Time Dilation: Is This a Reasonable Explanation?

[gatztopher]

TL;DR Summary

The speed of light is always the same no matter how fast you're going, so the closer to the speed of light you get, the slower time passes for you so that light you see continues to go the speed it's supposed to.

I thought of this description recently and I think it's pretty intuitive, but I've gotten some side eye telling it to friends and family (maybe because relativity is screwy, maybe because I'm confused, maybe both?) so I want to get some confirmation that it's reasonable. Here goes:

If you're in a car and there's a car going faster than you, its speed from your point of view is its speed minus your speed. So, say, if you're going 20mph and it's going 25mph, then it looks like it's just going 5mph. The speed of light, however, looks like it's going the same speed no matter how fast you're going. So what happens if you're going the speed of light minus 5mph? Instead of light looking like it's going 5mph, the passage of time slows down for you until you see light going the speed it's supposed to. That's time dilation.

What do you all think, does this explanation track?

 

[FactChecker]

That's a good start. Remember that everything looks normal to you in every direction as though you were not moving at all. I think that you will see that an outsider, who is "not moving" is the one who thinks that your clock and processes have slowed down. Consider how your time can look slow both in the direction of your motion and in the opposite direction. I think you will see that the outsider must think that your "synchronized" (in your opinion) clocks in both directions must be set very wrong. That is the "Relativity of Simultaneity" that is at the heart of Special Relativity.

 

[phinds]

What do you all think, does this explanation track?

Not even remotely. Time does NOT slow down for you. Your clock just keeps on ticking at the same one second per second that my clock does.

 

[PeterDonis]

the closer to the speed of light you get

Unfortunately, there is no invariant that corresponds to this. You can always find a frame in which you are at rest, no matter how "close" your speed is to the speed of light in some other frame.

 

[Halc]

TL;DR Summary: The speed of light is always the same no matter how fast you're going, so the closer to the speed of light you get, the slower time passes for you so that light you see continues to go the speed it's supposed to.

But speed is relative, so relative to say some neutrino generated in the sun, you're already moving awfully close to the speed of light, and yet you notice no slower passage of time, exactly per the principle of relativity which says essentially that physics is the same relative to any inertial frame, and thus there's no way to tell which of two things is 'moving faster'.

If you're in a car and there's a car going faster than you

Again, relative to that other car, it is you going faster since it is stationary and you're not. Speed is relative, not absolute like you using it in such statements.

its speed from your point of view is its speed minus your speed.

No, it's speed from your point of view is its speed relative to you. Not minus your speed since from your PoV you're stationary.

So, say, if you're going 20mph and it's going 25mph

Relative to what? If it's the road, say that. The statement is meaningless without some kind of reference.

So what happens if you're going the speed of light minus 5mph? Instead of light looking like it's going 5mph, the passage of time slows down for you until you see light going the speed it's supposed to. That's time dilation.6

That interpretation won't work since light going in the other direction wouldn't look like it's going at c.

 

[PeroK]

If you're in a car and there's a car going faster than you, its speed from your point of view is its speed minus your speed. So, say, if you're going 20mph and it's going 25mph, then it looks like it's just going 5mph.

This is not actually true. You need the (relativistic) velocity addition rule. See below.

The speed of light, however, looks like it's going the same speed no matter how fast you're going.

That is also a consequence of the velocity addition rule.

So what happens if you're going the speed of light minus 5mph?

As others have said, there is no sense in which you can be travelling at near the speed of light in an absolute sense. Only relative to something else.

The velocity transformation rule is:
$$u' = \frac{v + u}{1 + uv/c^2}$$Where $u$ is the velocity of some object as measured by someone who is travelling at velocity $v$ relative to you. And $u'$ is the velocity of that object as measured by you.

If, now, we take that object to be light, with velocity $u = c$, then you measure the speed of that light as:
$$u' = \frac{v + c}{1 + v/c} = c$$And we see that the speed of light is an invariant for any $v$, even if $v$ is the speed of light minus 5 mph.

 

[Nugatory]

What do you all think, does this explanation track?

It really doesn’t work at all. The difficulty is that it neither predicts nor explains the symmetry of time dilation: if you are moving relative to me I will find that your clock is slow compared to my normal-running one, but you will find with equal justification that your clock is running normally while mine is the slow one.

 

[jbriggs444]

TL;DR Summary: The speed of light is always the same no matter how fast you're going, so the closer to the speed of light you get, the slower time passes for you so that light you see continues to go the speed it's supposed to.

The problem with this is that the prediction from the quoted facts is opposite from the one that you have made: Time dilation and length contraction do not cancel. They multiply. Someone looks at you and sees that your moving clock is ticking slowly. They also see that your rulers are shortened. So their naive conclusion would be that you will see light going extra extra fast. The light has extra time (per your clocks) to travel a longer distance (per your rulers).

The reason that this naive conclusion does not hold turns out to hinge on the relativity of simultaneity.

Clocks at rest and synchronized in one inertial frame show a systematic mis-synchronization in the direction of relative motion when compared against clocks at rest and synchronized in another inertial frame.

Time dilation (and, in particular, symmetric time dilation) is what you get when you pay careful attention to clock synchronization issues. It is a comparison of your elapsed proper time against my difference in coordinate times. Or vice versa.

One of us can use a single stop watch. The other one of us has to use two different clocks that are synchronized in some manner. The guy using a stop watch measures a shorter time than the guy subtracting the two clock readings.

 

[Vanadium 50]

OP, I think the lesson here is to understand the conventional explanations fowards, backwards and sideways before concocting a new one of your own. You might come up with a better one, but not until you've absolutely nailed the conventional one.

 

[gatztopher]

Alright, granted that it is a very complicated topic and it resists simplification, but I do think, for the purposes of ELI5 (literally, I’m trying to explain it to my children), it’s helpful to point to time dilation as proportional to how close to the speed of light a person is going, and a way to resolve why a person can’t see light’s speed vary relative to their own.
I guess another, more amenable way to phrase it would be:
You see a beam of light and someone going the speed of light minus 5mph. You might think, as with a car going 5mph faster than your car, that they would see light moving 5mph. Instead what you see is that time has slowed down for them so much that they will see light going the speed it’s supposed to.

Am I wrong that that’s just an accurate (and dare I say succinct) description of time dilation?

 

[phinds]

Am I wrong

Completely. You clearly are not understanding what you have been told.

 

[Mister T]

Alright, granted that it is a very complicated topic and it resists simplification, but I do think, for the purposes of ELI5 (literally, I’m trying to explain it to my children), it’s helpful to point to time dilation as proportional to how close to the speed of light a person is going, and a way to resolve why a person can’t see light’s speed vary relative to their own.

It embeds in their mind the erroneous notion that speed is absolute. It is no more correct to say that the speed of a person is close to the speed of light than it is to say that the person is at rest.

 

[Ibix]

Am I wrong that that’s just an accurate (and dare I say succinct) description of time dilation?

I would say that there are three things I would measure about a person moving fast relative to me. Their rulers are short. Their clocks tick slowly. Their clocks are not synchronised. And if I take all this into account (especially the synchronisation issue, which is one of those things that sounds like a boring technical thing but is actually a statement that people in relative motion don't agree what "now" means everywhere, which is a critical insight), then I will understand why they measure light speed relative to them to be the same as I measure relative to me. And the really critical part is to point out that it's reciprocal. They see nothing odd about their clocks and rulers, but they see your rulers short and your clocks ticking slow and out of sync. So they understand why you measure light to be travelling at the same speed relative to you as they do, and their reasons are the same as yours, not the opposite. That's why it's called relativity. Neither is wrong; both are describing someone travelling near the speed of light relative to them.

The major problem with this is that the obvious followup question is to ask what happens if you meet up again - were my clocks slow or were yours? The answer is that the above assumes inertial movement at all times, but to meet up again requires at least one of you to turn round and come back. It actually turns out that the elapsed time for a clock is a measure of the "length" of its path through spacetime, and the one who took the "shorter" path experienced less time. There's no general prescription for saying which one that will be except to crank through the relevant integral, but in the specific case that one person remains inertial at all times (never accelerates or decelerates), that one will have experienced the most time.

 

[Nugatory]

I guess another, more amenable way to phrase it would be:
You see a beam of light and someone going the speed of light minus 5mph. You might think, as with a car going 5mph faster than your car, that they would see light moving 5mph. Instead what you see is that time has slowed down for them so much that they will see light going the speed it’s supposed to.

Am I wrong that that’s just an accurate (and dare I say succinct) description of time dilation?

I don’t think that any explanation that uses the phrase “time slows down” can be accurate, even at an ELI5 level. That phase misrepresents what time dilation is and inevitably takes you to the paradox of clock A being both faster and slower than clock B.
I must confess that I’d still be very tempted to use it with a child who has just figured out how to add speeds (probably not literally a five-year-old) but I would be aware that it’s not an ELI5, it’s me being unable to say what time dilation is at an ELI5 level.

Now if I could come up with an ELI5 explanation of relativity of simultaneity…. Then I could easily explain time dilation…. And teachers of relativity everywhere would regard me as the greatest hero of all time.

 

[Peter Strohmayer]

Without appearing to be a hero in front of my five-year-old granddaughter, I would first tell her that we measure lengths and times with the spread of light.

In every clock, there is ultimately something like a small beam of light that oscillates back and forth between two mirrors.

But with light rays - I would tell her further - it is different than with balls on the schoolyard: a ball thrown "equally hard" can overtake the other one, if one ball is thrown from a moving train, but the other one from the railroad embankment.

Light beams, meanwhile, are mysterious magical creatures. They cannot overtake each other. Even if two children with skateboards pass each other and at the moment they pass each other, each emits a light beam in the same direction, the two tips of the light beams spread out next to each other without one being able to overtake the other. Both light beams then arrive at their destination (e.g. the school gate) at the same time. This is always the case, regardless of the speed at which the skateboards whiz past each other.

My granddaughter is a smart kid. She would tell me with narrowed eyes that this can't be true. It won't be easy to convince her that I'm not pulling her leg. But eventually I will succeed because I tell her that time is something that is created in our hearts and that the ray of light is a mirror of our heart.

Once my granddaughter accepts this miracle, she will have understood the mystery of time and the special theory of relativity. Because then all I have to do is tell her that the two rays of light are nothing but the clock I was talking about.

If we then ask the two children with their skateboards how much time has passed between the event of their coming past each other (the emission of the light pulses) and the arrival of the light pulses at the school gate, then the child which has gone away from the school gate with the skateboard rightly claims that its light ray propagation (=time S) would be longer than the light ray propagation (=time S') of its friend who went with her skateboard towards the school gate.

And then I would say to her: some claim that the time would pass more slowly with the one who moves. Don't believe such people: the time that passes between two events depends rather on where events take place and in which direction children are moving with their skateboard.

 

[PeroK]

Light beams, meanwhile, are mysterious magical creatures. They cannot overtake each other. Even if two children with skateboards pass each other and at the moment they pass each other, each emits a light beam in the same direction, the two tips of the light beams spread out next to each other without one being able to overtake the other. Both light beams then arrive at their destination (e.g. the school gate) at the same time. This is always the case, regardless of the speed at which the skateboards whiz past each other.

That's true of sound as well. If both children shout or blow a horn, then the sound waves will propagate through the air, independent of the motion of the source.

But, if one of the children is moving relative to the air, then the speed of sound in her reference frame will depend on her motion relative to the air.

The distinctive thing about light is that it has the same speed in all inertial reference frames. The two beams in your example have the same speed in the reference frame of both skateboarders, despite their relative motion.

 

[Peter Strohmayer]

I have told my granddaughter not about sound waves but about emitted particles ("balls") because I do not want to confuse her - as one would have done 100 years ago - also with an ether.

My granddaughter is not so much impressed by the fact that each of the light pulses in the respective reference frame is measured by the respective skateborder at the same speed - this would be the case also with the balls - but by the additional assertion that the peaks of the two light pulses propagate together, so that their respective length of propagation is different from the point of view of the two skateborderers. Balls would never be able to fly together in such a situation.

 

[PeroK]

My granddaughter is not so much impressed by the fact that each of the light pulses in the respective reference frame is measured by the respective skateborder at the same speed - this would be the case also with the balls -

This is not the case. If you are on a moving train and playing with a ball, then the ball has a low speed. But, to someone watching you from the platform or tracks, the ball has the speed of the train plus or minus the speed that you measure.

Also, with the sound waves: both skateboarders will measure the same speed of sound relative to the air. But relative to them, the sound will move at different speeds.

Your model of relativity seems to be based on having the Earth's surface as an absolute reference frame, relative to which all speeds are measured. If you consider an observer at rest relative to the Solar System, then the speed of a ball or sound wave on Earth is not just the local speed relative to Earth's surface. It will depend on the speed of the Earth relative to them. But, this observer will still the speed of light pulses to be the same universal $c$.

 

[Peter Strohmayer]

You have misunderstood me.

I said: the balls are measured in the respective reference frame by the respective skateborder with the same speed. You speak of one ball, I of two, you speak of one light pulse, I of two.

My concept of relativity is based like yours on the fact that none of the reference systems (school gate, skate S, skate S') is preferred.

 

[Peter Strohmayer]

Everyone measures only the speed of his own ball.

It would be too difficult to explain to my granddaughter how one is supposed to measure the speed of the other's ball. Why should I do that? That would only complicate the explanation. After all, she's only five.

It would be even more difficult if one should measure the velocity of a light pulse of the other, because that would amount to nothing else than measuring the velocity of one's own light beam emitted in parallel. A small child cannot understand all this.

 

[PeroK]

Everyone measures only the speed of his own ball.

That's not correct. You can measure the speed of any object. All speed is relatve, after all.

It would be too difficult to explain to my granddaughter how one is supposed to measure the speed of the other's ball. Why should I do that?

It's no different from any other speed measurement. You don't have to be in a car to measure its speed. In fact, if you are in a car, its speed relative to you is zero.

It would be even more difficult if one should measure the velocity of a light pulse of the other, because that would amount to nothing else than measuring the velocity of one's own light beam emitted in parallel.

As both light beams have the same speed, it's no more difficult to measure one than the other.

A small child cannot understand all this.

Relativity is a university undergraduate level subject.

 

[Peter Strohmayer]

I did not claim that it is not possible to measure velocities of matter points (be it the coordinate velocity or the intrinsic velocity).

Isn't it boring to share school wisdom with each other?

I would appreciate it if you could tell me if I have told my granddaughter something that is clearly wrong. After all, it is possible that I should be more careful about certain phrases.

 

[PeroK]

I would appreciate it if you could tell me if I have told my granddaughter something that is clearly wrong. After all, it is possible that I should be more careful about certain phrases.

The fundamental point is this. In classical, Newtonian physics we have absolute time and space. This leads to a simple rule for velocity transformation between inertial reference frames:
$$u' = v + u$$Where $u$ and $u'$ is the velocity of an object, as measured in two reference frames, and $v$ is the relative velocity between the reference frames. You can see from this that there cannot be an invariant speed (such as the speed of light), because the transformation rule is simple addition.

In special relativity, the first postulate is that we have an invariant speed: the speed of light in vacuum, denoted by $c$.

This is incompatible with classical notions of time and space. That is the starting point for an understanding of special relativity. But, you must transform velocities between reference frames to see this. Or, indeed, transform time and space coordinates, which is what leads to the measurement of velocity in the first place.

 

[Ibix]

Light beams, meanwhile, are mysterious magical creatures. They cannot overtake each other. Even if two children with skateboards pass each other and at the moment they pass each other, each emits a light beam in the same direction, the two tips of the light beams spread out next to each other without one being able to overtake the other. Both light beams then arrive at their destination (e.g. the school gate) at the same time. This is always the case, regardless of the speed at which the skateboards whiz past each other.

The problem is that this misses out the key property of light, which is that its speed is frame invariant. The source independence of speed, which is what you describe above, is also a property of waves in a medium - so this alone is enough to rule out a pre-relativistic ballistic model of light, but not enough to arrive at relativity.

 

[Peter Strohmayer]

Source independence and independence of a frame of reference are terms which presuppose the understanding of how we can measure velocities (and there are two kinds of "velocity").

All this is unnecessary ballast (for a child).

The decisive thing is the limitation of the maximum propagation of an effect, shown by the example that no light pulse can overtake another, the resulting different lengths of the light propagation from the view of the respective observer and thus the different temporal distances of two events for observers moving relative to each other.

Is this wrong? Have I told nonsense to my granddaughter?

 

[Ibix]

The decisive thing is the limitation of the maximum propagation of an effect, shown by the example that no light pulse can overtake another,

But no sound pulse can overtake another either, so this cannot be the decisive thing.

The key point about light speed is its frame invariance, better illustrated by cars on a two-lane road. Standing on the footpath I see cars in the inside lane passing me at 30mph and cars in the outside lane passing at 60mph. A passenger in the inside lane sees me pass her at 30mph and cars in the outside lane pass her at 30mph in the opposite direction. A passenger in the outside lane sees me pass him at 60mph and cars in the inside lane pass at 30mph. Everyone agrees that a light ray propagating along the central reservation is doing 186,000 miles per second, no exceptions, no variations.

All this is unnecessary ballast (for a child).

I don't think I'd even try to explain this to anyone who wasn't at least at secondary school level.

 

[Peter Strohmayer]

"But no sound pulse can overtake another either, so this cannot be the decisive thing."

Inconsistency: If there is an aether for sound, but none for light, the fact that (also) no sound wave can overtake another one cannot be an argument that this cannot be the decisive thing.

Why do you argue always with the aether, which is abolished since 118 years? Shall I start with the ether to my granddaughter?

 

[Ibix]

Why do you argue always with the aether, which is abolished since 118 years?

I'm just pointing out that waves in a medium behave in the way you are describing as special to light. If you want to describe the thing that's unique about light speed, which is its frame invariance, shouldn't you describe that, and not its source independence which is true of other phenomena too?

 

[Nugatory]

Relativity is a university undergraduate level subject.

The most minimal "What is relativity and time dilation about?" explanation that I can think of presupposes that we understand Galilean relativity's velocity addition rule (although we don't call it that). Then we can say that "it doesn't work for light and that messes up the way we think about time and space; if you want more you're going to have to learn more math".

OP's hypothetical five-year-old won't have the prereq, but I'd be fine trying this on a middle-schooler.

 

[Peter Strohmayer]

I have presented the circumstance that each child measures its ball or its light pulse with the same speed as the other one as truth of the example on the schoolyard.

With mass particles this would have to lead inevitably to the fact that one ball overtakes the other. (In your words: the velocity of the respective ball depends - in relativistic addition - on the reference frame in which it is measured.) Therefore, it can never be on a par with its own ball.

The miracle - for children as for grayed scientists - is that one light pulse does not overtake the other. (In your words, the "speed of light" is not dependent on the reference frame in which it is measured. The light pulses of the two children are always on a par.) Therefore, the temporal distances of the two events must differ from each other. This is the simple core of the SRT.

I've described what you're missing.

 

[PeroK]

Why do you argue always with the aether, which is abolished since 118 years?

The question is: if there is no aether, in which reference frame does light propagate at $c$? Before Einsten, no one had a satisfactory answer to this question. Because: a) everyone assumed that light needed a medium in which to propagate; b) the invariance of $c$ was impossible owing to the laws of classical physics, as outlined above.

Einstein's amazing answer to the question: "in which reference frame does light propagate at $c$?", was "in all of them!". That took incredible insight, and considerable courage to publish. Not least, because in avoiding the need for an aether, Einstein had to overturn the assumed classical nature of space and time.

 

[Vanadium 50]

OP's hypothetical five-year-

I don't think thats the OP. But my advice in #9 applies to everyone.

 

[vanhees71]

The problem is that this misses out the key property of light, which is that its speed is frame invariant. The source independence of speed, which is what you describe above, is also a property of waves in a medium - so this alone is enough to rule out a pre-relativistic ballistic model of light, but not enough to arrive at relativity.

Of course that's right only for waves with a (phase) velocity of the speed of light in a vacuum. Sound waves or em. waves in a medium also relativistically behave differently. For a treatment of the relativistic Doppler effect of sound waves and other waves with phase velocities less than the speed of light in a vacuum, see

https://itp.uni-frankfurt.de/~hees/pf-faq/rela-waves.pdf

 

[Sagittarius A-Star]

that one light pulse does not overtake the other. (In your words, the "speed of light" is not dependent on the reference frame in which it is measured.

From the first statement does not follow the second. See @Ibix's posting #28.

 

[mpresic3]

I see that Gatztopher has a degree in physics. I know from the posts that the OP has some misconceptions regarding time dilation, and although I have not read all the responses has not addressed simultaneity.

I want to say, Gatztopher, take heart, my first conceptions of Special Relativity were very different and wrong from what I know today, after a few months on study. I think I had less than a week on relativity is freshman physics, and perhaps a week more in junior level classical mechanics etc. To become better versed in SR, find a good book, and read and think about all the concepts very deliberately. This is not a field you can learn overnight.

As far as having friends and family eyes pop out, this is understandable. My coversations with friends go something like this:

Me: Suppose I am going 25 MPH and a car passes me going 30 MPH, the car passing me looks like it is going at 5 MPH. (Using your example)

Friend: What difference does it make how the car looks to you, The car is going 30 MPH.

Me: Don't you see, to me, the car is going 5 MPH.

Friend: But you are moving so you cannot be a good judge of the speed. The cop on the side of the road isn't moving. That is why he/she can come after you after he gets you on the radar. Now where should we go for pizza.
'Your friends/family most likely did not have the lectures on SR that you have had.

As far as explaining relativity to children, I do not think you should get to far in the weeds, although children will likely shut out information they are not ready for. When I was 12, I found out a mu-meson (it was called that, back then), lives longer than expected because time slows down when you are moving close to the speed of light. This is a statement of the phenomenology, without a detailed explanation. I was pretty advanced but I did not begin to understand it until I was 18 to 19.

Don't get me wrong, I think it is excellent to expose (older) children to somewhat sophisticated concepts, but consider whether they are receptive or can comprehend rather advanced explanation. For example, we may tell 12 year olds the straight line is the shortest distance between two points, or the pythagorean theorem, but we generally do not introduce
geometric proofs for those statements till much later

There is good reason, apart from teachers understanding or misunderstanding that relativity is not taught in high schools, and even some colleges and universities.