I Does time dilation occur due to the speed limit of light or c?

[mucker]

In both cases you were moving inertially. There's no physical sense in which you can say you have a fixed absolute speed.

I've never said anything about an absolute speed. In both scenarios I said one observer is moving at 0.5c relative to the other observer, and in the other scenario I said someone is moving at 0.25c relative to the other observer, how does any of this imply I am talking about an absolute speed??

When I used the the word fixed speed (only in the last post) I still meant relative to the observer. I used the term fixed because you were being so pedantic about the speeds I was using in reference to c (i was using percentages of c), so I said let's use a fixed speed instead. You can't put this one on me, if you can't follow the post and didn't pick this up then that's your mistake not mine; it's clear that's what I am referring to as I've said it many times throughout this entire discussion. I shouldn't have to repeat every single detail in every single post I write just to protect myself from you constantly telling me I am wrong. I have specifcally stated the examples 3 times in other posts - the examples I gave haven't changed throughout this whole disucssions and I have reworded it 3 times already but in all cases I said one observer is moving relative to another. Granted I did not on the last one but I shouldn't need to if you are following the conversation

 

[mucker]

Look at it from our perspective: we don't know what your point is, so we can only address the problems we see in what you've written.

I want to get to the bottom of this, politely. I don't see how that is relevant in this context, you don't need to know someones point (although it certainly helps) to understand the question they asking. Sometimes I leave the "point" out. I do this for one of two reasons (which I am sure others do to):

• Sometimes it can detract from the question and people get hung up on the "point" rather than addressing the question and answer, then it just goes on and on and you never get your question answered.
• Sometimes to add the full context just takes too long and makes the post massive.

Either option I believe is fine when some context isn't needed and you just want a straight answer.

 

[jbriggs444]

what I meant was ~300km/s when I said c and ~600km/s when I said 2c. I didn’t mean, everything is increased by a multiplication of c (including c itself). So again, in those two examples a person would be moving at ~150km/s in both examples, but the speed of light would be faster in the latter

c is 300,000 km/s. 2c is 600,000 km/s. 1/2c is 150,000 km/s. Let's assume that you meant those numbers.

So you've changed out the universe and doubled the invariant speed. You had a guy in the first universe moving at 1/2 c (relative to a particular inertial frame against which his clock is observed). Now a guy in the second universe is moving at 1/4 c (relative to a particular inertial frame against which his clock is observed).

The observed time dilation is 15% in the first universe and 3% in the second. Increasing the speed of light has reduced the time dilation. And not linearly.

The relevant figure for purposes of time dilation and the like is speed expressed as a fraction of the invariant speed.

0.5c behaves the same whether you have a guy moving at 300,000 km/s in a universe where c is 600,000 km/s or a guy moving at 150,000 km/s in our own home universe.

0.25c behaves the same whether you have a guy moving at 75,000 km/s in our universe or a guy moving at 150,000 km/s in a universe where c is 600,000 km/s.

If you change the invariant speed, you change the geometry of the universe to match.

Edit: The idea of the existence of a speed standard that is shared between two different universes is problematic. How will you measure speed except as a fraction of the invariant speed? What is it about the two universes that you are keeping unchanged? And how can you know that it is unchanged.

 

[Sagittarius A-Star]

I just think it is a bit pedantic about the metre thing. It didn't need to brought up.

It is important to understand the "metre thing", because the definition of "1 meter" contains the invariant (and maximum) speed $c$ (as @PeroK mentioned already). In the SI-unit system the definition is:
$$1m := 1s * \frac{c}{299792458}$$
Source:
https://en.wikipedia.org/wiki/Metre#Speed_of_light_definition

The value of $c$ is only an artifact of the unit-system.

The calculation formula for time dilation contains the unit system-independent term $v/c$.

 

[Grasshopper]

Well it seems I will get shot down no matter what! The reason I took that approach this time is because I was getting shot down when asking the questions directly.
[...]

Regarding being "shot down" here, be careful not to read too much intent into words. A lot of the time people here are extremely concise and to the point, and it can come across as being "shot down," when it's really just someone stating a fact with no embellishment or fanfare. What I mean is, a lot of the times "You are wrong" simply means what you said is incorrect, and there is no intended connotation of derision at at all (where there may be on other forums). The goal isn't to feel superior or belittle people by this community. It's just to communicate physics correctly and clearly.

 

[Grasshopper]

Oh one other thing: these discussions about what the meter is are not pedantic. As you learn more about this topic (speaking from personal experience), you’ll find that the rabbit hole goes much deeper than you might think. And with respect to the meter specifically, when Einstein was first making his arguments about SR, he carefully looked at what it means to measure lengths or time intervals. And the more you learn, you’ll see it was for good reason.

As I said, the rabbit hole goes deeper than one might think (or as a physics professor told me, there are “subtleties” to SR that aren’t clear at first glance).

Good luck in your searching!

 

[Sagittarius A-Star]

pedantic

Being pedantic is required in math and physics.

 

[anuttarasammyak]

Thanks all, but that doesn't answer my question. What I am asking is if time dilation is caused by the finite speed of light or the speed in which we are moving relative to another observer?

I would like to show you the third choice : time dilation of another body is caused by its speed to us who are at rest in an IFR.

Do you say in your latter choice that our time pace depends on whether another one observe us or not ? When v=0.99999c elementary particle is produced in CERN accelerator, does the particle become an observer and influence our pace of time ?

 

[anuttarasammyak]

What I am asking is if time dilation is caused by the finite speed of light

..Well, yes, in a sense that time dilation has gamma factor defined as
$$\gamma:=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$
and if c were infinite, $\gamma$=1 for any finite v so no time dilation could take place.

 

[vanhees71]

In modern terms, the meter is defined in terms of the speed of light as @PeroK says, so you can't have a different speed of light.

You are correct that this definition scheme is new (2018) but the problem is not. The meter used to be defined as some fraction of the Earth's circumference. In such a system, if you change $c$ you have to change $\epsilon_0$, which changes the strength of the electromagnetic force, which changes the size of an atom (because they're held together by electrostatic forces), which changes the size of the Earth, which changes the definition of the meter in exactly the same way the modern definition would.

The new SI didn't change $c$ but kept it as it was defined since 1983.

The logic of the SI is driven by both the best theoretical knowledge about the natural laws we have today and the practical realization of the units as accurate as possible. That's why all starts with the definition of the second as a unit of time. It uses still the Cs hyperfine transition frequency as done since 1967:

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency $\Delta \nu_{\text{Cs}}$, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.

Then one uses the fact that to the best of our knowledge spacetime has to be described relativistically, and thus there is a universal limiting speed (having a priori nothing to do with the speed of light but it's always called the speed of light, because to the best of our empirical knowledge the em. field is massless, as discussed above) to define the metre as the unit of length:

The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit $\text{m} \cdot \text{s}^{-1}$, where the second is defined in terms of the caesium frequency $\Delta \nu_{\text{Cs}}$.

This is all as before. The great achievement of the 2019 redefinition of the SI units however is that the fundamental natural constants (except Newtons gravitational constant $G$) have been given defined values once and for all. Thus the kg as the unit of mass is now pretty abstractly defined as

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be $6.62607015 \cdot 10^{-34}$ when expressed in the unit J⋅s, which is equal to $\textbf{kg} \cdot m^2 \cdot s^{-1}$, where the metre and the second are defined in terms of $c$ and $\Delta \nu_{\text{Cs}}$.

The electromagnetic unit, the SI introduces for practical convenience (not so much for the convenience of theoretical physicists and students of electromagnetism though ;-)), an extra unit for electric charge or rather, for historical reasons, electrical current. It defines the elementary charge (the charge of a proton or the negative charge of an electron) to have a certain numerical value:

The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be $1.602176634 \cdot 10^{−19}$ when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of $\Delta \nu_{\text{Cs}}$.

Now the pretty artificial constants $\mu_0$ and $\epsilon_0$ are to be empirically determined, and this brings the greatest deviations between the old and new definitions of the units due to the uncertainty inherited from the unertainty in the measurement of the finestructure constant $\alpha=e^2/(4 \pi \epsilon_0 \hbar c)$. While $e$, $\hbar=h/(2 \pi)$ and $c$ are by definition exact, the vacuum permittivity $\epsilon_0$ has to be measured, and the most accurate way is to measure $\alpha$, and this has an relative uncertainty (CODATA 2018) of $1.5 \cdot 10^{-10}$. Correspondingly also the vacuum permeability has an uncertainty of this order too, because it is related with $\epsilon_0$ due to $\mu_0 \epsilon_0=1/c^2$.

 

[PeterDonis]

The reason I took that approach this time is because I was getting shot down when asking the questions directly.

You were? Where? Not in this thread.

 

[PeterDonis]

I don't see why it needs to be consistent for a hypothetical situation

If the scenario you propose isn't consistent, how can anyone possibly reason about it? It would be like asking, "if 2 plus 2 were 5, what would the universe look like?" How is anyone supposed to answer that?

I don’t see how I could have asked the question without using a hypothetical situation

The point isn't to never propose a hypothetical situation; the point is that if you do, it has to be consistent so that people can reason about it. You already know that there are two consistent models--finite invariant speed (relativity) and infinite invariant speed (Newtonian physics)--so you could just ask, hypothetically, if our universe were described by Newtonian physics instead of relativity, would there be time dilation? (That question has already been answered in this thread anyway--the answer is no.)

Or, if you aren't sure about, say, whether the speed of light can be consistently modeled as different from the invariant speed, you could ask if such a model exists. (And then you would have gotten the answer that @Ibix gave you in post #2.) And then, if such a model exists, you could ask if there is time dilation in that model, and what it depends on. (The answer to that is yes, and it depends on the spacetime structure implied by the finite invariant speed, not the speed of light.)

Maybe I shouldn’t have used relative speeds, let’s convert them to m/s to be clear about what I meant.

Relative speeds are in m/s (or whatever unit of speed you are using). So I don't understand why you would need to "convert" them.

In the last two cases (where you said they would be the same), what I meant was ~300km/s when I said c and ~600km/s when I said 2c.

In these two models, you are proposing that the speed of light is different, not the invariant speed, correct?

 

[Jsauce]

The way I reason about it is with a thought experiment. All observers will measure c to be the same, no matter their velocity relative to the inertial of the universe. So, if you are in a ship moving at 0.5 c and you measure c you will get the same result as a “stationary” ship, but the photons can’t be translating at 1.5c just because you are observing them, this is where I imagine the time dilation adjustment comes in. The photon translates the same “distance” in the universe frame in the same amount of universal frame “time”. So instead of the photon having an absolute speed of 1.5c it is actually still c in the universe frame.

 

[PeroK]

The way I reason about it is with a thought experiment. All observers will measure c to be the same, no matter their velocity relative to the inertial of the universe. So, if you are in a ship moving at 0.5 c and you measure c you will get the same result as a “stationary” ship, but the photons can’t be translating at 1.5c just because you are observing them, this is where I imagine the time dilation adjustment comes in. The photon translates the same “distance” in the universe frame in the same amount of universal frame “time”. So instead of the photon having an absolute speed of 1.5c it is actually still c in the universe frame.

This is all wrong. There is no "universal" frame of reference.

 

[anuttarasammyak]

the photons can’t be translating at 1.5c just because you are observing them, this is where I imagine the time dilation adjustment comes in.

Not only time dilation but also Lorentz contraction of space length take place. Say light starts and goals with time and space difference of T and X
$$\frac{X}{T}=c$$
It holds for observation in any IFR say
$$\frac{X_n}{T_n}=c$$
where An means A observed value in IFR#n with any numbering of IFRs. We have both no ways and no needs to say which IFR is "the universal frame".

 

[Jsauce]

This is all wrong. There is no "universal" frame of reference.

Sorry for my imprecise language, but I was referring to asymptotically flat space time.

 

[jbriggs444]

Not only time dilation but also Lorentz contraction of space length take place. Say light starts and goals with time and space difference of T and X
$$\frac{X}{T}=c$$
It holds for observation in any IFR say
$$\frac{X_n}{T_n}=c$$
where An means A observed value in IFR#n with any numbering of IFRs.

This is correct but, perhaps, misleading. Just as you say, there is time dilation and length contraction. If we blindly apply the formula for length contraction, we might say "our measured displacement was $X$. His measured displacement must be greater": $$X_n = \frac{X}{\sqrt{1-\frac{v^2}{c^2}}}$$If we blindly apply the formula for time dilation, we might say "our measured duration was T. So his measured duration must be less": $$T_n = T \sqrt{1-\frac{v^2}{c^2}}$$
The above seemingly correct but actually wrong-headed calculation would lead us to believe that$$c_n = \frac{X_n}{T_n} = \frac{c}{1-\frac{v^2}{c^2}}$$
A correct way of doing the calculation would be to do the full Lorentz transformation on the starting and ending events and thereby include the relativity of simultaneity.

We have both no ways and no needs to say which IFR is "the universal frame".

Agreed.

 

[Herman Trivilino]

The way I reason about it is with a thought experiment. All observers will measure c to be the same, no matter their velocity relative to the inertial of the universe.

But there is no such thing as velocity relative to the inertial of the universe. Besides not making sense, it seems you are clinging to the notion the universe somehow has a rest frame and that all velocities can be measured relative to it. That's equivalent to the notion of velocity being absolute.

Syo, if you are in a ship moving at 0.5 c and you measure c you will get the same result as a “stationary” ship, but the photons can’t be translating at 1.5c just because you are observing them, this is where I imagine the time dilation adjustment comes in.

No need to imagine any such thing. You are simply hung up on the Newtonian notion of adding speeds to combine them. Adding them is not the correct way. When you correctly combine c and 0.5c you get c, not 1.5 c.