# Does time really slow down in relativity, or is it an illusion caused by the Doppler shifting of light? [duplicate]

Does time really dilate, or is it only how we perceive time, which is in the form of light waves. When an object moves away from another object at very high speeds, the light takes longer to reach it so it gets Doppler shifted longer, creating the illusion of time for the object slowing down. Likewise observing a moving beam of light requires light from the beam to reach the eyes, so it won’t appear to go as fast as it really is going.

My question asks whether this Doppler shift is what slows time down in relativity.

• (1) Please jettison the idea of "relativistic mass" ASAP. It is an anachronism and will only confuse further study. (2) Wave-particle duality, while important in quantum mechanics, is not going to help you grasp relativity at this point – JEB Jul 11 '18 at 22:10
• None of the justifications for special relativity rely on the wave-particle duality, nor should they. Special relativity works just fine and makes sense even if you don't know that quantum mechanics exists (which isn't surprising, considering that Einstein came up with it before quantum mechanics was worked out). – probably_someone Jul 11 '18 at 22:14
• use "invarient mass". This remains the same, but a $\gamma$ factor alters the force required to accelerate it at high speed. – JMLCarter Jul 11 '18 at 22:14
• Time is really slowed by the effect of time dilation. Lots of sources for the an introductory read – JMLCarter Jul 11 '18 at 22:17
• Your title is asking about time changes, but the body seems to be asking very different questions. These concepts can be related, but aren't identical. Perhaps you could edit either the title or the question so they are in sync? – BowlOfRed Jul 11 '18 at 22:19

The effect of time dilation comes directly from the central postulates of special relativity, which are that a) the speed of light is the same in all inertial frames of reference, and (b) that the laws of physics are the same in all inertial frames of reference.

Consider an observer inside a railway car. The height to the mirror ceiling is $L$, and he fires a laser to see it go and return. From the definition of velocity, he sees that

$$v = \frac{dx}{dt} \quad = c = \frac{2L}{\Delta \tau},$$

where $\tau$ is the time he measures.

In the frame of reference of someone watching him pass by at speed $v$ (see the picture from Wiki), they similarly measure that

$$c = \frac{2\sqrt{L^2 + \frac{1}{4}v^2\Delta t^2}}{\Delta t},$$ where $\Delta t$ the time span in the ground frame. Combining these, you can show time dilation, as given by

$$\Delta \tau = \Delta t\sqrt{1-\left(\frac{v}{c}\right)^2}.$$

Since we know of the speed limit $v < c$, the root term is always less than 1, and thus the moving observer measures a smaller time.

This is a physical result. The observers measure different time spans for the light clock, and they are both equally valid in thinking their measured time is "correct". So the effect of time dilation arises directly from the assumptions of special relativity, not from the doppler effect.

For the doppler effect, a difference in wavelength can be given by

$$\frac{\Delta \lambda}{\lambda} = \frac{v}{c}.$$

The speed is related to the change in wavelength, so the fact that the object is moving relative to the observer means that the observer can only see a change in color, not in time. After all, if the source being observed is continually emitting light, then light will constantly arrive at the observer. So the observer would not detect a change in the arrival time of the light.

However, your reasoning could be applied to a car blinker accelerating away from us relativistically. At each blink, the clock would be farther away, and each pulse would take longer to reach us. However, this would still be the result of causality, and the nature of light, rather than the doppler effect itself. Also, a person in the relativistically-moving car would still measure a dilated time relative to us as observers.

Well the Doppler effect has nothing to do with this in any way. Time dilation is definitely a real phenomena and thus 'is not an illusion'.If it was then our GPS systems wouldn't function and you'd drive into a lake instead of reaching your favorite lakeside restaurant. There is a lot of mathematical support to the theory which would be best understood if you examine it yourself and hence I will refrain from explaining it. Basically Time dilation must occur to ensure that all fundamental laws (Maxwell's Laws and Newton's Laws) remain same in all inertial frame irrespective of their motion i.e. time dilation (and length contraction) justify non preference of any inertial frame. Also this phenomena is relative(as is motion). If a rocket is speeding away from you at relativistic speed you would see time in the rocket to be flowing slower as compared to on earth. And at the same time the astronauts in the rockets would feel time to flowing slower on earth w.r.t their rocket. To get the hang of this understanding that motion is purely relative is essential.

Ok, when you ask "does it really" you need to be careful.

Let's think about a motivational example where everything is easy. Think of a ladder leaning against a wall. The ladder is 5 meters long. And it contacts the wall and the floor such that it is 3 meters out at the bottom. So, sum-root-squares Pythagoras, it must contact the wall 4 meters up.

Now slip the ladder a bit so it contacts the floor 4 meters out. So blip blip it must now contact the wall 3 meters up.

The ladder is still 5 meters long. But it changes contact points with wall and floor. Does it REALLY change height? Yes. Does it REALLY change extent from the wall? Yes. Does it REALLY keep the same length? Yes.

Relativity is like that. In the Lorentz transform of coordinates, both $x$ and $t$ change. They change such that certain things remain constant, but their coordinate values change. Rotate a ladder and the length of the ladder is the same, but its width and height change. Lorentz transform an interval and the $x$ and $t$ values change, but the proper time along the interval remains the same.

What special relativity is telling you is, the time coordinate is part of the geometry. It's not exactly the same as the x, y, and z. But it is part of the scheme.

So what you need is the full Lorentz transform for x and t. Then you want to know what happens to the proper-length of an interval between two points. It's easier if you let one point be the origin and the other be a point at $(x,t)$. So, to get the x and t in a coordinate system for an observer moving to the right at $v$, who happens to have his origin coinciding with the $(x,t)$ origin, you get the following.

$$t^\prime = \gamma \left(t - \frac{vx}{c^2} \right)$$ $$x^\prime = \gamma (x-vt)$$

where $\gamma$ is defined as follows.

$$\gamma = \frac{1}{ \sqrt{1 - \frac{v^2}{c^2}} }$$

And from that you get (some algebra left for homework) the following.

$$x^2 -c^2 t^2 = (x^\prime)^2 -c^2 (t^\prime)^2$$

So you get this interval that is constant. The change in velocity is analogous to a rotation. The interval $x^2 -c^2 t^2$ is analogous to the length of the ladder. (Well, the length squared.) $x$ and $t$ are analogous to the extent up the wall and out from the wall.

So, yes, time REALLY does slow down. And length REALLY does get shorter. But these are coordinate values. The interval between the points is constant.

To begin to understand relativistic effects (yes, this is a long process for the most of people, not a boolean fact), you should first understand similar effects, but with more "simple" waves - sound waves. The fundamental properties of all waves are the same, and to be honest there is only one - emitted wave propogates at speed that is independent from speed of emitter itself. And that's what make all the relativity tricks. Including the most obvious one - Doppler effect. Imagine you are moving in your car and music plays. The car is a cabriolet because playing music in a closed cabin is irrelevant, because you drag the medium (air) with you. Thus we need a cabriolet to simulate waves that propogates in a vacuum, which you can't drag with your medium (like light). We will ignore all the aerodynamic hell around our cabriolet that is moving fast and give it one property - it doesn't drag medium. We always do these assumptions in our mind experiments in phisics, do we? And how fast you ask? Well, you can notice pitch distortion at speeds as high as 50 miles per hour. But faster - better. Professional musicians can recognise pitch changes at a speed of pedestrian. What annoys me in STR learning materials is this sample with train and its signal. Because in our sample with cabriolet there is a very significant and interesting detail which is absent in the sample with train (and this is crucial detail for understanding what's going on) - tempo. Music tempo. You can't hear changes in tempo in a train signal, an you can (and will) notice these changes with music. So, there are 4 interesting positions to observe sound relativistic effects:

• A driver with sound emitter behind him
• A driver with sound emitter in front of him
• Outside observer our car moving towards
• Outside observer our car moving from

What is interesting in the first case? The emitter is behind the driver (rear speakers). The driver is in a blue shift area of these waves. Will he notice that? Nope - because he is moving from these waves and compensate doppler blue shift with his own speed. What about second case? The driver is in a red area shift, but now he is moving towards sound waves and, again, compensate this shift by "hitting" "red" waves more frequently.

Now case with outside observer which sees how our driver approaches him. What does he hear? He hears accelerated playback of the song, i.e. high pitched, high tempo, less duration (say 1 min will be copmressed into just 50 seconds) version of the song. It's the same effect as DJ can make just spinning vinil disk faster. The observer that sees the back of the car hears opposite - stretched version of the song (longer duration, low pitched, low tempo).

Everything is the same for light waves including emitted with our cabriolet. The driver sees no changes at all, front observer sees blue shifted car with slightly accelerated actions of the driver, and the back observer sees red shifted colors with slightly slo-mo driver actions. But there is one interesting detail in addition to sound waves. Which is actually was a question topic =) Time dilation effect. What is it and why? Well, all processes (physical, chemical, literally all) that our life consist of are depend on the speed of signal propagation between A and B. By moving you decrease this speed and when you reach close to speed of this signal, things became even more interesting. Everything that is moving starts to be literally slower. Everything. That's what time dilation is. How slower? See formulas in other answers. But it is slower. Real deal. Live slo-mo. But you will not feel it. Because you live inside it. Within it. But your outside observers will! And that doppler effect with red shifted cabriolet and slo-mo driver will be affected by this even more! Red will be even more red, and slo-mo will be even more slower. What 's interesting, blue shift effect for the cars' front observer will not be "more blue", it will be "less blue" because of this time dilation (i.e additional red shift).

This tiny property of all waves - moving independently from speed of its source gives us all this mind-blowing tricks of nature. We literally live in the magic world.