.

Al

 

[Dale]

I think Fredrik's answer was accurate and complete. The physical cause of all of those effects is the simple fact that clocks measure timelike intervals (the formula provided) rather than coordinate time.

Those questions are then seen to all be akin to asking why does a ruler measure a longer distance on the hypotenuse of a right triangle. It is just geometry.

 

[G Hathaway]

I think Fredrik's answer was accurate and complete. The physical cause of all of those effects is the simple fact that clocks measure timelike intervals (the formula provided) rather than coordinate time.

Those questions are then seen to all be akin to asking why does a ruler measure a longer distance on the hypotenuse of a right triangle. It is just geometry.

What is "coordinate time"?

I mean, does a rotating frame of reference work?

 

[Dale]

Coordinate time is the timelike coordinate in any physical coordinate system. For SR intertial frames it is, by convention, the time as measured by a system of clocks at rest wrt each other and synchronized via the Einstein synchronization procedure. In non-inertial frames and in GR coordinate time has even less physical meaning.

 

[Fredrik]

He was asking what the physical causes were for differential clock rates.

The physical cause is that spacetime, and clocks, have the properties that are summarized by that formula. To ask why they have those properties is equivalent to asking why special relativity can predict the results of experiments so accurately. It's kind of a pointless question, since it can only be answered by another theory. General relativity (sort of) answers the question, but we can obviously ask the same question about general relativity.

 

[Al68]

I think Fredrik's answer was accurate and complete. The physical cause of all of those effects is the simple fact that clocks measure timelike intervals (the formula provided) rather than coordinate time.

Those questions are then seen to all be akin to asking why does a ruler measure a longer distance on the hypotenuse of a right triangle. It is just geometry.

Well, it would be a correct answer to say that it's caused by the fact that rulers measure length, or one could realize that he's really asking why the hypotenuse is longer, not literally why the ruler measures a longer distance. And the fact that rulers measure length doesn't "cause" the hypotenuse to be longer.

And the fact that clocks measure time like intervals don't "cause" the intervals to be what they are.

I guess if I ask my son why my fuel gauge reads empty after he borrows my car, he could correctly say that it is "caused" by the fact that the fuel gauge measures the amount of fuel in the tank. Should I be satisfied with that answer?

Al

 

[Al68]

The physical cause is that spacetime, and clocks, have the properties that are summarized by that formula. To ask why they have those properties is equivalent to asking why special relativity can predict the results of experiments so accurately. It's kind of a pointless question, since it can only be answered by another theory. General relativity (sort of) answers the question, but we can obviously ask the same question about general relativity.

Well, I guess it's semantics, but I wouldn't call that a "physical cause". I would say there is no physical cause for a clock to run slower as seen from one frame than from another. Nothing about a clock physically changes because I choose to look at it from different frames, so we don't need a physical cause.

Al

 

[Bob K]

Hi Fredrik,

I don't think that does anything to answer the OP's questions. None of his questions were about how to calculate what any clock measures. He was asking what the physical causes were for differential clock rates.

Al

Al: Your paraphrase is correct.

Some physical phenomenon occurs that causes a clock's rate of ticking and timecount to slow down when accelerated and to speed up when decelerated.

I want to know if anyone who frequents this physicsforums.com knows what is the physical cause of changes of a clock's rate of ticking and timecount inre acceleration/deceleration.

 

[HallsofIvy]

Then I guess the question is, what do YOU mean by a "physical reason". Indeed what do you mean by "clock rates" since that depends upon the coordinate frame from which you are observing the clock. Did you read Al68's second post, the one in which he says " It's kind of a pointless question, since it can only be answered by another theory"?

 

[Al68]

Al: Your paraphrase is correct.

Some physical phenomenon occurs that causes a clock's rate of ticking and timecount to slow down when accelerated and to speed up when decelerated.

I want to know if anyone who frequents this physicsforums.com knows what is the physical cause of changes of a clock's rate of ticking and timecount inre acceleration/deceleration.

Well, there is no physical reason because a clock's tick rate doesn't actually slow down in it's own frame. If I get on a spaceship and accelerate to half the speed of light, a clock on Earth will tick slower than a clock on my ship as viewed from the ship's frame. Nothing physical happened to the clock. It still ticks at the same rate it always did on earth. I just changed the reference frame from which I observe the clock. Likewise, the ship's clock will tick slower than Earth's clock in the Earth's reference frame. Nothing physical happened to the clock, I'm just using a different reference frame.

If I were sitting on the moon, and I measure the moons velocity relative to me to be zero, I could asked what made the moon "slow down" since it has a much higher speed relative to earth. The answer is that there is no physical cause for the moon to slow down, it's just due to the fact that I'm using a different reference frame. The same goes for clocks in SR.

Al

 

[G Hathaway]

Well, there is no physical reason because a clock's tick rate doesn't actually slow down in it's own frame. If I get on a spaceship and accelerate to half the speed of light, a clock on Earth will tick slower than a clock on my ship as viewed from the ship's frame. Nothing physical happened to the clock. It still ticks at the same rate it always did on earth. I just changed the reference frame from which I observe the clock. Likewise, the ship's clock will tick slower than Earth's clock in the Earth's reference frame. Nothing physical happened to the clock, I'm just using a different reference frame.

If I were sitting on the moon, and I measure the moons velocity relative to me to be zero, I could asked what made the moon "slow down" since it has a much higher speed relative to earth. The answer is that there is no physical cause for the moon to slow down, it's just due to the fact that I'm using a different reference frame. The same goes for clocks in SR.

Al

That is interesting that you say that the earth-twin-clock slows down from the point of view on the ship. And at the same time, the space-twin-clock slows down from the point of view on earth. They both slowed down by the same amount. How could they be different (twin paradox) when brought back together.

 

[Al68]

Then I guess the question is, what do YOU mean by a "physical reason". Indeed what do you mean by "clock rates" since that depends upon the coordinate frame from which you are observing the clock. Did you read Al68's second post, the one in which he says " It's kind of a pointless question, since it can only be answered by another theory"?

I don't think I said that. I don't think it's a pointless question at all. Unless I misunderstand the OP's question, he's under the impression that something physical "happens" to a clock that makes it run slower instead of the fact that a clock's tick rate just depends on reference frame, similar to other measurements, like momentum, kinetic energy, etc.

Al

 

[Al68]

That is interesting that you say that the earth-twin-clock slows down from the point of view on the ship. And at the same time, the space-twin-clock slows down from the point of view on earth. They both slowed down by the same amount. How could they be different (twin paradox) when brought back together.

Well, they run slow reciprocally by the same amount during inertial motion. During the turnaround the Earth's clock runs faster or "jumps" ahead in the ship's frame(s). In some explanations, this is attributed to the switching reference frames and noting the lack of simultaneity between the two inertial frames of the ship during the turnaround. Or, if we have a realistic acceleration at the turnaround, in the ship's accelerated frame, the Earth's clock "ticks faster" than the ship's in the ship's accelerated frame. Or during the acceleration, we consider a sequence of co-moving inertial frames, each with a corresponding "jump" in time of the Earth's clock due to lack of simultaneity between each sequential frame, which amounts to the same thing.

There are lots of threads on the twins paradox, and lots of different explanations, but in all of them, the fact that each sees the other's clock run slower is reciprocal during all inertial motion.

Al

 

[Dale]

Well, it would be a correct answer to say that it's caused by the fact that rulers measure length, or one could realize that he's really asking why the hypotenuse is longer, not literally why the ruler measures a longer distance. And the fact that rulers measure length doesn't "cause" the hypotenuse to be longer.

And the fact that clocks measure time like intervals don't "cause" the intervals to be what they are.

I understand what you are saying. I am trying to shift the OP's mindset from the idea that it is the clock which is different to the idea that it is the thing that is being measured by the clock which is different. I believe that is the same thing you are trying to get him to understand.

I guess if I ask my son why my fuel gauge reads empty after he borrows my car, he could correctly say that it is "caused" by the fact that the fuel gauge measures the amount of fuel in the tank. Should I be satisfied with that answer?

Although this is not related to thread I think that yes, you should be satisfied and even proud of such an answer. It shows a great deal of thought for a teenager since it completely, correctly, and honestly answers the question without getting him in trouble!

You should be pleased with such an answer although you may want to follow it up with a question that really interests you like where he went.

 

[Fredrik]

I guess if I ask my son why my fuel gauge reads empty after he borrows my car, he could correctly say that it is "caused" by the fact that the fuel gauge measures the amount of fuel in the tank. Should I be satisfied with that answer?

I don't think that's fair. The OP's question is more like "what's the physical reason why the reading on the fuel gauge decreases when the amount of fuel in the tank decreases".

And the fact that clocks measure time like intervals don't "cause" the intervals to be what they are.

He doesn't seem to be looking for the reason why Minkowski space is a good model of spacetime. If he is, then my answer is still what I said in #8. If the question is about the properties of spacetime, and of clocks, then my answer is still what I said in #3. If the question is "why does a clock (defined by the instructions on how to build one) measure the proper time of the curve in spacetime that represents its motion", then we're back to #8.

 

[Al68]

I don't think that's fair. The OP's question is more like "what's the physical reason why the reading on the fuel gauge decreases when the amount of fuel in the tank decreases".

Well, that's the question you and others have answered, but I got the distinct impression that he was asking what physically happened to the fuel, not how the gauge works.

And in the case of the clock viewed from a frame in relative motion, the answer would be that nothing physically happened to the clock. Viewing a clock from a different frame doesn't physically change the clock. Unless I completely misunderstand the OP's questions, that's what he's asking.

Al

 

[Al68]

I guess if I ask my son why my fuel gauge reads empty after he borrows my car, he could correctly say that it is "caused" by the fact that the fuel gauge measures the amount of fuel in the tank. Should I be satisfied with that answer?

Although this is not related to thread I think that yes, you should be satisfied and even proud of such an answer.

Proud, maybe. Pleased by his intelligence, yes. But not satisfied.

Al

 

[G Hathaway]

In this article, http://www.astro.ucla.edu/~wright/cosmo_02.htm, I note the author's use of the term "proper time."

Is this possibly Bob K's "absolute time"?

 

[Fredrik]

And in the case of the clock viewed from a frame in relative motion, the answer would be that nothing physically happened to the clock. Viewing a clock from a different frame doesn't physically change the clock. Unless I completely misunderstand the OP's questions, that's what he's asking.

I agree that nothing happened to the clock, and you're right to mention that explicitly. But we should also mention that the change in the clock's ticking rate reflects a property of spacetime. The fact that spacetime has that property (the property that makes what I said in #3 true) is the only thing that can be described as a "cause" of the changed ticking rate.

 

[Dale]

Bob K,

To understand what we are discussing here it is important to understand the geometric interpretration of relativity.

In a spacetime diagram a moving clock is a diagonal worldline while a stationary clock is a vertical worldline. A clock measures the interval along its worldline.

A rod is a physical device which measures distance and in Euclidean geometry a perpendicular line is the shortest distance between two parallel lines. There is no "physical difference" between a diagonal rod and a perpendicular rod. They give different measurements simply because they are measuring the length of different lines.

Similarly, a clock is a physical device which measures (timelike) intervals and in Minkowski geometry a perpendicular line is the longest interval between two parallel lines. There is no "physical difference" between a diagonal (moving) clock and a perpendicular (stationary) clock. They give different measurements simply because they are measuring the length of different lines.

Does that help?

 

[G Hathaway]

Bob K,

To understand what we are discussing here it is important to understand the geometric interpretration of relativity.

In a spacetime diagram a moving clock is a diagonal worldline while a stationary clock is a vertical worldline. A clock measures the interval along its worldline.

A rod is a physical device which measures distance and in Euclidean geometry a perpendicular line is the shortest distance between two parallel lines. There is no "physical difference" between a diagonal rod and a perpendicular rod. They give different measurements simply because they are measuring the length of different lines.

Similarly, a clock is a physical device which measures (timelike) intervals and in Minkowski geometry a perpendicular line is the longest interval between two parallel lines. There is no "physical difference" between a diagonal (moving) clock and a perpendicular (stationary) clock. They give different measurements simply because they are measuring the length of different lines.

Does that help?

As I understand it (on another message board) Bob K was banned. (For "crackpottery" it was claimed.) So he is unlikely to read this response. Should you wish to engage him (not recommended -- he is totally dogmatic that there is an absolute time) I could direct you to the right message board.

 

[Dale]

he is unlikely to read this response.

OK, hopefully it is helpful to someone else then.