When moving fast, you're too busy to age

[birulami]

Trying to understand special relativity, in particular the influence of speed on time, I came up with the following picture, and wonder how accurate it could be.

Suppose a spell is cast on you in your rocket drifting through space that stops everything moving all over the rocket: from the arms on the wall clock, to the quartz in your watch, down to the molecules and atoms active in chemical reactions and even further to the subatomic level to whatever may jiggle and wiggle about, everything stops --- total "freeze". Just to be sure, the spell even stops photons just where they are. (Ok, this is unphysical, but a spell is anyway.)

Do you think you and your rocket are getting older, are aging now? Most likely not, because you are not changing, no chemical reactions that make wrinkles and grey hair in the long run.

Do you think time passes in the rocket now? Tricky. To my knowledge there would be no way to prove that time passes, because everything came to a halt: no change, no way to measure time passing. Why not extend this a bit and say: "Without change, no time passes". Or even stronger: time *is* change.

If we can assume this for a moment, an interesting connection to special relativity appears. Suppose after releasing the above spell, another spell accelerates you and your rocket to the speed of light. Would you and your rocket still be able to change? No, because in addition to your forward motion the change would require additional velocity components for, say, the molecules to perform their chemical reaction. But the additional velocity is not available: speed of light cannot be topped. The situation at the speed of light is very much the same as described for the original spell: (relative) change of any kind within your body or the rocket is not possible. Consequently no time passes.

No need to say that this argument goes smooth for rockets slower than light if we assume that atomic and subatomic changes like chemical reactions require exchange of photons and similar "particles". These are going along with the rocket and only what is left towards the full speed of light can be invested in change. The faster you go, the lesser is left for change, i.e. for time passing.

As a side note we realize that in this picture time is a completely local phenomenon.

Does this picture have any credibility?

 

[Doc Al]

If we can assume this for a moment, an interesting connection to special relativity appears. Suppose after releasing the above spell, another spell accelerates you and your rocket to the speed of light.

Forget about you and your rocket traveling at the speed of light; such a scenario is prohibited by relativity, thus unphysical. But it's perfectly OK to consider what relativity says about sub-light speed rockets and clocks.

Would you and your rocket still be able to change? No, because in addition to your forward motion the change would require additional velocity components for, say, the molecules to perform their chemical reaction. But the additional velocity is not available: speed of light cannot be topped. The situation at the speed of light is very much the same as described for the original spell: (relative) change of any kind within your body or the rocket is not possible. Consequently no time passes.

You seem to think that somehow your velocity is absolute, not relative to some observer. Consider that right this second you are traveling at close to the speed of light with respect to some frame--yet everything seems to work as normal. When your rocket travels at a high speed relative to some observer, it is that observer-not you!-who measures your clocks as operationg slowly compared to his. As far as you are concerned, your clocks work just fine--but his clocks are running slowly.

No need to say that this argument goes smooth for rockets slower than light if we assume that atomic and subatomic changes like chemical reactions require exchange of photons and similar "particles". These are going along with the rocket and only what is left towards the full speed of light can be invested in change. The faster you go, the lesser is left for change, i.e. for time passing.

Again, the faster you go relative to some observer, the slower your clocks operate according to that observer, not you. Your speed relative to someone else has no effect whatsoever on anything going on in your rocket (whether chemical, atomic, subatomic, or whatever). That's the principle of relativity!

 

[birulami]

When your rocket travels at a high speed relative to some observer, it is that observer-not you!-who measures your clocks as operationg slowly compared to his.

This is exactly what I am saying. If I am in the speeding rocket, my clocks tick slower; in the extreme case they nearly stop ticking. Of course I myself cannot see, measure or prove this. How could I, without something that ticks at the "correct", "right" speed. Everthing in my system is slowed down completely in sync, so I cannot measure the slowdown.

There seems to be some "absolute" time lurking here, some point where the picture I described in my original post breaks. But to understand special relativity better, I would like to find out where it really breaks.

So this outside observer sees me speeding by and says to himself: "this guy's time runs slower and I imagine it happens like birulami described in his first post".

Now I in my rocket will say the same about this observer speeding by relative to me. And here the picture breaks, because only one of us can have the time slowed down relative to the other --- in that picture.

But if we consider for a moment, completely unphysical, that the outside observer sits in "the" absolute reference frame of the universe and I am the one who is "really" speeding by: how would we prove (measure) the asymmetry of our situations?

It seems obvious that --- in this picture --- the outside observer should be able to prove that my clocks run slow, but: With the time in my rocket slowed down, would not every measurement I make indicate that it is just the other way around, exactly like special relativity predicts?

I think an analysis of the measurement processes possible shows exactly that. But there is also a high chance that I made a mistake in the calculations or the descriptions of the measurement process. I wonder if someone could point me to a paper where this is elaborated, i.e. in summary: assume absolute reference frame, assume time dilation and length contraction according to velocity relative to absolute reference frame, prove that there would exists a measurement process that demonstrates the asymmetry between any reference frame and the absolute one or between any two reference frames.

 

[MeJennifer]

There seems to be some "absolute" time lurking here, some point where the picture I described in my original post breaks. But to understand special relativity better, I would like to find out where it really breaks.

My advice is not to think in terms of absolute time when you want to understand relativity better. The whole point in relativity is that there is neither absolute space nor absolute time.

And here the picture breaks, because only one of us can have the time slowed down relative to the other --- in that picture.

No, both will observe each others time to be slowed down.

But if we consider for a moment, completely unphysical, that the outside observer sits in "the" absolute reference frame of the universe and I am the one who is "really" speeding by: how would we prove (measure) the asymmetry of our situations?

Again, in relativity the point is that there is no absolute frame of reference and furthermore that there is absolutely no need for such an absolute frame of reference. So if you think in these terms you might get more confused.

It seems obvious that --- in this picture --- the outside observer should be able to prove that my clocks run slow, but: With the time in my rocket slowed down, would not every measurement I make indicate that it is just the other way around, exactly like special relativity predicts?

Well if you could prove that it would prove relativity wrong. But I would not hold my breath for it.

I wonder if someone could point me to a paper where this is elaborated, i.e. in summary: assume absolute reference frame, assume time dilation and length contraction according to velocity relative to absolute reference frame, prove that there would exists a measurement process that demonstrates the asymmetry between any reference frame and the absolute one or between any two reference frames.

There are many papers that assume absolute space and absolute time but they are not about the theory of relativity.
Some of them are not wrong, in that the numerical results are equal to the theory of relativity, theories like LET, but others are simply crackpot theories of the "Einstein is wrong and my special theory is right" kind.

 

[JesseM]

This is exactly what I am saying. If I am in the speeding rocket, my clocks tick slower; in the extreme case they nearly stop ticking.

They tick slower in the frame of someone who you are speeding past. In your frame, it is their clocks that tick slower. There's no reason to prefer one frame's description of the situation to another's.

So this outside observer sees me speeding by and says to himself: "this guy's time runs slower and I imagine it happens like birulami described in his first post".

Now I in my rocket will say the same about this observer speeding by relative to me. And here the picture breaks, because only one of us can have the time slowed down relative to the other --- in that picture.

But if we consider for a moment, completely unphysical, that the outside observer sits in "the" absolute reference frame of the universe and I am the one who is "really" speeding by: how would we prove (measure) the asymmetry of our situations?

It seems obvious that --- in this picture --- the outside observer should be able to prove that my clocks run slow, but: With the time in my rocket slowed down, would not every measurement I make indicate that it is just the other way around, exactly like special relativity predicts?

Yes, it's true that even if we imagine there is an absolute space and absolute time, as long as it's still true that observers moving at velocity v in absolute space and time will have their rulers shrunk by a factor of $$\sqrt{1 - v^2/c^2}$$ and the ticks of their clocks extended by $$1 / \sqrt{1 - v^2/c^2}$$ (and that this applies to all physical clocks and rulers, including things like biological aging), then if they sychronize their own clocks using Einstein's synchronization convention (which will lead the clocks to be out-of-sync with respect to absolute time) and use their own clocks and rulers to establish a coordinate system, then they will measure clocks which are at rest in absolute space to be slowed down and rulers at rest in absolute space to be shrunk with respect to their own clocks and rulers, even though their own clocks and rulers are "really" the ones slowed down and shrunk. So the hypothesis that there is such a thing as absolute time and space would not make any new physical predictions, and thus it would be more of a philosophical interpretation, there'd be no experiment we could do to break the symmetry and discover which frame's measurements were the "correct" ones even if such a thing were true. The only way to get a genuinely new physical prediction out of a belief in absolute time and space would be if there were some type of special physical ruler or clock that did not shrink/slow down by the amount predicted by relativity when moving in absolute space, or if there were some other phenomenon that did not behave identically in every frame (like tachyons which could be seen as moving backwards in time in every frame but one, so you could have FTL without causality violations).

 

[MeJennifer]

The only way to get a genuinely new physical prediction out of a belief in absolute time and space would be if there were some type of special physical ruler or clock that did not shrink/slow down by the amount predicted by relativity when moving in absolute space, or if there were some other phenomenon that did not behave identically in every frame (like tachyons which could be seen as moving backwards in time in every frame but one, so you could have FTL without causality violations).

Well the key difference between Lorentz ether theories and special relativity is that in Lorentz ether theories rulers shrink and clocks slow down while space and time remain static, but in special relativity it is space that shrinks (and thus rulers must shrink as well) and time that dilates (and thus clocks close down).
Space and time are static in Lorentz ether theories while in special relativity they are dynamic.

 

[JesseM]

Well the key difference between Lorentz ether theories and special relativity is that in Lorentz ether theories rulers shrink and clocks slow down while space and time remain static, but in special relativity it is space that shrinks (and thus rulers must shrink as well) and time that dilates (and thus clocks close down).
Space and time are static in Lorentz ether theories while in special relativity they are dynamic.

Unless you can translate these different verbal descriptions into theories which actually make distinct predictions, then they cannot qualify as distinct "theories" at all, they are more like the different "interpretations" of quantum mechanics, metaphysical hypotheses more than physical ones. There is nothing in the mathematics of SR that forces us to believe that "space shrinks and time slows down" rather than "rulers shrink and clocks slow down", I am not even sure what this distinction is supposed to mean on a more philosophical level.

 

[MeJennifer]

Not only are space and time not absolute in relativity there are actually an infinite number of spaces.
For instance a box X inside a larger box Y encloses the same space, but when box X is in relative motion inside box Y it is no longer a trivial case. The box Y and the space inside it are actually in relative motion with the box X and the space enclosing it!

Empty space can contract, expand and curve and it is the same with time.

The implications of the theory of relativity are most certainly profound!

 

[JesseM]

For instance a box X inside a larger box Y encloses the same space, but when box X is in relative motion inside box Y it is no longer a trivial case. The box Y and the space inside it are actually in relative motion with the box X and the space enclosing it!

It still seems to me you're talking about some kind of philosophical interpretation (and like I said, I don't even really understand what statements like this would mean philosophically), not making a statement about physics. Can you translate these statements into mathematical terms? Why would they be true in SR but not Newtonian physics, when in both cases there is no physical reason to prefer one inertial frame over another?

Empty space can contract, expand and curve and it is the same with time.

Yes, general relativity does feature effects like this, but I don't see how this relates to the statements you were making about special relativity. Certainly when a ruler shrinks relative to a particular reference frame in SR, it's not because space is contracting in anything resembling the GR sense.

 

[MeJennifer]

While it is true that expansion and curvature of space only apply to general relativity, contraction of space and dilation of time apply to both the special and general theory of relativity.

 

[JesseM]

While it is true that expansion and curvature of space only apply to general relativity, contraction of space and dilation of time apply to both the special and general theory of relativity.

But expansion/contraction of space in general relativity has a well-defined meaning in terms of the mathematical structure of the theory. Whatever you mean by "contraction of space" in SR, if you're contrasting it with the idea that the rulers themselves contract, that can't have a basis in the theory's structure since these two ways of thinking about it don't lead you to different predictions.

And to get into the subject of philosophical interpretations, it's true that an interpretation like the one birulami suggests would require you to believe in a sort of "metaphysically preferred reference frame" which I assume is not part of most physicist's philosophical interpretations of the theory, but then I don't think most physicist's interpretations would talk about "space contracting" either, I think many would just say that spacetime is the fundamental entity in relativity and "length" is just a property of how you slice up spacetime into spacelike cross-sections. As an analogy, suppose we have two cylinders of equal radius embedded at different angles in a block of solid ice, and then we slice the block into cross-sections; if we slice perpendicular to the axis of the first cylinder, that cylinder's cross section will be a circle, while the second cylinder's cross section will be an elongated ellipse, but we could have just as easily reversed the situation by slicing perpendicular to the second cylinder's axis. The fact that one cylinder's cross-section will be more elongated than the other is not due to either the cylinders or the ice expanding or contracting, it's just due to the geometry of taking 2D cross-sections of this 3D block, and the same could be said about taking 3D cross-sections of 4D spacetime.

 

[MeJennifer]

So let me get this right JesseM, are you stating that a box B in relative motion to an observer O, is contracted in the direction of motion but the space in the box in the direction of motion remains constant? And that a clock inside this box runs slower but that time remains constant inside this box?

 

[JesseM]

So let me get this right JesseM, are you stating that a box B in relative motion to an observer O, is contracted in the direction of motion but the space in the box in the direction of motion remains constant? And that a clock inside this box runs slower but that time remains constant inside this box?

I don't understand what the phrase "space in the box remains constant" means in physical terms, or the phrase "time remains constant inside the box". Please tell me what concrete predictions would be made by someone who someone who says they don't remain constant, as distinct from someone who says they do. If there is no difference in predictions, then you are making statements about philosophical interpretations rather than scientific theories, period. And as a matter of philosophical interpretation, I prefer to just think in terms of spacetime, so the volume inside the box at a particular moment is just an arbitrary matter of how you choose to take a 3D cross-section of 4D spacetime, just like the area of a 2D cross section of a tube embedded in ice will depend on the angle you slice the ice to make a cross section. The fact that the area varies with the angle would not be explained in terms of the ice itself expanding or contracting, nor would it be explained in terms of the tube expanding or contracting, so I don't see how it makes sense to explain volume changes with reference frame in terms of space expanding or contracting or in terms of the box expanding or contracting, both ways of describing the situation seem misleading to me just as they would be in the case of the block of ice.

 

[MeJennifer]

I don't understand what the phrase "space in the box remains constant" means in physical terms, or the phrase "time remains constant inside the box". Please tell me what concrete predictions would be made by someone who someone who says they don't remain constant, as distinct from someone who says they do. If there is no difference in predictions, then you are making statements about philosophical interpretations rather than scientific theories, period. And as a matter of philosophical interpretation, I prefer to just think in terms of spacetime, so the volume inside the box at a particular moment is just an arbitrary matter of how you choose to take a 3D cross-section of 4D spacetime, just like the area of a 2D cross section of a tube embedded in ice will depend on the angle you slice the ice to make a cross section. The fact that the area varies with the angle would not be explained in terms of the ice itself expanding or contracting, nor would it be explained in terms of the tube expanding or contracting, so I don't see how it makes sense to explain volume changes with reference frame in terms of space expanding or contracting or in terms of the box expanding or contracting, both ways of describing the situation seem misleading to me just as they would be in the case of the block of ice.

Ok, how about a photon going from the left side to the right side of the box, how much space does it travel according to you from observer O's perspective who is at rest to this moving box.

 

[JesseM]

Ok, how about a photon going from the left side to the right side of the box, how much space does it travel according to you from observer O's perspective who is at rest to this moving box.

If "how much space does it travel" just means "what is the coordinate distance it travels in O's rest frame", of course the answer is simply the rest length of the box. If it means something else, please explain. And what is the relevance of this question to your claim that, in a frame moving relative to the box, it's space itself that contracts rather than the box?

 

[MeJennifer]

And what is the relevance of this question to your claim that, in a frame moving relative to the box, it's space itself that contracts rather than the box?

That is not "my claim", the example with the box is from Albert Einstein himself.

Another example of space contraction in relativity is when a spaceship measures the distance between Earth and Andromeda and then takes off and travels near light speed, the distance will be a lot shorter due to space contraction. The folks in the ship could arrive there in a few days on their time if their speed was high enough.

Space and time are not static but dynamic in special relativity.

 

[JesseM]

That is not "my claim", the example with the box is from Albert Einstein himself.

I wasn't referring to the box example, I was referring to your claim that there is a difference between saying "the box contracts" and "space contracts", and that somehow relativity favors the second view. Did Einstein ever say anything which supports this claim of yours? If so, where? And again, what distinct physical predictions would be made by people favoring one view over the other? Do you disagree with the fundamental idea that two ideas about physics can only qualify as distinct "theories" if they make different predictions?

Another example of space contraction in relativity is when a spaceship measures the distance between Earth and Andromeda and then takes off and travels near light speed, the distance will be a lot shorter due to space contraction. The folks in the ship could arrive there in a few days on their time if their speed was high enough.

Of course this would also be predicted by someone who says that rulers shrink and clocks slow down. And it would also be predicted by someone like me who thinks that the fundamental reality is just a collection of worldlines in 4D spacetime, and that "the distance to the star" is just a question of what angle you slice spacetime, just like if you had two parallel tubes in a block of ice and created a cross section of it, the distance between the cross sections of the tubes would depend on the angle you sliced the ice.

Space and time are not static but dynamic in special relativity.

This statement has no scientific content. You can keep repeating it until you're blue in the face, but unless you can show how this claim leads to a single prediction different from someone whose interpretation of SR is different from yours, you're just philosophizing.

 

[birulami]

Yes, it's true that even if we imagine there is an absolute space and absolute time [...] So the hypothesis that there is such a thing as absolute time and space would not make any new physical predictions, and thus it would be more of a philosophical interpretation, there'd be no experiment we could do to break the symmetry and discover which frame's measurements were the "correct" ones even if such a thing were true.

Many thanks for clearing this up. I hope I can take your word for it. Personally I find it an interesting and actually helpful thought model to go with an absolute space/time and then prove that you cannot single it out, cannot detect it, and that special relativity is nevertheless just right. As you say. the assumption of such an undectable absolute frame of reference does not add any new predictitons to the theory. I see it similar to drawing lines and points on a piece of paper when learning euclidian geometry. Those lines and points on the paper don't add anything new to the axioms of the theory, but they help a lot in understanding.

What I don't understand is that I should be the only one who thinks the approach to special relativity as described above is easier than leaving out, even excorcising, the absolute reference frame from the beginning. I think a lot of people interested in the theory would find it easier to be told: imagine this absolute reference frame, assume the speed of light is c in this frame, then carefully design your ways to measure time and length and, like magic, you'll find that all your observers are symmetrically equivalent with regards to measurements of each others lengths and clock ticks. There is no way to pin down the absolute frame of reference, so just forget about it again.

Thanks for your answers.

 

[selfAdjoint]

What I don't understand is that I should be the only one who thinks the approach to special relativity as described above is easier than leaving out, even excorcising, the absolute reference frame from the beginning

I think it's because "There is no prefrerred frame" is a cleaner statement than "There is a preferred frame but you can never detect it". Imagine the name "Santa Claus" in place of the phrase "preferred frame".

And also, beginners often use a naive preferred frame in their assumption that they can have a viewpoint of two inertial frames related by a velocity that enables them to to tell "what really goes on". You have to break them of this bad habit so you teach no preferred frame.

 

[MeJennifer]

I think it's because "There is no preferred frame" is a cleaner statement than "There is a preferred frame but you can never detect it".

I agree 100%!

In special relativity there is no preferred frame, not even in principle. On the contrary the principle of relativity is that there is no preferred frame and that there is actually no need whatsoever to have one. So to "explain" special relativity from a hypothetical preferred frame is counter productive IMHO.

Of course you can assume an absolute frame with absolute space and time and assume that moving objects get contracted and their clocks slowed down with exactly the same results, but then your are really adopting the ontology of some Lorentz ether like theory and not special relativity!

 

[masudr]

Is MeJennifer confusing "space inside different boxes" with "different co-ordinate systems"? 'Cos really, all the co-ordinate systems are describing the same spacetime.

 

[MeJennifer]

Here is the whole box thing:

When a smaller box s is situated, relativity at rest, inside the hollow space of a larger box S, then the hollow space of s is a part of the hollow space of S, and the same "space," which contains both of them, belongs to each of the boxes. When s is in motion with respect to S, however, the concept is less simple. One is then inclined to think that s encloses always the same space, but a variable part of the space S. It then becomes necessary to apportion to each box its particular space, not thought of as bounded, and assume that these two spaces are in motion with respect to each other.

Before one has become aware of this complication, space appears as an unbounded medium or container in which material objects swim around. But it must be remembered that there is an infinite number of spaces, which are in motion with respect to each other.
The concept of space as something existing objectively and independent of things belongs to pre-scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relatively to each other. This latter idea is indeed unavoidable, but is far from having played a considerable role even in scientific thought.

 

[birulami]

Of course you can assume an absolute frame with absolute space and time and assume that moving objects get contracted and their clocks slowed down with exactly the same results, but then your are really adopting the ontology of some Lorentz ether like theory and not special relativity!

Thanks for this comment and for helping me understand all that. For a while already I was wondering what the difference really was between special relativity and "some Lorentz ether like theory". To get things straight, I would like to ask another question. To do so I want to refer to "some Lorentz ether like theory" as the model discussed in this thread and call it sLELT. The original Lorentz Ether Theory shall be LET and of course SRT is Special Relativity Theory.

May I understand your statement above as saying that indeed

• predictions(SRT) = predictions(sLELT)

except that sLELT makes use of an ether concept (or absolute frame of reference), which is not necessary to get to those predictions? The other question would be if

• predictions(SRT) = predictions(LET)

or if LET has a subtle difference in the precitions as compared to SRT.

If both equations, or at least the first, are true, it would clear up things a lot for me. The decision whether I then picture things in my mind rather according to SRT or sLELT or LET would turn out to be "only" philosophical.

 

[birulami]

And also, beginners often use a naive preferred frame in their assumption that they can have a viewpoint of two inertial frames related by a velocity that enables them to to tell "what really goes on". You have to break them of this bad habit so you teach no preferred frame.

Hmm, I think I am such a beginner still, but nevertheless it was a very interesting exercise to assume that I am in the absolute reference frame and that the speed of light is constant with regard to it. Easily it follows that the other observers' clocks run slow and their lenghts are contracted. The jaw dropping moment, however, came when I modeled how they see my clocks and my lengths, of course not knowing that they are in the "wrong" reference frame and therefore have "broken" clocks and "short" meters: they would come to the very conclusion that my clocks run slow and my lengths are contracted as if they are in the absolute frame of reference.

The funny thing is: all I threw in as an assumption was that the speed of light is constant with regard to the absolute frame of reference. Einsteins first postulate, that "all inertial frames are equivalent for the performance of physical experiments" (cited after Rindler), seems to be a consequence then --- at least for mutual measurements of length and time.