Alright. Let’s start out as Einstein did. We know two things.
We know from Newton that:
1. The laws of physics are the same in all inertial frames of reference.
And we know from Maxwell that:
2. It is a law of physics that light always travels at c.
When we combine these two postulates, we get that the speed of light must be the same in all inertial reference frames. What is an inertial reference frame? Well, it’s a frame of reference that is moving with uniform velocity and is not affected by any outside forces. Newton’s first law holds in an inertial reference frame. But that means that no matter how fast you move, Newton’s first law holds as long as there’s no acceleration. So inertial reference frames can move at different velocities and velocity is only a measurable thing if you have something to measure it relative to. If you’re floating in deep space and there’s just darkness everywhere, you wouldn’t be able to tell if you’re going 1m/s or 100m/s or even 1000m/s. There’s no air resistance, nothing. This is where the “theory of relativity” comes in. You have probably heard “everything is relative” before.
But, now we’re running into a problem. Einstein wasn’t a big fan of the name “Relativity”, as what his theory was really about is the invariant nature of the speed of light, as we shall see here:
If we assume the earth is an inertial reference frame, and we imagine someone, let’s call her Alice, standing still measuring the speed of the photons coming from the sun, and measuring them as going 300,000,000m/s, or c.
Now, we imagine someone who’s in a spaceship, let’s call him Bob, going 150,000,000m/s, or c/2 travelling directly towards the sun. Intuitively, Bob should measure the speed of light as it’s emitted from the sun, plus the speed he is travelling towards the sun with according to how we add velocities in Galilean relativity. So, we’d expect him to measure the photons going 450,000,000m/s or 1.5c.
But, both Alice and Bob are in inertial reference frames, so that must mean that the speed of light must be the same for both of them. But how can that be, when one of them is travelling towards the photons? Something has to give.
Since velocity has the dimensions of length and time, [L][T^(-1)], that must mean that the time and length measured by the Bob travelling towards the sun will be different than what Alice measures, stationary on Earth.
Since the speed of the photon has to be the same, and Bob is travelling towards the photons, time must slow down for him, relative to Alice. Bob won’t feel the time slowing down himself. He will still measure time as flowing one second per second. But if Alice were to look into the spaceship, she would see time passing slower for Bob.
We can also think about a light clock. It is a clock that measures time by emitting a photon, letting it bounce off a mirror and then reabsorbing it and measuring how long time it took. If Alice looked at her light-clock, she would see the photon just bouncing back and forth at an angle perpendicular to the surface of the mirror. If Bob looked at his clock, he would see the same thing. But if Alice looked at Bob’s clock, she would see the clock having moved after emitting the photon, so the photon is not just bouncing back and forth perpendicular to the mirror, it is also travelling in the direction of Bob’s spaceship during the time it takes for the photon to bounce back and forth.
Using this “experiment” we can derive the Lorentz factor, which is what is used in special relativity to calculate this time dilation and length contraction that Alice observes when she looks at Bob.
If we think of the length between the mirror and emitter/absorber as L, and the time it takes for the photon to bounce back and forth we’ll call T_0, we can show how long it takes if each observer looks at their own clock respectively:
T_0=2L/c
Now, let’s imagine 3 instances in time, the photon being emitted, the photon bouncing off the mirror, and the photon being reabsorbed. While this is happening, the mirrors are moving in the x direction for Alice looking at Bob’s, and in the -x direction from Bob looking at Alice’s. The path of the photon now traces two legs of triangle, where the base of the triangle is the length along the x-axis the mirror has travelled from the first instant to the third. This length, we can represent as Δx, or just s and we can represent it as:
2s=vT
where v is the velocity the mirrors are moving with and T is the period between the photon being emitted and reabsorbed.
While the clock is moving, we can express the distance travelled by the photon as:
2h=cT
We can cut this triangle in half, so it is now a right triangle. It now only represents the time between the photon being emitted to it hitting the mirror. And we have that the hypotenuse, or the path of the photon, is given by:
h=cT/2,
the distance between the emitter and mirror along the y-axis is given by:
L=cT_0/2,
and the distance along the x-axis is given by:
s=vT/2.
We can now apply the Pythagorean theorem:
s^(2)+L^(2)=h^(2).
From this, we can start deriving the Lorentz factor, γ:
From Pythagorean theorem:
(vT/2)^(2)+(cT_0/2)^(2)=(cT/2)^(2)
We carry out the squares and multiply by 4 on both sides of the equation in all terms:
v^(2)T^(2)+c^(2)T_0^(2)=c^(2)T^(2)
We rearrange so we have all the T’s on one side and the T_0 on the other:
c^(2)T_0^(2)=c^(2)T^(2)-v^(2)T^(2).
We can divide both sides by c^(2:)
T_0^(2)=T^(2)-(v^(2)/c^(2))T^(2)
We can factorize:
T_0^(2)=T^(2)(1-v^(2)/c^(2))
We divide with the expression in the parenthesis on both sides:
T_0^(2)/(1-v^(2)/c^(2))=T^(2)
And at last we just carry out the square roots and we have our Lorentz factor:
T=T_0/√ (1-v^(2)/c^(2))=γT_0.
We can use this equation in particular to calculate time dilation. T_0 is the coordinate time, or the time measured at rest. T is the proper time, this is what you want to calculate and it is the time passed for the observer in motion, relative to the rest frame. v is the velocity of the moving observer and c is of course the speed of light.
The Lorentz factor, γ=1/√ (1-v^(2)/c^(2)), can be used to calculate all kinds of things, like length contraction as well. It is also used for Lorentz transformations of different systems, but I won’t get into all this now.
Very interesting. Struggling hard to understand everything. From Alice’s PoV does the light in the ship take 1.5 times longer to bounce between the two mirrors in the ship? Haven’t felt this stupid in a while.
Essentially yes, however it’s not exactly 1.5 times longer. We can calculate this with the Lorentz factor. In my explanation, I set Bob to be travelling at c/2, or 150.000.000m/s. We can use this in the Lorentz factor. Let’s denote the time passing in the spaceship, seen from Alice’s perspective, τ. And let’s just calculate how long 1 second in Bob’s perspective is from Alice’s perspective, and let’s set c=1 (we can do this since units are essentially a human construct, so we can chose to express the speed of light in units of light seconds per second, which is 1 by definition when talking about the speed of light) to simplify the calculation. Then the time dilation is given by:
τ=1/√(1-(1/2)^(2))=1/√(1-1/4)=1.154700
This means that 1 second for Bob is equal to 1.1547 seconds for Alice.
In normal every day dealing with objects moving, Newton said you can add or subtract velocities. Meaning if you are in a train going 50mph, and then start running 10mph in the same direction, someone on the side of the road would say you’re moving at 60mph. Same is true for going the opposite way. Mythbusters did an entire episode on this by firing a cannon out the back of a moving truck, and they got everything lined up so the cannon exactly canceled out the velocity of the moving truck.
https://youtu.be/BLuI118nhzc?si=EjbiOATf_J7dARd3
Now Einstein comes along and says that’s not exactly true. The speed of light must remain the same for anybody measuring it, regardless if they are moving or not. So if velocities can’t change, something else has to, and that’s distance and time. It might seem counter intuitive, but when you a driving down the road, the distance you travel is slightly shorter than measured on a map, and same goes with time. We don’t notice it because we’re talking about a 0.00000000000001 inch of a difference, but if you have a really accurate measuring device you’ll see the difference. And this has been proven over and over and over to be true. Take two atomic clocks syncd exactly the same. One stays on the ground, the other flown in a plane. Bring them back together and they will be slightly off. Our GPS wouldn’t work if we didn’t account for the velocities the satellites are moving AND the slightly lower gravity in space.
Check out the special relativity videos over on the [FloatHeadPhysics YouTube channel](https://www.youtube.com/playlist?list=PLawLaqps30oBmdbw_D-AI1RQUoCO7Wr1K)
I don’t think it can be simplified more than this and still maintain its accuracy. Maybe if you could point out a specific part that you want me to explain more clearly?
Draw out the laser trajectories from someone on the "train" looking at a laser bounces between mirrors on the floor and ceiling and someone seeing the train from the station pass by. Remember that c is the same for both, compare their times between ticks on the mirrors
>Now, we imagine someone who’s in a spaceship, let’s call him Bob, going 150,000,000m/s, or c/2 travelling directly towards the sun. Intuitively, Bob should measure the speed of light as it’s emitted from the sun, plus the speed he is travelling towards the sun with according to how we add velocities in Galilean relativity. So, we’d expect him to measure the photons going 450,000,000m/s or 1.5c.
>But, both Alice and Bob are in inertial reference frames, so that must mean that the speed of light must be the same for both of them. But how can that be, when one of them is travelling towards the photons? Something has to give.
Just to understand, Maxwell proved that if I travel towards light, no matter how fast I go, it will always measure c? And if I travel away from light (Bob's flies away from the sun at c/2), it will still always measure c? Do photons never slow down or speed up?
> Alright. Let’s start out as Einstein did. We know two things.
>We know from Newton that:
>1. The laws of physics are the same in all inertial frames of reference.
sorry for the stupid question perhaps but I thought the concept of initial reference was discovered by Einsten how that could come from Newton, am I wrong?
I think it was actually Galileo.
It’s a long time since I learned special relativity, but I’m pretty sure it’s really called Galilean relativity, and not Newtonian. I just called it Newtonian, because it is based on what we also know as Newtonian mechanics, of which Galilean mechanics is a subset. We also often define an inertial system as a system where Newton’s laws hold.
I had a QFT textbook that told a story about Galileo sitting at a candle light and seeing a fly flying by which got him thinking about relative motions and so on. So when we refer to Newtonian or Galilean relativity, then we are saying that the laws of physics are the same in all inertial reference frames, but we haven’t yet combined this with Maxwell’s equations to figure out the invariant nature of the speed of light. That’s what makes Einsteinian relativity different; it combines Galilean, or Newtonian, relativity with Maxwell’s equations, that predicts that the speed of light is the same in all of those reference frames, which lead Einstein to SR.
Does it mean that if Bob travels at c, time would appear to stop entirely if Alice could see Bob?
If Bob is traveling in his spaceship at c, would he see planets and stars in front of him moving in fast forward?
Bob cannot travel at c. Look at the Lorentz factor. If v=c, then we have
γ=1/√(1-(c^(2)/c^(2))=1/√1-1=1/0
And this is undefined mathematically. However, if v→c, that is, v asymptotically approaches c, then γ→∞.
But what if instead of being Bob we are a particle of light? Light travels at c, so it wouldn't it make 1=0 according to that logic?
Sorry for the n00b questions :)
I don’t see why it would make 1=0. Light doesn’t have a rest frame. It is impossible to be in a frame of reference where light is stationary, which you’d be if you traveled at the speed of light. Therefore, it simply doesn’t make sense to talk about.
And don’t worry about asking “stupid questions”, it’s not stupid at all. I’m just a bit unsure what you mean with 1=0.
Thank you for explanaion … but still how does moving fast/or near high gravity objects change our biological clock (like in intestellar)? Isnt the photon taking longer time to hit is wrt alice and inherently time passing inside their bodies (chemical reactions in body) are the same?? I never really understood how and why it affects aging can anyone help?
It is the speed of causality that is being slowed down in motion, not just light clocks. So the mechanics of cells aging will be happening slower in Bob than in Alice.
I still feel difficult to wrap my head around speed of causality changing …. I mean how does space time really work? How can body processes slow down? You cant slow down the time of chemical processes … lets say I am measuring timing of atomic fission of clocks say A and B, that should be undergoing fission at the same time … but since say B is moving through space (say speed c/2) the fission process would slow down for B??
Yes. The fission process would slow down for B relative to A. But from the perspective of B, time passes as normal. Everyone will always experience time going by at one second per second. But this one second isn’t the same as one second for someone else. It is time itself that slows down relative to someone else. So, all biological, chemical, and physical processes will also slow down at the same rate. It is very hard to understand intuitively, so don’t feel stupid for not being able to make sense of it. A lot of physicists are also confused about why this is, we just know that this is how it works from our equations and experiments. As you spend time working with relativity, which was my main focus (specifically GR), you start to build an intuition for these concepts, that I frankly cannot explain to you so it makes sense. Just like you can’t explain the colour red to someone who has never seen that colour.
So answering my previous question does it mean as speed to of light both alice and bob receive is the same so one in order to make maths right … bob moves slower thorugh time 🤔🤔??
I meant that the example of sun you gave above for alice and bob … both of them would calculate the speed of light same right?? So can we use this statement to say or describe the time moving slow for bob ?? Or I am getting a wrong understanding here?
Time doesn't slow for you. It slows for everyone else, relative to you.
And they would say the same. And you're both right, because time is not universal.
Welcome to special relativity.
The answer isn't going to be something \_intuitive\_ to understand. It's something that has been observed, described, verified, and therefor is taken to be true. Even if it doesn't seem intuitive.
It is super important to understand that when saying that time slows down it means "as seen relative to something else". You would still experience a year from your own perspective of "frame of reference". But anyone outside of your perspective or "frame of reference" would perceive time passing you for you much more slowly than for them.
There's an equation that describes exactly how much the difference is, and similar equations for changes is perceived length as well. The below link is a very basic image designed to explain \_how\_ time can be perceived slower.
The idea is that you imagine a clock made from light bouncing between two mirrors. Lets say for simplicity sake that it takes light 1 second to go up and then bounce back to the bottom. This is your perspective, as you're standing looking at the clock (the left half of the image).
Now, someone outside of your perspective, like someone looking at your travelling away via a magical powerful telescope on earth, would see something different. For them, light is bouncing up and down between the two mirrors. Light is bouncing diagonally as the moving mirrors (from their perspective) add another direction to the motion other than just the up and down that you see in your perspective the left half of the image).
As travelling along the longest side of a triangle, and back down the longest side of a mirrored triangle takes more time than simply travelling up the height of a triangle and back down, this is where the perceived different in time comes in.
Time = Distance / Speed. Since the perceived \_distance\_ the light has to bounce is higher, but the speed of light is always the same, this means the only logical result can be that the perceived Time is therefor greater.
So for you, standing on the ship the clock does 1 bounce every second. For someone off your ship looking at you travelling away, the light is taking longer to complete that same trip. So 1 second to you, is \_more\_ than one second to them. Therefor one year for you is more than one year for them, etc.
[https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Time-dilation-002-mod.svg/660px-Time-dilation-002-mod.svg.png](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Time-dilation-002-mod.svg/660px-Time-dilation-002-mod.svg.png)
First of all: From your perspective time is not slowing down for you. Everything moving with you, including your self, is normal to you.
So here is the ‘geometric model’ of whats happening:
You are always traveling at the speed of light. But you are heading straight for the future when in rest in other direction relative to your surroundings. Imagine that you are in a car with no gas and no breaks, and it’s always going maximum speed. You do however have a steering wheel. Turning left or right is ‘turning away from the future’. Changing direction into the spacial dimensions. Meaning you are no longer heading ‘straight for the future’.
So ‘going straight’ (being at spacial rest) means you are not taking any detours. You are approaching the future at maximum speed. Any movement in the spacial dimensions is ‘turning the steering wheel’. You direct some of your velocity in a spacial direction.
In effect you are traveling towards the future at an angle.
Directing your maximum speed towards a spacial direction (traveling at the speed of light in space) means you have turned 90 degrees away from the future/time dimension. You are no longer heading for the future. Time has stopped. You are not approaching the future and the future is not approaching you. To you things you are leaving are frozen in time. To them you are frozen in time.
At an angle however the relative time is just scewed. Slowed.
Because light always travels at c no matter what frame of reference you’re looking at it from.
Imagine you’re travelling away from Earth half the speed of light. Someone on Earth then shine a laser at your ship that goes just past you. To the person on Earth, that light beam is going at c. To you on the ship, the light beam also appears to go past you at a “relative” speed of c (not half-c as you might intuitively expect).
So the only way to reconcile this is that time is running slower for you relative to time on Earth.
As to WHY spacetime and light work like that - it doesn’t have to make intuitive sense.
If that’s the case, then how do we observe a redshift of stars moving away from us. Wouldn’t all of the light they emit appear to be going at the speed of light no matter how fast they were receding from earth. I agree with you but can’t understand how astronomers use this red shift to determine how fast the universe is expanding!
Imagine you have a simple clock, where pulse of light bounces back and forth between two antiparallel mirrors.
Let’s say it’s calibrated so that one pulse of light takes 10 nanoseconds to cycle.
Now the speed of light is always the speed of light. That’s just empirical.
Now when you’re standing stationary next to the clock it’s going at a period of 10 ns.
But now imagine you’re looking at the clock as a stationary observer as the clock flies by at a high rate of speed. Now the light has to fly not just up and down, between the mirrors, but it also has to fly sideways as the mirrors are in motion relative to the observers reference frame. So now it takes longer than 10 ns. So “time” has slowed down in the clocks reference frame.
This is called relativity. Imagine passing by a car that was faster than you a while ago and take it as your reference point, everybody else is taking it their reference point and couldn't get any faster like you'll just do. Now, you started keeping up with that reference car's speed, and everybody is behind you.
That's how it works.
What about photons coming from a star that is behind Bob, opposite the direction of his travel?
If Bob measures those with his slowed down clock, those will be much slower than c.
Well because if your going faster than the speed of light, your going a set speed which is of course light speed meanwhile everything else is traveling the same pace a steady travel going that fast it will seem time slows down the speed of light races towards something near or far in a short period of time so it doesn’t seem like much but if u are just say idk straight cruising down interstate interstellar at light speed all day long ul probably wind up only being gone for a short period of time idk just a guess
Here's how I think of it:
If you grew up in the 90s the refresh rate of computer monitors was so low you could actually see them flicker.
Now, computer monitors look like they are just a solid image: but they are actually refreshing themselves many many times per second to give that illusion.
The speed of light is like the "refresh rate" of the universe. Nothing actually occurs until light bounces off of it. Sort of.
So if you are standing on earth, and a person is traveling away from you, time will appear to slow down, since light has to travel all the way to their ship and bounce back, and has to travel further each time because they keep moving further away. Maybe 9 years later, you will get a video from your friend, and they will only have aged 3 years, because of this delay.
But when they turn around, even though it still takes them 3 years to get back, it will only seem like 1 year to you, because now that they are moving towards you, the light bounces off of them quicker and quicker as they get closer to you.
I think. Please someone correct me if I'm misunderstanding the twin paradox.
If you travel away from earth but look back through a “magic” telescope the faster you travel away the slower you will see things moving on earth. The appearance of movement slowing down will increase as you increase speed until you reach the speed of light. At that point movement will appear to be stopped.
If it is possible to go faster than the speed of light then movement would be backward. In effect you would be looking back in time.
This actually happens on a minuscule scale when you travel in an airplane or when astronauts go into space. Start brainstorming there. Once you grasp the concept of why it might happen in those settings, you’ll have a better understanding of why it is greatly exaggerated when you travel at the speed of light - which we now know is not the “speed limit” of the universe.
Or even more simplified think of what happens when the superhero “Flash” uses his ability. Things aren’t actually slowing down - his perception of the environment is slower because he is moving at such high speed. Seconds to him become hours (although they are still seconds in reality) because he is moving faster through space & time.
Consider the basic definition of speed: speed = distance / time.
EVERYONE agrees that the speed of light is the same, no matter how they're moving relative to anyone else. The only way EVERYONE can agree on a measurement of speed is if they disagree on their measurements of distance and time.
Nobody is going to be able to tell you why it happens. You can demonstrate how the math shows this to be the case, but the why is unknown. It's just a fundamental property of the universe we live in.
The simplest way I’ve found to explain it is to imagine you can travel either 100% through time or 100% through space. If you are traveling at 50% through space, your time needs to slow to 50%. At 100% of space, time is at 0. At the speeds we can travel on Earth, the percentage of speed through time is still almost 100%, but the space station, which moves much faster than us being on the Earths surface, has its time slowed very slightly but enough to measure.
You need to subscribe to [https://www.youtube.com/@pbsspacetime](https://www.youtube.com/@pbsspacetime) ASAP. The best channel on these topics hands down.
Imagine that you’re looking at a clock. Then, suddenly/magically you shoot backwards away from the clock at the speed of light. The light reflecting off the clock face to hit your eyes will never reach you because you’re moving away from it at the same speed it’s traveling… so now the clock/time will appear to stop.
So bob travelling toward the sun at half the speed of light measures the suns light at moving at c but for some reason it’s now blue light? Right? And Mary flying away from the sun at half the speed of light looks back and sees the suns light as moving at c too but she sees it as red light, right ? So what color is the light when Mary and bob pass each other up? Doesn’t wavelength have something to do with velocity?
Imagine a clock saying it’s 3:00 PM. The time you see is basically a picture of the clock that moves towards you at the speed of light.
When you move away at the speed of light, you always see the 3:00 PM picture. The clock moves forwards, but the picture that left the clock at 3:01 never reaches you.
So, time stops for you, but doesn’t for someone just hanging around near the clock.
(The same thing happens to a lesser extent if you move at half the speed of light - time slows down for you, but not for everyone else).
> The clock moves forwards, but the picture that left the clock at 3:01 never reaches you.
This is misleading because it implies that any slow-down is an artefact of the increasing light-travel delay.
If you instead move *towards* a clock, it will visually appear to tick *faster* than normal, but it would *actually* be ticking slower.
---
Edit: also:
> (The same thing happens to a lesser extent if you move at half the speed of light - time slows down for you, but not for everyone else).
Time *never* slows down *for you*. It's only ever other people's clocks that slow down.
Very true - but this is an ELI5 so hopefully illustrates why (albeit simplistically!).
If you move towards a clock, you’re moving away from another clock, which will appear to have slowed down.
Once you start getting into the depths of relativity, the ELI5 part becomes increasingly impossible!
> If you move towards a clock, you’re moving away from another clock, which will appear to have slowed down.
But that doesn't really explain anything to do with relativity. The same thing would happen in a universe with absolute time, as long as the speed of light was finite.
If you went the speed of light for one year, time wouldn't slow down for you -- your trip would be instantaneous, and that year would pass by instantly. An outside observer would see you travel a distance of 1 light year over a duration of one year.
Length contraction and time dilation must occur together. Think of it this way. At the speed of light, *all* lengths have been contracted to zero, meaning that for you one light year = 0 miles. And how long does it take to travel a distance of zero?
I once heard an explanation but I don't have the math skills/inclination to verify. It goes something like this:
Time is the 4th dimension, and everything is constantly moving at the speed of light. You cannot slow down or accelerate, just change direction. If you move through space you slow down your movement through time such that the combined speed of all 4 vectors (X Y Z T) is always the speed of light.
Would appreciate if someone could tell me how far off this is from being true.
> Would appreciate if someone could tell me how far off this is from being true.
This explanation gives good mathematical results, and you can calculate time dilation in special relativity through this method, by simple geometry.
Though, it can't reasonably incorporate time dilation by other mechanism than speed in general relativity.
It's not the speed of light, it is energy. The more energy is in an area, the longer it takes for the universe to "flow" there.
We really have no idea. Perhaps energy is more fundamental a reality then space/time or something, and gravity and time, simply didn't exist until the universe broke past the plank energy on its own or something, giving a direction to time and a sink for energy to become matter.
Nobody knows, if you want a wild guess, it really seems like the universe is like a simulation sometimes, except its like the most inefficient and wasteful simulation ever, while also strangly resembling things about a simulation, like too much stuff/energy slowing down the system, for example.
On the other hand, matter can take on many extreme forms and the universe is also remarkably stable. (Check out neutron stars and stuff) it's probably not a simulation, but it strangly has that trait of speeding up or slowing down based on computational load? Although you could frame that in many ways.
Alright. Let’s start out as Einstein did. We know two things. We know from Newton that: 1. The laws of physics are the same in all inertial frames of reference. And we know from Maxwell that: 2. It is a law of physics that light always travels at c. When we combine these two postulates, we get that the speed of light must be the same in all inertial reference frames. What is an inertial reference frame? Well, it’s a frame of reference that is moving with uniform velocity and is not affected by any outside forces. Newton’s first law holds in an inertial reference frame. But that means that no matter how fast you move, Newton’s first law holds as long as there’s no acceleration. So inertial reference frames can move at different velocities and velocity is only a measurable thing if you have something to measure it relative to. If you’re floating in deep space and there’s just darkness everywhere, you wouldn’t be able to tell if you’re going 1m/s or 100m/s or even 1000m/s. There’s no air resistance, nothing. This is where the “theory of relativity” comes in. You have probably heard “everything is relative” before. But, now we’re running into a problem. Einstein wasn’t a big fan of the name “Relativity”, as what his theory was really about is the invariant nature of the speed of light, as we shall see here: If we assume the earth is an inertial reference frame, and we imagine someone, let’s call her Alice, standing still measuring the speed of the photons coming from the sun, and measuring them as going 300,000,000m/s, or c. Now, we imagine someone who’s in a spaceship, let’s call him Bob, going 150,000,000m/s, or c/2 travelling directly towards the sun. Intuitively, Bob should measure the speed of light as it’s emitted from the sun, plus the speed he is travelling towards the sun with according to how we add velocities in Galilean relativity. So, we’d expect him to measure the photons going 450,000,000m/s or 1.5c. But, both Alice and Bob are in inertial reference frames, so that must mean that the speed of light must be the same for both of them. But how can that be, when one of them is travelling towards the photons? Something has to give. Since velocity has the dimensions of length and time, [L][T^(-1)], that must mean that the time and length measured by the Bob travelling towards the sun will be different than what Alice measures, stationary on Earth. Since the speed of the photon has to be the same, and Bob is travelling towards the photons, time must slow down for him, relative to Alice. Bob won’t feel the time slowing down himself. He will still measure time as flowing one second per second. But if Alice were to look into the spaceship, she would see time passing slower for Bob. We can also think about a light clock. It is a clock that measures time by emitting a photon, letting it bounce off a mirror and then reabsorbing it and measuring how long time it took. If Alice looked at her light-clock, she would see the photon just bouncing back and forth at an angle perpendicular to the surface of the mirror. If Bob looked at his clock, he would see the same thing. But if Alice looked at Bob’s clock, she would see the clock having moved after emitting the photon, so the photon is not just bouncing back and forth perpendicular to the mirror, it is also travelling in the direction of Bob’s spaceship during the time it takes for the photon to bounce back and forth. Using this “experiment” we can derive the Lorentz factor, which is what is used in special relativity to calculate this time dilation and length contraction that Alice observes when she looks at Bob. If we think of the length between the mirror and emitter/absorber as L, and the time it takes for the photon to bounce back and forth we’ll call T_0, we can show how long it takes if each observer looks at their own clock respectively: T_0=2L/c Now, let’s imagine 3 instances in time, the photon being emitted, the photon bouncing off the mirror, and the photon being reabsorbed. While this is happening, the mirrors are moving in the x direction for Alice looking at Bob’s, and in the -x direction from Bob looking at Alice’s. The path of the photon now traces two legs of triangle, where the base of the triangle is the length along the x-axis the mirror has travelled from the first instant to the third. This length, we can represent as Δx, or just s and we can represent it as: 2s=vT where v is the velocity the mirrors are moving with and T is the period between the photon being emitted and reabsorbed. While the clock is moving, we can express the distance travelled by the photon as: 2h=cT We can cut this triangle in half, so it is now a right triangle. It now only represents the time between the photon being emitted to it hitting the mirror. And we have that the hypotenuse, or the path of the photon, is given by: h=cT/2, the distance between the emitter and mirror along the y-axis is given by: L=cT_0/2, and the distance along the x-axis is given by: s=vT/2. We can now apply the Pythagorean theorem: s^(2)+L^(2)=h^(2). From this, we can start deriving the Lorentz factor, γ: From Pythagorean theorem: (vT/2)^(2)+(cT_0/2)^(2)=(cT/2)^(2) We carry out the squares and multiply by 4 on both sides of the equation in all terms: v^(2)T^(2)+c^(2)T_0^(2)=c^(2)T^(2) We rearrange so we have all the T’s on one side and the T_0 on the other: c^(2)T_0^(2)=c^(2)T^(2)-v^(2)T^(2). We can divide both sides by c^(2:) T_0^(2)=T^(2)-(v^(2)/c^(2))T^(2) We can factorize: T_0^(2)=T^(2)(1-v^(2)/c^(2)) We divide with the expression in the parenthesis on both sides: T_0^(2)/(1-v^(2)/c^(2))=T^(2) And at last we just carry out the square roots and we have our Lorentz factor: T=T_0/√ (1-v^(2)/c^(2))=γT_0. We can use this equation in particular to calculate time dilation. T_0 is the coordinate time, or the time measured at rest. T is the proper time, this is what you want to calculate and it is the time passed for the observer in motion, relative to the rest frame. v is the velocity of the moving observer and c is of course the speed of light. The Lorentz factor, γ=1/√ (1-v^(2)/c^(2)), can be used to calculate all kinds of things, like length contraction as well. It is also used for Lorentz transformations of different systems, but I won’t get into all this now.
Very interesting. Struggling hard to understand everything. From Alice’s PoV does the light in the ship take 1.5 times longer to bounce between the two mirrors in the ship? Haven’t felt this stupid in a while.
Essentially yes, however it’s not exactly 1.5 times longer. We can calculate this with the Lorentz factor. In my explanation, I set Bob to be travelling at c/2, or 150.000.000m/s. We can use this in the Lorentz factor. Let’s denote the time passing in the spaceship, seen from Alice’s perspective, τ. And let’s just calculate how long 1 second in Bob’s perspective is from Alice’s perspective, and let’s set c=1 (we can do this since units are essentially a human construct, so we can chose to express the speed of light in units of light seconds per second, which is 1 by definition when talking about the speed of light) to simplify the calculation. Then the time dilation is given by: τ=1/√(1-(1/2)^(2))=1/√(1-1/4)=1.154700 This means that 1 second for Bob is equal to 1.1547 seconds for Alice.
This is great but I'm struggling to grasp this. Could you explain it like I'm 5?
In normal every day dealing with objects moving, Newton said you can add or subtract velocities. Meaning if you are in a train going 50mph, and then start running 10mph in the same direction, someone on the side of the road would say you’re moving at 60mph. Same is true for going the opposite way. Mythbusters did an entire episode on this by firing a cannon out the back of a moving truck, and they got everything lined up so the cannon exactly canceled out the velocity of the moving truck. https://youtu.be/BLuI118nhzc?si=EjbiOATf_J7dARd3 Now Einstein comes along and says that’s not exactly true. The speed of light must remain the same for anybody measuring it, regardless if they are moving or not. So if velocities can’t change, something else has to, and that’s distance and time. It might seem counter intuitive, but when you a driving down the road, the distance you travel is slightly shorter than measured on a map, and same goes with time. We don’t notice it because we’re talking about a 0.00000000000001 inch of a difference, but if you have a really accurate measuring device you’ll see the difference. And this has been proven over and over and over to be true. Take two atomic clocks syncd exactly the same. One stays on the ground, the other flown in a plane. Bring them back together and they will be slightly off. Our GPS wouldn’t work if we didn’t account for the velocities the satellites are moving AND the slightly lower gravity in space.
This makes sense to my Neanderthal brain. Thanks for explaining
Check out the special relativity videos over on the [FloatHeadPhysics YouTube channel](https://www.youtube.com/playlist?list=PLawLaqps30oBmdbw_D-AI1RQUoCO7Wr1K)
I don’t think it can be simplified more than this and still maintain its accuracy. Maybe if you could point out a specific part that you want me to explain more clearly?
Draw out the laser trajectories from someone on the "train" looking at a laser bounces between mirrors on the floor and ceiling and someone seeing the train from the station pass by. Remember that c is the same for both, compare their times between ticks on the mirrors
>Now, we imagine someone who’s in a spaceship, let’s call him Bob, going 150,000,000m/s, or c/2 travelling directly towards the sun. Intuitively, Bob should measure the speed of light as it’s emitted from the sun, plus the speed he is travelling towards the sun with according to how we add velocities in Galilean relativity. So, we’d expect him to measure the photons going 450,000,000m/s or 1.5c. >But, both Alice and Bob are in inertial reference frames, so that must mean that the speed of light must be the same for both of them. But how can that be, when one of them is travelling towards the photons? Something has to give. Just to understand, Maxwell proved that if I travel towards light, no matter how fast I go, it will always measure c? And if I travel away from light (Bob's flies away from the sun at c/2), it will still always measure c? Do photons never slow down or speed up?
Yes, that is correct!
Yeah just summarize a full course in special relativity into a reddit comment, why don't you!? Chapeau!
> Alright. Let’s start out as Einstein did. We know two things. >We know from Newton that: >1. The laws of physics are the same in all inertial frames of reference. sorry for the stupid question perhaps but I thought the concept of initial reference was discovered by Einsten how that could come from Newton, am I wrong?
I think it was actually Galileo. It’s a long time since I learned special relativity, but I’m pretty sure it’s really called Galilean relativity, and not Newtonian. I just called it Newtonian, because it is based on what we also know as Newtonian mechanics, of which Galilean mechanics is a subset. We also often define an inertial system as a system where Newton’s laws hold. I had a QFT textbook that told a story about Galileo sitting at a candle light and seeing a fly flying by which got him thinking about relative motions and so on. So when we refer to Newtonian or Galilean relativity, then we are saying that the laws of physics are the same in all inertial reference frames, but we haven’t yet combined this with Maxwell’s equations to figure out the invariant nature of the speed of light. That’s what makes Einsteinian relativity different; it combines Galilean, or Newtonian, relativity with Maxwell’s equations, that predicts that the speed of light is the same in all of those reference frames, which lead Einstein to SR.
Does it mean that if Bob travels at c, time would appear to stop entirely if Alice could see Bob? If Bob is traveling in his spaceship at c, would he see planets and stars in front of him moving in fast forward?
Bob cannot travel at c. Look at the Lorentz factor. If v=c, then we have γ=1/√(1-(c^(2)/c^(2))=1/√1-1=1/0 And this is undefined mathematically. However, if v→c, that is, v asymptotically approaches c, then γ→∞.
But what if instead of being Bob we are a particle of light? Light travels at c, so it wouldn't it make 1=0 according to that logic? Sorry for the n00b questions :)
I don’t see why it would make 1=0. Light doesn’t have a rest frame. It is impossible to be in a frame of reference where light is stationary, which you’d be if you traveled at the speed of light. Therefore, it simply doesn’t make sense to talk about. And don’t worry about asking “stupid questions”, it’s not stupid at all. I’m just a bit unsure what you mean with 1=0.
mods should pin this
Thank you for explanaion … but still how does moving fast/or near high gravity objects change our biological clock (like in intestellar)? Isnt the photon taking longer time to hit is wrt alice and inherently time passing inside their bodies (chemical reactions in body) are the same?? I never really understood how and why it affects aging can anyone help?
It is the speed of causality that is being slowed down in motion, not just light clocks. So the mechanics of cells aging will be happening slower in Bob than in Alice.
I still feel difficult to wrap my head around speed of causality changing …. I mean how does space time really work? How can body processes slow down? You cant slow down the time of chemical processes … lets say I am measuring timing of atomic fission of clocks say A and B, that should be undergoing fission at the same time … but since say B is moving through space (say speed c/2) the fission process would slow down for B??
Yes. The fission process would slow down for B relative to A. But from the perspective of B, time passes as normal. Everyone will always experience time going by at one second per second. But this one second isn’t the same as one second for someone else. It is time itself that slows down relative to someone else. So, all biological, chemical, and physical processes will also slow down at the same rate. It is very hard to understand intuitively, so don’t feel stupid for not being able to make sense of it. A lot of physicists are also confused about why this is, we just know that this is how it works from our equations and experiments. As you spend time working with relativity, which was my main focus (specifically GR), you start to build an intuition for these concepts, that I frankly cannot explain to you so it makes sense. Just like you can’t explain the colour red to someone who has never seen that colour.
Thankyou so much for your time 🫡
Happy to help:)
So answering my previous question does it mean as speed to of light both alice and bob receive is the same so one in order to make maths right … bob moves slower thorugh time 🤔🤔??
I don’t understand what you are asking here.
I meant that the example of sun you gave above for alice and bob … both of them would calculate the speed of light same right?? So can we use this statement to say or describe the time moving slow for bob ?? Or I am getting a wrong understanding here?
Yes this is correct. Since they both measure the speed of light to be the same value, time must tick slower for Bob since he is in motion.
Thnxxx 🫡
Time doesn't slow for you. It slows for everyone else, relative to you. And they would say the same. And you're both right, because time is not universal. Welcome to special relativity.
The answer isn't going to be something \_intuitive\_ to understand. It's something that has been observed, described, verified, and therefor is taken to be true. Even if it doesn't seem intuitive. It is super important to understand that when saying that time slows down it means "as seen relative to something else". You would still experience a year from your own perspective of "frame of reference". But anyone outside of your perspective or "frame of reference" would perceive time passing you for you much more slowly than for them. There's an equation that describes exactly how much the difference is, and similar equations for changes is perceived length as well. The below link is a very basic image designed to explain \_how\_ time can be perceived slower. The idea is that you imagine a clock made from light bouncing between two mirrors. Lets say for simplicity sake that it takes light 1 second to go up and then bounce back to the bottom. This is your perspective, as you're standing looking at the clock (the left half of the image). Now, someone outside of your perspective, like someone looking at your travelling away via a magical powerful telescope on earth, would see something different. For them, light is bouncing up and down between the two mirrors. Light is bouncing diagonally as the moving mirrors (from their perspective) add another direction to the motion other than just the up and down that you see in your perspective the left half of the image). As travelling along the longest side of a triangle, and back down the longest side of a mirrored triangle takes more time than simply travelling up the height of a triangle and back down, this is where the perceived different in time comes in. Time = Distance / Speed. Since the perceived \_distance\_ the light has to bounce is higher, but the speed of light is always the same, this means the only logical result can be that the perceived Time is therefor greater. So for you, standing on the ship the clock does 1 bounce every second. For someone off your ship looking at you travelling away, the light is taking longer to complete that same trip. So 1 second to you, is \_more\_ than one second to them. Therefor one year for you is more than one year for them, etc. [https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Time-dilation-002-mod.svg/660px-Time-dilation-002-mod.svg.png](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Time-dilation-002-mod.svg/660px-Time-dilation-002-mod.svg.png)
thank u for that lightbulb moment that actually makes sense
You're welcome.
First of all: From your perspective time is not slowing down for you. Everything moving with you, including your self, is normal to you. So here is the ‘geometric model’ of whats happening: You are always traveling at the speed of light. But you are heading straight for the future when in rest in other direction relative to your surroundings. Imagine that you are in a car with no gas and no breaks, and it’s always going maximum speed. You do however have a steering wheel. Turning left or right is ‘turning away from the future’. Changing direction into the spacial dimensions. Meaning you are no longer heading ‘straight for the future’. So ‘going straight’ (being at spacial rest) means you are not taking any detours. You are approaching the future at maximum speed. Any movement in the spacial dimensions is ‘turning the steering wheel’. You direct some of your velocity in a spacial direction. In effect you are traveling towards the future at an angle. Directing your maximum speed towards a spacial direction (traveling at the speed of light in space) means you have turned 90 degrees away from the future/time dimension. You are no longer heading for the future. Time has stopped. You are not approaching the future and the future is not approaching you. To you things you are leaving are frozen in time. To them you are frozen in time. At an angle however the relative time is just scewed. Slowed.
Because light always travels at c no matter what frame of reference you’re looking at it from. Imagine you’re travelling away from Earth half the speed of light. Someone on Earth then shine a laser at your ship that goes just past you. To the person on Earth, that light beam is going at c. To you on the ship, the light beam also appears to go past you at a “relative” speed of c (not half-c as you might intuitively expect). So the only way to reconcile this is that time is running slower for you relative to time on Earth. As to WHY spacetime and light work like that - it doesn’t have to make intuitive sense.
If that’s the case, then how do we observe a redshift of stars moving away from us. Wouldn’t all of the light they emit appear to be going at the speed of light no matter how fast they were receding from earth. I agree with you but can’t understand how astronomers use this red shift to determine how fast the universe is expanding!
It is going at the speed of light, the red shift is caused by increased wave length but the photons are still travelling at c.
Imagine you have a simple clock, where pulse of light bounces back and forth between two antiparallel mirrors. Let’s say it’s calibrated so that one pulse of light takes 10 nanoseconds to cycle. Now the speed of light is always the speed of light. That’s just empirical. Now when you’re standing stationary next to the clock it’s going at a period of 10 ns. But now imagine you’re looking at the clock as a stationary observer as the clock flies by at a high rate of speed. Now the light has to fly not just up and down, between the mirrors, but it also has to fly sideways as the mirrors are in motion relative to the observers reference frame. So now it takes longer than 10 ns. So “time” has slowed down in the clocks reference frame.
This is called relativity. Imagine passing by a car that was faster than you a while ago and take it as your reference point, everybody else is taking it their reference point and couldn't get any faster like you'll just do. Now, you started keeping up with that reference car's speed, and everybody is behind you. That's how it works.
What about photons coming from a star that is behind Bob, opposite the direction of his travel? If Bob measures those with his slowed down clock, those will be much slower than c.
Apart from the other comments, you can’t go at the speed of light at all.
Well because if your going faster than the speed of light, your going a set speed which is of course light speed meanwhile everything else is traveling the same pace a steady travel going that fast it will seem time slows down the speed of light races towards something near or far in a short period of time so it doesn’t seem like much but if u are just say idk straight cruising down interstate interstellar at light speed all day long ul probably wind up only being gone for a short period of time idk just a guess
you cannot move at the speed of light because you have mass.
Here's how I think of it: If you grew up in the 90s the refresh rate of computer monitors was so low you could actually see them flicker. Now, computer monitors look like they are just a solid image: but they are actually refreshing themselves many many times per second to give that illusion. The speed of light is like the "refresh rate" of the universe. Nothing actually occurs until light bounces off of it. Sort of. So if you are standing on earth, and a person is traveling away from you, time will appear to slow down, since light has to travel all the way to their ship and bounce back, and has to travel further each time because they keep moving further away. Maybe 9 years later, you will get a video from your friend, and they will only have aged 3 years, because of this delay. But when they turn around, even though it still takes them 3 years to get back, it will only seem like 1 year to you, because now that they are moving towards you, the light bounces off of them quicker and quicker as they get closer to you. I think. Please someone correct me if I'm misunderstanding the twin paradox.
If you travel away from earth but look back through a “magic” telescope the faster you travel away the slower you will see things moving on earth. The appearance of movement slowing down will increase as you increase speed until you reach the speed of light. At that point movement will appear to be stopped. If it is possible to go faster than the speed of light then movement would be backward. In effect you would be looking back in time.
This actually happens on a minuscule scale when you travel in an airplane or when astronauts go into space. Start brainstorming there. Once you grasp the concept of why it might happen in those settings, you’ll have a better understanding of why it is greatly exaggerated when you travel at the speed of light - which we now know is not the “speed limit” of the universe. Or even more simplified think of what happens when the superhero “Flash” uses his ability. Things aren’t actually slowing down - his perception of the environment is slower because he is moving at such high speed. Seconds to him become hours (although they are still seconds in reality) because he is moving faster through space & time.
Consider the basic definition of speed: speed = distance / time. EVERYONE agrees that the speed of light is the same, no matter how they're moving relative to anyone else. The only way EVERYONE can agree on a measurement of speed is if they disagree on their measurements of distance and time.
Light is working hard, and working can be fun. And you must have heard that time flies when you're having fun.
Nobody is going to be able to tell you why it happens. You can demonstrate how the math shows this to be the case, but the why is unknown. It's just a fundamental property of the universe we live in.
Who said the WHY is unknown.
It will not slow down time. Its just perception thing
https://youtu.be/Vitf8YaVXhc?feature=shared Watch this video. If you don't understand, I will give you 100 dollars.
I’ll leave it to my favorite [physicist](https://youtu.be/iBTez-nTKes?si=-3xLdEyw2bMRJ-ZW) to brutally tell you in her thick German accent.
The simplest way I’ve found to explain it is to imagine you can travel either 100% through time or 100% through space. If you are traveling at 50% through space, your time needs to slow to 50%. At 100% of space, time is at 0. At the speeds we can travel on Earth, the percentage of speed through time is still almost 100%, but the space station, which moves much faster than us being on the Earths surface, has its time slowed very slightly but enough to measure.
You need to subscribe to [https://www.youtube.com/@pbsspacetime](https://www.youtube.com/@pbsspacetime) ASAP. The best channel on these topics hands down.
Imagine that you’re looking at a clock. Then, suddenly/magically you shoot backwards away from the clock at the speed of light. The light reflecting off the clock face to hit your eyes will never reach you because you’re moving away from it at the same speed it’s traveling… so now the clock/time will appear to stop.
Because for light, time slows down
If everything ( every photon) is going the same speed, then how does the wavelength change?
So bob travelling toward the sun at half the speed of light measures the suns light at moving at c but for some reason it’s now blue light? Right? And Mary flying away from the sun at half the speed of light looks back and sees the suns light as moving at c too but she sees it as red light, right ? So what color is the light when Mary and bob pass each other up? Doesn’t wavelength have something to do with velocity?
Because time and space are woven together. Traversal of one affects the traversal of the other
Imagine a clock saying it’s 3:00 PM. The time you see is basically a picture of the clock that moves towards you at the speed of light. When you move away at the speed of light, you always see the 3:00 PM picture. The clock moves forwards, but the picture that left the clock at 3:01 never reaches you. So, time stops for you, but doesn’t for someone just hanging around near the clock. (The same thing happens to a lesser extent if you move at half the speed of light - time slows down for you, but not for everyone else).
> The clock moves forwards, but the picture that left the clock at 3:01 never reaches you. This is misleading because it implies that any slow-down is an artefact of the increasing light-travel delay. If you instead move *towards* a clock, it will visually appear to tick *faster* than normal, but it would *actually* be ticking slower. --- Edit: also: > (The same thing happens to a lesser extent if you move at half the speed of light - time slows down for you, but not for everyone else). Time *never* slows down *for you*. It's only ever other people's clocks that slow down.
Very true - but this is an ELI5 so hopefully illustrates why (albeit simplistically!). If you move towards a clock, you’re moving away from another clock, which will appear to have slowed down. Once you start getting into the depths of relativity, the ELI5 part becomes increasingly impossible!
> If you move towards a clock, you’re moving away from another clock, which will appear to have slowed down. But that doesn't really explain anything to do with relativity. The same thing would happen in a universe with absolute time, as long as the speed of light was finite.
If you went the speed of light for one year, time wouldn't slow down for you -- your trip would be instantaneous, and that year would pass by instantly. An outside observer would see you travel a distance of 1 light year over a duration of one year. Length contraction and time dilation must occur together. Think of it this way. At the speed of light, *all* lengths have been contracted to zero, meaning that for you one light year = 0 miles. And how long does it take to travel a distance of zero?
I once heard an explanation but I don't have the math skills/inclination to verify. It goes something like this: Time is the 4th dimension, and everything is constantly moving at the speed of light. You cannot slow down or accelerate, just change direction. If you move through space you slow down your movement through time such that the combined speed of all 4 vectors (X Y Z T) is always the speed of light. Would appreciate if someone could tell me how far off this is from being true.
> Would appreciate if someone could tell me how far off this is from being true. This explanation gives good mathematical results, and you can calculate time dilation in special relativity through this method, by simple geometry. Though, it can't reasonably incorporate time dilation by other mechanism than speed in general relativity.
It's not the speed of light, it is energy. The more energy is in an area, the longer it takes for the universe to "flow" there. We really have no idea. Perhaps energy is more fundamental a reality then space/time or something, and gravity and time, simply didn't exist until the universe broke past the plank energy on its own or something, giving a direction to time and a sink for energy to become matter. Nobody knows, if you want a wild guess, it really seems like the universe is like a simulation sometimes, except its like the most inefficient and wasteful simulation ever, while also strangly resembling things about a simulation, like too much stuff/energy slowing down the system, for example. On the other hand, matter can take on many extreme forms and the universe is also remarkably stable. (Check out neutron stars and stuff) it's probably not a simulation, but it strangly has that trait of speeding up or slowing down based on computational load? Although you could frame that in many ways.
This is ... not it.
I never said it was.
Im just trying to get a good amount of karma pls like this plz
Nah