Time dilation interpretation

[teacher94]

Which is to say that it is a comparison of clocks.
Which is to say that time is what clocks measure.

So time does not exist as an independent concept?!! It exists only in sense of comparing how many cyles of an event fit in one cyle of another event? Therefore relative?

 

[jbriggs444]

So time does not exist as an independent concept?!! It exists only in sense of comparing how many cyles of an event fit in one cyle of another event? Therefore relative?

We can measure it. With clocks. Proper time exists in that empirical sense.
We can agree on and validate standards of synchronization and extend this notion of time to coordinate systems.

Coordinate time is relative -- to a set of coordinates.
Proper time is invariant.

 

[Sagittarius A-Star]

So time does not exist as an independent concept?!! It exists only in sense of comparing how many cyles of an event fit in one cyle of another event? Therefore relative?

The reason for calling time "relative" is, that the time-interval ##\Delta t## between two events depends on, which reference frame you choose. Invariant is the spacetime interval between the events. The square of it is, with (+---) convention:
##(\Delta s)^2 = (c \Delta t)^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2##

 

[Nugatory]

No matter how you look at time boils down to how many events happen in the span of another event, for example how many times the pendulum swings in the span of a free falling motion of a ball.

Yes, provided that the pendulum and the ball are for all practical purposes colocated, in which case we are measuring proper time along a timelike worldline (strictly speaking, within a sufficiently small timelike worldtube). Everyone agree that this proper time cannot be "affected or changed"; it is also, as Einstein said, what a clock measures.

It gets trickier when we work with events that are not for all practical purposes colocated, as when we conclude that a clock moving relative to us is running slow relative to our own clock. Now the measurement relies on additional assumptions (most crucially, what it means to say that two physically separated events happen "at the same time") that should be stated precisely. The "time slows down...." presentations hide these additional assumptions and obscure what is really going on.

 

[Nugatory]

So time does not exist as an independent concept?!! It exists only in sense of comparing how many cyles of an event fit in one cyle of another event? Therefore relative?

Throughout this thread, you have been (as does everyone who hasn't learned relativity, including many people who think they have) using the word "time" to refer to two different things: proper time which is what a clock measures, and coordinate time which is the timestamps that we attach to events ("that firecracker over there exploded at 3:00 PM"). These are completely different things, and confusing them is the root of most relativity confusion. Proper time is "real" in the sense that it is a physical quantity that can be measured, and everyone will agree about the results of such measurements. It's as real and non-relative as any other physical quantity. Coordinate time is relative, in the sense that people in motion relative to one another will naturally assign different coordinate times to the same event.

In normal life we nearly always choose to assign coordinate times in such a way that they are numerically equal to our proper time, and of course we are all moving slowly enough relative to one another that our proper times are pretty much indistinguishable (it takes something like the Hafele-Keating experiment to notice any difference) so it's easy to lump them all together under the single inadequately specified word "time".

We have many older threads here about the difference between the two concepts of time, and I will repeat my earlier suggestion about the early chapters of Taylor and Wheeler.

 

[Sagittarius A-Star]

The justification for the slow of evey process by the same factor could be justified by saying that object that move fast have large kinetic energy which in itself is mass since mass and energy are the same this will result in every particle in that object being heavier so it moves slower.

Here is a calculation for a simple mass-spring-system in motion, using "relativistic mass":
https://www.mathpages.com/home/kmath068/kmath068.htm

It is better to speak about "energy" (as you did) instead of "relativistic mass" to avoid confusion with "invariant mass".

Here is a similar calculation for a balance-wheel-clock:

The period of oscillation of the balance wheel in it's rest-frame ##S## for non-relativistic angular velocity is:
##T = 2\pi\sqrt{I/\kappa}##

For simplicity assume, that the frame ##S'## moves with relativistic velocity in direction of the wheel axis.

The spring constant in transversal direction must transform in the same way as transversal forces do:
## \kappa' = \kappa/\gamma##

The moment of inertia in transversal direction must transform in the same way as ##E/c^2## does:
##I' = I \gamma##
$$T' = 2\pi\sqrt{I'/\kappa'} = 2\pi\sqrt{\gamma^2 * I/\kappa} = \gamma T$$
The "relativistic mass" ##m_R## and therefore also ##E/c^2## depend on the choosen reference frame and also on the conventional Einstein clock synchronization, as time-dilation does. Their calculation includes the time-dilation factor ##\gamma##:
##m_R = \gamma m_0##
##E/c^2 = \gamma E_0/c^2##

 

[gmax137]

Suppose Alice passes you, at one-fourth the speed of light. If she could see your clock, she would say it is running slow, by a factor called "gamma."

##\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##

In this case, ##\gamma_{Alice}=\frac{1}{\sqrt{1-0.25^2}} = 1.033##

Now suppose at the same time, Bob also passes you, but he's going one-half the speed of light.
In this case, ##\gamma_{Bob}=\frac{1}{\sqrt{1-0.5^2}} = 1.155##

So how "slow" is your clock? It depends on who you ask! For you, it reads "proper time" since you are carrying it along with you. Alice and Bob disagree on how slow your clock is. This disagrrement has nothing to do with how fast your biological processes are "really" running. There is no "really" except for your proper time.

EDITed to fix up some confusing words.

 

[Sagittarius A-Star]

It gets trickier when we work with events that are not for all practical purposes colocated, as when we conclude that a clock moving relative to us is running slow relative to our own clock. Now the measurement relies on additional assumptions (most crucially, what it means to say that two physically separated events happen "at the same time") that should be stated precisely. The "time slows down...." presentations hide these additional assumptions and obscure what is really going on.

As an example for this, I define a reference frame ##\bar S## (##\bar x, \bar t##) with anisotropic speed of light, given a standard inertial coordinate system ##S## (##x, t##), with ##|k|<1##:

##\bar x = x##
##\bar t = t + \frac{kx}{c}##

https://www.mathpages.com/home/kmath229/kmath229.htm

The spacetime interval between two ticks of a clock moving with velocity ##\bar v = \frac{v}{1+ k\frac{v}{c}}## in positive ##\bar x## direction is:
##\Delta s^2 = c^2 (\Delta\bar t - \frac{k\Delta\bar x}{c})^2 - \Delta \bar x^2##
##\Rightarrow##
##\frac{\Delta \tau}{\Delta \bar t} = \sqrt{(1 - k\frac{\bar v}{c})^2 - \bar v^2/c^2} = \frac{1}{1+ k\frac{v}{c}} \sqrt{1 - v^2/c^2}##

But usually, time-dilation is define with reference to a standard inertial coordinate system, which is based on the Einstein-synchronization (##k = 0##).

Measurement equipment for the transversal Doppler effect to test time-dilation is constructed under the assumption of isotropic one-way speed of light.

 

[Sagittarius A-Star]

Alice and Bob disagree on how slow your clock is.

All agree on the spacetime-interval between two ticks of my clock.

 

[pervect]

TL;DR Summary: Hi, i am not a physicist but i have the intuition that time dilation is just slow in the movement of particle's and causality instead of slow in time itself and that this does not affect photons. I understand that there is no way to distinguish between a slow in time and a slow in movement and causality but would the math still work the same if we assume this interpretation of time dilation? Thank you

Hi, i am not a physicist but i have the intuition that time dilation is just slow in the movement of particle's and causality instead of slow in time itself and that this does not affect photons. I understand that there is no way to distinguish between a slow in time and a slow in movement and causality but would the math still work the same if we assume this interpretation of time dilation? Thank you

It's possible to regard a photon as the limiting case of a non-photon (i.e. a massive particle) that moves very very fast. Such a massive particle can't ever quite reach the limiting speed that a photon does, but it can come arbitrarily close.

It's unclear to me exactly what your proposal is, but this might be a useful case to consider. What would you see as the difference between a very fast moving particle, for instance at .9999 c, and a photon moving at 1.0 c? It would be helpful if you could describe some experiment or thought experiment that would illustrate what it is you're trying to describe.

On a somewhat related note, it'd be helpful if you could explain what you think time dilation is. I have to admit that it'd be helpful mostly in criticizing your idea, which you may not want to hear, but that's a separate issue. Discussion is supposed to involve the exchange of ideas, in the end, as opposed to validation. At least, that's the view I take.

I regard time dilation as the ration of proper time (which is the sort of time a clock, such as a wristwatch, measures) to coordinate time, for instance, but I'm not sure saying that will make sense to you. I have a sense (which may be wrong), that you think there is some sort of universal, agreed-upon notion of time, and that you regard time dilation as the ratio of the proper / wristwatch time to this universal underlying time. I would be very critical of this idea, but it'd be somewhat useless to say more if I was totally off the track of what you were trying to ask.

 

[Dale]

So time does not exist as an independent concept?!! It exists only in sense of comparing how many cyles of an event fit in one cyle of another event? Therefore relative?

You have to be careful here. The definition of (proper) time is that it is the thing that a clock measures. That is different from saying that time is a clock.

A measuring device measures something. A scale measures mass, a ruler measures length, a clock measures time. Mass is not a scale, it is the thing measured by a scale. Length is not a ruler, it is the thing measured by a ruler. Time is not a clock, it is the thing measured by a clock.

Also, proper time is not relative, it is invariant. All reference frames agree on the reading of any clock, therefore the thing that a clock measures must be an invariant.

 

[jkourany]

If you assume that every possible physical process is slowed, then there are a couple of questions:
1) How would you distinguish between that and time dilation?
2) How can you explain every possible physical process slowing down exactly the same amount? That is a lot to explain. On the other hand, you can just say that there is time dilation and everything else follows.

It also seems to me that what dilates is the frequency of decay of all particles with mass and not time itself. That would be why people age slower traveling away from earth and coming back to earth, because every atom in them decayed slower than those at earth. Traveling clocks slowed because the caesium atoms decay slowed down taking more time to tick the number of cycles we count to say one second has passed. So it seems speed is affecting matter not time.

 

[Ibix]

So it seems speed is affecting matter not time.

How do you explain the reciprocal nature of this? If I am moving fast with respect to you, you see my clocks slowed but I see your clocks slowed. Which of us is "affected by speed"?

And you can build clocks that work using light bouncing between mirrors. We will both agree that light travels at the same speed, but will both agree that the other's clocks are slow.

The fundamental problem is trying to go down any kind of "time (or whatever other word you think you can use to avoid using the word time) is slowed" route at all. It's a terrible description of the reality of relativity, as I believe I said on the previous page.

 

[Sagittarius A-Star]

So it seems speed is affecting matter not time.

The squared spacetime-interval ##s^2 = c^2 (\Delta t)^2 - (\Delta x) ^2 - (\Delta y) ^2 - (\Delta z) ^2## between two ticks of the clock is invariant. That means, it is the same in each inertial reference frame.

In the inertial restframe of the clock, the squared spatial distance ##(\Delta x) ^2 + (\Delta y) ^2 + (\Delta z) ^2## between the ticks is zero.

In an inertial reference frame, in with the clock is moving, the squared spatial distance between the ticks is greater than zero, therefore, also the (coordinate-)time interval ##\Delta t## between the ticks must be greater than in the rest frame of the clock.

 

[FactChecker]

How do you explain the reciprocal nature of this? If I am moving fast with respect to you, you see my clocks slowed but I see your clocks slowed. Which of us is "affected by speed"?

Very good point. The central fact is that a stationary person observes the clock of a moving person as it goes from one location to another. It is the difference in synchronized clocks in different locations that forces the reciprocal property. So the slowing of a moving clock is the direct, logical, result of the spacetime distortion of a moving reference frame.

 

[Dale]

So it seems speed is affecting matter not time.

There are a number of issues with that approach. @Ibix mentioned that it doesn’t explain the reciprocal nature of time dilation.

Another problem is that it requires a lot of unexplained coincidence. If it isn’t time then why does EM’s effect dilate the same as the strong force and the weak force and gravity?

But in my mind the biggest problem is that it is scientifically meaningless. If you cannot propose a specific experiment whose measured outcome would depend on the difference between “speed is affecting matter not time” vs “speed is affecting time” then nature doesn’t care about the difference between the two. If there is no possible experimental difference then the distinction is all in your mind and doesn’t describe anything about the universe.

 

[jbriggs444]

Traveling clocks slowed because the caesium atoms decay slowed down taking more time to tick the number of cycles we count to say one second has passed.

Atomic clocks stabilized using the hyperfine transition in caesium-133 do not operate by having caesium-133 atoms decay. The operating principle is not based on counting out caesium-133 half lives.

In a manner of speaking, it is not the transition rate that is important. It is the transition energy. Energy yields a time measure according to ##E=h \nu##.

The official definition of the second was first given by the BIPM at the 13th General Conference on Weights and Measures in 1967 as: "The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." At its 1997 meeting the BIPM added to the previous definition the following specification: "This definition refers to a caesium atom at rest at a temperature of 0 K."[3]

It is no coincidence that this definition can be realized by constructing an atomic clock.

In a caesium beam frequency reference, timing signals are derived from a high stability voltage-controlled quartz crystal oscillator (VCXO) that is tunable over a narrow range. The output frequency of the VCXO (typically 5 MHz) is multiplied by a frequency synthesizer to obtain microwaves at the frequency of the caesium atomic hyperfine transition (about 9192.6317 MHz). The output of the frequency synthesizer is amplified and applied to a chamber containing caesium gas which absorbs the microwaves. The output current of the caesium chamber increases as absorption increases.

The remainder of the circuitry simply adjusts the running frequency of the VCXO to maximize the output current of the caesium chamber which keeps the oscillator tuned to the resonance frequency of the hyperfine transition.[46]

Paraphrasing... You have this chamber with a caesium gas. It is able to absorb microwaves corresponding to the hyperfine transition. You have this quartz oscillator that can be tuned slightly. You tune the oscillator so that it produces microwaves that are optimally absorbed by the caesium gas. The quartz oscillator is then your clock.

It is just like the clock in your smart phone. It has a quartz oscillator. It is just that the quartz oscillator in an atomic clock is stabilized using that clever caesium arrangement.

But all of the above is nothing but technical details. At the end of the day it is still a physical process. Time dilation affects all physical processes. As others have pointed out, whether it affects time itself or merely affects "all physical processes" is philosophical wool gathering, not science.

 

[FactChecker]

As others have pointed out, whether it affects time itself or merely affects "all physical processes" is philosophical wool gathering, not science.

Occam's razor: When presented with competing hypotheses about the same prediction, one should prefer the one that requires the fewest assumptions.
It's not a law of logic, mathematics, or physics; it's just a preference for simplicity and testability.

 

[jbriggs444]

Occam's razor: When presented with competing hypotheses about the same prediction, one should prefer the one that requires the fewest assumptions.
It's not a law of logic, mathematics, or physics; it's just a preference for simplicity and testability.

Brevity is the soul of wit