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

[mucker]

The universal speed limit is c, and as a consequence light is confined to that limit. I was thinking about the time dilation in SR and was wondering if this is result of reaching speeds close to the speed of light or because of reaching speed close to c?

For example, let's say light could be instantaneous would we still experience time dilation as we approached c relative to another body? In other words is the time dilation directly related to the finite speed of light itself or simply that we are going a lot faster relative to another body?

I know the above doesn’t make sense btw as (even theoretically) it would mean c wouldn’t have a universal speed limit anymore. I am just giving the example above to illustrate my point in asking if the time dilation is due to light speed of c.

 

[Ibix]

You can certainly construct theories of massive photons where light does not travel at $c$. In fact, using such theories you can measure the mass of the photon which we now know to be less than 10^-54kg or something like that. In the case that a photon does have mass it's just like any particle and can be stopped - it's just so light (pardon the pun) that a mosquito sneezing ten miles away makes it accelerate to almost $c$. So we model it as massless, but you should be aware of the possibility that it might have a tiny mass that we just haven't differentiated from zero yet (especially in online discussion where people who think they're philosophers like to pontificate about the conditional nature of scientific knowledge which they think scientists don't know about).

So the constant $c$ would have the same importance to relativity that it does now even if light didn't travel at that speed. We'd just have to stop calling it the speed of light.

 

[PeroK]

The universal speed limit is c, and as a consequence light is confined to that limit. I was thinking about the time dilation in SR and was wondering if this is result of reaching speeds close to the speed of light or because of reaching speed close to c?

For example, let's say light could be instantaneous would we still experience time dilation as we approached c relative to another body? In other words is the time dilation directly related to the finite speed of light itself or simply that we are going a lot faster relative to another body?

I know the above doesn’t make sense btw as (even theoretically) it would mean c wouldn’t have a universal speed limit anymore. I am just giving the example above to illustrate my point in asking if the time dilation is due to light speed of c.

If you start with some simple assumptions about the homogeneity and isotropy of space and time, then you can deduce in a couple of pages that there are only two possibilities. The first is Newtonian space and time, with the Galilean transformation between inertial reference frames. The second is SR with some universal constant $c$ and the Lorentz transformation.

In this development of SR there is no need to consider electromagnetic radiation (I.e. light) - although that was the historical path to SR.

It's then your theories of EM radiation and particle physics that determine that massless particles travel at the universal speed $c$.

In general, when learning SR, I found it useful not to put too much emphasis on EM signals and focus on SR as the natural theory of spacetime arising as described above.

Although I cautioned against using too many sources, there is a development of the above on the University of Maryland website.

 

[Nugatory]

would we still experience time dilation as we approached c relative to another body?

We don’t experience time dilation at all - right now you are moving at very close to the speed of light relative to something and that doesn’t affect your experience of anything.

Time dilation is best understood as an example of relativity of simultaneity. You and I are moving relative to one another; our wristwatches both read noon at the same time; later your wristwatch reads 12:20 at the same time that mine reads 12:40 using my rest frame’s “at the same time”; but using your rest frame’s “at the same time” my wristwatch reads 12:10 at the same time that yours reads 12:20. We both conclude that the other’s watch is running slow by a factor of two, and we’re both right.

And to answer the question in your thread title: time dilation, length contraction, and the speed limit are all logical consequences of assuming that there is an invariant speed. Once we assume that the speed of light is invariant, all the rest follows.

 

[mucker]

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 am finding it difficult to explain what I am asking so I will use two scenarios to help explain it:

In one, the laws of the universe are as we know and someone is moving at 0.5c relative to another, the usual observations play out as expected, let’s say here the time dilation is double (I don’t know the exact multiplier but it doesn’t matter to illustrate my point).

In the second scenario light speed is doubled (2c – for some context: I am using this so that the light can reach the observer quicker) but we are now moving at exactly the same speed as before relative to another body (which would now be 0.25c of the new c, not that this matters), all other things being equal, would I experience double the time dilation like in scenario one? In other words, as I said before, is the time dilation, length contraction etc a consequence of the strict speed of light itself (causing a delay for when we observe it), or is it simply that we are moving (the same speed in both examples here) extremely fast relative to another body?

I am going somewhere with this btw, but I’d like to understand the above first (if it is possible to discuss theoretically). thanks!

I could be talking utter BS btw, but this is part of me learning and trying to understand I bit more- maybe there is no way to decouple c and the speed of light, even theoretically

 

[jbriggs444]

In one, the laws of the universe are as we know and someone is moving at 0.5c relative to another, the usual observations play out as expected, let’s say here the time dilation is double (I don’t know the exact multiplier but it doesn’t matter to illustrate my point).

Details do matter. If you don't sweat the details, it is easy to get the big stuff wrong. Which is where you seem to be flailing around now.

For a relative velocity of 0.5 c, the time dilation factor $\gamma$ is given by $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. It works about to be about 1.15. Each frame sees clocks at rest in the other running about 15% slow.

In the second scenario light speed is doubled (2c – for some context: I am using this so that the light can reach the observer quicker) but we are now moving at exactly the same speed as before relative to another body (which would now be 0.25c of the new c, not that this matters), all other things being equal, would I experience double the time dilation like in scenario one?

So now we have a new universe but a similar scenario with a relative velocity of 0.25 c. The relativistic $\gamma$ is now approximately 1.0328. We now have a time dilation where each frame sees clocks at rest in the other to be running about 3% slow.

No. Doubling the speed of light universal speed limit does not double time dilation. It reduces it instead.

Doubling a suitably slow signaling speed does not affect time dilation at all. However, doubling it so that one can send signals faster than the universal speed limit gives rise to serious problems with causality.

Time dilation is not some sort of illusion having to do with signal delay. It is (in some sense) the underlying reality that is revealed when we carefully account for the observational effects of signal delay.

In a better sense, time dilation has to do with the details of the accounting. It involves coordinate systems and hyperbolic rotations and the resulting discrepancies between coordinate values in two coordinate systems at angles to one another.

Edit: As @Ibix has already pointed out, if light does not travel at the universal speed limit then the "speed of light" would not even be a thing. Light could then move at any speed less than c. It would not have a single defined speed.

 

[Sagittarius A-Star]

is the time dilation, length contraction etc a consequence of the strict speed of light itself (causing a delay for when we observe it)

Time dilation of a moving clock in your rest frame does not depend on the delay, by which you observe events.

The results indicate that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames. Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co-exist.

Source:
https://arxiv.org/abs/physics/0207109

 

[Dale]

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?

Time dilation has nothing whatsoever to do with the finite speed of light. No relativistic effects are based on the finite speed of light.

It has to do with the invariant speed and the speed you are moving relative to some specified inertial frame.

 

[mucker]

And there you go! Thank you Dale. You’re a very good teacher and can always get the point I am making and what I am essentially asking.

 

[Dale]

Thanks, but I would have answered the OP the same way everyone else did if I had seen it earlier. Your clarification was important.

 

[mucker]

For example, let's say light could be instantaneous would we still experience time dilation as we approached c relative to another body? In other words is the time dilation directly related to the finite speed of light itself or simply that we are going a lot faster relative to another body?

I hope you are being modest! ;-) This quote is from my op. I don’t see how this different to my last post, but anyhow…

 

[PeroK]

I hope you are being modest! ;-) This quote is from my op. I don’t see how this different to my last post, but anyhow…

This is an example of imprecise language. What you mean is "the finite time that light signals take to reach an observer".

Note that when I explained the difference between an observer and a reference frame in a previous post you replied that you understood that already. Clearly you do not understand this as your question is based on that misunderstanding.

I know it sounds harsh, but if you pretend you grasp something when you do not you are only fooling yourself.

 

[jbriggs444]

For example, let's say light could be instantaneous

If the speed of light is "instantaneous", that implies a standard of simultaneity against which we judge it to be instantaneous.

You have two obvious distasteful alternatives (along with some more exotic and unpalatable ones).

1. Instantaneous signaling only works in one reference frame. We use the standard of simultaneity from that frame. This violates one of the underlying tenets of special relativity (the principle of relativity) and the theory is falsified.

It is not proper to ask about what a theory predicts when using a phenomenon that violates the theory.

2. Instantaneous signaling works in all reference frames. The principle of relativity is upheld. We can use the standard of simultaneity for any valid frame.

But by picking frames of reference carefully we can now have signals propagating backward in time. Effect precedes cause and paradoxes ensue.

 

[pinball1970]

I am confused with a few points
Namely mass and the speed of light

My assumptions :

I thought the speed of light was determined via Maxwell and that this is a finite number.

Secondly I thought ONLY a massless particle can travel at the speed of light in a vacuum and a photon is such a particle.

Lastly a massive particle could never reach the speed of light due to the Energy mass equation derived by Einstein.

There may be other reasons but I thought that was a big one.

This is off topic not wildly off but a little off.

 

[ergospherical]

Nowadays $c$ is an exactly defined number. Putting $\mathbf{j} = 0$ and $\rho = 0$, $\nabla \times (\nabla \times \mathbf{E}) = - \dfrac{1}{c} \dfrac{\partial}{\partial t} \nabla \times \mathbf{B} \implies \nabla(\underbrace{\nabla \cdot \mathbf{E}}_{=0}) - \nabla^2 \mathbf{E} = -\dfrac{1}{c^2} \dfrac{\partial^2 \mathbf{E}}{\partial t^2}$. Similar for $\mathbf{B}$.

 

[Dale]

Secondly I thought ONLY a massless particle can travel at the speed of light in a vacuum and a photon is such a particle.

The point made above is that we have been able to experimentally determine that the photon has a mass $m_{\gamma} < 1 \ 10^{-18} \text{ eV}$. So we believe it to be exactly zero, but in principle we could find out through future experiments that the mass is not zero but something like $m_{\gamma} = 3.5 \ 10^{-20} \text{ eV}$. I.e. it could be non-zero but simply so small that we have not been able to detect the difference yet.

 

[pinball1970]

The point made above is that we have been able to experimentally determine that the photon has a mass $m_{\gamma} < 1 \ 10^{-18} \text{ eV}$. So we believe it to be exactly zero, but in principle we could find out through future experiments that the mass is not zero but something like $m_{\gamma} = 3.5 \ 10^{-20} \text{ eV}$. I.e. it could be non-zero but simply so small that we have not been able to de

Thanks Dale. I think my problem is not understanding other parts to this.
I thought I had a basic grasp of some of the principles.

 

[Grasshopper]

Looking at the algebra it seems to me like it boils down to whether the invariant speed limit is finite or infinite. If it’s finite, you get SR (and time dilation), and if it’s infinite you get Galileo (and no time dilation).

I know I’ll probably get chastised for suggesting that an infinite speed is invariant, since infinity isn’t a number, but as everyone knows if you let c approach infinity in the Lorentz factor the limit is 1, and presumably all finite numbers are infinitely less than infinity.

I’m interested to know the flaws or validity in thinking of it this way.

 

[mucker]

Looking at the algebra it seems to me like it boils down to whether the invariant speed limit is finite or infinite. If it’s finite, you get SR (and time dilation), and if it’s infinite you get Galileo (and no time dilation)

This is exactly where I was going with my OP and trying to draw to that conclusion. I felt that it was so obvious (where I was going with it, not the conclusion) that I specifically didn't need to state it. It's exactly what I was implying when I ask if the time dilation is caused by the finite speed of light or because we are moving close to c. It's why I gave several examples of all things being equal except the speed of light. IE I gave one where it was instantaneous, one at c (as we know it to be) and one where speed of light would be 2c. In all three scenarios where the speed of light is the only thing that changes, I believe we would experience time dilation differently (none in the case of instantaneous), but not one person clarified this.

I was fearful of drawing the same conclusion as Grasshopper, because god help me if I was wrong! People love a good chiding and I wouldn’t have heard the end of it. So instead, I posed the scenarios and asked others what they would conclude, they could get chided instead lol.

But instead, everyone just wanted to point out how it can’t work with the current known laws, or how it would break SR, or it breaks something else. It really frustrates me when people do this, I mean I even stipulate my posts with “let’s say” or “imagine if” to specifically point out I am talking hypothetically so I can deepen my understanding. Instead of going with the flow so said person (me in this case) can “walk it through” so to speak and come to the realisations themselves, everyone just shoots you down right off the bat with why it wouldn’t work due said SR postulates. Does no one here realize that the best way to learn is taking what you think you know and applying it to another scenario? The whole the point of the post was to see if I was grasping parts on the subject matter – since the speed of light and c are always the same (except in rare circumstances like light going through water) I was trying give them separate values so I could “figure out” if it was the speed of light (as in the delay to reach you) or moving really fast (relative to another body) causes time dilation. The only way to do that, was to propose a hypothetical situation where light and c are different speeds and ask what the results would be on time dilation. But most people didn’t even want to entertain this.

Also Dale I misunderstood your reply when I said you answered my question. I already understood what you said, hopefully the above clarifies what I was asking, seems I need to clearer.

 

[PeterDonis]

Looking at the algebra it seems to me like it boils down to whether the invariant speed limit is finite or infinite. If it’s finite, you get SR (and time dilation), and if it’s infinite you get Galileo (and no time dilation).

Yes, this is correct.

I know I’ll probably get chastised for suggesting that an infinite speed is invariant

A mathematician might want a more rigorous formulation, but most physicists are quite happy with that level of sloppiness.

I gave one where it was instantaneous, one at c (as we know it to be) and one where speed of light would be 2c.

The last two scenarios are not actually different. As @Grasshopper said, there are only two alternatives: either the invariant speed is finite or it is infinite. There is not a continuous range of models with finite invariant speed, just with the invariant speed having different numerical values. There is only a binary, discrete choice of models, finite or infinite invariant speed.

I was fearful of drawing the same conclusion as Grasshopper, because god help me if I was wrong!

And now you see the drawbacks of that approach. Instead of trying to tiptoe around the actual question you want to ask, you should just ask it directly.

Does no one here realize that the best way to learn is taking what you think you know and applying it to another scenario?

That's not what you did in your OP (see further comments below). All you did in your OP was, as you have already admitted, to not ask the question you actually wanted to ask because you were afraid of being shot down, so instead you tried to tiptoe around it, and guess what? You got shot down anyway.

The only way to do that, was to propose a hypothetical situation where light and c are different speeds and ask what the results would be on time dilation. But most people didn’t even want to entertain this.

That's because just uttering words doesn't magically define a consistent alternative model that people can reason from, and people can't "entertain" something that they can't even find a consistent meaning for. "A hypothetical situation where light and c are different speeds" is just word salad unless you have a consistent mathematical model that those words refer to. @Ibix tried to point you at one possible such model in post #2, but all you said was that that didn't answer your question.

 

[PeroK]

A mathematician might want a more rigorous formulation, but most physicists are quite happy with that level of slosloppiness.

It seems simpler to say there is no invariant speed, rather than drag infinity into it!

 

[Grasshopper]

This is exactly where I was going with my OP and trying to draw to that conclusion. I felt that it was so obvious (where I was going with it, not the conclusion) that I specifically didn't need to state it. It's exactly what I was implying when I ask if the time dilation is caused by the finite speed of light or because we are moving close to c. It's why I gave several examples of all things being equal except the speed of light. IE I gave one where it was instantaneous, one at c (as we know it to be) and one where speed of light would be 2c. In all three scenarios where the speed of light is the only thing that changes, I believe we would experience time dilation differently (none in the case of instantaneous), but not one person clarified this.

I was fearful of drawing the same conclusion as Grasshopper, because god help me if I was wrong! People love a good chiding and I wouldn’t have heard the end of it. So instead, I posed the scenarios and asked others what they would conclude, they could get chided instead lol.

But instead, everyone just wanted to point out how it can’t work with the current known laws, or how it would break SR, or it breaks something else. It really frustrates me when people do this, I mean I even stipulate my posts with “let’s say” or “imagine if” to specifically point out I am talking hypothetically so I can deepen my understanding. Instead of going with the flow so said person (me in this case) can “walk it through” so to speak and come to the realisations themselves, everyone just shoots you down right off the bat with why it wouldn’t work due said SR postulates. Does no one here realize that the best way to learn is taking what you think you know and applying it to another scenario? The whole the point of the post was to see if I was grasping parts on the subject matter – since the speed of light and c are always the same (except in rare circumstances like light going through water) I was trying give them separate values so I could “figure out” if it was the speed of light (as in the delay to reach you) or moving really fast (relative to another body) causes time dilation. The only way to do that, was to propose a hypothetical situation where light and c are different speeds and ask what the results would be on time dilation. But most people didn’t even want to entertain this.

Also Dale I misunderstood your reply when I said you answered my question. I already understood what you said, hopefully the above clarifies what I was asking, seems I need to clearer.

Well to be fair, while I appreciate the sentiment, where I was coming from was the general transformation derivation alluded to by PeroK, after making assumptions about isotropy and homogeneity space and time.

With those assumptions, you’ll end up with only three possibilities: one which doesn’t seem to make any rational sense (since it treats space and time too similarly), one that is the Galileo transformation, and one that is the Lorentz transformation.

In particular, you can follow along here:

https://www.mathpages.com/home/kmath307/kmath307.htm

In that you get to a point where a particular constant k makes all the difference, and it can have values (with a suitable conversion factor) of -1, 0 or 1. The -1 case is the one that makes no sense, because it implies we can move around through time at will like we do through space. The other two lead to the Galileo and Lorentz transformations, the former having an infinite invariant speed and the latter a finite invariant speed (if k = 0, the square root is 1, so there is no finite speed limit; while if k = 1, the limit is when v^2 approaches 1, which in these units mean v approaches the finite speed limit; because otherwise you’d have an imaginary root or divide by zero).

 

[Grasshopper]

It seems simpler to say there is no invariant speed, rather than drag infinity into it!

That’s true, but it feels to me like there’s a sense of symmetry when I think of it that way, like they are two subsets of a larger whole.

 

[mucker]

you were afraid of being shot down, so instead you tried to tiptoe around it, and guess what? You got shot down anyway.

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.

That's because just uttering words doesn't magically define a consistent alternative model that people can reason from

Maybe this is the sticking point. I don't see why it needs to be consistent for a hypothetical situation for the purpose of learning – in fact by hypothesising nonsense (so to speak) and walking through it, is where a revelation can happen for the student. I don’t see how I could have asked the question without using a hypothetical situation, are you saying I could have? If so, care to elaborate?

The last two scenarios are not actually different. As @Grasshopper said, there are only two alternatives: either the invariant speed is finite or it is infinite. There is not a continuous range of models with finite invariant speed, just with the invariant speed having different numerical values. There is only a binary, discrete choice of models, finite or infinite invariant speed.

This one might be a misunderstanding, me not being clear, or me being wrong so let me clarify one part. Maybe I shouldn’t have used relative speeds, let’s convert them to m/s to be clear about what I meant. 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. 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. With me clarifying that now, would the last two still be the same? To be clear, I am agreeing that time dilation occurs in both, I am only asking if the time dilation would be different due to the faster speed of light.

 

[PeroK]

The metre is defined in terms of the speed of light. By postulating a different speed of light all you do is redefine the metre.

In any case, physically and mathematically the two cases are identical. There's no new physics by changing the numerical calue of the speed of light.

Advanced texts on relativity tend to take the speed of light to be $1$. Which is at first sight quite simple but also quite subtle.

 

[mucker]

The metre is defined in terms of the speed of light. By postulating a different speed of light all you do is redefine the metre.

Dude sometimes i wonder if you are trolling me lol. It never used to be, and you knew what I meant!

 

[Ibix]

Dude sometimes i wonder if you are trolling me lol. It never used to be, and you knew what I meant!

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 problem with asking about counterfactual physical laws is that very often they don't make any sense, often for reasons that are quite subtle. As @PeterDonis says, there are only two types of light speed: finite and infinite, and attempting to work your way around that will just lead you down a deep rabbit hole of metrology to get to the answer Peter first stated. That's fine if that's what you want to do, but I think it's something of a tangent to what you are actually interested in.

On a meta point, I think what you are doing is rushing ahead to the fun stuff without nailing down the basics. Then you come and ask us for help when you can't follow the fun stuff and we say "you need to nail down the basics before you can understand the fun stuff". I usually draw an analogy with learning an instrument. You need to learn to read music and the boring mechanics of finger placement and all that dull stuff and you need to practice, practice, practice before you can play well.

 

[mucker]

I just think it is a bit pedantic about the metre thing. It didn't need to brought up. think it was pretty obvious what I meant even though I used a poor metric to illustrate my point. It was obvious what I was getting at is that in both examples you would flying at the same fixed speed. In any case, I am getting nowhere here. I hear your points Ibex and will take them onboard.

 

[PeroK]

I just think it is a bit pedantic about the metre thing. It didn't need to brought up. think it was pretty obvious what I meant even though I used a poor metric to illustrate my point. It was obvious what I was getting at is that in both examples you would flying at the same fixed speed. In any case, I am getting nowhere here. I hear your points Ibex and will take them onboard.

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

These are not pedantic points but core concepts in SR.

 

[Ibix]

It didn't need to brought up. think it was pretty obvious what I meant even though I used a poor metric to illustrate my point.

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.

It's extremely common for the first asking of a question not to get what you want. There's an art to asking questions in order to get useful replies and we all have to learn it. It will help if you ask a direct question and don't leave out the real question! Even if your reasoning were shaky or outright wrong somebody would have answered along with all the corrections to the reasoning. It'll also help if you try to explain why answers you get don't answer what you want to know. That back-and-forth is how we arrive at a joint understanding of what it is you need help with.

 

[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.