Delta1212

I would wager there is a high probability that they are exactly equal in their degree of truth.

You can't. Things only move with respect to other things. There is no "real" velocity at which anything is traveling. All motion is relative to something else, hence the name.

There was a point when this was my entire online posting philosophy. The angrier I'd get, the nicer I made my posts.

Um, Einstein's recognition of the constancy of the speed of light wasn't derived by random daydreaming. It was brought about as a result of the presence of c in Maxwell's equations. Einstein's great conceptual leap was realizing that this constant meant that the equations would break down if the speed of light was variable dependent upon the observer's speed, and then working through the implications of that gave rise to Special Relativity. He didn't just randomly have SR pop into his head one day. It very much arose out of knowledge of existing physics and the mathematics underlying it. Whatever source told you otherwise is mistaken and probably drew from the famous anecdote of Einstein coming up with the idea for SR by imagining himself sitting on a beam of light which, like the story of Newton coming up with the idea for gravity when an apple fell off a tree, is frequently used to, usually unintentionally, mislead people about how much pre-existing knowledge and mathematical work actually went into developing these theories. As it happens, Einstein did imagine himself observing light from the perspective of a photon, but there are any number of ways that you could do that which would be physically meaningless. The only reason this thought of his was important was that he realized that the observation you would typically expect to make in that situation (i.e. Light not moving with respect to you) would result in a violation of the field equations for light, which would make that observation impossible, and leads to the conclusion that light has the same speed with respect to every observer. If he hadn't had that familiarity with Maxwell's equations, it would have been impossible to realize they were being violated by his little thought experiment and he would have been unable to draw any conclusions from it at all. So yes, he had the idea for SR before he had worked out all the math for it, but he got the idea from working with the pre-existing math for describing the behavior of light. He wasn't a starving artist who suddenly had a great physics idea out of nowhere. One of his most famous quotes, regarding standing on the shoulders of giants, states as much. He built on what had come before, and he knew it. He certainly built more than most, but he was still starting from the point others had left off at.

You have to understand what is meant by a law of physics. It means that the same rules apply no matter what (inertial) frame you are in, but certain things are not rules. There is no rule that clocks in different frames must tick at the same rate as yours. In fact, the rule, applied to all frames, is the opposite. Every frame will measure the clocks in every other frame as being slower. It's counter-intuitive at first glance, but it's a consistent rule across every frame. Similarly, it is not a rule that every frame will measure the same difference in speed between light and any given moving object (e.g. See light as traveling at c + the velocity of the source). It is a rule that every frame will observe light traveling at exactly c (in a vacuum). Knowing that these rules apply in every frame the same way allows us to figure out what events "look like" in that frame, even when we are not currently in it. So if you were to travel one lightyears distant, you could calculate how much time would have passed on Earth should you turn around and travel back, and you could determine that the distance you traveled is greater as seen from Earth than as seen by you, and consequently took more time as seen from Earth than as experienced by you. And you could decide that Earth's frame is valid, and that your time was dilated rather than theirs. Until you actually turn around (and, by accelerating, cease to be in an inertial frame) the Earth could say the same thing about you. There is nothing stopping any frame from treating any other frame as "standard" and, by applying the rules, coming out with a model of how things look that is perfectly consistent with the experiences of its own frame. Because every frame can do this with every other frame, there is no uniquely "standard" frame, and everything is, well, relative. Observations from different frames may not be identical, but they will always be consistent with each other when you know the rules by which they operate.

This is true of basically everyone on some level. People do not like to lose, and many times an argument stops being about what is actually true and starts being about beating the person you're arguing with. Some people fall into that pattern more easily than others, but most people will fall into it under certain conditions.

You can't define time in one frame by the number of clock ticks in another frame. Both frames will read a single clock tick the same number of times, but won't agree on how much time passed between ticks. For instance, if you define a "day" as 1000 pulses of the pulsar, the pulsar obviously won't pulse a different number of times per day, by definition, but each frame is going to wildly disagree on how long a day is. Going by that definition of a day, one frame might experience a day (ie 1000 pulsar ticks) in a span roughly equivalent to what we think of as a day, while someone in the other frame lives out their entire life and dies of old age before "tomorrow" arrives. Labeling 1000 ticks of a clock in one frame as one unit of time in every frame that can see that clock doesn't suddenly make all of the frames agree on the elapsed time, it just means they disagree on how long that unit lasts. Calling it a day doesn't mean it will last a day in every frame, and saying every frame experienced one "day" doesn't mean anything if they don't agree on how long a day is.

The problem with reconciling GR with QM isn't merely "one is deterministic and the other is probabilistic." The issue won't be resolved by determining that the universe is "really" deterministic or "really" probabilistic. Anything that replaces QM and/or GR has to do so in a way that not only describes behavior accurately in areas where these two theories are inconsistent, but it also has to predict behavior that is identical to what both theories currently predict in the realms in which they have each been very thoroughly tested and confirmed.

Personally, I think it looks like a screaming stick figure chasing a ~ with arms out stretched.

No. No matter how far away or where the pulsar is positioned, it will be moving with respect to one or both of the travel/stay-at-home. As such, regular old time dilation applies and they will measure the pulsar as "ticking" at different rates. Time dilation is not the same thing as Doppler shift.

I'm not sure time asymmetry is really the proper term to use, but yes, something moving away from you doesn't just look like something moving toward you shown in reverse.

I'm not sure that is specific enough of a question to provide a meaningful answer. What kind of program? What kind of interface?

The abrupt change is a result of the difference in light delay. While the object is traveling toward you, each photon bouncing off of it is starting a little closer to the Earth, so it will have slightly less travel time than the last photon to bounce off of the object, and will arrive on Earth sooner after the previous one than it left. When the object is traveling away from Earth, each successive photon is slightly farther away from Earth, so it has to travel farther and the gap between when the first arrives and the second arrives will be slightly longer than the gap between the first and second bouncing off the object. This creates the illusion that objects moving toward you are faster than they really are, and objects moving away from you are slower than they really are, though it's only really noticeable at large fractions of light speed. When the object reaches you, it transitions from the blue-shift "sped up" appearance to the red-shifted "slowed down" appearance, which creates the illusion of rapid deceleration even though the object is still actually traveling along an inertial path and doesn't feel any net forces.

Assuming the interior just disappeared, gravity would decrease dramatically, and the crust would probably break apart and fall in on itself.

That's actually interesting. I can sort of see why that would happen, but I need to look at it a bit more in-depth. Either way, thanks for the info. Though yeah, it doesn't really change anything especially impactful about what I was trying to say. Still always good to learn new things.

Realizing that clocks with different inertial paths but identical acceleration would have different elapsed times is actually what got me over that common conceptual hurdle of "maybe time dilation occurs during acceleration!"

T4-T3 yields the time between when the astronomer receives the light from Tom turning around (at a 1 year delay) and when the astronomer receives the light from Tom's return (at no delay). However, at T3, the astronomer sees Tom turn around at a point on the timeline that the astronomer believes is T2, because the astronomer knows there is a 1 year delay. Therefore to get the time that the astronomer observes Tom to take in a mathematical, rather than visual, sense, you must subtract the time that the astronomer calculates Tom turned around (T2) from his arrival. So the astronomer observes Tom's turnaround as being at T2 when the astronomer sees the light from Tom's turnaround at T3. Part of the difficulty in communicating the concept here, I think, is simply that the term 'observe' can mean a lot of different things depending on how you're using it. Actually, here's a good example of how this works in a manner that is more relatable to every day experience. Have you ever tried to figure out how far away lightning is by measuring the time between the flash and the thunder? So let's use sound as a stand in for light, because both travel at a constant speed (for a given medium), but sound is slower so the effects of distance are more apparent in our every day perceptions whereas light is far too fast for the delay to be intuitively understandable based on every day experience. So let's start with the lightning. In the case of Tom, you know how far away Tom is, and you know when the light from Tom arrives, so you need to know when Tom turned around. So say you're in the basement where you can't see the lightning (because frankly it's extraneous to the metaphor), but you hear the thunder. At exactly 5 pm, you hear thunder. At exactly 5:01 lightning strikes your house. You later learn that the other lightning strike hit a church 12 miles away. Sound travels about a fifth of a mile per second, so it took 60 seconds for the sound to reach you. You "heard" one minute pass between the thunder from the first strike and the thunder from lightning striking your house, but you observed that two minutes passed between the strikes. That's the same way the astronomer "sees" Tom turn around one year before arriving but observes that it was two years. Now, you're wondering what it looks like when Tom arrives at Earth after traveling at a speed that looks ridiculously fast. Sound actually helps here, too. An object traveling at the speed of sound can be observed approaching but it will be entirely silent until it arrives, at which point all the sound that it created during the trip arrives simultaneously in the form of a sonic boom. Obviously, nothing can travel at light speed, but an object traveling just below the speed of sound will behave similarly to how something traveling just below the speed of light will. So a slightly sub-sonic object will be Doppler shifted into very high frequencies, the way a siren sounds higher pitched while traveling toward you than when traveling away. The sound will also be sped up because the object emitting the sound is almost keeping pace with the waves it emits, so all the sound it emits arrives only slightly before it does and has to play in full. If a jet with a loudspeaker blaring someone's voice was traveling at you at just below the speed of sound, the voice would be very loud, very high pitch and speak very quickly until the loud speaker reached you. When it was directly at your position (assuming it didn't hit you) you would briefly hear the voice at the exact speed, volume and pitch at which it was being broadcast. Then once it passed you, you would hear it at a lower pitch, more softly and slowed down slightly. It's the same with light. An object traveling toward you will be bluer, appear to be traveling faster and be brighter than one traveling away from you. This is true of literally anything moving toward or away from you, but the speeds we're used to working with on a daily basis, even our fastest vehicles/weapons/whatever, move at such tiny fractions of the speed of light that the difference is literally imperceptible and we don't notice. Once you are dealing with largest enough distances and speeds, though, light behaves more like how we experience sound. So an object traveling toward you at 0.9999c will look like a movie that someone hit fast forward on in addition to being bluer and brighter, but once it reaches you, it will no longer be traveling toward you and it will look like it is moving at exactly the speed it is moving at, look exactly the color you'd normally see it at and be as bright as normal. In fact, if it isn't on a collision course with you, but will pass right next to you instead, less of its speed will be pointed "at" you as it gets closer until it is parallel with your position and it momentarily isn't moving toward or away from you. In this case, it will look as if it is decelerating the whole way until it's traveling at it's actual velocity as it passes you, and then continues decelerating as it moves away. This is, again, only true of something moving toward you but not on a perfect collision course. In that case, you won't see it traveling at its actually velocity until it hits you, but it will hit you with the force of something traveling 0.967c, not 29c. Hopefully something in there made some sense. If there's something specific confusing you, and some way you'd prefer it explained, let me know and I'll see if I can answer it in a more reasonable timeframe than this last time.

Well, yes.

If one of the sides has a length of 0, it's not a triangle. It's a line.

That's not a cross, it's a targeting reticle. Someone is planning to blow up the sun.

To clarify, are you asking how something can hit you with the force of a subliminal object when you see it traveling many times faster than the speed of light, or are you asking what it would look like when that object reached you when it has looked like it was traveling at many times the speed of light?

Yes. As long as you realize that it didn't actually take one day to travel all that way from Earth's FOR because you have to take Doppler shift into account when calculating actual speed. Light is like a postcard. It tells you where someone was when they sent it. It doesn't tell you where they are now. If someone sends you a postcard saying they just arrived in Hawaii for their vacation, and the card doesn't reach you for 5 days, you don't assume that their vacation was two days long when they return two days after you receive the card. You look at the postmark to see when the card was sent, and can then determine they spent a week away, even though it "looks" like they spent two days. With light, you have to measure from the time the light was sent, rather than the time you received the light, in order to measure something's actual velocity. If something is keeping pace with the original light that reflected toward Earth, they can arrive very soon after it, and it will "look" like they moved much more quickly than is physically possible. That doesn't mean they actually did, of course.

But what you see is not what happened, and c is only a speed limit for things that actually happen, not for things you see. Let's say that instead of waving, he turns on a lightbulb. How long after you see him flick the switch will you see the light from the bulb reach you?

Here, let's say that I've got a flashlight that is pointed towards Earth and traveling along the path of the accelerated twin in the twin paradox at neutrino speeds, so just barely under c. Let's say it falls 1 light day behind c per month (which is actually considerably slower than neutrinos) for the sake of math. The flashlight flicks on and then off once a month. After the first month, the flashlight is 29 light days away from Earth when it flickers. The photons take 29 days to reach Earth, so 59 days after the flashlight leaves, the Earth sees the flashlight 29 light days away. This gives the flashlight an apparent velocity of just under 0.5c from Earth. Let's put up a quick timeline of dates: Day 30: Flashlight flickers 29 light days from Earth (velocity: 29/30c or 0.967c) Day 59: Earth sees flashlight flicker 29 light days away (apparent velocity: 29/59c or 0.492c) Day 60: Flashlight flickers 58 light days away from Earth (velocity: 0.967c) Day 90: Flashlight flickers 87 light days away. (velocity: 0.967c) Day 118: Earth sees flashlight flicker 58 light days away. (apparent velocity: 0.492c) Day 120: Flashlight flickers at 116 light days. (apparent velocity: 0.967c) Day 150: Flashlight flickers at 145 light days. (apparent velocity: 0.967c) Day 180: Flashlight flickers at 174 light days. (apparent velocity: 0.967c) Day 177: Earth sees flashlight flicker 87 light days away. (apparent velocity: 0.492c) Day 210: Flashlight flickers at 203 light days. (apparent velocity: 0.967c) Day 236: Earth sees flashlight flicker 116 light days away. (apparent velocity: 0.492c) Day 240: Flashlight flickers at 232 light days. (apparent velocity: 0.967c) Day 270: Flashlight flickers at 261 light days. (apparent velocity: 0.967c) Day 295: Earth sees flashlight flicker 145 light days away. (apparent velocity: 0.492c) Day 300: Flashlight flickers at 290 light days. (apparent velocity: 0.967c) Day 330: Flashlight flickers at 319 light days. (apparent velocity: 0.967c) Day 354: Earth sees flashlight flicker 174 light days away. (apparent velocity: 0.492c) Day 360: Flashlight flickers at 348 light days, then turns around and heads back to Earth at the same velocity. (velocity: 0.967c) Day 390: Flashlight flickers at 319 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 413: Earth sees flashlight flicker 203 light days away. (apparent velocity: 0.492c) Day 420: Flashlight flickers at 290 light days. Covered 29 light days in 30 days. (velocity: 0.967c) Day 450: Flashlight flickers at 261 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 472: Earth sees flashlight flicker 232 light days away. (apparent velocity: 0.492c) Day 480: Flashlight flickers at 232 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 510: Flashlight flickers at 203light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 531: Earth sees flashlight flicker 261 light days away. (apparent velocity: 0.492c) Day 540: Flashlight flickers at 174 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 570: Flashlight flickers at 145 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 590: Earth sees flashlight flicker 290 light days away. (apparent velocity: 0.492c) Day 600: Flashlight flickers at 116 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 630: Flashlight flickers at 87 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 649: Earth sees flashlight flicker 319 light days away. (apparent velocity: 0.492c) Day 660: Flashlight flickers at 58 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 690: Flashlight flickers at 29 light days away. Covered 29 light days in 30 days. (velocity: 0.967c) Day 708: Earth sees flashlight flicker at 348 light days. (apparent velocity: 0.492c) Day 709: Earth sees flashlight flicker at 319 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 710: Earth sees flashlight flicker at 290 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 711: Earth sees flashlight flicker at 261 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 712: Earth sees flashlight flicker at 232 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 713: Earth sees flashlight flicker at 203 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 714: Earth sees flashlight flicker at 174 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 715: Earth sees flashlight flicker at 145 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 716: Earth sees flashlight flicker at 116 light days. Covered 29 light days in 1 day. (apparent velocity: 29c). Day 717: Earth sees flashlight flicker at 87 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 718: Earth sees flashlight flicker at 58 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 719: Earth sees flashlight flicker at 29 light days. Covered 29 light days in 1 day. (apparent velocity: 29c) Day 720: Flashlight reaches Earth. Covered 29 light days in 30 days (velocity: 0.967c). Earth sees flashlight reach Earth. Covered 29 light days in 1 day. (Apparent velocity: 29c). Now, can you point to one of the dates marking Earth's observations that is incorrect, and tell me what the correct day on which Earth would observe the flashlight at that distance would be?

The issue that you're running into is that, 'apparent' velocity doesn't have a cap of c the way actual velocity does. Things are allowed to look like they are traveling up to a speed approximately equivalent to instantaneous. Let's say there's a supernova 10,000 light years away. It releases neutrinos, which travel at very close to the speed of light. Earth sees the supernova, and an hour later, the neutrinos arrive, having fallen slightly behind the photons over the course of the trip. Well, it had only been an hour since Earth saw the release of the neutrinos, so their apparent velocity from Earth must have been 10,000 ly per hour.