# Time Dilation. I don't get it!

#### JesseM

JesseM said:
Did you mean "all movement between objects of mass and light is absolute, including acceleration" to be a physical statement?
In fact it is the core of Einstein's relativity theory!
What's at the core of his theory is that light moves at c in every inertial coordinate system, or equivalently that each inertial observer will measure the speed of light to be c if he uses rulers and clocks at rest relative to himself. But your claim that "the traveler always travels at 0c relative to light" doesn't make sense in either of these terms.

Again, please provide some rigorous definition--whether expressed in terms of coordinate systems or in terms of physical measurements--of what you mean in general by the phrase "A is moving at velocity v relative to B", in such a way that if A=the traveler and B=the light beam, v would equal 0 rather than c. If you can't do this, then your statement cannot possibly make any sense as physics.
MeJennifer said:
For an unaccelerated object light aways escapes at a speed of c while during the acceleration of an object this is no longer the case. Again feel free to give a situation that is in contradiction with this.
It's not that I think your statement is clearly wrong, it's just that I have no idea what you even mean. I would certainly agree that in the coordinate system of an unaccelerated object light always escapes at a speed of c, and that in the coordinate system of an accelerating object this would not necessarily be the case, but you claim not to be talking about coordinate systems. So what are you talking about? Surely it's meaningless to ask "how fast is the light escaping" without having in mind either a coordinate system or a physical procedure for measuring speed?

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#### MeJennifer

Perhaps you are confused by the term acceleration.
In Newtonian thinking a comet falling towards the earth due to the earth's gravity is accelerating but in relativity the rock is not accelerating at all.
When I talk about acceleration it is not some coordinate specific thing but a physical thing. An unaccelerated object is on a geodesic in space-time while an accelerated object is not. Acceleration is a measurable physical quantity.

Show me a case where an object of mass that is not accelerating is either emitting or absorbing light at a speed different from c, or a case where an object that is accelerating (as in relativity not in some coordinate specific sense) is emitting or absorbing light at the speed of c.

I wager that you will not find a case like that.

So the speed differential between such an object of mass and emitted or absorbed light is always c unless the mass object accelerates. From this we can conclude that the mass object must be at rest compared to light and thus the speed of a mass object relative to light is always 0c unless it accelerates. Also if light would be emitted in all directions forming a sphere the unacellerated mass object would aways be exactly in the middle and the sphere's radius would grow by c. The relative motion of this mass object, so the motion compared with other mass objects, would be completely irrelevant to this phenomenon.

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#### JesseM

Perhaps you are confused by the term acceleration.
In Newtonian thinking a comet falling towards the earth due to the earth's gravity is accelerating but in relativity the rock is not accelerating at all.
When I talk about acceleration it is not some coordinate specific thing but a physical thing. An unaccelerated object is on a geodesic in space-time while an accelerated object is not. Acceleration is a measurable physical quantity.
Of course acceleration is a measurable physical quantity, but you measure it using rulers and clocks. You are still not answering any of my questions about what measurements you are thinking of when you say things like "the traveler always travels at 0c relative to light" and "For an unaccelerated object light aways escapes at a speed of c while during the acceleration of an object this is no longer the case." The first quote does not obviously have anything to do with acceleration, and the second quote would seem to imply you're talking about how an accelerated vs. unaccelerated observer would measure the speed of light, not how to measure whether the observer himself is accelerating, which I agree is unambiguous.
MeJennifer said:
Show me a case where an object of mass that is not accelerating is either emitting or absorbing light at a speed different from c or a case where an object that is accelerating (as in relativity not in some coordinate specific sense) is emitting or absorbing light at the speed of c.
Who is supposed to be measuring the speed of light, and using what method??? If you have an accelerating object emitting light, but the speed of light is being measured by an unaccelerating observer's rulers and clocks, than the light will be measured to be travelling at c. The speed of light has everything to do with what coordinate system you are using, or what set of rulers and clocks are being used to perform the measurement, and nothing to do with whether the object emitting the light is accelerating or not.
MeJennifer said:
So the speed differential between such an object of mass and emitted or absorbed light is always c unless the mass object accelerates. From this we can conclude that the mass object must be at rest compared to light and thus the speed of a mass object relative to light is always 0c unless it accelerates.
You still have provided absolutely no justification for why the second sentence makes sense. In all of physics, "the speed of A relative to B" means either the speed that A measures B to be moving (or vice versa), or perhaps the speed that some third observer sees the distance between A and B changing (the 'closing speed'). But in both of these cases, to say the relative speed is 0c would mean that the distance between A and B is remaining unchanged, so they are measured to be at rest with respect to each other, but that clearly isn't the case with the light beam. So, either you have invented some totally new definition of what it means to say "A is moving at speed v relative to B", or else you have no well thought-out basis for this statement. If you have in fact invented a new definition, it should be simple for you to answer this question I posted earlier:
please provide some rigorous definition--whether expressed in terms of coordinate systems or in terms of physical measurements--of what you mean in general by the phrase "A is moving at velocity v relative to B", in such a way that if A=the traveler and B=the light beam, v would equal 0 rather than c.
MeJennifer said:
Also if light would be emitted in all directions forming a sphere the unacellerated mass object would aways be exactly in the middle and the sphere's radius would grow by c.
As measured by rulers and clocks (or coordinate system) which are at rest relative to the unaccelerated object. On the other hand, if you measure things using rulers and clocks which are moving at constant velocity relative to the unaccelerated object, you will still measure an expanding sphere of light, but the center will be the mark on your ruler where the light was originally emitted, while the object itself will be moving away from this mark and will be closer to one part of the sphere than the other.

In any case, I still have no idea how you think the expanding light-sphere sheds any light on your statement that the emitter is moving at 0c relative to the light. Once again, please provide some general definition of what you mean by "A is travelling at speed v relative to B", such that if we plug in A=the emitter and B=the light, we conclude that v=0 rather than v=c, as would be concluded by most ordinary definitions of "relative speed".

#### MeJennifer

If you have an accelerating object emitting light, but the speed of light is being measured by an unaccelerating observer's rulers and clocks, than the light will be measured to be travelling at c.
In your case you would be measuring the absorbing speed of light by an unaccelerated observer. What makes you think that the fact that light was emitted by an accelerated object has anything to do wth the results of the measurement?
It does not in relativity.

Again light is always emitted and absorbed at the speed of c unless the observer is accelerating. Frankly this is a rather obvious statement, I really do not see what your problem is with it.

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#### JesseM

In your case you would be measuring the absorbing speed of light by an unaccelerated observer. What makes you think that the fact that light was emitted by an accelerated object has anything to do wth the results of the measurement?
Of course I don't think this, but I was asking the question to try to make sense of what you were arguing, which is still completely unclear to me.
MeJennifer said:
Again light is always emitted and absorbed at the speed of c unless the observer is accelerating. Frankly this is a rather obvious statement, I really do not see what your problem is with it.
The statement's meaning is obvious if you are talking about the speed of light in an accelerated observer's coordinate system, but I have no idea what it could mean independently of a statement about coordinate systems. Again, do you have any specific notion of how this accelerating observer is measuring the speed of light? If not, how does it make sense to talk about the "speed" of anything outside of either a coordinate system or a well-defined measurement procedure?

Also, you still have not addressed my other question about what you mean when you talk about a relative speed of 0c rather than 1c between an inertial observer and a light beam:
please provide some rigorous definition--whether expressed in terms of coordinate systems or in terms of physical measurements--of what you mean in general by the phrase "A is moving at velocity v relative to B", in such a way that if A=the traveler and B=the light beam, v would equal 0 rather than c.

#### MeJennifer

Also, you still have not addressed my other question about what you mean when you talk about a relative speed of 0c rather than 1c between an inertial observer and a light beam:
Again it is obvious, how could you posibly reason that the relative speed of the mass object is c?
A non accelerating mass object emitting light in all directions will create a growing sphere growing with the speed of c and with the mass object always in the middle. How could you possibly argue that the mass object is going with any speed except 0 relative to the speed that the light is escaping from it?
Furthermore the relative speed of the mass object in question compared to other mass objects is completely irrelevant to this.

#### JesseM

Again it is obvious, how could you posibly reason that the relative speed of the mass object is c?
Er, because the only definition of "relative speed" in physics is the rate that the distance grows between two things, and the distance between the object and the light is growing at a rate of 1 light year per year. According to every definition I know of, to say the "relative speed" between the two is 0c means they are maintaining a constant distance.
MeJennifer said:
A non accelerating mass object emitting light in all directions will create a growing sphere growing with the speed of c and with the mass object always in the middle. How could you possibly argue that the mass object is going with any speed except 0 relative to the speed that the light is escaping from it?
Obviously in the object's own rest frame, its speed is 0 (and the object only stays at the center of the expanding light-sphere in this frame, in other inertial frames it will move closer to one side of the sphere than the other). But according to all standard definitions this is not the speed of the object relative to the light, it is the speed of the object relative to its own frame.

If we're living in a Newtonian universe, and I'm driving at 30 mph down the road, and one car is going at 10 mph in the opposite direction while another is going at 70 mph in the same direction, then if all three cars start from a single location, my car will always remain at the center of the expanding line segment whose edges are defined by the positions of the two other cars--would you say that this somehow means my speed is 0 relative to these cars, in spite of the fact that each one is moving away from me at 40 mph?

Once again, if you don't have some general definition of what you mean by "relative speed", which can cover cases that don't involve light like the case of cars moving relative to one another at sublight speeds, then you're simply talking gibberish.

#### MeJennifer

Obviously in the object's own rest frame, its speed is 0 (and the object only stays at the center of the expanding light-sphere in this frame, in other inertial frames it will move closer to one side of the sphere than the other).
I suppose you mean that for all other observers who are in relative motion to the object in question the object does not stay in the center right? Well that is true, and that is where the Lorentz transformations come in. The other observers see it like that because they are in relative motion with the object in question.

If we're living in a Newtonian universe, and I'm driving at 30 mph down the road, and one car is going at 10 mph in the opposite direction while another is going at 70 mph in the same direction, then if all three cars start from a single location, my car will always remain at the center of the expanding line segment whose edges are defined by the positions of the two other cars--would you say that this somehow means my speed is 0 relative to these cars, in spite of the fact that each one is moving away from me at 40 mph?
Right, but the point is that we are not living in a Newtonian universe! For light things are rather different as Einstein discovered about a century ago! He discovered that when we are in an inertial state we cannot "catch up" with light, that our speed differential is always c.
It is interesting because your example is exactly what puzzled Einstein. "Why doesn't it work for light this way" is what he thought. And now it seems to puzzle you.
One of the basics in relativity is the fact that light is always emitted from and absorbed by an unaccelerated mass object at a fixed speed, and this speed is c. It does not matter if something is moving at x relative to another object of mass, it could move at 99.99999% relative to my big toe, it is totally irrelevant. You can make up 100 of your frames that are in relative motion but it would not matter in the least.
For light the object is always standing still unless it is accelerating.

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#### JesseM

Right, but the point is that we are not living in a Newtonian universe! for light things are rather different as Einstein discovered about a century ago!
I only had it be a Newtonian universe to make the math a little easier, but you could also pick an example of objects moving at sublight speeds in SR. For example, suppose in your frame I am moving at 0.6c, and there is another ship moving at 0.385c in the opposite direction, while a second ship is moving at 0.946c in the same direction. In this case, in my own rest frame, both ships would be moving at 0.8c in opposite directions from me, so I would remain at the center of the expanding line segment with the edges defined by the positions of the ships. Would you therefore say that somehow my speed relative to the ships is 0c rather than, say, 0.8c (the speed of each ship in my rest frame), or 1.185c and 0.346c (the speed with which the distance between my ship and each of the other ships is growing in your own frame)?
MeJennifer said:
One of the basics in relativity is the fact that light is always emitted from and absorbed by an unaccelerated mass object at a fixed speed, and this speed is c. It does not matter if something is moving at x relative to another object of mass, it could move at 99.99999% relative to my big toe, it it is totally irrelevant.
Yes, I certainly agree with this, at least if we are looking at things from an inertial reference frame.
MeJennifer said:
For light the object is always standing still unless it is accelerating.
This statement has no obvious connection to the previous one, it seems like a non sequitur. What does it mean to talk about what things look like "for light"? Light has no rest frame in relativity, as I'm sure you know. And even if we consider something like how another ship moving at v relative to me will see me in the limit as v approaches c, for the other ship my own velocity would approach c in this limit, not 0.

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#### MeJennifer

I only had it be a Newtonian universe to make the math a little easier, but you could also pick an example of objects moving at sublight speeds in SR. For example, suppose in your frame I am moving at 0.6c, and there is another ship moving at 0.385c in the opposite direction, while a second ship is moving at 0.946c in the same direction. In this case, in my own rest frame, both ships would be moving at 0.8c in opposite directions from me, so I would remain at the center of the expanding line segment with the edges defined by the positions of the ships. Would you therefore say that somehow my speed relative to the ships is 0c rather than 0.8c?
No of course not, we are not talking about light here but about relative motion of mass objects, something entirely different.
With light it is different.

You say it has something to do with frames, but a frame is simply a concept. There is nothing physical about frames, and in GR they are next to completely useless. All we have is objects of mass that are or are not in relative motion with other obects of mass, inertial v.s. accelerated state and the speed of light, and the fact that light always is emitted and always escapes at c and that that is independent of relative motion.
These are the building blocks of relativity not frames!

I do not see one bit of a problem with the statement that for light all mass objects either stand still or accelerate even if that means you cannot construct one of your frames on it.

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#### JesseM

No of course not, we are not talking about light here but about relative motion of mass objects, something entirely different.
With light it is different.
So you're using a definition of "relative speed" which somehow only makes sense when applied to light, the definition cannot be applied to anything else? Under your definition, there is only one possible "relative speed", and it is 0c?
MeJennifer said:
You say it has something to do with frames, but a frame is simply a concept.
Yes, but it is a concept defined in terms of actual measurements.
MeJennifer said:
There is nothing physical about frames, and in GR they are next to completely useless.
Not really, you still use coordinate systems in GR, and for them to have physical meaning you still need some notion of a measurement procedure which can tell you what coordinates a given event should be defined.
MeJennifer said:
All we have is objects of mass that are or are not in relative motion with other obects of mass
The words "relative motion" are meaningless unless you define it in terms of some measurement procedure.
MeJennifer said:
inertial v.s. accelerated state and the speed of light, and the fact that light always is emitted and always escapes at c and that that is independent of relative motion.
Speed is meaningless unless you define it in terms of some measurement procedure. You don't need "frames" per se for your statement to be correct, it is also correct if you just define "speed" in terms of measurements on rulers and clocks moving inertially (and if you're measuring one-way speed as opposed to round-trip speed, you also need to specify that clocks at different points on the ruler are synchronized according to the Einstein synchronization convention). But if you don't define speed in terms of either coordinate systems or measurements on physical rulers and clocks, your statement is meaningless.

If your objection is just to frames and not to the idea that we need to measure speed physically, what physical measurement procedure are you imagining that will lead us to the conclusion that a sublight object is moving at 0c "for light"? How does a light beam measure the speed of another object relative to itself? You can't get a ruler or clock moving at that speed, and again, if you consider the observations of an observer moving away from the object in the limit as his speed relative to the object approaches c, then according to measurements on his own rulers and clocks the object's velocity approaches c in this limit, not 0.

#### MeJennifer

If your objection is just to frames and not to the idea that we need to measure speed physically, what physical measurement procedure are you imagining that will lead us to the conclusion that a sublight object is moving at 0c "for light"?
I have not objection to frames, unless they are viewed as some hidden reality of space or space-time.

what physical measurement procedure are you imagining that will lead us to the conclusion that a sublight object is moving at 0c "for light"?
There is no movement relative to the speed of light Jesse, if there were we would not be able to state that light always gets emitted or absorbed at the speed c. We would instead measure that if something moved at say 0.2c that light would be emitted at 0.8c in the direction of movement. This is obviously not the case. So it is clear, at least to me, that relative movement between objects of mass is entirely irrelevant to light.

For light there is no movement.
Consider space-time with the Minkowski metric. Observer the angle between the worldline of an accelerated mass particle and photon, does the "speed" of the mass particle make any difference whatsoever? No it does not, the angle remains the same.

Lorentz effects are caused by relative movements of mass objects.
But here we also should be a bit more selective.
An effect can only be observed once there is change in the rate of change of the distance between the observer and the measured object. If the rate of change remains constant one could at most infer that the rate of change in the past was different, but one cannot actually observe length contraction, time dilation or increase of relativistic mass.
So it is more accurate to say that the Lorentz effect can only be observed if the rate of change of the distance between an observer and a mass object changes.

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#### JesseM

There is no movement relative to the speed of light
What does it mean to talk about movement relative to a speed rather than relative to an object or particle (such as a photon)?
MeJennifer said:
Jesse, if there were we would not be able to state that light always gets emitted or absorbed at the speed c.
Physically, the statement that light alwasy gets emitted or absorbed at the speed of c just means that whenever you measure its speed using inertial rulers and clocks, you find its speed is c. Speed is not a theological or philosophical concept--do you agree that all statements about speeds must be ultimately be justified in terms of some set of physical measurements? If so, please explain what you mean by "the speed of a mass object relative to light is always 0c" in terms of actual physical measurements.
MeJennifer said:
For light there is no movement.
I have no idea what the physical meaning of this statement is supposed to be. If it is not a theological or philosophical claim, then please explain what it means in terms of physical measurements.

#### MeJennifer

I have no idea what the physical meaning of this statement is supposed to be. If it is not a theological or philosophical claim, then please explain what it means in terms of physical measurements.
Did you ever study a space-time diagram for a photon, a so-called null interval? I suppose you did. How much "movement" of mass objects does a light beam encounter from one spacetime event to another? I hope you will see that it is in fact none whatsoever. So why is it that you have trouble with my statement?

#### JesseM

Did you ever study a space-time diagram for a photon, a so-called null interval? I suppose you did. How much "movement" of mass objects does a light beam encounter from one spacetime event to another? I hope you will see that it is in fact none whatsoever. So why is it that you have trouble with my statement?
I don't know what this means either. When you talk about spacetime events "encountered" by a light beam, are you talking solely about events on the light beam's own worldline? If so, what does it mean for anyone (whether a sublight observer or a light beam) to measure the "movement" of any other object based only on the intersections between their own worldline and the object's worldline? Normally measuring movement depends on recording two different positions of an object at different times, if you only measure the position once you don't conclude the object is at rest, you just don't have enough information to measure its speed.

#### eiapeteides

OK Guys. Now you really confused the hell out of me! The only remaining question I actually had was:

Is the Lorentz contraction a real physical effect or is it a mere optical illusion due to the relative motion between the one who measures the length of an object and the measured object?

#### pervect

Staff Emeritus
What sort of experiment would you perform to tell if it is "real" or an "optical illusion"?

#### eiapeteides

I can't think of anything. But just because "I" can not distinguish between them doesn't make "Real" and "Illusion" the same?

#### JesseM

I can't think of anything. But just because "I" can not distinguish between them doesn't make "Real" and "Illusion" the same?
If it helps, it's not an optical effect, length contraction is what you get when you factor out light signal delays, or when you measure "length" using only local measurements. For example, suppose there was a rod that was 10 meters long in its own rest frame, and it was moving past you at 0.6c. If you held out a ruler which had a bunch of synchronized clocks attached to each marking, then if the back end of the rod was passing the 0-meter mark when the clock there read exactly 12:00, then the front end would be passing the 8-meter mark when the clock at that marking also read exactly 12:00, so you could use these simultaneous local measurements to judge that the length of the rod in your frame had shrunk to 8 meters, just as the length contraction equation predicts.

Of course, it's important to understand that the concept of what it means for a pair of clocks to be "synchronized" differs from frame to frame, so that even though in your frame both clocks tick 12:00 "at the same time", other frames would assign these events different time-coordinates. If you're interested, on this thread I provided an illustration of how two rulers moving past each other at relativistic speeds, with clocks at each marking, would view one another in their own rest frame, and how the fact that they define simultaneity differently can explain why each one measures the other to be shrunken.

Since the question of which ruler is shrunken also depends on your choice of frames, this makes it ambiguous whether length contraction should be called a "real physical effect"--like I said, it isn't optical, but it isn't frame-independent either, and usually physicists would only define a quantity or observation as truly "physical" if it would be agreed upon by all observers.

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#### pervect

Staff Emeritus
I can't think of anything. But just because "I" can not distinguish between them doesn't make "Real" and "Illusion" the same?
Nope - but it does make the answer to your question a matter of philosphy, rather than science, unless you can pin your question down better.

There generally isn't any end or resolution to philospohical arguments, but a scientific argument can ultimately be resolved by the court of experiment.
A corollary to this is that most (though perhaps not all) scientists stop arguing when they realize they only disagree about things that can't be tested, i.e. that they are arguing about philosophy rather than science.

For what it's worth, I tend to regard oberver independent quantites as being more "real" or at least more fundamental than observer dependent quantities. This POV leads to the view that the Lorentz interval, being independent of the observer, is a more fundamental property of nature than length. But you won't necessarily find total agreement on this point, though I personally think the physics is easier when one views things in this way.

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