md65536

You're describing a (frame-dependent) moment, or an instant in time, rather than an interval of time. To describe things like "bolt here, one there" etc., you're describing events, ie. anything with a location and a time. The coordinates you use to describe the events come from a system of coordinates, in this case you're using the coordinate system of the observer, ie. the inertial frame in which your chosen observer is at rest. In those coordinates, the 2 lightning events have the same time value. The relationship you're talking about describes any pair of events separated by a space-like interval in flat spacetime, because you can always find an inertial frame in which 2 space-like separated events happen at the same time. Or, find other observers where the lightning bolts aren't simultaneous. So, there's nothing special about the 2 events being simultaneous, unless there's something special about the observer you chose. "The interval between the events is space-like" is something all observers agree on, to describe the relationship.

Yes, it's definitely an ad hominem attack. I still see the same pattern of posts on this site over many years, where newer users must deal with people who like "crackpot bashing for sport". If one of the regulars posted a question about a suspicious video about science, would you treat their post the same way? Would you focus on their name while completely ignoring the content of the post? Did you even read the post, or did you conclude all you needed to know by the title, nickname, and some assumptions? What exactly is "not even wrong" about OP's post? "you seem very tacky"??? Why do this?

I think the helicopter is below the "true horizon" in those videos (represented by the lake surface), and hills behind it make the visible horizon higher. The simplest explanation is the video producers fabricated the shot because they didn't have the footage that they wanted to illustrate the narrative. That's pervasive in modern media, and only increasing. They add, remove, combine, edit, recolor, enhance, and create the shots they want if they don't have them. They basically assemble the story they want to tell, from pieces of the story they shot. Scenes are not always in the right order or even in context, and here you have proof that they're edited. Discovery Channel shows like this aren't video evidence of scientific experiments conducted by scientists, they're science-themed entertainment. Another common thing you'll see is footage of insects, or stop-motion of plants growing, and you'll hear loud, clear chewing noises, or the "sound of plants growing", but most of the time it's just a separate sound track added in post exactly like they would do for movie sound effects. Everything is edited and processed and repackaged these days. The raw footage would be boring and dry and not fit the exciting action film percussion soundtrack. I imagine that editing is such a common practice that the producers might not have even considered that people would treat it as scientific evidence. I think the "target circle" was added in post as well. I don't think you looked very closely, they're not just the same birds, they're the same pixels frame after frame. You can see it in OP's images. They're the same shot, and one is edited. That's not something I'd expect to see on Discovery. But maybe they could blow something up when they're talking about the laser, and say "Now that's what I call doing science!"

Ah, okay, that experiment can be set up in a lot of different ways and the details will be different. If you mean it's common that each is positioned at their respective midpoints between the events when they pass, it's only because you've chosen those observers. You could choose other observers who don't have that in common. If you mean that both frames agree on where the midpoint of the train and platform are located relative to their ends, yes that's true because the length contraction factor in the direction of motion is the same everywhere (the front half and back half of the train are length-contracted by the same factor). But it is true, if you had a bunch of trains running parallel at different speeds, the 'midpoints' on each train between the two events, would all momentarily coincide. Basically, all observers would agree that the "forward" char marks on all trains line up together at some time (at the moment the lightning strikes them, of course!), and the middles line up at some time, and the "rear" char marks line up at some time. Also, a 1/4 mark of the length between the marks lines up at some time, etc.

Yessssss... but What you described can be true, but there are complications you should understand. Lets say the lightning bolts hit the 2 ends of the train simultaneously in the train frame, and M1 is in the middle of the train, and sees the lightning bolts simultaneously at the same moment M passes on the embankment (at a negligible distance from M1). Then M also sees them simultaneously. And yes, each says "The ends of the train where the char marks are, are both the same distance from me at the moment that I see the lightning." First, because of length contraction, there isn't a fixed distance they agree on. M1 might say "Both ends of the train are 100m away from me and are at rest." M might say "Both ends of the train are 80m (say) away from me and are moving." Second, because the train is moving for M, the locations of the char marks are not the locations of the lightning strikes! M can say "The lightning struck at locations x1 and x2, but by the time I'd seen them, the char marks (which were equidistant from me when I saw the lightning) had moved to locations x1+delta and x2+delta." Observer M is not at the midpoint of x1 and x2 in her frame, but at that point plus delta. M and M1, while momentarily at the same location, do not agree that that location is the midpoint of the lightning strikes, in their respective frames.

A lot of the cautious best practices depend on whether you're talking about a battery pack or a single cell. I'm not sure if charging a single cell to 4.2 v will have a noticeable effect, but if you charge a 2-cell series pack to 8.4 v, and they're not perfectly balanced, you might eg. charge one to 4.15 v and the other to 4.25 v, more likely shortening its life. Avoiding charging to full might make a pack last longer, but do nothing for charging a single cell? Letting a cell drop below 3 v once might shorten its life a little, but driving it negative in a very unbalanced battery pack will quickly cause damage. Charging with lower current is better. "Rapid charging" devices likely have shortened life span. It's also something to be aware of with replacement batteries, because a charger made for a 2400 mAh cell might stress a 2000 mAh cell. Charging at an excessively low current would be the easiest on a cell.

I just quoted the wiki page. I can't explain other than with another quote from the page: "But because the principle is so vague, many distinct statements can be (and have been) made that would qualify as a Mach principle, and some of these are false." Definitely Mach's principle doesn't answer the questions here. I see it more as philosophical in that it provides questions that can't be answered, or at least aren't settled by science. I disagree that there's evidence of what would be observed if all matter was taken away, as far as I know no one has performed such an experiment! The evidence is based on extrapolation from what we currently observe. Does the Higgs mechanism depend on other fundamental constants or measurements? I think to settle this, and to answer OP's questions about a massless universe etc, you'd first have to know if and how the fundamental constants etc. would change in such a case. You'd have to settle Mach's principle in general. I think Mach7 is not true based on current evidence, best current theoretical models, and the assumption that some specific aspects of Mach's principle are not true.

This is a variation of a variation of Mach's Principle https://en.wikipedia.org/wiki/Mach's_principle "Mach7: If you take away all matter, there is no more space." I think that if time and distance are emergent properties of the universe then nothing requires spacetime, because everything could be described in terms of whatever they're emergent from. Eg. maybe causal connections could be described using topology without geometry. In that case, c is a property of the relationship between distance and time, something describing how things are connected in the underlying universe and emerging as a speed in our possibly emergent observations and measurements of that universe. As an example or analogy, consider the emergent 3d space depicted by a 2d hologram. The observable depths and distances of that 3d space are not needed to describe the hologram completely.

But the frequency of the light changes depending on the motion of the emitter. Why is the frequency different if it's not actually in motion?

Based on others' answers, I think I'm misunderstanding what you mean by this. What you described here is fine, if you set up the experiment to get those results. Having the lightbulbs next to the observer is a good idea, because if they light up at the same time and at the same place, that can be considered a single event, and then everyone in every reference frame will agree on whether the bulbs lit at the same time or not. Similarly you can set it up so that M and M1 are at the same place at the moments the light bulbs light (ie. their world lines intersect at that event) and then everyone can agree on the simultaneity of those events. Is that what you are describing? On the other hand, adding transformers and bulbs can unnecessarily complicate things, and obfuscate what you're trying to get a grip on. Simplification is usually better. What you might be missing, is that just because the two light bulbs light at the same time, the events that caused them (in this case the lightning bolts) might not have occurred at the same time, because the information from the 2 events might not have taken the same time to get to the 2 bulbs. The simpler case is that M and M1 can both see the lightning bolts appearing simultaneous, but still disagree on whether they're "really" simultaneous, because they can disagree on their distances to the two lightning bolts. It applies the same to wires and bulbs, because you can measure the timing of the signals through the wires using light signals, and you'll get consistent results. So that suggests some "definite facts" that you're looking for: The events you're describing, and the causal relationships between them, and the light cones describing those relations, are all definite and not dependent on frame of reference.

"The interval between the two events is space-like" describes everything you're talking about here, and it has a precise definition. "Event" has a precise definition as well. There no problem here. A lightning bolt could also be described not as a single event, but as something with spatial and temporal extent. Then it could be described with some other precise definitions that effectively describe sets of events, such as "world line". If "coexist" is given a precise definition, it would be fine, but there are already words that suffice, and it's a problem if you want it to mean something more or other than the definition you give it.

If your brain was in a simulation, where every stimulus you received was somehow artificial, that could mean that everything you know (which you acquired through stimuli) might be made up. You probably wouldn't need to distinguish external stimuli (eg. the sense of touching things) vs. internal (eg. having a memory of having lived your life up to this point). That would mean the senses of remembering things could be made up... so maybe it is simulating a few minutes or just one moment in time, including any made-up memories of time before that. It could also mean that things like atoms could be made up too. Maybe the knowledge of atoms or even of there being 3 spatial dimensions is an artificial reality that is simulated in some other reality with no atoms and a different number of dimensions. As for whether it could be one "identity" being simulated, or everyone---or to put it another way, "what if I'm just a figment of someone else's mind?" etc.---I guess that's an open philosophical question related to whether there is some physical form to the feeling of having an identity, or if it's just emergent from the configuration of other physical things like brain cells. If you simulated an object's sense of being, like if you simulated the thought "I think, therefore I am" in something that otherwise wouldn't think that on its own, does that thought have any physical presence? I can think about these ideas and write them down, and I get the sense that I'm thinking them, but if other senses (eg. of touching something) could be simulated, why not the sense of having thought things? I feel like I'm here, but if that could be simulated, I don't think I'd need to exist at all. I don't see how I could prove to myself that I exist, IF the only way to test it is by sensing whether I exist, AND if what is sensed can be simulated. By a really coarse analogy, if I write a story about a character that realizes it exists, I can write convincing thoughts for it with dialog like, "I know I'm only a character in a story, but I exist!" By creating those "thoughts" on paper, I'm not making them real. You wouldn't read that dialog and claim that as evidence that the character has become real. If I myself could think up some thought test that proves to me that I exist, I could write a fictional character having those same thoughts, and yet that wouldn't really prove to anyone that the character really exists and can think. How can I as a person prove that I'm not just someone else's thought, if any action I could take to prove it could also be their thought? How could you know that the feeling of being real, is itself real?

That's not a square, only a rhombus.

Interesting shape! Am I understanding correctly that 2 opposite corners of the cut face are on the middles of edges (diagonal length 10√2) and the other two are on opposite corners of the cube (diagonal length 10√3)?

1. 2.

Maybe I missed the point, but the extract is basically explaining that in relativity, you deal with spacetime, not just space or just time. When you do, the things described in the text become simple. It's simple and mathematical, and the nature of the subject doesn't complicate it. If anything it seems to make issues irrelevant.

... continued from previous post. But why stop there?! From here, I think you could add any number of wormholes from anywhere to anywhere, as long as they each linked two events using the same t parameter as all the other wormholes, ie. they each connected two events that were the same instant according to a single common frame of reference, and you wouldn't create any causality paradoxes. But then!, I think you could also add any number of wormholes, each with a different time parameter (so, some wormhole entrances link an event in your frame's present to an event in your frame's past and at a great distance, others to an event in your frame's future at a distance), without causality paradoxes, as long as you kept sufficient distance between the multiple wormholes' endpoints. For any worldline that goes through multiple wormholes, as long as you keep its events far apart enough to stay outside of earlier events' past light cones, there's no causality paradox. I think!)

If you could travel at all faster than light, multiple times in different directions, you could create paradoxes. I don't think the instantaneousness of it matters at all, unless you can apply it arbitrarily in different frames of reference. For a counter example without paradoxes (I think), if spacetime is multiply connected between A and B, where one connection is flat spacetime with a proper distance of 10 LY between A and B, and another connection is a stable wormhole between A and B, allowing instantaneous travel in either direction at any time t in one given inertial frame of reference---or in other words, you could instantly travel from A to B and back, and you could even have B earlier than A (or vice versa) in your frame of reference, but not so early that it's in A's past light cone, AND you can travel back from B to A, but never to an earlier time than you left A---then I think no causality paradoxes are possible without something more. Even though you can transmit information in 2 directions faster than light, and try to exploit the 2 different-length connections between A and B, there's no frame of reference in which information from an event at A can be sent to an earlier event at A. (Same with B and everywhere else.) The parameter t of the events never decreases. The difference here is, arbitrary travel at faster than light over great distances allows traveling to earlier times in both directions. HOWEVER, traveling through the wormhole I described is not traveling a great distance, and it can be done at low speed. So it's instantaneous travel, but not technically "moving faster than light". Just getting there faster via a shortcut. The difference is important because it's the changes in relative simultaneity across great distances that are exploited in (impossible) FTL time travel, and that doesn't apply to the wormhole here. I suspect it might not apply to the Alcubierre "warp" drive either. (Just a further thought on the example above. Say you tried to cause a paradox by switching between different frames of reference. You could start in one frame F such that a traveler leaves A in 2020, travels through the wormhole, and arrives at B "earlier" in your frame of reference. Then you could switch to another frame F' so that if the traveler leaves B just after it arrived, back through the wormhole, it can now arrive in a time at A that is "earlier" again than it left B, but in this other frame F'. However, you'll also find that in this new frame F', the first event where the traveler left A for B, is earlier (by the same amount) than the event of it arriving at B, and in this frame (like in any) you find that the traveler still arrives back at A after it left, without paradox.)

Yes, it's not a problem as long as everyone understands a statement consistently. Even "traveling to someone's future" could be discussed without confusion if someone defined what that meant and everyone agreed on it. Combining this and OP's example: Say there are 2 events, A-2020 ("now" at A) and B-2020 ("now" at B). A ship (or message) travels FTL from A-2020 to B-2020. It travels from "the present" at A to "the present" at B (that is the present relative to the two events, in A & B's shared frame of reference). Then say B immediately accelerates away from A. In the new frame of reference, A's clock could "now" (according to B) read 2019. The event A-2020 is in the future of B-2020 in this frame. It's not in its future light cone, but in its elsewhere, and in the future relative to B's plane of simultaneity at B-2020. Then if B immediately sent a message instantly to A-2019 say, A in 2019 could receive information from A-2020, an event in A-2019's own future. In this example there's no mention of relative past or future until there's relative motion. Also, B receiving a message, accelerating, and sending a message, if done all at once, could be considered a single event. In both examples, the time travel requires two different inertial frames, with the corresponding two different ways that "now" or "instant" apply to the distant events. You send a message "instantly" using one frame's definition of an instant across space, and send another in a different definition of an instant. Also! in this example, B doesn't need to accelerate at all. If it were inertial and moving relative to A, the only change is that it doesn't agree with A about "now". In this case, the original ship or signal from A-2020 arriving at B-2020 (with B moving away from A and B saying that it is "now" 2019 at A), B can say that it originated from an event that has not yet happened in its frame of reference. However since that event's still outside of its future light cone, that alone doesn't violate causality yet.

But that's not a paradox. I think that a one-way teleporting of information would not break causality (not sure though). To make the situation into a paradox you'd have to add something to it. You could assume generalization and 2-way travel, but I think you could also add restrictions to make a paradox impossible (use one-way wormholes or black holes). Yes, I think without more specifics, we can't conclude that there's for sure a paradox, or no possibility of a paradox. What does it mean for B to be five years in A's future? Can you explain in terms of events or coordinates? My reading of the description is that A and B can be assumed to be at rest, 10 ly apart. Say they have clocks sync'd to year 2020. The events are the ship leaves A when A's clock reads 2020, and arrives at B when B's clock reads 2020. 5 years in A's future is 2025? And B is in 2025? I'm obviously not getting that right but I don't see any meaning of an object being in another object's future. An event can be in another event's future, but I don't see any events here that can be described like that.

After thinking about this, I think this is not a paradox. Instead of "space ship" you could have said "tachyon". You haven't described the ship doing anything that would break causality or do anything paradoxical. If by "you travel" you mean literally a person, then you can come up with something paradoxical, but it's not a paradox yet. (Edit: As for the rest of what you wrote after the above, I don't think it's right. Especially anything that adds a paradox, the paradox seems to come from an incorrect description.) Relativity doesn't specifically disallow nor predict the possibility of faster-than-light particles. Or wormholes for that matter. You can't accelerate something massive to the speed of light or faster, but if something's traveling faster than light already, it doesn't break anything. You can't use FTL to transmit information, because then you could break causality, but you haven't described any information transmitted, or anything else that would be a paradox. I think we'd all (anyone here talking about relativity) agree that if something doesn't agree with "common sense" or intuition, that doesn't make it a paradox. But then, when you describe something that "common sense" says disagrees with relativity, such as something traveling faster than light, we tend to jump to the conclusion that it does, along with any assumptions needed (eg. I might assume you're talking about accelerating a person from rest). There's a difference between a common sense paradox like this, and an actual paradox that's not theoretically possible.

This doesn't sound like a scientific argument. Besides, you haven't described anything that you're seeing that is at all different than if you'd never stepped through the wormhole. You're seeing light from about a hundred years of Earth's worldline arrive at planet P. Why describe it as a story? Why not speak of events and light cones, etc? Why not use defined scientific terms? Your story doesn't help at all explain the meaning of "[you] are in effect travelling into the 'future' [...] of the person standing 2 m away from you". I doubt you could explain the meaning in that, because it seems meaningless. Can you point out a specific error in what J.C.MacSwell wrote? You dismissed it, but I don't see any error in it.

I disagree. J.C.MacSwell has merely described the situation that others set up, in real terms like frames of reference, without any assumption about how that situation was arrived at. No false claims were made. Your idea of "traveling into the future of a person" doesn't make sense to me in any of the frames mentioned (which events are you comparing, and in which frame? If the events are in the same place (star B), it seems to describe only events in a mutual present). I don't see any paradoxes mentioned yet, but one could be built from the situation. In the frame of reference of an object moving slower than c in the direction from A to B, the ship arrives at B before it leaves A, which I don't think is itself a paradox, but can lead to one.

Here's a bit of a meander through how I understand this topic. There are other ways to look at it that you might prefer. First, if you move a light clock across a timelike interval in a particular frame, you can derive the time dilation factor for the moving clock using Pythagoras theorem. It looks quite similar to the scene you described in the initial post. I'd take a look at this if you've never seen it, I could post a video. If you repeat this for a bunch of different frames, you'll find you're looking at a bunch of different triangles that all have one of their sides in common: the side representing the proper time measured by the clock. Or working in the opposite direction: If you look at the time dilation factor with these equations: t/tau = 1/sqrt(1-v^2/c^2), and r = vt, you get (c tau)^2 = (ct)^2 -r^2, the spacetime interval. You can also consider space-like intervals, and either add a ruler (a proper length) instead of a light clock, and/or replace the proper lengths with times measured by light passing over those lengths, effectively swapping time and distance to get the same situation as above. From this you have a simple geometric picture of the spacetime interval components, in a triangle that gets stretched for different frames of reference, but has one side remaining invariant, and you can see the equation of the spacetime interval in the Pythagoras theorem. I get the sense that you're trying to say something like, "The spacetime interval is some natural measure of separation, and the fact that it's invariant must say something fundamental about relativity." The way I see it, the definition of the interval was chosen because it's something that is invariant---proper time---and as seen above, simply relates time and distance in different frames. Rather than starting by defining it and then assuming it is invariant, I think we start by defining it as something that is already assumed to be invariant. Rather than deriving relativity from it, I'd say the opposite is true; since it represents the measurements (eg. of time) in a particular frame, it shows that Newtonian time in a "rest frame" can be derived from special relativity. Like Markus's video suggests, it shows that not everything becomes relative when going from a Newtonian model to SR. The fact that proper time is invariant is not saying anything more (to me at least) than that 1) there's a single measure of time between a pair of events in a single frame (same as with Newtonian time). Or, different clocks sharing a rest frame don't measure time differently, and 2) while different observers measure time differently than each other, they all agree on the (proper) measurements that each other is making.

Thanks for that. Is the repeated use of the word "true" in the video not a standard scientific term (even misleading)? If someone said that if a measure of something being length contracted isn't a true measure of length, I'd argue that's wrong, whereas saying it's not its proper length is using a scientific term. About exact specification of intervals: If you have 2 events and you don't care about their locations, only their relative separation, then you're talking about their spacetime interval. Further if you don't care about how they're measured in one particular frame of reference, then all you need to completely specify the interval is the one value, s^2. So in OP's example, suppose that s^2 is about 39999.9999999999889111 light seconds squared. This describes two events that, in one frame, are separated by say 1000 meters and 200 seconds. But it also describes the same two events that, in another frame, are in the same place and separated by 199.99999999999997227774 seconds. The latter is a measure of the proper time between the two events. (Sorry for those numbers, but if I don't use that many digits, the 1000 meters gets completely lost to rounding.) But also... that same s^2 describes the same 2 events separated by billions of light years and billions of years, in yet another frame. It also describes 2 completely different events a long time ago in a galaxy far far away that had the same separation relative to each other. This seems to imply that all light-like intervals are "the same." They all have s^2 = 0. What this means physically, is that if you have a light signal from A to B, no matter how near or far they are in your frame of reference, you can find other frames of reference where that light signal is arbitrarily short, and others where it is arbitrarily long. Those all describe the same thing, and there is no one frame in which the distance or timing of the light signal is "proper". An exception is the interval between an event and itself??? That seems to produce a valid interval where s^2 = 0, yet there are no frames of reference that can separate the events in time or space. I've never seen any mention of this. Is "spacetime interval" only defined for two different points?