# Einstein's Cellphone: Talking at the Speed of Light

Thought experiment:

You’re in a vehicle that can travel up to 99% the speed of light, around the earth’s equator. This vehicle has fantastic cell coverage, and never loses its signal. You initiate a call to your best friend before getting up to speed, and he/she is siting still in their couch, while you begin your acceleration to zoom around the earth…

…What would this phone call be like? Once you reached the limit of C, Would the relativistic effects make having a conversation nigh impossible?

Assuming you’re in some sort of huge particle accelerator-like structure spanning the entire earth, I would assume that as you approached the speed of light the other party on the phone would appear to talk very, very fast, while to them you would appear to talk very, very slow.

You cannot reach c, however, so there’s no answer to that part of the question. Purely as a thought experiment similar to “what if I could ride on a photon” I suppose you could say that time would pass you by in an instant. stars will die and be born in no time, galaxies would collide and the universe would continue to expand until there is nothing before you could say “oh shit!”.

Of course the earth and your method of transport would have long been destroyed, so most likely you would go from alive to dead (as either your vehicle fails, the earth is swallowed by the red giant: Sol, or some other disaster strikes) in no time at all.

I think it’d be a normal conversation with the exception of the doppler effect when the train’s going towards and away from the friend. I suppose that’s hardly normal. Since the voices are going into a machine in their own reference frame and the signal travels the same no matter the reference frame, it would work out fine I believe.

Interesting.

It was my understanding, that for each observer it looks like the other clock (your best friend’s clock) is the one running slow. So, wouldn’t my friend’s voice sound like it’s slowing down, and to him, my voice would sound like it’s slowing down.

I realize you can actually reach C, but if you can go fast enough, you can feel some pretty huge relative effects.

No contribution, just an amusing ad at the bottom:

Saint Einstein Tees
Geneuis loves you Socially awkward tees
www.CottonFactory.com

That should read can’t actually reach C” :smack:

The doppler effect wouldn’t change the frequency of the vioces since they are stationary to the individual phone but it would effect the frequency of the signal so assuming the phone could only send/recieve within a band of frequencies, it would be a normal conversation that suddenly cuts off

Ahh, correct. I didn’t think of that aspect SaintCad.

Would there be any way around that technical problem, so that the signal would still maintain broadcast? Something that could compensate for the redshift?

Not in this case. You’re thinking of two people moving relative to each other at a constant speed.

In the OP, you’re going in a circle around the earth. To go in a circle, you have to be constantly accelerating (your overall speed might not be changing, but the direction is always changing, so you’re accelerating). If one person is accelerating and the other isn’t, the accelerating person’s time runs slower.
For the cell phone communications, I can’t think of a theoretical reason why the phone on the accelerating ship couldn’t adjust it’s internal frequency so the earth-bound tower always receives a constant frequency. (The ship phone has no internal way of knowing what the time dialation shift is, but it can figure it out by by observing the transmissions from the earth tower). But there may be a reason I can’t think of. The engineering issues wouldn’t be easy, though…

If you are interested, check out Heinlein’s Time for the Stars, which deals with this exact issue, substituting telepathy for cell phones.

Aside from the problem of tower coverage (you’re orbiting the Earth at something like 7 times a second), you also have the problem that the Doppler shift is going to make receiving the signal from the tower virtually impossible. Once you match the speed of the tower’s transmission signal through the atmosphere, some very high percentage of c, the waves won’t be resolvable any more (i.e., you’ll be flying between the waves without them being able to catch up). If you fly faster than the signal can travel, you’ll be plowing backwards (as it were) through the transmission.

I don’t recall Heinlein’s story resolving how telepathy is physically transmitted, so he may have done some hand-waving to get the signal to catch up to the relativistic recipient.

How can you travel faster than an EM trasmission, if you’re traveling at sub-luminal speeds? I thought that no matter how fast you accelerate, the speed of light will always measure out to C.

The atmosphere is not a vacuum. Radio waves will travel somewhat slower than c in the air. Not much slower, though.

In the story the brother that stayed on Earth was put into some sort of deep sleep/trance/whatever and his body functions slowed down enough to just barely communicate with his twin on the ship.

What if it wasn’t a cellphone, but a phone with a cord thousands of miles long?

Assuming your cord didn’t break, there’d just be a lag of however long your cord is divided by whatever the speed of electricity is in your cord.

So, to sum up:

Assuming you could adjust for the redshift, and maintain a constant signal (I’m going with a complete analog system here, no digital), it would be a very costly and severely engineered way of making your friend sound like Alvin from the Chipmunks. And you, to him, would begin to sound like a baritone, and take forever to complete a sentence.

I’m assuming your pitch would ascend or descend out of human range before long. But not before your friend was talking so fast, you couldn’t understand him. Or you are talking so slowly, that you become unintelligible as well.

Then, by the time you get bored and end the call, you step on the brakes, and eventually come to a stop. You’d get out, and the sun would be a bloated red giant in the sky, the humans have evolved into something else entirely and left the earth for a more pleasant home elsewhere in the galaxy, and earth’s mean temperature is 200°F+ and you die a miserable death.

Just imagine if it had video chat. That would be hilarious.

One more thing:

Wouldn’t you get turned into a puddle of goo from the “centrifugal”* force, even if your speed was constant, and got to that speed slowly?

*I understand there’s no such thing; it’s really the effects of inertia acting on a rotating body.