A Common Misunderstanding Of Special Relativity

[Doctordick]

AnssiH has been very helpful in showing me how my presentations are misunderstood. With Anssi's help I have now composed a third version of my presentation and arranged for it to be published as a standard book soon to be available on Amazon.com.

On the other hand, it has come to my attention that one very serious aspect of my presentation has been overlooked by Anssi. I have been thinking about that aspect and have decided to present it here as I am sure that if it wasn't clear to Anssi, it was probably overlooked by everyone else also. It is a direct consequence of special relativity (both my presentation and Einstein's) and, when examined from the perspective of my presentation, applies directly to general relativity also.

It has to do with how things actually appear to an observer; an issue seldom examined carefully by the professionals. Let me construct a subtle thought experiment worth examining.

Suppose we have an individual making some careful examinations from a spaceship traveling at a high enough velocity to make special relativity an important issue in the examinations I am about to describe. I want to exactly represent the following examinations from both the rest frame (the frame in which the spaceship is traveling at a high velocity) and the frame within which the space ship is at rest. Dimensions in the frame of the space ship will be primed.

First of all, the correct transformations between the two frames are expressly given by the following well known special relativistic relationships:
 

[math]
x'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[x-vt]
\;\;\;\;
and
\;\;\;\;
t'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[t-\frac{vx}{c^2}]
[/math]

Regarding the other relationships, y'=y and z'=z so these coordinates do not require a careful analysis. On the other hand, any measurements involving x and x' must be carefully looked at.

In this thought experiment, there will be a metal panel at the rear of the spaceship orthogonal to the path of the ship. In that panel, there will be two holes each a specific distance from the center line of the ship. Note that both the rest observer and the observer on the ship will agree as to the separation of those two holes (they are no more than measurements in the y-z direction).

At the front end of the ship, on a plane also orthogonal to the path of the ship and on a line directly represented by same y-z direction used to specify the two holes above (once again symmetric to the center line of the ship) there will be two photon detectors which can be moved to any desired position along that line. Note that once again, both the rest observer and the observer on the ship will agree as to the separation of those detectors (their positions are again no more than measurements in the y-z direction).

For any star viewed directly to the rear of the ship, those two detectors may be set to a position to detect that that star simultaneously: i.e., [math]t_{1}'[/math] must exactly equal [math]t_{2}'[/math]

Since those two detectors are in exactly the same y-z plane at the moment of that detection the x separation of the two events is exactly zero in both reference frames and thus, though t' may not be the same as t, the difference between [math]t_{1}[/math] and [math]t_{2}[/math] must also be zero: i.e., these two specific events are seen as exactly simultaneous in both frames.

Now this posses a seriously interesting geometric issue.

Let us now examine the triangle formed by the two detectors and the star being detected. Clearly the rest observer will observe that the photons pass through the two holes at the rear of the ship and impact the detectors at the front of the ship and as such define a very specific geometric construct.

If that ship were actually at rest at t=0, that geometric construct would provide a means of measuring the distance to the star being detected. However, if the ship were moving at a high velocity, as measured in the ships frame of reference, the geometric construct is exactly the same as that which would have been measured if the ship were at rest. This implies the distance to the star as calculated on board the moving ship would be exactly the same as that calculated were the ship at rest.

That result implies a rather astounding consequence. Using their observations both the rest observer and the moving observer would map the universe with identical separations between the stars. This is not at all what is implied by the standard interpretations of special relativity. What is important here is that we have avoided bringing in the issue of general simultaneity, the central complication of any relativistic calculation.

If anyone can see an error in this presentation, please put forth a logical argument which defeats the conclusion.

Thanks for your attention -- Dick

Edited May 17, 2014 by Doctordick

[Rade]

This is not at all what is implied by the standard interpretations of special relativity.

Exactly what is your understanding of "what is implied by the standard interpretations of special relativity" ? Your requested defeat hinges on your answer to this request.

[AnssiH]

Exactly what is your understanding of "what is implied by the standard interpretations of special relativity" ?

 

Obviously he means the standard Lorentz length contraction. As in, under relativistic definitions the universe would be taken as length contracted, while optically the distances would not appear length contracted. Length contraction is after all just a direct consequence of changing your notion of simultaneity (simultaneity between the front and the end of an object needs to be established in order to measure the length of a moving object), and changing your notion of simultaneity in SR is a convention, which is performed in order to maintain the speed of light as isotropic between the frames in your coordinate representation of the situation.

 

That is just to say, reality does not change its form just because you decide to represent it from a different coordinate system.

 

As of the OP, quite interesting... I though about it from different angles for quite some time, especially the effects of aberration. I think those effects should at least be mentioned because it would affect what things look like optically.

 

I.e, stars directly in front of the ship would appear to be further away for the moving ship, while the stars towards the rear would appear to be closer. Only when calculating away the optical effect of aberration, the stars would appear to be in identical distances (seems to me).

 

Here's what I'm thinking in more detail;

Represent the situation from the non-primed frame, and imagine a stationary ship and moving ship super-imposed on top of each others so that the rear plates are in the same position just as the light from the star is passing through the holes.

 

Let's say the speed of the moving ship is such that it is represented as length contracted into half the length of the stationary ship. (that's about 0.87c)

 

Imagine the situation moving forwards up to the point the light beams hit the front detectors of the stationary ship. The spatial separation between the photon detections defines the distance to the star, as calculated by the stationary ship.

 

By this time the beam has traveled only 26% of the length of the moving ship, while the separation between the beams is already identical to the beams that have travelled through the entire length of the stationary ship.

 

If there was a photon detector at that location in the moving ship, it would already imply the star appears to be closer than it does for the stationary ship, at the moment the ships have only partially passed each others.

 

If you do similar analysis to measure a star in front of the ship, the result is the star appears to be further away.

 

Am I forgetting something?

 

-Anssi

Edited January 5, 2014 by AnssiH

[AnssiH]

Oh and the book he mentions, for those who have been interested of following DD's argument, the book is by far the clearest representation so far. Just the fact that it's all composed into one book is helpful, and I think quite large number of unfortunate ambiguities have been fixed. For anyone who's interested, I'm sure he'll mention it when it's available for anyone to pick it up, or maybe you can ask your local library to carry a copy.

[Doctordick]

 

Am I forgetting something?

 

Hi Anssi,

 

I was slow to respond to this because I couldn't follow what you meant by “aberration” which commonly means a deviation from normal. So I googled “aberration of light” and, except for aberration due a non-flat mirror, all the cases of “aberration of light” depended upon a velocity of the source relative to the observer or vice-versa.

 

I think you are misunderstanding the example I presented. To either observer, at rest or moving with the ship, the only information available is the path of the ship (a specific straight line as there is no acceleration), the distance between the two surfaces measured along that line (as measured in their own rest frame, something determined by the original design of the space ship), the distance off that line to the hole in the first surface and the distance off that line to the detector on the second surface.

 

The detection of the photon is marked as the origin of both coordinate systems. Thus it is, when the observers calculate the distance to the object being detected via the geometry of the experiment, they must obtain exactly the same result. What is important here is that the image of events and the “apparent” simultaneity of the events standing behind that image is identical to what would be obtained if one presumed the speed of light was infinite.

 

“In 185 CE, Chinese astronomers recorded the appearance of a bright star in the sky, and observed that it took about eight months to fade from the sky. It was observed to sparkle like a star and did not move across the heavens like a comet. These observations are consistent with the appearance of a supernova, and this is believed to be the oldest confirmed record of a supernova event by humankind.” -- google “first observed super nova”

 

My point in making that quote is that the event appeared to occur in 185 BC (CE means before the current era.) It is “hypothesized” that it occurred 10,000–20,000 years ago via the assumption that the light required that long to get to us. The only real information available to us is where they appear to be: i.e., essentially simultaneous with the present as it appears to us.

 

There are two very different perceptions as to what the universe looks like: one as calculated consistent with our scientific concepts of the rules of the universe and another which is no more than what we see when we look. Failure to recognize the difference between these two views is a relatively important issue and presuming they are identical is patently false.

 

Have fun -- Dick

[Bombadil]

Now this posses a seriously interesting geometric issue.

 

Let us now examine the triangle formed by the two detectors and the star being detected. Clearly the rest observer will observe that the photons pass through the two holes at the rear of the ship and impact the detectors at the front of the ship and as such define a very specific geometric construct.

 

If that ship were actually at rest at t=0, that geometric construct would provide a means of measuring the distance to the star being detected. However, if the ship were moving at a high velocity, as measured in the ships frame of reference, the geometric construct is exactly the same as that which would have been measured if the ship were at rest. This implies the distance to the star as calculated on board the moving ship would be exactly the same as that calculated were the ship at rest.

 

That result implies a rather astounding consequence. Using their observations both the rest observer and the moving observer would map the universe with identical separations between the stars. This is not at all what is implied by the standard interpretations of special relativity. What is important here is that we have avoided bringing in the issue of general simultaneity, the central complication of any relativistic calculation.

 

Isn't this assuming that both observers will measure the angle that the light hits the photon detector to be the same?

 

That is the light enters though the window in the back of the ship, the observer on board of the ship will assume that he is at rest and so the light must make a straight line from the back window to where it hits the photon detector, meanwhile the observer that sees the ship zooming past him will see that the ship has in fact moved while the light was inside of the ship, he will then have the option of correcting for this factor and pointing out where the light would hit had he been stationary or he can do like the observer on board the ship and assume that the light made a straight line.

 

Both choices must result in a different distance measurement since it changes the distance between the light impacts along that axis that is not scaled because it is orthogonal to the direction of travel.

 

Note I have not done the length contraction calculations (which if I am understanding correctly will make the ship appear shorter) in which case this will also play a role in this, since it will play a role in determining how long it takes the light to get from one end of the ship to the other, and so will result in yet a different distance between the photon detectors. It may be that when this is considered it will be found that the ship winds up counteracting the time that the light is inside of the ship by making the ship smaller although I would expect this to play a similar but opposite role if the light was to enter though the front of the ship. So perhaps you have already done this calculation, and this is what you are trying to draw attention to.

[Doctordick]

Isn't this assuming that both observers will measure the angle that the light hits the photon detector to be the same?

Yes! I am not assuming that at all but rather demonstrating that it must be the same. You, on the other hand, are totally misinterpreting the situation!

 

That is the light enters though the window in the back of the ship, the observer on board of the ship will assume that he is at rest and so the light must make a straight line from the back window to where it hits the photon detector, ...

This is a correct analysis of the situation as seen on the ship!

 

...meanwhile the observer that sees the ship zooming past him...

The measurement being made by the other observer has absolutely nothing to do with the “ship zooming past him” other than the fact that t and t' (the time coordinates used by the two observers: i.e., the origins used by the two) happen to be defined to both be zero at the moment the detector detects the relevant photon.

 

... will see that the ship has in fact moved while the light was inside of the ship, he will then have the option of correcting for this factor and pointing out where the light would hit had he been stationary or he can do like the observer on board the ship and assume that the light made a straight line.

Here you are assuming the rest observer is checking the moving observer's observation. If you read what I said carefully, you would comprehend that the rest observer is not checking the moving observers measurements at all but is rather performing an equivalent measurement in his own frame.

 

... you are misunderstanding the example I presented. To either observer, at rest or moving with the ship, the only information available is the path of the ship (a specific straight line as there is no acceleration), the distance between the two surfaces measured along that line (as measured in their own rest frame, something determined by the original design of the space ship), the distance off that line to the hole in the first surface and the distance off that line to the detector on the second surface.

The rest observer is using the manufacture's drawings for the length of the ship; not the apparent length he deduces from the relativistic transformations. In my example they are both using exactly the same length reference! If you are bothered by the fact that the rest observer cannot make his measurement at the same time as the moving observer because the ship is in the way, note that the only important issue is the position of the ship's detector at the moment the detector detected the photon on board the ship (that gives the moment at which the measurement was made from the moving ship's frame of reference). Since the ship is moving, that distance measure will change with time! The position of that detector at the moment the detection was made defines the specific moment of interest. The rest observer (at rest with respect to the distant object to which the measurement is being made) can delay his experiment to whatever time is convenient as he is not moving with respect to the distant object and he will obtain the same answer no matter when he goes to make the measurement!

 

Note I have not done the length contraction calculations (which if I am understanding correctly will make the ship appear shorter) in which case this will also play a role ...

Again, you are talking about converting the ship's experiment into the rest frame of the other observer. That is not at all what I am talking about. I am talking about how things appear to the person on the ship relative to how they appear to the rest observer! I have set the problem up such that no conversion whatsoever is required between the two coordinate systems actual measurements.

 

There are two very different perceptions as to what the universe looks like: one as calculated consistent with our scientific concepts of the rules of the universe and another which is no more than what we see when we look. Failure to recognize the difference between these two views is a relatively important issue and presuming they are identical is patently false.

 

... in this, since it will play a role in determining how long it takes the light to get from one end of the ship to the other, and so will result in yet a different distance between the photon detectors. It may be that when this is considered it will be found that the ship winds up counteracting the time that the light is inside of the ship by making the ship smaller although I would expect this to play a similar but opposite role if the light was to enter though the front of the ship. So perhaps you have already done this calculation, and this is what you are trying to draw attention to.

No, that is exactly what I am trying to draw your attention away from!! What you see and what you calculate to be the correct answer to be are two very different things.

 

Please examine the presentation I have put forth more carefully.

 

Have fun -- Dick

[AnssiH]

I was slow to respond to this because I couldn't follow what you meant by “aberration” which commonly means a deviation from normal.

 

Oh yeah, sorry about that, I realized that when I was writing and wrote "aberration of light" at first, but looks like that part got lost in some edit before I posted... :I

 

But now that you know what I mean, I'll just say "aberration"

 

So I googled “aberration of light” and, except for aberration due a non-flat mirror, all the cases of “aberration of light” depended upon a velocity of the source relative to the observer or vice-versa.

 

I came to think about aberration of light because your thought experiment reminded me of something I was thinking about some 10 years ago. I realized later there was a term of it, namely, "aberration of light".

 

I'll explain in detail in the end of the post what I'm thinking exactly, and why it appears to me it has to have an effect in your thought experiment too. If I'm making a mistake we should be able to spot it. But either way it is, it's not really relevant to the point you were trying to raise, so;

 

“In 185 CE, Chinese astronomers recorded the appearance of a bright star in the sky, and observed that it took about eight months to fade from the sky. It was observed to sparkle like a star and did not move across the heavens like a comet. These observations are consistent with the appearance of a supernova, and this is believed to be the oldest confirmed record of a supernova event by humankind.” -- google “first observed super nova”

 

My point in making that quote is that the event appeared to occur in 185 BC (CE means before the current era.) It is “hypothesized” that it occurred 10,000–20,000 years ago via the assumption that the light required that long to get to us. The only real information available to us is where they appear to be: i.e., essentially simultaneous with the present as it appears to us.

 

There are two very different perceptions as to what the universe looks like: one as calculated consistent with our scientific concepts of the rules of the universe and another which is no more than what we see when we look. Failure to recognize the difference between these two views is a relatively important issue and presuming they are identical is patently false.

 

Yup, so true. It always bothers me a bit that on the other hand we are using relativistic convention to describe the universe, but on the other hand we imply partially newtonian convention when people talk about a supernova we see now having happened "20 000 years ago". 20 000 years ago in what sense? If there is no preferred frame, then there is an infinite number of reference frames where that supernova bursted a split second before we saw it. Or at least pointing that out would be consistent to the definitions we are using.

 

People also almost always talk vaguely or even inconsistently when they describe C as being the speed limit for our space ships, and as a result people always seem to think we literally could not get to places faster than whatever the distance is in light years. Have you ever seen a single science fiction film where they have actually just built a damn fast space ship that would work according to the definitions of special relativity, instead of spending years in hyper sleep? I can't think of a single one. I bet a lot of people would think "but you can't do that according to relativity", but of course you can, doh!

 

Note I have not done the length contraction calculations (which if I am understanding correctly will make the ship appear shorter) in which case this will also play a role in this

 

It doesn't play any role in this because the length of the ship is always defined in ships own frame for their own calculations. The calculated distance of the star is entirely a function of distance between the detected photons, and length contraction doesn't affect that at all, which would be exactly DD's point and he is absolutely right about that.

 

If aberration has an optical effect in this, then the distance between the photons when they hit the back wall is different between the ships at the precise moment the ships are passing each others (if we imagine this in terms of two different ships, other one "parked", other one passing by). But so, let's investigate my thoughts in detail and see if we can find an error;

 

The obvious case first;

 

Imagine a "rest" reference frame, and a cube shaped room floating stationary in space, with a hole in the ceiling.

 

Imagine a laser pointer, also stationary, beaming a pulse of light through the hole. The beam is shot down orthogonally to the floor, so if there is an observer directly below the hole, he will see the beam coming through the hole.

 

Now imagine the same situation, but the room is moving in our reference frame past the laser pointer (which is still stationary). The velocity of the room is parallel to its floor. The laser shoots a beam of light just before the room is passing underneath, so that the beam of light will go through the hole, and continue down into the room.

 

The beam of light cannot possibly hit the floor right underneath the hole since the room is moving sideways in the reference frame, while the light is moving directly downwards. When the beam hits the floor, it will be in a location that is off-set from the hole by some distance that depends on the speed of the room.

 

If there is an observer directly under the hole, it cannot possibly see the laser beam.

 

If there is an observer in the spot where the beam would hit the observer, it would see the flick of the laser beam, and the laser pointer itself, right at the hole. That is to say, it could not possibly see them directly overhead, it would have to see them off in an angle. That angle is towards the direction of motion of the room.

 

Obvious symmetries apply; in the frame of the room, the laser pointer is moving very fast, and it appears to shoot its light off in an angle that is not orthogonal to the floor of the room.

 

Replace the laser pointer with a light coming from a star, and the same rules apply; the "moving" room sees the star off in an angle that is different than how the "stationary" room sees it in, and it is entirely a function of the speed of the room.

 

Note also that, if an observer is in motion inside the room, then the same effect must apply to the observer itself; That observer cannot possibly see the starlight as if its coming through the hole, he must see it as if its coming through the ceiling next to the hole! Edit: Nope, that would be my first mistake right there! The room itself would have to appear skewed to the observer by the same amount, including the hole. Silly hat to me! The rest seems correct to me still.

 

Now, let's open up the ceiling and the walls entirely, think about the entire circumference of the room as it is accelerating near the speed of light as plotted in some reference frame. As the room is gaining velocity in relation to the rest of the visible stars, the stars all must appear to be moving towards the front (towards the accelerated direction) of the ship. Even stars that the room is receding from, must appear optically as if they are somewhere near the front of the ship. Only the objects that are DIRECTLY behind (or front) are not affected at all. Eventually the rest of the stars would just be a speck in front of the ship (except that doppler shift would probably lose the speck too, but that's another story...).

 

If this effect was not accounted for and compensated away, navigating a space ship would be quite troublesome!

 

I think this effect raises an interesting question. I've sometimes wondered why is it that the entire universe is practically stationary in relativistic terms; every massive object we are detecting sits in a very small range of possible velocities.

 

If you think about the possible reference frames - thinking in terms of special relativity - then the vast majority of those frames - from our perspective - are sitting arbitrarily close to C in some direction. So close that we could not possibly detect the difference between the velocities of objects "occupying" those frames.

 

Imagine clusters of massive objects in reference frames that to us look practically like C, would it be possible to detect theose objects in any way? What would they look like with fully doppler shifted light when they are receding, or when they are approaching us? Even if we could detect that light, it would have to come off with full aberration in effect 90 degrees "off-angle", and the entire cluster of objects in or near that reference frame would be visually shrunk into a single speck of light in one direction.

 

If that cluster of object would pass us at any distance, and if its light was detectable, would it, by the definitions of physics, look exactly identical to one photon being detected from that one angle parallel to its direction of motion? Just one photon hidden among a sea of photons we get from objects that are close to our velocity?

 

If that's true, then wouldn't a constant battery of such clusters in all kinds of reference frames in all directions around us, look just like random background radiation that is always centered around us no matter which way we move or look?

 

In addition, since these objects would have to be taken as lorentz contracted, at some velocity they would have to be reduced to so short distance that it would be theoretically impossible to detect them in any way, right? Everything would just move pass each others undetected, except for random noise from things that happen to reside in appropriate reference frames to be detectable in some way?

 

Or to be little bit more epistemological, if we take a massive object and place it in a reference frame arbitrarily close to C so not to be detectable, could such a thing be called "massive object" at all, or something else? Even if, by accelerating near their frame, they would look like normal stars and galaxies? I think there are interesting epistemological questions here.

 

Okay so back to the space ship with two holes. If there was a hole in the exact middle of the back plate of the ship, then aberration could not possibly have any effect. But then also distance measurement could not be performed. The holes that are off-center from the direction of motion and the star behind the ship, would get the light beam coming in in an angle that would have to be affected by aberration effect analogous to the room experiment;

 

We first plot the situation in a frame where the star is stationary, and also the ship is stationary in some distance from the star. That distance is calculated from the distance between the two light beams hitting the front wall (and knowing the construction of the ship). We call this frame "the lab frame"

 

Add another ship that is moving in great speed in this lab frame, moving away from the star, and about to pass the stationary ship (we can imagine it slips straight through the parked ship for clarity).

 

The moment that the front plates of the ships are passing each others, is our simultaneity reference, and that's the moment we want to check the distance between the beams.

 

As plotted in lab frame:

For the parked ship, the photons that hit the front wall at the moment of measurement, entered the ship when the rear end was exactly where it still is.

 

Still as plotted in the lab frame;

For the moving ship, the photons hitting the front wall at the moment of measurement must have entered the ship when the rear end was still closer to the star (even with length contraction taken into account), and the photons must have entered at whatever angle that location would imply. Since then, the beam has been expanding inside the ship while trying to catch the front wall. When it finally hits the front wall, the distance between the beams would have to be larger than is measured inside the stationary ship at the same moment (of the passing of the front plates).

 

Still as plotted in the lab frame;

If the speed of the moving ship is almost C in lab frame, the light may be plotted as having entered the holes of the ship back when the star was still very close to it (i.e. beams entered in extremely high angle), and it has been making its way through the ship throughout the journey, finally hitting the front of the ship at very high angle, making the distance measurement extremely skewed.

 

As plotted in the frame of the "moving" ship, the star is in motion receding from the ship at the rear, and up ahead, the other ship is approaching rear-first. Aberration from all the stars in lab frame is in full effect (everything near the lab frame is skewed forwards), and as seen by either of the holes at the back, the star directly behind is also visually skewed towards the front of the ship by the same mechanism as described with the room thought experiment, making it appear right in the middle behind the ship, but close according to the beam angles.

 

At the moment the front plates co-incide is again the moment of measurement (simultaneity agreed by both ships). In this frame of the "moving" ship we would have to plot the "parked" ship as flying towards the beams of light in such a way that each beam is plotted to be expanding inside the ship only for a brief moment (the ship is also plotted as length contracted but that's just an additional to plain aberration); the beam separation at the moment of measurement would have to be less inside the "parked" ship, making it appear the star is further away.

 

That view gets you entirely consistent and symmetrical transformation between the frames, but since navigating to any star would be impossible if this effect was not accounted for (not to mention the effect would look different when looking out from different locations inside the ship), each space ship would have to see it as an optical illusion of a sort, and navigate either by compensating to some agreed upon frame (the center of cosmic background radiation for instance), or maybe develop a convention to always use the reference frame of some star of interest (that has some useful velocity) as the "correct" one.

 

And if they did that, then yes, they would still calculate the distance to the different stars as identical as you said in the OP. That's why I said this is not really relevant to your point per se, but it should be mentioned as long as we talk about what things optically "look like", not "how things should be plotted".

 

And yeah, for anyone wondering, the stars directly front would not look skewed closer to the ship, they would look skewed further away.

 

-Anssi

Edited January 7, 2014 by AnssiH

[AnssiH]

Okay, since this stuff ticks me off so much, I decided to find a random documentary about the subject just to point out how something like special relativity is almost always misprepresented in rather obvious ways, without anyone raising an eye-brow.

 

Take this:

 

I'm sure Michio Kaku is meaning well, but I really don't think he should be allowed to represent things the way he always does. But, not only is he allowed to keep doing this, he is regarded as one of the big physicists. In his Wikipedia page, there is no "criticism" section at all. Well, allow me. Here's some of the things where he misrepresents standard special relativity;

 

2:30 - "So far no one has build a vehicle that can travel even at a fraction of [light speed]"

 

No, everything we have ever built or could possibly build could move at any speed within C, as seen by any frame, which is a direct logical extension of "no preferred frame" mantra. If it's staying together when stationary, it is already moving at breakneck speeds. The question in terms of interstellar travel is entirely a problem of finding ways to maintain high enough acceleration for long enough to get to places, nothing to do with "speed".

 

Next, he goes on to explain how hard it is to move at the speed of light by talking about how much energy a particle accelerator is using to accelerate particles near the speed of light, adding "after 30 years of trying, they have not been able to push an electron past the speed of light".

 

This could be tricky to explain correctly but he should at least try. More accurately that all is to say, as seen from the rest frame of the device that is doing the pushing (with electromagnetic radiation that is taken to propagate at speed C in itself), the electron will not move faster than C, and furthermore the relationships between the definitions of energy and mass and time mean we cannot observe the electron in our frame as moving faster than C. The time dilation of the electron would have to be pushed down to 0, conversely meaning it needs to be seen as receiving energy in 0 amount of time to change its velocity; that's the same as infinite energy.

 

What ticks me off is he again makes it seem like there's a magical speed boundary in the universe that just stops the particle from moving faster.

 

"Since we can't even push an electron closer to a speed of light, let alone a space ship."

Not analogous problems at all, and in many ways it is theoretically easier with a spaceship. It's kind of hard to build prolonged acceleration mechanisms inside an electron, after all!

 

Next section he goes on to talk about how this spaceship problem has got something to do with "keeping an infinite mass moving" and it requiring "more energy than there is in the universe", just to sound cool.

 

Except that when you are on a spaceship, you are changing your frame all the time and you never get to any sort of infinite mass problem. Oops.

 

5:10 "Even if you got to this magical speed, the ship would be crushed to nothing"

 

Aahhh! :doh:

So wrong it's not even wrong!

 

Yeah in terms of the definitions of SR, mathematically a massive object at the speed of light is length contracted into nothing... ...except for one little thing; by the VERY SAME definitions there is no such thing as massive object moving at that velocity. Which is related to the stuff about the particle accelerator.

 

And no, if such thing was happening, it would not be "crushed", as length contraction is just a specific length DEFINITION, as its seen due to relativistic definition of simultaneity, nothing happens to the object in its own perspective.

 

And no, if you keep accelerating an object it never approaches any magical wall, it just keeps accelerating happily and getting to places ever faster (which is represented by length contraction so the velocity of things won't exceed C)

 

It is only if you decide to plot the spaceship in some particular reference frame, that as per definitions of SR, it will appear to be just approaching C forever and ever, getting more and more time dilated (which represents the fact that on-board the acceleration is constant)

 

It just sounds so cool to claim that a spaceship would hit a cosmic speed wall and get crushed, I guess. Someone should get fired is what should be happening right about now.

 

Yeah and in the next section we learn that we can exceed the speed of light without breaking the rules of relativity (except that it is fairly trivial to show those rules to be inconsistent if we can get to places faster...), and the reason we can break that speed limit is because reality is like pizza dough. I SO saw that coming.

 

And obviously we all know how pizza will solve this so maybe I won't have to go any further... ...for now... (you guys can play this game too, point out the next silly thing he says!)

 

-Anssi

Edited January 8, 2014 by AnssiH

[Doctordick]

Hi Anssi,

Your post of January 7 was essentially quite correct except for a couple of issues that should be noticed.
 

But either way it is, it's not really relevant to the point you were trying to raise, so; ...

“Not really relevant” is the most accurate assessment! I think you understand the issues quite well; however, I will make some comments which I feel clarify the issues a bit.
 

People also almost always talk vaguely or even inconsistently when they describe C as being the speed limit for our space ships, and as a result people always seem to think we literally could not get to places faster than whatever the distance is in light years.

The problem there is the definition of “faster”! Who's clock are we supposed to be using to judge how fast we are getting there?
 

Have you ever seen a single science fiction film where they have actually just built a damn fast space ship that would work according to the definitions of special relativity, instead of spending years in hyper sleep? I can't think of a single one. I bet a lot of people would think "but you can't do that according to relativity", but of course you can, doh!

An interesting fact associated with that issue is the fact that the acceleration of gravity at the surface of the earth, 9.8 meters per second per second, is almost exactly one light year per year per year. That is to say, if one's space ship could accelerate at 97 percent of one g indefinitely (actually a pretty comfortable environment), one could quite easily visit any star in the universe in a quite reasonable time “as measured on the ship”. Any of you guys who think they can do the math ought to work it out once.

The speed of light is 299,792,458 meters per second and there are roughly 365 days, 6 hours, 9 minutes and 9.7676 seconds for the earth to complete one orbit of the sun on average. That comes out to be 31,558,149.7676 second in one year. It follows that one light year in meters is 299,792,458 meters times 31,558,149.7676 seconds. Dividing that by 31,558,149.7676 seconds squared (inverse year in seconds squared) yields 299,792,458 divided by 31,558,149.7676 seconds which is almost exactly 9.5 meters per second per second; roughly 97 percent the acceleration of gravity at the surface of the earth. That makes rough calculations a rather easy thing to do.

Meanwhile back to Anssi's post
 

If this effect was not accounted for and compensated away, navigating a space ship would be quite troublesome!

What you should have pointed out is the fact that the aberration you are discussing is effectively an observable consequence in a purely Newtonian universe: i.e., it has nothing to do with the relativistic transformations! In fact, you then include the relativistic transformations (which I have already shown do not yield the actual correct appearances)
 

 

[math]
x'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[x-vt]
\;\;\;\;
and
\;\;\;\;
t'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[t-\frac{vx}{c^2}]
[/math]

 

which do nothing more than exaggerate the consequences of the distortion of the aberration which interests you. Since the Newtonian picture already includes that aberration, appearances should be exactly what is seen in the Newtonian picture of events. Your “one photon” picture is a direct consequence of exaggerating the supposed relativistic contraction to an utter unrealistic extreme. As I mentioned earlier, one must be very careful when it comes to recognizing those two very different perceptions as to what the universe looks like.

However, it does bring up another subtle effect which arises from general relativistic consequences.

The official scientific factual assertion is that the universe is some 3.8 billion years old and was created by something referred to as the “big bang”. Suppose this assertion is false. Suppose the the universe is actually a steady state solution and has always existed. Since our finite and changing knowledge of what exists leads to the conclusion that time is no more than a mechanism for ordering this knowledge (see pages 17 to 20 of my book if you ever get a chance to see it). That fact seriously implies the infinite nature of the unknown information, a factor the official scientific presumption simply does not handle. There is a subtle but fascinating fact embedded in that observation.

So let us examine such an infinite universe. In my book, the hypothetical tau axis is introduced on page 24 allows geometric points to represent any and all possible circumstances. Momentum in the tau direction maps directly into the concept of mass which is shown to lead directly to gravitational forces. That fact has a very important impact on what the universe looks like.

At this point it is very important to notice that time measures are influenced by both relative velocity and gravitational effects. The official scientific position does not seriously address that issue. When looking at the universe, the gravitational effects are seen as unimportant and the time changes seen at large distances are seen as entirely due to velocity differences. If we live in a steady state universe, one should expect exactly the reverse: velocity differences should, for the most part, be negligible and gravitational effects might be the more important issue.

Note that, regarding gravitational effects, we appear to reside at the center of the universe (approximately anyway). If we pick some galaxy, say half way to the edge of the apparent universe, their image of the universe would be quite the same as ours: they also would think they resided at the center of the universe. If the universe were indeed in a steady state, they would see the edge of the apparent universe (by observing and mapping the various galaxies) closer to them when viewed in our direction than they would map into the apparent universe in the opposite direction as referenced by those specific galaxies: i.e., they would see more of that steady state universe than we do when looking away from us and less than we do when looking in our direction.

In other words, suppose the apparent edge of the universe is a direct consequence of gravitational effects and not velocity effects. The edge of the universe would constitute the radial distance where the gravitation effects reach the point where the clocks rate of measure goes to zero. Certainly no stars beyond that point could impose any gravitational effects on our observations (no quantized photon exchanges could be possible; see page 100 of my book). That implies the two galaxies discussed above would each see the other as not being in the center of the universe: i.e., they would see each other as residing at a different gravitational potential.

Clearly both would see the universe as finite in size. But, more important, that perspective would be in error. The apparent edge of the universe would be the consequence of gravitation effects. The actual universe could extend right out to infinity. That implies two possible important errors in those scientific observations supposedly standing behind our view of the universe. First of all, the observed shift in time the scientists attribute to doppler effects would be due to gravitational effects and the apparent velocities of the distant stars away from us (which approach the speed of light as the edge of the universe is reached) simply vanishes. Everything in the observable universe ends up with a rather limited velocity.

That clearly explains Anssi's complaint that the observable velocities of galaxies orthogonal to the distance from us are quite small relative to the speed of light.
 

I think this effect raises an interesting question. I've sometimes wondered why is it that the entire universe is practically stationary in relativistic terms; every massive object we are detecting sits in a very small range of possible velocities.
...
I think there are interesting epistemological questions here.

It also explains why that observation must be necessary. If the universe is described by a steady state, anything traveling at any seriously relativistic velocity would have left the observable universe long ago.
 

Okay so back to the space ship with two holes. If there was a hole in the exact middle of the back plate of the ship, then aberration could not possibly have any effect. But then also distance measurement could not be performed. The holes that are off-center from the direction of motion and the star behind the ship, would get the light beam coming in in an angle that would have to be affected by aberration effect analogous to the room experiment;

Again, the aberration is a Newtonian effect and has to do with the time the photon came through the hole. Note that both the rest observer and the observer on the ship will see the photon as going through the hole and as activating the detector. Since the important moment is the actual detection, the geometric construct of the two observers is identical. That is why I laid the thing out the way I did; to make the time the photon came through the hole immaterial.
 

For the moving ship, the photons hitting the front wall at the moment of measurement must have entered the ship when the rear end was still closer to the star (even with length contraction taken into account), and the photons must have entered at whatever angle that location would imply. Since then, the beam has been expanding inside the ship while trying to catch the front wall. When it finally hits the front wall, the distance between the beams would have to be larger than is measured inside the stationary ship at the same moment (of the passing of the front plates).

The use of the term “photons” is the source of the confusion here. What must be realized is that the “photon” being detected was emitted by the “star” when the star was at some specific apparent position. During the time it takes that photon to reach the detector, the position of the star when the photon was emitted does not change at all: i.e., the hole was closer to the star by exactly the length of the ship as seen from the ships frame of reference. This is the underlying basis of the geometry used in the calculation.
 

That view gets you entirely consistent and symmetrical transformation between the frames, but since navigating to any star would be impossible if this effect was not accounted for (not to mention the effect would look different when looking out from different locations inside the ship), each space ship would have to see it as an optical illusion of a sort, and navigate either by compensating to some agreed upon frame (the center of cosmic background radiation for instance), or maybe develop a convention to always use the reference frame of some star of interest (that has some useful velocity) as the "correct" one.

The crew on the ship would simply see those stars as moving rapidly past them: i.e., in their reference frame, the star would have moved further to the rear by the original photon hit the floor. Their life would be much easier if they worked off a map rather than the actual observations when things are moving rapidly. It actually reminds me of an event which happened when I was very young. My father was trying to teach my grandfather how to drive a car (my grandfather had never ridden in anything faster than a wagon pulled by a walking draft horse). After about a month, my father gave up the issue entirely. My grandfather simply could not see things from the moving perspective. He made it quite clear that everything moving towards him from ahead of the car was just a blur. He simply could not focus on anything moving towards him with any reasonable velocity. It is quite clear that we actually posses a mental map of that moving road which he was never able to acquire.
 

And yeah, for anyone wondering, the stars directly front would not look skewed closer to the ship, they would look skewed further away.

I have a strong feeling that the issue is not quite as you present it. I think you are using calculations to determine what you will see which are not necessarily accurate. Sort of like my grandfather's view.

Have fun -- Dick

 

Edited May 19, 2014 by Doctordick

[Bombadil]

Here you are assuming the rest observer is checking the moving observer's observation. If you read what I said carefully, you would comprehend that the rest observer is not checking the moving observers measurements at all but is rather performing an equivalent measurement in his own frame.

 

So both observers have identical ships? If this is the case and both observers are measuring the distance between the photon detectors and between the windows then you have not proven that both observers will measure the same distance on their ship as on the other ship.

 

Now you also don't seem to be making it very clear how you plan to actually calculate the distance to the star and so my first thought is that you are going to use an angle side angle representation of the triangle formed so that you don't actually have to measure the length of the ship. And so this brings me to the question of how are you going to actually measure these angles? Certainly you don't plan to use a protractor.

 

With this in mind there is one point witch seems to suggest what you are thinking and that is when you say,

 

In this thought experiment, there will be a metal panel at the rear of the spaceship orthogonal to the path of the ship. In that panel, there will be two holes each a specific distance from the center line of the ship. Note that both the rest observer and the observer on the ship will agree as to the separation of those two holes (they are no more than measurements in the y-z direction).

 

That you are placing holes in the back of the ship implies that you want to use the distance between them and the location of them to measure the angles of the triangle. Formed between the incoming light and the photon detectors.

 

Now you of course agree that we still must know the length of the ship to actually measure the distance to the star, which you make clear when you say

 

The rest observer is using the manufacture's drawings for the length of the ship; not the apparent length he deduces from the relativistic transformations. In my example they are both using exactly the same length reference! If you are bothered by the fact that the rest observer cannot make his measurement at the same time as the moving observer because the ship is in the way, note that the only important issue is the position of the ship's detector at the moment the detector detected the photon on board the ship (that gives the moment at which the measurement was made from the moving ship's frame of reference). Since the ship is moving, that distance measure will change with time! The position of that detector at the moment the detection was made defines the specific moment of interest. The rest observer (at rest with respect to the distant object to which the measurement is being made) can delay his experiment to whatever time is convenient as he is not moving with respect to the distant object and he will obtain the same answer no matter when he goes to make the measurement!

 

The problem is not that I am bothered by the idea that the rest observer cannot make his measurements at the same time as the moving observer, but rather that this whole idea seems to rest on the idea that we can just measure the distance between the photon detectors and then from knowing the length of the ship we can calculate the distance to the star, which is clearly impossible as this supplies only two sides of a triangle which is not necessarily a right triangle.

 

My point is we must still measure the distance between the windows where the light enters the ship, so my question is when do you want to make this measurement? We are of course assuming that the ship is traveling fast enough that this number is making noticeable changes even in very shot periods of time.

 

As a consequence when we make this measurement it seems quite reasonable that if the ship later reverses the direction of travel so that the light now enters through the front of the ship and is detected at the back of the ship, that is the ship is now traveling in the opposite direction with the same speed we would expect that the distance between the windows would have to be changed to get the light at the other end of the ship to be picked up at the same points.

 

That view gets you entirely consistent and symmetrical transformation between the frames, but since navigating to any star would be impossible if this effect was not accounted for (not to mention the effect would look different when looking out from different locations inside the ship), each space ship would have to see it as an optical illusion of a sort, and navigate either by compensating to some agreed upon frame (the center of cosmic background radiation for instance), or maybe develop a convention to always use the reference frame of some star of interest (that has some useful velocity) as the "correct" one.

 

And if they did that, then yes, they would still calculate the distance to the different stars as identical as you said in the OP. That's why I said this is not really relevant to your point per se, but it should be mentioned as long as we talk about what things optically "look like", not "how things should be plotted".

 

I think that I can agree with you when you say that the measurement of the distances to the stars as made by observers on the ship and observers at rest will disagree in their frame that they are in, however if they can agree on a convention of some sort then it is certainly possible to solve this problem and they can both come to agree on the location of the star of interest.

 

However I don't know that I can agree on your analysis of where the stars should appear to be as it seems incomplete as you don't supply a method of measuring the angle of the incoming light.

 

The problem here is that unless we can come to some agreement on when to make the needed measurements I can see no way for either observer to say at what angle it is hitting the side of the ship. If you just want to refer to the plans that the ship was made from that is fine but we must then develop a method of timing that will result in measuring the ship that will give this same answer so that we can measure where the light enters the ship, until we do this I can see no way to say at what angle the light enters the ship.

 

Of course there is the flip side to this which is that after we have agreed on a way of making the measurements it would be very difficult to prove that our choice was the right choice after all without actually preferring the experiment.

[AnssiH]

The problem there is the definition of “faster”! Who's clock are we supposed to be using to judge how fast we are getting there?

 

Exactly. People almost always just consider Earth's frame, but seems to me that accelerating frame of the ship is far more relevant for the crew on board in quite many ways... :D

 

An interesting fact associated with that issue is the fact that the acceleration of gravity at the surface of the earth, 9.8 meters per second per second, is almost exactly one light year per year per year. That is to say, if one's space ship could accelerate at 97 percent of one g indefinitely (actually a pretty comfortable environment), one could quite easily visit any star in the universe in a quite reasonable time “as measured on the ship”. Any of you guys who think they can do the math ought to work it out once. :rolleyes:

 

Yeah, it's not something I could have figured out in a hurry, but here's someone else's attempt;

 

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

 

If he hasn't made mistakes, 1 g acceleration works out as 28 years to travel 2 000 000 light years (in earth frame), even if you decelerate back to earth's frame for half of the trip.

 

What you should have pointed out is the fact that the aberration you are discussing is effectively an observable consequence in a purely Newtonian universe: i.e., it has nothing to do with the relativistic transformations!

 

Yup. Albeit the expected amount of aberration is little different between newtonian view and special relativitistic view, as represented by length contraction or time dilation, whichever way one wants to view it. Probably the easiest way to see it is to consider that room with a hole on the ceiling, traveling arbitrarily close to C in a lab frame.

 

In newtonian view, the light that looks orthogonal to the floor of the room in the lab frame, is expected to appear in 45 degree angle in the ship's frame.

 

In relativistic view, the ship must be taken as extremely length contracted in the lab frame, which yields the result that the light coming through the hole is plotted to hit the top of the back wall instantly; from the room the light appears to be coming from the extreme front angle, almost parallel to the direction of travel.

 

Of course the crew inside the room doesn't take themselves to be length contracted, but as long as those relativistic definitions are valid (i.e. self-consistent), the crew must nevertheless also see the light hitting the top of their back wall; the light must appear to be coming from the extreme front angle.

 

Obviously that is not the same thing as assuming the crew would see the beams inside their space ship as forming a length contracted triangle; obviously they would not. It is just to say that the expected amount of aberration is different between newtonian view and special relativity. And in both cases, if the crew knows what to expect, and if their expectations are valid, they would have to be compensating that effect out of their calculations, otherwise they would be knowingly calculating wrong distances :D

 

Your “one photon” picture is a direct consequence of exaggerating the supposed relativistic contraction to an utter unrealistic extreme.

 

If relativistic aberration is valid, it's not such an unrealistic extreme as just after few years of acceleration in 1 g would be expected to cause almost all of visible universe to appear almost directly in front of the ship :I

 

If it's true, it is also a little odd in my opinion... But on that token;

 

However, it does bring up another subtle effect which arises from general relativistic consequences.

 

The official scientific factual assertion is that the universe is some 3.8 billion years old and was created by something referred to as the “big bang”. Suppose this assertion is false. Suppose the the universe is actually a steady state solution and has always existed. Since our finite and changing knowledge of what exists leads to the conclusion that time is no more than a mechanism for ordering this knowledge (see pages 17 to 20 of my book if you ever get a chance to see it). That fact seriously implies the infinite nature of the unknown information, a factor the official scientific presumption simply does not handle. There is a subtle but fascinating fact embedded in that observation.

 

Personally I find it odd that people have such a hard time conceptualizing the idea that reality does not have a beginning. In my view taking big bang theory as a creation myth is just as naive and ignorant as any "religious" creation story. The desire to estimate the age of the universe is pretty much a joke in my view, because it's almost impossible to define what is meant by that. And the fact that the age estimate is being continuously tweaked when the age estimates of some stars imply that they are older than the universe, when those age estimates are performed via analyzing radiactive decay. There are so many assumptions upon assumptions in those analyses that I just have hard time of thinking about them as anything but wildly speculative.

 

It has become a modern creation myth simply because people love to have simple explanations they can conceptualize in their minds without thinking too much. And if they were interested of thinking about it, they would probably realize there are some pretty serious epistemological problems with that whole idea. Even if it could be proved that the observable universe is not a stable solution, taking the observable universe = reality itself is just as self centered and narcissistic as saying God created man as his image.

 

And yeah, I have no problems considering stable solutions, in many ways I find them more plausible than unstable solutions, for similar reasons than you do (having nothing to do with ontological considerations, but purely epistemological considerations).

 

In other words, suppose the apparent edge of the universe is a direct consequence of gravitational effects and not velocity effects. The edge of the universe would constitute the radial distance where the gravitation effects reach the point where the clocks rate of measure goes to zero. Certainly no stars beyond that point could impose any gravitational effects on our observations (no quantized photon exchanges could be possible; see page 100 of my book). That implies the two galaxies discussed above would each see the other as not being in the center of the universe: i.e., they would see each other as residing at a different gravitational potential.

 

I find all those ideas very interesting. In general the observation that when the universe is viewed from any particular location, there exists a distance where our object definitions essentially break down, is quite interesting. And if is valid, i.e. can be epistemologically proven, it sits with me quite a bit better than naive realistic idea of invisible framework of space that is stretching faster than light.

 

The use of the term “photons” is the source of the confusion here. What must be realized is that the “photon” being detected was emitted by the “star” when the star was at some specific apparent position. During the time it takes that photon to reach the detector, the position of the star when the photon was emitted does not change at all: i.e., the hole was closer to the star by exactly the length of the ship as seen from the ships frame of reference. This is the underlying basis of the geometry used in the calculation.

 

Yes, correct in terms of (lack of) visual effects of length contraction, but it is also the reason why the aberration effect was not accounted for in your thought experiment; if the speed of the light is effectively seen as instantaneous when it is traveling inside the ship, then there's no expectation for the aberration effect.

 

If it takes "time" for the light to travel through the ship, then there exists different expectations for different velocities of the ship (as different versions are plotted in some lab frame), in terms of observable aberration inside the ship.

 

Basically the situation for different cases must be plottable to a single frame, and if they are expected to show different results in that frame (because the faster the ship is "escaping" the light beams, the more time the light beams are expected to expand inside the ship), then they must be expected to show different results no matter which frame things are plotted to or transformed to.

 

The only slightly counter intuitive part of that whole thing is that, when the star is plotted as moving (when the light was emitted), the ship must expect to get an aberration effect off of it just the same... But little thought experiments suggest it must be so.

 

The crew on the ship would simply see those stars as moving rapidly past them: i.e., in their reference frame, the star would have moved further to the rear by the original photon hit the floor. Their life would be much easier if they worked off a map rather than the actual observations when things are moving rapidly.

 

Indeed, that would have to happen.

 

It actually reminds me of an event which happened when I was very young. My father was trying to teach my grandfather how to drive a car (my grandfather had never ridden in anything faster than a wagon pulled by a walking draft horse). After about a month, my father gave up the issue entirely. My grandfather simply could not see things from the moving perspective. He made it quite clear that everything moving towards him from ahead of the car was just a blur. He simply could not focus on anything moving towards him with any reasonable velocity. It is quite clear that we actually posses a mental map of that moving road which he was never able to acquire.

 

Heh yeah, I don't doubt that story. We are processing incomprehensible amount of information just to comprehend what is around us...

 

I have a strong feeling that the issue is not quite as you present it. I think you are using calculations to determine what you will see which are not necessarily accurate. Sort of like my grandfather's view.

 

Entirely possible. Also I'm sure I am neglecting some effects that could be relevant in a practical situation. In that page I linked to in the beginning of this post I noticed one interesting little comment; he mentions that the doppler shifted background radiation at near light speeds would be seen as so energetic it would just melt all the known metals... If that's true, that could throw a wrench in our interstellar travel plans...

 

-Anssi

[AnssiH]

Now you also don't seem to be making it very clear how you plan to actually calculate the distance to the star and so my first thought is that you are going to use an angle side angle representation of the triangle formed so that you don't actually have to measure the length of the ship. And so this brings me to the question of how are you going to actually measure these angles? Certainly you don't plan to use a protractor.

 

In the thought experiment the star was seen as being directly behind the ship in terms of direction of travel (or in other words, the star's velocity is seen as directly receding from the ship). It's best to approximate it as a point like source.

 

If you take those two holes, and draw lines from the holes towards the front wall, directly parallel to the length of the ship (parallel to the direction of travel/star's apparent velocity), you can mark those positions.

 

Any light coming from a point light source behind he ship would be coming through the holes in such angles they would not quite hit the positions you marked. Knowing the distance between the holes and the wall, you can figure out the angles of the beams. And if you work out where those beams would cross, you get the calculated distance to the source. (plus you'd need to compensate for whatever aberration effect you expect to affect the situation)

 

And yeah the "ships are identical"; best think of it as the same ship in different circumstances.

 

If you just want to refer to the plans that the ship was made from that is fine but we must then develop a method of timing that will result in measuring the ship that will give this same answer so that we can measure where the light enters the ship, until we do this I can see no way to say at what angle the light enters the ship.

 

The punchline here is kind of exactly the fact that it is not possible to prove "where" the light enters the ship, because "where" cannot be defined. It is not possible to measure the lengths of moving things without knowing the speed of information (light) to all directions. It is not possible to measure the one-way speed of light without synchronizing clocks. And it is not possible to synchronize clocks without knowing the speed of light, so there's no way around that problem.

 

Relativity is a self-coherent collection of definitions that yield a convention for representing the universe in a self consistent manner. As an ontological idea its just a metaphysical circle of beliefs that cannot be proven. I believe what DD was kind of wanting to draw attention on is the very true fact that length contraction is not in itself an observable thing. It is just a result of plotting information in a framework where each inertial frame has got its own simultaneity notion, established by the idea that the speed of light is always represented as C to all directions, and simultaneity and object lengths are adjusted to compensate (to make the picture self-consistend across frames).

 

-Anssi

Edited January 17, 2014 by AnssiH

[Bombadil]

I'm sure Michio Kaku is meaning well, but I really don't think he should be allowed to represent things the way he always does. But, not only is he allowed to keep doing this, he is regarded as one of the big physicists. In his Wikipedia page, there is no "criticism" section at all. Well, allow me. Here's some of the things where he misrepresents standard special relativity;

 

In truth I think of Michio Kaku as little more then a public face that is meant to try to shorten the gap between the scifi fans and the physicists, although I wonder if some of the stuff he says isn't closer to scifi then not, and I also wonder at times if he's not doing more harm then good. In truth I can't hardly stand watching him at times, but I don't think that I am missing anything by not watching him either although I did watch the video that you posted, partly just so that I could say that I did.

 

Oh by the way, the part that I find almost the best is when they start saying that... oh we can bend space time but we need a huge amount of energy without actually giving any number and then say it is actually negative energy that we need and then say something about the size of Jupiter. The best part though or maybe the worst part depending on your view is the end where you get to see the responses of the people that he is talking to, they actually believe everything that he just said.

 

If you want to watch someone that is doing a better job at explaining things then watch Leonard Susskind in the Stanford lectures, at least he is not trying to dumb it down to the point of making anyone think that all you have to do is talk big to be a physicist and he is not trying to hide all of the math. On the other hand he is probably so far ahead of most people that they would rather listen to someone like Michio Kaku say it wrong just because they can at least pretend to understand Michio Kaku, where Leonard Susskind is probably just an old man in front of a board writing gibberish to most people. Also Leonard Susskind spends most of his time in those lectures, due to their nature, just explaining mathematics to the point that he says he is doing relativity when what he is really doing is an introduction to differential geometry.

 

Any light coming from a point light source behind he ship would be coming through the holes in such angles they would not quite hit the positions you marked. Knowing the distance between the holes and the wall, you can figure out the angles of the beams. And if you work out where those beams would cross, you get the calculated distance to the source. (plus you'd need to compensate for whatever aberration effect you expect to affect the situation)

 

My point is that if the windows in the back of the ship are fixed then I see no reason to assume that when the moving ship and the stationary ship make their measurements that they will come to the same measurements of where the photon detectors are, in fact I expect them to be different.

 

The punchline here is kind of exactly the fact that it is not possible to prove "where" the light enters the ship, because "where" cannot be defined. It is not possible to measure the lengths of moving things without knowing the speed of information (light) to all directions. It is not possible to measure the one-way speed of light without synchronizing clocks. And it is not possible to synchronize clocks without knowing the speed of light, so there's no way around that problem.

 

Really, you can't imagine a way to measure the speed of light in one direction? I'll admit that different things are assumed and it has to be done carefully but I can imagine a means of doing it. Just take two discs that are nontransparent and connect them together with a rod, and put one hole in each where you have carefully measured the angel between the holes if you were to lay the discs on top of each other.

 

To actually make the measurement, just start spinning this thing by the rod, so that it looks like a pair of tires, then look at it from one end so that all that is seen is one of the disks spinning. Set a laser on the other end pointing at the same height as the hole so that there is one position of the wheel where it will shine though one of the holes, now notice that when the speed of rotation of the disks is just right the laser will make it all the way though both holes and can be picked up on the other side of the device.

 

We can then, by knowing how long the device is, how fast it is rotating and the angel between the holes, calculate the speed of the light.

 

 

Relativity is a self-coherent collection of definitions that yield a convention for representing the universe in a self consistent manner. As an ontological idea its just a metaphysical circle of beliefs that cannot be proven. I believe what DD was kind of wanting to draw attention on is the very true fact that length contraction is not in itself an observable thing. It is just a result of plotting information in a framework where each inertial frame has got its own simultaneity notion, established by the idea that the speed of light is always represented as C to all directions, and simultaneity and object lengths are adjusted to compensate (to make the picture self-consistend across frames).

 

I think this kind of misses the point here which I see as two fold. Firstly if the measurements are done consistently it really makes no difference if we use an instrument, a thought experiment, or do it ourselves, we are going to get the same result. And if we where to actually have a ship that we could get up to say 98% of the speed of light and we had the technology to do the thought experiments, would we come to the same measurements, not to say they are real or not but rather to say put in a life or death scenario is it really going to work like that.

 

To say that “I believe what DD was kind of wanting to draw attention on is the very true fact that length contraction is not in itself an observable thing.” is kind of like saying to me that the math is wrong. If the math says that there is going to be a measurable length contraction and we are consistent, then I think that you had better expect to see length contraction when you get in a ship and set the computer for prolonged acceleration at 32ft sec sec we will see the universe around us look differently then if we hadn't been accelerating at 32 ft sec sec, not to say it is real just to say you are going to see it if the model is consistent.

[Doctordick]

In my original post to this thread, I said the following:
 

First of all, the correct transformations between the two frames are expressly given by the following well known special relativistic relationships:

[math]
x'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[x-vt]
\;\;\;\;
and
\;\;\;\;
t'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[t-\frac{vx}{c^2}]
[/math]

 

Regarding the other relationships, y'=y and z'=z so these coordinates do not require a careful analysis. On the other hand, any measurements involving x and x' must be carefully looked at.

The issue I was trying to bring up is the fact that these transformations do not define how the universe appears to an observer in these two frames. They are rather, the appropriate transformations to the space-time plots required to make the physics equations valid; an assertion quite different from "how the universe appears".

Given any specific collection of dynamic events, "how the universe appears" requires specific corrections from that specified "space-time plot" of events. These corrections have to include the consequences of the finite speed of light. "How the universe appears" is very definitely not at all as it is represented in that "space-time" plot specified as one's frame of reference! In fact, "how the universe appears" is more accurately represented by the assumption that the speed of light is infinite: i.e., when we look out at the stars, they appear to be in specific locations which are not at all the locations held as correct in that abstract "space-time plot". From the perspective of the standard "space-time plot" the observed locations (what we see when we look) are where those stars were years ago (the nearest stars are light years away) to billions of years ago (most of the stars we see).
 

To say that “I believe what DD was kind of wanting to draw attention on is the very true fact that length contraction is not in itself an observable thing.” is kind of like saying to me that the math is wrong. If the math says that there is going to be a measurable length contraction and we are consistent, then I think that you had better expect to see length contraction when you get in a ship and set the computer for prolonged acceleration at 32ft sec sec we will see the universe around us look differently then if we hadn't been accelerating at 32 ft sec sec, not to say it is real just to say you are going to see it if the model is consistent.

No, I am not saying "the math is wrong"; what I am saying is that when you simply convert the representation from frame #1 to frame #2 you have not finished the job! In order to get an accurate picture of what you will see when you look, you must further take into account the length of time the light takes to get to your eyes. What that means is that it looks like it came from where it was at an earlier time. How much earlier depends on how far away it was.

 

Really, you can't imagine a way to measure the speed of light in one direction? I'll admit that different things are assumed and it has to be done carefully but I can imagine a means of doing it. Just take two discs that are nontransparent and connect them together with a rod, and put one hole in each where you have carefully measured the angel between the holes if you were to lay the discs on top of each other.

That word should be "angle".
 

To actually make the measurement, just start spinning this thing by the rod, so that it looks like a pair of tires, then look at it from one end so that all that is seen is one of the disks spinning. Set a laser on the other end pointing at the same height as the hole so that there is one position of the wheel where it will shine though one of the holes, now notice that when the speed of rotation of the disks is just right the laser will make it all the way though both holes and can be picked up on the other side of the device.

We can then, by knowing how long the device is, how fast it is rotating and the angel between the holes, calculate the speed of the light.

What you are failing to take into account is the fact that the above measurement presumes the speed of light is the same in both directions. An observer moving with respect to you will say that the length of the rod is different from what you are presuming and the time between the positions of the holes when the laser went through was different than what you presumed. He would assert the speed of light as measured by your device was too small in one direction and too large in the other. In fact, those differences are exactly what is being represented in the equations at the top of this post.

In fact, if you were to assert that there was only one correct frame of reference (say frame #1) such as "the rest frame of the universe" and both of you used that reference frame to define all your measurements, you would obtain identical results. On the other hand, making the required corrections due to the different velocities of light in different directions would make the physics equations quite a bit more cumbersome. Electric fields and other phenomena (some of which are presumed due to virtual photon exchange) would also be distorted. In fact, time measurements would be distorted as the round trip of light would be longer in the moving frame. But those effects are very small if the relative velocities are small compared to "c"; they are nevertheless quite complex corrections.

Instead of my earlier example, consider two pinhole cameras separated by some specified distance orthogonal to the plane of the film. Given the distance between the pinholes and the distance to the film, the pictures provide a geometric reference (analogous to bifocal vision) which allows a calculation of the distance to the pictured points of light. Clearly the pattern of points at a specific instant would be the same for both observers (being in the y,z plane). The time attached to the picture would be different as the two will differ as to the rate at which time is passing but that issue is immaterial to the geometric constructs. The only significant issue is the supposed difference in that distance from the pinholes to the film. And, exactly what does the relativistic transform say about that issue? The two observers will disagree about that distance. Each will say that the other's camera is foreshortened as compared to theirs (they will disagree as to who is at rest). Furthermore, they will also see the positions of the objects being photographed as being shortened in the x direction by the other's calculation.

But let us look at that issue from the perspective of the fundamental units used by each of those observers. They are both going to be working with some fundamental length standard. For the sake of argument, let that standard be the length of the camera from the pinholes to the film. The "rest" observer (which could be either) will assert the other camera is foreshortened so they are getting incorrect calculations. However, what results are they obtaining? The "rest" observer will assert that the moving observer sees the rest universe (his representation) as foreshortened. By what amount is it foreshortened? Well, don't you find it strange that the foreshortening factor is exactly the same?

In essence, the moving observer will obtain exactly the same picture of the universe as the rest observer. They will each say that the others calculation is in error as it is foreshortened in comparison to theirs. But the reference length they are using is also foreshortened by the same factor thus their actual answers will be the same. Only their time measurements will actually be different. In order to understand that difference you would have to read my book.

Have fun -- Dick

 

Edited May 19, 2014 by Doctordick

[AnssiH]

My point is that if the windows in the back of the ship are fixed then I see no reason to assume that when the moving ship and the stationary ship make their measurements that they will come to the same measurements of where the photon detectors are, in fact I expect them to be different.

 

You left out the most important bit; by which mechanism do you expect them to be different? In terms of relativity, they are expected to be the same, apart from an aberration effect that has an expected magnitude, and is taken to be an optical illusion.

 

If you expect them to be different, then it would be meaningful to describe what mechanism are you thinking?

 

Really, you can't imagine a way to measure the speed of light in one direction? I'll admit that different things are assumed and it has to be done carefully but I can imagine a means of doing it. Just take two discs that are nontransparent and connect them together with a rod, and put one hole in each where you have carefully measured the angel between the holes if you were to lay the discs on top of each other.

 

To actually make the measurement, just start spinning this thing by the rod, so that it looks like a pair of tires, then look at it from one end so that all that is seen is one of the disks spinning. Set a laser on the other end pointing at the same height as the hole so that there is one position of the wheel where it will shine though one of the holes, now notice that when the speed of rotation of the disks is just right the laser will make it all the way though both holes and can be picked up on the other side of the device.

 

We can then, by knowing how long the device is, how fast it is rotating and the angel between the holes, calculate the speed of the light.

 

I could easily find references that explain why one-way speed of light measurements are impossible, but it's much more fun and more useful to think these issues through yourself, let's talk through the whole thing. It's very important issue to understand actually because there are very fundamental reasons as to why it is so. It's quite a shame that it's not very often mentioned...

 

First we need to carefully define what we are measuring; We have a rod of particular length, and we want to measure the time it takes for the light to travel the length of that rod.

 

What we mean by "the time it takes" must also be defined. Clocks are electromagnetic devices undergoing some cyclical process, where the cycles can be measured. A simplest possible clock would be two mirrors and a photon bouncing between, where we count the cycles.

 

Two-way speed is dead easy; we just place a mirror at the other end of the rod, and have the same clock register the departure and the arrival of a beam of light. Count the clock cycles in between these events, and you get the two-way average speed.

 

For one-way speed we use two clocks, one to register the departure, and the other to register the arrival.

 

And now we have the problem; to make a meaningful measurement, we must have synchronized clocks. But we don't know if the clocks are synchronized, without checking it. We can only check it via light signals, so we would have to know the one-way speed of light to check. Also, we can't first synchronize them at one end and then move them to their locations, since clocks are electromagnetic devices, so we don't know what impact does moving them have to their rate of operation, without knowing the one-way speed of light (and without being able to check after moving what happened to the clocks).

 

Furthermore, it turns out that if you just assume any one-way speed of light, and compensate the opposite direction speed until you get the same average as you already measured, you will always get the same observable results no matter what you defined your one-way speed of light to be.

 

This leads to an important realization that all physicists were well aware of over a hundred years ago; you cannot prove simultaneity of two separated events. To prove the simultaneity, you would have to know one-way speed of light, which you cannot measure, because you'd need to already know what it is, to setup any meaningful experiment.

 

Effectively in your proposal you are assuming that you know the simultaneity of events (regarding how those wheels actually rotate in relation to each others), which is based on the critical error; an unprovable assumption that electromagnetic information is propagating at constant speed to all directions in your frame; the very property we were supposed to measure has already been assumed to be known at the initial setup.

 

Since one-way speed of light is not a measurable property of the nature, it is in some sense "immaterial". And that is exactly the heart of special relativity; because it can't be measured, it can also be defined as being C in all directions, in all inertial frames.

 

The freedom to define C this way, e.g., to define simultaneity to suit your purpose in any frame, is exactly the crux of special relativity. What you have to keep in mind though is that it is a valid method (of many valid methods) of translating a particular inertial frame representation of something into a different inertial frame representation. If you choose to represent a spaceship from a different inertial frame, nothing actually happens to that spaceship just because you chose to represent it in different manner.

 

The converse is equally true, when the spaceship accelerates from one inertial frame to another, it will not actually shrink in any provable manner; just the way it is represented from the old frame is such that it is plotted as being shrunk. Most relativity representations say things like "the crew doesn't know the ship has shrunk because they have also shrunk", which is absolutely a misrepresentation of relativity. If the ship did actually shrunk, it would be because there is a preferred frame. If there is no preferred frame, it is a representational effect; a function of the frame you chose to plot the situation in.

 

And if the crew on-board want to represent the rest of the universe from their new frame, they must represent the universe as shrunk if they are using the SR convention correctly (which is a valid convention), but equally so, their act of choosing to do so does not actually shrink the rest of the universe.

 

I think this kind of misses the point here which I see as two fold. Firstly if the measurements are done consistently it really makes no difference if we use an instrument, a thought experiment, or do it ourselves, we are going to get the same result. And if we where to actually have a ship that we could get up to say 98% of the speed of light and we had the technology to do the thought experiments, would we come to the same measurements, not to say they are real or not but rather to say put in a life or death scenario is it really going to work like that.

 

To me, thought experiments are not assertions about reality, they are just logical examinations to the consequences of some definitions. Whether or not those definitions are valid, or whether they are true to reality, are much broader subjects. The definitions we are talking about in this particular thread, I would consider to be approximately valid with quite reasonable accuracy.

 

To say that “I believe what DD was kind of wanting to draw attention on is the very true fact that length contraction is not in itself an observable thing.” is kind of like saying to me that the math is wrong. If the math says that there is going to be a measurable length contraction and we are consistent, then I think that you had better expect to see length contraction when you get in a ship and set the computer for prolonged acceleration at 32ft sec sec we will see the universe around us look differently then if we hadn't been accelerating at 32 ft sec sec, not to say it is real just to say you are going to see it if the model is consistent.

 

ACtually what DD was saying was in complete accordance to the math of relativity. It was exactly the expectations in the case that relativity is valid.

 

See that's exactly where the problem is, the way that relativity is usually represented is to imply that things like length contractions are real observable things that we would simply see if we were moving at those speeds. And when someone points out otherwise, it is easily taken to be a contradiction of relativity, when it is not. The problem is, relativity is often represented vaguely, or plain misprepresented, even by "reliable sources". There are many ways to say these things, and if someone says "the spaceship is seen as length contracted", they could mean the spaceship is represented or plotted in a spacetime diagram as length contracted, or it is optically seen as length contracted, or both.

 

In actual fact, in terms of relativity, it is just the way things are plotted in spacetime diagrams, and that fact is usually lost in most representations of relativity, although it is blatantly obvious if you understand the fundamental underpinnings of relativity.

 

-Anssi

[Rade]

See that's exactly where the problem is, the way that relativity is usually represented is to imply that things like length contractions are real observable things that we would simply see if we were moving at those speeds.

? Evidence of "Optical" Lorentz contraction was reported here in Physical Review Letters. So, yes, Lorentz length contraction of "real" objects can really be observed, just takes some thinking how to design the experiment. If the basis of this thread topic is to claim it is impossible to design an experiment to optically observe "real" Lorentz contraction, then the premise of this thread topic is based on a false assumption.

 

Are there no professional physicists that moderate this area of the forum to respond to the false claim that it is impossible in theory to devise an experiment for humans to optically observe Lorentz contraction ?

===

 

APS » Journals » Phys. Rev. Lett. » Volume 75 » Issue 7

 

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Phys. Rev. Lett. 75, 1372–1375 (1995)

Lorentz Contraction of Flux Quanta Observed in Experiments with Annular Josephson Tunnel Junctions

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A. Laub, T. Doderer, S. G. Lachenmann, and R. P. Huebener

Lehrstuhl Experimentalphysik II, University of Tübingen, D-72076 Tübingen, Germany

 

V. A. Oboznov

Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow district, 142432, Russia

 

Received 28 April 1995; published in the issue dated 14 August 1995

 

Vortices (magnetic flux quanta) in Josephson tunnel junctions can move at velocities near the propagation velocity of light in the junction, and they undergo the Lorentz contraction. In annular junctions, pairs of vortices and antivortices are created; these move in opposite directions and collide with each other. Using low-temperature scanning electron microscopy, we can visualize the collision region. We observe the contraction of the collision region with increasing vortex velocity. With the assumption that the length of the collision region is proportional to the length of the vortices, we can directly image the Lorentz contraction of magnetic flux quanta.

 

© 1995 The American Physical Society