Why does time slow down as you approach C?

[Darius Macab]

I was talking with my friend and the best answer i could come up with is "It does." But, i could not explain why. Could you guys help me out?

Thanks

DM

 

[mathman]

Lorentz transformation. See section in following:

http://en.wikipedia.org/wiki/Special_relativity

 

[Isaacsname]

On a more simplistic level, you are experiencing time at your own rate. If you traveled above c ( currently thought to be impossible, sans new CERN reports in the news about neutrinos ) everything else in the universe would be standing still relative to you. Time is never truly at a fixed rate of passage for anything, it's completely dependent on your velocity relative to everything else.

At least that's how I'll look at it until shown to be incorrect.

 

[Curl]

because the speed of light could not be a constant if time was the same for everyone in all frames of reference.

but c is a constant therefore time must be different in inertial frames at different speeds.

 

[phinds]

WHOA HERE ... unless I have this totally wrong, time does NOT slow down for you when you get near the speed of light. It APPEARS to other inertial frames of reference to have slowed down but to YOU it doesn't seem to slow down at all. To you it seems like things in the OTHER frames of reference have slowed down (and of course, they would disagree).

 

[Pengwuino]

WHOA HERE ... unless I have this totally wrong, time does NOT slow down for you when you get near the speed of light. It APPEARS to other inertial frames of reference to have slowed down but to YOU it doesn't seem to slow down at all. To you it seems like things in the OTHER frames of reference have slowed down (and of course, they would disagree).

Indeed.

Also, the explanation to 'why' is pretty complicated and can't be summed up in 1 line. Experimentally it has been shown that the speed of light for any observer moving at any velocity relative to anything else will be constant.

The question relates to how one measures distance and velocities and times. For example, if an observer at rest sees a train moving 100mph to the right and another observer is driving by the train going 60mph, the person in the car will only measure the train going at 40mph. So typically, observers measure objects traveling at different speeds depending on their own velocities. Experimentally, however, it has been shown that the speed of light is measured as the same velocity for all observers, regardless of their velocity!

Since any velocity measurement is simply a change in distance during some change in time, for two observers to measure something at the same velocity yet the observers themselves are moving at different velocities during those measurements, something has to be different with how they measure time and distance. The details of that, given correctly by the Lorentz transformations, tell us that people will measure time changing differently and specifically, the observer moving relative to the guy initially at rest will experience a slower time change.

 

[YummyFur]

I was listening recently to an audio book by Brian Greene 'the fabric of the cosmos' and he used a very simple analogy concerning spacetime. If you travel north east, then it would take you longer to get to a line that was north of your starting point than if you simply traveled north, because some of the distance component has been transferred to the easterly direction.

Similarly seeing as space and time are two aspects of the one spacetime, then if you are not moving time is going as fast as it can. But once you start moving in space then the time component slows down because some of the time component of spacetime is being used up by traveling through space.

So if you travel at the speed of light then you are traveling through space as fast as you can so you are using all the time component of your spacetime motion on traveling through space. Therefore time stands still.

This is how I understood what was being said, anyway.

 

[phinds]

the observer moving relative to the guy initially at rest will experience a slower time change.

Hm ... I wonder if that's really the right way to say it. As I understand it, the guy moving will not EXPERIENCE a slower time change but he will have UNDERGONE a slower time change even though not experiencing it. I think this is more than semantic nitpicking.

The guy who travels off at 99.99% of the speed of light (forget about getting squashed by initial G force in this thought experiment) and travels in a huge arc back to the starting point will feel that he has been traveling through time at a perfectly normal rate, but when he gets back he'll see that a clock on the ground that was synchronized with his to start with is now far into the future of his clock even though he EXPERIENCED time as normal.

 

[Volkl]

Time slows down for the observers only, like when entering the event horizon of a black hole to an observer outside the object entering will appear to take forever to fall in, however if you are in the object you would pass right through it in no time at all.

 

[Pengwuino]

Hm ... I wonder if that's really the right way to say it. As I understand it, the guy moving will not EXPERIENCE a slower time change but he will have UNDERGONE a slower time change even though not experiencing it. I think this is more than semantic nitpicking.

The guy who travels off at 99.99% of the speed of light (forget about getting squashed by initial G force in this thought experiment) and travels in a huge arc back to the starting point will feel that he has been traveling through time at a perfectly normal rate, but when he gets back he'll see that a clock on the ground that was synchronized with his to start with is now far into the future of his clock even though he EXPERIENCED time as normal.

Yes that was a poor way of stating it. He will experience time like usual, but upon returning to compare, his clock will have advanced much less than the original one.

 

[feihong47]

So suppose I start a stopwatch and I start traveling at the speed of light C for 100 seconds and then returned to my original stopwatch. how many seconds will have lapsed on my stopwatch?

 

[ModusPwnd]

Depends on how close to the speed of light you go. You can't go c... But you can get closer to closer to c and as you get closer and closer you can make the stopwatch lapse as much as you want.

 

[feihong47]

well, I was wondering how you'd solve that numerically. Say I went 99% of C for 100 s, assuming C is 3x10^8 m/s. How much time would have elapsed on my stopwatch?

 

[Ignea_unda]

well, I was wondering how you'd solve that numerically. Say I went 99% of C for 100 s, assuming C is 3x10^8 m/s. How much time would have elapsed on my stopwatch?

If the stopwatch you are using to measure out that 100s is on your body when you travel that fast, 100s.

If the stopwatch is not moving at all,

\gamma = \frac{1}{\sqrt{1-\beta^2}}
with
\beta = \frac{v}{c}
and
\Delta t = \frac{\tau}{\gamma}
Hence,

t = 14.1067 s
Now, if you went 0.9999c,
t = 1.41418 s
And if you were only going 0.5c
t = 96.8246 s

So, notice that you really have to be traveling VERY close to the speed of light to see an effect.

----EDIT----

This is the time you would experience out of the stationary frame's 100s. If you want to see how long the other would experience just multiply 100s by gamma.

Secondly, I fixed my numbers, the were a bit off.

 

[Volkl]

Gravity has the same effect on time. I.e. Flying a clock in a plane can cause a difference.
Would flying around the sun at 1/2 the speed of light in a gravitational field that was immensely stronger than that on Earth cause the clock to differ in the same manner as they would if there was no gravity but you were going very close to the speed of light? I know the answer is yes, just curious if anyone knows how the gravitational effect changes the difference in the clocks in comparison to the speed concept? Then we will know which way might be achievable before the other. Or is the combo the best approach? Sending yourself into the future might be useful if you were gravely sick for instance, or just currious :)

 

[GarryS]

WHOA HERE ... unless I have this totally wrong, time does NOT slow down for you when you get near the speed of light. It APPEARS to other inertial frames of reference to have slowed down but to YOU it doesn't seem to slow down at all. To you it seems like things in the OTHER frames of reference have slowed down (and of course, they would disagree).

Then why does one person age more than the other?

 

[phinds]

Then why does one person age more than the other?

Have you read the thread? Read posts 8 & 10

 

[3nTr0pY]

I really like the 'photon clock' explanation. Imagine you have a photon clock which measures one second as the time it takes a photon to go up a distance d, bounce off a mirror and go back down a distance d. Now imagine you have this photon clock on a train moving at speed v.

Relative to you, the photon clock isn't moving, so the time it takes for the photon to go up and down is simply 2d/c, where c is the speed of light. However, I am outside of the train looking in. I see the photon moving to the side as well as up and down, because the train is moving at speed v. Since the speed of light is a constant, I measure the time for the photon to go up and down as a value greater than 2d/c because the distance traveled by the photon is further.

Thus for me, a greater time has elapsed than for you, even though we have both seen the same event occurring. And so we conclude that the faster you move, the more time slows down.

 

[ghwellsjr]

No matter how much you have accelerated in the past, you are still just as far from the speed of light as you were before you started. You will still measure the speed of light to be c just like before.

Furthermore, even though an observer you left behind sees and measures time for you to be going slower, you see and measure his time to be going slower by the same amount, even though he never accelerated. You are both in the same boat as far as "time slowing down" or as far as "approaching c" goes. To you, he appears to be the one who is traveling at some high rate of speed and therefore "approaching c" and to him, you are the one who is moving at the same high rate of speed and therefore "approaching c".

And to top it off, you don't even have to accelerate at all to have your "time slowing down" or "approaching c". All you have to do is transform a frame in which you are at rest to one in which you are "approaching c" as close as you want and in that frame your time will be slowed down as much as you want. Then, you can see what happens if you actually accelerate in the opposite direction approaching c and then, according to that frame, your time will be speeding up.

 

[akshayxyz]

Hm ... I wonder if that's really the right way to say it. As I understand it, the guy moving will not EXPERIENCE a slower time change but he will have UNDERGONE a slower time change even though not experiencing it. I think this is more than semantic nitpicking.

The guy who travels off at 99.99% of the speed of light (forget about getting squashed by initial G force in this thought experiment) and travels in a huge arc back to the starting point will feel that he has been traveling through time at a perfectly normal rate, but when he gets back he'll see that a clock on the ground that was synchronized with his to start with is now far into the future of his clock even though he EXPERIENCED time as normal.

Hi,
I am out of touch in physics for more than a decade, so please excuse my obsolete and corrupt memory/understanding of the concepts...

As per my understanding velocity is a vector quantity, and if the traveler indeed comes back to the starting point - while travelling in the arc - the velocity vector relative to the stationary clock will not always be 0.9999c, half of the journey time should dilate, and the other half, it would be other wise... so when he does comes back and stops, there should not be any time difference.


The time dilation effect should come into picture, when the person traveling at 99.99%c, tries to read the stationary clock - since that information from stationary clock can at best be sent at c... so the 1 second ticks sent by stationary clock to the person traveling at 99.99% c, will not be 1 second ticks read as per the clock with the traveling man... and vice versa ( if the stationary person tries to read the clock traveling at 99.99%c)


So, if the traveller continue traveling at 99.99%c, in the direction away from the stationary clock - the time ticks sent by stationary clock when read on traveller's clock will appear dilated - relatively.


However, I am not sure what happens, when the traveller takes a U-turn and approaches the stationary clock... and if it must come to rest to read the clock, there would be a process of deceleration also - and it would no more be non-accelerating frames of observation...the traveller must read the stationary clock, while maintaining the constant speed.

 

[ghwellsjr]

Hi,
I am out of touch in physics for more than a decade, so please excuse my obsolete and corrupt memory/understanding of the concepts...

As per my understanding velocity is a vector quantity, and if the traveler indeed comes back to the starting point - while travelling in the arc - the velocity vector relative to the stationary clock will not always be 0.9999c, half of the journey time should dilate, and the other half, it would be other wise... so when he does comes back and stops, there should not be any time difference.

No, it doesn't matter his direction, his speed is what counts relative to some frame, in this case the stationary clock. So the traveling clock always experiences the same time dilation throughout the entire journey.

The time dilation effect should come into picture, when the person traveling at 99.99%c, tries to read the stationary clock - since that information from stationary clock can at best be sent at c... so the 1 second ticks sent by stationary clock to the person traveling at 99.99% c, will not be 1 second ticks read as per the clock with the traveling man... and vice versa ( if the stationary person tries to read the clock traveling at 99.99%c)

You are correct, each observer will read the other one's clock as ticking slower by exactly the same amount but here we are not talking about time dilation, we are talking about Relativistic Doppler which is what each observer actually sees of the other one's clock. The amount of slowdown that they see is not the amount of time dilation.

So, if the traveller continue traveling at 99.99%c, in the direction away from the stationary clock - the time ticks sent by stationary clock when read on traveller's clock will appear dilated - relatively.


However, I am not sure what happens, when the traveller takes a U-turn and approaches the stationary clock... and if it must come to rest to read the clock, there would be a process of deceleration also - and it would no more be non-accelerating frames of observation...the traveller must read the stationary clock, while maintaining the constant speed.

What happens when the traveler makes the U-turn, is that he immediately sees the stationary clock speed up. This the Relativistic Doppler in the other direction, exactly the inverse factor, but time dilation is still going on.

The stationary observer does not see this happen in the traveler's clock until a long time later. It is this imbalance in the times that each one sees of the other's clock running slow then fast that accounts for the difference in the clocks elapsed time when they rejoin.

 

[ThomasT]

Then why does one person age more than the other?

Because the frequency of an oscillator is directly related to the speed at which the oscillator is moving. This includes the atoms that constitute the biological oscillators of an organism. So, the faster you move, the less you age.

While the mainstream geometrical interpretation (Minkowski) of SR is quantitatively correct, there's no detailed mechanistic understanding of differential aging yet -- though the quantitatively equivalent Lorentz ether theory is a step in that direction.

As others have noted, nobody will feel like they're aging any differently as their speed increases or decreases, and their own clocks won't appear to them to be slowing down or speeding up. But they will feel something if their speed increases or decreases, and it's during these intervals of changing speeds that the changes in biological oscillators, as well as the, say, crystal oscillator that's the basis of a reference clock, are occurring.

But this shouldn't be confused with what's actually determining the accumulated difference in age between, say, a person at rest on Earth and a person moving at an average of, say, .5 c in a spaceship. This accumulated difference is solely determined by the duration of intervals wrt which there are differences in speed between the two.

 

[Naty1]

While the mainstream geometrical interpretation (Minkowski) of SR is quantitatively correct, there's no detailed mechanistic understanding of differential aging yet -- though the quantitatively equivalent Lorentz ether theory is a step in that direction.

That's what I was thinking as I read the posts above...nothing wrong with the above explanations as ways of thinking about it. I like Brian Greene's explanation and have used it myself, but nobody really knows WHY the speed of light is constant while distance and time vary among inertial frames.

It's akin to asking WHY the electron has the mass...or the charge... it does...or why we have the four fundamental forces we observe...we know they are there but not WHY.

good discusssion overall.

 

[ghwellsjr]

Then why does one person age more than the other?

Because the frequency of an oscillator is directly related to the speed at which the oscillator is moving. This includes the atoms that constitute the biological oscillators of an organism. So, the faster you move, the less you age.

While the mainstream geometrical interpretation (Minkowski) of SR is quantitatively correct, there's no detailed mechanistic understanding of differential aging yet -- though the quantitatively equivalent Lorentz ether theory is a step in that direction.

As others have noted, nobody will feel like they're aging any differently as their speed increases or decreases, and their own clocks won't appear to them to be slowing down or speeding up. But they will feel something if their speed increases or decreases, and it's during these intervals of changing speeds that the changes in biological oscillators, as well as the, say, crystal oscillator that's the basis of a reference clock, are occurring.

But this shouldn't be confused with what's actually determining the accumulated difference in age between, say, a person at rest on Earth and a person moving at an average of, say, .5 c in a spaceship. This accumulated difference is solely determined by the duration of intervals wrt which there are differences in speed between the two.

So you're saying that the person that accelerated to 0.5c is accumulating less age than the person at rest because of the time duration that he spends at that speed? And this is better explained by LET than SR? And that if he increases his speed, his clock slows down and if he decreases his speed, his clock speeds up? It sure sounds like you are promoting an absolute state of rest. Can you explain further, because I'm afraid that Garry will get a wrong impression?

 

[ThomasT]

So you're saying that the person that accelerated to 0.5c is accumulating less age than the person at rest because of the time duration that he spends at that speed?

The difference in time (or age) that the (earthbound and travelling) biological oscillators accumulate during an interval is due to their difference in speed during that interval. A traveller moving at an average of, say, .5c for a roundtrip interval of, say, 30 years (earth time) will have aged noticeably less than the earthbound person (by an amount given by the Lorentz transformation).

And that if he increases his speed, his clock slows down and if he decreases his speed, his clock speeds up?

Yes.

And this is better explained by LET than SR?

Not necessarily. They're quantitatively equivalent. But to even begin to have a mechanistic understanding of why an oscillator's frequency decreases as the oscillator's speed increases, and vice versa, then you'd have to have the oscillator interacting with something.

As I mentioned, LET is a step in that direction. But it's certainly not a detailed account of what's happening with oscillator's as they move about. And SR is even less detailed in that regard.

It sure sounds like you are promoting an absolute state of rest.

I don't know what that might refer to. Relativity says that the laws of physics don't depend on states of motion, and, so far, that seems to be the case.

I do think that we can reasonably infer the existence of a wave/particle reality underlying our observations, and that while SR obviates that view it certainly doesn't rule it out.

Can you explain further, because I'm afraid that Garry will get a wrong impression?

What I suggested is that the frequency of an oscillator is directly related to the speed at which the oscillator is moving, and that there's currently no detailed mechanical explanation of how a change in the speed of an oscillator produces a change in the frequency of the oscillator.

What other impression might he get from anything I've said?

 

[ghwellsjr]

What other impression might he get from anything I've said?

His specific question was prompted by the statement that time dilation is reciprocal.

WHOA HERE ... unless I have this totally wrong, time does NOT slow down for you when you get near the speed of light. It APPEARS to other inertial frames of reference to have slowed down but to YOU it doesn't seem to slow down at all. To you it seems like things in the OTHER frames of reference have slowed down (and of course, they would disagree).

Then why does one person age more than the other?

Your posts state that it all is a result of one person having a speed while the other one is at rest. You seem to be stating the opposite of what phinds was saying. Can't you incorporate the reciprocal nature of time dilation into your discussion and explain why the "person at rest on earth" could be the one with the slowed down "biological oscillators" just as validly as the person moving at 0.5c in a spaceship?

 

[akshayxyz]

@ghwellsjr
thanks for the response.

I still have doubts about the 'twin paradox'.
Lets take the example of stationary A and moving B (lets say at .9999c).
As you also agreed - "You are correct, each observer will read the other one's clock as ticking slower by exactly the same amount".

Lets say at some instant B sends message/tick to A, that he is 10 y/o as per B's clock. A would get this message let's say when A is 20 y/o (as per A's clock). and vice-versa.

Now at that instant (when at receives that message), would B also not have aged to 20? Even though A would not know about it.
So, essentially both should age at same rate (from neutral perspective), and it should just be the time gap in knowledge of their ages with each other.

 

[ThomasT]

Thanks for the feedback ghwellsjr. You and DaleSpam (primarily, but many others also) are helping me to learn how to think and talk about this stuff. I've gone from believing that differential aging is just a matter of 'perspective' (don't ask what I was thinking at the time), to understanding it as a well supported physical fact of nature, to incorrectly stating the role that acceleration plays, to hopefully refining my understanding (and any statements) regarding that, and any inferences that might follow from that.

Now to the comments:

His specific question was prompted by the statement that time dilation is reciprocal.

Ok, but his question was about differential aging not time dilation. Time dilation is symmetric, and is due to the SR conventions applied by observers in relative motion wrt each other in a relativistic universe (ie., apparently our universe, wherein the speed of light is constant and the same for all observers regardless of their state of motion).

On the other hand, differential aging is asymmetric, and is due to the real physical effects undergone by an oscillator as a function of its speed.

Your posts state that it all is a result of one person having a speed while the other one is at rest.

That's just one scenario, that is, where one person and his clock move about at relativistic speeds wrt the Earth while the other person and his clock remain at rest wrt the earth.

You seem to be stating the opposite of what phinds was saying.

phinds said (I'm paraphrasing) that each observer would see the other's clock as slowing down, and that each observer would see his own clock as not slowing down. And I said that, "As others have noted, nobody will feel like they're aging any differently as their speed increases or decreases, and their own clocks won't appear to them to be slowing down or speeding up". Which doesn't contradict what phinds said.

Can't you incorporate the reciprocal nature of time dilation into your discussion and explain why the "person at rest on earth" could be the one with the slowed down "biological oscillators" just as validly as the person moving at 0.5c in a spaceship?

No, because SR predicts, and analogous experiments support the expectation, that the person moving at 0.5c in a spaceship would be the one who actually aged less, and with that the inference that the traveller's biological and reference clock oscillators' periods actually physically dilated.

 

[ghwellsjr]

@ghwellsjr
thanks for the response.

I still have doubts about the 'twin paradox'.
Lets take the example of stationary A and moving B (lets say at .9999c).
As you also agreed - "You are correct, each observer will read the other one's clock as ticking slower by exactly the same amount".

Lets say at some instant B sends message/tick to A, that he is 10 y/o as per B's clock. A would get this message let's say when A is 20 y/o (as per A's clock). and vice-versa.

Now at that instant (when at receives that message), would B also not have aged to 20? Even though A would not know about it.
So, essentially both should age at same rate (from neutral perspective), and it should just be the time gap in knowledge of their ages with each other.

You can say precisely what each twin will see of the other one's clock, but there is no neutral perspective from which you can identify an instant that applies to both of them.

 

[ThomasT]

I still have doubts about the 'twin paradox'.
Lets take the example of stationary A and moving B (lets say at .9999c).

Lets say at some instant B sends message/tick to A, that he is 10 y/o as per B's clock. A would get this message let's say when A is 20 y/o (as per A's clock). and vice-versa.

Now at that instant (when at receives that message), would B also not have aged to 20?

You specified that A is stationary and B is moving at .9999c, which means that B is aging and his clock is accumulating time slower than A by a factor of 70.7.

So, essentially both should age at same rate (from neutral perspective) ...

By "neutral perspective" I assume you mean some common referent. Like say A is on Earth, so he's stationary wrt the Earth, and B is moving at .9999c wrt A and the Earth. Ok, so when the Earth-Sun system marks 10 years, then A will have aged 10 years and A's clock will have accumulated 10 years, but B will have aged (and B's clock will have accumulated) only about 51 days and 15 hours.

Also, what ghwellsjr and other commenters more knowledgeable than I am have said. I don't think I've contradicted any of that. I wanted to respond to your post because I too had doubts about the reality of differential aging. But the preponderance of experimental evidence supporting it is pretty convincing ... strange as it might seem, at first anyway. And differential aging actually becomes sort of inuitive when you consider that what seems like empty space interspersed with ponderable objects is actually a seamless hotbed of all sorts of underlying interactional activity. So the periods of atomic oscillators are physically related to their speed of movement, and changes in their frequencies are due to accelerations involving changes in speed. Still something of a mystery as to exactly how that works, but not really strange or weird.