Interpreting Time, Mass & Length in Special Relativity

[MeJennifer]

In the theory of special relativity when two observers are in relative motion with each other then each observer measures an increase in mass, a slower clock rate and a contraction of length in the other observer's frame of reference.

How are we to interpret this according to the theory of special relativity?
Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

Edit: highlighted text to clarify the questions.

 

[clj4]

In the theory of special relativity when two observers are in relative motion with each other then each observer measures an increase in mass, a slower clock rate and a contraction of length in the other observer's frame of reference.

How are we to interpret this according to the theory of special relativity?
Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

You are asking two different questions in one sentence. And the question is very poorly phrased.

1. The effect is reciprocal . All frames behave identically in SR .
2. The effect is also measurable for:
- time dilation (Ives-Stilwell measure time dilation thru the Transverse Doppler Effect, the muons reach the Earth due to time dilation)
- mass increase (particle in nuclear accelerators are known to experience
increased resistance to further speed increase as a function of their instantaneous speed)

To my best knowledge, the effect has not been measured directly for:
- length contraction but the effect has called upon in the explanation of MMX. See here:
http://en.wikibooks.org/wiki/Special_Relativity:_aether

 

[MeJennifer]

You are asking two different questions in one sentence. And the question is very poorly phrased.

Basically I am asking:

Is the reciprocal effect actually happening to both frames or is this reciprocal effect a distortion of reality?

 

[Mickey]

Length contraction is not directly observable, because light beams coming from the object each travel different distances to reach an observer. Here is a nice applet that illustrates why we would not see length contraction:

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/Flash/ContractInvisible.html

As it happens, we end up seeing a rotation!

 

[Jorrie]

Basically I am asking: Is the reciprocal effect actually happening to both frames or is this reciprocal effect a distortion of reality?

My take on this is that it is just the way one frame observes the other, so it is obviously reciprocal and nothing is physically happening to either frame.

In my engineering view, it is a measurement phenomenon and not a physical one. We measure the elapsed time for the muon to travel to Earth's surface as being longer than it's (statistical) lifetime, but that is because we are not present at the two events (the muon's birth and arrival at Earth's surface). For the muon, present at both events, nothing strange happens – it does not have our 'measurement problem'!

 

[Hans de Vries]

In the theory of special relativity when two observers are in relative motion with each other then each observer measures an increase in mass, a slower clock rate and a contraction of length in the other observer's frame of reference.

How are we to interpret this according to the theory of special relativity?
Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

Edit: highlighted text to clarify the questions.

It's a reality rather than a distortion. Still there is only one reality in
4D space-time.

For instance: The Lorentz contraction is the result of the non-simultaneity
of Special Relativity. To see this we can imagine that we instantaneously
"freeze" a bypassing traveler. Walking around him we can now see him
"hanging in the air", indeed being contracted in the direction in which he
was moving.

The traveler however will complain that his front was stopped first, before
his back was frozen in time, and argues that this is the reason of his
compressed state. You can give him your "freezing device" and do the
experiment the other way around. This time you'll be the one who is
Lorentz contracted.


Regards, Hans

 

[clj4]

Length contraction is not directly observable, because light beams coming from the object each travel different distances to reach an observer. Here is a nice applet that illustrates why we would not see length contraction:

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/Flash/ContractInvisible.html

As it happens, we end up seeing a rotation!

Correct, this is the well-known Terrell-Penrose effect

http://en.wikipedia.org/wiki/The_Terrell-Penrose_Effect

 

[pervect]

In the theory of special relativity when two observers are in relative motion with each other then each observer measures an increase in mass, a slower clock rate and a contraction of length in the other observer's frame of reference.

How are we to interpret this according to the theory of special relativity?
Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

Edit: highlighted text to clarify the questions.

Generally speaking, what is "real" or "actual" is a philosphical question. Philosophical questions, by definition, don't have any definite answers, so one is free to assume that any particular phenomenon is "real" or "appearance" as desired.

While philosophical questions don't make any actual difference, i.e. they don't make any experimental predictions, or else they wouldn't be philosophical, there is usually a philosophy that makes any particular theory the most understandable.

For relativity, I would say that this philosophy is the idea that the Lorentz interval is "real" and "fundamental". Invariant mass is also in the same category. "Time" and "space" are less fundamental than the Lorentz interval.

Of course, like any philosophy, one is not forced to this belief, it's just a matter of convenience and possibly communication.

 

[MeJennifer]

For relativity, I would say that this philosophy is the idea that the Lorentz interval is "real" and "fundamental". Invariant mass is also in the same category. "Time" and "space" are less fundamental than the Lorentz interval.

Indeed, that seems to be the crux in the theory of relativity.

But at the same time, we postulate a fundamental speed, e.g. the speed of a light signal.
What else is speed than a measure of distance/duration?

If we consider time and space, and thus, speed less fundamental, then reflectively, observer A, seeing a light beam going towards observer B, must conclude that B sees this light at the same speed because of B's Lorentz distorted measurement of speed.

If A and B are in relative motion should one not logically conclude that the identical observer speed of light is due to the Lorentz distortion, rather than that the Lorentz distortion is due to the constancy of the speed of light?

 

[jtbell]

Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

As Pervect noted, it depends on your definition of "reality". Do you expect "reality" to be the same in different reference frames? If not, whose reference frame do you prefer?

I think a legitimate point of view is that length contraction itself (to use it as an example) is not "real", in the sense that the object itself doesn't "perceive" the contraction in its own reference frame. Nevertheless, length contraction has real physical consequences in other reference frames.

As an analogy, suppose that a friend is standing in front of you, some distance away. She's holding a meter stick, oriented horizontally and perpendicular to your line of sight. There's a light behind her so all you can see is a silhouette.

She turns the meter stick so that it's oriented at an angle to your line of sight, but still horizontal. To you, the meter stick now appears to be shorter. It's not really shorter, of course. Nevertheless, the apparent shortening has real physical consequences, because your friend can now walk towards you, through a door which is less than a meter wide, without the meter stick hitting the doorframe!

 

[pervect]

Indeed, that seems to be the crux in the theory of relativity.

But at the same time, we postulate a fundamental speed, e.g. the speed of a light signal.
What else is speed than a measure of distance/duration?

If we consider time and space, and thus, speed less fundamental, then reflectively, observer A, seeing a light beam going towards observer B, must conclude that B sees this light at the same speed because of B's Lorentz distorted measurement of speed.

If A and B are in relative motion should one not logically conclude that the identical observer speed of light is due to the Lorentz distortion, rather than that the Lorentz distortion is due to the constancy of the speed of light?

Speed can also be regarded geometrically as a measure of the angle that two world lines form where they meet.

As the ratio of two intervals ("lengths"), speed becomes dimensionless.

However, you make a good point in that time is different from space, and the Lorentz interval does not in and of itself distinguish them, except by the sign of the interval.

We find it convenient in relativity to use the same units to measure time and space. Furthermore, time and space "mix together" in the Lorentz transform - an interval that one observer sees as having only time components will appear to have both time and space components when viewed by another observer, for example.

However, I would stop short of suggesting that time and space are actually the same thing. Closely related and intertwined, yes, but (according to my philosophy, anyway) not quite identical.

 

[MeJennifer]

However, you make a good point in that time is different from space, and the Lorentz interval does not in and of itself distinguish them, except by the sign of the interval.

True. Apparently time or space but not both is imaginary in SR's mathematics.

But are we actually measuring time here?
Can we univocally conclude that just because a clock runs slower in motion or in a curved area, that time slows down there?

 

[jtbell]

How would you define "time," if not by the ticking of a (suitably idealized) clock?

 

[MeJennifer]

How would you define "time," if not by the ticking of a (suitably idealized) clock?

Well, obviously the number of ticks a clock gives per unit of time depends on its relative speed and the influence of space-time curvature.

I suppose the best we can do at the moment is measuring against a clock at rest relative to the CMB and not influenced by a gravitational field.

 

[pervect]

But are we actually measuring time here?
Can we univocally conclude that just because a clock runs slower in motion or in a curved area, that time slows down there?

In general we can't, and probably don't want to, conclude that "time slows down" at all.

Rather, in most approaches, we regard clocks as always keeping time, i.e. time is what clocks keep, just as space is what rulers measure.

We regard time dilation as being relative, i.e. "this clock runs slower than that clock". Operationally, we also usually require that there be some sort of stationary (not changing with time) path between the clocks in order to make the comparison.

Also note that curvature doesn't directly cause time dilation. Clock A, at a hollowed out spot at the center of the Earth, runs slower than clock B at infinity (when compared as above) - but (ignoring the sun, planets, and the rest of the universe for this example) space-time is flat both for clock A and for clock B.

 

[yogi]

If you want clarity on the subject, you can go back to Eddington's enlightening statement: "Length contraction is true, but its not really true."

Measurements between frames in relative motion are distorted - they are real only to the extent the measurments are real. As Pervect observes - its more of a philosophical viewpoint as to what is real - the difficultly is provoked by trying to reconcile the observed slowing of clocks in relatively moving frames (each apparently running slower than the other) and the actuality of a resultant real time difference that comes about in some experiments. (e.g., the proverbeal twin paradox).

 

[Hans de Vries]

Can we univocally conclude that just because a clock runs slower in motion or in a curved area, that time slows down there?

In SR, all physical processes (including clocks) proceed slower when moving.

Now what is the REASON? Consider the following clock:

A photon bounces back and forward between two mirrors.

It ticks and gives you a way to measure it's proper time. Let the photon
bounce on the x-axis and then let the clock move in the y-direction.
(the simplest case). The clock will now tick slower because the photon
has to follow a longer (zigzag) path. Remember? The more space is
covered the less "proper time" proceeds: ds^2=dt^2-dx^2-dy^2-dz^2

Here you have the basic reason:

All physical, chemical and biological processes go slower because more
time is required to exchange information between the constituents of
the process (the elementary particles). Regards, Hans

 

[clj4]

In SR, all physical processes (including clocks) proceed slower when moving.

Now what is the REASON? Consider the following clock:

A photon bounces back and forward between two mirrors.

It ticks and gives you a way to measure it's proper time. Let the photon
bounce on the x-axis and then let the clock move in the y-direction.
(the simplest case). The clock will now tick slower because the photon
has to follow a longer (zigzag) path. Remember? The more space is
covered the less "proper time" proceeds: ds^2=dt^2-dx^2-dy^2-dz^2

Here you have the basic reason:

All physical, chemical and biological processes go slower because more
time is required to exchange information between the constituents of
the process (the elementary particles).


Regards, Hans

The complete statement is:

In SR, all physical processes (including clocks) proceed slower when moving when viewed from another frames of reference

In your light clock example, the slowdown is as viewed from a frame of reference wrt the clock is moving with speed v. From the point of view of the frame of the clock, the time still pases at the rate of 1 second per second.

 

[jcsd]

Well if soemthign is moving then it's another refernce frame to the person who sees it moving, that's a given.

To tell the truth though it's not strictly true either as accelerated movement can make things proceed faster.

 

[MeJennifer]

In SR, all physical processes (including clocks) proceed slower when moving.

I do not disagree with you that that is what is factually happening.

However that does not seem to be the assumption in the theory of special relativity. In SR it seems that the question as to who is moving is not relevant, since the movement is considered relative.

Regardless of the assumption if movement is relative, it is clear that there must be some sort of "uncertainty" principle at works with regard to knowing if something is moving or not.

But when we consider the "twin" thought experiment, we are confronted with an asymmetrical situation.

Is there a paradox? No, but only if one assumes that the movement was not relative.

In general we can't, and probably don't want to, conclude that "time slows down" at all.

Rather, in most approaches, we regard clocks as always keeping time, i.e. time is what clocks keep, just as space is what rulers measure.

Well what you write here is confusing to me.

To me it seems that one either assumes that time is just that what clocks register or one assumes that clocks are influenced by movement and thus not always are able to accurately represent time.
So what is the position from the perspective of SR?

For instance, in SR, with regards to the "twin" thought experiment, do any of the clocks slow down and does time slow down anywere?

the difficultly is provoked by trying to reconcile the observed slowing of clocks in relatively moving frames (each apparently running slower than the other) and the actuality of a resultant real time difference that comes about in some experiments. (e.g., the proverbeal twin paradox).

So how is this resolved in the special theory of relativity. Since it asserts that the movement is relative.

 

[pervect]

What counts in the end is experimental predictions.

If you set up an experiment where one twin travels at a high velocity, accelerates and turns around, and then returns to a twin that has stayed in a single inertial frame, everyone agrees that the twin who has remained inertial has the longer elapsed time.

In a similar vein, one can say with definiteness that when one compares two clocks, one on a mountain top, and another in a valley, that the clock on the mountaintop will tick appear to tick faster when compared by light signals that have a constant propagation time. One can even have two clocks start out in a valley, carry one up to the mountain (via slow clock transport), let it sit for a while, then carry it back, and one will find that the clock that remained in the valley has less elapsed time.

Now there are a number of ways to explain this all philosphically, as long as one can get to the same conclusions in the end, one can take several different philosphical positions about what is "real" and what is "not real".

So my advice is not to worry too much when the phiolsophical parts of the answers differ. Focus on some experimental results (even thought experiments) - those are what must agree.

 

[MeJennifer]

So my advice is not to worry too much when the phiolsophical parts of the answers differ. Focus on some experimental results (even thought experiments) - those are what must agree.

First of all I am not worried and second I think it is rather stupid to tell people to stop thinking about the meaning of theories. That is just a bad educational advice IMHO!

 

[bernhard.rothenstein]

In the theory of special relativity when two observers are in relative motion with each other then each observer measures an increase in mass, a slower clock rate and a contraction of length in the other observer's frame of reference.

How are we to interpret this according to the theory of special relativity?
Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

i think that you could add to the physical quantities you mention the electric field, the magnetic field and many others which behave in the same way and special relativity becomes involved when two observers in rtelative motion measure the same physical quantity say the reading of the same clock, the mass of the same bullet, the electric field generated by the same electric charge...and as long as we do not take into account Heisenberg, the measurements performed in one of the reference frames does not influence the results of the measurements performed in the other one
sine ira et studion

 

[yogi]

First of all I am not worried and second I think it is rather stupid to tell people to stop thinking about the meaning of theories. That is just a bad educational advice IMHO!

I think Pervect is saying - ultimately the correct theory must fit the facts - in the meantime we have different theories and can only determine which is true when every conceivable test has been completed. Example - when Einstein first published SR in 1905 he was willing to combine a theory based upon apparent observatiions in relatively moving frames to arrive at a result where one clock had accumulated more time than the other when they were compared in the same frame...it was a direct consequence of the arithmetic and the invariance of the spacetime interval - one clock had been put in motion so that it traveled in the rest frame of the other (the traveling clock experienced both a spatial and temporal distance, whereas the rest clock only experienced a temporal excursion). Later in 1918 he wrote another paper attempting to reconcile time dilation (the traveling twin lost time) with GR by inroducing the notion of pseudo gravitational field that whould give the correct answer based upon the turn-around acceleratin field - so you have a group of authors following that line of reasoning (Max Born, Ron Lederman and some others) claiming GR is needed to explain the twin paradox. The interesting fact is that both formulations give the correct result for the actual time difference.

 

[pervect]

First of all I am not worried and second I think it is rather stupid to tell people to stop thinking about the meaning of theories. That is just a bad educational advice IMHO!

You are missing the point. The object is to think about the matter deeply enough to realize what differences are important, and what differences are not important - not to stop thinking.

There are a lot of questions that may appear at first glance to be important, perhaps even vital, but have no testable consequences. As long as one is positive that there are not testable consequences, one is free to adopt either viewpoint in such cases. People being people, different people will make different assumptions in such cases. When there are no testable consequences, arguing about "who is right" is just a pointless exercise.

Differing philosophical assumptions are often a barrier to communications, in spite of the fact that they don't have any testable consequences. One might wish that everyone had the same philosophy, but it just isn't going to happen.

Basically, arguing over untestable philosphical questions is a lot like arguing about religion - it's a waste of time.

I would suggest that the optimum point of view is to try to understand as many different way of looking at a problem as possible. While they may all be ultimately equivalent in terms of result, sometimes finding solutions to a specific problem or coming up with alternate theories is simpler using one viewpoint than another.

 

[MeJennifer]

In SR, all physical processes (including clocks) proceed slower when moving.

Now what is the REASON? Consider the following clock:

A photon bounces back and forward between two mirrors.

It ticks and gives you a way to measure it's proper time. Let the photon
bounce on the x-axis and then let the clock move in the y-direction.
(the simplest case). The clock will now tick slower because the photon
has to follow a longer (zigzag) path. Remember? The more space is
covered the less "proper time" proceeds: ds^2=dt^2-dx^2-dy^2-dz^2

Here you have the basic reason:

All physical, chemical and biological processes go slower because more
time is required to exchange information between the constituents of
the process (the elementary particles).


Regards, Hans

Again I completely agree with you. But that reason is not derivable from the theory of special relativity.

While any Lorentz based theory would make such a conclusion, SR only "concludes" that because of the postulate of the constancy of light. Seems like a clear case of mixing up cause and effect!

To me it seems straight forward that in absolute space and time any object that moves will encounter a length contraction and a slowing down of all clocks simply because it moves in relation to the electromagnetic waves! Not magic, no paradoxes and no relativity here.

But that is not the approach in SR at all, the approach in SR is the postulate of the constancy of light, which was supposedly proven by the MM experiment. An experiment that simply measures the roundtrip time of light not the one way time.
It is like saying you proved that a cyclist who goes from A to B and back with a strong head wind in the B direction takes just as much time in each direction because the combined speed is equal to the combined speed if there were no wind in the first place.

 

[jcsd]

That reason is derivable from special relativity, it is a result of the principle of relativity (the first postulate of special relativity). If physical processes (and therefore chemcial and bilogical process as they are at their most basic level physical processes) proceed differently in different inertial frames this would be in contradiction of the principle of relativity.

 

[MeJennifer]

That reason is derivable from special relativity, it is a result of the principle of relativity (the first postulate of special relativity). If physical processes (and therefore chemcial and bilogical process as they are at their most basic level physical processes) proceed differently in different inertial frames this would be in contradiction of the principle of relativity.

The twin experiment is a proof that physical processes go slower in a frame that is moving. Furthermore they go slower as well when there is a gravitational field.

 

[clj4]

Again I completely agree with you. But that reason is not derivable from the theory of special relativity.

While any Lorentz based theory would make such a conclusion, SR only "concludes" that because of the postulate of the constancy of light. Seems like a clear case of mixing up cause and effect!

To me it seems straight forward that in absolute space and time any object that moves will encounter a length contraction and a slowing down of all clocks simply because it moves in relation to the electromagnetic waves! Not magic, no paradoxes and no relativity here.

But that is not the approach in SR at all, the approach in SR is the postulate of the constancy of light, which was supposedly proven by the MM experiment. An experiment that simply measures the roundtrip time of light not the one way time.
It is like saying you proved that a cyclist who goes from A to B and back with a strong head wind in the B direction takes just as much time in each direction because the combined speed is equal to the combined speed if there were no wind in the first place.

Are you aware that in ADDITION to MMX type of experiments which test average light speed there is a whole class of experiments that have tested the light speed isotropy?
So, sorry , buddy, relativity is build on the very strong foundation, the attack " yes, you are measuring two ways and you are averaging different numbers to come up with c" is not going to work. Try selling "aetherists" concepts on other websites, not here.

 

[clj4]

The twin experiment is a proof that physical processes go slower in a frame that is moving. Furthermore they go slower as well when there is a gravitational field.

Nonsense. The clocks run at the rate of 1 sec per sec in all systems. You are misrepresenting relativistic time dilation. There were hundreds of demonstrations based on Minkowski diagrams of the twin paradox that absolutely contradict what you just said. I am sure pervect will be more than happy to send you one.