Lorentz Contraction ?s and Implication

[Apophenia]

Unfortunately, my knowledge on this is limited to wiki which I trust is relatively correct but I would like to clear up some ambiguity. (I don't mind technical but please back it up with a general explanation since I am completely new to this. The general explanations I value more.)

Wiki quote: "In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer."

I read the first statement in wiki and already have questions. Now it says "detected by an observer of the object". Is this saying it is merely an observer effect, i.e., the object only contracts apparent to the observer who is seeing it with relative velocity; the object relative to itself does not contract?

If in fact Lorentz contraction states that an object actually shortens:
Is the general explanation that space is the introduced substance that contracts with the implication that the object shortens without changing it's internal material characteristics (other than space if that is considered an intrinsic property of matter)?

 

[PAllen]

A measures B to contract; B measures A to contract. Which is real? Only plausible answers are both or neither (there are reputable advocates of both positions, with the difference being, in part, the lack of definition of 'real'). I have the feeling you want to pick the illogical answer that one is real and the other is not.

 

[tiny-tim]

Hi Apophenia!

Now it says "detected by an observer of the object". Is this saying it is merely an observer effect, i.e., the object only contracts apparent to the observer who is seeing it with relative velocity; the object relative to itself does not contract?

The object relative to itself does not contract.

Its length is measured (this is a better word than "detected") by any observer with a different velocity, as being shorter.

The example I like best is a train moving past two barriers.

The barriers are 100 metres apart, and they sweep down simultaneously (as seen by a stationary observer) so as to just miss the front and back of the train (at the same time).

So the stationary observer measures the train as being 100 metres long!

(The train is in fact slightly longer, say 101 metres, but its length is measured as contracted)

But the driver measures the train as 101 metres (not contracted),

and he measures the distance between the barriers as 99 metres (contracted) …

so how can the 101m train fit between the 99m barriers??

Because the driver measures time differently … the further away something is, the earlier the time is (compared with the stationary observer) …

in particular, the driver measures the front barrier as always lower than the rear barrier …

so by the time the rear barrier comes down, the rear of the train has had enough extra time to just sneak in under it!

 

[danR]

Lorentz regarded the contraction as real, and involving a literal 'decrease' in the space between atoms.

This is not the modern picture, and in fact it is meaningless to talk about length contraction. What is decreasing is the measure of the length, as far as an observer moving at a different velocity from the object is concerned, is able to measure it.

Edit: these guys got ahead of me. Disregard what I wrote. Unless it is usefully simpler (and approximately accurate).

 

[Apophenia]

A measures B to contract; B measures A to contract. Which is real? Only plausible answers are both or neither (there are reputable advocates of both positions, with the difference being, in part, the lack of definition of 'real'). I have the feeling you want to pick the illogical answer that one is real and the other is not.

"...both or neither"...I have a feeling to pick neither actually. So how would a reputable advocate of saying it neither is real explain himself while remaining within the bounds of generally accepted science? or within the bounds of recognized scientific speculation? I would define real as the object actually experiencing a contraction; a relativity of actual form not a relativity of the perception of form (measurement). If that is not what they mean by neither or real then please explain. Thanks PAllen.

Hi Apophenia!

The object relative to itself does not contract.

Its length is measured (this is a better word than "detected") by any observer with a different velocity, as being shorter.

The example I like best is a train moving past two barriers.

The barriers are 100 metres apart, and they sweep down simultaneously (as seen by a stationary observer) so as to just miss the front and back of the train (at the same time).

So the stationary observer measures the train as being 100 metres long!

(The train is in fact slightly longer, say 101 metres, but its length is measured as contracted)

But the driver measures the train as 101 metres (not contracted),

and he measures the distance between the barriers as 99 metres (contracted) …

so how can the 101m train fit between the 99m barriers??

Because the driver measures time differently … the further away something is, the earlier the time is (compared with the stationary observer) …

in particular, the driver measures the front barrier as always lower than the rear barrier …

so by the time the rear barrier comes down, the rear of the train has had enough extra time to just sneak in under it!

Just to be certain I understand correctly: the phenomenon is proposed to be a relativity of measurement not a relativity of actual matter? The barrier distance is relative to the observer but in some absolute sense (if it can be taken) the barriers are only one distance?

Also the relativity of measurement is independent of the perception of light? Light takes time to travel so if the observer relies on information observed from light emitted by barriers he would have to take that into consideration. That's a specific example, but I am fairly certain what you and it suggests is that the information is instantly observed (by whatever means), correct?

Thanks Tiny-Tim

 

[1977ub]

If A uses logic and light beams to come to conclusions that various events removed from him spatially are simultaneous with certain things happening to him where he is, then one aspect (feature? bug?) of this decision is that B, moving relative to him will be decided - again using his method of determining lengths and distances - to be shortened and with a slower clock. And B, using this same idea of remote simultaneity aka inertial reference frame - will come to a similar conclusion about A. If we understand nothing else from this, we must understand that contrary to the classical view, A & B won't decide that the same events are simultaneous, and won't decide that all clocks move at the same rate. If we reject this appealing idea of the inertial reference frame where certain things at a distance are simultaneous with events where we are, then we don't have to worry about contracting rods or slowing clocks...

 

[Nugatory]

Just to be certain I understand correctly: the phenomenon is proposed to be a relativity of measurement not a relativity of actual matter?

Neither. It's a relativity of simultaneity. How do you define the length of an object? It's easy if it's at rest relative to you - you find one end, you find the other end, and then you measure the distance between them. But if it's moving relative to you, then it's harder because the first end won't stay put while you're finding the other end and measuring. Instead, you have to find the positions of both ends at the same time (tinytim's gates serve that purpose, or if you had a long line of stationary observers standing along its path, you could ask whoever finds an end of the object passing by them at exactly noon to raise their hand); now you have two points that are rest so you can measure the distance between them.

But the length that you measure depends on the claim that two events (front of object here, rear of object there) were simultaneous. Different observers moving at different speeds relative to each other will disagree about the simultaneity of events and therefore the location of the endpoints of the distance being measured.

If you haven't already done so, you might want to google for the "pole-barn paradox"

 

[1977ub]

If the train has clocks at either end with little ink stamps attached, and if the gates that come down each give a little 'smack' to the end of the train, and someone on the train is confident that all clocks on the train are synchronized, then the times that get tattooed on the gates will be different. When someone at the station says "we just proved that your train is shorter" someone in the train will point to the times stamped on the gates and say "no way, the rear gate smacked the back end of the train much later than the front gate smacked the front end!"

 

[Nugatory]

Also the relativity of measurement is independent of the perception of light? Light takes time to travel so if the observer relies on information observed from light emitted by barriers he would have to take that into consideration.

Yes. Time dilation and length contraction is what's left over after we've allowed for light-travel time. For example... When my clock reads zero someone passes me at .5c, and as he passes I notice that his clock also reads zero. I keep watching his clock as it moves away, so after 6 seconds I see the light that left his clock when he had been traveling for 4 seconds and was 2 light-seconds away. I see this clock reading when my clock reads 6 seconds, and I say to myself "aha - that's what his clock said when my clock said 4, because it took the light 2 seconds to get to me and my clock says 6 now". Time dilation says that the time I see on his clock won't be 4 seconds, but some smaller value.

 

[bobc2]

...Wiki quote: "In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer."

I read the first statement in wiki and already have questions. Now it says "detected by an observer of the object". Is this saying it is merely an observer effect, i.e., the object only contracts apparent to the observer who is seeing it with relative velocity; the object relative to itself does not contract?

The problem in answering your questions directly is that the so-called Lorentz ether theory (LET) has been modified a few times from the late 1880's until after Einstein's 1905 special relativity theory (SR).

Going back to the early Lorentz theory, the answer is that an object in motion actually physically shortens in the direction of motion. This was not just an "apparant" effect; the contraction was physically real (although an observer moving with the object, carrying his measuring stick, would not detect the contraction, because he and his measuring stick were also contracted). This was considered a result having to do with electromagnetic interaction times among the particles making up the object. Accordingly, an object at rest would not contract.

In current Lorentz ether theory even an object at rest in ether would be observed by an observer in motion to have contracted, simply because that's the way the final mathematics worked (having been applied in this manner to agree with physical observations, lab experiments, and thought-experiment results). For observers A and B in motion with respect to each other, A sees B as contracted and B sees A as contracted. Thus, ether is no longer compatible with LET (at least as related to the cause of contraction). The contraction observed for either A to B or B to A is the same effect as is manifest with special relativity theory. Einstein emphasized the equivalence of observers, that no one frame of reference is preferred over another. Thus, there is now no difference in the application of the Lorentz (actually, Poincare') transformations between LET and SR. They are now the same theory. There is no longer any point in arguing over which theory is to be preferred--they are the same theory. However, everyone acknowledges that Einstein enhanced the theory in a most dramatic and convincing fashion and identified a number of significant implications of the theory, resulting in it being identified for all time as Einstein's theory of special relativity. As Wolfgang Rindler put it, "...ether theory eventually disappeared into oblivion."

Poincare' continued to embrace the concept of ether, however (not as needed for contraction, but rather as needed as a medium for electromagnetic waves to wave in, i.e., travel in). But, with the modern mathematical basis and usage, the question of whether there is an ether is no longer relevant to LET. If one wishes to have an ether, he should develop a new theory separate from LET/SR to accommodate that concept. And of course it would have to include aspects to account for the same special effects we are familiar with in SR.

 

[Dale]

So how would a reputable advocate of saying it neither is real explain himself while remaining within the bounds of generally accepted science?

There isn't a standard scientific definition of "real", so all you have to do is to define it to make length contraction unreal. One easy way to do that is to say that a necessary condition for something to be "real" is that it must be frame invariant.

I tend to not worry much about such questions. They hinge entirely on the definition of "real", and without a standard scientific definition such discussions always devolve into either a shouting match or a semantic debate.

 

[Apophenia]

Neither. It's a relativity of simultaneity. How do you define the length of an object? It's easy if it's at rest relative to you - you find one end, you find the other end, and then you measure the distance between them. But if it's moving relative to you, then it's harder because the first end won't stay put while you're finding the other end and measuring. Instead, you have to find the positions of both ends at the same time (tinytim's gates serve that purpose, or if you had a long line of stationary observers standing along its path, you could ask whoever finds an end of the object passing by them at exactly noon to raise their hand); now you have two points that are rest so you can measure the distance between them.

But the length that you measure depends on the claim that two events (front of object here, rear of object there) were simultaneous. Different observers moving at different speeds relative to each other will disagree about the simultaneity of events and therefore the location of the endpoints of the distance being measured.

If you haven't already done so, you might want to google for the "pole-barn paradox"

Ok, I think I have some sort of grasp on what you are referring to from the train-and-platform with light emitting source thought experiment in this:

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

Im sorry if I seem to be ignoring what you reference but I looked at it and I could not understand what it was trying to convey; to be honest it all seemed like semantics but I found the train/platform helpful.

I think for one to understand you have to think of light being constant in all frames. For the train-platform though experiment, and correct me if I am wrong, the motion of the emitting light source does not matter since we are saying c is constant in all frames; or specifically in the thought experiment the lack of motion of the emitting source. I don't quite understand how that translates to a relativity of simultaneity (it seems that it is merely a definition to say there can be simultaneity in an absolute sense) but I understand that the observation of light compared to the train car is relative between observers on the car and on the platform precisely because a difference between the emitting source velocity and train velocity does not affect the speed of light.

If light did not behave constant in all reference frames what would this imply in relation to what is discussed on this thread and the relativity of simultaneity?

Say light traveling through a vacuum is actually something like terminal velocity for an object traveling through air. If you have source with a given velocity v' emit the object at it's terminal velocity vt. The total velocity vt+v' would quickly diminish to vt. and because objects in the universe travel at far less the speed of light the emitting sources speed is a very small diminishing factor; it would diminish rather quickly or seemingly instantaneously to c. Actually, considering the nothingness of a vacuum has mass and energy (postulated virtual particles - ) it would not seem that far fetched although it is speculation. Depending on how quickly it diminishes it should be verifiable though so the speculation is probably all bogus. Anyway, what would a non constant c imply in any manifestation?

 

[Apophenia]

There isn't a standard scientific definition of "real", so all you have to do is to define it to make length contraction unreal. One easy way to do that is to say that a necessary condition for something to be "real" is that it must be frame invariant.

I tend to not worry much about such questions. They hinge entirely on the definition of "real", and without a standard scientific definition such discussions always devolve into either a shouting match or a semantic debate.

Yeah, good point; I agree with you for the most part.

But I do think asking whether or not the object is implied to "physically contract by whatever means" (meaning contract atomic or spatially or whatever the object is reducible to) in a relative frame is 100% scientifically valid and testable although directly measuring something like that seems an impossible feat. Does it really contract (to an observers frame)? That's what I would define as real.
There should not be a relativity of objectivity unless of course you acknowledge there is no truth or objectivity.

 

[Nugatory]

I think for one to understand you have to think of light being constant in all frames. For the train-platform though experiment, and correct me if I am wrong, the motion of the emitting light source does not matter since we are saying c is constant in all frames; or specifically in the thought experiment the lack of motion of the emitting source.

That's right. This is one of the two postulates of special relativity (I expect that by now you've found Einstein's 1905 paper - if not, do a google search for "The electrodynamics of moving bodies"); it is very strongly hinted at by Maxwell's equations; and it is very strongly suggested by a number of negative results of experiments that try to measure variation in the speed of light.

I don't quite understand how that translates to a relativity of simultaneity (it seems that it is merely a definition to say there can be simultaneity in an absolute sense) but I understand that the observation of light compared to the train car is relative between observers on the car and on the platform precisely because a difference between the emitting source velocity and train velocity does not affect the speed of light.

You can't construct an internally consistent set of coordinate transforms that both maintain a constant speed of light and that allow us to say that all observers will agree about the simultaneity or not of the emission and absorption times of light signals. That's basically how the constant speed of light "translates to" (I would prefer to say "drives us, through counterintuitive but inexorable logic, to") relativity of simultaneity.

It's worth noting that although popular treatments of relativity tend to focus on time dilation, length contraction, and other gee-whiz cool stuff, the relativity of simultaneity is the more fundamental effect.

If light did not behave constant in all reference frames what would this imply in relation to what is discussed on this thread and the relativity of simultaneity?

We'd have a very different physics, and depending on exactly what non-constant behavior you have in mind we might be able to salvage the notion of absolute time and non-relative simultaneity. We'd also have a theory that dismally fails to match an amazing amount of experimental data.

Say light traveling through a vacuum is actually something like terminal velocity for an object traveling through air. If you have source with a given velocity v' emit the object at it's terminal velocity vt. The total velocity vt+v' would quickly diminish to vt. and because objects in the universe travel at far less the speed of light the emitting sources speed is a very small diminishing factor; it would diminish rather quickly or seemingly instantaneously to c. Actually, considering the nothingness of a vacuum has mass and energy (postulated virtual particles - ) it would not seem that far fetched although it is speculation. Depending on how quickly it diminishes it should be verifiable though so the speculation is probably all bogus. Anyway, what would a non constant c imply in any manifestation?

Now you're goading the moderators again
But seriously, kidding aside:
1) If the time that takes for this hypothetical faster-than-c speed to decay down to c is small enough that we can't detect it and it seems as if light instantaneously reaches the speed c... A bit of slicing with Occam's razor says we might as well construct our theories as if the speed of light is always c. We're going to be stuck with the counterintuitive but experimentally confirmed predictions of special relativity anyways.
2) We already have a perfectly good, mathematically sound, and solidly experimentally validated theory of electromagnetism that way predates relativity: Maxwell's theory. And this theory predicts electromagnetic radiation traveling in a vacuum at speed c; indeed, the problem that Einstein solved was how to reconcile this theory with our intuition about how time and space should behave.

Between #1 and #2, and the total lack of conflicting experimental evidence, I'm happy with the postulate that the speed of light in vacuum is constant.

3) In another thread recently, I said that if someone is talking to you about "virtual particles" and not also showing you a page full of equations... They're oversimplifying enough that you shouldn't be building any new ideas on that foundation.

 

[DrewD]

I think you have to say that it is real even though it may be impossible to "directly measure" in the way that you could measure the length of something at rest wrt you.

The example that help make it click for me was muon decay. There was an experiment done (I think many times) that confirmed the predictions of time dilation. In a very quick synopsis, more muons reach sea level than would be expected given the speed they are traveling and the life time of a muon. It seems then that the muon's "clock" ticks more slowly when they are moving.

That doesn't directly relate to you issue with length contraction, but think about it from the muon's point of view. The distance between wherever they originate in space and sea level would seem unattainable to a stationary muon. However, when one is moving near the speed of light the distance is shorter and the reality of that change can be seen by the fact more muons can make it across that distance before they decay.

Perhaps invoking strange particles isn't a helpful way to think about it, but this for me sealed the deal. This is not just a thought experiment. This is a real thing that happens constantly that shouldn't happen if length contraction were just an illusion.

 

[Nugatory]

But I do think asking whether or not the object is implied to "physically contract by whatever means" (meaning contract atomic or spatially or whatever the object is reducible to) in a relative frame is 100% scientifically valid and testable although directly measuring something like that seems an impossible feat. Does it really contract (to an observers frame)? That's what I would define as real.

You've seen mfb's observations about the muon decay measurements. It's easy enough to explain these from the standpoint of the observer at rest relative to Earth's atmosphere by saying that time is running slow for the moving muon. But from the muon's point of view... It seems real enough that the muon traversed the Earth's atmosphere, and it wouldn't have lived long enough to do that if 100-odd kilometers it passed through weren't contracted.

 

[Apophenia]

Now you're goading the moderators again
But seriously, kidding aside:

I apologize for this. I understand PF is here for more of a learning tool but I find it impossible in my own character to avoid bringing thought out. Einstein would agree with me here although I think he would want to "destroy" me in general. haha

Occam's razor also suggests NO! to string theory, multiverse, and other ad hoc science to reconcile quantum anomalies that people actually get PAID FOR STUDYING! i do agree with it on a NO for string theory in particular though. Haha.

As for the virtual particles; I don't recognize that as objective fact but there is currently a limit and maybe a definite limit on the potential of what we can observe. that's why scientists make ad hoc in the first place otherwise let's "microscope "empty" space"! I think you get what I am saying; speculation is necessary sometimes. I am not genius enough with mathematics or intuition of the universe to accomplish what is essentially a Newton or einstein so unfortunately I can only use limited intuition; not pages of mathematics. Ad hoc is intuitive though.As for the light in ether stuff:

Einstein reduces to Newton on small velocities; btw can anyone show me the equation for this; and point to where the term (im assuming a relative velocity over the speed of light... to some effect) drops out.

An absolute frame with that variable light can reduce to Einstein with essentially all if not most velocities. The nitpicking here is for truth not the practicality of mathematical models of the universe.In response to the Maxwell statements, I read this on another forum from a gold member:

"Maxwell's equations do not predict that the speed of light is the same in every frame of reference."
So, Maxwell predicts speed c in a vacuum but not a constant speed in all frames it seems.

From Mattson, but he goes on to say why (not trying to take his words out of context).
https://www.physicsforums.com/showthread.php?t=30922

 

[Apophenia]

You've seen mfb's observations about the muon decay measurements. It's easy enough to explain these from the standpoint of the observer at rest relative to Earth's atmosphere by saying that time is running slow for the moving muon. But from the muon's point of view... It seems real enough that the muon traversed the Earth's atmosphere, and it wouldn't have lived long enough to do that if 100-odd kilometers it passed through weren't contracted.

Wouldnt that have more to do with gravitational time dilation not Lorentz contraction?
Lorentz contraction I guess would be implied through the atmosphere (distance muon must travel) being contracted?

When discussing these phenomenon I think its easier to separate them; i.e., measure GTD with a stationary clock. If I want to talk strictly of Lorentz contraction then I would want to separate the object from a gravitational source.

Are there predictions saying look: the muons considering only GTD would hit the Earth in this amount but if it were GTD + Lorentz contraction then it would be a greater amount that we predict by this number. <- supported by data. Basically, is the data quantitative as well as qualitative?

 

[nitsuj]

Yeah, good point; I agree with you for the most part.

But I do think asking whether or not the object is implied to "physically contract by whatever means" (meaning contract atomic or spatially or whatever the object is reducible to) in a relative frame is 100% scientifically valid and testable although directly measuring something like that seems an impossible feat. Does it really contract (to an observers frame)? That's what I would define as real.
There should not be a relativity of objectivity unless of course you acknowledge there is no truth or objectivity.

It is a really good point Dalespams mentions.

Reducing the size of the contracting object (to atoms as you mention) just shifts the issue to said object (atoms / space / what have you).

It wouldn't clarify the "realness" of length contract, read about invariants, try to understand why Dalespam considers invariant measurements more "real" than those performed which highlight relativity of simultaneity.

to help clarify more about length contract, look for the scenario that describes two ships traveling / accelerating at the same speed attached by a string.

as the ships approach c and length contraction becomes remarkable, what happens to the string and what are the perspectives (explanations) of the observers on both ships. It's a good scenario and for me highlighted that length contraction is not "within" spacetime, but merely orientation of how the dimensions are defined, which more specifically is conventionality of simultaneity.

relativity of simultaneity is kinda strange, but learning about it in conjunction with spacetime diagrams (focusing on how simultaneous is defined by the diagram) helps becoming familiar ( & comfortable with) length contraction.

 

[Dale]

But I do think asking whether or not the object is implied to "physically contract by whatever means" (meaning contract atomic or spatially or whatever the object is reducible to) in a relative frame is 100% scientifically valid and testable although directly measuring something like that seems an impossible feat.

You seem to have some sort of obsession with using vague and undefined terms like "real" and "physical". There is no need to do that here. The term "length" is well-defined with standard experiments to measure it. Those experiments are scientifically valid and testable.

Does it really contract (to an observers frame)? That's what I would define as real.

Another terrible definition. My personal recommendation to you: stick with well defined terms, if you cannot ask a question without using undefined terms then don't ask the question since it is literally nonsense.

Personally, I don't see what is the big deal. We already know that there are many very useful quantities which are frame-variant. Velocity, momentum, energy, etc. It turns out that length is one such quantity.

 

[Dale]

"Maxwell's equations do not predict that the speed of light is the same in every frame of reference."
So, Maxwell predicts speed c in a vacuum but not a constant speed in all frames it seems.

Maxwell's equations do predict that the speed of light is c in every frame in which they are valid. In order to get a different prediction you have to add a frame-dependent modification to Maxwell's equations that is not there currently.

 

[1977ub]

Does it really contract (to an observers frame)?

To claim an object has a particular length, you need to choose a frame first. Whichever frame you choose will determine the length you end up with. That's doubly true if there are any factors which lead an object to morph or change its shape. You might even decide that length itself is a mathematical side-effect and not "real" ... ?

 

[tiny-tim]

Hi Apophenia!

Just to be certain I understand correctly: the phenomenon is proposed to be a relativity of measurement not a relativity of actual matter? The barrier distance is relative to the observer but in some absolute sense (if it can be taken) the barriers are only one distance?

i gave you two (different) measurements of the distance between the barriers, one for each observer

Also the relativity of measurement is independent of the perception of light? Light takes time to travel so if the observer relies on information observed from light emitted by barriers he would have to take that into consideration. That's a specific example, but I am fairly certain what you and it suggests is that the information is instantly observed (by whatever means), correct?

yes, if he is measuring by using light (eg by looking), then he has to take the speed of light into account in judging simultaneity (or he could just stand exactly in the middle, so it didn't matter)

(that gives the same result as if he could measure instantaneously)

… I found the train/platform helpful.

I think for one to understand you have to think of light being constant in all frames. For the train-platform though experiment, and correct me if I am wrong, the motion of the emitting light source does not matter since we are saying c is constant in all frames; or specifically in the thought experiment the lack of motion of the emitting source. I don't quite understand how that translates to a relativity of simultaneity (it seems that it is merely a definition to say there can be simultaneity in an absolute sense) but I understand that the observation of light compared to the train car is relative between observers on the car and on the platform precisely because a difference between the emitting source velocity and train velocity does not affect the speed of light.

If light did not behave constant in all reference frames what would this imply in relation to what is discussed on this thread and the relativity of simultaneity?

forget about the speed of light being constant

all you need to know is that simultaneity is relative …

ie, what is simultaneous for one observer is not simultaneous for another

Einstein reduces to Newton on small velocities; btw can anyone show me the equation for this; and point to where the term (im assuming a relative velocity over the speed of light... to some effect) drops out.

if c = ∞, then √(1 - v²/c²) = 1,

and so the lorentz transformaion becomes:

x' = x - vt
t' = t​

which is Newtonian

 

[Naty1]

Getting your head around the ideas of relativity takes some time and some new ways of thinking. I try to keep a few basic ideas in mind:

For special relativty: [flat spacetime]

What you and I observe is in general not identical even if we are very close together!

Local time always ticks at the same constant rate.

Light is always measured at 'c'...both locally and distant.

Time [clock rates] and observed distance between different observers [moving at relative velocities] vary.

So: light speed is a constant, time and distance are not.

So for example, if I am sitting here typing and you go whizzing by at a speed which is a significant proportion of 'c', we each observe the other's clock ticking slower and see each other foreshortened along the direction of motion.

//////////
In general relativity, not only the relative speed from SR but relative gravitational potential also affects clock rates. So the above rules require some modification.

 

[Nugatory]

Wouldnt that have more to do with gravitational time dilation not Lorentz contraction?

No. The gravitational time dilation between 4000 miles away from the center of the Earth (that is, the surface of the earth) and 4100 miles away is a second or so per century. The time dilation and length contraction effect for a particle moving near the speed of light are many billions of times greater, and that's what we're seeing with muon measurements.

The gravitational time dilation in these experiments is completely unmeasurable.

Lorentz contraction I guess would be implied through the atmosphere (distance muon must travel) being contracted?

Yes. Earth-bound observer sees a time-dilated slowly-aging muon living long enough to make it through one hundred uncontracted miles; Muon-riding observer sees a non-time-dilated muon living a normal undilated shorter life as it covers a contracted distance.

 

[Apophenia]

It's a good scenario and for me highlighted that length contraction is not "within" spacetime, but merely orientation of how the dimensions are defined, which more specifically is conventionality of simultaneity.

relativity of simultaneity is kinda strange, but learning about it in conjunction with spacetime diagrams (focusing on how simultaneous is defined by the diagram) helps becoming familiar ( & comfortable with) length contraction.

I seem to be getting confilicting views from some of you guys although it may just be interpretation. It makes sense to me when you put it "merely an orientation of how dimensions are defined".

You seem to have some sort of obsession with using vague and undefined terms like "real" and "physical". There is no need to do that here. The term "length" is well-defined with standard experiments to measure it. Those experiments are scientifically valid and testable.

Another terrible definition. My personal recommendation to you: stick with well defined terms, if you cannot ask a question without using undefined terms then don't ask the question since it is literally nonsense.

Personally, I don't see what is the big deal. We already know that there are many very useful quantities which are frame-variant. Velocity, momentum, energy, etc. It turns out that length is one such quantity.

I think I alluded to what I refer as real multiple times in relation to Lorentz contraction. Very straightforward question would be: does it affect particles? The muon reply would seem to answer some of that. That is the simplest way I can put it. If that is open to semantics than I don't know how to ask what I want to. I understand completely why the issue may not matter to the macroscopic result but am intently curious and think any scientist should be.

However, like "nitsuj" was saying if it is a relativity of dimension definition then I suppose the question itself which I am asking does not make sense. Which I am fine with.

 

[Apophenia]

No. The gravitational time dilation between 4000 miles away from the center of the Earth (that is, the surface of the earth) and 4100 miles away is a second or so per century. The time dilation and length contraction effect for a particle moving near the speed of light are many billions of times greater, and that's what we're seeing with muon measurements.

The gravitational time dilation in these experiments is completely unmeasurable.

Yes. Earth-bound observer sees a time-dilated slowly-aging muon living long enough to make it through one hundred uncontracted miles; Muon-riding observer sees a non-time-dilated muon living a normal undilated shorter life as it covers a contracted distance.

Ok, right. I seemed to forget the muon is traveling near c!

Would the Earth bound observer also potentially see the muon with contracted dimensions if somehow possible?

 

[Dale]

I think I alluded to what I refer as real multiple times in relation to Lorentz contraction. Very straightforward question would be: does it affect particles? The muon reply would seem to answer some of that. That is the simplest way I can put it.

Rather than try to categorize length contraction as either "real" or "physical" or not I tend to simply describe its characteristics and leave it at that. So I would say:

"Length is a measurable, frame variant quantity"

That avoids the inherent problems with using poorly defined categories. Furthermore, the "measurable, frame variant" category is filled with useful things such as: velocity, energy, momentum, duration, force, power, electric fields, magnetic fields, pressure, etc. So even if I cannot say that it is "real" or "physical" I can feel comfortable using it in physics since I recognize the value of many of the other quantities in the same category.

 

[Apophenia]

Rather than try to categorize length contraction as either "real" or "physical" or not I tend to simply describe its characteristics and leave it at that. So I would say:

"Length is a measurable, frame variant quantity"

That avoids the inherent problems with using poorly defined categories. Furthermore, the "measurable, frame variant" category is filled with useful things such as: velocity, energy, momentum, duration, force, power, electric fields, magnetic fields, pressure, etc. So even if I cannot say that it is "real" or "physical" I can feel comfortable using it in physics since I recognize the value of many of the other quantities in the same category.

I understand you and regardless of how it seems I would agree 100% on "feel comfortable using it". We know it works as far as are experimental precision suggests; I would use it !The main thing that particularly bothers me (take the muon traveling through atmosphere case):
Again I may just be looking at it the wrong way but these are how I see the possibilities of what it infers with LC:

The mindless constituents of the muon seemingly "know" they are traveling at a speed v and the dimensions of atmospheric space ahead of them should contract.

How do we describe know? The only scientific answer would seem to be a mechanistic approach,i.e., particle interaction (in whatever process). I do think a micro view of everything explains more completely everything macro.

Just something to think about, but it should be thought about and much more so than string theory. come on.

 

[Nugatory]

Ok, right. I seemed to forget the muon is traveling near c!

Would the Earth bound observer also potentially see the muon with contracted dimensions if somehow possible?

See the digression below, but to answer the question I think you're trying to ask...

There is no remotely practical way to observe the diameter of a muon: What could we build the ruler out of? The thing is (enormously) smaller than the atoms that we use to build measuring devices out of, far smaller than the wavelength of the light that we might use to observe it, and the thing is so small that quantum mechanical effects get in the way... It would make as much sense to drive an automobile back and forth over a grain of sand in an attempt to read its size off of the car's odometer.

If it were not a muon coming down at relativistic velocities, but instead some macroscopic object, then yes, it would appear contracted to the earth-bound observer.

Of course no one has any experience with macroscopic objects moving at relativistic velocities. An ordinary meter stick moving at a speed sufficient to produce a five-fold contraction would hit the Earth like a 100 megaton hydrogen bomb (I did the calculation in my head - if I'm way off some other reader will correct me, but it's a big explosion in any case) and flatten every building and tree for tens of miles around. This is why we don't/can't do direct length contraction experiments with macroscopic objects.

(Digression: You are typing too quickly, as your question has the same logical structure as "Would the earth-bound observer also potentially see X if seeing X were somehow possible?", and the answer to that is clearly, tautologically, and unhelpfully "yes" for just about any X no matter how absurd.)

 

[PAllen]

(I did the calculation in my head - if I'm way off some other reader will correct me, but it's a big explosion in any case)

A cute rule to know that I've checked very carefully, is that for gamma factor k, each gram of matter has KE equivalent to 20 kilotons (= 1 Nagasaki atom bomb) per k. So for gamma of 5, that is 100 kilotons TNT per gram. Perhaps 1 kg (which would leag to 100 megatons) is a bit heavier than the average meter stick.

 

[Nugatory]

A cute rule to know that I've checked very carefully, is that for gamma factor k, each gram of matter has KE equivalent to 20 kilotons (= 1 Nagasaki atom bomb). So for gamma of 5, that is 100 kilotons TNT per gram. Perhaps 1 kg (which would lead to 100 megatons) is a bit heavier than the average meter stick.

I assumed 1KG for the mass of the meter stick - a bit heavy as you say, but easy to calculate with because I also selected the gamma factor of 5 to make it easy to work with 1MT=5x10¹⁵ Joules (easy to remember after you've said it fast a few times - "5-10-15").

But I think I should have chosen gamma=6 because the rest mass of the meter stick is rather broadly redistributed but doesn't convert to energy?

 

[Apophenia]

See the digression below, but to answer the question I think you're trying to ask...
If it were not a muon coming down at relativistic velocities, but instead some macroscopic object, then yes, it would appear contracted to the earth-bound observer.

Of course no one has any experience with macroscopic objects moving at relativistic velocities. An ordinary meter stick moving at a speed sufficient to produce a five-fold contraction would hit the Earth like a 100 megaton hydrogen bomb (I did the calculation in my head - if I'm way off some other reader will correct me, but it's a big explosion in any case) and flatten every building and tree for tens of miles around. This is why we don't/can't do direct length contraction experiments with macroscopic objects.

(Digression: You are typing too quickly, as your question has the same logical structure as "Would the earth-bound observer also potentially see X if seeing X were somehow possible?", and the answer to that is clearly, tautologically, and unhelpfully "yes" for just about any X no matter how absurd.)

...helpful to me. I just want to distinguish what constitutes observers and such. For example, anything not within the frame of the muon is contracted as observed from the muon and visa versa.

Yes, the question was completely hypothetical.
Thanks.

 

[PAllen]

I assumed 1KG for the mass of the meter stick - a bit heavy as you say, but easy to calculate with because I also selected the gamma factor of 5 to make it easy to work with 1MT=5x10¹⁵ Joules (easy to remember after you've said it fast a few times - "5-10-15").

But I think I should have chosen gamma=6 because the rest mass of the meter stick is rather broadly redistributed but doesn't convert to energy?

Well, the 100 megatons is pure KE, so it will go somewhere if the meter stick hits the earth. It's really hard to find data from experiments that could answer details on questions like this. There was thread here a while ago speculating on what happens if a base ball 'appears' at the pitcher's mound going at .99c towards home plate? The consensus was that it would release only about 1% of its KE (still a lot) by home plate. But try looking for information about the mean free path of nitrogen nucleii in material similar to a baseball, at .99c. Relativistic ion colliders use neither baseball targets nor nitrogen ions.

 

[Dale]

I understand completely why the issue may not matter to the macroscopic result but am intently curious and think any scientist should be.

Scientists should be curious, but they also need to be logical. Part of being logical is making sure to use well defined terms. Being curious doesn't justify being sloppy in your thinking.