Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Des on 09/05/2011 02:30:06
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Des asked the Naked Scientists:
Hi there,
this may be well off the mark, but, is the reason why time slows down more and more as you travel closer to the speed of light because time and space are part of each other ie "spacetime".Â
Space is expanding and therefore as you travel faster you are catching up with that expansion and time itself. And so time travels more slowly as you catch up to it?
Kind regards
Des Enright
What do you think?
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You're right in that they are intimately connected.
Think of two mirrors at rest relative yourself, then let a light-corn bounce between them. As it does you will find the path that light-corn to take being a straight path, back and forth, a little like a pendulum.
Now let the mirrors move with you staying at earth, it won't matter if you look at them while accelerating, or after as they start to 'coast' in space. From your point of view the light-corn suddenly will move slower, due to you finding that light-corn having a longer path between the mirrors, that as it has to traverse more 'space' as the mirrors it bounce between constantly moves away from you. Also you will find the path it takes to be a diagonal one as it 'tags' after the mirrors in a zigzag motion relative you, being still.
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You being still falls under SR but the mirror when accelerating falls under GR,and so as a 'system' you both belong to GR there. After the acceleration when it just 'coasts' you will both belong to SR.
Now imagine that you would move with those mirrors, being 'at rest' with them.
First of all, when will you be able to prove that you are moving?
The acceleration right?
How do you think that light-corn will behave then? Will it start to zigzag? According to you, being 'at rest' with the mirrors :) That just means that you and the mirrors now are traveling together, being still relative each other.
Contrast that to when you've stopped accelerating, instead uniformly moving (coasting).
Do you expect to see the light-corn zigzag? You still being at rest relative the mirrors?
Do you think there is a difference between the acceleration and later uniform motion?
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And as a over course.
For the last one, imagine each scenario of the two above. Accelerating and uniformly moving. The only difference being that you now are enclosed inside a very large black box. It's really, really black in there as the engineers forgot all about the windows. Will the lightcorn behave differently?
So, in which scenario are you able to say that you are 'moving' inside that black box.
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When you've done those, you will know what I think I know :)
And you're right, the mirrors becomes the light clock. And 'space' is a geometry that is intimately connected to 'time' expressed in 'gravity'. Gravity is what bends, distort and 'deform' space. And there is nowhere I know that you will find a 'space' without gravity. Even where you can't measure it, as in a free fall, it is still there. It's just you coming to be 'at rest' momentarily relative it.
So SpaceTime, not Space & Time.
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The important thing always to remember is that time only flows more slowly for outside observers observing you. You would not notice any difference in the flow of time around you in things moving with you, although you would see big changes in the layout, appearance and behaviour of distant objects.
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As you approach the speed of light it requires more and more energy to carry on accelerating up to the speed of light. More energy is equivalent to more mass. More mass is equivalent to a slower passage of time (gravitational time dilation).
The speed of light is a constant.
Speed is distance divided by time.
Therefore, either distance has to shrink or the passage of time has to contract to maintain that constant.
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As you approach the speed of light it requires more and more energy to carry on accelerating up to the speed of light. More energy is equivalent to more mass. More mass is equivalent to a slower passage of time (gravitational time dilation).
That isn't true. The kind of mass you gain by moving fast isn't the same as gravitational mass. There are two kinds of mass used in relativity, and you're confusing relativistic mass (which goes up when you move fast) with rest mass (which doesn't).
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Is speed related to mass? If so much energy is required to move at the speed of light that it can't be done, then how does light do it?
And we know light does do exactly that, it travels at the speed of light, so what energy causes the light to travel at such high speed?
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You have three questions there:
Is speed related to mass?
There are two kinds of mass in special relativity: relativistic mass and invariant mass. Invariant mass is the more useful quantity for figuring out gravitational force, etc. Relativistic mass is only useful because it makes E=mc2 hold. If you use invariant mass, you need to fix up the formula to read:
E2=m02c4+p2c2,
where that m0 is rest mass.
If so much energy is required to move at the speed of light that it can't be done, then how does light do it?
Only objects with zero rest mass can move at the speed of light. However, those objects are always moving at the speed of light, no matter what. Light doesn't need to speed up, since it is never moving (in a vacuum) at any speed other than the speed of light.
And we know light does do exactly that, it travels at the speed of light, so what energy causes the light to travel at such high speed?
That seems to be one of the fundamental properties of the universe. Maybe some future theory will come along and answer why light speed is the limit and why massless things move at that speed, but for now it's just an assumption in relativity that happens to match very well with what we see experimentally.
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As you approach the speed of light it requires more and more energy to carry on accelerating up to the speed of light. More energy is equivalent to more mass. More mass is equivalent to a slower passage of time (gravitational time dilation).
That isn't true. The kind of mass you gain by moving fast isn't the same as gravitational mass. There are two kinds of mass used in relativity, and you're confusing relativistic mass (which goes up when you move fast) with rest mass (which doesn't).
I do understand the difference in rest mass and relativistic mass but what specifically isn't true?
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More mass is equivalent to a slower passage of time (gravitational time dilation).
Which type of mass are you talking about here?
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More mass is equivalent to a slower passage of time (gravitational time dilation).
Which type of mass are you talking about here?
Relativistic mass
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More mass is equivalent to a slower passage of time (gravitational time dilation).
Which type of mass are you talking about here?
Relativistic mass
That's the problem. Relativistic mass is not equivalent to gravitational time dilation. Invariant mass does.
If your mass is moving and you want to compute it's effect on space-time, you need to use the stress-energy tensor, which accounts for the energy and momentum of motion. This is definitely not the relativistic mass either.
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More mass is equivalent to a slower passage of time (gravitational time dilation).
Which type of mass are you talking about here?
Relativistic mass
That's the problem. Relativistic mass is not equivalent to gravitational time dilation. Invariant mass does.
If your mass is moving and you want to compute it's effect on space-time, you need to use the stress-energy tensor, which accounts for the energy and momentum of motion. This is definitely not the relativistic mass either.
What does cause the passage of time to dilate when travelling at near to the speed of light?
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It's a consequence of special relativity: that everyone in an inertial reference frame measures the speed of light to be constant.
Also, it's important to remember that time dilation is only apparent when two observers in different reference frames compare clocks. If I'm traveling near the speed of light, I don't notice anything funny happening on board my spaceship, since it's all in the same reference frame as me so all the clocks run the same as mine.
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There is a direct correlation between time dilation and relativistic mass, they both have the same relativistic dilation for any unique observer.
That being said, there is a corresponding length contraction or space contraction. If you look at matter's wave counterpart, space contraction corresponds to relativistic frequency red (or blue) shift (only the relativistic part)...
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More mass is equivalent to a slower passage of time (gravitational time dilation).
Which type of mass are you talking about here?
Relativistic mass
That's the problem. Relativistic mass is not equivalent to gravitational time dilation. Invariant mass does.
If your mass is moving and you want to compute it's effect on space-time, you need to use the stress-energy tensor, which accounts for the energy and momentum of motion. This is definitely not the relativistic mass either.
What does cause the passage of time to dilate when travelling at near to the speed of light?
The relativity denies an ether, therefore only field communication can slow down time.
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It's a consequence of special relativity: that everyone in an inertial reference frame measures the speed of light to be constant.
Also, it's important to remember that time dilation is only apparent when two observers in different reference frames compare clocks. If I'm traveling near the speed of light, I don't notice anything funny happening on board my spaceship, since it's all in the same reference frame as me so all the clocks run the same as mine.
Does the speed of the passage of time in the spacecraft actually slow down or not? From the crews point of view it obviously would not. They are part of that frame of reference and wouldn't notice anything amiss, even if the spaceship accelerated up to the speed of light, in which case they would be frozen in time. So can we actually say that mass travelling at the speed of light experiences the passage of time?
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They are part of that frame of reference and wouldn't notice anything amiss, even if the spaceship accelerated up to the speed of light, in which case they would be frozen in time. So can we actually say that mass travelling at the speed of light experiences the passage of time?
Mass can't move at the speed of light, so that question can't be answered. Trying to answer it by plugging v=c into the Lorentz factor leads to nonsensical results because the entire theory was derived under the assumption that the case where v=c cannot be handled for objects with mass.
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There is a direct correlation between time dilation and relativistic mass, they both have the same relativistic dilation for any unique observer.
Energy and time transform in similar ways when you change inertial reference frames. Relativistic mass is just a fancy word for energy. The factor you're talking about is hardly unique to energy and time, since it's part of the equations that define how space and time transform. Any quantities which live in space and time are going to transform in ways where that same factor shows up. It's called the Lorentz factor.
http://en.wikipedia.org/wiki/Lorentz_factor
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yes, but it is not so fancy if you believe in Einstein's Equivalence Principle.
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They are part of that frame of reference and wouldn't notice anything amiss, even if the spaceship accelerated up to the speed of light, in which case they would be frozen in time. So can we actually say that mass travelling at the speed of light experiences the passage of time?
Mass can't move at the speed of light, so that question can't be answered. Trying to answer it by plugging v=c into the Lorentz factor leads to nonsensical results because the entire theory was derived under the assumption that the case where v=c cannot be handled for objects with mass.
I was simply continuing the example you gave. The trend being nothing that travels at the speed of light experiences any passage of time.
yes, but it is not so fancy if you believe in Einstein's Equivalence Principle.
At last.
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They are part of that frame of reference and wouldn't notice anything amiss, even if the spaceship accelerated up to the speed of light, in which case they would be frozen in time. So can we actually say that mass travelling at the speed of light experiences the passage of time?
Mass can't move at the speed of light, so that question can't be answered. Trying to answer it by plugging v=c into the Lorentz factor leads to nonsensical results because the entire theory was derived under the assumption that the case where v=c cannot be handled for objects with mass.
I was simply continuing the example you gave. The trend being nothing that travels at the speed of light experiences any passage of time.
I never said that. In fact, I've told you a few times that you can't apply special relativity to v=c. In fact, one of those places was right here:
http://www.thenakedscientists.com/forum/index.php?topic=39022.msg354305#msg354305
yes, but it is not so fancy if you believe in Einstein's Equivalence Principle.
At last.
Can you explain what you mean by this? If you're invoking the equivalence principle of general relativity on top of special relativity, you now have 4 masses in play: inertial mass, gravitational mass, relativistic mass and rest mass. And relativistic mass still isn't equivalent to inertial or gravitational mass.
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There is also a fairly simple thought experiment that shows that relativistic mass is not the mass you want to think about as causing gravity. Say I have a rocket ship traveling by the earth incredibly fast. An observer on the earth will calculate the rocket ship's relativistic mass and say, "Wow! That has so much mass it will have to become a black hole!" The observer on the ship, of course, sees his mass as the rest mass and doesn't turn into a black hole.
It would be somewhat absurd for this ship to be a black hole and not a black hole at the same time.
The resolution is that you can't just plug relativistic mass (or invariant mass, for that matter) into the equations of general relativity by itself. You need to actually use the entire stress-energy tensor which has 16 terms to it, specifying the energy, momentum as well as flow of energy and momentum in space and time.
The only time where you can just plug in mass and nothing else is when things are perfectly stationary. And of course in this case, relativistic and rest mass agree.
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And relativistic mass still isn't equivalent to inertial or gravitational mass.
Yes it is JP, I have read an article of a physicist working at CERN explaining that the relativistic mass of 2 protons colliding in the LHC have each a maximum of about 7500*m0 (m0 being the proton's rest mass). The total energy produced by the collision is 15000*m0. He said that they never observed any discrepancy between relativistic mass, inertial mass and gravitational mass. He was answering to the question of the difference between gravitational mass and relativistic mass. Each proton is perceiving the other proton's mass increase as a true mass and they are much smaller in size, which makes the collisions more difficult to obtain.
E = (m0^2*c^4+p^2*c^2)^1/2 = m*c^2 where m is the relativistic mass.
If i find the article, i will post it.
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You better do that CPT :)
As far as I know the difference between relativistic mass and invariant (matter) is that both equivalently are able to translate into 'Energy' but only the invariant mass will be there in any experiment measuring the mass in that 'frame of reference'. That is, for example, you being at rest versus whatever you want to measure a mass from/on.
Relativistic mass is 'real' in the same manner as 'potential energy' is real. What that means is that you by choosing your possible frame of 'interaction' aka a collision will get different results on what this relativistic mass or potential energy is.
A simple proof of that is all 'uniform motion' where, according to the equivalence principle, it won't matter what you expect your 'speed' to be (relative some origin, for example Earth). You won't be able to define that speed in a black box scenario from any experiments and so you will be able to define your speed from zero to any value relative what you measure against.
With no possibility to define a speed your relativistic mass also will be questionable. What's not expected to be questionable though is that invariant mass, expected to be the same in any frame thought up.
Relativistic mass and potential energy are both definition using comparisons between 'frames of reference' and as you can have several different frames simultaneously to compare between, like several spacecrafts at 'different accelerations (as well as uniformly moving) you will find yourself to have a different potential energy. As for your relativistic mass it is in fact so that you either will measure it against some frame of origin, or possibly CBM or blue shift and from there calculate a possible 'interaction' with the energy released in a collision. But, as far as I know, it will not be present in the atoms 'jiggling' in those ships moving relative some frame of definition.
What you seem to state there is that there is?
Show the proofs, I'm interested :)
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my point of view is the same as yours, i don't understand what you mean. Invariant mass is rest mass, inertial mass and gravitational mass are relativistic mass and are frame dependent, obviously. Gravitational mass is often wrongly associated to invariant mass but they are not the same in GR.
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It's that citation you used actually, I presumed it was your point of view too?
"(?)He said that they never observed any discrepancy between relativistic mass, inertial mass and gravitational mass(?) He was answering to the question of the difference between gravitational mass and relativistic mass. (ahh?)... Each proton is perceiving the other proton's mass increase as a true mass and they are much smaller in size..
The only way I can make sense of such a statement should be in its 'interaction', measuring the 'energy' released. If it is meant as a proof of 'relativistic mass', and so the protons 'potential energy' to be one and the same at all times, they will need to prove it to be so without comparing versus 'interactions', as different 'interactions' will give you different answers. And so it comes back to being 'at rest' versus what you measure the 'relativistic energy' 'Potential energy', etc, against.
And there you only will find the invariant mass, as I see it, discussing uniform motion. The problem here is acceleration, it depends on how you look at that. Is a acceleration a definition of something that never begets 'instants' of uniform motion, or is it a 'jumping' from state to state?
In the first definition you have acceleration as something differing from the idea of QM where everything in some manner needs to be 'quanta', a discrepancy that here translates into motion as a 'smooth phenomena' not fitting QM. In the other definition you will find that you suddenly can translate any acceleration to something similar to 'the photoelectric effect' and 'black body radiation', meaning that all accelerations are equivalent to a infinite (? not really as we have 'c' but?) amount of 'uniform motions' jumping from one state to another as defined by our arrow of time.
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First, you have to accept that the relativistic mass is inertial mass and the proof of that is in all particles accelerators. Then, you have to accept the Equivalence Principle that says that Gravitational mass and Inertial mass are the same. At collision time, the 7500m0 for each proton is for the lab's observer frame, the 15000m0 is for 1 proton viewed from the other. Any measurement made within any unique inertial frame cannot differentiate relativistic, inertial and gravitational mass... That is the Equivalence Principle. We must agree on definitions first. We will all agree about that :)... You can only measure by interacting...
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"the Equivalence Principle that says that Gravitational mass and Inertial mass are the same."
I don't dispute that gravity act as an acceleration? After all that is the essence of the Equivalence principle when it comes to accelerations and gravity. But where exactly did he state that relativistic mass is invariant?
As I remember it he never liked the idea of 'relativistic mass' himself? As for what made sense to me in that experiment, it was, as I said if you try to read it, that it had to be the 'measurements' aka interactions. And also that it was this way of defining relativistic mass as 'really, really, there' that sounded wrong to my ears. The fact is that for you to measure any existing real effects on a object moving, as defined against any other frame of reference, you will have to be 'at rest' with it. And there you will find no 'extra energy' in that moving object, no matter its velocity. That means that no 'atoms' in it will 'jiggle' due to its motion.
And that's why the definition of invariant mass makes a better sense to me.
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Assuming moving in a vacuum, classically defined as having no resistance, creating no 'friction'. When it comes to accelerating, creating a gravity, the definition of a friction less vacuum becomes slightly weird, but as I see it, having to do with the room time getting 'compressed'.
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Ask yourself, if a Lorentz contraction is real, is that equal to a compression?
If so, shouldn't the atoms in the Lorentz contracted ship heat up as they are compressed in the axis of the motion? And If you think that this is possible, how about the rest of the Lorentz contracted universe then? As seen from the ship? Also 'heated up'?
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Relativistic mass is not invariant, nor inertial mass or gravitational mass. Only rest mass is invariant. We don't have the same definitions...
For a proton having a relativistic mass of 7500m0 in the accelerator frame (corresponding to a fixed speed), the accelerator pushing the proton will perceived the proton as having an inertial mass of 7500m0.
Yes, i agree that invariant mass is more fundamental. If all matter is made of light, then relative movement of matter imply Relativity... :o)
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Ok, here's the points I've been trying to make in perhaps a simpler form:
1) If gravity is fully determined by mass alone, then you have to be in a reference frame where the mass is stationary. In this case, the rest mass and relativistic mass are equal.
2) If your mass is moving, you cannot compute the gravitational curvature of space-time from mass alone--neither relativistic mass nor rest mass tells the whole story. In this case, you need to compute the stress-energy tensor, which has 16 components (10 of which are unique). You need to obviously know a lot more than just a single number for mass to compute the gravitational field here.
My original point was to argue against MikeS's claim that higher relativistic mass equals more time dilation, since things aren't so simple as that. If you believe that relativistic mass alone is enough to determine the gravitational effects, then you believe that fast moving particles spontaneously form black holes for some observers and not others--which is false.
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Yeah JP, I was wondering when we would introduce the stress energy tensor :) That one is about the room time geometry to me and as such perfectly reasonable, then again, I'm slightly weird :)
You're perfectly correct.
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CPT, you have a point in that it will take more energy the faster something moves, and if you like you can translate that energy drain into moving a greater (invariant) mass at a slower velocity, begetting the same numbers. It's a equivalence of sorts I agree, but it's you pushing, or dragging, that object expending energy in a accelerator. In itself it does not change any invariant mass, at least not due to any motion in a perfect vacuum.
The reason I think so is that all particles accelerated in a vacuum otherwise, at some state as I see it,should start to glow, melt into some weird plasma, whatever :) And as they don't?
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It's not really such a great analogue thinking of it again as those particles constantly are interacting with a electromagnetic field, getting up to speed. But I still think I'm right there.
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The point I was getting around to making has since been covered but I will mention it anyway. As I see it there is only energy and mass in the universe. One kind of energy can be converted into another so from the point of view of E=mc2 only energy needs to de considered. Likewise with mass, there is rest mass and all of the other kinds. But the other kinds are simply rest mass plus energy of one kind or another. Even rest mass has gravitational (kinetic) energy. So from E=mc2 we only need to consider energy and mass.
JP
Going back to the space-ship.
As it accelerates up to the speed of light it experiences no passage of time and its length has diminished to zero (?). It would seem that the space-ship has possibly lost two of the four dimensions of space time. If this were the case then its mass would only have to compress two spacial dimensions out of existence to become a singularity not the usual four of space time. Just a thought.
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JP
Going back to the space-ship.
As it accelerates up to the speed of light it experiences no passage of time and its length has diminished to zero (?). It would seem that the space-ship has possibly lost two of the four dimensions of space time. If this were the case then its mass would only have to compress two spacial dimensions out of existence to become a singularity not the usual four of space time. Just a thought.
Fortunately it can't reach light speed, so we don't have to worry about it becoming a singularity in any dimensions.
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Think of two mirrors at rest relative yourself, then let a light-corn bounce between them. As it does you will find the path that light-corn to take being a straight path, back and forth, a little like a pendulum.
Now let the mirrors move with you staying at earth, it won't matter if you look at them while accelerating, or after as they start to 'coast' in space. From your point of view the light-corn suddenly will move slower, due to you finding that light-corn having a longer path between the mirrors, that as it has to traverse more 'space' as the mirrors it bounce between constantly moves away from you. Also you will find the path it takes to be a diagonal one as it 'tags' after the mirrors in a zigzag motion relative you, being still.
First of all, what is a "light-corn"?
Now, even though I see the light moving diagonally, thus farther, I would also the the overall movement of the mirrors. That movement would have to be added to the movement across (from mirror to mirror), and would fully explain how a longer diagonal distance could be traversed in the SAME amount of time. So, why would there be any need for time dilation?
Imagine two children tossing a ball back and forth in a car. If the car begins to move, the ball will have to travel a longer distance, even much longer since the car will be moving quite fast compared to the side to side velocity of the ball. If I only took into consideration the distance the ball was traveling diagonally, I would have to experience an immense amount of time dilation. Of course, that is not the case at all because I would also have to take into account the forward speed of the car that would be added to the speed of the ball which would fully account for why the ball can travel a long diagonal distance in the same time as the short distance it traveled while the car was stationary. So, no time dilation. So, I'm still confused. Why does time slow down with relative speed.
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Why does time slow down with relative speed.
My understanding is that in the case of the ball in the car; when the car is moving an outside observer would measure the speed of the ball to be greater because of the addition of speeds.
On the other hand an outside observer would measure the speed of light as being the same when the mirrors were moving as when they were stationary. Thus the situation is quite different.
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The answer isn't that straightforward. First you have to accept the validity of 'frames of reference', being comparisons between different points in space and time. Then you have to accept the idea of all inertially moving observers being equivalent. Then you have to introduce a absolute frame of reference, relative all those 'inertial observers' (uniform motion, or being in 'free falls', acting on you without resistance) called 'c'. Then you need to notice that 'c' only can be 'c' relative such a 'inertial observer', and that any acceleration will distort the path giving it a different value according to the original definition. And I'm most certainly missing important points, but they should do for now I hope?
One description that catches the idea is someone bouncing a ball in a railroad wagon. To the guy inside the ball goes straight down and up. To the guy standing at the embankment, watching the train go past him, you can imagine the balls path to then form a V. If we assume the train to have a 'uniform speed' we can pretend that it is a inertially moving object from the point of the guy standing at the side watching it. This is not a very good example but it works to show you the idea behind it. That depending on observer we will see a different motion, and also define it as taking a different time. I have a link describing it better than I ever will :) Special Theory of Relativity: Clocks and Rods. (http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_clocks_rods/index.html) SR is a space without 'gravity', just as a 'free fall' can be seen as, ignoring tidal forces as the earth rotating.