md65536

1 hour ago, geordief said:

I won't attempt to  patch it up as  I would probably make a bad job worse.

I think you should! If you think it's a bad job and don't know how to make it better, then we haven't done a good job in explaining it. There are aspects of this topic that I'm going to keep getting wrong until I see it in the right way. I know for myself it'll take repetition, to keep looking at it.

Besides, I don't think that you did a bad job. Originally you didn't specify the two events of the interval precisely, but 1) it was good enough to understand what you implied, and 2) the imprecision only changes the 200 seconds value by +/- 3.3 microseconds, so imprecision is not a problem there.

I'm not concerned with the exactness of the example interval, but I'm concerned about the meaning of it especially with respect to multiple frames of reference.

1 hour ago, joigus said:

The problem is under-determined.

Maybe I misunderstood something...

No, I think you're right. When OP wrote,

On 10/16/2020 at 7:33 PM, geordief said:

Am I right to say that the spatial measurement component of the spacetime interval  between the 2 events is the 1000 metres and the time component ( ie the ct component) is the 200 light.seconds taken by the signal to make the round trip and return to the vicinity of its emission?

you're basically saying that the 200 LS is imprecise or an assumption about where the reflection point is. I was treating it as though it was supplying the previously missing information, but that's not explicit.

2 hours ago, joigus said:

It is not specified well enough by Euclidean distances only. This may be at the root of the problem that @md65536 sees.

No, I didn't see that as a problem. The original spec is, "So we have 2 events ; the emission and the recapture of the signal," and "200 light.seconds taken by the signal to make the round trip." It's not specified where the reflection point is, but I don't think that matters because it's only used to establish the time between the two events, and that's given.

For me the light reflection path is irrelevant. It's only used here as a clock, and any stationary clock would do. Yes, there are light-like intervals between the reflection point and each of the 2 events, but I wasn't thinking of those.

I think I've completely confused the meaning of hyperbolic angle, which I tried to relate to the derivative dr/dt.

With a given invariant spacetime interval, a change in the t and r parameters doesn't involve moving along a world line between the two events. It involves rotating the fixed interval through different frames of reference, to vary the t and r components that make up the same fixed interval. If you do consider a particle moving along such a world line, it's moving through different points along that line, ie. different events, each of which makes a different spacetime interval between it and the initial event. (Though, in the case of light-like paths, all of those intervals are 0! But they can still be rotated so that different observers measure light between the two events traveling a different distance during a different time. Lol I'm sure there's a simpler way to look at this.)

You're in over my head! Hopefully someone else can help?

That's the derivative of a hyperbola. I don't see it saying anything about switching places. When y (or r) is small, it changes quickly. As y gets bigger, it approaches x (or ct), and the rate of change approaches constant; a unit hyperbola asymptotically approaches the line y=x.

If you take the spacetime interval and make r a function of t, I think what that means physically is... It describes how the spatial distance of the interval changes as a function of the time component of the interval, as you go through different frames of reference. The infinitesimal changes in t for example would mean, if you change inertial frames by just a little (ie. with infinitesimal change of speed), the time and spatial distance components of the interval change like a hyperbolic function does. Or, an infinitesimal change in speed corresponds with an infinitesimal hyperbolic rotation of the spacetime interval.

Edit: I'll leave that there but it's wrong! When both x and y are very large, an infinitesimal rotation (I think) can still mean a huge change in x and y. So to correct that: A small change in inertial frame involves an infinitesimal change in t and an infinitesimal change in r. However, as speed approaches c, a small change in speed (but huge change in rapidity) can involve a huge change in t and r. That makes sense with respect to velocity composition, right? Maybe it's correct to say "an infinitesimal change in rapidity corresponds with an infinitesimal hyperbolic rotation of the spacetime interval", but I might change my mind again after learning more...

16 hours ago, michel123456 said:

Is that your objection? (still searching the quote)

"If it's not moving, it's not Lorentz contracted" seems like a good rule to me.

"If it's moving, it's length-contracted" could be made into a rule of thumb, but it's problematic (point particles, c, distances between relatively moving points, I think don't easily fit).

"If B is moving, then (something else) is length contracted" is not a rule as you seem to think.

I don't remember stating a rule though, so you might not find it. I did ask you which of certain objects (not distances) were moving and which were length-contracted. Misinterpreting things like that, and misinterpreting what SR says, and assuming it says something that you've invented, is a recurring problem here.

I wrote:

Quote

The distance between the dice must contract the same as an object of the same length.

Not that it'll matter for you, but it would have been helpful if I'd instead said something like that the "rest or proper distance between the dice is contracted in the frame where they're moving." If you're talking about a length being contracted, it's only relative to the length measured in another frame. Here the frames of reference are implied, but if you want to think about rules, it'd be better to be explicit about frames.

If you want to think of a distance being contracted, think of a ruler that is measuring the distance. If that ruler is moving (in frame F) then distances being measured using that ruler are contracted (in frame F). If you're talking about measuring a distance to B, as measured by X, using X's ruler (that is not moving relative to X), then distances as measured using that (relatively) stationary ruler are not contracted according to X. I expect you to either ignore or twist this idea. Also, this is just my attempt to explain things as far as they make sense to me. It's not an "official rule of SR", and if it disagrees with SR or can be so easily misinterpreted, it's not a good rule. Certainly there are clearer and/or more precise ways to explain it.

1 hour ago, michel123456 said:

Applying MD's rule:

From the FOR of X, Is B moving?

If B is moving then the distance is contracted.

What rule is that? That's not my rule.

33 minutes ago, michel123456 said:

Now, if you keep in mind that the situation must be so that you cannot know who is the "moving" and who is the "at rest", you get the confusion I struggle with.

You don't know how to tell if something is moving?

4 hours ago, michel123456 said:

Show me.

What are you trying to achieve here? I'd say the question of whether or not you will learn relativity is answered, your refusal to do so is just too strong. I think you've convinced others that you're interested in relativity, even though you've stated that you're not. I don't see what's in it for you, to waste time on this. Do you hope to have your mind changed? Do you hope to change anyone's mind? I'm fairly certain, no one's changing their minds here. This will go on to page 140+. Would you persist, knowing you'll never change the mind of someone who understands relativity?

For others, how long is it worth persisting if the result is what we currently have? (For myself, it's only worth it to write about relativity in this thread if I'm doing it for myself, not to try to inform michel123456.)

When you say "hyperbolic rotation", michel123456 reads "pirouette". You can't force-feed understanding to someone willing to put in the effort to avoid it.

It's meters or lightseconds or any distance units, squared. The use of distance units is apparently a convention, see https://physics.stackexchange.com/questions/519707/is-the-unit-for-spacetime-intervals-time-or-space-distance

Yes, for a time-like interval, the time component will be greater than the spatial.

For time-like (or light-like for that matter) intervals, the ratio of r/t is the constant speed of a particle that moves between the two events.

ct/r would be the ratio of the distance that light travels between the two events (along any path that gets it there, like your 200 lightsecond example) to the straight-line spatial distance between the two events, in the given frame. This ratio is frame-dependent, and undefined in frames where r=0.

(ct)^2/r^2... I'm not sure of any meaning to that. As squares, the equation of the interval s^2 (a constant) =(ct)^2-r^2 is that of a hyperbola, and relates to the pythagorean theorem.

Conventionally in SR "observer" refers to a frame of reference. If you used that convention (not that you have to, just that it can be helpful to think in these terms), then A and B are the same observer when they're not moving relative to each other. They measure times and distances the same. Local measurements differ, like the relative timing of perceived light from distant events, that each can see (ie. locally measure) in different orders, but that doesn't matter in your example.

A and B measure the same as each other, the time between the two events, and the distance between the two events. They measure an interval with a length of negligibly less than two seconds.

A moving observer (another reference frame) would measure a generally different time between the two events, and a different distance between the two events, but end up with the exact same interval length.

The interval you're describing is a timelike interval (meaning a clock could travel between the events, and record its length as a proper time). The time component that A measures is simply c multiplied by the time on A's clock measured between the events. But of course that's the distance that A measures light traveling in that time, so you're right that it is 200 light seconds.

The reflection point being 100 light seconds away doesn't really matter either, for the interval you're describing. Basically you're measuring the time between the events using a very big light clock that ticks just once between the events. A smaller light clock that reflects a light signal multiple times, can measure the same thing.

I don't care whether you ever learn relativity. It's still interesting to find errors in what seems like paradoxes, but you're just adding complication on top of previous errors. Why not go simpler instead of more complicated? You don't have a solid foundation to build on, but you're building anyway.

9 hours ago, michel123456 said:

diag 6

Exactly the same diagram with annotated the point Xb that is on the rod of B at 0.6 LH from him. X will reach this point in 45 min from the FOR of B. It is the same point Xb that is shown in diag 3.

I think that's wrong. How do you get that X takes 45 minutes?

If B starts at E, and the length to X is length-contracted to 0.6 LH (in B's frame), then X is already at that location (in B's frame) at B's time 0.

A problem when introducing rods like this is that you can't just compare both ends of a rod at a single time that applies in multiple frames. You have to consider relativity of simultaneity (the real one, not "what I'm calling RoS" etc). You could always label the events that you're describing, in the frames you're describing (so it's not just an x-coordinate like Xb, but an x and a time coordinate, and they're different in different frames).

But I still think you're wasting your time. I think you would do better trying to learn Galilean relativity.

9 hours ago, Eise said:

I would suggest, that you do not try to press relativity in the way you are used to think about time and distances. Try to understand relativity as it is, lookup simple derivations. If you do not understand some step in the derivation, come here and ask. The terms in which you are thinking bear no fruit in understanding relativity.

Yes, I agree. Even without the derivations, just much simpler examples, starting with the basics and without already deciding the answers before looking at the examples. One of the many problems here is that we're all looking at a relatively complicated example and trying to explain/understand step 10 of it, and Michel is effectively saying "I replaced step 3 with my own ideas, but can you keep explaining step 10 over and over? You're doing it wrong because I'm getting different results."

Though, I still think giving up and not misusing the language of SR is a good option for him.

6 hours ago, michel123456 said:

But when @Eise  quoted @Janus & explained the "However" part, that made sense to you, and it was about Relativity.

Correct! Their numbers made sense and I could repeat the calculations of SR to get them, and when they referred to "relativity of simultaneity" they were using the established meaning of the term. Your numbers are based only on a denial of time dilation (your "?=30" is based only on having B's clock match X's, nothing else), and you use your own personal redefinition of RoS that seems to mean some combination of "light is delayed, and I've modified Galilean relativity so that it is not symmetric".

Anyway, I'm not interested in discussing your alternative model, so... good day, sir.

1 hour ago, michel123456 said:

I believe that in the FOR of B, X does not start to move instantaneously.

I see. That kind of makes sense... B measures a shorter trip but a delayed start and ends up with the same time that X has.

That's not special relativity. There's no point in discussing what special relativity predicts any further, if we're talking SR while you're talking about your own ideas in the language of SR. I could demonstrate why "when B starts moving relative to X, X is delayed before moving relative to B" is inconsistent, but if you have no problem picking aspects of relativity that you like while rejecting others, you'll continue finding ways to make the numbers add up to whatever you want, with no regard for consistency.

You won't understand relativity while ignoring what it predicts. I don't think that's a problem, and I don't think you do either. Not everyone needs to understand it. Sorry it didn't work out.

6 hours ago, michel123456 said:

You should read again the statement. It is about B's clock.

Bold emphasis mine:

On 10/12/2020 at 4:02 AM, michel123456 said:

45+?=75 says "The amount of time that B's clock ticks while B travels, plus the time on B's clock when X begins equals the time on X's clock then B arrives."

That's your statement, it's about two clocks.

6 hours ago, michel123456 said:

It states that you must add to B's clock the RoS caused by the fact that E and X are not experienced in simultaneity by B.

I can't imagine how to explain why this is wrong if you don't understand that you're talking about different clocks. Are you purposefully making statements that you know are nonsense? (A strawman to defeat) Or do you think your statement makes sense and is true?

8 hours ago, michel123456 said:

Taking from your statements, reversed, that should give:

45+?=75 says "The amount of time that B's clock ticks while B travels, plus the time on B's clock when X begins equals the time on X's clock then B arrives."

And we can assume that the result should be:

?=30min.

But that's incorrect. Times on B's clock don't add up to times on X's clock.

Do you at least understand that you're talking about 2 different clocks? I know it's only page 12 but do you understand that much so far?

5 hours ago, Eise said:

I might repeat a few things that md65536 might already have said, but repeating in other words might help...

Agreed, there are so many ways to describe the concepts, and different people "get it" different ways, plus I often make mistakes. It's too bad this isn't in the relativity forum and might be read by others who'll get it. There's always something that makes more sense with someone else's explanation.

5 hours ago, Eise said:

E.g. when a stick is moving in the direction of its length, and one measures it by measuring the begin point and the end point at the same time, i.e. simultaneously, one get the 'correct length' (the proper length). However, observers in different FORs from the stick's FOR do not agree on 'the same time'. Therefore from the FOR of the stick other FOR's do not do that. They measure at different times, and so they get the length of the stick wrong.

I don't agree, as worded. Different observers do measure the ends of the stick simultaneously in their respective frames, and they get the correct relative length of the stick. But it's true those measurement times are different for different observers. The proper length is measured when the stick's at rest, it's not enough to measure at a single time, because any observer can do the latter.

(Not mentioned here, but also it's no good to measure the length at times that are simultaneous in the stick's rest frame, because in other frames the stick moves between those two times.)

The thread's question needs interpretation, and I might be interpreting it differently than others. I think that what you're asking is how much mass you would need to make everything in the universe gravitationally bound to it, despite the current rate of expansion.

If I'm thinking about it right, any constant rate of expansion will result in a constant-size cosmic horizon, beyond which it is impossible for matter to be gravitationally bound across that distance. The reason is that the matter would have to be falling in faster than the speed of light, to overcome the expansion of space between it and the mass. The horizon is determined by expansion alone, so making a more massive BH won't help... except...

If you had matter right on the cosmic horizon, you'd need to basically have it falling in at a speed of c to overcome expansion. That would imply a BH with an event horizon at the same radius as the cosmic horizon??? (assuming Schwarzschild BH) But then, if you had a BH even close to that size, matter on the cosmic horizon would be a lot closer to it than if it were a point mass, so wouldn't it fall in anyway? Or does it work out that the gravitational influence of a BH is still the same as if it were a point mass?

This seems really weird, because even if we completely ignore expansion for a moment, wouldn't this mean that the gravitational influence of a BH is roughly proportional to 1/r^2, while the mass is proportional to 1/r, no matter how big it is? That seems to imply that if you could have a BH of unlimited mass, you could make it so that the Schwarzschild radius is so large that an object outside it is so extremely far away from the center of the BH that the gravitational acceleration is small, even if it is near the horizon. Am I thinking about this correctly? How would an infalling observer describe the BH? It seems that the event horizon (a lightlike surface) would still pass by it at the speed of light, despite minimal acceleration. Meanwhile it seems like another observer, hovering farther away, outside the horizon, could easily avoid falling in, and see that same event horizon as stationary. Where's the error in my thinking?

Back to expansion, would it even make sense to talk about a constant rate of expansion of spacetime, in a volume that is entirely occupied by a massive BH? The BH curves the spacetime so extremely that the volume inside the horizon is not a part of the same spacetime outside??? Does curved spacetime expand the same as flat spacetime? Would a volume containing a large BH expand the same as a volume of empty space?

9 hours ago, michel123456 said:

1. why is there no use of RoS in stage 2? (the question mark on the sketch)

Another answer based only on the sketch: 27+48=75 basically says "The amount of time that X's clock ticks while B travels, plus the time on X's clock when B begins, equals the arrival time on X's clock of 1:15"

27+48=75 expresses the sentence from B's frame. 75+0=75 expresses the exact same sentence, from the E+X frame of reference. Those are sensible statements because they're adding times measured by the same clock.

45+?=75 says "The amount of time that B's clock ticks while B travels, plus ??? equals the time on X's clock then B arrives." That doesn't make sense, because those times are measured by different clocks.

5 hours ago, michel123456 said:

That is fine.

 

 

My questions are thus the followings,

 

1. why is there no use of RoS in stage 2? (the question mark on the sketch)

 

2.I am confused about the calculation procedure generally: why does it go one way (here from up to down) instead of going forth & back?

The 3 "stages" sound good to me... Please don't go backward from this point, where the details are no longer fine!

Answers: 1. RoS concerns the simultaneity of separated clocks or events, in this case the time at Earth relative to the time at X. It's not showing up yet because you're not comparing the times of things at E and X.

However, your stages 2 and 3 are describing the same calculations. They're just "what is measured in B's inertial frame." RoS can be used in stage 2 to explain why, when B is arriving at X, B can find that X's clock is at 1:15 while E's clock is only at 0:27. Both have recorded 27 minutes passing (according to inertial B) during B's trip, but X started with a clock 48 minutes ahead (according to inertial B). Meanwhile, in the E+X frame, these same clocks are synchronized. That's relativity of simultaneity.

2. There's no reason, the "stages" are just calculations from different frames. You can calculate from any frame in any order that you want, and you don't have to do them all. Any one frame of reference can make all the measurements necessary, assuming all the clocks are accessible to them, to calculate the proper times mentioned here (B arrives at X at 1:15 on X's clock and 0:45 on B's clock, all frames of reference can show that on their own, using the initial conditions described above. 0:27 on E's clock is a coordinate time (measured by B from a distance) and is a frame dependent measure, differing in different frames again due to RoS).

It doesn't make sense to line up all the stages as you did in the diagram. They're times measured by different clocks. By analogy, imagine if you made a map lining up all the countries in the world and attaching them vertically. It would show relative lengths of countries, but it wouldn't show how they're actually connected.

5 hours ago, Markus Hanke said:

Perhaps even more surprisingly, an electron at rest within a curved spacetime background (e.g. an electron confined in a vacuum tube at rest relative to earth) does not radiate, even though a comoving accelerometer would show non-zero proper acceleration. In some sense this is expected, since anything different would violate local conservation of energy; nonetheless, it is somewhat counterintuitive result.

This is one of those cases where common sense and intuition are at odds with GR, and one has no option but to work through the (extremely tedious, in this case) maths.

Actually, that does make intuitive sense in retrospect (cheating, OR if your common sense considers enough information).

The intuition is that an electron radiating EM energy, is associated with "change" rather than proper acceleration. An electron at rest relative to Earth isn't changing relative to an EM field. Instead it should be expected to radiate if you moved an EM field around it.

In freefall, the electron isn't changing in terms of inertia due to spacetime curvature, but it is (or can be) changing with respect to the EM field. So, no proper acceleration, but radiation is possible.

But I agree about the maths; intuition is useless if it doesn't reflect what the maths say.

2 hours ago, sgabc123 said:

I believe that if I accelerated every particle in the universe, including your beverage, just not your car, you're spilling your drink, and nobody else notices.  It's still all relative.  The only reason we would never assume such a thing is because we know it's wildly impractical to accelerate the entire universe.

This is an argument similar to Mach's principle. I think scientific theories neither support nor refute it.

How would you even conceptually accelerate everything? You could for example use a uniform gravitational field throughout the universe. But then, you could detect gravitational time dilation between different points, where there currently is none.

On the other hand, could you use frame dragging to cancel out those effects? I don't know enough about frame dragging to say anything, except that it's conceivable to me that if you rotated the entire universe around your body, frame dragging might cause your arms to pull away from your body, ie. a possible way to make Mach's principle true.

I can think of two opposing ideas here. One is that physical quantities are typically defined according to things that can be measured. Eg. time is defined as what a clock measures. It might be okay to say proper acceleration is what an accelerometer measures? Another is that measuring devices generally are not perfect. For example if you apply force directly to the cantilever in an accelerometer, it says that the body itself is accelerating, which it isn't. A test for whether an effect is "real" might be, "Does this effect affect *every* measuring device, or just individuals?" For example, a pendulum clock on a ship might tick slowly, but that doesn't mean time is slowing down, because a cesium clock would not tick slowly. On a rocket traveling at relativistic speed, time really is slower than a stationary clock, because all clocks on the rocket tick slowly.

If you manipulated everything in the universe so that everything accelerated, but all possible things that can measure acceleration are adjusted so that they don't detect it, then practically I'd say that there is no difference between that and things not accelerating at all. Philosophically I think this is called empiricism. If there really is no possible way to detect a difference between two things, I'd say there's no difference.

2 hours ago, swansont said:

If I accelerate an electron - a fundamental particle - it will emit radiation. This does not happen with constant velocity. So no. This is fundamental.

Would an electron in freefall in a gravitational field radiate? I'm guessing it wouldn't, so it emits when it is properly accelerated? But that would still give you a way (eg. using specific gravitational fields) to accelerate things and have them not detect proper acceleration? Could you say that for practical purposes, proper acceleration is a locally measurable difference in acceleration (or force) applied to different nearby points?

1 hour ago, sgabc123 said:

If there is no cosmic stage, if speed is only meaningful relative to other things, how can change in speed be absolute/not relative?

Coordinate speed is relative, but proper speed is absolute. Coordinate acceleration is relative, but proper acceleration is absolute.

Even relative speeds can have absolute consequences. For example, if two objects have a relative speed and they collide, that collision is absolute. When things have a speed relative to other things, that can be measured. Acceleration can involve different parts of things having different relative speeds at different times. For example, if a cantilever in an accelerometer momentarily has a non-zero speed relative to the rest of the device, the device measures a proper acceleration. If you think of a "cosmic stage" there may be a mystery, but the practical measurements aren't mysterious.

1 hour ago, sgabc123 said:

There must be something about acceleration that is more fundamental that simply a change in velocity. 

That's metaphysics. If you look at just the physics, you can see in the equations how the change in velocity adds up (given enough time and distance). The "something more", if it isn't in the equations, is probably not going to be something measurable (unless you discover something new experimentally), so you can interpret it however you want and invent whatever "something more" you want, without it having any bearing on observed reality, which in my opinion is why metaphysics is philosophy, not science.

1 hour ago, sgabc123 said:

Why can't it be the other twin that stayed in place the whole time, and the rest of the universe accelerated away and back, and moved through multiple frames?

There are 2 possible results. One is, you manipulate the universe so that the two twins experience the exact same thing as they do in the simpler case, for example using gravitational fields and gravitational time dilation instead of just Lorentz time dilation. You might also use frame dragging and calculate the effect of all the mass in the entire universe on the twins. In this case, by making the twins experience exactly the same thing as before, by definition they're going to experience the same difference in aging, and you end up with the same result. Even though you moved the entire universe around instead of the twin to get an exact equivalent of simple acceleration, you still get that the twin that felt the effect of acceleration is the one that ages less.

Second possibility is that you modify things so that they don't have the same experience as in the simpler case. In this case, depending on gravitational time dilation etc., you can get different results, eg. make it so the other twin ages less. But that should be expected; if you change the experiment you can change the results.

If "something moving relative to the rest of the universe" is measurably exactly the same as "the universe moving relative to something", then you can't experimentally say that one is really happening and the other isn't. To say they're different would be metaphysics. I think this would be the Machian viewpoint that MigL mentioned. I think an anti-Machian viewpoint would be that speculatively, there must always be a measurable difference between accelerating something around the universe, vs. accelerating the universe around the something?

That said, I think it would be very difficult to figure out how to manipulate the entire real universe so that there's no measurable difference from just accelerating a twin. In a toy universe containing only the twins, it should be easier.

What's the paradox? The title implies that "yourself" played both black and white. White won the game. You were both black and white. You won as white and lost as black. There's nothing paradoxical about that, and not even a feeling of doubt about those answers, let alone a sense that it's unsolvable.

What am I missing? Is there some assumption that is somehow a tautology, something like "You can't be your own adversary"? "One entity cannot be two different things at once?" I can't think of any assumption that I agree with that would require a contradiction in answering the questions. What is the gist of the argument that it's unsolvable?

5 hours ago, MSC said:

I have my answer, but people won't like it.

I would bet money that you're right! I'm curious about your reasoning though.

2 hours ago, MSC said:

What if I told you that in this riddle, two persons are playing. One lost, one won.

White won, "you" were playing white. No other person was mentioned. The title implies your opponent was yourself. If you are calling "yourself" two persons, that's fine, I see nothing paradoxical about that.

Ignoring the title, the story describes an opponent who is not seen when the game is won. It could describe a game against someone else, who stood up and walked around after playing their final move. Not only is there no paradox, there are multiple consistent interpretations. Is it "unsolvable" because you've left out information?

But I suspect that the two people are both you, and that somehow that seems impossible to you. I suspect that one person is described as "two persons" for the meaning of "playing a game for two persons", and then the meaning of "two persons" is switched, without it being obvious to you, to mean "two persons refers to separate individuals".

1 hour ago, swansont said:

It’s what everybody has explained. What’s not fine is the implication that anyone has suggested that it’s not the case. What’s the point of deny something that nobody is claiming?

It's a strawman argument, and his entire argument.

"These numbers don't make sense; there is something wrong with relativity."

> Those aren't the numbers that special relativity predicts.

"But they have to be! It's the only way that relativity can be right!"