**Physicist**: Back in the day, Galileo came up with the “Galilean Equivalence Principle” (GEP) which states that all the laws of physics work exactly the same, regardless of how fast you’re moving, or indeed whether or not you’re moving. (Acceleration is a different story. Acceleration screws everything up.) What Einstein did was to tenaciously hold onto the GEP, regardless of what common sense and everyone around told him. It turns out that the speed of light can be derived from a study of physical laws. But if physics is the same for everybody, then the speed of light (hereafter “C”) must be the same for everybody. The new principle, that the laws of physics are independent of velocity and that C is the same for everybody, is called the Einstein Equivalence Principle (EEP).

*Moving faster makes time slow down*: I’ve found that the best way to understand this is to actually do the calculation, then sit back and think about it. Now, if a relativistic argument doesn’t hinge on the invariance of C, then it isn’t relativistic. So ask yourself “What do the speed of light and time have to do with each other?”. A good way to explore the connection is a “light clock”. A light clock is a pair of mirrors, a fixed distance apart, that bounce a photon back and forth and *clicks* at every bounce. What follows is essentially the exact thought experiment that Einstein proposed to derive how time is affected by movement.

Let’s say Alice is holding a light clock, and Bob is watching her run by, while holding it, with speed V. Alice is standing still (according to Alice), and the time, , between ticks is easy to figure out: it’s just . From Bob’s perspective the photon in the clock doesn’t just travel up and down, it must also travel sideways, to keep up with Alice. The additional sideways motion means that the photon has to cover a greater distance, and since it travels at a fixed speed (EEP y’all!) it must take more time. The exact amount of time can be figured out by thinking about the distances involved. Mix in a pinch of Pythagoras and Boom!: the time between ticks for Bob. So Bob sees Alice’s clock ticking slower than Alice does. You can easily reverse this experiment (just give Bob a clock), and you’ll see that Alice sees Bob’s clock running slow in exactly the same way.

It turns out that the really useful quantity here is the ratio: . This equation is called “gamma”. It’s so important in relativity I’ll say it again: .

It may seem at first glance that the different measurements are an illusion of some kind, like things in the distance looking smaller and slower, but unfortunately that’s not the case. For Alice the light definitely travels a shorter distance, and the clock ticks faster. For Bob the light really does travel a greater distance, and the clock ticks slower. If you’re wondering why there’s no paradox, or want more details, then find yourself a book on relativity. There are plenty. Or look up Lorentz boosts. (The very short answer is that position is also important.)

*The lower the slower*: Less commonly known, is that the lower you are in a gravity well, the slower time passes. So someone on a mountain will age (very, very slightly) faster than someone in a valley. This falls into the realm of general relativity, and the derivation is substantially more difficult. Einstein crapped out special relativity in a few months, but it took him another 10 years to get general relativity figured out. Here’s a good way to picture why (but not quite derive how) acceleration causes nearby points to experience time differently:

Alice and Bob (again) are sitting at opposite ends of an accelerating rocket (that is to say; the rocket is on, so they’re speeding up). Alice is sitting at the Apex (top) of the rocket and she’s shining a red light toward Bob at the Bottom of the rocket. It takes some time (not much) for the light to get from the Apex of the rocket to the Bottom. In that time Bob has had a chance to speed up a little, so by the time the light gets to him it will be a little bit blue-shifted. Again, Alice sees red light at the Apex and Bob sees blue light at the Bottom.

The time between wave crests for Bob are short, the time between wave crests for Alice are long. Say for example that the blueshift increases the frequency by a factor of two, and Alice counts 10 crests per second. Then Bob will count 20 crests per second (No new crests are being added in between the top and the bottom of the rocket). Therefore, 2 seconds of Alice’s time happens in 1 second of Bob’s time. Alice is moving through time faster.

Einstein’s insight (a way bigger jump than the EEP) was that gravitational acceleration and inertial acceleration are one and the same. So the acceleration that pushes you down in a rocket does all the same things that the acceleration due to gravity does. There’s no way to tell if the rocket is on and you’re flying through space, or if the rocket is off and you’re still on the launch pad.

It’s worth mentioning that the first time you read this it should be very difficult to understand. Relativity = mind bending.

Hello. Everything you all explain is clear to me and is correct…and when you think about it is pretty simple. But…time isn’t moving…light is moving and a clocks mechanism is moving at certain speeds and all that moves in opposed to each other reacts due to different speeds…but again no one is thinking of time as a stillness. Therefore:

If I am starring at a clock which has one minute to 12 and I am travelling away from the clock at the speed of light, meaning that the image of the clock ticking one minute to 12 is moving towards my eyes the same speed as I am travelling, therefore it will allways be one to 12 for me but for other people who are standing by the clock,time will pass normally. So it is said that i will not age and everyone else will…..don’t think so.I will age the same as they do. If I counted seconds in my mind(not looking at the watch or my wrist watch)while travelling away,time would be the same.Why?If i didn’t travell into space,but rather around the clock at the speed of light, no one would see me,I wouldn’t see reality but an after image….but i could still count the same as the clock at the beginning of the story.My wrist watch may be off by years.But would age the same. A pilot in a jet counts time the same as you do, and it doesn’t matter how fast he goes. Clocks can trick you and make you think of time as something that moves.

For example…I talk to a friend: Hey lets count 10 seconds together but I will make a trillion laps around the world at the speed of light during our count. Ok? And go!

1,2,3,4,5,6,7,8,9,10.He would be 10 seconds older and so would I!

But than again….this is just my opinion;)

David: I understood your example of “time” is “mechanical” movement of the clock and also time-space dilemma when you move away from the clock @ the speed of light but why time is slowing down with you travelling @ speed of light wearing that wrist watch?

Hello. Please read Vocation’s comments.

Maybe it will be clearer to you than.

For what it’s worth,I for one am 100 percent with his statement.

You only see something…that doesn’t mean that it is what you see…understand?

You are looking at the past…but it is not the past over there,is it? You are only deceaving

yourself. And that is what I tried to say in my previous statement.

I am stating that the movie “Interstellar” is wrong 😉

I still don’t understand how alice would see the photon reach her at the same time as she was when she wasn’t moving sideways but Bob would definitely see a time difference

David: you have to trust a bit more in the people who actually learned A LOT about this. They are quite capable of understanding these kind of simple things. What you are presenting here is known as the Dunning-Kruger effect;

https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

What you are referring to in your post is only the socalled Doppler effect, and has nothing to do with the actual time dilation;

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

Time dilation means all laws of physics are going at a slower rate, including how fast your mind works, so you won’t notice a thing. Altogether with that effect, you have the Doppler effect, which is what you described, which has no influence at all on what is actually happening, but is only about what is seen, which are two completely different things.

There are only 2 constants at a base of special relativity;

* a constant speed of light measured by every observer, regardless of their relative motion or of the motion of the source of the light

* all laws of physics are the same for all observers in uniform motion relative to one another

Yes, I understand your point.

But first of all:

David says:

September 19, 2015 at 9:25 am

But than again…this is just my opinion;)

After my comment, telling me that I am presenting the Dunning-Kruger effect, is just rude.

Second:

How speed of light is held to be constant, when light going through Water travels with slower than light going through air, or when light travels through matters at ABSOLUTE ZERO temperature, travels at the speed of a bicycle ?What about longitudinal waves that appear to travel much faster than light? Or what about the proven mathematical correlation between particles that where once in contact but are now lightyears apart yet which under Bell’s Theorem seem to be instantaneously connected?

Third: I know we are all talking about vacuum measuring,but you cannot use something effected by speed to measure time with. You can use something which is not effected by anything.

Fourth:I know that GPS proves Einstain was right.(doesn’t prove that the expiration date of the satellite is wrong from Earths point.

Fifth:Imagine I am in a shuttle and moving at…whatever…lets say half the speed of light.From a point, my clock is ticking faster than the speed of light? Just depending on how I am facing my clock(laser clock)I can change various outcomes of time measured?

Six:You can’t prove I am wrong because you do not have a grandpa twin …you can prove time measuring differences on time measuring devices. Nothing else.

The mistake that Einstein said was incorrect with relativity was that he did not take into account electricity and magnetism. This is now being included and the new learning has thrown relativity out the window.

Any way….please make an experiment with two humans and show me. And than….if you are correct…..than you can be rude.

Till than…you are relatively correct.

@David

Great questions!

The important thing about the speed of light is the speed, not the light itself. There’s a post here that talks about that a bit. When light travels through a material is does a lot of starting and stopping; on average it travels slower, but when it moves it’s still moving at the usual speed (post here). Importantly, the speed of light through different materials has nothing at all to do with relativity.

There are effects that seem to travel faster than light, but they never actually involve things doing so. A good example is this experiment. It sounds exciting, but even the folk who did that particular experiment are quick to say that they never actually got anything to go faster than light.

Bell’s theorem implies some pretty wild stuff about how the universe works, but unfortunately it doesn’t involve anything going faster than light either. Every now and again someone will come along and propose a method of using entanglement to “cheat” relativity, but without exception there’s always been a flaw in their reasoning and their experiments never work (post here).

Just a quick note, Einstein’s original paper was titled (in German) “On the Electrodynamics of Moving Bodies”. The theory of relativity was originally written to explain the relationship between electric and magnetic fields; EM is built into its bones.

Thank you very much for explaining, I understand.

Quick thought: Lets say that we can go fast as near 300 000 km/h in a brand new rocket. And we launch the rocket(very slowly in comparison to the speed of light) and position our selves near the Moon from where we are going to engage in that high speed.

Where is 0 km/h from where we will start? Does anyone know? Because we measure speed relative to Earth right?

We already are on a vessel. Our galaxy, which is also on a vessel of kind.So we already are moving at high speeds and we would start at those speeds…so we basically wouldn’t have to reach 300 000,rather find a direction to which to go in order to maximize our speed relative to the stillness in space which is 0 km/h? Yes?

Or a better question? Is it possible to reach 0 km/h?

Hi David,

Speed is relative, so everything can be seen as moving at 0 km/h, or ‘almost’ the speed of light. Light will always be seen as moving at it’s same steady speed, as observed from any of these observers, so light is actually a completely different realm than the realm of matter.

@David

“you can prove time measuring differences on time measuring devices. Nothing else.”

Actually it’s worse. You can only prove counting differences on counting devices. There are no devices that measure time. There are devices that count vibrations, oscillations or other periodically occurring physical events.

Some of these physical phenomena are affected by motion. But there is no proof that any of those motions or differences in motion are at all related to some mysterious thing called time. Clocks count. They do not sample something a yield a reading.

Sorry for the typo. I meant to say at the end that clocks do not sample something AND yield reading.

Einstein theory of relativity States that as you travel near the speed of light that time slows down and matter shrinks. The first time I saw this in modern physics, I thought it was only relative and did not really affect the individual in the accelerated time frame I started to rationalize how this could be true. In our low energy state the hydrogen atom has 100000 to 1 distance between the nucleus and the electron as you increase your speed, to the speed of light the distance between the nucleus and the electron decrease to 1 to 1 this cause everything to shrink. Also time will slow down and then eventually stop at the speed of light. The reason time stops is based on Einstein proven theory that speed of light is a constant no matter what reference frame you are in. Speed is equal to distance divide by time to keep the speed of light a constant when you distance shrink time must also decrease equally to to keep speed of light constant. To accelerate to the speed of light you must increase energy into object, by increase the energy into an object this will cause the electrons to move closer to the nucleus in the atom. This happens because the increase in energy overcomes the repulsive nuclear force, between the nucleus and the electrons. Note: This affect is the same as increasing the gravitational field around an object. The gravitational field over comes the nuclear force causing the electrons to move closer to the nucleus. This agrees with Einstein theory about the warpage of space time (space shrinking and time slowing down around massive objects)

That’s always the weird thing about time. It really only exists in particles interacting with the Higgs field: matter. Empty spacetime in essence holds no time: it’s just a mathematical means to understand how matter behaves within it. Photons have no time; they don’t ‘age’, and have no frame of reference.

From our ‘matter’ point of view it almost seems they should have a frame of reference, but if our particles wouldn’t interact with (or far less well said; be slowed down by) the Higgs, then space and time couldn’t be derived out of the difference between these fields/particles.

If we had just decided to use the lightsecond (299799458 m) as a distance unit, then c would have been equal to 1, and we wouldn’t have had to use it to translate E to M anymore in E=Mc^2 * lorentzfactor. Also it would’ve added to our intuition on how time and space are very much entwined.

Steven, once you reach inertial motion of an object, after some initial accelerating, there are no forces doing anything anymore, so you can’t really compare that to gravity, which is effectively similar to continuous acceleration. An object is ‘flattened’ in the direction it’s moving, relative to the observer, so to another observer, in another frame of reference, the same object is flat in a completely different direction.

If it was simply the compression of a moving object by electrons moving closer to the nucleus, and time going slower, then all *other* objects from it’s own viewpoint would seem to be larger, with time going faster. But the thing about relativity is that both observers will obverse the other as being shrinked and going slower. So c acts like a sort of mirror, that way.

This is why c is much more than just the speed of light: it’s a universal constant. It’s the connection of energy to mass, and space to time, and this is also why we need to think of our mathematical spacetime grid changing, depending on the frame of reference of the observer, to be able keep a correct helicopter view of all possible events within it. How this changes for different frames of reference, is all expressed with mathematical structures, known as tensors.

this is for david,

I’m bill, riverside ca.

I understand the theory why time slows down at light speed, but does it really?

I mean, five minutes is five minutes right?

or would my wrist watch actually run slower if I were traveling at light speed and return to find everybody decades older?

could you send me an email with your response?

thanks

bill

Hi, I think both examples (the light clock and the rocket) do not explain or prove that time passes faster or slower depending on speed of an object. I think both proves are flawed. Let me explain:

– the light clock: Your experiment starts off with a photon being bounced between absolutely parallel mirrors. The distance the photon travels is defined by the distance between the two mirrors. The direction of the photon is given by the mirrors it bounces off from. The mirrors being exactly parallel, the photon’s direction is exactly perpendicular to the mirrors. If I move the box with the mirrors while the photon is moving, the location where the photon hits the mirror the next time is different. The direction of the photon does not change only because I move the box. Eventually when I move the box horizontally enough the photon which is on its way from one mirror to the other will hit the wall of the box and the experiment is dead. For the experiment to keep working with the box in motion the mirrors would need to be slightly tilted in the direction of the motion, directing the photon to the location the center of the mirror will be when the photon hits that mirror. The distance of the photon travelled this way is longer because it now travels slightly at an angle. The duration the photon takes for that distance is exactly the same whether measured by the Bob or Alice. Your experiment wrongly assumes that the photon somehow magically changes direction because the box is moving, but it does not!

– the rocket experiment is flawed too. Let me explain:

First, let’s assume that both Bob and Alice send out the same type of white light from their sources of light (not to confuse the blue and red any further).

We both agree that the light spreads at the same speed for both of them.

Let’s assume it is a huge rocket that stands on the ground and light takes exactly one second to travel from Bob to Alice. It also takes one second to travel from Alice to Bob (there is no motion yet), the light is neither shifted to red or blue for either of them.

Now, assume the rocket moves upwards at half the speed of light. A photon sent from Alice to Bob will now take 2/3 of a second (because the photon will travel at C and the movement of the rocket will shorten the distance by 1/3). Because Bob is now hit by higher frequency light, the light he preceives as blue shifted. The opposite is valid for Alice. She sort of runs away from Bob’s light source. A photon sent from Bob to her will take 1.5 seconds exactly (the time the light takes to travel from bottom to top of the rocket plus the distance the rocket travels in space during that one second). Alice is now hit by lower frequency light. She perceives the light as redshifted.

While Bob and Alice see different wave lenghts and different colors their time or their clocks still show exactly the same lapse of time. In other words when our rocket moves at half the speed of light for 10 seconds, both Bob and Alice will have spent the exact same 10 seconds, one seing red the other seeing blue light. the fact that one sees higher frequency light and the other sees lower frequency light has no influence on how fast time has passed for them.

Now, I realize I as a non physicist and non-mathematician stand alone with this argument amongst a world of geniuses and against a world of proves and experiments that confirm what you are stating is correct. Still, the arguments and so called proves you mention here do not make logical sense to me. I am very open to stand corrected and made understand

@Urs

You seem to confuse inert speed with acceleration in both your arguments.

– Einstein´s light clock

Einstein´s clock is *inert* during the thought experiment that shows how time is affected by motion. So there´s no acceleration needed to show this. This results in a saw tooth type of motion of the photon, as seen from the observer that sees the light clock from a train that moves with constant speed. In other words: for the observer outside the train, the photon is moving sideways. The observer in the train disagrees, and will say it is only moving up and down. Same would go with a bumping ball within the train, for that matter…

Once acceleration comes into play, you´re very right: there´s no reason for the photon between the mirrors to start moving sideways, if the train suddenly started to move. And it won´t. But this is not part of the thought experiment. Photons do have momentum, like the bumping ball, even though they don´t have a rest mass. So if there would be a laser light behind a top semitransparent mirror that points straight down to a parallel mirror at the bottom, and start shooting light downward, it won´t move straight down, as seen from the observer outside the train, if the train was moving sideways. This momentum originates from the energy within the photon (energy = mass).

– rocket experiment

Here, the rocket in Physicist´s example is accelerating, whereas it is moving at a constant speed in your given example.

To follow your example with the rocket moving at a constant speed of 0.5c: first of all, there´s no length contraction of that amount with a speed of only 0.5c. At 0.6c there is a length contraction of 0.8, as seen from a static observer. Since Alice and Bob are no static observers, since they´re both on the rocket, this length contraction won´t be noticed, because of their time dilation. This time dilation will make it appear for both Alice and Bob that their lights are white, and not blue or red shifted at all, since they’re not accelerating. Frequency has a time element.

As seen from a static observer, the light sent from the bottom arrives later at the top of the rocket that’s moving upwards at a constant speed, and light sent from the top arrives sooner at the bottom. But we also observe a time difference between the clocks of Alice and Bob, that is not there for Alice and Bob. This time difference exactly compensates for this.

SUPPOSE WHILE TRAVELING AT HIGH SPEED I AM HOLDING A CLOCK , WOULD THE TIME DILATE IN MY CLOCK TOO?

Regarding experimental evidence for time dilation based two initially synchronous clocks; one clock “at rest” on earth and another, now faster, clock in motion on an aircraft circling the earth, wouldn’t the “stationary” clock on earth be moving relative to the clock on the aircraft, thus run faster relative to it? In other words, if observer 1 stayed on earth with clock 1 and observer 2 stayed in the aircraft with clock 2, wouldn’t each observer view their respective clocks as being slow since the other was moving relative to them? If so, explanation for physical evidence from this experiment?

Another way to consider my question is from a symmetry perspective; since both clocks are moving relative to the other, why asymmetry in the outcome?

Eric, the asymmetry originates from one accelerating, where the other is not. Both travelers will always deduce the other having slower time, but during the turnaround point/phase, a lot is changing in the view of the traveler (the other aging rapidly), but not in view of the one that isn’t accelerating.

This is most clearly shown using Minkowski spacetime: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime_rel_sim/index.html

Tom, thanks for you quick reply. It makes sense that both deduce the other as time-dilated. Regarding effects due to acceleration at the turnaround point / phase, even that would seem to be symmetric in that each observer is remaining still relative to their inertial reference frame and the other would be experiencing the acceleration / turn around. With respect to my question on the empirical evidence based in accurate clocks (one at rest and one flown flown for a while at modest speed), my question (conundrum) stems from the aforementioned perspective consideration. I understand that both observers should perceive other’s time as dialated, but if the looked at each other’s clocks (mechanical/ physical objects) would they read the same thing – an assymmetry? Why would one inertial reference frame be dominant.

Best and Happy New Year!

@Eric

This post on the twin paradox and this post on the asymmetry you’re talking about should answer your question.

While velocity is relative, acceleration is not. Observers in different reference frames can disagree about how fast a given thing is moving, but they don’t disagree on whether or not it’s accelerating. When you accelerate you feel a push in some direction, but that doesn’t mean that everything else in the universe also feels a push.

Thanks Tom. That makes a lot of sense.

Interesting read on Hafele-Keating that considers potential errors and bias in the experiment; lack of observer-based time dialation in particular (rather reliance on assumption that earth geocentric inertial reference frame is dominant).

http://thescientificworldview.blogspot.com/2011/02/time-dilation-and-hafele-and-keating.html?m=1

To me, special and general relativity make mathematical and physical sense (light speed constant in all reference frames, space-time planes). It is the failure of H-K experiment to demonstrate basic prediction of SR relative to each clock’s own reference frame that I am concerned with. Perhaps this experiment was indeed flawed. What additional experimental evidence support time dialation? Preferably that which confirms reciprocal observations of time-dialation independent of a “master reference frame”.

Time travelling is also possible through wormholes right?

I agree with Ur and Tom’s arguments still don’t convince me that the thought experiments are accurate.

The light clock – While the observer on the train perceives the light only travelling in a perpendicular motion, the light is indeed also travelling sideways with the train. Whether that train is going at a steady speed, accelerating, or decelerating, the light is travelling sideways at the same speed of the train and the observer on the train. Just because the observer perceives the vertical motion doesn’t negate the fact that the light did in fact travel along the hypotenuse of motion combined by the vertical separation of the mirrors and the horizontal motion of the train. It therefore took exactly the same amount of time to “tick” the clock and the exact same amount of time passed for both observers. Even though Alice only perceived a vertical light shift, time didn’t change for her, only the illusion that the path the light took was purely vertical.

Rocket experiment – Whether they experience the wavelengths slower or faster than the other, time doesn’t change. Over some time period Alice emits a single wave of light. Over the same time period Bob will experience that light as either bluer (if the rocket is accelerating due to the time lag it took the light to travel the length of the rocket) or redder if the rocket is decelerating. Just because Bob experienced the light waves differently he was not experiencing time differently.

Time is a human construct designed to put things in order so that we can understand them better. Sadly it has gotten tied in with mathematical formulas of acceleration but has no real existence in the universe except in our minds. We count the transitions of a cesium atom and call that time but who’s to say that gravity and acceleration (which compresses atoms in much the same way as gravity) are really only affecting the performance of the atom (in a predictable manner) and not affecting time, a human notion invented to be able to catch the bus.

Hi Nukdookum,

You have to understand that the constant speed of light was not theorized by this thought experiment. It doesn’t prove anything. A constant speed of light was first experimentally discovered. The thought experiment of the light clock is merely a way of showing what observations you´d get with this experimentally verified phenomenon of constant light speed, and that relative time dilation is merely a necessary element in it, to be able to have that phenomenon within a non-conflicting world. It’s a necessary piece of the puzzle (and there are more piece than just time dilation). And it’s also one that’s been proven experimentally.

Of you’d conclude it only looks as though the light only moves vertically for the observer on the train, but that this is really an illusion, because he knows he is actually moving on the train (ignoring earth’s rotation, the movement of our earth around the sun and the total movement of our local galaxy group), so the light is also really moving sideways with the train, and there´s actually no time dilation at all, then you would inevitably have to conclude you would measure the light clock passing slower than an atomic or mechanical clock inside the train. You think a light clock is therefore simply a bad clock? Do you believe we should measure light arriving at earth more slowly, because a star that emitted it moved away from us? Or faster because the star was moving towards us?

If you, on the other hand, do trust experiments, and believe light is somehow always measured at a constant speed, but time simply never dilates, you’ll inevitably get conflicts. The traveler inside the train will ‘subjectively’ observe a light pulse going straight down, and is unable to account for ‘the real length of the path’ by considering all those other movements, like the train on earth, the earth’s rotation, the earth around the sun, and our local galaxy group moving.

The thing is, it is always measured at a constant speed, for any seemingly ‘subjective’ distance, without accounting for anything. So it is actually measured faster than light speed, if you would account for all those other movements.

So when scientists say the earth is 13.7B years old, when are they measuring from?

What if someone measured the time hovering above the Big Bang?

What if someone measured the time from the exact point the earth is now just hovering waiting for the universe to exapnd until the earth appeared here?

What if someone measured time from a parallel universe as far away as we can imagine?

What if someone measured time while hurling through space parallel to the energy that would eventually become atoms and matter, and molecules and rocks and planets and eventually become earth? Since they’re moving really fast, lot’s more time passes by to them?

How’s this relate to the event horizon of a black hole? I know that if Bob heads into a black hole, and Frank watches, time appears normal to bob while Frank would see him slow down and approach the event horizon until he appears to move so slow he appears to freeze in place. If light is a continuos stream, light would take an increasingly larger amount of time to get to Frank’s eye…

But what if light only emitted at a really fast rate on and off? Assume for comprehension purposes it’s one per second. Wouldn’t Frank eventually start to see Bob appear like a strobe light slowing down in frequency from one second to one minute to one hour and one per day as Bob appeared to accelerate because it would take longer and longer for the “on” light to reach? Or would the beam of light be so distorted from the movement away from Frank that as Bob accelerated, the one second of light would last increasingly longer?

What if Bob looked back at Frank? Wouldn’t he see Frank disappearing really fast and appear smaller really fast? Why is it the opposite for Frank if Bob is moving away really fast? If they’re moving apart from each other at the same speed shouldn’t it be the same? Are we talking about the lights reflecting off of Frank that Bob’s seeing or is Frank emitting photons that make seeing him possible?

Sorry for all the questions… I’m confused!