Lately, a bunch of videos have been popping up on my Instagram feed where Neil DeGrass Tyson explains that photons do not experience time. Since learning about special relativity, his reasoning really rubs me the wrong way because it's completely flawed.
Special relativity deals with how things like distance and time differ depending on relative motion between inertial frames of reference. If an object is in an inertial frame, that means it is not experiencing acceleration. While you're sitting on your couch, it may seem that you're not experiencing acceleration since you aren't moving, but you are at least experiencing gravitational acceleration. So you're not actually in an inertial frame. If you were in an inertial frame, you would be experiecing weightlessness.
An object moving at a constant speed and direction (i.e. a constant velocity) is in an inertial frame. That is true regardless of the speed or direction which means there can be multiple inertial frame all in motion relative to each other.
No matter what frame of reference you are in, time will tick at the same rate with respect to yourself. In other words, whether you're moving very fast, very slow, or not at all relative to something else (like the earth), you will not notice a difference in the rate at which time ticks in your frame of reference. However, if an object is moving relative to you, time in its frame of reference will tick at a different rate relative to you. The difference in the rate at which time ticks in different frames of reference is called time dilation.
Let's say you're in an inertial frame, and you're watching something fly by at some fraction of the speed of light relative to you, and you want to know the rate at which time for that object is ticking relative to you. You can calculate it using the formula for time dilation, which is derived from the Lorentz transformation. The equation is:
Δt′=Δt√1−v2c2
See here for an explanation of where this forumula comes from.
Δt is the amount of time that has passed in the frame that is moving relative to you.
Δt' is the amount of time that has passed in your stationary reference frame.
𝑣 is the velocity of the moving frame.
c is the speed of light, which is the same in both frames. This is one of the postulates of special relativity, which will become important in a minute.
Notice that if the "moving" frame isn't moving (i.e. 𝑣 = 0), then Δt = Δt'. In other words, if there's no relative motion between the two inertial frames, time will tick at the same rate in both.
Notice, on the other hand, that the higher the velocity of the moving frame, the smaller the denominator. The smaller the denominator, the larger the whole fraction. Since the fraction is equal to Δt', it follows that the faster an object is moving relative to you, the more time will pass in your frame than in the moving frame. That means time is ticking slower in the moving frame compared to your frame.
Now, imagine what happens when the moving object approaches the speed of light. Notice it can never actually reach the speed of light because if 𝑣 = c, then the denominator = 0, and that don't make no kinda sense. But we can take the limit of Δt' as 𝑣 approaches c. When we do, we discover that Δt' approaches infinity as 𝑣 approaches c. That means in your frame of reference, if something were moving close to the speed of light relative to you, its time would be nearly at a stand still.
Neil thinks that photons don't experience time. His reasoning is that since photons move at the speed of light, it must be that from our point of view, time is not moving at all in the photon's frame of reference.
But there is a huge boo boo in Neil's reasoning. One of the postulates of special relativity is that light has the same speed in all inertial frames. If we imagined an object moving at a constant velocity relative to us, it would have its own inertial frame. It would not be moving in its own inertial frame. But there is no inertial frame for light. There is no frame in which light is not moving. So it's completely meaningless to talk about a photon's inertial frame. A photon does not have an inertial frame. Neil's major boo boo is to treat a photon like an ordinary object in an inertial frame. That's nonsense.
Another mistake is that by treating the photon like an ordinary object moving at the speed of light, and applying the time dilation equation to it, he'd have to be dividing by zero, which doesn't make sense. The time dilation equation shows that an inertial frame can get arbitrarily close to the speed of light, but it can't reach the speed of light. You can't apply the time dilation equation to anything moving at the speed of light, and that includes light itself.
It wasn't long ago that Neil's reasoning would've made sense to me. Thankfully, I've discovered FloatHeadPhysics on YouTube, and he has really helped to straighten out a lot of confusion I was having while trying to understand special relativity. He has one video where he addressed the subject of whether light experiences time. I highly recommend this video because it explains very clearly what's wrong with Neil's reasoning. Neil is simply forgetting the postulates of special relativity.
It just shows to go you that even physicists can get stuff wrong. You have to be especially cautious when it comes to popularizers, and Neil is one of the worst. I saw another video where he butchered the Andromeda Paradox.
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