Special relativity:Reality or measurment error(?

[ShayanJ]

In the books I've read about relativity the introduction is a definition of simultaneity which is given by the famous train and track example.I've thought a lot about it and concluded that the difference is just in the measurment.I mean the man on train thinks thunders are not simultanous and the man on the ground thinks they are but doesn't mean there is no absolute meaning of simultaneity and it just shows the measurment error.So I concluded that special relativity is a theory which gives us the exact amount of error in measurments caused by taking different frames of references not sth that happens in reality but I read in articles that special relativity's implications are seen in nature and so they happen in reality.
this makes me confused.I really need help about it.
thanks

 

[bcrowell]

The key is that there is no way to tell whose measurement is the correct one and whose is in error.

 

[Mentz114]

In the train thought experiment, two events are defined as simultaneous for an observer if the light from the events reaches the observer at the same time on his clock. Applying this criterion to the train and platform observer, one concludes that the events cannot be perceived as simultaneous by both observers - unless the events are very close together.

The point is that there is no definition of simultaneity that allows all frames to agree whether two spatially separated events are simultaneous or not.

 

[ghwellsjr]

The issue of simultaneity has nothing to do with measurement error because it has nothing to do with measurement. It has only to do with definition.

If there were an absolute aether reference frame that we could identify by measurement or if we could agree to define a single reference frame to be the one that all measurements would be made from, then we wouldn't have the problem of simultaneity because all events would be measured relative to the one reference frame.

Instead, Einstein's second postulate is that the unmeasureable one-way speed of light in any arbitrary reference frame is a constant so that simultaneity can be rationally and reasonably defined within that one reference frame, but this means that events that are defined to be simultaneous in that reference frame will not be simultaneous in another reference frame with its own conflicting definition of simultaneity.

Thus, we have the relativity of simultaneity. The only way to not have it is to have only one reference frame but Mother Nature won't tell us which it is and people just won't agree on an arbitrary one.

 

[Dale]

the man on train thinks thunders are not simultanous and the man on the ground thinks they are but doesn't mean there is no absolute meaning of simultaneity and it just shows the measurment error

Can you justify this statement? What absolute meaning of simultaneity could there possibly be if all measurements are intrinsically subject to such a measurement error?

 

[JesseM]

The key is that there is no way to tell whose measurement is the correct one and whose is in error.

Yes, this. The key physical notion of relativity is that all the fundamental laws of physics will obey the same equations in any of the inertial coordinate systems defined in the way Einstein defined them, i.e. the laws are invariant under the Lorentz transformation which relates these frames to one another. You could define a different set of coordinate systems which didn't disagree about simultaneity, but if the laws of physics are Lorentz-invariant as relativity predicts, then they will not be invariant in this different set of coordinate systems, the equations will have to be written differently in different frames.

Also note that you are free to believe that one inertial frame's definition of simultaneity is "correct" in some absolute metaphysical sense, as long as there is no physical experiment that will actually distinguish the "correct" inertial frame from any other inertial frame this does not conflict with SR, which is just meant to be a physical theory and not a metaphysical one.

 

[ShayanJ]

Can you justify this statement? What absolute meaning of simultaneity could there possibly be if all measurements are intrinsically subject to such a measurement error?

I accept that we can't tell for sure two events are simultanous or not but that doesn't mean there is not such a notion in nature.I mean two thunders can be simultanous,the problem is we can't understand.and relativity I think says that we can never understand.
So a question arises.I understand from your speeches that relativity says for example if a car goes with a speed not small compared with c,we measure its length smaller than its rest length.But is it really shrunk?will it fall in a hole which is smaller than its rest length but bigger than its real length(if such a thing exists)?
what about time dialation?does it really happen or its just measurment error?do twins become non-twins after one of them having a trip with a speed comparable with c?
Or what about this example:imagine I have an electron and a magnet at my hand and take the frame connected to me the inertial frame.Now there is another frame moving with constant speed relative to mine.there is a magnet in the second frame.the electron and magnet in my frame have no effect on each other but the my electron and second magnet apply forces to each other because they're moving relative to each other.does such an effect exists or its again a measurment error?
But I think all these questions boil down to a hard philosophical question.Is reality apart from our understanding?I mean if we can NEVER understand weather two events are simultanous or not,is there such a notion?i think yes but frankly talking I don't know how to conclude it,and that gets me in doubt.
(WOW its more complicated (and interesting) than I thought)

 

[russ_watters]

what about time dialation?does it really happen or its just measurment error?do twins become non-twins after one of them having a trip with a speed comparable with c?

Yes, it actually happens. Read the sticky on the experimental basis of SR.

 

[Grep]

I accept that we can't tell for sure two events are simultanous or not but that doesn't mean there is not such a notion in nature.I mean two thunders can be simultanous,the problem is we can't understand.and relativity I think says that we can never understand.

Leaving behind even the notion that no reference frame is special in terms of getting to define what was simultaneous. Even more, how can you even say two things were really, truly simultaneous? The most you can say is, in your frame of reference, it was simultaneous to at least within a certain margin of error.

But were two events really truly simultaneous? No matter how small a slice of time you come up with, can I not divide it in half and come up with an even smaller slice? Even if there's a smallest increment of time, it would be amazingly, impractically small (let's say Planck Time). And as far as I know, there's little reason to believe Planck Time is literally the smallest possible increment of time. How simultaneous is simultaneous?

Just for fun, from the Wiki on Planck Time: "As of 2010, the smallest time interval that was directly measured was on the order of 20 attoseconds (10^−18 s), or about 3.7 × 10^26 Planck times."

That's pretty quick, I'll give it that. Don't blink!

So a question arises.I understand from your speeches that relativity says for example a car goes with a speed not small compared with c,we measure its length smaller than its rest length.But is it really shrunk?will it fall in a hole which is smaller than its rest length but bigger than its real length(if such a thing exists)?
(WOW its more complicated (and interesting) than I thought)

For this, read "A Special Relativity Paradox: The Barn and the Pole" at: http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html . That explains the basic idea of what you're asking, only with a pole and a barn instead of a car and a hole.

 

[atyy]

Time dilation: is "measurement error" in some sense in that it relates the "time" of one inertial reference frame that is moving at constant velocity relative to the "time" of another inertial reference frame. This time is called "coordinate time", and is just one of 4 labels for events in spacetime. Events that are simultaneous according to one reference frame's "time" are not simultaneous according to another reference frame's "time".

But the twin paradox is not measurement error, it is about real aging, on which all inertial frames will agree.

 

[Dale]

I accept that we can't tell for sure two events are simultanous or not but that doesn't mean there is not such a notion in nature.

What does it mean, even in principle, for something which is completely undetectable to be "in nature"? Usually undetectable things like ghosts are considered "supernatural", not "in nature". If something is completely undetectable through any natural means then it seems much more likely to be a fantasy than something natural.

I would sooner believe in ghosts than undetectable absolute reference frames. But, as long as you consistently treat your absolute reference frame as undetectable you won't get wrong answers.

 

[ShayanJ]

I mean forget about humans just for a moment.Now imagine a cload.it is thundering.for some reasons,two of its thunders come at the same time(God dammit,now I should ask which time)
i don't know.My brain is coming out through my body holes.I think I need a year thought to fully understand and accept relativity.Now I understand what they mean by telling "Einstein was a genius".
I'm just confused.I accept both ideas and non of them.I'm becoming crazy. :zzz:
Hey.I know its not a proper place to ask this,But can you start from the beginning?

 

[atyy]

Now imagine a cload.it is thundering.for some reasons,two of its thunders come at the same time(God dammit,now I should ask which time)

Exactly - what does one mean by "same time"? That is the key to special relativity - Einstein defined "same time" in a particular way.

 

[ShayanJ]

I think you mean \tau.Can we call it "universal time"?
And so can we define an absolute meaning of simultaneity with it?
If we can,we can tell that every frame of reference which its time is the same as \tau is the preferred one,unless no frame of refrence has such a time?
Are these sentences correct(from now on I can't really trust my reasonings)
Can we tell that the philosophical basics of relativity (cause the mathematical basics of it I think is lorentz transformations)is the conclusions about time and \tau?

 

[Grep]

I'm just confused.I accept both ideas and non of them.I'm becoming crazy. :zzz:
Hey.I know its not a proper place to ask this,But can you start from the beginning?

I think at this point you might want to read up a lot. It's a simple theory with a lot of non-intuitive results. It could take us a lot of typing to explain it clearly, here.

I have a few books that explain it well, but for online material, you might try:
Wikibooks on SR: http://en.wikibooks.org/wiki/Special_Relativity
You can even download a PDF of the book.

Or maybe just the regular Wiki: http://en.wikipedia.org/wiki/Special_relativity

I also highly suggest the SR section of the Physics FAQ at: http://math.ucr.edu/home/baez/physics/
Most of the tricky bits about SR that come up a lot are explained in that FAQ, and it's well worth the read. And the rest of the FAQ is pretty cool too.

Enjoy, it's a great topic!

 

[JesseM]

I think you mean \tau.Can we call it "universal time"?
And so can we define an absolute meaning of simultaneity with it?

No, \tau is what's called proper time, it's only defined along individual worldlines, giving the time between two events on a given worldline as measured by a clock that moves along that worldline (sort of like how in 2D geometry, you could define the "path length" between two points on a given curve). It's only about the difference between two events, the actual value of proper time assigned to a particular event is totally arbitrary, for example if two events A and B on a given worldline have a difference in proper time of 20 seconds, you're free to label A as \tau = 0 \, s and B as \tau = 20 \, s, or to label A as \tau = 100 \, s and B as \tau = 120 \, s, the differences are all that has any physical significance. For this reason it wouldn't make sense to ask whether two events along different worldlines happened at the "same proper time" or "different proper times", any more than you can ask whether two points on different curves in a 2D plane are at the "same path length" or "different path lengths".

As for good intros to SR, you might take a look at the references given on this thread.

 

[Dale]

I mean forget about humans just for a moment.Now imagine a cload.it is thundering.for some reasons,two of its thunders come at the same time

I agree, let's forget about humans just for a moment. In what way does it matter if the two lightnings strike at the same time? Neither lightning bolt caused the other, so why does it matter to nature which order they came in? The answer is that it doesn't. The order only matters to humans not nature. Simultaneity is a matter of human convention, nature doesn't care about simultaneity, only causality. A cause will always precede an effect in all reference frames, and the rest is human book-keeping, not nature.

I think I need a year thought to fully understand and accept relativity.

That's not too bad, it took me 7 years. Of course, I didn't have a place like PF to ask questions.

 

[atyy]

I think you mean \tau.Can we call it "universal time"?
And so can we define an absolute meaning of simultaneity with it?
If we can,we can tell that every frame of reference which its time is the same as \tau is the preferred one,unless no frame of refrence has such a time?
Are these sentences correct(from now on I can't really trust my reasonings)
Can we tell that the philosophical basics of relativity (cause the mathematical basics of it I think is lorentz transformations)is the conclusions about time and \tau?

You cannot proceed until you define "universal time" operationally - what set of physical procedures do you use to define "universal time"?

 

[closet mathemetician]

The way I think about this is that you can't have any knowledge of any event that happens anywhere until the light from that event reaches you. From your perspective, it doesn't "happen" until the light from the event reaches you. For all events that emit light at some time and at some position in space, everyone else any distance away from that event will see it happen in the future relative to the event frame.

Now, that doesn't mean that two events can't happen at a single time, there are just limits on our ability to KNOW that they happened at that time. If two events occur at the same time in different points of space, each event will see the other event in the future of its own frame.

Suppose the sun explodes at precisely noon today. At noon, I'll be sitting here at work doing my thing, oblivious to what has occurred. I won't, and can't know about it until about 8 seconds later. So for all purposes to me that matter it happened at 12:08 not at 12:00.

 

[JesseM]

The way I think about this is that you can't have any knowledge of any event that happens anywhere until the light from that event reaches you. From your perspective, it doesn't "happen" until the light from the event reaches you. For all events that emit light at some time and at some position in space, everyone else any distance away from that event will see it happen in the future relative to the event frame.

Now, that doesn't mean that two events can't happen at a single time, there are just limits on our ability to KNOW that they happened at that time. If two events occur at the same time in different points of space, each event will see the other event in the future of its own frame.

Suppose the sun explodes at precisely noon today. At noon, I'll be sitting here at work doing my thing, oblivious to what has occurred. I won't, and can't know about it until about 8 seconds later. So for all purposes to me that matter it happened at 12:08 not at 12:00.

It's true that there are light delays, but when physicists talk about what is measured in a given frame, they are talking about what coordinates are assigned to events after you factor out light delays--for example, if you know the Sun is 8-light minutes away from the Earth as measured in the Earth's rest frame, then if you see the Sun explode at 12:08 you can retrospectively conclude it "really" happened at 12:00 in your frame, and thus was simultaneous in your frame with the event of a clock on Earth reading 12:00. The relativity of simultaneity says that when observers at rest in different frames assign times to events in this "retroactive" way that filters out light delays (each assuming that light moves at c in their frame), they will still disagree about whether a given pair of events at different points in space were "simultaneous" or not.

 

[ShayanJ]

I think I understood.
From the first potulate of special relativity,simultaneity doesn't have a physical meaning and so there is no such notion in nature.
But another question arises which I expressed in the following experiment.
Imagine I'm in a spacecraft with transparent walls.I'm still on the ground.another guy is out of space craft.I take the refrence frame connected to the spacecraft as my preferred refrence frame.then i make a device which lights a LED when it hears two simultanous voices.then I start moving up with an speed comparable to c.then I sound two horns simultanous near my device while I'm moving.i see the LED lighting but the man on the ground should not see it lighting.But this is a contradiction.we can't say LED lighted and also didn't light.
What's the problem?

 

[Mentz114]

I think I understood.
From the first potulate of special relativity,simultaneity doesn't have a physical meaning and so there is no such notion in nature.
But another question arises which I expressed in the following experiment.
Imagine I'm in a spacecraft with transparent walls.I'm still on the ground.another guy is out of space craft.I take the refrence frame connected to the spacecraft as my preferred refrence frame.then i make a device which lights a LED when it hears two simultanous voices.then I start moving up with an speed comparable to c.then I sound two horns simultanous near my device while I'm moving.i see the LED lighting but the man on the ground should not see it lighting.But this is a contradiction.we can't say LED lighted and also didn't light.
What's the problem?

Interesting, but no paradox. If you'll allow me to redo the experiment using a device which lights an LED when two beams of light strike it at the same time, it is easier.

Suppose you put two clocks which can send a laser beam at both ends of the ship and place the device midway between them. The clocks are synchronised by sending a light pulse from the middle to both clocks. At some prearranged time the clocks send their beams to the device, and the LED lights up. I've drawn a spacetime diagram which shows the ends of the ship, and the synchronisation pulse, then the clocks sending their signals. Read the diagram from the bottom up, which is the way time is flowing. The first diagram is the ships frame. The synch pulses travel out from the center to start the clocks. Four time units later the clocks send their beams which hit the device simultaneously in the ship frame. The second diagram shows the ship from a moving frame. As you can see, the beams still hit the device at the same time.

The reason is that the 'two' events we are interested in ( the crossing of the light beams ) is actually one event, whose existence is frame independent.

 

[ghwellsjr]

But another question arises which I expressed in the following experiment.
Imagine I'm in a spacecraft with transparent walls.I'm still on the ground.another guy is out of space craft.I take the refrence frame connected to the spacecraft as my preferred refrence frame.then i make a device which lights a LED when it hears two simultanous voices.then I start moving up with an speed comparable to c.then I sound two horns simultanous near my device while I'm moving.i see the LED lighting but the man on the ground should not see it lighting.But this is a contradiction.we can't say LED lighted and also didn't light.
What's the problem?

From the description of your experiment, I don't see why you think the observer on the ground would not see the LED flash. Is it that you think he would not "see" the two thunder sounds arriving at the same time and would conclude that the LED should not flash and so it doesn't for him even though it does for you, the traveler?

 

[michelcolman]

I think I understood.
From the first potulate of special relativity,simultaneity doesn't have a physical meaning and so there is no such notion in nature.
But another question arises which I expressed in the following experiment.
Imagine I'm in a spacecraft with transparent walls.I'm still on the ground.another guy is out of space craft.I take the refrence frame connected to the spacecraft as my preferred refrence frame.then i make a device which lights a LED when it hears two simultanous voices.then I start moving up with an speed comparable to c.then I sound two horns simultanous near my device while I'm moving.i see the LED lighting but the man on the ground should not see it lighting.But this is a contradiction.we can't say LED lighted and also didn't light.
What's the problem?

The device has to listen to the two horns to tell whether or not they were simultaneous. The sound has to actually travel to the device. All observers will agree that both sounds will arrive at the device at the same time. But they did not leave the horns at the same time, because the speed of sound in the two directions was not the same (thanks to relativistic addition of speeds). So, from the stationary observer, the horns did not sound simultaneously, but their sound did arrive at the device simultaneously.

By the way, my favorite example of the "reality" of relativity (to show it's not just an observational thing) is the train passing paradox: two 100 meter trains can pass each other on an 80 meter section of double track if their speed is at least 0.6c. Actually, that's not even the paradox yet, it gets interesting when you look at things from the point of view of a driver. But just the fact that they're able to pass each other at all, really drives home the reality of the theory.

 

[ShayanJ]

Hey mentz and michel,you're giving two different explanations.Please agree on one of them.
And mentz I can't understand how these crossing of light beams can be one event.Please explain more.

 

[michelcolman]

Hey mentz and michel,you're giving two different explanations.Please agree on one of them.
And mentz I can't understand how these crossing of light beams can be one event.Please explain more.

I kept your original experiment. Mentz modified it a little bit using light signals instead of the sound of the horns. But the explanations are very similar. In mentz's example too, the device receives signals (light instead of sound, but that does not really matter) from both sides simultaneously, but the signals were not emitted by the (light)horns simultaneously. So the fact that the LED lights up, only means that the device (which is itself an observer traveling with the ship) sees/hears the horns at the same time. All observers agree on that. They just disagree on when the horns themselves were activated.

You can apply the same kind of reasoning on the train with the two bolts of lightning:

Suppose the train has a speed of 0.5c, you are standing next to the track, and at the precise time that the middle of the train is passing next to you, you see simultaneous flashes of lightning from left and right, one on the front and one on the back of the train. Since the train is moving, this means the lightning strike at the back must have happened first, because a few moments ago, the back end was further away and the front end was closer, so light had to travel a longer distance from the back than from the front. However, for someone on board the train, both happened simultaneously because the light travels relative to the train and had to travel the same distance. Everybody agrees that the light from both sides arrived at the center of the train at the same time, but that does not means the events themselves happened at the same time.

 

[ShayanJ]

Hey I'm really happy 'cause I think I understand it.
I just want to ask how the mass increase is concluded?
What about mass-energy equivalence?
And I didn't understand the train example.what you mean they can pass each other?please explain it more clearly.
thanks

 

[Mentz114]

I just want to add to michelcoleman's explanation an answer to this

how these crossing of light beams can be one event.Please explain more.

If two people meet and shake hands then I think we can agree this is one event although two worldlines are involved, because they are in the same place at the same time, within reasonable limits. The same can be said for the event when the lightbeams hit the receiver.

 

[michelcolman]

And I didn't understand the train example.what you mean they can pass each other?please explain it more clearly.
thanks

High speed not only changes time (clocks running more slowly), it also changes lengths and distances. If a 100 meter long train is passing you with a speed of 0.6c, it will only be 80 meters long. That's not just some observational effect, it really is shorter. You could for example check it with a sensor that times the passage of the front and back of the train, and multiply that time with its speed. But if you are on the train, you will still measure it as 100 meters because it is not moving relative to you. You would explain the result of the sensor next to the track by saying its clock is running slowly.

If you read that last sentence, you might be tempted to say "see, it was just an observational error after all". But if two 100 meter long trains in opposite directions are approaching an 80 meter section of double track, which would normally be too short for the trains to pass each other, they can make it just fine if they are going at a speed of 0.6c! This would be completely impossible if length contraction was not "real".


The funny thing is what happens when you look at the situation from the point of view of one of the train drivers. He will still experience his own train as being 100 meters long (because it is not moving relative to him), but the section of double track, which was originally 80 meters, is now only 64 meters long because it is moving at 0.6c relative to him! How can he pass the other train then, if his train is so much longer than the double track?

Fortunately for him, the other train that is coming towards him, is traveling at 0.88c (relativistic addition of 0.6c + 0.6c = 0.88c). This means it will have contracted to only 47 meters long. When the front end of the long train is reaching the end of the double track (and the back end is still sticking out on the other side), he just misses the back of the short train. That short train now still has 17 meters to go before its front reaches the other end. When it gets there, it just misses the back end of the long train which enters the double track just in time.

So you see, the two observers agree that the two trains can pass each other safely, but they have a completely different explanation, because they do not agree on simultaneity. For the first observer, the ends of the trains pass each other at exactly the same time on both sides. For the other, they pass each other at one end first, and at the other end later.


For more examples, check out the wikipedia entry for "Relativity", near the bottom under "See also": "Paradoxes"

 

[ShayanJ]

This question is not related to the previous ones but I don't want to make a new thread for it.
Imagine we have a source of light which can emit photons in two direcions.We take the refrence frame connected to the light source,our preferred refrence frame.Then we emit photons from two sides simultanously(So photons move in opposite direcions).If we use relativistic velocity composition formula to obtain the speed of one of the photons relative to the other one,we obtain c.What it means?How can you explain it?
thanks

 

[ghwellsjr]

I did a Google search on the phrase "relativistic velocity composition formula" and found only 14 hits but I couldn't get a clear definition of the formula. I would think a legitimate formula would have hundreds, if not thousands, of hits. Could you please point to a reference that defines it? The reason I ask is that I have never heard of a formula that would allow you to obtain the speed of one photon relative to another one.

 

[matheinste]

This question is not related to the previous ones but I don't want to make a new thread for it.
Imagine we have a source of light which can emit photons in two direcions.We take the refrence frame connected to the light source,our preferred refrence frame.Then we emit photons from two sides simultanously(So photons move in opposite direcions).If we use relativistic velocity composition formula to obtain the speed of one of the photons relative to the other one,we obtain c.What it means?How can you explain it?
thanks

It is just a consequence of putting in a legitimate?? value, c, (for a massless particle) for velocities into the SR relative velocity formula. Remember the formula returns the value of the velocity of one photon as measured?? from the other photon's point of view. Of course whether or not a photon has a valid reference frame, or point of view, is often the subject of some, mostly informed and thought provoking, heated argument in this forum. However, I prefer to avoid the question and stick to subluminal speeds.

Matheinste.

 

[Daverz]

I did a Google search on the phrase "relativistic velocity composition formula" and found only 14 hits but I couldn't get a clear definition of the formula. I would think a legitimate formula would have hundreds, if not thousands, of hits. Could you please point to a reference that defines it? The reason I ask is that I have never heard of a formula that would allow you to obtain the speed of one photon relative to another one.

Huh? Google says "564,000 results". Try

Try http://www.google.com/search?q=relativiistic+velocity+addition

 

[ShayanJ]

I have another question.In SR there is a notion called rest mass.but we know sth which is at rest in one frame of refrence,is moving in another.So How can we define rest mass when there is nothing called rest?

 

[ghwellsjr]

I did a Google search on the phrase "relativistic velocity composition formula" and found only 14 hits but I couldn't get a clear definition of the formula. I would think a legitimate formula would have hundreds, if not thousands, of hits. Could you please point to a reference that defines it? The reason I ask is that I have never heard of a formula that would allow you to obtain the speed of one photon relative to another one.

Huh? Google says "564,000 results". Try

Try http://www.google.com/search?q=relativiistic+velocity+addition

You have to put quotes around a phrase (and it helps if you spell it right), otherwise it searches for the words anywhere in a document. Now, when I do it, it finds 15 hits, because it found this webpage.

In any case, I'm still waiting for an answer to my question.

 

[ghwellsjr]

I have another question.In SR there is a notion called rest mass.but we know sth which is at rest in one frame of refrence,is moving in another.So How can we define rest mass when there is nothing called rest?

In SR, you must select just one frame at a time. Anything at rest in that frame will exhibit its rest mass.

 

[jester1989]

Hey! read 1 of the TS original questions. super interesting. So if we have a 2m car, a 1m hole and an stationary observer. now the 2m car is accelerated to approx c. then the observer measures the car nw, it is less than 1m, will it fall into the hole? (since the hole is not moving wrt to observer, even if he measures it again, it will still b 1m right?)

hmm from the car driver pt of view, he will always measure his car at 2m right? but he will see the hole contract? if so...then he (even more) won't fall into the hole from his pt of view.

 

[John232]

The car would contract he just wouldn't be able to measure it with a contracted ruler, so he would measure his car to still be 2m but it could still be smaller than the hole.

Same problem of two observers both measuring each other to contract doesn't fit into one single reality. I would think that since the car does the acceleration it is the one that actually contracts, but then acceleration doesn't cause spacetime dialation...

Earth has never contracted due to an object traveling close to the speed of light either.

 

[JesseM]

I did a Google search on the phrase "relativistic velocity composition formula" and found only 14 hits but I couldn't get a clear definition of the formula.

Usually terms for equations don't actually have the word "formula" at the end of them, if you search for "relativistic velocity composition" you get 1,990 hits and if you search for the more common synonym "relativistic velocity addition" you get 10,300 hits.

 

[jester1989]

why would it still be smaller than the hole? if the stationary observer measures it again(when it is traveling at near speed now) but this time it is less than 1m, shouldn't it fall into the hole?

sry if i seem slow. this concept is quite non intuitive.=x

 

[John232]

The saying goes that you can't measure your own length contraction because your ruler would contract by the same amount. So he would measure himself as being the same size but he would still be contracted to a smaller size.

But, he would only be contracted in the direction of motion so if he was traveling head on into the hole then he still wouldn't fit because his ship would still be just as wide.